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…

Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations

NASA Astrophysics Data System (ADS)

Shallal, Muhannad A.; Jabbar, Hawraz N.; Ali, Khalid K.

2018-03-01

In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation. The method is used to obtain analytic solutions for the space-time fractional Klein-Gordon and coupled conformable space-time fractional Boussinesq equations. The fractional complex transforms and the properties of modified Riemann-Liouville derivative have been used to convert these equations into nonlinear ordinary differential equations.

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.

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.

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.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

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

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

The valuation of currency options by fractional Brownian motion.

PubMed

Shokrollahi, Foad; Kılıçman, Adem

2016-01-01

This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use.

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Differentiated meteorites and the components of chondrites

NASA Technical Reports Server (NTRS)

Wasson, J. T.

1984-01-01

Findings are summarized from research conducted to develop a detailed classification of all kinds of meteorites in an effort to determine the conditions in the solar nebula, the processes that produced chemical fractionations in chondrites and formed chondrules, as well as ascertain the processes that occurred in the parent bodies of differentiated meteorites (which preserve a partial record of the chondritic materials from which they formed). Fractionation patterns within iron meteorite groups are analyzed.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

NASA Technical Reports Server (NTRS)

Chang, F.-C.

1973-01-01

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

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

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.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

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

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Blood flow problem in the presence of magnetic particles through a circular cylinder using Caputo-Fabrizio fractional derivative

NASA Astrophysics Data System (ADS)

Uddin, Salah; Mohamad, Mahathir; Khalid, Kamil; Abdulhammed, Mohammed; Saifullah Rusiman, Mohd; Che – Him, Norziha; Roslan, Rozaini

2018-04-01

In this paper, the flow of blood mixed with magnetic particles subjected to uniform transverse magnetic field and pressure gradient in an axisymmetric circular cylinder is studied by using a new trend of fractional derivative without singular kernel. The governing equations are fractional partial differential equations derived based on the Caputo-Fabrizio time-fractional derivatives NFDt. The current result agrees considerably well with that of the previous Caputo fractional derivatives UFDt.

High-order fractional partial differential equation transform for molecular surface construction.

PubMed

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations

PubMed Central

Zhao, Xiaofeng; McGough, Robert J.

2016-01-01

The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations. PMID:27250193

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.

High-order fractional partial differential equation transform for molecular surface construction

PubMed Central

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation. PMID:24364020

Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

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.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

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.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Pricing geometric Asian rainbow options under fractional Brownian motion

NASA Astrophysics Data System (ADS)

Wang, Lu; Zhang, Rong; Yang, Lin; Su, Yang; Ma, Feng

2018-03-01

In this paper, we explore the pricing of the assets of Asian rainbow options under the condition that the assets have self-similar and long-range dependence characteristics. Based on the principle of no arbitrage, stochastic differential equation, and partial differential equation, we obtain the pricing formula for two-asset rainbow options under fractional Brownian motion. Next, our Monte Carlo simulation experiments show that the derived pricing formula is accurate and effective. Finally, our sensitivity analysis of the influence of important parameters, such as the risk-free rate, Hurst exponent, and correlation coefficient, on the prices of Asian rainbow options further illustrate the rationality of our pricing model.

Generalized Functions for the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

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

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

Heat transfer at microscopic level in a MHD fractional inertial flow confined between non-isothermal boundaries

NASA Astrophysics Data System (ADS)

Shoaib Anwar, Muhammad; Rasheed, Amer

2017-07-01

Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.

A new modification in the exponential rational function method for nonlinear fractional differential equations

NASA Astrophysics Data System (ADS)

Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-02-01

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

Origin and evolution of the Nakhla meteorite inferred from the Sm-Nd and U-Pb systematics and REE, Ba, Sr, Rb and K abundances

NASA Technical Reports Server (NTRS)

Nakamura, N.; Unruh, D. M.; Tatsumoto, M.; Hutchison, R.

1982-01-01

Analyses of whole rock and mineral separates from the Nakhla meteorite are carried out by means of Sm-Nd and U-Tn-Pb systematics and by determining their REE, Ba, Sr, Rb, and K concentrations. Results show that the Sm-Nd age of the meteorite is 1.26 + or - 0.7 b.y., while the high initial epsilon(Nd) value of +16 suggests that Nakhla was derived from a light REE-depleted, old planetary mantle source. A three-stage Sm-Nd evolution model is developed and used in combination with LIL element data and estimated partition coefficients in order to test partial melting and fractional crystallization models and to estimate LIL abundances in a possible Nakhla source. The calculations indicate that partial melting of the source followed by extensive fractional crystallization of the partial melt could account for the REE abundances in the Nakhla constituent minerals. It is concluded that the significantly younger age of Nakhla than the youngest lunar rock, the young differentiation age inferred from U-Th-Pb data, and the estimated LIL abundances suggest that this meteorite may have been derived from a relatively large, well-differentiated planetary body such as Mars.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Coal-oil slurry preparation

DOEpatents

Tao, John C.

1983-01-01

A pumpable slurry of pulverized coal in a coal-derived hydrocarbon oil carrier which slurry is useful as a low-ash, low-sulfur clean fuel, is produced from a high sulfur-containing coal. The initial pulverized coal is separated by gravity differentiation into (1) a high density refuse fraction containing the major portion of non-coal mineral products and sulfur, (2) a lowest density fraction of low sulfur content and (3) a middlings fraction of intermediate sulfur and ash content. The refuse fraction (1) is gasified by partial combustion producing a crude gas product from which a hydrogen stream is separated for use in hydrogenative liquefaction of the middlings fraction (3). The lowest density fraction (2) is mixed with the liquefied coal product to provide the desired fuel slurry. Preferably there is also separately recovered from the coal liquefaction LPG and pipeline gas.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

First-principles investigations of equilibrium Ca, Mg, Si and O isotope fractionations between silicate melts and minerals

NASA Astrophysics Data System (ADS)

Qi, Y.; Liu, X.; Kang, J.; He, L.

2017-12-01

Equilibrium isotope fractionation factors are essential for using stable isotope data to study many geosciences processes such as planetary differentiation and mantle evolution. The mass-dependent equilibrium isotope fractionation is primarily controlled by the difference in bond energies triggered by the isotope substitution. With the recent advances in computational capabilities, first-principles calculation has become a reliable tool to investigate equilibrium isotopic fractionations, greatly improving our understanding of the factors controlling isotope fractionations. It is important to understand the isotope fractionation between melts and minerals because magmatism is critical for creating and shaping the Earth. However, because isotope fractionation between melts and minerals is small at high temperature, it is difficult to experimentally calibrate such small signature. Due to the disordered and dynamic character of melts, calculations of equilibrium isotope fractionation of melts are more challenging than that for gaseous molecules or minerals. Here, we apply first-principles molecular dynamics method to calculate equilibrium Ca, Mg, Si, and O isotope fractionations between silicate melts and minerals. Our results show that equilibrium Mg, Si, and O isotope fractionations between olivine and pure Mg2SiO4 melt are close to zero at high temperature (e.g. δ26Mgmelt-ol = 0.03 ± 0.04‰, δ30Simelt-ol = -0.06 ± 0.07‰, δ18Omelt-ol = 0.07‰ ± 0.08 at 1500 K). Equilibrium Ca, Mg, Si, and O isotope fractionations between diopside and basalt melt (67% CaMgSi2O6 + 33% CaAl2Si2O8) are also negligible at high temperature (e.g. δ44/40Camelt-cpx = -0.01 ± 0.02‰, δ26Mgmelt-cpx = -0.05 ± 0.14‰, δ30Simelt-cpx = 0.04 ± 0.04‰, δ18Omelt-cpx = 0.03 ± 0.07‰ at 1500 K). These results are consistent with the observations in natural samples that there is no significant Ca, Mg, Si, and O isotope fractionation during mantle partial melting, demonstrating the reliability of our methods. Thus, our results can be used to understand stable isotope fractionation during partial melting of mantle peridotite or fractional crystallization during magmatic differentiation. The first-principles molecular dynamics method is a promising tool to obtain equilibrium fractionation of more isotope systems for complicate liquids.

Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel

NASA Astrophysics Data System (ADS)

Abdulhameed, M.; Vieru, D.; Roslan, R.

2017-10-01

This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological analysis and medical diagnosis.

Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.

PubMed

Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

2014-01-01

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

PubMed Central

Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

2014-01-01

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. PMID:27433525

Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model

NASA Astrophysics Data System (ADS)

Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad

2017-02-01

The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.

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.

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

Abu Hamed, M.; Nepomnyashchy, A. A.

2016-08-01

The dynamics of a curved front in a plane between two stable phases with equal potentials is modeled via two-dimensional fractional in time partial differential equation. A closed equation governing a slow motion of a small-curvature front is derived and applied for two typical examples of the potential function. Approximate axisymmetric and non-axisymmetric solutions are obtained.

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Another elementary proof of the Jordan form of a matrix

NASA Astrophysics Data System (ADS)

Budhi, Wono Setya

2012-05-01

In this paper we establish the Jordan Form for a matrix using the elementary concepts of vector differentiation and partial fractions. The idea comes from the resolvent of the operator. For the matrix, the Laurent series is finite and easy to compute through rational representation. We also give a proof of some famous theorems in matrix analysis as consequences from the result.

The effects of complex chemistry on triple flames

NASA Technical Reports Server (NTRS)

Echekki, T.; Chen, J. H.

1996-01-01

The structure, ignition, and stabilization mechanisms for a methanol (CH3OH)-air triple flame are studied using Direct Numerical Simulations (DNS). The methanol (CH3OH)-air triple flame is found to burn with an asymmetric shape due to the different chemical and transport processes characterizing the mixture. The excess fuel, methanol (CH3OH), on the rich premixed flame branch is replaced by more stable fuels CO and H2, which burn at the diffusion flame. On the lean premixed flame side, a higher concentration of O2 leaks through to the diffusion flame. The general structure of the triple point features the contribution of both differential diffusion of radicals and heat. A mixture fraction-temperature phase plane description of the triple flame structure is proposed to highlight some interesting features in partially premixed combustion. The effects of differential diffusion at the triple point add to the contribution of hydrodynamic effects in the stabilization of the triple flame. Differential diffusion effects are measured using two methods: a direct computation using diffusion velocities and an indirect computation based on the difference between the normalized mixture fractions of C and H. The mixture fraction approach does not clearly identify the effects of differential diffusion, in particular at the curved triple point, because of ambiguities in the contribution of carbon and hydrogen atoms' carrying species.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Chemical Zoning of Feldspars in Lunar Granitoids: Implications for the Origins of Lunar Silicic Magmas

NASA Technical Reports Server (NTRS)

Mills, R. D; Simon, J. I.; Alexander, C.M. O'D.; Wang, J.; Christoffersen, R.; Rahman, Z..

2014-01-01

Fine-scale chemical and textural measurements of alkali and plagioclase feldspars in the Apollo granitoids (ex. Fig. 1) can be used to address their petrologic origin(s). Recent findings suggest that these granitoids may hold clues of global importance, rather than of only local significance for small-scale fractionation. Observations of morphological features that resemble silicic domes on the unsampled portion of the Moon suggest that local, sizable net-works of high-silica melt (>65 wt % SiO2) were present during crust-formation. Remote sensing data from these regions suggest high concentrations of Si and heat-producing elements (K, U, and Th). To help under-stand the role of high-silica melts in the chemical differentiation of the Moon, three questions must be answered: (1) when were these magmas generated?, (2) what was the source material?, and (3) were these magmas produced from internal differentiation. or impact melting and crystallization? Here we focus on #3. It is difficult to produce high-silica melts solely by fractional crystallization. Partial melting of preexisting crust may therefore also have been important and pos-sibly the primary mechanism that produced the silicic magmas on the Moon. Experimental studies demonstrate that partial melting of gabbroic rock under mildly hydrated conditions can produce high-silica compositions and it has been suggested by that partial melting by basaltic underplating is the mechanism by which high-silica melts were produced on the Moon. TEM and SIMS analyses, coordinated with isotopic dating and tracer studies, can help test whether the minerals in the Apollo granitoids formed in a plutonic setting or were the result of impact-induced partial melting. We analyzed granitoid clasts from 3 Apollo samples: polymict breccia 12013,141, crystalline-matrix breccia 14303,353, and breccia 15405,78

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Comparative investigation of five nanoparticles in flow of viscous fluid with Joule heating and slip due to rotating disk

NASA Astrophysics Data System (ADS)

Qayyum, Sumaira; Khan, Muhammad Ijaz; Hayat, Tasawar; Alsaedi, Ahmed

2018-04-01

Present article addresses the comparative study for flow of five water based nanofluids. Flow in presence of Joule heating is generated by rotating disk with variable thickness. Nanofluids are suspension of Silver (Ag), Copper (Cu), Copper oxide (CuO), Aluminum oxide or Alumina (Al2O3), Titanium oxide or titania (TiO2) and water. Boundary layer approximation is applied to partial differential equations. Using Von Karman transformations the partial differential equations are converted to ordinary differential equations. Convergent series solutions are obtained. Graphical results are presented to examine the behaviors of axial, radial and tangential velocities, temperature, skin friction and Nusselt number. It is observed that radial, axial and tangential velocities decay for slip parameters. Axial velocity decays for larger nanoparticle volume fraction. Effect of nanofluids on velocities dominant than base material. Temperature rises for larger Eckert number and temperature of silver water nanofluid is more because of its higher thermal conductivity. Surface drag force reduces for higher slip parameters. Transfer of heat is more for larger disk thickness index.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Amniotic-Fluid Stem Cells: Growth Dynamics and Differentiation Potential after a CD-117-Based Selection Procedure

PubMed Central

Arnhold, S.; Glüer, S.; Hartmann, K.; Raabe, O.; Addicks, K.; Wenisch, S.; Hoopmann, M.

2011-01-01

Amniotic fluid (AF) has become an interesting source of fetal stem cells. However, AF contains heterogeneous and multiple, partially differentiated cell types. After isolation from the amniotic fluid, cells were characterized regarding their morphology and growth dynamics. They were sorted by magnetic associated cell sorting using the surface marker CD 117. In order to show stem cell characteristics such as pluripotency and to evaluate a possible therapeutic application of these cells, AF fluid-derived stem cells were differentiated along the adipogenic, osteogenic, and chondrogenic as well as the neuronal lineage under hypoxic conditions. Our findings reveal that magnetic associated cell sorting (MACS) does not markedly influence growth characteristics as demonstrated by the generation doubling time. There was, however, an effect regarding an altered adipogenic, osteogenic, and chondrogenic differentiation capacity in the selected cell fraction. In contrast, in the unselected cell population neuronal differentiation is enhanced. PMID:21437196

A Geochemical Study of Postshield Volcanism and the Generation of Trachyte on West Maui, HI

NASA Astrophysics Data System (ADS)

Trenkler, M. L.; Cousens, B.

2016-12-01

The West Maui Volcano provides a complete evolutionary history of a fully developed Hawaiian volcano described by three main phases: (1) the tholeiitic shield-building stage of the Wailuku Basalts; (2) the postshield alkalic stage Honolua Volcanics; and (3) the rejuvenated stage Lahaina Volcanics of silica-undersaturated rocks. On West Maui, the postshield Honolua Volcanics erupted highly differentiated rocks (benmoreite to trachyte), with little to no intermediate alkalic rocks, upon cessation of tholeiitic shield building. Utilizing K-Ar dated samples, we present 35 new major and trace element analyses of shield, postshield, and rejuvenated stage lavas on West Maui in an attempt to identify the mechanisms present during evolution from basalt to trachyte over a defined temporal and spatial range. Wailuku basalts are dominated by olivine fractionation, whereas decreasing Sc and CaO/Al2O3 with increasing degree of differentiation indicate Honolua benmoreites and trachytes heavily fractionated clinopyroxene. Major element trends are consistent with crystallization of titano-magnetite, potassium feldspar, and minor apatite. Trace element patterns of the Honolua Volcanics are uniform with strong enrichments in LILE and the LREEs indicating fractionation and lower degrees of partial melting compared to Wailuku basalts. The HREEs are enriched relative to shield basalts with Gd/Yb values of 2.0-2.8 as a result of high degrees of fractionation and the presence of crystalizing apatite. Major and trace element trends follow the evolution of the postshield Hawi Volcanics of Kohala, where alkalic basalts differentiate up to trachyte. Compared to shield lavas, the Honolua Volcanics represent a drastic decrease in magma supply rates, infrequent eruptions, and magma residence times long enough to produce highly differentiated magmas with no significant mafic magma input.

Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control.

PubMed

He, Ding-Xin; Ling, Guang; Guan, Zhi-Hong; Hu, Bin; Liao, Rui-Quan

2018-02-01

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

Differential levels of metabolic activity in isolated versus confluent/partially confluent HeLa cells are analyzed by autofluorescent NAD(P)H using multi-photon FLIM microscopy

NASA Astrophysics Data System (ADS)

Chandler, Andrea; Chandler, Aaron; Wallrabe, Horst; Periasamy, Ammasi

2017-02-01

NAD(P)H is a known biomarker for cellular metabolism; a higher ratio of enzyme-bound NAD(P)H to free/unbound NAD(P)H indicates an increase in metabolic activity. Free NADH has a shorter fluorescence lifetime (τ1), the bound version (τ2) a longer lifetime. FLIM's unique capability to establish inter alia the relative fractions of τ1 (a1%) and τ2 (a2%) in each pixel, determines the level of metabolic activity. The relative abundances of bound NAD(P)H were analyzed for single cells, confluent and partially confluent cells within 3 Fields-of-View (FoVs). A gradient of increasing a 2% levels of bound NAD(P)H from single, partially confluent to confluent cells was observed.

Estrogenic activity of isoflavonoids from the stem bark of the tropical tree Amphimas pterocarpoides, a source of traditional medicines.

PubMed

Tchoumtchoua, Job; Makropoulou, Maria; Ateba, Sylvain Benjamin; Boulaka, Athina; Halabalaki, Maria; Lambrinidis, George; Meligova, Aggeliki K; Mbanya, Jean Claude; Mikros, Emmanuel; Skaltsounis, Alexios-Leandros; Mitsiou, Dimitra J; Njamen, Dieudonne; Alexis, Michael N

2016-04-01

Various preparations of the African tree Amphimas pterocarpoides Harms are traditionally used to treat endocrine- related adverse health conditions. In the ovariectomized rat, the enriched in phenolics fraction of the methanol extract of stem bark of A. pterocarpoides acted as vaginotrophic agent of considerably weaker uterotrophic activity compared to estradiol. Evaluation of the fraction and 11 isoflavonoids isolated therefrom using Ishikawa cells and estrogen receptor (ER) isotype-specific reporter cells suggested that the estrogenic activity of the fraction could be attributed primarily to daidzein and dihydroglycitein and secondarily to glycitein. The potency-based selectivity of daidzein, dihydroglycitein and glycitein for gene expression through ERβ versus ERα, expressed relative to estradiol, was 37, 27 and 20, respectively. However, the rank order of relative-to-estradiol potencies of induction of alkaline phosphatase in Ishikawa cells, a reliable marker of estrogenic activity, was daidzein>dihydroglycitein>glycitein. The considerably higher estrogenic activity of dihydroglycitein compared to glycitein could be attributed to the partial agonist/antagonist activity of dihydroglycitein through ERβ. Calculation of theoretical free energies of binding predicted the partial agonism/antagonism of dihydroglycitein through ERβ. The fraction and the isolated isoflavonoids promoted lactogenic differentiation of HC11 mammary epithelial cells at least as effectively as premenopausal levels of estradiol. This data suggests that the estrogenic activity of the fraction likely depends on the metabolism of glycitein to dihydroglycitein; that the fraction could exert vaginotrophic activity likely without challenging endocrine cancer risk more than estrogen-alone supplementation; and that the fraction's safety for the reproductive track warrants a more detailed evaluation. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

One input-class and two input-class classifications for differentiating olive oil from other edible vegetable oils by use of the normal-phase liquid chromatography fingerprint of the methyl-transesterified fraction.

PubMed

Jiménez-Carvelo, Ana M; Pérez-Castaño, Estefanía; González-Casado, Antonio; Cuadros-Rodríguez, Luis

2017-04-15

A new method for differentiation of olive oil (independently of the quality category) from other vegetable oils (canola, safflower, corn, peanut, seeds, grapeseed, palm, linseed, sesame and soybean) has been developed. The analytical procedure for chromatographic fingerprinting of the methyl-transesterified fraction of each vegetable oil, using normal-phase liquid chromatography, is described and the chemometric strategies applied and discussed. Some chemometric methods, such as k-nearest neighbours (kNN), partial least squared-discriminant analysis (PLS-DA), support vector machine classification analysis (SVM-C), and soft independent modelling of class analogies (SIMCA), were applied to build classification models. Performance of the classification was evaluated and ranked using several classification quality metrics. The discriminant analysis, based on the use of one input-class, (plus a dummy class) was applied for the first time in this study. Copyright © 2016 Elsevier Ltd. All rights reserved.

Ar-Ar and I-Xe Ages of Caddo County and Thermal History of IAB Iron Meteorites

NASA Technical Reports Server (NTRS)

Bogard, Donald D.; Garrison, Daniel H.; Takeda, Hiroshi

2005-01-01

Inclusions in IAB iron meteorites include non-chondritic silicate and those with more primitive chondritic silicate composition. Coarse-grained gabbroic material rich in plagioclase and diopside occurs in the Caddo County IAB iron meteorite and represents a new type of chemically differentiated, extra-terrestrial, andesitic silicate. Other parts of Caddo contain mostly andesitic material. Caddo thus exhibits petrologic characteristics of parent body metamorphism of a chondrite-like parent and inhomogeneous segregation of melts. Proposed IAB formation models include parent body partial melting and fractional crystallization or incomplete differentiation due to internal heat sources, and impact/induced melting and mixing. Benedix et al. prefer a hybrid model whereby the IAB parent body largely melted, then underwent collisional breakup, partial mixing of phases, and reassembly. Most reported 129I- Xe-129 ages of IABs are greater than 4.56 Gyr and a few are greater than or = 4.567 Gyr. These oldest ages exceed the 4.567 Gyr Pb-Pb age of Ca, Al-rich inclusions in primitive meteorites,

Rotating flow of a nanofluid due to an exponentially stretching surface with suction

NASA Astrophysics Data System (ADS)

Salleh, Siti Nur Alwani; Bachok, Norfifah; Arifin, Norihan Md

2017-08-01

An analysis of the rotating nanofluid flow past an exponentially stretched surface with the presence of suction is studied in this work. Three different types of nanoparticles, namely, copper, titania and alumina are considered. The system of ordinary differential equations is computed numerically using a shooting method in Maple software after being transformed from the partial differential equations. This transformation has considered the similarity transformations in exponential form. The physical effect of the rotation, suction and nanoparticle volume fraction parameters on the rotating flow and heat transfer phenomena is investigated and has been described in detail through graphs. The dual solutions are found to appear when the governing parameters reach a certain range.

Isentropic expansion and related thermodynamic properties of non-ionic amphiphile-water mixtures.

PubMed

Reis, João Carlos R; Douhéret, Gérard; Davis, Michael I; Fjellanger, Inger Johanne; Høiland, Harald

2008-01-28

A concise thermodynamic formalism is developed for the molar isentropic thermal expansion, ES,m = ( partial differential Vm/ partial differential T)(Sm,x), and the ideal and excess quantities for the molar, apparent molar and partial molar isentropic expansions of binary liquid mixtures. Ultrasound speeds were determined by means of the pulse-echo-overlap method in aqueous mixtures of 2-methylpropan-2-ol at 298.15 K over the entire composition range. These data complement selected extensive literature data on density, isobaric heat capacity and ultrasound speed for 9 amphiphile (methanol, ethanol, propan-1-ol, propan-2-ol, 2-methylpropan-2-ol, ethane-1,2-diol, 2-methoxyethanol, 2-ethoxyethanol or 2-butoxyethanol)-water binary systems, which form the basis of tables listing molar and excess molar isobaric expansions and heat capacities, and molar and excess molar isentropic compressions and expansions at 298.15 K and at 65 fixed mole fractions spanning the entire composition range and fine-grained in the water-rich region. The dependence on composition of these 9 systems is graphically depicted for the excess molar isobaric and isentropic expansions and for the excess partial molar isobaric and isentropic expansions of the amphiphile. The analysis shows that isentropic thermal expansion properties give a much stronger response to amphiphile-water molecular interactions than do their isobaric counterparts. Depending on the pair property-system, the maximum excess molar isentropic value is generally twenty- to a hundred-fold greater than the corresponding maximum isobaric value, and occurs at a lower mole fraction of the amphiphile. Values at infinite dilution of the 9 amphiphiles in water are given for the excess partial molar isobaric heat capacity, isentropic compression, isobaric expansion and isentropic expansion. These values are interpreted in terms of the changes occurring when amphiphile molecules cluster into an oligomeric form. Present results are discussed from theoretical and experimental thermodynamic viewpoints. It is concluded that isentropic thermal expansion properties constitute a new distinct resource for revealing particular features and trends in complex mixing processes, and that analyses using these new properties compare favourably with conventional approaches.

Modelling the seismic properties of fast-spreading ridge crustal Low-Velocity Zones: insights from Oman gabbro textures

NASA Astrophysics Data System (ADS)

Lamoureux, Gwenaëlle; Ildefonse, Benoı̂t; Mainprice, David

1999-11-01

Although considerable progress has been made in the study of fast-spreading, mid-ocean ridge magma chambers over the past fifteen years, the fraction of melt present in the chamber remains poorly constrained and controversial. We present new constraints obtained by modelling the seismic properties of partially molten gabbros at the ridge axis. P-wave velocities at low frequencies are calculated in the foliation/lineation reference frame using a differential effective medium technique. The model takes into account the lattice preferred orientation of the crystalline phase and the average shape of the melt phase. The structural parameters are obtained from the Oman ophiolite. The structural reference frame is given by the general trend of the gabbro foliation and the melt fraction and shape are estimated using the textures of nine upper gabbro samples. The estimated melt fraction and shape depend on the assumptions regarding which part of the observed textures represent the melt in the gabbroic mush of the magma chamber. However, we can put limits on the reasonable values for the melt fraction and shape. Our results are consistent with a melt fraction of the order of 10 to 20% in the Low-Velocity Zone (i.e. the magma chamber), which is anisotropically distributed with the melt pockets preferentially aligned parallel to the foliation and approximated by oblate ellipsoids with approximate dimensions of 4 : 4 : 1. These results are also consistent with the seismic structure of the East Pacific rise at 9°30'. The anisotropic melt distribution can, at least partially, explain the vertical velocity gradient described in the LVZ.

On Partial Fraction Expansion with Multiple Poles. Classroom Notes

ERIC Educational Resources Information Center

Hou, Shui-Hung; Hou, Edwin Sui-Hoi

2004-01-01

A simple and novel method for evaluating the partial fraction expansion of proper rational functions is presented. The technique involves simultaneous determination of the partial fraction coefficients associated with each of the multiple poles in the expansion in turn. Only synthetic division is required, which makes the process very suitable for…

How to Compute the Partial Fraction Decomposition without Really Trying

ERIC Educational Resources Information Center

Brazier, Richard; Boman, Eugene

2007-01-01

For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

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.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Improvement of dry fractionation ethanol fermentation by partial germ supplementation

USDA-ARS?s Scientific Manuscript database

Ethanol fermentation of dry fractionated grits (corn endosperm pieces) containing different levels of germ was studied using the dry grind process. Partial removal of germ fraction allows for marketing the germ fraction and potentially more efficient fermentation. Grits obtained from a dry milling p...

Melting Heat in Radiative Flow of Carbon Nanotubes with Homogeneous-Heterogeneous Reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Muhammad, Khursheed; Muhammad, Taseer; Alsaedi, Ahmed

2018-04-01

The present article provides mathematical modeling for melting heat and thermal radiation in stagnation-point flow of carbon nanotubes towards a nonlinear stretchable surface of variable thickness. The process of homogeneous-heterogeneous reactions is considered. Diffusion coefficients are considered equal for both reactant and autocatalyst. Water and gasoline oil are taken as base fluids. The conversion of partial differential system to ordinary differential system is done by suitable transformations. Optimal homotopy technique is employed for the solutions development of velocity, temperature, concentration, skin friction and local Nusselt number. Graphical results for various values of pertinent parameters are displayed and discussed. Our results indicate that the skin friction coefficient and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Ashorynejad, H. R.; Sheikholeslami, M.; Pop, I.; Ganji, D. D.

2013-03-01

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge-Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al2O3) and titanium oxide (TiO2) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.

The Component Slope Linear Model for Calculating Intensive Partial Molar Properties: Application to Waste Glasses

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

Reynolds, Jacob G.

2013-01-11

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a changemore » in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOH-NaAl(OH{sub 4}H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results detennined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components.« less

Inflammatory Biomarkers Predict Heart Failure Severity and Prognosis in Patients With Heart Failure With Preserved Ejection Fraction: A Holistic Proteomic Approach.

PubMed

Hage, Camilla; Michaëlsson, Erik; Linde, Cecilia; Donal, Erwan; Daubert, Jean-Claude; Gan, Li-Ming; Lund, Lars H

2017-02-01

Underlying mechanisms in heart failure (HF) with preserved ejection fraction remain unknown. We investigated cardiovascular plasma biomarkers in HF with preserved ejection fraction and their correlation to diastolic dysfunction, functional class, pathophysiological processes, and prognosis. In 86 stable patients with HF and EF ≥45% in the Karolinska Rennes (KaRen) biomarker substudy, biomarkers were quantified by a multiplex immunoassay. Orthogonal projection to latent structures by partial least square analysis was performed on 87 biomarkers and 240 clinical variables, ranking biomarkers associated with New York Heart Association (NYHA) Functional class and the composite outcome (all-cause mortality and HF hospitalization). Biomarkers significantly correlated with outcome were analyzed by multivariable Cox regression and correlations with echocardiographic measurements performed. The orthogonal partial least square outcome-predicting biomarker pattern was run against the Ingenuity Pathway Analysis (IPA) database, containing annotated data from the public domain. The orthogonal partial least square analyses identified 32 biomarkers correlated with NYHA class and 28 predicting outcomes. Among outcome-predicting biomarkers, growth/differentiation factor-15 was the strongest and an additional 7 were also significant in Cox regression analyses when adjusted for age, sex, and N-terminal probrain natriuretic peptide: adrenomedullin (hazard ratio per log increase 2.53), agouti-related protein; (1.48), chitinase-3-like protein 1 (1.35), C-C motif chemokine 20 (1.35), fatty acid-binding protein (1.33), tumor necrosis factor receptor 1 (2.29), and TNF-related apoptosis-inducing ligand (0.34). Twenty-three of them correlated with diastolic dysfunction (E/e') and 5 with left atrial volume index. The IPA suggested that increased inflammation, immune activation with decreased necrosis and apoptosis preceded poor outcome. In HF with preserved ejection fraction, novel biomarkers of inflammation predict HF severity and prognosis that may complement or even outperform traditional markers, such as N-terminal probrain natriuretic peptide. These findings lend support to a hypothesis implicating global systemic inflammation in HF with preserved ejection fraction. URL: http://www.clinicaltrials.gov; Unique identifier: NCT00774709. © 2017 American Heart Association, Inc.

Inhibition of partially purified K+/H+-ATPase from guinea-pig isolated and enriched parietal cells by substituted benzimidazoles.

PubMed Central

Beil, W.; Sewing, K. F.

1984-01-01

The cellular and subcellular distributions of adenosinetriphosphatases (ATPases) were examined in guinea-pig gastric mucosal cells. All cell types displayed Mg2+-ATPase and bicarbonate (HCO3-)-stimulated ATPase activity. K+-ATPase was located only in fractions derived from parietal cells. Differential and density-gradient centrifugation of material prepared from parietal cells revealed that K+-ATPase activity was located in a tubulo-vesicular membrane fraction. Enzyme activity was ten fold greater in this fraction than in a crude parietal cell homogenate. The substituted benzimidazoles, omeprazole and picoprazole, inhibited K+-ATPase (IC50 1.8 +/- 0.5 mumol l-1 and 3.1 +/- 0.4 mumol l-1, respectively). Detailed kinetic analysis indicated that these compounds were non-competitive and reversible inhibitors of the enzyme. In contrast cimetidine and verapamil were without effect on the enzyme. The relevance of the inhibition of K+-ATPase to the antisecretory activity of the benzimidazoles, in experimental animals and man, is discussed. PMID:6146367

Modelling the petrogenesis of high Rb/Sr silicic magmas

USGS Publications Warehouse

Halliday, A.N.; Davidson, J.P.; Hildreth, W.; Holden, P.

1991-01-01

Rhyolites can be highly evolved with Sr contents as low as 0.1 ppm and Rb Sr > 2,000. In contrast, granite batholiths are commonly comprised of rocks with Rb Sr 100. Mass-balance modelling of source compositions, differentiation and contamination using the trace-element geochemistry of granites are therefore commonly in error because of the failure to account for evolved differentiates that may have been erupted from the system. Rhyolitic magmas with very low Sr concentrations (???1 ppm) cannot be explained by any partial melting models involving typical crustal source compositions. The only plausible mechanism for the production of such rhyolites is Rayleigh fractional crystallization involving substantial volumes of cumulates. A variety of methods for modelling the differentiation of magmas with extremely high Rb/Sr is discussed. In each case it is concluded that the bulk partition coefficients for Sr have to be large. In the simplest models, the bulk DSr of the most evolved types is modelled as > 50. Evidence from phenocryst/glass/whole-rock concentrations supports high Sr partition coefficients in feldspars from high silica rhyolites. However, the low modal abundance of plagioclase commonly observed in such rocks is difficult to reconcile with such simple fractionation models of the observed trace-element trends. In certain cases, this may be because the apparent trace-element trend defined by the suite of cognetic rhyolites is the product of different batches of magma with separate differentiation histories accumulating in the magma chamber roof zone. ?? 1991.

Lunar and terrestrial crust formation

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

Walker, D.

1983-11-15

Planetary crusts may be accreted, produced in primordial differentiation, or built up piecemeal by serial magmatism. The existence of old, polygenetic, laterally heterogeneous, partial melt rocks in the lunar highlands suggests that the moon produced its early crust by serial magmatism. This view can be reconciled with lunar Eu anomalies, previously thought to support the magma ocean model of crust formation, if complications in the fractionation of mare basalts are reconized. Phase equilibrium and magmatic density information for mare basalts suggest a model in which plagioclase fractionation can occur even though plagioclase is not a near-liquidus phase. The crytic fractionationmore » of clinopryoxene in MORB provides a precedent for this model. The necessity for a lunar magma ocean is questioned, but a role for a terrestrial magma ocean of sorts at depth is suggested.« less

Characteristics of a leucine aminoacyl transfer RNA synthetase from Tritrichomonas augusta.

PubMed

Horner, J; Champney, W S; Samuels, R

1991-04-01

This study has investigated the characteristics of a leucine aminoacyl transfer RNA synthetase enzyme from Tritrichomonas augusta. Differential centrifugation and DEAE-cellulose column chromatography were used for partial enzyme purification. The column purification increased the synthetase activity 125-fold over the unfractionated cell extract. The conditions for maximum [3H] leucine charging were 37 degrees C for 20 min, with protein at 180 micrograms ml-1 using yeast leucine tRNA as an acceptor. The optimal reaction conditions were 14 mM-Mg acetate, 3 mM-ATP, 3 mM-spermidine and 5.5 mM-putrescine. Acceptor activity with T. augusta transfer RNA was 8-fold higher than with yeast transfer RNA and 25-fold higher than with Escherichia coli transfer RNA. The partially purified enzyme fraction had comparable changing activities for both leucine and valine.

Periodicity and positivity of a class of fractional differential equations.

PubMed

Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

2016-01-01

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

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…

Oscillation of a class of fractional differential equations with damping term.

PubMed

Qin, Huizeng; Zheng, Bin

2013-01-01

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

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).

The component slope linear model for calculating intensive partial molar properties /application to waste glasses and aluminate solutions

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

Reynolds, Jacob G.

2013-01-11

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a changemore » in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOH-NaAl(OH){sub 4}-H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results determined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components.« less

The Component Slope Linear Model for Calculating Intensive Partial Molar Properties: Application to Waste Glasses and Aluminate Solutions - 13099

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

Reynolds, Jacob G.

2013-07-01

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a changemore » in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOHNaAl(OH){sub 4}-H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results determined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components. (authors)« less

Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: A revised model

NASA Astrophysics Data System (ADS)

Jusoh, R.; Nazar, R.; Pop, I.

2018-03-01

A reformulation of the three-dimensional flow of a nanofluid by employing Buongiorno's model is presented. A new boundary condition is implemented in this study with the assumption of nanoparticle mass flux at the surface is zero. This condition is practically more realistic since the nanoparticle fraction at the boundary is latently controlled. This study is devoted to investigate the impact of the velocity slip and suction to the flow and heat transfer characteristics of nanofluid. The governing partial differential equations corresponding to the momentum, energy, and concentration are reduced to the ordinary differential equations by utilizing the appropriate transformation. Numerical solutions of the ordinary differential equations are obtained by using the built-in bvp4c function in Matlab. Graphical illustrations displaying the physical influence of the several nanofluid parameters on the flow velocity, temperature, and nanoparticle volume fraction profiles, as well as the skin friction coefficient and the local Nusselt number are provided. The present study discovers the existence of dual solutions at a certain range of parameters. Surprisingly, both of the solutions merge at the stretching sheet indicating that the presence of the velocity slip affects the skin friction coefficients. Stability analysis is carried out to determine the stability and reliability of the solutions. It is found that the first solution is stable while the second solution is not stable.

The stable Cr isotopic compositions of chondrites and silicate planetary reservoirs

NASA Astrophysics Data System (ADS)

Schoenberg, Ronny; Merdian, Alexandra; Holmden, Chris; Kleinhanns, Ilka C.; Haßler, Kathrin; Wille, Martin; Reitter, Elmar

2016-06-01

The depletion of chromium in Earth's mantle (∼2700 ppm) in comparison to chondrites (∼4400 ppm) indicates significant incorporation of chromium into the core during our planet's metal-silicate differentiation, assuming that there was no significant escape of the moderately volatile element chromium during the accretionary phase of Earth. Stable Cr isotope compositions - expressed as the ‰-difference in 53Cr/52Cr from the terrestrial reference material SRM979 (δ53/52CrSRM979 values) - of planetary silicate reservoirs might thus yield information about the conditions of planetary metal segregation processes when compared to chondrites. The stable Cr isotopic compositions of 7 carbonaceous chondrites, 11 ordinary chondrites, 5 HED achondrites and 2 martian meteorites determined by a double spike MC-ICP-MS method are within uncertainties indistinguishable from each other and from the previously determined δ53/52CrSRM979 value of -0.124 ± 0.101‰ for the igneous silicate Earth. Extensive quality tests support the accuracy of the stable Cr isotope determinations of various meteorites and terrestrial silicates reported here. The uniformity in stable Cr isotope compositions of samples from planetary silicate mantles and undifferentiated meteorites indicates that metal-silicate differentiation of Earth, Mars and the HED parent body did not cause measurable stable Cr isotope fractionation between these two reservoirs. Our results also imply that the accretionary disc, at least in the inner solar system, was homogeneous in its stable Cr isotopic composition and that potential volatility loss of chromium during accretion of the terrestrial planets was not accompanied by measurable stable isotopic fractionation. Small but reproducible variations in δ53/52CrSRM979 values of terrestrial magmatic rocks point to natural stable Cr isotope variations within Earth's silicate reservoirs. Further and more detailed studies are required to investigate whether silicate differentiation processes, such as partial mantle melting and crystal fractionation, can cause stable Cr isotopic fractionation on Earth and other planetary bodies.

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).

Structural physical approximation for the realization of the optimal singlet fraction with two measurements

NASA Astrophysics Data System (ADS)

Adhikari, Satyabrata

2018-04-01

Structural physical approximation (SPA) has been exploited to approximate nonphysical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of SPA to partial transpose is less than 2/9 then the two-qubit state is entangled. We find application of SPA to partial transpose in the estimation of the optimal singlet fraction. We show that the optimal singlet fraction can be expressed in terms of the minimum eigenvalue of SPA to partial transpose. We also show that the optimal singlet fraction can be realized using Hong-Ou-Mandel interferometry with only two detectors. Further we have shown that the generated hybrid entangled state between a qubit and a binary coherent state can be used as a resource state in quantum teleportation.

Leukotriene B4 omega-hydroxylase in human polymorphonuclear leukocytes. Partial purification and identification as a cytochrome P-450.

PubMed

Shak, S; Goldstein, I M

1985-09-01

Human polymorphonuclear leukocytes (PMN) not only synthesize and respond to leukotriene B4 (LTB4), but also catabolize this mediator of inflammation rapidly and specifically by omega-oxidation. To characterize the enzyme(s) responsible for omega-oxidation of LTB4, human PMN were disrupted by sonication and subjected to differential centrifugation to yield membrane, granule, and cytosol fractions (identified by biochemical markers). LTB4 omega-hydroxylase activity was concentrated (together with NADPH cytochrome c reductase activity) only in the membrane fraction (specific activity increased 10-fold as compared to whole sonicates, 41% recovery). Negligible activity was detected in granule or cytosol fractions. LTB4 omega-hydroxylase activity in isolated PMN membranes was linear with respect to duration of incubation and protein concentration, was maximal at pH 7.4, had a Km for LTB4 of 0.6 microM, and was dependent on oxygen and on reduced pyridine nucleotides (apparent Km for NADPH = 0.5 microM; apparent Km for NADH = 223 microM). The LTB4 omega-hydroxylase was inhibited significantly by carbon monoxide, ferricytochrome c, SKF-525A, and Triton X-100, but was not affected by alpha-naphthoflavone, azide, cyanide, catalase, and superoxide dismutase. Finally, isolated PMN membranes exhibited a carbon monoxide difference spectrum with a peak at 452 nm. Thus, we have partially purified the LTB4 omega-hydroxylase in human PMN and identified the enzyme as a membrane-associated, NADPH-dependent cytochrome P-450.

Petrogenesis of high-Ti and low-Ti basalts: high-pressure and high-temperature experimental study

NASA Astrophysics Data System (ADS)

Yang, J.; WANG, C.; Jin, Z.

2017-12-01

Geochemical and petrological studies have revealed the existence of high-Ti and low-Ti basalts in large igneous provinces. However, the petrogenesis of them are still under debate. Several different mechanisms have been proposed: (1) the high-Ti basalts are formed by the melting of mantle plume containing recycled oceanic crust or delaminated lower crust (Spandler et al., 2008) while low-Ti basalts are formed by the melting of subcontinental lithospheric mantle (Xiao et al., 2004); (2) both of them are from mantle plume or asthenospheric source, but the production of high-Ti basalts are associated with the thick lithosphere and relevant low degrees of melting while the low-Ti basalts are controlled by the thin lithosphere with high degrees of melting (Arndt et al., 1993; Xu et al., 2001). Almost all authors emphasize the role of partial melting but less discuss the crystallization differentiation process. The low Mg# (< 0.7) of these basalts provides that they are far away from direct melting of mantle peridotite. In addition, seismic data indicate unusually high seismic velocities bodies beneath LIPs which explained by the fractionated cumulates from picritic magmas (Farnetani et al., 1996). Therefore, we believed that the crystallization differentiation process might play a more significant role in the genesis of high-Ti and low-Ti basalts. In order to investigate the generation of these basalts, a series of high pressure and high temperature partial crystallization experiments were performed by using piston-cylinder and multi-anvil press at pressures of 1.5, 3.0 and 5.0 GPa and a temperature range of 1200-1700°. Two synthetic picrite glass with different chemical compositions were used as starting materials. Our experimental results show that Ti is preferred to be concentrated in the residual melt during crystallization differentiation. For the same melt fraction, the residual melt of higher pressure experiments has relatively higher TiO2 concentration and higher Mg#. Thus, we propose that most of the high-Ti and low-Ti basalts are inherited from picritic parental magmas which could be formed by high degree partial melting of garnet peridotite. The high-Ti basalts are generated through relatively high pressure crystallization process while the low-Ti basalts are generated at relatively low pressure.

Cytotoxic and antiproliferative effects induced by a non terpenoid polar extract of A. indica seeds on 3T6 murine fibroblasts in culture.

PubMed

Di Ilio, Vincenzo; Pasquariello, Nicoletta; van der Esch, Andrew S; Cristofaro, Massimo; Scarsella, Gianfranco; Risuleo, Gianfranco

2006-07-01

Neem oil is a natural product obtained from the seeds of the tree Azadirachta indica. Its composition is very complex and the oil exhibits a number of biological activities. The most studied component is the terpenoid azadirachtin which is used for its insecticidal and putative antimicrobial properties. In this report we investigate the biological activity of partially purified components of the oil obtained from A. indica. We show that the semi-purified fractions have moderate to strong cytotoxicity. However, this is not attributable to azadirachtin but to other active compounds present in the mixture. Each fraction was further purified by appropriate extraction procedures and we observed a differential cytotoxicity in the various sub-fractions. This led us to investigate the mode of cell death. After treatment with the oil fractions we observed positivity to TUNEL staining and extensive internucleosomal DNA degradation both indicating apoptotic death. The anti-proliferative properties of the neem oil-derived compounds were also assayed by evaluation of the nuclear PCNA levels (Proliferating Cell Nuclear Antigen). PCNA is significantly reduced in cells treated with a specific fraction of neem oil. Finally, our results strongly suggest a possible involvement of the mitochondrial pathway in the apoptotic death.

Rotating flow over a stretching sheet in nanofluid using Buongiorno model and thermophysical properties of nanoliquids

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.

2017-08-01

The boundary layer flow and heat transfer in rotating nanofluid over a stretching sheet using Buongiorno model and thermophysical properties of nanoliquids is studied. Four types of nanoparticles, namely silver (Ag), copper (Cu), alumina (Al2O3) and titania (TiO2) are used in our analysis with water as the base fluid (Prandtl number, Pr = 6.2). The nonlinear partial differential equations are transformed into ordinary differential equations by using the similarity transformation. The numerical solutions of these equation is obtained using shooting method in Maple software. The numerical results is concentrated on the effects of nanoparticle volume fraction φ, Brownian motion Nb, thermophoresis Nt, rotation Ω and suction S parameters on the skin friction coefficient and heat transfer rate. Dual solutions are observed in a certain range of the rotating parameter.

Numerical simulation of convective heat transfer of nonhomogeneous nanofluid using Buongiorno model

NASA Astrophysics Data System (ADS)

Sayyar, Ramin Onsor; Saghafian, Mohsen

2017-08-01

The aim is to study the assessment of the flow and convective heat transfer of laminar developing flow of Al2O3-water nanofluid inside a vertical tube. A finite volume method procedure on a structured grid was used to solve the governing partial differential equations. The adopted model (Buongiorno model) assumes that the nanofluid is a mixture of a base fluid and nanoparticles, with the relative motion caused by Brownian motion and thermophoretic diffusion. The results showed the distribution of nanoparticles remained almost uniform except in a region near the hot wall where nanoparticles volume fraction were reduced as a result of thermophoresis. The simulation results also indicated there is an optimal volume fraction about 1-2% of the nanoparticles at each Reynolds number for which the maximum performance evaluation criteria can be obtained. The difference between Nusselt number and nondimensional pressure drop calculated based on two phase model and the one calculated based on single phase model was less than 5% at all nanoparticles volume fractions and can be neglected. In natural convection, for 4% of nanoparticles volume fraction, in Gr = 10 more than 15% enhancement of Nusselt number was achieved but in Gr = 300 it was less than 1%.

Enforcing realizability in explicit multi-component species transport

PubMed Central

McDermott, Randall J.; Floyd, Jason E.

2015-01-01

We propose a strategy to guarantee realizability of species mass fractions in explicit time integration of the partial differential equations governing fire dynamics, which is a multi-component transport problem (realizability requires all mass fractions are greater than or equal to zero and that the sum equals unity). For a mixture of n species, the conventional strategy is to solve for n − 1 species mass fractions and to obtain the nth (or “background”) species mass fraction from one minus the sum of the others. The numerical difficulties inherent in the background species approach are discussed and the potential for realizability violations is illustrated. The new strategy solves all n species transport equations and obtains density from the sum of the species mass densities. To guarantee realizability the species mass densities must remain positive (semidefinite). A scalar boundedness correction is proposed that is based on a minimal diffusion operator. The overall scheme is implemented in a publicly available large-eddy simulation code called the Fire Dynamics Simulator. A set of test cases is presented to verify that the new strategy enforces realizability, does not generate spurious mass, and maintains second-order accuracy for transport. PMID:26692634

Correcting the initialization of models with fractional derivatives via history-dependent conditions

NASA Astrophysics Data System (ADS)

Du, Maolin; Wang, Zaihua

2016-04-01

Fractional differential equations are more and more used in modeling memory (history-dependent, non-local, or hereditary) phenomena. Conventional initial values of fractional differential equations are defined at a point, while recent works define initial conditions over histories. We prove that the conventional initialization of fractional differential equations with a Riemann-Liouville derivative is wrong with a simple counter-example. The initial values were assumed to be arbitrarily given for a typical fractional differential equation, but we find one of these values can only be zero. We show that fractional differential equations are of infinite dimensions, and the initial conditions, initial histories, are defined as functions over intervals. We obtain the equivalent integral equation for Caputo case. With a simple fractional model of materials, we illustrate that the recovery behavior is correct with the initial creep history, but is wrong with initial values at the starting point of the recovery. We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.

Partial volume segmentation in 3D of lesions and tissues in magnetic resonance images

NASA Astrophysics Data System (ADS)

Johnston, Brian; Atkins, M. Stella; Booth, Kellogg S.

1994-05-01

An important first step in diagnosis and treatment planning using tomographic imaging is differentiating and quantifying diseased as well as healthy tissue. One of the difficulties encountered in solving this problem to date has been distinguishing the partial volume constituents of each voxel in the image volume. Most proposed solutions to this problem involve analysis of planar images, in sequence, in two dimensions only. We have extended a model-based method of image segmentation which applies the technique of iterated conditional modes in three dimensions. A minimum of user intervention is required to train the algorithm. Partial volume estimates for each voxel in the image are obtained yielding fractional compositions of multiple tissue types for individual voxels. A multispectral approach is applied, where spatially registered data sets are available. The algorithm is simple and has been parallelized using a dataflow programming environment to reduce the computational burden. The algorithm has been used to segment dual echo MRI data sets of multiple sclerosis patients using lesions, gray matter, white matter, and cerebrospinal fluid as the partial volume constituents. The results of the application of the algorithm to these datasets is presented and compared to the manual lesion segmentation of the same data.

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Long-Term Dynamics of Autonomous Fractional Differential Equations

NASA Astrophysics Data System (ADS)

Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

The multispecies modeling of the premixed, laminar steady-state ozone flame

NASA Technical Reports Server (NTRS)

Heimerl, J. M.; Coffee, T. P.

1980-01-01

Species dependent kinetic, transport and thermodynamic coefficients were employed in a one dimensional model of the premixed, laminar, steady state ozone flame. Convenient expressions for these coefficients are reported. They are based on independent measurements, no arbitrary parameters are used. The governing equations are solved using a relaxation technique and the partial differential equation package, PDECOL. Species and temperature profiles and the burning velocities are found over the range of initial ozone mole fraction of 0.25 to 1.00. The computed burning velocities are no more than 30% greater than the measurements of Streng and Grosses. Comparison with the computed results of Warnatz shows agreement within + or - 12%, even though quite different expressions for some of the kinetic coefficients were used. These differences are most obvious in the atomic oxygen and temperature profiles at an initial ozone mole fraction of unity.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

3D magneto-convective heat transfer in CNT-nanofluid filled cavity under partially active magnetic field

NASA Astrophysics Data System (ADS)

Al-Rashed, Abdullah A. A. A.; Kolsi, Lioua; Oztop, Hakan F.; Aydi, Abdelkarim; Malekshah, Emad Hasani; Abu-Hamdeh, Nidal; Borjini, Mohamed Naceur

2018-05-01

A computational study has been performed to investigate the effects of partially active magnetic field on natural convection heat transfer in CNT-nanofluid filled and three-dimensional differentially heated closed space. Two cases are considered to see this effect as magnetic field is applied to upper half (Case I) and lower half (Case II) while remaining walls are insulated. The finite volume method is used to solve governing equations and results are obtained for different governing parameters as Hartmann number (0 ≤ Ha ≤ 100), nanoparticle volume fraction (0 ≤ φ ≤ 0.05) and height of the active zone (0 ≤ LB ≤ 1). It is found that location of magnetic field plays an important role even at the same Hartmann number. Thus, it can be a good parameter to control heat and fluid flow inside the closed space.

Glass transition behavior of the vitrification solutions containing propanediol, dimethyl sulfoxide and polyvinyl alcohol.

PubMed

Wang, Hai-Yan; Lu, Shu-Shen; Lun, Zhao-Rong

2009-02-01

Knowledge of the glass transition behavior of vitrification solutions is important for research and planning of the cryopreservation of biological materials by vitrification. This brief communication shows the analysis for the glass transition and glass stability of the multi-component vitrification solutions containing propanediol (PE), dimethyl sulfoxide (Me2SO) and polyvinyl alcohol (PVA) by using differential scanning calorimetry (DSC) during the cooling and subsequent warming between 25 and -150 degrees C. The glass formation of the solutions was enhanced by introduction of PVA. Partial glass formed during cooling and the fractions of free water in the partial glass matrix increased with the increasing of PVA concentration, which caused slight decline of glass transition temperature, T(g). Exothermic peaks of devitrification were delayed and broadened, which may result from the inhibition of ice nucleation or recrystallization of PVA.

Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using (G‧/G2) -expansion method

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Ullah, Rahmat; Ahmed, Naveed; Khan, Umar

This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs) by applying a relatively new method known as (G‧/G2) -expansion method. Solutions of space-time fractional Sharma-Tasso-Olever (STO) equation of fractional order and (3+1)-dimensional KdV-Zakharov Kuznetsov (KdV-ZK) equation of fractional order are reckoned to demonstrate the validity of this method. The fractional derivative version of modified Riemann-Liouville, linked with Fractional complex transform is employed to transform fractional differential equations into the corresponding ordinary differential equations.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Iron Isotope Fractionation in the Bushveld Igneous Complex Provide Insight into Fractional Crystallization

NASA Astrophysics Data System (ADS)

Rios, K. L.; Feineman, M. D.; Bybee, G. M.

2016-12-01

Dated at 2.056 Ga and encompassing an estimated 65,000 km2 in surface area and 650,000 km3 in volume the Bushveld Igneous Complex in South Africa contains the largest and most unique layered mafic intrusion in the world. It contains 80-90% of the world's minable platinum group elements. Scientists are interested in understanding the origin of this intrusion due to its massive size, unique assemblage of minerals, and strongly zoned stratigraphy. Iron isotopes may help us to understand the roles of partial mantle melting and fractional crystallization in magma genesis and differentiation. For example, it may be possible to determine what role fractional crystallization of oxides and sulfides played in the formation of the Rustenburg Layered Suite (RLS) by comparing δ56Fe in samples from the Lower, Critical, Main and Upper Zones. The use of MC-ICPMS has made it more routine to study the fractionation of stable iron isotopes in natural systems; however, this technique has only been applied in a few studies of the RLS, mostly restricted to the Upper Main and Upper Zones. In this study δ56Fe was determined in Upper Zone magnetite, Critical Zone chromitite and Critical Zone sulfides using MC-ICP-MS. Previous research has shown that early crystallizing mafic phases incorporate the lighter 54Fe isotope leaving a residual magma with a higher δ56Fe value. Therefore, if the Upper Zone magma represents a high-degree differentiate of the parental Bushveld magma, then magmas from the Upper Zone would be expected to have a higher δ56Fe than magmas contributing to the Lower, Critical and Main Zones. The results of this experiment were indeed consistent with this hypothesis. The δ56Fe values recorded for the three sample types were: magnetite 0.19 ±0.03‰; sulfides -0.45 ±0.03‰ to -0.81 ±0.03‰; and chromitite 0.03 ±0.05‰. The sulfides of the Critical Zone are isotopically lighter than would be predicted based on equilibrium sulfide-melt fractionation, if the parental melt of the Critical Zone were in equilibrium with previously published whole rock data for Upper Zone. This is consistent with interpretations of the Upper Zone as a high degree differentiate of the Bushveld Parental Magma.

Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent diffusion coefficient.

PubMed

Chen, Juan; Cui, Baotong; Chen, YangQuan

2018-06-11

This paper presents a boundary feedback control design for a fractional reaction diffusion (FRD) system with a space-dependent (non-constant) diffusion coefficient via the backstepping method. The contribution of this paper is to generalize the results of backstepping-based boundary feedback control for a FRD system with a space-independent (constant) diffusion coefficient to the case of space-dependent diffusivity. For the boundary stabilization problem of this case, a designed integral transformation treats it as a problem of solving a hyperbolic partial differential equation (PDE) of transformation's kernel, then the well posedness of the kernel PDE is solved for the plant with non-constant diffusivity. Furthermore, by the fractional Lyapunov stability (Mittag-Leffler stability) theory and the backstepping-based boundary feedback controller, the Mittag-Leffler stability of the closed-loop FRD system with non-constant diffusivity is proved. Finally, an extensive numerical example for this closed-loop FRD system with non-constant diffusivity is presented to verify the effectiveness of our proposed controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Experimental test of the viscous anisotropy hypothesis for partially molten rocks

PubMed Central

Qi, Chao; Kohlstedt, David L.; Katz, Richard F.; Takei, Yasuko

2015-01-01

Chemical differentiation of rocky planets occurs by melt segregation away from the region of melting. The mechanics of this process, however, are complex and incompletely understood. In partially molten rocks undergoing shear deformation, melt pockets between grains align coherently in the stress field; it has been hypothesized that this anisotropy in microstructure creates an anisotropy in the viscosity of the aggregate. With the inclusion of anisotropic viscosity, continuum, two-phase-flow models reproduce the emergence and angle of melt-enriched bands that form in laboratory experiments. In the same theoretical context, these models also predict sample-scale melt migration due to a gradient in shear stress. Under torsional deformation, melt is expected to segregate radially inward. Here we present torsional deformation experiments on partially molten rocks that test this prediction. Microstructural analyses of the distribution of melt and solid reveal a radial gradient in melt fraction, with more melt toward the center of the cylinder. The extent of this radial melt segregation grows with progressive strain, consistent with theory. The agreement between theoretical prediction and experimental observation provides a validation of this theory. PMID:26417107

Experimental test of the viscous anisotropy hypothesis for partially molten rocks.

PubMed

Qi, Chao; Kohlstedt, David L; Katz, Richard F; Takei, Yasuko

2015-10-13

Chemical differentiation of rocky planets occurs by melt segregation away from the region of melting. The mechanics of this process, however, are complex and incompletely understood. In partially molten rocks undergoing shear deformation, melt pockets between grains align coherently in the stress field; it has been hypothesized that this anisotropy in microstructure creates an anisotropy in the viscosity of the aggregate. With the inclusion of anisotropic viscosity, continuum, two-phase-flow models reproduce the emergence and angle of melt-enriched bands that form in laboratory experiments. In the same theoretical context, these models also predict sample-scale melt migration due to a gradient in shear stress. Under torsional deformation, melt is expected to segregate radially inward. Here we present torsional deformation experiments on partially molten rocks that test this prediction. Microstructural analyses of the distribution of melt and solid reveal a radial gradient in melt fraction, with more melt toward the center of the cylinder. The extent of this radial melt segregation grows with progressive strain, consistent with theory. The agreement between theoretical prediction and experimental observation provides a validation of this theory.

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale.

PubMed

Katgert, Gijs; Latka, Andrzej; Möbius, Matthias E; van Hecke, Martin

2009-06-01

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

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

Some properties for integro-differential operator defined by a fractional formal.

PubMed

Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

2016-01-01

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Diffusion-driven D/H fractionation in silicates during hydration, dehydration and degassing

NASA Astrophysics Data System (ADS)

Roskosz, Mathieu; Laporte, Didier; Deloule, Etienne; Ingrin, Jannick; Remusat, Laurent; Depecker, Christophe; Leroux, Hugues

2017-04-01

Understanding how degassing occurs during accretion and differentiation is crucial to explain the water budget of planetary bodies. In this context, the hydrogen isotopic signature of water in mantle minerals and melts is particularly useful to trace reservoirs and their interactions. Nonetheless, little is known on the influence of mantle processes on the D/H signatures of silicates. In this study, we performed controlled hydration/dehydration experiments. We explore the possibility that diffusion-driven fractionation could affect the D/H signature of partially hydrated amorphous or molten silicates and nominally anhydrous minerals (NAMs). High purity synthetic fused silica samples were annealed at between 200 and 1000°C at 20 mbar water partial pressure for 1 to 30 days. Dehydration of initially hydrated silica was also performed at 1000°C for a few hours. A set of rhyolitic samples previously synthesized in order to study bubble nucleation during magma decompression was also analyzed. Finally a natural grossular monocrystal (Zillertaler Alps, Austria), partially dehydrated in air at 800°C for 10 hours was studied. Water content and speciation were measured both by Fourier-Transform Infra-Red and Raman spectroscopies. Isotopic analyses were performed with the IMS 1270 and 1280 ion microprobes. The silica samples, the rhyolitic glasses and the grossular monocrystal exhibit typical water concentration profiles. In all cases, water speciation does not change significantly along concentration profiles. Concerning D/H signatures, no isotopic variation is detectable across amorphous silica and rhyolitic glasses. The situation is however very different in the grossular monocrystal. A strong isotopic gradient appears correlated to the water concentration profile. Our data are interpreted in terms of diffusion mechanisms in both amorphous (and molten) silicates and NAMs. Hydration, dehydration and magma degassing are probably not able to promote large diffusion-driven fractionation of hydrogen in amorphous silicates. Conversely, the diffusion of water through the structure of NAMs affects the overall isotopic composition of dissolved water.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Existence of a coupled system of fractional differential equations

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

Ibrahim, Rabha W.; Siri, Zailan

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

Fractional Poisson Fields and Martingales

NASA Astrophysics Data System (ADS)

Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely

2018-02-01

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

A new medical image segmentation model based on fractional order differentiation and level set

NASA Astrophysics Data System (ADS)

Chen, Bo; Huang, Shan; Xie, Feifei; Li, Lihong; Chen, Wensheng; Liang, Zhengrong

2018-03-01

Segmenting medical images is still a challenging task for both traditional local and global methods because the image intensity inhomogeneous. In this paper, two contributions are made: (i) on the one hand, a new hybrid model is proposed for medical image segmentation, which is built based on fractional order differentiation, level set description and curve evolution; and (ii) on the other hand, three popular definitions of Fourier-domain, Grünwald-Letnikov (G-L) and Riemann-Liouville (R-L) fractional order differentiation are investigated and compared through experimental results. Because of the merits of enhancing high frequency features of images and preserving low frequency features of images in a nonlinear manner by the fractional order differentiation definitions, one fractional order differentiation definition is used in our hybrid model to perform segmentation of inhomogeneous images. The proposed hybrid model also integrates fractional order differentiation, fractional order gradient magnitude and difference image information. The widely-used dice similarity coefficient metric is employed to evaluate quantitatively the segmentation results. Firstly, experimental results demonstrated that a slight difference exists among the three expressions of Fourier-domain, G-L, RL fractional order differentiation. This outcome supports our selection of one of the three definitions in our hybrid model. Secondly, further experiments were performed for comparison between our hybrid segmentation model and other existing segmentation models. A noticeable gain was seen by our hybrid model in segmenting intensity inhomogeneous images.

Simulation of the modulation transfer function dependent on the partial Fourier fraction in dynamic contrast enhancement magnetic resonance imaging.

PubMed

Takatsu, Yasuo; Ueyama, Tsuyoshi; Miyati, Tosiaki; Yamamura, Kenichirou

2016-12-01

The image characteristics in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) depend on the partial Fourier fraction and contrast medium concentration. These characteristics were assessed and the modulation transfer function (MTF) was calculated by computer simulation. A digital phantom was created from signal intensity data acquired at different contrast medium concentrations on a breast model. The frequency images [created by fast Fourier transform (FFT)] were divided into 512 parts and rearranged to form a new image. The inverse FFT of this image yielded the MTF. From the reference data, three linear models (low, medium, and high) and three exponential models (slow, medium, and rapid) of the signal intensity were created. Smaller partial Fourier fractions, and higher gradients in the linear models, corresponded to faster MTF decline. The MTF more gradually decreased in the exponential models than in the linear models. The MTF, which reflects the image characteristics in DCE-MRI, was more degraded as the partial Fourier fraction decreased.

Leaching behaviour, mechanical and durability properties of mortar containing municipal incineration bottom ash

NASA Astrophysics Data System (ADS)

Morales Hernandez, Maria B.

The review of municipal solid waste (MSW) management scheme has indicated that the amount of MSW sent to incineration plants will increase in the UK in coming years. Therefore, the amount of municipal solid waste incineration (MSWI) residues generated will increase significantly. MSWI residues are divided into MSWI fly ash (MSWI-FA) and MSWI bottom ash (MSWI-BA). MSWI-FA is classified as hazardous residue thereby requires special treatment before disposal. MSWI-BA is mostly disposed in landfill sites. MSWI-BA fraction with particle size diameter below approximately 2mm has low engineering properties and may have an adverse effect on the environment due to its high porosity, solubility and leachability of possible toxic compounds. This research programme has investigated new potential uses and leaching behaviour of mortar containing MSWI-BA with particle size diameters below 2.36mm. Fraction of MSWI-BA with particle size diameters (φ) below 2.36 mm (φ <2.36) was divided into different sub-fractions to evaluate their influence on compressive strength of concrete when used as partial replacement of cement or sand. MSWI-BA fraction with φ <212mum (fine fraction) and 212mum < φ2.36mm (coarse fraction) used as partial replacement of cement and sand respectively, showed higher compressive strength compared with the other fractions examined. In addition, replacing sand with the coarse fraction of MSWI-BA exhibited similar or higher strength than the reference mix. Examination of physical and chemical properties of the fine and coarse fractions of MSWI-BA unbound indicated that both fractions had potential to be used as replacement of cement or sand. However, the evaluation of their leaching behaviour suggested that they should be bound in cement-based systems to avoid leaching of potential toxic elements. Evaluation of physical, mechanical and sulfate resistance properties of mortars containing 15% of the fine fraction of MSWI-BA as a partial replacement of cement and 50% of the coarse fraction as partial replacement of sand indicated potential uses in concrete production. In addition, the leachability of mortar specimens containing 15% and 50% of MSWI-BA as partial replacement of cement and sand respectively was significantly reduced when compared to unbound MSWI-BA fractions.

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.

Adiponectin is partially associated with exosomes in mouse serum.

PubMed

Phoonsawat, Worrawalan; Aoki-Yoshida, Ayako; Tsuruta, Takeshi; Sonoyama, Kei

2014-06-06

Exosomes are membrane vesicles 30-120 nm in diameter that are released by many cell types and carry a cargo of proteins, lipids, mRNA, and microRNA. Cultured adipocytes reportedly release exosomes that may play a role in cell-to-cell communication during the development of metabolic diseases. However, the characteristics and function of exosomes released from adipocytes in vivo remain to be elucidated. Clearly, adipocyte-derived exosomes could exist in the circulation and may be associated with adipocyte-specific proteins such as adipocytokines. We isolated exosomes from serum of mice by differential centrifugation and analyzed adiponectin, leptin, and resistin in the exosome fraction. Western blotting detected adiponectin but no leptin and only trace amounts of resistin in the exosome fraction. The adiponectin signal in the exosome fraction was decreased by proteinase K treatment and completely quenched by a combination of proteinase K and Triton X-100. Quantitative ELISA showed that the exosome fraction contains considerable amounts of adiponectin, but not leptin or resistin. The concentration of adiponectin in the serum and the ratio of adiponectin to total protein in the exosome fraction were lower in obese mice than in lean mice. These results suggest that a portion of adiponectin exists as a transmembrane protein in the exosomes in mouse serum. We propose adiponectin as a marker of exosomes released from adipocytes in vivo. Copyright © 2014 Elsevier Inc. All rights reserved.

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Vapor sensing using polymer/carbon black composites in the percolative conduction regime.

PubMed

Sisk, Brian C; Lewis, Nathan S

2006-08-29

To investigate the behavior of chemiresistive vapor sensors operating below or around the percolation threshold, chemiresistors have been formed from composites of insulating organic polymers and low mass fractions of conductive carbon black (CB, 1-12% w/w). Such sensors produced extremely large relative differential resistance changes above certain threshold vapor concentrations. At high analyte partial pressures, these sensors exhibited better signal/noise characteristics and were typically less mutually correlated in their vapor response properties than composites formed using higher mass fractions of CB in the same set of polymer sorption layers. The responses of the low-mass-fraction CB sensors were, however, less repeatable, and their nonlinear response as a function of analyte concentration required more complicated calibration schemes to identify and quantify analyte vapors to compensate for drift of a sensor array and to compensate for variability in response between sensor arrays. Because of their much larger response signals, the low-mass-fraction CB sensors might be especially well suited for use with low-precision analog-to-digital signal readout electronics. These sensors serve well as a complement to composites formed from higher mass fractions of CB and have yielded insight into the tradeoffs of signal-to-noise improvements vs complexity of signal processing algorithms necessitated by the use of nonlinearly responding detectors in array-based sensing schemes.

Numerical Investigation on Absorption Enhancement of Black Carbon Aerosols Partially Coated With Nonabsorbing Organics

NASA Astrophysics Data System (ADS)

Zhang, Xiaolin; Mao, Mao; Yin, Yan; Wang, Bin

2018-01-01

This study numerically evaluates the effects of aerosol microphysics, including coated volume fraction of black carbon (BC), shell/core ratio, and size distribution, on the absorption enhancement (Eab) of polydisperse BC aggregates partially coated by organics, which is calculated by the exact multiple-sphere T-matrix method. The coated volume fraction of BC plays a substantial role in determining the absorption enhancement of partially coated BC aggregates, which typically have an Eab in the range of 1.0-2.0 with a larger value for larger coated volume fraction of BC as the shell/core ratio, BC geometry, and size distribution are fixed. The shell/core ratio, BC geometry, and size distribution have little impact on the Eab of coated BC with small coated volume fraction of BC, while they become significant for large coated volume fraction of BC. The Eab of partially coated BC particles can be slightly less than 1.0 for the large BC in the accumulation mode exhibiting large shell/core ratio and small coated volume fraction of BC, indicating that the absorption shows even slight decrease relative to uncoated BC particles. For partially coated BC aggregates in the accumulation and coarse modes, the refractive index uncertainties of BC result in the Eab differences of less than 9% and 2%, respectively, while those of organics can induce larger variations with the maximum differences up to 22% and 18%, respectively. Our study indicates that accounting for particle coating microphysics, particularly the coated volume fraction of BC, can potentially help to understand the differences in observations of largely variable absorption enhancements over various regions.

[Carbon monoxide tests in a steady state. Uptake and transfer capacity, normal values and lower limits].

PubMed

Ramonatxo, M; Préfaut, C; Guerrero, H; Moutou, H; Bansard, X; Chardon, G

1982-01-01

The aim of this study was to establish data which would best demonstrate the variations of different tests using Carbon Monoxide as a tracer gas (total and partial functional uptake coefficient and transfer capacity) to establish mean values and lower limits of normal of these tests. Multivariate statistical analysis was used; in the first stage a connection was sought between the fractional uptake coefficient (partial and total) to other parameters, comparing subjects and data. In the second stage the comparison was refined by eliminating the least useful data, trying, despite a small loss of material, to reveal the most important connections, linear or otherwise. The fractional uptake coefficients varied according to sex, also the variation of the partial alveolar-expired fractional uptake equivalent (DuACO) was largely a function of respiratory rate and tidal volume. The alveolar-arterial partial fractional uptake equivalent (DuaCO) depended more on respiratory frequency and age. Finally the total fractional uptake coefficient (DuCO) and the transfer capacity corrected per liter of ventilation (TLCO/V) were functions of these parameters. The last stage of this work, after taking account of the statistical observations consistent with the facts of these physiological hypotheses led to a search for a better way of approaching the laws linking the collected data to the fractional uptake coefficient. The lower limits of normal were arbitrarily defined, separating those 5% of subjects deviating most strongly from the mean. As a result, the relationship between the lower limit of normal and the theoretical mean value was 90% for the partial and total fractional uptake coefficient and 70% for the transfer capacity corrected per liter of ventilation.

Apollo 15 Mg- and Fe-norites - A redefinition of the Mg-suite differentiation trend

NASA Technical Reports Server (NTRS)

Lindstrom, M. M.; Marvin, U. B.; Mittlefehldt, D. W.

1989-01-01

The Apollo 15 highland rocks from the Apennine Front include clasts of mafic plutonic rocks from deep in the lunar crust that were brought to the surface by the Imbrium and Serenitatis impacts. The Apollo 15 norites exhibit wide variations in mineral and bulk compositions and include Fe-norites that plot between the three major pristine rock fields on a diagram of Mg' in mafic minerals vs An in paglioclase. Based on assemblages and compositions of minerals, and on ratios of elemental abundances, it is concluded that these Apollo 15 Fe-norites are differentiated members of the Mg-norite suite. The Apollo 15 and 17 norites and troctolites form a closely related suite of rocks, whose variations in mineral compositions represent the main differentiation trend of the Mg-suite. This trend in mineral compositions has a steeper slope than the previous Mg-suite field. The parent magmas for these Mg-suite rocks formed by partial melting deep in the lunar mantle. Differentiation by fractional crystallization may also have included assimilation of crustal components as the magmas rose from the mantle and crystallized plutons in the lower crust.

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).

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.

2017-12-01

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.

Fractionation products of basaltic komatiite magmas at lower crustal pressures: implications for genesis of silicic magmas in the Archean

NASA Astrophysics Data System (ADS)

Mandler, B. E.; Grove, T. L.

2015-12-01

Hypotheses for the origin of crustal silicic magmas include both partial melting of basalts and fractional crystallization of mantle-derived melts[1]. Both are recognized as important processes in modern environments. When it comes to Archean rocks, however, partial melting hypotheses dominate the literature. Tonalite-trondhjemite-granodiorite (TTG)-type silicic magmas, ubiquitous in the Archean, are widely thought to be produced by partial melting of subducted, delaminated or otherwise deeply buried hydrated basalts[2]. The potential for a fractional crystallization origin for TTG-type magmas remains largely unexplored. To rectify this asymmetry in approaches to modern vs. ancient rocks, we have performed experiments at high pressures and temperatures to closely simulate fractional crystallization of a basaltic komatiite magma in the lowermost crust. These represent the first experimental determinations of the fractionation products of komatiite-type magmas at elevated pressures. The aim is to test the possibility of a genetic link between basaltic komatiites and TTGs, which are both magmas found predominantly in Archean terranes and less so in modern environments. We will present the 12-kbar fractionation paths of both Al-depleted and Al-undepleted basaltic komatiite magmas, and discuss their implications for the relative importance of magmatic fractionation vs. partial melting in producing more evolved, silicic magmas in the Archean. [1] Annen et al., J. Petrol., 47, 505-539, 2006. [2] Moyen J-F. & Martin H., Lithos, 148, 312-336, 2012.

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates.

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

A remark on fractional differential equation involving I-function

NASA Astrophysics Data System (ADS)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

Experimental Investigation of Turbulence-Chemistry Interaction in High-Reynolds-Number Turbulent Partially Premixed Flames

DTIC Science & Technology

2016-06-23

4 . TITLE AND SUBTITLE [U] Experimental investigation of turbulence-chemistry interaction in high-Reynolds-number 5a. CONTRACT NUMBER turbulent...nonpremixed/partially premixed flames and turbulence-chemistry interaction. Turbulent mixing of mixture fraction has been studied extensively [ 4 , 14]. In a...two-feed non-premixed flame, the mixture fraction is defined as: ξ = Y − Yo YF − Yo (1) where Y is a conserved quantity such as the mass fraction of any

Impact of textural anisotropy on syn-kinematic partial melting of natural gneisses: an experimental approach.

NASA Astrophysics Data System (ADS)

Ganzhorn, Anne-Céline; Trap, Pierre; Arbaret, Laurent; Champallier, Rémi; Fauconnier, Julien; Labrousse, Loic; Prouteau, Gaëlle

2015-04-01

Partial melting of continental crust is a strong weakening process controlling its rheological behavior and ductile flow of orogens. This strength weakening due to partial melting is commonly constrained experimentally on synthetic starting material with derived rheological law. Such analog starting materials are preferentially used because of their well-constrained composition to test the impact of melt fraction, melt viscosity and melt distribution upon rheology. In nature, incipient melting appears in particular locations where mineral and water contents are favorable, leading to stromatic migmatites with foliation-parallel leucosomes. In addition, leucosomes are commonly located in dilatants structural sites like boudin-necks, in pressure shadows, or in fractures within more competent layers of migmatites. The compositional layering is an important parameter controlling melt flow and rheological behavior of migmatite but has not been tackled experimentally for natural starting material. In this contribution we performed in-situ deformation experiments on natural rock samples in order to test the effect of initial gneissic layering on melt distribution, melt flow and rheological response. In-situ deformation experiments using a Paterson apparatus were performed on two partially melted natural gneissic rocks, named NOP1 & PX28. NOP1, sampled in the Western Gneiss Region (Norway), is biotite-muscovite bearing gneiss with a week foliation and no gneissic layering. PX28, sampled from the Sioule Valley series (French Massif Central), is a paragneiss with a very well pronounced layering with quartz-feldspar-rich and biotite-muscovite-rich layers. Experiments were conducted under pure shear condition at axial strain rate varying from 5*10-6 to 10-3 s-1. The main stress component was maintained perpendicular to the main plane of anisotropy. Confining pressure was 3 kbar and temperature ranges were 750°C and 850-900°C for NOP1 and PX28, respectively. For the 750°C experiments NOP1 was previously hydrated at room pressure and temperature. According to melt fraction, deformation of partially molten gneiss induced different strain patterns. For low melt fraction, at 750°C, deformation within the initially isotropic gneiss NOP1 is localized along large scales shear-zones oriented at about 60° from main stress component σ1. In these zones quartz grains are broken and micas are sheared. Melt is present as thin film (≥20 µm) at muscovite-quartz grain boundaries and intrudes quartz aggregates as injections parallel to σ1. For higher melt fraction, at 850°C, deformation is homogeneously distributed. In the layered gneiss PX28, deformation is partitioned between mica-rich and quartz-rich layers. For low melt fraction, at 850°C, numerous conjugate shear-bands crosscut mica-rich layers. Melt is present around muscovite grains and intrudes quartz grains in the favor of fractures. For high melt fractions, at 900°C, melt assisted creep within mica-rich layers is responsible for boudinage of the quartz-feldspar rich layers. Melt-induced veining assists the transport of melt toward inter-boudin zones. Finite strain pattern and melt distribution after deformation of PX28 attest for appearance of strong pressure gradients leading to efficient melt flow. The subsequent melt redistribution strongly enhance strain partitioning and strength weakening, as shown by differential stress vs. strain graphs. Our experiments have successfully reproduced microstructures commonly observed in migmatitic gneisses like boudinage of less fertile layers. Comparison between non-layered and layered gneisses attest for strong influence of compositional anisotropies inherited from the protolith upon melt distribution and migmatite strength.

On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer order m as a multi-order (1, 1,…, 1), the Gelfond-Leontiev generalized differentiation operators, many other integral and differential operators in Calculus that have been used in various topics, some of them not related to FC at all, others involved in differential and integral equations for treating fractional order models.

Classifying Acute Respiratory Distress Syndrome Severity: Correcting the Arterial Oxygen Partial Pressure to Fractional Inspired Oxygen at Altitude.

PubMed

Pérez-Padilla, Rogelio; Hernández-Cárdenas, Carmen Margarita; Lugo-Goytia, Gustavo

2016-01-01

In the well-known Berlin definition of acute respiratory distress syndrome (ARDS), there is a recommended adjustment for arterial oxygen partial pressure to fractional inspired oxygen (PaO2/FIO2) at altitude, but without a reference as to how it was derived.

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.

The effect of partially stabilized zirconia on the biological properties of HA/HDPE composites in vitro.

PubMed

Sadi, A Yari; Shokrgozar, M A; Homaeigohar, S Sh; Hosseinalipour, M; Khavandi, A; Javadpour, J

2006-05-01

The effect of partially stabilized zirconia (PSZ) on the biological properties of the hyroxyapatite - high density polyethylene (HA/HDPE) composites was studied by investigating the simultaneous effect of hydroxyapatite and PSZ volume fractions on the in vitro response of human osteoblast cells. The biocompatibility of composite samples with different volume fraction of HA and PSZ powders was assessed by proliferation, alkaline phosphatase (ALP) and cell attachment assays on the osteoblast cell line (G-292) in different time periods. The effect of composites on the behavior of G-292 cells was compared with those of HDPE and TPS (Tissue Culture Poly Styrene as negative control) samples. Results showed a higher proliferation rate of G-292 cells in the presence of composite samples as compared to the HDPE sample after 7 and 14 days of incubation period. ALP production rate in all composite samples was higher than HDPE and TPS samples. The number of adhered cells on the composite samples was higher than the number adhered on the HDPE and TPS samples after the above mentioned incubation periods. These findings indicates that the addition of PSZ does not have any adverse affect on the biocompatibility of HA/HDPE composites. In fact in some experiments PSZ added HA/HDPE composites performed better in proliferation, differentiation and attachment of osteoblastic cells.

Fractionation of carbon and hydrogen isotopes by methane-oxidizing bacteria

USGS Publications Warehouse

Coleman, D.D.; Risatti, J.B.; Schoell, M.

1981-01-01

Carbon isotopic analysis of methane has become a popular technique in the exploration for oil and gas because it can be used to differentiate between thermogenic and microbial gas and can sometimes be used for gas-source rock correlations. Methane-oxidizing bacteria, however, can significantly change the carbon isotopic composition of methane; the origin of gas that has been partially oxidized by these bacteria could therefore be misinterpreted. We cultured methane-oxidizing bacteria at two different temperatures and monitored the carbon and hydrogen isotopic compositions of the residual methane. The residual methane was enriched in both 13C and D. For both isotopic species, the enrichment at equivalent levels of conversion was greater at 26??C than at 11.5??C. The change in ??D relative to the change in ??13C was independent of temperature within the range studied. One culture exhibited a change in the fractionation pattern for carbon (but not for hydrogen) midway through the experiment, suggesting that bacterial oxidation of methane may occur via more than one pathway. The change in the ??D value for the residual methane was from 8 to 14 times greater than the change in the ??13C value, indicating that combined carbon and hydrogen isotopic analysis may be an effective way of identifying methane which has been subjected to partial oxidation by bacteria. ?? 1981.

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 .

Mixed convection flow of sodium alginate (SA-NaAlg) based molybdenum disulphide (MoS2) nanofluids: Maxwell Garnetts and Brinkman models

NASA Astrophysics Data System (ADS)

Ahmed, Tarek Nabil; Khan, Ilyas

2018-03-01

This article aims to study the mixed convection heat transfer in non-Newtonian nanofluids over an infinite vertical plate. Mixed convection is caused due to buoyancy force and sudden plate motion. Sodium alginate (SA-NaAlg) is considered as non-Newtonian base fluid and molybdenum disulphide (MoS2) as nanoparticles are suspended in it. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively. The flow is modeled in the form of partial differential equations with imposed physical conditions. Exact solutions for velocity and temperature fields are developed by means of the Laplace transform technique. Numerical computations are performed for different governing parameters such as non-Newtonian parameter, Grashof number and nanoparticle volume fraction and the results are plotted in various graphs. Results for skin friction and Nusselt number are presented in tabular form which show that increasing nanoparticle volume fraction leads to heat transfer enhancement and increasing skin friction.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

A unifying fractional wave equation for compressional and shear waves.

PubMed

Holm, Sverre; Sinkus, Ralph

2010-01-01

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

NASA Astrophysics Data System (ADS)

Wilson, F.; Neukirch, T.

2018-01-01

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.

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

Sphingomyelins and ceramides with VLCPUFAs are excluded from low-density raft-like domains in differentiating spermatogenic cells[S

PubMed Central

Santiago Valtierra, Florencia X.; Mateos, Melina V.; Aveldaño, Marta I.; Oresti, Gerardo M.

2017-01-01

Rat spermatogenic cells contain sphingomyelins (SMs) and ceramides (Cers) with very long-chain PUFAs (VLCPUFAs) in nonhydroxylated (n-V) and 2-hydroxylated (h-V) forms. How these atypical species distribute among membrane fractions during differentiation was investigated here using a detergent-free procedure to isolate a small light raft-like low-density fraction and a large heavy fraction, mostly derived from the plasma membrane of spermatocytes, round spermatids, and late spermatids. The light fraction contained cholesterol, glycerophospholipids (GPLs), and SM with the same saturated fatty acids in all three stages. In the heavy fraction, as PUFA increased in the GPL and VLCPUFA in SM from spermatocytes to spermatids, the concentration of cholesterol was also augmented. The heavy fraction had mostly n-V SM in spermatocytes, but accumulated h-V SM and h-V Cer in spermatids. A fraction containing intracellular membranes had less SM and more Cer than the latter, but in both fractions SM and Cer species with h-V increased over species with n-V with differentiation. This accretion of h-V was consistent with the differentiation-dependent expression of fatty acid 2-hydroxylase (Fa2h), as it increased significantly from spermatocytes to spermatids. The non-raft region of the plasma membrane is thus the main target of the dynamic lipid synthesis and remodeling that is involved in germ cell differentiation. PMID:28082410

Iron isotope fractionation during magmatic differentiation in Kilauea Iki lava lake.

PubMed

Teng, Fang-Zhen; Dauphas, Nicolas; Helz, Rosalind T

2008-06-20

Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stagemeltveins are 0.2 permil (per thousand) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2 per thousand lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.

Iron isotope fractionation during magmatic differentiation in Kilauea Iki lava lake

USGS Publications Warehouse

Teng, F.-Z.; Dauphas, N.; Helz, R.T.

2008-01-01

Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stage melt veins are 0.2 per mil (???) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2??? lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.

Production of mildly alkaline basalts at complex ocean ridge settings: Perspectives from basalts emitted during the 2010 eruption at the Eyjafjallajökull volcano, Iceland

NASA Astrophysics Data System (ADS)

Viccaro, Marco; Nicotra, Eugenio; Urso, Salvatore

2015-11-01

The early phase of the 2010 eruption at the Eyjafjallajökull volcano (Iceland) produced poorly evolved mildly alkaline basalts that have a signature more enriched with respect to the typically depleted basalts emitted at ocean ridges. The whole rock geochemistry of these basaltic magmas offers a great opportunity to investigate the mantle source characteristics and reasons leading to this enriched fingerprint in proximity of the ocean ridge system. Some basaltic products of Katla volcano, ∼25 km east of Eyjafjallajökull, have been chosen from the literature, as they display a similar mildly alkaline signature and can be therefore useful to explore the same target. Major and trace element variations of the whole rock suggest a very limited evolutionary degree for the 2010 Eyjafjallajökull products and the selected Katla magmas, highlighting the minor role played by differentiation processes such as fractional crystallization. Nevertheless, effects of the limited fractionation have been erased through re-equilibration of the major and trace element abundances at primary conditions. Concentrations of Th after re-equilibration have been assumed as indexes of the partial melting degree, given the high incompatibility of the element, and enrichment ratios calculated for each trace element. Especially for LILE (Rb, Ba, K, Sr), the pattern of resulting enrichment ratios well matches that obtained from fractional melting of peridotite bearing hydrous phases (amphibole/phlogopite). This put forward the idea that magmas have been generated through partial melting of enriched mantle domains where hydrous minerals have been stabilized as a consequence of metasomatic processes. Refertilization of the mantle has been attributed to intrusion of hydrous silicate melts and fractional crystallization of hydrous cumulates. These refertilizing melts, inherited from an ancient subducted oceanic crust, intruded into a depleted oceanic lithosphere that remained stored for a long time (hundreds of Ma or Ga) before being re-entrained in partial melting. This means that magmas could have acquired their main geochemical differences in response of the variable depletion/enrichment degree of the heterogeneous mantle portion tapped at rather shallow depth (≤100 km). Our finding is another tessera in the open debate on the plume-related vs. non plume-related origin of Icelandic magmatism.

Partial-fraction expansion and inverse Laplace transform of a rational function with real coefficients

NASA Technical Reports Server (NTRS)

Chang, F.-C.; Mott, H.

1974-01-01

This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.

Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

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.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

NASA Astrophysics Data System (ADS)

Banerjee, Joydip; Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu

2017-04-01

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag-Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero - rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials d x (and d t) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δ x) α (and (Δ t) α ) with 0 < α < 1; called as `fractional differentials'. For arbitrarily small Δ x and Δ t (tending towards zero), these `fractional' differentials are greater than Δ x (and Δ t), i.e. (Δ x) α > Δ x and (Δ t) α > Δ t. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.

A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2017-09-01

In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

Fractional dynamics pharmacokinetics–pharmacodynamic models

PubMed Central

2010-01-01

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

NASA Astrophysics Data System (ADS)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Gamma-glutamyltransferase fractions in human plasma and bile: characteristic and biogenesis.

PubMed

Fornaciari, Irene; Fierabracci, Vanna; Corti, Alessandro; Aziz Elawadi, Hassan; Lorenzini, Evelina; Emdin, Michele; Paolicchi, Aldo; Franzini, Maria

2014-01-01

Total plasma gamma-glutamyltransferase (GGT) activity is a sensitive, non-specific marker of liver dysfunction. Four GGT fractions (b-, m-, s-, f-GGT) were described in plasma and their differential specificity in the diagnosis of liver diseases was suggested. Nevertheless fractional GGT properties have not been investigated yet. The aim of this study was to characterize the molecular nature of fractional GGT in both human plasma and bile. Plasma was obtained from healthy volunteers; whereas bile was collected from patients undergoing liver transplantation. Molecular weight (MW), density, distribution by centrifugal sedimentation and sensitivity to both detergent (deoxycholic acid) and protease (papain) were evaluated. A partial purification of b-GGT was obtained by ultracentrifugation. Plasma b-GGT fraction showed a MW of 2000 kDa and a density between 1.063-1.210 g/ml. Detergent converted b-GGT into s-GGT, whereas papain alone did not produce any effect. Plasma m-GGT and s-GGT showed a MW of 1,000 and 200 kDa, and densities between 1.006-1.063 g/ml and 1.063-1.210 g/ml respectively. Both fractions were unaffected by deoxycholic acid, while GGT activity was recovered into f-GGT peak after papain treatment. Plasma f-GGT showed a MW of 70 kDa and a density higher than 1.21 g/ml. We identified only two chromatographic peaks, in bile, showing similar characteristics as plasma b- and f-GGT fractions. These evidences, together with centrifugal sedimentation properties and immunogold electronic microscopy data, indicate that b-GGT is constituted of membrane microvesicles in both bile and plasma, m-GGT and s-GGT might be constituted of bile-acid micelles, while f-GGT represents the free-soluble form of the enzyme.

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.

Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow

NASA Astrophysics Data System (ADS)

Ali, Farhad; Imtiaz, Anees; Khan, Ilyas; Sheikh, Nadeem Ahmad

2018-06-01

In the sixteenth century, medical specialists were of the conclusion that magnet can be utilized for the treatment or wipe out the illnesses from the body. On this basis, the research on magnet advances day by day for the treatment of different types of diseases in mankind. This study aims to investigate the effect of magnetic field and their applications in human body specifically in blood. Blood is a non-Newtonian fluid because its viscosity depends strongly on the fraction of volume occupied by red cells also called the hematocrit. Therefore, in this paper blood is considered as an example of non-Newtonian Casson fluid. The blood flow is considered in a vertical cylinder together with heat transfer due to mixed conviction caused by buoyancy force and the external pressure gradient. Effect of magnetic field on the velocities of blood and magnetic particles is also considered. The problem is modelled using the Caputo-Fabrizio derivative approach. The governing fractional partial differential equations are solved using Laplace and Hankel transformation techniques and exact solutions are obtained. Effects of different parameters such as Grashof number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field are shown graphically. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field.

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

Microgravity modifies protein kinase C isoform translocation in the human monocytic cell line U937 and human peripheral blood T-cells

NASA Technical Reports Server (NTRS)

Hatton, Jason P.; Gaubert, Francois; Cazenave, Jean-Pierre; Schmitt, Didier; Hashemi, B. B. (Principal Investigator); Hughes-Fulford, M. (Principal Investigator)

2002-01-01

Individual protein kinase C (PKC) isoforms fulfill distinct roles in the regulation of the commitment to differentiation, cell cycle arrest, and apoptosis in both monocytes and T-cells. The human monocyte like cell line U937 and T-cells were exposed to microgravity, during spaceflight and the translocation (a critical step in PKC signaling) of individual isoforms to cell particulate fraction examined. PKC activating phorbol esters induced a rapid translocation of several PKC isoforms to the particulate fraction of U937 monocytes under terrestrial gravity (1 g) conditions in the laboratory. In microgravity, the translocation of PKC beta II, delta, and epsilon in response to phorbol esters was reduced in microgravity compared to 1 g, but was enhanced in weak hypergravity (1.4 g). All isoforms showed a net increase in particulate PKC following phorbol ester stimulation, except PKC delta which showed a net decrease in microgravity. In T-cells, phorbol ester induced translocation of PKC delta was reduced in microgravity, compared to 1 g, while PKC beta II translocation was not significantly different at the two g-levels. These data show that microgravity differentially alters the translocation of individual PKC isoforms in monocytes and T-cells, thus providing a partial explanation for the modifications previously observed in the activation of these cell types under microgravity.

Adult murine CNS stem cells express aquaporin channels.

PubMed

La Porta, Caterina A M; Gena, Patrizia; Gritti, Angela; Fascio, Umberto; Svelto, Maria; Calamita, Giuseppe

2006-02-01

Fluid homoeostasis is of critical importance in many functions of the CNS (central nervous system) as indicated by the fact that dysregulation of cell volume underlies clinical conditions such as brain oedema and hypoxia. Water balance is also important during neurogenesis as neural stem cells move considerable amounts of water into or out of the cell to rapidly change their volume during differentiation. Consistent with the relevance of water transport in CNS, multiple AQP (aquaporin) water channels have been recognized and partially characterized in brain cell function. However, the presence and distribution of AQPs in CNS stem cells has not yet been assessed. In the present study, we investigate the expression and subcellular localization of AQPs in murine ANSCs (adult neural stem cells). Considerable AQP8 mRNAs were found in ANSCs where, as expected, the transcript of two additional AQPs, AQP4 and AQP9, was also detected. Immunoblotting with subcellular membrane fractions of ANSCs showed predominant expression of AQP8 in the mitochondria-enriched fraction. This result was consistent with the spotted immunoreactivity profile encountered within the ANSCs by confocal immunofluorescence. AQP8 may have a role in mitochondrial volume regulation during ANSC differentiation. Recognition of AQPs in ANSCs is a step forward in our knowledge of water homoeostasis in the CNS and provides useful information for the purposes of stem cell technology.

Gender-dimorphic effects of adipose-derived stromal vascular fractions on HUVECs exposed to oxidative stress.

PubMed

Lim, Soyeon; Kim, Il-Kwon; Choi, Jung-Won; Seo, Hyang-Hee; Lim, Kyu Hee; Lee, Seahyoung; Lee, Hoon-Bum; Kim, Sang Woo; Hwang, Ki-Chul

2017-01-01

Stromal vascular fractions (SVFs) are a heterogeneous collection of cells within adipose tissue that are being studied for various clinical indications. In this study, we aimed to determine whether SVF transplantation into impaired tissues has differential effects on inflammatory and angiogenetic properties with regard to gender. As reactive oxygen species have been implicated in cardiovascular disease development, we investigated differences in gene and protein expression related to inflammation and angiogenesis in HUVECs co-cultured with adipose-derived SVFs from male (M group) and female (F group) individuals under oxidative stress conditions. The expression of several inflammatory (interleukin (IL)-33) and angiogenetic (platelet-derived growth factor (PDGF)) factors differed dramatically between male and female donors. Anti-inflammatory and pro-angiogenetic responses were observed in HUVECs co-cultured with SVFs under oxidative stress conditions, and these characteristics may exhibit partially differential effects according to gender. Using network analysis, we showed that co-culturing HUVECs with SVFs ameliorated pyroptosis/apoptosis via an increase in oxidative stress. Activation of caspase-1 and IL-1B was significantly altered in HUVECs co-cultured with SVFs from female donors. These findings regarding gender-dimorphic regulation of adipose-derived SVFs provide valuable information that can be used for evidence-based gender-specific clinical treatment of SVF transplantation for understanding of cardiovascular disease, allowing for the development of additional treatment.

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

Moments of the electron energy spectrum and partial branching fraction of B{yields}X{sub c}e{nu} decays at the Belle detector

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

Urquijo, P.; Barberio, E.; Dalseno, J.

2007-02-01

We report a measurement of the inclusive electron energy spectrum for charmed semileptonic decays of B mesons in a 140 fb{sup -1} data sample collected at the {upsilon}(4S) resonance with the Belle detector at the KEKB asymmetric energy e{sup +}e{sup -} collider. We determine the first four moments of the electron energy spectrum for threshold values of the electron energy between 0.4 and 2.0 GeV. In addition, we provide values of the partial branching fraction (zeroth moment) for the same electron threshold energies, and independent measurements of the B{sup +} and B{sup 0} partial branching fractions at 0.4 GeV andmore » 0.6 GeV electron threshold energies. We measure the independent B{sup +} and B{sup 0} partial branching fractions with electron threshold energies of 0.4 GeV to be {delta}B(B{sup +}{yields}X{sub c}e{nu})=(10.79{+-}0.25(stat.){+-}0.27(sys.))% and {delta}B(B{sup 0}{yields}X{sub c}e{nu})=(10.08{+-}0.30(stat.){+-}0.22(sys.))%. Full correlations between all measurements are evaluated.« less

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

NASA Astrophysics Data System (ADS)

Ravi Kanth, A. S. V.; Aruna, K.

2016-12-01

In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

NASA Technical Reports Server (NTRS)

Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

2002-01-01

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

Isotope mass fractionation during evaporation of Mg2SiO4

NASA Technical Reports Server (NTRS)

Davis, Andrew M.; Clayton, Robert N.; Mayeda, Toshiko K.; Hashimoto, Akihiko

1990-01-01

Synthetic forsterite (Mg2SiO4) was partially evaporated in vacuum for various durations and at different temperatures. The residual charges obtained when molten Mg2SiO4 was evaporated to 12 percent of its initial mass were enriched in heavy isotopes by about 20, 30, and 15 per mil/amu for O, Mg, and Si, respectively, whereas solid forsterite evaporated to a similar residual mass fraction showed negligible fractionations. These results imply that calcium and aluminum-rich refractory inclusions in carbonaceous chondrites must have been at least partially molten in the primordial solar nebula if the observed large mass fractionation effects were caused by evaporation processes in the nebula.

Fractional Brownian motion of an Al nanosphere in liquid Al-Si alloy under electron-beam irradiation

NASA Astrophysics Data System (ADS)

Yokota, Takeshi; Howe, J. M.; Jesser, W. A.; Murayama, M.

2004-05-01

Fractional forces and Brownian motion are expected to govern the behavior of nanoscale metallic solids in liquids, but such systems have not been studied. We investigated the motion of a crystalline Al nanosphere inside a partially molten Al-Si alloy particle, using an electron beam to both stimulate and observe the motion of the nanosphere. The irregular motion observed was quantified as antipersistant fractional Brownian motion. Analysis of possible phenomena contributing to the motion demonstrates that the incident electrons provide the fractional force that moves the Al nanosphere and that gravity and the oxide shell on the partially molten particle cause the antipersistant behavior.

Isolation of Autolysosomes from Tobacco BY-2 Cells.

PubMed

Takatsuka, Chihiro; Inoue-Aono, Yuko; Moriyasu, Yuji

2017-01-01

Autolysosomes are organelles that sequester and degrade a portion of the cytoplasm during autophagy. Although autophagosomes are short lived compared to other organelles such as mitochondria, plastids, and peroxisomes, many autolysosomes accumulate in tobacco BY-2 cells cultured under sucrose starvation conditions in the presence of a cysteine protease inhibitor. We here describe our methodology for isolating autolysosomes from BY-2 cells by conventional cell fractionation using a Percoll gradient. The autolysosome fraction separates clearly from fractions containing mitochondria and peroxisomes. It contains acid phosphatase, vacuolar H + -ATPase, and protease activity. Electron micrographs show that the fraction contains partially degraded cytoplasm seen in autolysosomes before isolation although an autolysosome structure is only partially preserved.

[Correlation between the inspired fraction of oxygen, maternal partial oxygen pressure, and fetal partial oxygen pressure during cesarean section of normal pregnancies].

PubMed

Castro, Carlos Henrique Viana de; Cruvinel, Marcos Guilherme Cunha; Carneiro, Fabiano Soares; Silva, Yerkes Pereira; Cabral, Antônio Carlos Vieira; Bessa, Roberto Cardoso

2009-01-01

Despite changes in pulmonary function, maternal oxygenation is maintained during obstetric regional blocks. But in those situations, the administration of supplementary oxygen to parturients is a common practice. Good fetal oxygenation is the main justification; however, this has not been proven. The objective of this randomized, prospective study was to test the hypothesis of whether maternal hyperoxia is correlated with an increase in fetal gasometric parameters in elective cesarean sections. Arterial blood gases of 20 parturients undergoing spinal block with different inspired fractions of oxygen were evaluated and correlated with fetal arterial blood gases. An increase in maternal inspired fraction of oxygen did not show any correlation with an increase of fetal partial oxygen pressure. Induction of maternal hyperoxia by the administration of supplementary oxygen did not increase fetal partial oxygen pressure. Fetal gasometric parameters did not change even when maternal parameters changed, induced by hyperoxia, during cesarean section under spinal block.

On the local fractional derivative of everywhere non-differentiable continuous functions on intervals

NASA Astrophysics Data System (ADS)

Liu, Cheng-shi

2017-01-01

We first prove that for a continuous function f(x) defined on an open interval, the Kolvankar-Gangal's (or equivalently Chen-Yan-Zhang's) local fractional derivative f(α)(x) is not continuous, and then prove that it is impossible that the KG derivative f(α)(x) exists everywhere on the interval and satisfies f(α)(x) ≠ 0 in the same time. In addition, we give a criterion of the nonexistence of the local fractional derivative of everywhere non-differentiable continuous functions. Furthermore, we construct two simple nowhere differentiable continuous functions on (0, 1) and prove that they have no the local fractional derivatives everywhere.

Assessment of simulated high-dose partial-body irradiation by PCC-R assay.

PubMed

Romero, Ivonne; García, Omar; Lamadrid, Ana I; Gregoire, Eric; González, Jorge E; Morales, Wilfredo; Martin, Cécile; Barquinero, Joan-Francesc; Voisin, Philippe

2013-09-01

The estimation of the dose and the irradiated fraction of the body is important information in the primary medical response in case of a radiological accident. The PCC-R assay has been developed for high-dose estimations, but little attention has been given to its applicability for partial-body irradiations. In the present work we estimated the doses and the percentage of the irradiated fraction in simulated partial-body radiation exposures at high doses using the PCC-R assay. Peripheral whole blood of three healthy donors was exposed to doses from 0-20 Gy, with ⁶⁰Co gamma radiation. To simulate partial body irradiations, irradiated and non-irradiated blood was mixed to obtain proportions of irradiated blood from 10-90%. Lymphocyte cultures were treated with Colcemid and Calyculin-A before harvest. Conventional and triage scores were performed for each dose, proportion of irradiated blood and donor. The Papworth's u test was used to evaluate the PCC-R distribution per cell. A dose-response relationship was fitted according to the maximum likelihood method using the frequencies of PCC-R obtained from 100% irradiated blood. The dose to the partially irradiated blood was estimated using the Contaminated Poisson method. A new D₀ value of 10.9 Gy was calculated and used to estimate the initial fraction of irradiated cells. The results presented here indicate that by PCC-R it is possible to distinguish between simulated partial- and whole-body irradiations by the u-test, and to accurately estimate the dose from 10-20 Gy, and the initial fraction of irradiated cells in the interval from 10-90%.

Eliminating the blood-flow confounding effect in intravoxel incoherent motion (IVIM) using the non-negative least square analysis in liver.

PubMed

Gambarota, Giulio; Hitti, Eric; Leporq, Benjamin; Saint-Jalmes, Hervé; Beuf, Olivier

2017-01-01

Tissue perfusion measurements using intravoxel incoherent motion (IVIM) diffusion-MRI are of interest for investigations of liver pathologies. A confounding factor in the perfusion quantification is the partial volume between liver tissue and large blood vessels. The aim of this study was to assess and correct for this partial volume effect in the estimation of the perfusion fraction. MRI experiments were performed at 3 Tesla with a diffusion-MRI sequence at 12 b-values. Diffusion signal decays in liver were analyzed using the non-negative least square (NNLS) method and the biexponential fitting approach. In some voxels, the NNLS analysis yielded a very fast-decaying component that was assigned to partial volume with the blood flowing in large vessels. Partial volume correction was performed by biexponential curve fitting, where the first data point (b = 0 s/mm 2 ) was eliminated in voxels with a very fast-decaying component. Biexponential fitting with partial volume correction yielded parametric maps with perfusion fraction values smaller than biexponential fitting without partial volume correction. The results of the current study indicate that the NNLS analysis in combination with biexponential curve fitting allows to correct for partial volume effects originating from blood flow in IVIM perfusion fraction measurements. Magn Reson Med 77:310-317, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Planetesimal core formation with partial silicate melting using in-situ high P, high T, deformation x-ray microtomography

NASA Astrophysics Data System (ADS)

Anzures, B. A.; Watson, H. C.; Yu, T.; Wang, Y.

2017-12-01

Differentiation is a defining moment in formation of terrestrial planets and asteroids. Smaller planetesimals likely didn't reach high enough temperatures for widescale melting. However, we infer that core formation must have occurred within a few million years from Hf-W dating. In lieu of a global magma ocean, planetesimals likely formed through inefficient percolation. Here, we used in-situ high temperature, high pressure, x-ray microtomography to track the 3-D evolution of the sample at mantle conditions as it underwent shear deformation. Lattice-Boltzmann simulations for permeability were used to characterize the efficiency of melt percolation. Mixtures of KLB1 peridotite plus 6.0 to 12.0 vol% FeS were pre-sintered to achieve an initial equilibrium microstructure, and then imaged through several consecutive cycles of heating and deformation. The maximum calculated melt segregation velocity was found to be 0.37 cm/yr for 6 vol.% FeS and 0.61 cm/year for 12 vol.% FeS, both below the minimum velocity of 3.3 cm/year required for a 100km planetesimal to fully differentiate within 3 million years. However, permeability is also a function of grain size and thus the samples having smaller grains than predicted for small planetesimals could have contributed to low permeability and also low migration velocity. The two-phase (sulfide melt and silicate melt) flow at higher melt fractions (6 vol.% and 12 vol.% FeS) was an extension of a similar study1 containing only sulfide melt at lower melt fraction (4.5 vol.% FeS). Contrary to the previous study, deformation did result in increased permeability until the sample was sheared by twisting the opposing Drickamer anvils by 360 degrees. Also, the presence of silicate melt caused the FeS melt to coalesce into less connected pathways as the experiment with 6 vol.% FeS was found to be less permeable than the one with 4.5 vol.% FeS but without any partial melt. The preliminary data from this study suggests that impacts as well as higher temperature leading to partial melting of the silicate portion of the mantle could have contributed to fast enough core formation. 1. Todd, K.A., Watson, H.C., Yu, T., Wang, Y., American Mineralogist, 101.9, 1996-2004, 2016

Teaching a New Method of Partial Fraction Decomposition to Senior Secondary Students: Results and Analysis from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong; Leung, Allen

2012-01-01

In this paper, we introduce a new approach to compute the partial fraction decompositions of rational functions and describe the results of its trials at three secondary schools in Hong Kong. The data were collected via quizzes, questionnaire and interviews. In general, according to the responses from the teachers and students concerned, this new…

Tissue-transglutaminase contributes to neutrophil granulocyte differentiation and functions.

PubMed

Balajthy, Zoltán; Csomós, Krisztián; Vámosi, György; Szántó, Attila; Lanotte, Michel; Fésüs, László

2006-09-15

Promyelocytic NB4 leukemia cells undergo differentiation to granulocytes following retinoic acid treatment. Here we report that tissue transglutaminase (TG2), a protein cross-linking enzyme, was induced, then partially translocated into the nucleus, and became strongly associated with the chromatin during the differentiation process. The transglutaminase-catalyzed cross-link content of both the cytosolic and the nuclear protein fractions increased while NB4 cells underwent cellular maturation. Inhibition of cross-linking activity of TG2 by monodansylcadaverin in these cells led to diminished nitroblue tetrazolium (NBT) positivity, production of less superoxide anion, and decreased expression of GP91PHOX, the membrane-associated subunit of NADPH oxidase. Neutrophils isolated from TG2(-/-) mice showed diminished NBT reduction capacity, reduced superoxide anion formation, and down-regulation of the gp91phox subunit of NADPH oxidase, compared with wild-type cells. It was also observed that TG2(-/-) mice exhibited increased neutrophil phagocytic activity, but had attenuated neutrophil chemotaxis and impaired neutrophil extravasation with higher neutrophil counts in their circulation during yeast extract-induced peritonitis. These results clearly suggest that TG2 may modulate the expression of genes related to neutrophil functions and is involved in several intracellular and extracellular functions of extravasating neutrophil.

Origin of major element chemical trends in DSDP Leg 37 basalts, Mid-Atlantic Ridge

USGS Publications Warehouse

Byerly, G.R.; Wright, T.L.

1978-01-01

In this paper we summarize the major element chemical variation for basalts from the Deep Sea Drilling Project Leg 37 and relate it to stratigraphic position in each of five drilling sites. Least-squares techniques are successfully used to quantify the nature and extent of alteration in these basalts, and to correct the major element analysis back to a magmatic, or alteration-free, composition on the assumption that alteration takes place in two ways: (1) secondary minerals are introduced into veins and vesicles, and (2) CO2 and H2O react with components in the rock to form a simple alteration assemblage. A chemical stratigraphy is defined for these basalts by grouping lavas whose chemistries are related by low-pressure phenocryst-liquid differentiation as identified by least-squares calculation. Major chemical-stratigraphic units are as much as 200 m thick; correlations of these units can be made between the holes at site 332 (about 100 m apart), but not between the other sites. Compositions of parental magmas are calculated by extrapolating low-pressure variations to a constant value of 9% MgO. The differences in these extrapolated compositions reflect high-pressure processes, and suggest that clinopyroxene may be an important phase in either intermediate-level fractionation of basaltic liquids, or as a residual phase during the partial melting which produces these basaltic liquids. Several of the basaltic liquids calculated as parental to the Leg 37 basalts have CaO contents greater than 14% and indicate that the oceanic mantle is richer in CaO and Al2O3 than values used in pyrolite models for the upper mantle. A model for magma generation and eruption beneath the Mid-Atlantic Ridge embodies the following characteristics: 1. (1) Separate magma batches are generated in the mantle. 2. (2) Each of these may be erupted directly or stored at shallow depth where significant fractionation takes place. Common fractionation processes are inferred to be gravitative settling of olivine, flotation (?) of plagioclase, and flow differentiation of an olivine-plagioclase-augite assemblage. 3. (3) Eruption of fractionated lava derived from earlier magma batches may alternate with eruption of younger less-fractionated or unfractionated magma. ?? 1978.

Temporal constraints on magma generation and differentiation in a continental volcano: Buckland, eastern Australia

NASA Astrophysics Data System (ADS)

Crossingham, Tracey J.; Ubide, Teresa; Vasconcelos, Paulo M.; Knesel, Kurt M.; Mallmann, Guilherme

2018-03-01

The eastern margin of the Australian continent hosts a large number of Cenozoic intraplate volcanoes along a 2000 km long track. Here, we study mafic lavas from the Buckland volcano, Queensland, located in the northern (older) segment of this track, to assess magma generation and differentiation through time. The rocks are aphanitic to microporphyritic basalts, trachy-basalts and basanites. Incompatible element geochemistry together with Sr-Nd-Pb isotope ratios indicate that magmas formed from an enriched mantle I (EMI)-like garnet-bearing source with variable degrees of crustal contamination. Whole rock elemental variations suggest fractionation of olivine, plagioclase, clinopyroxene and/or magnetite. There is no petrographic or geochemical evidence of magma mixing in the studied rocks (e.g., lack of recycled minerals), suggesting a relatively quick ascent from the source to the surface without major storage at shallow levels. 40Ar/39Ar geochronology reveals two stages of volcanism: 30.3 ± 0.1 Ma and 27.4 ± 0.2 Ma. The Old Buckland (30.3 ± 0.1 Ma) melts have negative K anomalies, and incompatible element ratios suggest the occurrence of residual hydrous minerals in a metasomatised mantle source. We therefore infer that at the onset of volcanism, deep-mantle-derived magmas interacted with metasomatised sub-continental lithospheric mantle (SCLM). Major and trace element data, clinopyroxene thermobarometry and thermodynamic modelling indicate magma evolution by assimilation and fractional crystallisation (AFC) during ascent through the crust. Following a hiatus in volcanic activity of 2.5 Ma, eruption of Young Buckland (27.4 ± 0.2 Ma) lavas marked a shift towards more alkaline compositions. Trace element compositions indicate lower degrees of partial melting and a lack of interaction with metasomatic components. Young Buckland lavas become progressively more SiO2-saturated up stratigraphy, suggesting an increase in the degree of partial melting with time. Young Buckland lavas also have more radiogenic 87Sr/86Sr and 207Pb/204Pb ratios and less radiogenic 143Nd/144Nd ratios up stratigraphy. These isotopic variations, together with coupled increases in Pb and K and decreases in Ce/Pb (27.22 to 11.09) and Nb/U (68.30 to 29.96), suggest that crustal contamination also increased with time. By placing absolute age and stratigraphic constraints on the Buckland lavas, we have been able to ascertain differentiation signatures imposed on mantle-derived melts during ascent through the continental lithosphere over 3 Ma. Our study provides new constraints on magma generation and differentiation in continental intraplate volcanic systems.

Elemental composition of the Martian crust.

PubMed

McSween, Harry Y; Taylor, G Jeffrey; Wyatt, Michael B

2009-05-08

The composition of Mars' crust records the planet's integrated geologic history and provides clues to its differentiation. Spacecraft and meteorite data now provide a global view of the chemistry of the igneous crust that can be used to assess this history. Surface rocks on Mars are dominantly tholeiitic basalts formed by extensive partial melting and are not highly weathered. Siliceous or calc-alkaline rocks produced by melting and/or fractional crystallization of hydrated, recycled mantle sources, and silica-poor rocks produced by limited melting of alkali-rich mantle sources, are uncommon or absent. Spacecraft data suggest that martian meteorites are not representative of older, more voluminous crust and prompt questions about their use in defining diagnostic geochemical characteristics and in constraining mantle compositional models for Mars.

The Effects of Core Composition on Iron Isotope Fractionation During Planetary Differentiation

NASA Astrophysics Data System (ADS)

Elardo, S. M.; Shahar, A.; Caracas, R.; Mock, T. D.; Sio, C. K. I.

2018-05-01

High pressure and temperature isotope exchange experiments and density functional theory calculations show how the composition of planetary cores affects the fractionation of iron isotopes during planetary differentiation.

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…

The Effect of Thermal Cycling on Crystal-Liquid Separation During Lunar Magma Ocean Differentiation

NASA Technical Reports Server (NTRS)

Mills, Ryan D.

2013-01-01

Differentiation of magma oceans likely involves a mixture of fractional and equilibrium crystallization [1]. The existence of: 1) large volumes of anorthosite in the lunar highlands and 2) the incompatible- rich (KREEP) reservoir suggests that fractional crystallization may have dominated during differentiation of the Moon. For this to have occurred, crystal fractionation must have been remarkably efficient. Several authors [e.g. 2, 3] have hypothesized that equilibrium crystallization would have dominated early in differentiation of magma oceans because of crystal entrainment during turbulent convection. However, recent numerical modeling [4] suggests that crystal settling could have occurred throughout the entire solidification history of the lunar magma ocean if crystals were large and crystal fraction was low. These results indicate that the crystal size distribution could have played an important role in differentiation of the lunar magma ocean. Here, I suggest that thermal cycling from tidal heating during lunar magma ocean crystallization caused crystals to coarsen, leading to efficient crystal-liquid separation.

Oxygen isotopes reveal crustal contamination and a large, still partially molten magma chamber in Chaîne des Puys (French Massif Central)

NASA Astrophysics Data System (ADS)

France, Lydéric; Demacon, Mickael; Gurenko, Andrey A.; Briot, Danielle

2016-09-01

The two main magmatic properties associated with explosive eruptions are high viscosity of silica-rich magmas and/or high volatile contents. Magmatic processes responsible for the genesis of such magmas are differentiation through crystallization, and crustal contamination (or assimilation) as this process has the potential to enhance crystallization and add volatiles to the initial budget. In the Chaîne des Puy series (French Massif Central), silica- and H2O-rich magmas were only emitted during the most recent eruptions (ca. 6-15 ka). Here, we use in situ measurements of oxygen isotopes in zircons from two of the main trachytic eruptions from the Chaîne des Puys to track the crustal contamination component in a sequence that was previously presented as an archetypal fractional crystallization series. Zircons from Sarcoui volcano and Puy de Dôme display homogeneous oxygen isotope compositions with δ18O = 5.6 ± 0.25‰ and 5.6 ± 0.3‰, respectively, and have therefore crystallized from homogeneous melts with δ18Omelt = 7.1 ± 0.3‰. Compared to mantle derived melts resulting from pure fractional crystallization (δ18Odif.mant. = 6.4 ± 0.4‰), those δ18Omelt values are enriched in 18O and support a significant role of crustal contamination in the genesis of silica-rich melts in the Chaîne des Puys. Assimilation-fractional-crystallization models highlight that the degree of contamination was probably restricted to 5.5-9.5% with Rcrystallization/Rassimilation varying between 8 and 14. The very strong intra-site homogeneity of the isotopic data highlights that magmas were well homogenized before eruption, and consequently that crustal contamination was not the trigger of silica-rich eruptions in the Chaîne des Puys. The exceptionally strong inter-site homogeneity of the isotopic data brings to light that Sarcoui volcano and Puy de Dôme were fed by a single large magma chamber. Our results, together with recent thermo-kinetic models and an experimental simulation (Martel et al., 2013), support the existence of a large ( 6-15 km3), still partially molten mid-crustal reservoir (10-12 km deep) that is filled with silica-rich magma. Calculated oxygen isotope compositions of the trachytic melts that crystallized the analyzed zircons for Puy de Dôme, Sarcoui dome, and Sarcoui phreatomagmatic deposits, and the range of values for each analyzed zircon grain. The range for trachytes obtained by pure fractional crystallization of mantle melts is given for comparison. See text for details on calculations. Chemical differentiation trend of Chaîne des Puys magmas (data from Boivin et al., 2009), and results of the fractional crystallization models presented herein and in Table 3. L1 is obtained after the first step of differentiation, and L2 after the second. The composition of Sarcoui trachytes is identified by an X. S3.1. Core-rim variations for oxygen isotope compositions of the studied zircons. S3.2. Oxygen isotope compositions of the various zircon domains observed with cathodoluminescence imaging (dark versus bright), and for zircons with different types of zoning (oscillatory versus sector). No systematic variation is observed.

Antileukemic Potential of Momordica charantia Seed Extracts on Human Myeloid Leukemic HL60 Cells

PubMed Central

Soundararajan, Ramani; Prabha, Punit; Rai, Umesh; Dixit, Aparna

2012-01-01

Momordica charantia (bitter gourd) has been used in the traditional system of medicine for the treatment of various diseases. Anticancer activity of M. charantia extracts has been demonstrated by numerous in vitro and in vivo studies. In the present study, we investigated the differentiation inducing potential of fractionated M. charantia seed extracts in human myeloid HL60 cells. We found that the HL60 cells treated with the fractionated seed extracts differentiated into granulocytic lineage as characterized by NBT staining, CD11b expression, and specific esterase activity. The differentiation inducing principle was found to be heat-stable, and organic in nature. The differentiation was accompanied by a downregulation of c-myc transcript, indicating the involvement of c-myc pathway, at least in part, in differentiation. Taken together these results indicate that fractionated extracts of M. charantia seeds possess differentiation inducing activity and therefore can be evaluated for their potential use in differentiation therapy for leukemia in combination with other inducers of differentiation. PMID:22654956

Geochemical evolution of Jurassic diorites from the Bristol Lake region, California, USA, and the role of assimilation

USGS Publications Warehouse

Young, E.D.; Wooden, J.L.; Shieh, Y.-N.; Farber, D.

1992-01-01

Late Jurassic dioritic plutons from the Bristol Lake region of the eastern Mojave Desert share several geochemical attributes with high-alumina basalts, continental hawaiite basalts, and high-K are andesites including: high K2O concentrations; high Al2O3 (16-19 weight %); elevated Zr/TiO2; LREE (light-rare-earth-element) enrichment (La/YbCN=6.3-13.3); and high Nb. Pearce element ratio analysis supported by petrographic relations demonstrates that P, Hf, and Zr were conserved during differentiation. Abundances of conserved elements suggest that dioritic plutons from neighboring ranges were derived from similar parental melts. In the most voluminous suite, correlated variations in elemental concentrations and (87Sr/86Sr)i indicate differentiation by fractional crystallization of hornblende and plagioclase combined with assimilation of a component characterized by abundant radiogenic Sr. Levenberg-Marquardt and Monte Carlo techniques were used to obtain optimal solutions to non-linear inverse models for fractional crystallization-assimilation processes. Results show that the assimilated material was chemically analogous to lower crustal mafic granulites and that the mass ratio of contaminant to parental magma was on the order of 0.1. Lack of enrichment in 18O with differentiation is consistent with the model results. Elemental concentrations and O, Sr, and Nd isotopic data point to a hydrous REE-enriched subcontinental lithospheric source similar to that which produced some Cenozoic continental hawaiites from the southern Cordillera. Isotopic compositions of associated granitoids suggest that partial melting of this subcontinental lithosphere may have been an important process in the development of the Late Jurassic plutonic arc of the eastern Mojave Desert. ?? 1992 Springer-Verlag.

FPLC and liquid-chromatography mass spectrometry identify candidate necrosis-inducing proteins from culture filtrates of the fungal wheat pathogen Zymoseptoria tritici.

PubMed

Ben M'Barek, Sarrah; Cordewener, Jan H G; Tabib Ghaffary, Seyed M; van der Lee, Theo A J; Liu, Zhaohui; Mirzadi Gohari, Amir; Mehrabi, Rahim; America, Antoine H P; Robert, Olivier; Friesen, Timothy L; Hamza, Sonia; Stergiopoulos, Ioannis; de Wit, Pierre J G M; Kema, Gerrit H J

2015-06-01

Culture filtrates (CFs) of the fungal wheat pathogen Zymoseptoria tritici were assayed for necrosis-inducing activity after infiltration in leaves of various wheat cultivars. Active fractions were partially purified and characterized. The necrosis-inducing factors in CFs are proteinaceous, heat stable and their necrosis-inducing activity is temperature and light dependent. The in planta activity of CFs was tested by a time series of proteinase K (PK) co-infiltrations, which was unable to affect activity 30min after CF infiltrations. This suggests that the necrosis inducing proteins (NIPs) are either absent from the apoplast and likely actively transported into mesophyll cells or protected from the protease by association with a receptor. Alternatively, plant cell death signaling pathways might be fully engaged during the first 30min and cannot be reversed even after PK treatment. Further fractionation of the CFs with the highest necrosis-inducing activity involved fast performance liquid chromatography, SDS-PAGE and mass spectrometry. This revealed that most of the proteins present in the fractions have not been described before. The two most prominent ZtNIP encoding candidates were heterologously expressed in Pichia pastoris and subsequent infiltration assays showed their differential activity in a range of wheat cultivars. Copyright © 2015 Elsevier Inc. All rights reserved.

Non-chondritic iron isotope ratios in planetary mantles as a result of core formation

NASA Astrophysics Data System (ADS)

Elardo, Stephen M.; Shahar, Anat

2017-02-01

Information about the materials and conditions involved in planetary formation and differentiation in the early Solar System is recorded in iron isotope ratios. Samples from Earth, the Moon, Mars and the asteroid Vesta reveal significant variations in iron isotope ratios, but the sources of these variations remain uncertain. Here we present experiments that demonstrate that under the conditions of planetary core formation expected for the Moon, Mars and Vesta, iron isotopes fractionate between metal and silicate due to the presence of nickel, and enrich the bodies' mantles in isotopically light iron. However, the effect of nickel diminishes at higher temperatures: under conditions expected for Earth's core formation, we infer little fractionation of iron isotopes. From our experimental results and existing conceptual models of magma ocean crystallization and mantle partial melting, we find that nickel-induced fractionation can explain iron isotope variability found in planetary samples without invoking nebular or accretionary processes. We suggest that near-chondritic iron isotope ratios of basalts from Mars and Vesta, as well as the most primitive lunar basalts, were achieved by melting of isotopically light mantles, whereas the heavy iron isotope ratios of terrestrial ocean floor basalts are the result of melting of near-chondritic Earth mantle.

A new fractional order derivative based active contour model for colon wall segmentation

NASA Astrophysics Data System (ADS)

Chen, Bo; Li, Lihong C.; Wang, Huafeng; Wei, Xinzhou; Huang, Shan; Chen, Wensheng; Liang, Zhengrong

2018-02-01

Segmentation of colon wall plays an important role in advancing computed tomographic colonography (CTC) toward a screening modality. Due to the low contrast of CT attenuation around colon wall, accurate segmentation of the boundary of both inner and outer wall is very challenging. In this paper, based on the geodesic active contour model, we develop a new model for colon wall segmentation. First, tagged materials in CTC images were automatically removed via a partial volume (PV) based electronic colon cleansing (ECC) strategy. We then present a new fractional order derivative based active contour model to segment the volumetric colon wall from the cleansed CTC images. In this model, the regionbased Chan-Vese model is incorporated as an energy term to the whole model so that not only edge/gradient information but also region/volume information is taken into account in the segmentation process. Furthermore, a fractional order differentiation derivative energy term is also developed in the new model to preserve the low frequency information and improve the noise immunity of the new segmentation model. The proposed colon wall segmentation approach was validated on 16 patient CTC scans. Experimental results indicate that the present scheme is very promising towards automatically segmenting colon wall, thus facilitating computer aided detection of initial colonic polyp candidates via CTC.

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Partially Turboelectric Aircraft Drive Key Performance Parameters

NASA Technical Reports Server (NTRS)

Jansen, Ralph H.; Duffy, Kirsten P.; Brown, Gerald V.

2017-01-01

The purpose of this paper is to propose electric drive specific power, electric drive efficiency, and electrical propulsion fraction as the key performance parameters for a partially turboelectric aircraft power system and to investigate their impact on the overall aircraft performance. Breguet range equations for a base conventional turbofan aircraft and a partially turboelectric aircraft are found. The benefits and costs that may result from the partially turboelectric system are enumerated. A break even analysis is conducted to find the minimum allowable electric drive specific power and efficiency, for a given electrical propulsion fraction, that can preserve the range, fuel weight, operating empty weight, and payload weight of the conventional aircraft. Current and future power system performance is compared to the required performance to determine the potential benefit.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

Differential Association of the Na+/H+ Exchanger Regulatory Factor (NHERF) Family of Adaptor Proteins with the Raft-and the Non-Raft Brush Border Membrane Fractions of NHE3

PubMed Central

Sultan, Ayesha; Luo, Min; Yu, Qin; Riederer, Brigitte; Xia, Weiliang; Chen, Mingmin; Lissner, Simone; Gessner, Johannes E.; Donowitz, Mark; Yun, C. Chris; deJonge, Hugo; Lamprecht, Georg; Seidler, Ursula

2014-01-01

Background/Aims Trafficking, brush border membrane (BBM) retention, and signal-specific regulation of the Na+/H+ exchanger NHE3 is regulated by the Na+/H+ Exchanger Regulatory Factor (NHERF) family of PDZ-adaptor proteins, which enable the formation of multiprotein complexes. It is unclear, however, what determines signal specificity of these NHERFs. Thus, we studied the association of NHE3, NHERF1 (EBP50), NHERF2 (E3KARP), and NHERF3 (PDZK1) with lipid rafts in murine small intestinal BBM. Methods Detergent resistant membranes (“lipid rafts”) were isolated by floatation of Triton X-incubated small intestinal BBM from a variety of knockout mouse strains in an Optiprep step gradient. Acid-activated NHE3 activity was measured fluorometrically in BCECF-loaded microdissected villi, or by assessment of CO2/HCO3− mediated increase in fluid absorption in perfused jejunal loops of anethetized mice. Results NHE3 was found to partially associate with lipid rafts in the native BBM, and NHE3 raft association had an impact on NHE3 transport activity and regulation in vivo. NHERF1, 2 and 3 were differentially distributed to rafts and non-rafts, with NHERF2 being most raft-associated and NHERF3 entirely non-raft associated. NHERF2 expression enhanced the localization of NHE3 to membrane rafts. The use of acid sphingomyelinase-deficient mice, which have altered membrane lipid as well as lipid raft composition, allowed us to test the validity of the lipid raft concept in vivo. Conclusions The differential association of the NHERFs with the raft-associated and the non-raft fraction of NHE3 in the brush border membrane is one component of the differential and signal-specific NHE3 regulation by the different NHERFs. PMID:24297041

Differential association of the Na+/H+ Exchanger Regulatory Factor (NHERF) family of adaptor proteins with the raft- and the non-raft brush border membrane fractions of NHE3.

PubMed

Sultan, Ayesha; Luo, Min; Yu, Qin; Riederer, Brigitte; Xia, Weiliang; Chen, Mingmin; Lissner, Simone; Gessner, Johannes E; Donowitz, Mark; Yun, C Chris; deJonge, Hugo; Lamprecht, Georg; Seidler, Ursula

2013-01-01

Trafficking, brush border membrane (BBM) retention, and signal-specific regulation of the Na+/H+ exchanger NHE3 is regulated by the Na+/H+ Exchanger Regulatory Factor (NHERF) family of PDZ-adaptor proteins, which enable the formation of multiprotein complexes. It is unclear, however, what determines signal specificity of these NHERFs. Thus, we studied the association of NHE3, NHERF1 (EBP50), NHERF2 (E3KARP), and NHERF3 (PDZK1) with lipid rafts in murine small intestinal BBM. Detergent resistant membranes ("lipid rafts") were isolated by floatation of Triton X-incubated small intestinal BBM from a variety of knockout mouse strains in an Optiprep step gradient. Acid-activated NHE3 activity was measured fluorometrically in BCECF-loaded microdissected villi, or by assessment of CO2/HCO3(-) mediated increase in fluid absorption in perfused jejunal loops of anethetized mice. NHE3 was found to partially associate with lipid rafts in the native BBM, and NHE3 raft association had an impact on NHE3 transport activity and regulation in vivo. NHERF1, 2 and 3 were differentially distributed to rafts and non-rafts, with NHERF2 being most raft-associated and NHERF3 entirely non-raft associated. NHERF2 expression enhanced the localization of NHE3 to membrane rafts. The use of acid sphingomyelinase-deficient mice, which have altered membrane lipid as well as lipid raft composition, allowed us to test the validity of the lipid raft concept in vivo. The differential association of the NHERFs with the raft-associated and the non-raft fraction of NHE3 in the brush border membrane is one component of the differential and signal-specific NHE3 regulation by the different NHERFs. © 2013 S. Karger AG, Basel.

Three-year outcomes of a once daily fractionation scheme for accelerated partial breast irradiation (APBI) using 3-D conformal radiotherapy (3D-CRT)

PubMed Central

Goyal, Sharad; Daroui, Parima; Khan, Atif J; Kearney, Thomas; Kirstein, Laurie; Haffty, Bruce G

2013-01-01

The aim of this study was to report 3-year outcomes of toxicity, cosmesis, and local control using a once daily fractionation scheme (49.95 Gy in 3.33 Gy once daily fractions) for accelerated partial breast irradiation (APBI) using three-dimensional conformal radiotherapy (3D-CRT). Between July 2008 and August 2010, women aged ≥40 years with ductal carcinoma in situ or node-negative invasive breast cancer ≤3 cm in diameter, treated with breast-conserving surgery achieving negative margins, were accrued to a prospective study. Women were treated with APBI using 3–5 photon beams, delivering 49.95 Gy over 15 once daily fractions over 3 weeks. Patients were assessed for toxicities, cosmesis, and local control rates before APBI and at specified time points. Thirty-four patients (mean age 60 years) with Tis 0 (n = 9) and T1N0 (n = 25) breast cancer were treated and followed up for an average of 39 months. Only 3% (1/34) patients experienced a grade 3 subcutaneous fibrosis and breast edema and 97% of the patients had good/excellent cosmetic outcome at 3 years. The 3-year rate of ipsilateral breast tumor recurrence (IBTR) was 0% while the rate of contralateral breast events was 6%. The 3-year disease-free survival (DFS), overall survival (OS), and breast cancer-specific survival (BCSS) was 94%, 100%, and 100%, respectively. Our novel accelerated partial breast fractionation scheme of 15 once daily fractions of 3.33 Gy (49.95 Gy total) is a remarkably well-tolerated regimen of 3D-CRT-based APBI. A larger cohort of patients is needed to further ascertain the toxicity of this accelerated partial breast regimen. PMID:24403270

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.

Raman spectroscopy differentiates squamous cell carcinoma (SCC) from normal skin following treatment with a high-powered CO2 laser.

PubMed

Fox, Sara A; Shanblatt, Ashley A; Beckman, Hugh; Strasswimmer, John; Terentis, Andrew C

2014-12-01

The number of cases of non-melanoma skin cancer (NMSC), which include squamous cell carcinoma (SCC) and basal cell carcinoma (BCC), continues to rise as the aging population grows. Mohs micrographic surgery has become the treatment of choice in many cases but is not always necessary or feasible. Ablation with a high-powered CO2 laser offers the advantage of highly precise, hemostatic tissue removal. However, confirmation of complete cancer removal following ablation is difficult. In this study we tested for the first time the feasibility of using Raman spectroscopy as an in situ diagnostic method to differentiate NMSC from normal tissue following partial ablation with a high-powered CO2 laser. Twenty-five tissue samples were obtained from eleven patients undergoing Mohs micrographic surgery to remove NMSC tumors. Laser treatment was performed with a SmartXide DOT Fractional CO2 Laser (DEKA Laser Technologies, Inc.) emitting a wavelength of 10.6 μm. Treatment levels ranged from 20 mJ to 1200 mJ total energy delivered per laser treatment spot (350 μm spot size). Raman spectra were collected from both untreated and CO2 laser-treated samples using a 785 nm diode laser. Principal Component Analysis (PCA) and Binary Logistic Regression (LR) were used to classify spectra as originating from either normal or NMSC tissue, and from treated or untreated tissue. Partial laser ablation did not adversely affect the ability of Raman spectroscopy to differentiate normal from cancerous residual tissue, with the spectral classification model correctly identifying SCC tissue with 95% sensitivity and 100% specificity following partial laser ablation, compared with 92% sensitivity and 60% selectivity for untreated NMSC tissue. The main biochemical difference identified between normal and NMSC tissue was high levels of collagen in the normal tissue, which was lacking in the NMSC tissue. The feasibility of a combined high-powered CO2 laser ablation, Raman diagnostic procedure for the treatment of NMSC is demonstrated since CO2 laser treatment does not hinder the ability of Raman spectroscopy to differentiate normal from diseased tissue. This combined approach could be employed clinically to greatly enhance the speed and effectiveness of NMSC treatment in many cases. © 2014 Wiley Periodicals, Inc.

Differential expression of human lysyl hydroxylase genes, lysine hydroxylation, and cross-linking of type I collagen during osteoblastic differentiation in vitro

NASA Technical Reports Server (NTRS)

Uzawa, K.; Grzesik, W. J.; Nishiura, T.; Kuznetsov, S. A.; Robey, P. G.; Brenner, D. A.; Yamauchi, M.

1999-01-01

The pattern of lysyl hydroxylation in the nontriple helical domains of collagen is critical in determining the cross-linking pathways that are tissue specific. We hypothesized that the tissue specificity of type I collagen cross-linking is, in part, due to the differential expression of lysyl hydroxylase genes (Procollagen-lysine,2-oxyglutarate,5-dioxygenase 1, 2, and 3 [PLOD1, PLOD2, and PLOD3]). In this study, we have examined the expression patterns of these three genes during the course of in vitro differentiation of human osteoprogenitor cells (bone marrow stromal cells [BMSCs]) and normal skin fibroblasts (NSFs). In addition, using the medium and cell layer/matrix fractions in these cultures, lysine hydroxylation of type I collagen alpha chains and collagen cross-linking chemistries have been characterized. High levels of PLOD1 and PLOD3 genes were expressed in both BMSCs and NSFs, and the expression levels did not change in the course of differentiation. In contrast to the PLOD1 and PLOD3 genes, both cell types showed low PLOD2 gene expression in undifferentiated and early differentiated conditions. However, fully differentiated BMSCs, but not NSFs, exhibited a significantly elevated level (6-fold increase) of PLOD2 mRNA. This increase coincided with the onset of matrix mineralization and with the increase in lysyl hydroxylation in the nontriple helical domains of alpha chains of type I collagen molecule. Furthermore, the collagen cross-links that are derived from the nontriple helical hydroxylysine-aldehyde were found only in fully differentiated BMSC cultures. The data suggests that PLOD2 expression is associated with lysine hydroxylation in the nontriple helical domains of collagen and, thus, could be partially responsible for the tissue-specific collagen cross-linking pattern.

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…

Copper isotope behavior during extreme magma differentiation and degassing: a case study on Laacher See phonolite tephra (East Eifel, Germany)

NASA Astrophysics Data System (ADS)

Huang, Jian; Liu, Sheng-Ao; Wörner, Gerhard; Yu, Huimin; Xiao, Yilin

2016-09-01

Copper (Cu) isotopic analyses were performed on a set of samples from the Laacher See tephra (LST) (Eifel, Germany) to investigate whether Cu isotopes are fractionated during extreme magma differentiation and degassing. The LST represents a continuous fractional crystallization series from parental basanite through mafic to highly differentiated phonolites. Samples analyzed here include phonolites of variable degrees of differentiation, phonolite-basanite hybrid rocks formed by mixing basanite and phonolite magmas, and basanite-derived mega-crystals (i.e., clinopyroxene, amphibole, phlogopite). In addition, we analyzed a series of mafic parental lavas from surrounding volcanic centers to constrain the Cu isotopic features of the Eifel mantle. Mafic phonolites show strong depletion in Cu compared to their parental basanites from ~50 to ~3 ppm, indicating sulfide fractionation during the basanite-to-phonolite differentiation. Mass balance calculations, based on the most Cu-rich hybrid rock (δ65Cu = -0.21 ‰, [Cu] = 46.2 ppm), show that the parental basanite magmas have δ65Cu of ca. -0.21 ‰, lighter than those of the mafic phonolites (~0.11 ‰). This suggests that sulfide fractionation preferentially removes the lighter Cu isotope (63Cu) in S-saturated magmas. By contrast, all phonolites have a limited range of Cu contents (1.1 to 4.0 ppm) with no systematic variations with S, suggesting that Cu is not controlled by sulfide fractionation during the evolution of mafic to highly differentiated phonolites. The identical δ65Cu values (0.11 ± 0.03 ‰, 2SD, n = 10) of the phonolites, irrespective of highly diverse composition and extents of differentiation, indicate that fractional crystallization of silicates (e.g., plagioclase, sanidine, amphibole, pyroxene, olivine), Fe-Ti-oxides and phosphate (e.g., apatite) generates insignificant Cu isotope fractionation. The lack of correlations between δ65Cu and volatile contents (e.g., S, Cl) in the LST sequence implies that volcanic degassing causes no detectable Cu isotope fractionation of igneous rocks. Eifel basalts and mega-crystals have variable δ65Cu (-0.18 to 0.21 ‰) that are uncorrelated to MgO and Cu, suggesting that such variations were not caused by differentiation but reflect the Cu isotopic heterogeneity of the Eifel mantle source due to metasomatism by fluids derived from hydrothermally altered oceanic lithosphere.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

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.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Design of an all-optical fractional-order differentiator with terahertz bandwidth based on a fiber Bragg grating in transmission.

PubMed

Liu, Xin; Shu, Xuewen

2017-08-20

All-optical fractional-order temporal differentiators with bandwidths reaching terahertz (THz) values are demonstrated with transmissive fiber Bragg gratings. Since the designed fractional-order differentiator is a minimum phase function, the reflective phase of the designed function can be chosen arbitrarily. As examples, we first design several 0.5th-order differentiators with bandwidths reaching the THz range for comparison. The reflective phases of the 0.5th-order differentiators are chosen to be linear phase, quadratic phase, cubic phase, and biquadratic phase, respectively. We find that both the maximum coupling coefficient and the spatial resolution of the designed grating increase when the reflective phase varies from quadratic function to cubic function to biquadratic function. Furthermore, when the reflective phase is chosen to be a quadratic function, the obtained grating coupling coefficient and period are more likely to be achieved in practice. Then we design fractional-order differentiators with different orders when the reflective phase is chosen to be a quadratic function. We see that when the designed order of the differentiator increases, the obtained maximum coupling coefficient also increases while the oscillation of the coupling coefficient decreases. Finally, we give the numerical performance of the designed 0.5th-order differentiator by showing its temporal response and calculating its cross-correlation coefficient.

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.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

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.

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.

Fast-HPLC Fingerprinting to Discriminate Olive Oil from Other Edible Vegetable Oils by Multivariate Classification Methods.

PubMed

Jiménez-Carvelo, Ana M; González-Casado, Antonio; Pérez-Castaño, Estefanía; Cuadros-Rodríguez, Luis

2017-03-01

A new analytical method for the differentiation of olive oil from other vegetable oils using reversed-phase LC and applying chemometric techniques was developed. A 3 cm short column was used to obtain the chromatographic fingerprint of the methyl-transesterified fraction of each vegetable oil. The chromatographic analysis took only 4 min. The multivariate classification methods used were k-nearest neighbors, partial least-squares (PLS) discriminant analysis, one-class PLS, support vector machine classification, and soft independent modeling of class analogies. The discrimination of olive oil from other vegetable edible oils was evaluated by several classification quality metrics. Several strategies for the classification of the olive oil were used: one input-class, two input-class, and pseudo two input-class.

Isolation and characterization of the CNBr peptides from the proteolytically derived N-terminal fragment of ovine opsin.

PubMed Central

Brett, M; Findlay, J B

1983-01-01

Ovine rhodopsin may be cleaved in situ by Staphylococcus aureus V8 proteinase into two membrane-bound fragments designated V8-L (27 000 mol.wt.) and V8-S (12 000 mol.wt.). After purification of the proteolysed complex by affinity chromatography in detergent using concanavalin A immobilized on Sepharose 4B, the two polypeptide fragments may be separated by gel-permeation chromatography on Sephadex LH-60. Digestion of the N-terminal-derived V8-L fragment with CNBr in 70% (v/v) trifluoroacetic acid resulted in a peptide mixture that could be fractionated by procedures involving gel-permeation chromatography in organic and aqueous solvents and the use of differential solubility. The complete or partial sequences of all ten peptides are reported. PMID:6224479

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.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

PubMed Central

Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

2013-01-01

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

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.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Electrical conductivity of basaltic and carbonatite melt-bearing peridotites at high pressures: Implications for melt distribution and melt fraction in the upper mantle

NASA Astrophysics Data System (ADS)

Yoshino, Takashi; Laumonier, Mickael; McIsaac, Elizabeth; Katsura, Tomoo

2010-07-01

Electrical impedance measurements were performed on two types of partial molten samples with basaltic and carbonatitic melts in a Kawai-type multi-anvil apparatus in order to investigate melt fraction-conductivity relationships and melt distribution of the partial molten mantle peridotite under high pressure. The silicate samples were composed of San Carlos olivine with various amounts of mid-ocean ridge basalt (MORB), and the carbonate samples were a mixture of San Carlos olivine with various amounts of carbonatite. High-pressure experiments on the silicate and carbonate systems were performed up to 1600 K at 1.5 GPa and up to at least 1650 K at 3 GPa, respectively. The sample conductivity increased with increasing melt fraction. Carbonatite-bearing samples show approximately one order of magnitude higher conductivity than basalt-bearing ones at the similar melt fraction. A linear relationship between log conductivity ( σbulk) and log melt fraction ( ϕ) can be expressed well by the Archie's law (Archie, 1942) ( σbulk/ σmelt = Cϕn) with parameters C = 0.68 and 0.97, n = 0.87 and 1.13 for silicate and carbonate systems, respectively. Comparison of the electrical conductivity data with theoretical predictions for melt distribution indicates that the model assuming that the grain boundary is completely wetted by melt is the most preferable melt geometry. The gradual change of conductivity with melt fraction suggests no permeability jump due to melt percolation at a certain melt fraction. The melt fraction of the partial molten region in the upper mantle can be estimated to be 1-3% and ˜ 0.3% for basaltic melt and carbonatite melt, respectively.

The distribution of zirconium and hafnium in terrestrial rocks, meteorites and the moon

NASA Technical Reports Server (NTRS)

Ehmann, W. D.; Chyi, L. L.; Garg, A. N.; Ali, M. Z.

1979-01-01

It is shown that Zr and Hf are not always fractionated in terrestrial igneous differentiation or regional metamorphism. Data do support a Zr-Hf fractionation in the differentiation of the alkali olivine magma at St. Helena Island. A strong Zr-Hf fractionation exists among lunar rocks and minerals. Ilmenite is an excellent concentrator of Zr and Hf and always exhibits high Zr/Hf ratios. Chondritic meteorites exhibit rather uniform Zr abundances and Zr/Hf ratios but a distinct Zr-Hf fractionation is observed among the eucrite and diogenite achondrites.

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.

Rapid determination of chemical composition and classification of bamboo fractions using visible-near infrared spectroscopy coupled with multivariate data analysis.

PubMed

Yang, Zhong; Li, Kang; Zhang, Maomao; Xin, Donglin; Zhang, Junhua

2016-01-01

During conversion of bamboo into biofuels and chemicals, it is necessary to efficiently predict the chemical composition and digestibility of biomass. However, traditional methods for determination of lignocellulosic biomass composition are expensive and time consuming. In this work, a novel and fast method for quantitative and qualitative analysis of chemical composition and enzymatic digestibilities of juvenile bamboo and mature bamboo fractions (bamboo green, bamboo timber, bamboo yellow, bamboo node, and bamboo branch) using visible-near infrared spectra was evaluated. The developed partial least squares models yielded coefficients of determination in calibration of 0.88, 0.94, and 0.96, for cellulose, xylan, and lignin of bamboo fractions in raw spectra, respectively. After visible-near infrared spectra being pretreated, the corresponding coefficients of determination in calibration yielded by the developed partial least squares models are 0.994, 0.990, and 0.996, respectively. The score plots of principal component analysis of mature bamboo, juvenile bamboo, and different fractions of mature bamboo were obviously distinguished in raw spectra. Based on partial least squares discriminant analysis, the classification accuracies of mature bamboo, juvenile bamboo, and different fractions of bamboo (bamboo green, bamboo timber, bamboo yellow, and bamboo branch) all reached 100 %. In addition, high accuracies of evaluation of the enzymatic digestibilities of bamboo fractions after pretreatment with aqueous ammonia were also observed. The results showed the potential of visible-near infrared spectroscopy in combination with multivariate analysis in efficiently analyzing the chemical composition and hydrolysabilities of lignocellulosic biomass, such as bamboo fractions.

Use of Stirred Suspension Bioreactors for Male Germ Cell Enrichment.

PubMed

Sakib, Sadman; Dores, Camila; Rancourt, Derrick; Dobrinski, Ina

2016-01-01

Spermatogenesis is a stem cell based system. Both therapeutic and biomedical research applications of spermatogonial stem cells require a large number of cells. However, there are only few germ line stem cells in the testis, contained in the fraction of undifferentiated spermatogonia. The lack of specific markers makes it difficult to isolate these cells. The long term maintenance and proliferation of nonrodent germ cells in culture has so far been met with limited success, partially due to the lack of highly enriched starting populations. Differential plating, which depends on the differential adhesion properties of testicular somatic and germ cells to tissue culture dishes, has been the method of choice for germ cell enrichment, especially for nonrodent germ cells. However, for large animals, this process becomes labor intensive and increases variability due to the need for extensive handling. Here, we describe the use of stirred suspension bioreactors, as a novel system for enriching undifferentiated germ cells from 1-week-old pigs. This method capitalizes on the adherent properties of somatic cells within a controlled environment, thus promoting the enrichment of progenitor cells with minimal handling and variability.

Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet

NASA Astrophysics Data System (ADS)

Siddheshwar, Pradeep Ganapathi; Nerolu, Meenakshi; Pažanin, Igor

2017-08-01

Flow of a Newtonian nanoliquid due to a curved stretching sheet and heat transfer in it is studied. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations with variable coefficients by using a similarity transformation. The flow characteristics are studied using plots of flow velocity components and the skin-friction coefficient as a function of suction-injection parameter, curvature, and volume fraction. Prescribed surface temperature and prescribed surface heat flux are considered for studying the temperature distribution in the flow. The thermophysical properties of 20 nanoliquids are considered in the investigation by modeling them through the use of phenomenological laws and mixture theory. The results of the corresponding problem involving a plane stretching sheet is obtained as a particular case of those obtained in the present paper. Skin friction coefficient and Nusselt number are evaluated and it is observed that skin friction coefficient decreases with concentration of nanoparticles in the absence as well as presence of suction where as Nusselt number increases with increase in concentration of nanoparticles in a dilute range.

Purification of fetal mouse hepatoblasts by magnetic beads coated with monoclonal anti-e-cadherin antibodies and their in vitro culture.

PubMed

Nitou, Miho; Sugiyama, Yoshinori; Ishikawa, Katsutoshi; Shiojiri, Nobuyoshi

2002-10-01

A simple, rapid, and reproducible method of fetal hepatoblast purification was established to investigate mechanisms controlling interactions between hepatoblasts and nonparenchymal cells during liver development. Because E-cadherin is exclusively expressed on the cell membrane of hepatoblasts, magnetic beads coated with monoclonal antibodies to an extracellular epitope of its molecule were used to purify hepatoblasts from a cell suspension prepared from 12.5-day fetal mouse livers. The purity and yield in the hepatoblast fraction prepared in our protocol were more than 90% and approximately 30%, respectively. The nonparenchymal fraction rarely contained hepatoblasts; the rate of hepatoblast contamination in this fraction was less than 1%. Separate cultures of these two fractions were compared with cocultures of both fractions. In culture of the hepatoblast fraction, hepatoblasts formed aggregates similar to a bunch of grapes via their loose adhesion, floating in the medium after 24 h, and dissociated into single cells from the aggregates after 120 h of culture. By contrast, in the mixed culture, the majority of hepatoblasts formed multicellular spheroids after 24 h, and these spheroids changed into monolayer cell sheets after 120 h of culture. The cells comprising these monolayer sheets abundantly expressed albumin and carbamoylphosphate synthase I. In the mixed culture, fibroblastic cells also proliferated extensively with spreading on glass slides and surrounded the hepatoblast or hepatocyte colonies. On the other hand, fibroblastic cells spreading on glass slides decreased gradually in cultures of the nonparenchymal cell fraction alone. These findings indicated that the coexistence of hepatoblasts and nonparenchymal cells may be essential for their mutual survival, proliferation, differentiation, and morphogenesis. The conditioned medium of fetal liver cell cultures could partially replace the effects of the nonparenchymal cells on hepatoblasts in vitro. Our isolation protocol for fetal mouse hepatoblasts using immunobeads can greatly facilitate studies on mechanisms of cell-cell interactions during liver development.

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.

Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems.

PubMed

Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A

2016-01-01

This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

LES/PDF studies of joint statistics of mixture fraction and progress variable in piloted methane jet flames with inhomogeneous inlet flows

NASA Astrophysics Data System (ADS)

Zhang, Pei; Barlow, Robert; Masri, Assaad; Wang, Haifeng

2016-11-01

The mixture fraction and progress variable are often used as independent variables for describing turbulent premixed and non-premixed flames. There is a growing interest in using these two variables for describing partially premixed flames. The joint statistical distribution of the mixture fraction and progress variable is of great interest in developing models for partially premixed flames. In this work, we conduct predictive studies of the joint statistics of mixture fraction and progress variable in a series of piloted methane jet flames with inhomogeneous inlet flows. The employed models combine large eddy simulations with the Monte Carlo probability density function (PDF) method. The joint PDFs and marginal PDFs are examined in detail by comparing the model predictions and the measurements. Different presumed shapes of the joint PDFs are also evaluated.

The Effect of Large Melt Fraction on the Deformation Behavior of Peridotite: Implications for the Rheology of Io' Mantle

NASA Technical Reports Server (NTRS)

Scott, T.; Kohlstedt, D. L.

2004-01-01

One key constraint needed for refinement of the interior geochemical and geodynamic models of Io is the viscosity of the convecting partially- molten silicate mantle. To date, laboratory studies of partially molten mantle rocks have reached melt fractions up to approx.0.12, a value much smaller than thought to be appropriate for the asthenosphere of Io where the degree of partial melting may be 0.15 0.40 or higher. Therefore, we have performed a series of high temperature, triaxial compressive creep experiments on dry synthetic peridotites in a gas medium apparatus at a confining pressure of 300 MPa and temperatures from 1473 to 1573 K in order to understand the influence of large amounts of melt (0.15 < phi < 0.40) on the rheological behavior of partially molten rocks.

Measurement of branching fractions and rate asymmetries in the rare decays B→K (*)l⁺l⁻

DOE PAGES

Lees, J. P.; Poireau, V.; Tisserand, V.; ...

2012-08-24

In a sample of 471×10⁶ BB¯¯¯ events collected with the BABAR detector at the PEP-II e⁺e⁻ collider we study the rare decays B→K (*)l⁺l⁻, where l⁺l⁻ is either e⁺e⁻ or μ⁺μ⁻. We report results on partial branching fractions and isospin asymmetries in seven bins of dilepton mass-squared. We further present CP and lepton-flavor asymmetries for dilepton masses below and above the J/ψ resonance. We find no evidence for CP or lepton-flavor violation. The partial branching fractions and isospin asymmetries are consistent with the Standard Model predictions and with results from other experiments.

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

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Ford, Neville J.; Connolly, Joseph A.

2009-07-01

We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

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.

On new fractional Hermite-Hadamard type inequalities for n-time differentiable quasi-convex functions and P-functions

NASA Astrophysics Data System (ADS)

Set, Erhan; Özdemir, M. Emin; Alan, E. Aykan

2017-04-01

In this article, by using the Hölder's inequality and power mean inequality the authors establish several inequalities of Hermite-Hadamard type for n- time differentiable quasi-convex functions and P- functions involving Riemann-Liouville fractional integrals.

Electromagnetic field computation at fractal dimensions

NASA Astrophysics Data System (ADS)

Zubair, M.; Ang, Y. S.; Ang, L. K.

According to Mandelbrot's work on fractals, many objects are in fractional dimensions that the traditional calculus or differential equations are not sufficient. Thus fractional models solving the relevant differential equations are critical to understand the physical dynamics of such objects. In this work, we develop computational electromagnetics or Maxwell equations in fractional dimensions. For a given degree of imperfection, impurity, roughness, anisotropy or inhomogeneity, we consider the complicated object can be formulated into a fractional dimensional continuous object characterized by an effective fractional dimension D, which can be calculated from a self-developed algorithm. With this non-integer value of D, we develop the computational methods to design and analyze the EM scattering problems involving rough surfaces or irregularities in an efficient framework. The fractional electromagnetic based model can be extended to other key differential equations such as Schrodinger or Dirac equations, which will be useful for design of novel 2D materials stacked up in complicated device configuration for applications in electronics and photonics. This work is supported by Singapore Temasek Laboratories (TL) Seed Grant (IGDS S16 02 05 1).

Measurements of the S-wave fraction in B 0 → K + π - μ + μ - decays and the B 0 → K ∗(892)0 μ + μ - differential branching fraction

NASA Astrophysics Data System (ADS)

Aaij, R.; Adeva, B.; Adinolfi, M.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; d'Argent, P.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Bay, A.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Bellee, V.; Belloli, N.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bertolin, A.; Bettler, M.-O.; van Beuzekom, M.; Bifani, S.; Billoir, P.; Bird, T.; Birnkraut, A.; Bitadze, A.; Bizzeti, A.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Boettcher, T.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borisyak, M.; Borsato, M.; Bossu, F.; Boubdir, M.; Bowcock, T. J. V.; Bowen, E.; Bozzi, C.; Braun, S.; Britsch, M.; Britton, T.; Brodzicka, J.; Buchanan, E.; Burr, C.; Bursche, A.; Buytaert, J.; Cadeddu, S.; Calabrese, R.; Calvi, M.; Calvo Gomez, M.; Campana, P.; Campora Perez, D.; Capriotti, L.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carniti, P.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Cassina, L.; Castillo Garcia, L.; Cattaneo, M.; Cauet, Ch.; Cavallero, G.; Cenci, R.; Charles, M.; Charpentier, Ph.; Chatzikonstantinidis, G.; Chefdeville, M.; Chen, S.; Cheung, S.-F.; Chobanova, V.; Chrzaszcz, M.; Cid Vidal, X.; Ciezarek, G.; Clarke, P. E. L.; Clemencic, M.; Cliff, H. V.; Closier, J.; Coco, V.; Cogan, J.; Cogneras, E.; Cogoni, V.; Cojocariu, L.; Collazuol, G.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coquereau, S.; Corti, G.; Corvo, M.; Couturier, B.; Cowan, G. A.; Craik, D. C.; Crocombe, A.; Cruz Torres, M.; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; Dall'Occo, E.; Dalseno, J.; David, P. N. Y.; Davis, A.; De Aguiar Francisco, O.; De Bruyn, K.; De Capua, S.; De Cian, M.; De Miranda, J. M.; De Paula, L.; De Simone, P.; Dean, C.-T.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Demmer, M.; Derkach, D.; Deschamps, O.; Dettori, F.; Dey, B.; Di Canto, A.; Dijkstra, H.; Dordei, F.; Dorigo, M.; Dosil Suárez, A.; Dovbnya, A.; Dreimanis, K.; Dufour, L.; Dujany, G.; Dungs, K.; Durante, P.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Déléage, N.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; Elsasser, Ch.; Ely, S.; Esen, S.; Evans, H. M.; Evans, T.; Falabella, A.; Farley, N.; Farry, S.; Fay, R.; Ferguson, D.; Fernandez Albor, V.; Ferrari, F.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fiorini, M.; Firlej, M.; Fitzpatrick, C.; Fiutowski, T.; Fleuret, F.; Fohl, K.; Fontana, M.; Fontanelli, F.; Forshaw, D. C.; Forty, R.; Frank, M.; Frei, C.; Frosini, M.; Fu, J.; Furfaro, E.; Färber, C.; Gallas Torreira, A.; Galli, D.; Gallorini, S.; Gambetta, S.; Gandelman, M.; Gandini, P.; Gao, Y.; García Pardiñas, J.; Garra Tico, J.; Garrido, L.; Garsed, P. J.; Gascon, D.; Gaspar, C.; Gavardi, L.; Gazzoni, G.; Gerick, D.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gianì, S.; Gibson, V.; Girard, O. G.; Giubega, L.; Gizdov, K.; Gligorov, V. V.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gorelov, I. V.; Gotti, C.; Grabalosa Gándara, M.; Graciani Diaz, R.; Granado Cardoso, L. A.; Graugés, E.; Graverini, E.; Graziani, G.; Grecu, A.; Griffith, P.; Grillo, L.; Grünberg, O.; Gushchin, E.; Guz, Yu.; Gys, T.; Göbel, C.; Hadavizadeh, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S. C.; Hall, S.; Hamilton, B.; Han, X.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S. T.; Harrison, J.; He, J.; Head, T.; Heister, A.; Hennessy, K.; Henrard, P.; Henry, L.; Hernando Morata, J. A.; van Herwijnen, E.; Heß, M.; Hicheur, A.; Hill, D.; Hombach, C.; Hulsbergen, W.; Humair, T.; Hushchyn, M.; Hussain, N.; Hutchcroft, D.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jalocha, J.; Jans, E.; Jawahery, A.; John, M.; Johnson, D.; Jones, C. R.; Joram, C.; Jost, B.; Jurik, N.; Kandybei, S.; Kanso, W.; Karacson, M.; Karbach, T. M.; Karodia, S.; Kecke, M.; Kelsey, M.; Kenyon, I. R.; Kenzie, M.; Ketel, T.; Khairullin, E.; Khanji, B.; Khurewathanakul, C.; Kirn, T.; Klaver, S.; Klimaszewski, K.; Kolpin, M.; Komarov, I.; Koopman, R. F.; Koppenburg, P.; Kozachuk, A.; Kozeiha, M.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krokovny, P.; Kruse, F.; Krzemien, W.; Kucewicz, W.; Kucharczyk, M.; Kudryavtsev, V.; Kuonen, A. K.; Kurek, K.; Kvaratskheliya, T.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lanfranchi, G.; Langenbruch, C.; Langhans, B.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.-P.; Leflat, A.; Lefrançois, J.; Lefèvre, R.; Lemaitre, F.; Lemos Cid, E.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Likhomanenko, T.; Lindner, R.; Linn, C.; Lionetto, F.; Liu, B.; Liu, X.; Loh, D.; Longstaff, I.; Lopes, J. H.; Lucchesi, D.; Lucio Martinez, M.; Luo, H.; Lupato, A.; Luppi, E.; Lupton, O.; Lusiani, A.; Lyu, X.; Machefert, F.; Maciuc, F.; Maev, O.; Maguire, K.; Malde, S.; Malinin, A.; Maltsev, T.; Manca, G.; Mancinelli, G.; Manning, P.; Maratas, J.; Marchand, J. F.; Marconi, U.; Marin Benito, C.; Marino, P.; Marks, J.; Martellotti, G.; Martin, M.; Martinelli, M.; Martinez Santos, D.; Martinez Vidal, F.; Martins Tostes, D.; Massacrier, L. M.; Massafferri, A.; Matev, R.; Mathad, A.; Mathe, Z.; Matteuzzi, C.; Mauri, A.; Maurin, B.; Mazurov, A.; McCann, M.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Melnychuk, D.; Merk, M.; Michielin, E.; Milanes, D. A.; Minard, M.-N.; Mitzel, D. S.; Molina Rodriguez, J.; Monroy, I. A.; Monteil, S.; Morandin, M.; Morawski, P.; Mordà, A.; Morello, M. J.; Moron, J.; Morris, A. B.; Mountain, R.; Muheim, F.; Mulder, M.; Mussini, M.; Müller, D.; Müller, J.; Müller, K.; Müller, V.; Naik, P.; Nakada, T.; Nandakumar, R.; Nandi, A.; Nasteva, I.; Needham, M.; Neri, N.; Neubert, S.; Neufeld, N.; Neuner, M.; Nguyen, A. D.; Nguyen-Mau, C.; Niess, V.; Nieswand, S.; Niet, R.; Nikitin, N.; Nikodem, T.; Novoselov, A.; O'Hanlon, D. P.; Oblakowska-Mucha, A.; Obraztsov, V.; Ogilvy, S.; Oldeman, R.; Onderwater, C. J. G.; Otalora Goicochea, J. M.; Otto, A.; Owen, P.; Oyanguren, A.; Palano, A.; Palombo, F.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Pappalardo, L. L.; Pappenheimer, C.; Parker, W.; Parkes, C.; Passaleva, G.; Patel, G. D.; Patel, M.; Patrignani, C.; Pearce, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perret, P.; Pescatore, L.; Petridis, K.; Petrolini, A.; Petrov, A.; Petruzzo, M.; Picatoste Olloqui, E.; Pietrzyk, B.; Pikies, M.; Pinci, D.; Pistone, A.; Piucci, A.; Playfer, S.; Plo Casasus, M.; Poikela, T.; Polci, F.; Poluektov, A.; Polyakov, I.; Polycarpo, E.; Pomery, G. J.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Price, E.; Price, J. D.; Prisciandaro, J.; Pritchard, A.; Prouve, C.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Quagliani, R.; Rachwal, B.; Rademacker, J. H.; Rama, M.; Ramos Pernas, M.; Rangel, M. S.; Raniuk, I.; Raven, G.; Redi, F.; Reichert, S.; dos Reis, A. C.; Remon Alepuz, C.; Renaudin, V.; Ricciardi, S.; Richards, S.; Rihl, M.; Rinnert, K.; Rives Molina, V.; Robbe, P.; Rodrigues, A. B.; Rodrigues, E.; Rodriguez Lopez, J. A.; Rodriguez Perez, P.; Rogozhnikov, A.; Roiser, S.; Romanovskiy, V.; Romero Vidal, A.; Ronayne, J. W.; Rotondo, M.; Ruf, T.; Ruiz Valls, P.; Saborido Silva, J. J.; Sagidova, N.; Saitta, B.; Salustino Guimaraes, V.; Sanchez Mayordomo, C.; Sanmartin Sedes, B.; Santacesaria, R.; Santamarina Rios, C.; Santimaria, M.; Santovetti, E.; Sarti, A.; Satriano, C.; Satta, A.; Saunders, D. M.; Savrina, D.; Schael, S.; Schellenberg, M.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmelzer, T.; Schmidt, B.; Schneider, O.; Schopper, A.; Schubert, K.; Schubiger, M.; Schune, M.-H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Semennikov, A.; Sergi, A.; Serra, N.; Serrano, J.; Sestini, L.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, V.; Shires, A.; Siddi, B. G.; Silva Coutinho, R.; Silva de Oliveira, L.; Simi, G.; Sirendi, M.; Skidmore, N.; Skwarnicki, T.; Smith, E.; Smith, I. T.; Smith, J.; Smith, M.; Snoek, H.; Sokoloff, M. D.; Soler, F. J. P.; Souza, D.; Souza De Paula, B.; Spaan, B.; Spradlin, P.; Sridharan, S.; Stagni, F.; Stahl, M.; Stahl, S.; Stefko, P.; Stefkova, S.; Steinkamp, O.; Stenyakin, O.; Stevenson, S.; Stoica, S.; Stone, S.; Storaci, B.; Stracka, S.; Straticiuc, M.; Straumann, U.; Sun, L.; Sutcliffe, W.; Swientek, K.; Syropoulos, V.; Szczekowski, M.; Szumlak, T.; T'Jampens, S.; Tayduganov, A.; Tekampe, T.; Tellarini, G.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tomassetti, L.; Tonelli, D.; Topp-Joergensen, S.; Tournefier, E.; Tourneur, S.; Trabelsi, K.; Traill, M.; Tran, M. T.; Tresch, M.; Trisovic, A.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Ukleja, A.; Ustyuzhanin, A.; Uwer, U.; Vacca, C.; Vagnoni, V.; Valat, S.; Valenti, G.; Vallier, A.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vecchi, S.; van Veghel, M.; Velthuis, J. J.; Veltri, M.; Veneziano, G.; Venkateswaran, A.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vieites Diaz, M.; Vilasis-Cardona, X.; Volkov, V.; Vollhardt, A.; Voneki, B.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voß, C.; de Vries, J. A.; Vázquez Sierra, C.; Waldi, R.; Wallace, C.; Wallace, R.; Walsh, J.; Wang, J.; Ward, D. R.; Watson, N. K.; Websdale, D.; Weiden, A.; Whitehead, M.; Wicht, J.; Wilkinson, G.; Wilkinson, M.; Williams, M.; Williams, M. P.; Williams, M.; Williams, T.; Wilson, F. F.; Wimberley, J.; Wishahi, J.; Wislicki, W.; Witek, M.; Wormser, G.; Wotton, S. A.; Wraight, K.; Wright, S.; Wyllie, K.; Xie, Y.; Xing, Z.; Xu, Z.; Yang, Z.; Yin, H.; Yu, J.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zarebski, K. A.; Zavertyaev, M.; Zhang, L.; Zhang, Y.; Zhang, Y.; Zhelezov, A.; Zheng, Y.; Zhokhov, A.; Zhukov, V.; Zucchelli, S.

2016-11-01

A measurement of the differential branching fraction of the decay B 0 → K ∗(892)0 μ + μ - is presented together with a determination of the S-wave fraction of the K + π - system in the decay B 0 → K +π- μ + μ -. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb-1 collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q 2. Precise theoretical predictions for the differential branching fraction of B 0 → K ∗(892)0 μ + μ - decays are available for the q 2 region 1 .1 < q 2 < 6 .0 GeV2 /c 4. In this q 2 region, for the K +π- invariant mass range 796 < m Kπ < 996 MeV /c 2, the S-wave fraction of the K +π- system in B 0 → K +π- μ + μ - decays is found to be {F}S=0.101± 0.017(stat)± 0.009(syst), and the differential branching fraction of B 0 → K ∗(892)0 μ + μ - decays is determined to be dB/d{q}^2=(0.{392}_{-0.019}^{+0.020}(stat)± 0.010(syst)± 0.027(norm))× 1{0}^{-7}{c}^4/{GeV}^2.

Toxicity and cosmesis following partial breast irradiation consisting of 40 Gy in 10 daily fractions.

PubMed

Trovo, Marco; Roncadin, Mario; Polesel, Jerry; Piccoli, Erica; Mileto, Mario; Micheli, Elvia; Perin, Tiziana; Carbone, Antonino; Massarut, Samuele; Trovo, Mauro G

2013-10-01

To assess the toxicity and cosmetic results in breast cancer patients undergoing adjuvant partial breast irradiation (PBI) to a total dose of 40 Gy in 10 daily fractions (4 Gy/fraction). Patients affected by early-stage breast cancer were enrolled in this phase II trial. Patients had to be 60 years old and treated with breast conservative surgery for early stage (pT1-T2 pN0-N1a) invasive ductal carcinoma. 77 patients were enrolled. Median follow-up was 18 months. The proposed schedule was well tolerated. One patient reported Grade 3 pain at the site of irradiation. Four (5%) patients experience Grade 2 erythema. Late Grade 2 and 1 fibrosis was observed in 3 (4%) and 14 (18%) patients, respectively. Cosmesis was judged "good/excellent" and "poor" in 75 (97%) and in 2 (3%) patients, respectively. 40 Gy in 10 daily fractions, 4 Gy/fraction, is a well tolerated regimen to deliver PBI. Copyright © 2013 Elsevier Ltd. All rights reserved.

Development of fraction comparison strategies: A latent transition analysis.

PubMed

Rinne, Luke F; Ye, Ai; Jordan, Nancy C

2017-04-01

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item blocks showed that most children initially exhibited a "whole number bias," indicating that larger numbers in numerators and denominators produce larger fraction values. However, some children instead chose fractions with smaller numerators and denominators, demonstrating a partial understanding that smaller numbers can yield larger fractions. Latent transition analysis showed that most children eventually adopted normative comparison strategies. Children who exhibited a partial understanding by choosing fractions with smaller numbers were more likely to adopt normative comparison strategies earlier than those with larger number biases. Controlling for general math achievement and other cognitive abilities, whole number line estimation accuracy predicted the probability of transitioning to normative comparison strategies. Exploratory factor analyses showed that over time, children appeared to increasingly represent fractions as discrete magnitudes when simpler strategies were unavailable. These results support the integrated theory of numerical development, which posits that an understanding of numbers as magnitudes unifies the process of learning whole numbers and fractions. The findings contrast with conceptual change theories, which propose that children must move from a view of numbers as counting units to a new view that accommodates fractions to overcome whole number bias. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Discrete fractional solutions of a Legendre equation

NASA Astrophysics Data System (ADS)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

[Biochemical characterization of fractionated rat liver chromatin in experimental D-hypovitaminosis and after administration of steroidal drugs].

PubMed

Levitskiĭ, E L; Kholodova, Iu D; Gubskiĭ, Iu I; Primak, R G; Chabannyĭ, V N; Kindruk, N L; Mozzhukhina, T G; Lenchevskaia, L K; Mironova, V N; Saad, L M

1993-01-01

Marked changes in the structural and functional characteristics of liver nuclear chromatin fractions are observed under experimental D-hypovitaminosis, which differ in the degree of transcriptional activity. DNA-polymerase activity and activity of the fraction, enriched with RNA-polymerase I, increases in the active fraction. Free radical LPO reactions are modified in the chromatin fraction with low activity and to the less degree in the active one. Disturbances of chromatine structural properties are caused with the change in the protein and lipid components of chromatin. Administration of ecdysterone preparations (separately and together with vitamin D3) has a partial corrective effect on structural and functional organization of nuclear chromatine. At the action of ecdysterone normalization of LPO reactions modified by pathological changes is observed in the chromatin fraction with low activity and to the less degree in the active one. This kind of influence corrects to the less degree chromatin functional activity and quantitative and qualitative modifications of its protein component. Simultaneous influence of ecdysterone and vitamin D3 leads to the partial normalization of the biochemical indices studied (except for those which characterize LPO reactions) mainly in the active chromatin fraction.

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.

Evolution of the Craters of the Moon Lavas from primitive Snake River Plain basalts: inferences from plagioclase-melt thermobarometers and whole rock compositions

NASA Astrophysics Data System (ADS)

Vaid, N.; Putirka, K.; Kuntz, M.

2005-12-01

The volcanic rocks of the Craters of the Mon Lava field provide an ideal laboratory for testing models of magma transport and evolution. Their compositions, relative ages and volumes are well known, as are the fractionation processes leading to their evolution (Leeman, 1976). The COM is somewhat distinctive in the Snake River Plain (SRP) region, due to its evolved character, and an apparent compositional segregation from associated SRP basalts. Some have suggested that the high Fe liquids of the COM demand an origin separate from that of SRP basalts, possibly involving an Fe-enriched mantle, while others have suggested that the COM lavas may be derived by fractionation at moderate depths (30 km). In either case, there are important implications in regard to mantle composition and the nature and distribution of thermal energy. We use plagioclase-melt pairs and an analysis of whole rock compositions in attempt to test models of COM magmatic evolution. Plagioclase-melt thermobarometers provide rough estimates of crystallization depths, and show that COM and SRP lavas partially crystallized at similar depths of 14 +/- 6 km. However, plagioclase crystallization temperatures for SRP basalts (1400 +/- 25 K; Kings Bowl, Cerro Grande, North and South Robbers) exceed temperatures for COM lavas (1358 +/- 45 K) by 40 K. Our data also show that fractional crystallization (ol + plag) can explain the evolution of surrounding SRP basalt flows, and that the most evolved SRP basalts approach primitive COM lava compositions. The most primitive of COM magmas appear to be characterized by the appearance of apatite + magnetite as fractionating phases. Our results thus confirm the geochemical model of Leeman (1976) and the physical model of Kuntz (1992), with the added insight that SRP basalts are parental to the more evolved COM lavas, through low-pressure fractional crystallization in the upper crust. The principal differences between SRP and COM magmas appear to relate more to the presence or absence of density contrasts in the crust than differences in composition or temperature of mantle source materials. SRP basalts lie near the axis of the SRP where the granitic upper crust may have been obliterated by earlier volcanic episodes. In contrast, COM lavas, whose vents lie off axis, appear to have been trapped within the upper crust for longer periods, sufficient for further differentiation. Finally, SRP rhyolite compositions lie on the same fractionation trend as COM and SRP lavas, at very low values of MgO. We propose that highly evolved lavas throughout the SRP may form by fractional crystallization mechanisms alone, rather than through the partial melting and remobilization of preexisting felsic crustal materials.

Molybdenum mineralization related to the Yangtze's lower crust and differentiation in the Dabie Orogen: Evidence from the geochemical features of the Yaochong porphyry Mo deposit

NASA Astrophysics Data System (ADS)

Liu, Qing-Quan; Li, Bin; Shao, Yong-Jun; Lu, An-Huai; Lai, Jian-Qing; Li, Yong-Feng; Luo, Zheng-Zhuan

2017-06-01

The Dabie Orogen is a world-class case for large amounts of Mo mineralization in that it contains at least 10 porphyry Mo deposits with Mo metal reserves over 3 Mt from the time period of 156-110 Ma. However, the principal mechanism for the Mo mineralization remains controversial due to the lack of a precise definition of its source and shallow ore-forming process, which is essential to understand these rare large Mo deposits. Detailed geochronology, geochemistry, and isotopic data for ore-related granites and minerals were analyzed in order to place constraints on the massive Mo mineralization in the Dabie Orogen in eastern China. The Yaochong molybdenum orebodies were hosted in the transition belt and alteration zone between the granitic stocks and the Dabie Complex and were characterized as numerous veinlets with potassic, phyllic and propylitic alterations. The buried Yaochong granitic intrusions and associated molybdenum mineralization yield Early Cretaceous ages of magmatic activities at ca. 138 Ma and extremely similar Re-Os isotope ages for the corresponding Mo metallogenic event at ca. 137 Ma. The Yaochong monzogranite and granite porphyry belong to the highly fractionated I-type granites, which are believed to be derived from the dominantly Yangtze's lower crust mixed with the Northern Dabie Complex due to their geochemical and isotope features. The elemental diversity and isotopic homogeneity suggest that the formation of the Yaochong monzogranite involved the fractionation of biotite, garnet and minor feldspar and accessory minerals combined with a weak crustal assimilation process. In contrast, the granite porphyry was possibly generated by the partial melting of the same mixed lower continental crust via the differentiation process involving the fractionation of feldspar, apatite, and/or titanite. Fractional crystallization processes can significantly elevate the molybdenum concentration in the residual melts. The biotite fractional crystallization results in removal of molybdenum from the vestigial magma since molybdenum is compatible with it, which may account for the barren monzogranite with a low-grade molybdenum mineralization. The ore-bearing granite porphyry has more source materials from the Yangtze's lower crust, which may have contributed most of the molybdenum for the porphyry-related molybdenum deposits in the Dabie metallogenic zone. This porphyry molybdenum aggregation may have been deposited in a post-collision or intracontinental extensional setting.

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.

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

The Vertical Linear Fractional Initialization Problem

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

PubMed

Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

2016-08-01

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Cannibalism of olivine-rich cumulate xenoliths during the 1998 eruption of Piton de la Fournaise (La Réunion hotspot): Implications for the generation of magma diversity

NASA Astrophysics Data System (ADS)

Salaün, A.; Villemant, B.; Semet, M. P.; Staudacher, T.

2010-12-01

Contrasting with its unusual isotopic homogeneity compared to other hotspot volcanoes, Piton de la Fournaise has produced a large diversity of basaltic magmas over its 0.5 Ma history: picrites and two types of transitional basalts with distinct petrological and chemical compositions. A minor group of evolved basalts (anomalous group of basalts or AGB) is enriched in both compatible (Mg, Fe, Ti, Cr, and Ni) and incompatible (K, Th, and La) elements and depleted in Ca and Si relative to the dominant group of evolved basalts. The 1998 eruption simultaneously produced the two basaltic types at two distinct vents (Hudson vent: AGB, Kapor vent: common basalt) but from the same feeding conduit. Glasses of both magmas are close in composition and belong to the single differentiation trend defined by all 1998-2007 glass compositions. Thermodynamic model (MELTS code) shows that AGB-type magmas cannot be produced by high pressure (> 1 GPa) clinopyroxene fractionation as previously proposed and that all melts of the 1998-2007 activity period are produced by low pressure (< 800 MPa) crystal fractionation from the most primitive basalt (MgO ~ 9%). Modal composition of 1998 lavas (mass balance calculation and SEM image analysis) and olivine crystal composition show that Hudson lavas have assimilated significant fractions of olivine xenocrysts contrary to Kapor lavas. In addition, the higher incompatible element contents of Hudson lavas suggest contamination by a differentiated (trachytic) melt. All AGB share the following characteristics: (i) evolved glass compositions, (ii) 5-10% olivine xenocrysts, and (iii) vents located in a narrow region at the summit of the edifice. They are interpreted as the result of the assimilation of olivine-rich xenoliths either by evolved melts or by basaltic melts contaminated by low fractions of differentiated melts produced from interstitial glass frequently coating cumulates minerals or resulting from partial melting of cumulates bearing pyroxene or plagioclase (wehrlitic to gabbroic cumulates). The scarcity of AGB magmas is attributed to their shallow transfer path in rarely intruded lateral zones of Piton de la Fournaise volcano: wehrlitic to gabbroic cumulates bodies are either heterogeneously distributed within the edifice or have been depleted in low melting point components in the 'Rift Zone' where most of the recent eruptive events are emplaced. These results emphasize the exceptional chemical homogeneity of the primary basaltic melt involved in volcanic activity of Piton de la Fournaise hotspot for 0.5 Ma and the increasingly recognized role of magma-wall rock interactions in erupted magma compositions.

A proposal for unification of fatigue crack growth law

NASA Astrophysics Data System (ADS)

Kobelev, V.

2017-05-01

In the present paper, the new fractional-differential dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach are proposed. The anticipated unified propagation function describes the infinitesimal crack length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification fractional-differential functions with different number of fitting parameters are proposed. An alternative, threshold formulations for the fractional-differential propagation functions are suggested. The mean stress dependence is the immediate consequence from the considered laws. The corresponding formulas for crack length over the number of cycles are derived in closed form.

The effects of magmatic processes and crustal recycling on the molybdenum stable isotopic composition of Mid-Ocean Ridge Basalts

NASA Astrophysics Data System (ADS)

Bezard, Rachel; Fischer-Gödde, Mario; Hamelin, Cédric; Brennecka, Gregory A.; Kleine, Thorsten

2016-11-01

Molybdenum (Mo) stable isotopes hold great potential to investigate the processes involved in planetary formation and differentiation. However their use is currently hampered by the lack of understanding of the dominant controls driving mass-dependent fractionations at high temperature. Here we investigate the role of magmatic processes and mantle source heterogeneities on the Mo isotope composition of Mid-Ocean Ridges Basalts (MORBs) using samples from two contrasting ridge segments: (1) the extremely fast spreading Pacific-Antarctic (66-41°S) section devoid of plume influence and; (2) the slow spreading Mohns-Knipovich segment (77-71°N) intercepted by the Jan Mayen Plume (71°N). We show that significant variations in Mo stable isotope composition exist in MORBs with δ98/95Mo ranging from - 0.24 ‰ to + 0.15 ‰ (relative to NIST SRM3134). The absence of correlation between δ98/95Mo and indices of magma differentiation or partial melting suggests a negligible impact of these processes on the isotopic variations observed. On the other hand, the δ98/95Mo variations seem to be associated with changes in radiogenic isotope signatures and rare earth element ratios (e.g., (La/Sm)N), suggesting mantle source heterogeneities as a dominant factor for the δ98/95Mo variations amongst MORBs. The heaviest Mo isotope compositions correspond to the most enriched signatures, suggesting that recycled crustal components are isotopically heavy compared to the uncontaminated depleted mantle. The uncontaminated depleted mantle shows slightly sub-chondritic δ98/95Mo, which cannot be produced by core formation and, therefore, more likely result from extensive anterior partial melting of the mantle. Consequently, the primitive δ98/95Mo composition of the depleted mantle appears overprinted by the effects of both partial melting and crustal recycling.

The jammed-to-mobile transition in frozen sand under stress

NASA Astrophysics Data System (ADS)

Durham, W. B.; Pathare, A.; Stern, L. A.; Lenferink, H. J.

2009-12-01

We conducted laboratory deformation experiments on sand-rich mixtures of sand + ice under sufficient confinement to inhibit macroscopic dilation. Dry sand packs constrained not to dilate when they are under a shearing load reach an immobile or “jammed” state, as load-supporting “force chains” of sand particles form after a small amount of strain and cannot be broken without volume expansion. Our research objective here was to find the minimum volume fraction of ice required to overcome the jammed state. The result surprised us: the required volume fraction is not a fixed number, but depends on the packing characteristics of the sand in question. Experiments were carried out in a triaxial gas deformation rig at confining pressures (60 - 200 MPa) always at least twice the level of differential stresses (11 - 50 MPa) in order to suppress dilatancy. Run temperatures were 223 - 243 K. We used two kinds of quartz sand, one well-sorted, with a maximum dry packing density (MDPD) of about 0.68 sand by volume, and the other a mixture of two sizes, having a higher MDPD of 0.75. Ice volume fraction ranged from well below saturation (where unfilled porosity necessarily remained) to slightly greater than the value of porosity at MDPD. We tested these frozen sands in compression under constant applied differential stress (creep). Strain rates were very low at these conditions, and runs took days or weeks to complete. The amount of strain required to reach the jammed state in ice-undersaturated samples was approximately 0.04, and did not show an obvious dependence on ice content. For both sands, the onset of mobility occurred at approximately 5% above the value of pore volume at MDPD. Furthermore, viscosity of mobile frozen sand near the transition point was extremely sensitive to ice fraction, which implies that at geologic strain rates, far slower than we can reach in the lab, the ice fraction at transition may lie closer to that at MDPD. Cryogenic scanning electron microscopy shows that fracturing of sand grains occurs in ice-undersaturated samples, but gradually disappears as saturation is reached. There are no fractured sand grains in deforming mobile frozen sand packs. One application of this work is to the regolith of Mars at mid-latitudes and poleward, where significant ice is expected to be present. Partially relaxed (“softened”) landforms such as craters require the presence of ice, but also suggest strengths far higher than that of ice. The extreme sensitivity of viscosity to ice content near the mobility boundary, and the near coincidence of mobility and saturation at MDPD together suggest a plausible explanation for partial landform softening on Mars that does not require a fortuitous ice content or an unrealistically brief period of saturation; namely, that the water content of the Martian regolith lies at or near saturation. If true, we can estimate the historical water content of the Martian regolith for reasonable soil densities as being between 120 and 240 global meters of water for the upper kilometer of crust. This is somewhat lower than previous estimates.

Long noncoding RNAs in gastric cancer: functions and clinical applications

PubMed Central

Wang, Jiajun; Sun, Jingxu; Wang, Jun; Song, Yongxi; Gao, Peng; Shi, Jinxin; Chen, Ping; Wang, Zhenning

2016-01-01

Over the last two decades, genome-wide studies have revealed that only a small fraction of the human genome encodes proteins; long noncoding RNAs (lncRNAs) account for 98% of the total genome. These RNA molecules, which are >200 nt in length, play important roles in diverse biological processes, including the immune response, stem cell pluripotency, cell proliferation, apoptosis, differentiation, invasion, and metastasis by regulating gene expression at the epigenetic, transcriptional, and posttranscriptional levels. However, the detailed molecular mechanisms underlying lncRNA function are only partially understood. Recent studies showed that many lncRNAs are aberrantly expressed in gastric cancer (GC) tissues, gastric juice, plasma, and cells, and these alterations are linked to the occurrence, progression, and outcome of GC. Here, we review the current knowledge of the biological functions and clinical aspects of lncRNAs in GC. PMID:26929639

Lu-Hf and Sm-Nd Isotopic Studies of Shergottites and Nakhlites: Implications for Martian Mantle Sources

NASA Technical Reports Server (NTRS)

Debaille, V.; Yin, Q.-Z.; Brandon, A. D.; Jacobsen, B.; Treiman, A. H.

2007-01-01

We present a new Lu-Hf and Sm-Nd isotope systematics study of four enriched shergottites (Zagami, Shergotty, NWA856 and Los Angeles), and three nakhlites (Nakhla, MIL03346 and Yamato 000593) in order to further understand processes occurring during the early differentiation of Mars and the crystallization of its magma ocean. Two fractions of the terrestrial petrological analogue of nakhlites, the Archaean Theo's flow (Ontario, Canada) were also measured. The coupling of Nd and Hf isotopes provide direct insights on the mineralogy of the melt sources. In contrast to Sm/Nd, Lu/Hf ratios can be very large in minerals such as garnet. Selective partial melting of garnet bearing mantle sources can therefore lead to characteristic Lu/Hf signatures that can be recognized with Hf-176/Hf-177Hf ratios.

Impact of equalizing currents on losses and torque ripples in electrical machines with fractional slot concentrated windings

NASA Astrophysics Data System (ADS)

Toporkov, D. M.; Vialcev, G. B.

2017-10-01

The implementation of parallel branches is a commonly used manufacturing method of the realizing of fractional slot concentrated windings in electrical machines. If the rotor eccentricity is enabled in a machine with parallel branches, the equalizing currents can arise. The simulation approach of the equalizing currents in parallel branches of an electrical machine winding based on magnetic field calculation by using Finite Elements Method is discussed in the paper. The high accuracy of the model is provided by the dynamic improvement of the inductances in the differential equation system describing a machine. The pre-computed table flux linkage functions are used for that. The functions are the dependences of the flux linkage of parallel branches on the branches currents and rotor position angle. The functions permit to calculate self-inductances and mutual inductances by partial derivative. The calculated results obtained for the electric machine specimen are presented. The results received show that the adverse combination of design solutions and the rotor eccentricity leads to a high value of the equalizing currents and windings heating. Additional torque ripples also arise. The additional ripples harmonic content is not similar to the cogging torque or ripples caused by the rotor eccentricity.

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

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...

Histogram analysis of diffusion kurtosis imaging derived maps may distinguish between low and high grade gliomas before surgery.

PubMed

Qi, Xi-Xun; Shi, Da-Fa; Ren, Si-Xie; Zhang, Su-Ya; Li, Long; Li, Qing-Chang; Guan, Li-Ming

2018-04-01

To investigate the value of histogram analysis of diffusion kurtosis imaging (DKI) maps in the evaluation of glioma grading. A total of 39 glioma patients who underwent preoperative magnetic resonance imaging (MRI) were classified into low-grade (13 cases) and high-grade (26 cases) glioma groups. Parametric DKI maps were derived, and histogram metrics between low- and high-grade gliomas were analysed. The optimum diagnostic thresholds of the parameters, area under the receiver operating characteristic curve (AUC), sensitivity, and specificity were achieved using a receiver operating characteristic (ROC). Significant differences were observed not only in 12 metrics of histogram DKI parameters (P<0.05), but also in mean diffusivity (MD) and mean kurtosis (MK) values, including age as a covariate (F=19.127, P<0.001 and F=20.894, P<0.001, respectively), between low- and high-grade gliomas. Mean MK was the best independent predictor of differentiating glioma grades (B=18.934, 22.237 adjusted for age, P<0.05). The partial correlation coefficient between fractional anisotropy (FA) and kurtosis fractional anisotropy (KFA) was 0.675 (P<0.001). The AUC of the mean MK, sensitivity, and specificity were 0.925, 88.5% and 84.6%, respectively. DKI parameters can effectively distinguish between low- and high-grade gliomas. Mean MK is the best independent predictor of differentiating glioma grades. • DKI is a new and important method. • DKI can provide additional information on microstructural architecture. • Histogram analysis of DKI may be more effective in glioma grading.

Intrusive rocks of the Wadi Hamad Area, North Eastern Desert, Egypt: Change of magma composition with maturity of Neoproterozoic continental island arc and the role of collisional plutonism in the differentiation of arc crust

NASA Astrophysics Data System (ADS)

Basta, Fawzy F.; Maurice, Ayman E.; Bakhit, Bottros R.; Azer, Mokhles K.; El-Sobky, Atef F.

2017-09-01

The igneous rocks of the Wadi Hamad area are exposed in the northernmost segment of the Arabian-Nubian Shield (ANS). These rocks represent part of crustal section of Neoproterozoic continental island arc which is intruded by late to post-collisional alkali feldspar granites. The subduction-related intrusives comprise earlier gabbro-diorites and later granodiorites-granites. Subduction setting of these intrusives is indicated by medium- to high-K calc-alkaline affinity, Ta-Nb troughs on the spider diagrams and pyroxene and biotite compositions similar to those crystallized from arc magmas. The collisional alkali feldspar granites have high-K highly fractionated calc-alkaline nature and their spider diagrams almost devoid of Ta-Nb troughs. The earlier subduction gabbro-diorites have lower alkalis, LREE, Nb, Zr and Hf values compared with the later subduction granodiorites-granites, which display more LILE-enriched spider diagrams with shallower Ta-Nb troughs, reflecting variation of magma composition with arc evolution. The later subduction granitoids were generated by lower degree of partial melting of mantle wedge and contain higher arc crustal component compared with the earlier subduction gabbro-diorites. The highly silicic alkali feldspar granites represent extensively evolved melts derived from partial melting of intermediate arc crustal sources during the collisional stage. Re-melting of arc crustal sources during the collisional stage results in geochemical differentiation of the continental arc crust and the silicic collisional plutonism drives the composition of its upper part towards that of mature continental crust.

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Reproductive isolation between populations of Iris atropurpurea is associated with ecological differentiation

PubMed Central

Yardeni, Gil; Tessler, Naama; Imbert, Eric; Sapir, Yuval

2016-01-01

Background and Aims Speciation is often described as a continuous dynamic process, expressed by different magnitudes of reproductive isolation (RI) among groups in different levels of divergence. Studying intraspecific partial RI can shed light on mechanisms underlying processes of population divergence. Intraspecific divergence can be driven by spatially stochastic accumulation of genetic differences following reduced gene flow, resulting in increased RI with increased geographical distance, or by local adaptation, resulting in increased RI with environmental difference. Methods We tested for RI as a function of both geographical distance and ecological differentiation in Iris atropurpurea, an endemic Israeli coastal plant. We crossed plants in the Netanya Iris Reserve population with plants from 14 populations across the species’ full distribution, and calculated RI and reproductive success based on fruit set, seed set and fraction of seed viability. Key Results We found that total RI was not significantly associated with geographical distance, but significantly increased with ecological distance. Similarly, reproductive success of the crosses, estimated while controlling for the dependency of each component on the previous stage, significantly reduced with increased ecological distance. Conclusions Our results indicate that the rise of post-pollination reproductive barriers in I. atropurpurea is more affected by ecological differentiation between populations than by geographical distance, supporting the hypothesis that ecological differentiation is predominant over isolation by distance and by reduced gene flow in this species. These findings also affect conservation management, such as genetic rescue, in the highly fragmented and endangered I. atropurpurea. PMID:27436798

Contrasting Effects of Carbon and Sulfur on Fe-Isotope Fractionation between Metal and Silicate Melt during Planetary Core Formation

NASA Astrophysics Data System (ADS)

Elardo, S. M.; Shahar, A.

2015-12-01

There are numerous studies that show well-resolved Fe isotope fractionations in igneous materials from different planetary bodies. Potential explanations for these fractionations include a non-chondritic bulk planetary Fe isotopic composition, and equilibrium fractionation between Fe-alloys or minerals and silicate melts during planetary differentiation, mantle melting, or fractional crystallization. This is further complicated by the fact that these processes are not mutually exclusive, making the interpretation of Fe isotope data a complex task. Here we present new experimental results investigating the effect of C on Fe isotope fractionation between molten peridotite and an Fe-alloy. Experiments were conducted at 1 GPa and 1850° C for 0.5 - 3 hours on a mixture of an 54Fe-spiked peridotite and Fe-metal with and without Ni metal in an end-loaded piston cylinder at the Geophysical Laboratory. Carbon saturation was achieved with a graphite capsule, and resulted in C contents of the Fe-alloy in our experiments ranging from 3.8 - 4.9 wt. %. The metal and silicate phases from half of each experiment were separated manually and dissolved in concentrated acids. Iron was separated from matrix elements by anion exchange chromatagraphy. Iron-isotopic compositions were determined with the Nu Plasma II MC-ICP-MS at GL. The other half of each experiment was used for quantitative microbeam analysis. Equilibrium was assessed with a time series and the three-isotope exchange method. The Ni-free experiments resulted in no resolvable Fe isotope fractionation between the Fe-C-alloy and molten silicate. This is in contrast to the results of Shahar et al. (2015) which showed a fractionation for Δ57Fe of ~0.18 ‰ between a peridotite and an Fe-alloy with a similar S abundance to C in these experiments. The one experiment thus far that contained Ni (~4 wt. % in the alloy) showed a resolvable fractionation between the Fe-Ni-C alloy and silicate of ~0.10 ‰. Shahar et al. found a similar magnitude fractionation to our Ni bearing experiment in experiments with no C or S. The difference in temperature (1650° C in Shahar et al. vs. 1850° C here) may be partially responsible for these discrepancies. Ongoing experiments will further investigate the effects of C and other light elements on Fe isotope fractionation during core segregation.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement.

PubMed

Mazzocco, Michèle M M; Myers, Gwen F; Lewis, Katherine E; Hanich, Laurie B; Murphy, Melissa M

2013-06-01

Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to one-half, fraction pairs with common denominators) differentiates those with mathematics learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics and whether long-term learning trajectories of this knowledge also differentiate these groups. We confirmed that although fourth graders with TA (n=93) were more accurate in evaluating "one-half" fractions than in evaluating "non-half" fractions (until they reached ceiling performance levels on both types of fractions), children with MLD (n=11) did not show a one-half advantage until Grade 7 and did not reach ceiling performance even by Grade 8. Both the MLD and LA groups had early difficulties with fractions, but by Grade 5 the LA group approached performance levels of the TA group and deviated from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short-lived for the TA group (because ceiling level was achieved across formats), whereas it was slightly more persistent for the LA group and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties vary across children with math difficulties (MLD or LA). Copyright © 2013 Elsevier Inc. All rights reserved.

Petrogenesis of Western Cascades Silicic Volcanics Near Sweet Home, Oregon

NASA Astrophysics Data System (ADS)

Cook, G. W.; White, C. M.

2002-12-01

Silicic lavas in the Menagerie Wilderness east of Sweet Home, Oregon are Oligocene to Miocene in age and range in composition from dacite (low K) to trachydacite (high K) and rhyolite (medium K). Three distinct silicic centers have been distinguished through a combination of field observation, chemistry and petrography. Phenocryst assemblages in rocks of the centers are plagioclase-hornblende-magnetite (Rooster Rock rhyolite), plagioclase-quartz-magnetite (Soda Fork rhyolite) and quartz-plagioclase-biotite-hornblende-magnetite (Moose Mt. rhyolite). The silicic volcanics in the study area are similar in terms of mineral content and overall chemical composition. Despite this, chemical evidence suggests that the three centers are petrologically unrelated. REE variations and least squares modeling of major element compositions are consistent with fractionation of plagioclase and hornblende. The rhyolites have moderate Eu anomalies and have flat MREE and HREE signatures. Least squares models and bivariate plots of major and trace elements also suggest fractionation of the aforementioned phases for both the andesite to dacite, and dacite to rhyolite steps. Comparisons with similar silicic centers show the Menagerie rocks share affinities with High Cascades rocks thought to have been derived through fractional crystallization (Crater Lake and South Sister). Plots of ratios of incompatible trace elements were utilized to determine if assimilation played some role alongside fractional crystallization in differentiation. Plots of Ba/La vs. Ba, Rb/Zr vs. Rb and Rb/Th vs. Rb show systematic positive increases in the ratios between a plausible parent magma (icelandite) and the rhyolites. These increases are not easily explained by fractional crystallization but can be modeled by assimilation of silicic crust. Overall, it seems likely that the three centers evolved independently through similar petrogenetic processes from an andesitic parent. The most plausible petrogenetic scenario involves some combination of fractional crystallization and assimilation of partial melts of silicic crust.

Water uptake by fresh Indonesian peat burning particles is limited by water-soluble organic matter

NASA Astrophysics Data System (ADS)

Chen, Jing; Hapsari Budisulistiorini, Sri; Itoh, Masayuki; Lee, Wen-Chien; Miyakawa, Takuma; Komazaki, Yuichi; Qing Yang, Liu Dong; Kuwata, Mikinori

2017-09-01

The relationship between hygroscopic properties and chemical characteristics of Indonesian biomass burning (BB) particles, which are dominantly generated from peatland fires, was investigated using a humidified tandem differential mobility analyzer. In addition to peat, acacia (a popular species at plantation) and fern (a pioneering species after disturbance by fire) were used for experiments. Fresh Indonesian peat burning particles are almost non-hygroscopic (mean hygroscopicity parameter, κ < 0.06) due to predominant contribution of water-insoluble organics. The range of κ spans from 0.02 to 0.04 (dry diameter = 100 nm, hereinafter) for Riau peat burning particles, while that for Central Kalimantan ranges from 0.05 to 0.06. Fern combustion particles are more hygroscopic (κ = 0. 08), whereas the acacia burning particles have a mediate κ value (0.04). These results suggest that κ is significantly dependent on biomass types. This variance in κ is partially determined by fractions of water-soluble organic carbon (WSOC), as demonstrated by a correlation analysis (R = 0.65). κ of water-soluble organic matter is also quantified, incorporating the 1-octanol-water partitioning method. κ values for the water extracts are high, especially for peat burning particles (A0 (a whole part of the water-soluble fraction): κ = 0.18, A1 (highly water-soluble fraction): κ = 0.30). This result stresses the importance of both the WSOC fraction and κ of the water-soluble fraction in determining the hygroscopicity of organic aerosol particles. Values of κ correlate positively (R = 0.89) with the fraction of m/z 44 ion signal quantified using a mass spectrometric technique, demonstrating the importance of highly oxygenated organic compounds to the water uptake by Indonesian BB particles. These results provide an experimentally validated reference for hygroscopicity of organics-dominated particles, thus contributing to more accurate estimation of environmental and climatic impacts driven by Indonesian BB particles on both regional and global scales.

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.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Persea americana Mill. Seed: Fractionation, Characterization, and Effects on Human Keratinocytes and Fibroblasts

PubMed Central

Ramos-Jerz, Maria del R.; Villanueva, Socorro; Jerz, Gerold; Winterhalter, Peter; Deters, Alexandra M.

2013-01-01

Methanolic avocado (Persea americana Mill., Lauraceae) seed extracts were separated by preparative HSCCC. Partition and HSCCC fractions were principally characterized by LC-ESI-MS/MS analysis. Their in vitro influence was investigated on proliferation, differentiation, cell viability, and gene expression on HaCaT and normal human epidermal keratinocytes (NHEK) and normal human dermal fibroblasts (NHDF). The methanol-water partition (M) from avocado seeds and HSCCC fraction 3 (M.3) were mostly composed of chlorogenic acid and its isomers. Both reduced NHDF but enhanced HaCaT keratinocytes proliferation. HSCCC fraction M.2 composed of quinic acid among chlorogenic acid and its isomers inhibited proliferation and directly induced differentiation of keratinocytes as observed on gene and protein level. Furthermore, M.2 increased NHDF proliferation via upregulation of growth factor receptors. Salidrosides and ABA derivatives present in HSCCC fraction M.6 increased NHDF and keratinocyte proliferation that resulted in differentiation. The residual solvent fraction M.7 contained among low concentrations of ABA derivatives high amounts of proanthocyanidins B1 and B2 as well as an A-type trimer and stimulated proliferation of normal cells and inhibited the proliferation of immortalized HaCaT keratinocytes. PMID:24371457

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.

Copper isotope fractionation during partial melting and melt percolation in the upper mantle: Evidence from massif peridotites in Ivrea-Verbano Zone, Italian Alps

NASA Astrophysics Data System (ADS)

Huang, Jian; Huang, Fang; Wang, Zaicong; Zhang, Xingchao; Yu, Huimin

2017-08-01

To investigate the behavior of Cu isotopes during partial melting and melt percolation in the mantle, we have analyzed Cu isotopic compositions of a suite of well-characterized Paleozoic peridotites from the Balmuccia and Baldissero massifs in the Ivrea-Verbano Zone (IVZ, Northern Italy). Our results show that fresh lherzolites and harzburgites have a large variation of δ65Cu ranging from -0.133 to 0.379‰, which are negatively correlated with Al2O3 contents as well as incompatible platinum-group (e.g., Pd) and chalcophile element (e.g., Cu, S, Se, and Te) contents. The high δ65Cu can be explained by Cu isotope fractionation during partial melting of a sulfide-bearing peridotite source, with the light isotope (63Cu) preferentially entering the melts. The low δ65Cu can be attributed to precipitation of sulfides enriched in 63Cu during sulfur-saturated melt percolation. Replacive dunites from the Balmuccia massif display high δ65Cu from 0.544 to 0.610‰ with lower Re, Pd, S, Se, and Te contents and lower Pd/Ir ratios relative to lherzolites, which may result from dissolution of sulfides during interactions between S-undersaturated melts and lherzolites at high melt/rock ratios. Thus, our results suggest that partial melting and melt percolation largely account for the Cu isotopic heterogeneity of the upper mantle. The correlation between δ65Cu and Cu contents of the lherzolites and harzburgites was used to model Cu isotope fractionation during partial melting of a sulfide-bearing peridotite, because Cu is predominantly hosted in sulfide. The modelling results indicate an isotope fractionation factor of αmelt-peridotite = 0.99980-0.99965 (i.e., 103lnαmelt-peridotite = -0.20 to -0.35‰). In order to explain the Cu isotopic systematics of komatiites and mid-ocean ridge basalts reported previously, the estimated αmelt-peridotite was used to simulate Cu isotopic variations in melts generated by variable degrees of mantle melting. The results suggest that high degrees (>25%) of partial melting extracts nearly all source Cu and it cannot produce Cu isotope fractionation in komatiites relative to their mantle source, and that sulfide segregation during magma evolution have modified Cu isotopic compositions of mid-ocean ridge basalts.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

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.

Quantitative characterization of 3-dimensional melt distribution in partially molten olivine-basalt aggregates using X-ray synchrotron microtomography

NASA Astrophysics Data System (ADS)

Zhu, W.; Gaetani, G. A.; Fusseis, F.

2009-12-01

Quantitative knowledge of the distribution of small amounts of silicate melt in peridotite and of its influence on permeability are critical to our understanding of melt migration and segregation processes in the upper mantle. Estimates for the permeability of partially molten rock require 3D melt distribution at the grain-scale. Existing studies of melt distribution, carried out on 2D slices through experimental charges, have produced divergent models for melt distribution at small melt fractions. While some studies conclude that small amounts of melt are distributed primarily along triple junctions [e.g., Wark et al., 2003], others predict an important role for melt distribution along grain boundaries at low melt fractions [e.g., Faul 1997]. Using X-ray synchrotron microtomography, we have obtained the first high quality non-destructive imaging of 3D melt distribution in olivine-basalt aggregates. Textually equilibrated partially molten samples consisting of magnesian olivine plus 2, 5, 10, or 20% primitive basalt were synthesized at 1.5 GPa and 1350°C in experiments lasting 264-336 hours. Microtomographic images of melt distribution were obtained on cylindrical cores, 1 mm in diameter, at a spatial resolution of 1 micron. Textual information such as melt channel size, dihedral angle and channel connectivity was then quantified using AVIZO and MATLAB. Our results indicate that as melt fraction decreases, melt becomes increasingly distributed along 3 grain junctions, in agreement with theoretical predictions. We do not find significant amounts of melt along grain boundaries at low melt fractions. We found that the true dihedral angle ranges from 50 to 70°, in agreements with results using 2D microcopy. Comparison between the samples provides a quantitative characterization of how melt fraction affects melt distribution including connectivity. The geometrical data have been incorporated into our network model to obtain macroscale transport properties for partially molten dunite. Results from this tomographic study thus provide constraints on rates of melt migration and melt extraction within the partially molten regions beneath ocean ridges. Fig 1. Melt channels in an olivine-basalt sample with 10 vol% melt.

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.

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.

Fractionation of carbon isotopes by phytoplankton and estimates of ancient CO2 levels

NASA Technical Reports Server (NTRS)

Freeman, K. H.; Hayes, J. M.

1992-01-01

Reports of the 13C content of marine particulate organic carbon are compiled and on the basis of GEOSECS data and temperatures, concentrations, and isotopic compositions of dissolved CO2 in the waters in which the related phytoplankton grew are estimated. In this way, the fractionation of carbon isotopes during photosynthetic fixation of CO2 is found to be significantly correlated with concentrations of dissolved CO2. Because ancient carbon isotopic fractionations have been determined from analyses of sedimentary porphyrins [Popp et al., 1989], the relationship between isotopic fractionation and concentrations of dissolved CO2 developed here can be employed to estimate concentrations of CO2 dissolved in ancient oceans and, in turn, partial pressures of CO2 in ancient atmospheres. The calculations take into account the temperature dependence of chemical and isotopic equilibria in the dissolved-inorganic-carbon system and of air-sea equilibria. Paleoenvironmental temperatures for each sample are estimated from reconstructions of paleogeography, latitudinal temperature gradients, and secular changes in low-latitude sea surface temperature. It is estimated that atmospheric partial pressures of CO2 were over 1000 micro atm 160 - 100 Ma ago, then declined to values near 300 micro atm during the next 100 Ma. Analysis of a high-resolution record of carbon isotopic fractionation at the Cenomanian-Turonian boundary suggests that the partial pressure of CO2 in the atmosphere was drawn down from values near 840 micro atm to values near 700 micro atm during the anoxic event.

Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

NASA Astrophysics Data System (ADS)

Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R.

2017-06-01

This paper is intended to provide exponentially accurate Galerkin, Petrov-Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre-Gauss and Laguerre-Gauss-Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov-Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov-Galerkin methods are listed at the end.

Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement

PubMed Central

Mazzocco, Michèle M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

2014-01-01

Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to “one-half,” and fraction pairs with common denominators) differentiates those with mathematical learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics, and whether long term learning trajectories of this knowledge also differentiate these groups. We confirmed that although 4th graders with LA (n = 18) or TA (n = 93) are more accurate evaluating one-half vs. non-half fractions (until they reach ceiling performance levels on both types of fractions), children with MLD (n=11) do not show a one-half advantage until Grade 7 and do not reach ceiling performance even by Grade 8. Both the MLD and LA groups have early difficulties with fractions, but by Grade 5 the LA group approaches performance levels of the TA group and deviates from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short lived for the TA group (because ceiling level was achieved across formats), slightly more persistent for the LA group, and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties varies across children with math difficulties (MLD or LA). PMID:23587941

Devices, systems, and methods for microscale isoelectric fractionation

DOEpatents

Sommer, Gregory J.; Hatch, Anson V.; Wang, Ying-Chih; Singh, Anup K.

2016-08-09

Embodiments of the present invention provide devices, systems, and methods for microscale isoelectric fractionation. Analytes in a sample may be isolated according to their isoelectric point within a fractionation microchannel. A microfluidic device according to an embodiment of the invention includes a substrate at least partially defining a fractionation microchannel. The fractionation microchannel has at least one cross-sectional dimension equal to or less than 1 mm. A plurality of membranes of different pHs are disposed in the microchannel. Analytes having an isoelectric point between the pH of the membranes may be collected in a region of the fractionation channel between the first and second membranes through isoelectric fractionation.

Devices, systems, and methods for microscale isoelectric fractionation

DOEpatents

Sommer, Gregory J; Hatch, Anson V; Wang, Ying-Chih; Singh, Anup K

2015-04-14

Embodiments of the present invention provide devices, systems, and methods for microscale isoelectric fractionation. Analytes in a sample may be isolated according to their isoelectric point within a fractionation microchannel. A microfluidic device according to an embodiment of the invention includes a substrate at least partially defining a fractionation microchannel. The fractionation microchannel has at least one cross-sectional dimension equal to or less than 1 mm. A plurality of membranes of different pHs are disposed in the microchannel. Analytes having an isoelectric point between the pH of the membranes may be collected in a region of the fractionation channel between the first and second membranes through isoelectric fractionation.

High δ56Fe values in Samoan basalts

NASA Astrophysics Data System (ADS)

Konter, J. G.; Pietruszka, A. J.; Hanan, B. B.; Finlayson, V.

2014-12-01

Fe isotope fractionation spans ~0-0.4 permil in igneous systems, which cannot all be attributed to variable source compositions since peridotites barely overlap these compositions. Other processes may fractionate Fe isotopes such as variations in the degree of partial melting, magmatic differentiation, fluid addition related to the final stages of melt evolution, and kinetic fractionation related to diffusion. An important observation in igneous systems is the trend of increasing Fe isotope values against an index of magmatic fractionation (e.g. SiO2; [1]). The data strongly curve from δ56Fe >0.3 permil for SiO2 >70 wt% down to values around 0.09 permil from ~65 wt% down to 40 wt% SiO2 of basalts. However, ocean island basalts (OIBs) have a slightly larger δ56Fe variability than mid ocean ridge basalts (MORBs; [e.g. 2]). We present Fe isotope data on samples from the Samoan Islands (OIB) that have unusually high δ56Fe values for their SiO2 content. We rule out alteration by using fresh samples, and further test for the effects of magmatic processes on the δ56Fe values. In order to model the largest possible fractionation, unusually small degrees of melting with extreme fractionation factors are modeled with fractional crystallization of olivine alone, but such processing fails to fractionate the Fe isotopes to the observed values. Moreover, Samoan lavas likely also fractionated clinopyroxene, and its lower fractionation factor would limit the final δ56Fe value of the melt. We therefore suggest the mantle source of Samoan lavas must have had unusually high δ56Fe. However, there is no clear correlation with the highly radiogenic isotope signatures that reflect the unique source compositions of Samoa. Instead, increasing melt extraction correlates with lower δ56Fe values in peridotites assumed to be driven by the preference for the melt phase by heavy Fe3+, while high values may be related to metasomatism [3]. The latter would be in line with metasomatized xenoliths from Samoa [4]. [1] Heimann et al., 2008, doi:10.1016/j.gca.2008.06.009 [2] Teng et al., 2013, doi:10.1016/j.gca.2012.12.027 [3] Williams et al., 2004, doi: 10.1126/science.1095679 [4] Hauri et al., 1993, doi: 10.1038/365221a0

Chain confinement, phase transitions, and lamellar structure in semicrystalline polymers, polymer blends and polymer nanocomposites

NASA Astrophysics Data System (ADS)

Chen, Huipeng

Recent studies suggest that there are three phase fractions in semicrystalline polymers, the crystalline, the mobile amorphous and the rigid amorphous phases. Due to the distinct properties of the rigid amorphous fraction, RAF, it has been investigated for more than twenty years. In this thesis, a general method using quasi-isothermal temperature-modulated differential scaning calorimetry, DSC, is provided for the first time to obtain the temperature dependent RAF and the other two fractions, crystalline fraction and mobile amorphous fraction, MAF. For poly(ethylene terephthalate), PET, our results show RAF was vitrified during quasi-isothermal cooling after crystallization had been completed and became totally devitrified during quasi-isothermal heating before the start of melting. Several years after people initially discovered the existence of RAF, another issue arose relating to the physical location of RAF and mobile amorphous fraction, MAF, within a lamellar stack model. Two very different models to describe the location of RAF were proposed. In the Heterogeneous Stack Model, HET, RAF is located outside the lamellar stacks. In the Homogeneous Stack Model, HSM, RAF was located inside the lamellar stacks. To determine the lamellar structure of semicrystalline polymers comprising three phase, a general method is given in this thesis by using a combination of the DSC and small angle X-ray scattering, SAXS techniques. It has been applied to Nylon 6, isotactic polystyrene, iPS, and PET. It was found for all of these materials, the HSM model is correct to describe the lamellar structure. In addition to the determination of lamellar structures, this method can also provide the exact fraction of MAF inside and outside lamellar stacks for binary polymer blends. For binary polymer blends, MAF, normally is located partially inside and partially outside the lamellar stacks. However, the quantification of the MAF inside and outside the lamellar stacks has now been provided and is applied to the iPS/atactic polystyrene, aPS, blends. The fractions of MAF inside and outside the lamellar stacks were quantified for the first time. For A/B binary polymer blends, it has been reported that if B is already crystalline, the crystalline fraction would serve as a restriction on the subsequent growth of the crystallizable partner A, while amorphous fraction could be diffused from the crystalline growth front of the crystallizing A component. Considering the effect of RAF on binary blends, a new concept is provided: like the crystals, the RAF of one polymer component may inhibit the growth of crystals of the other blend partner. The non-isothermal crystallization of PET/poly(lactic acid), PLA, blends were investigated and the results confirmed the new concept is correct: PET forms a large amount of RAF and inhibits crystal formation in PLA. Then, we broadened the concept of RAF and investigated the RAF in recent 'hot' materials, polymer nanocomposites. It was found the fraction of RAF greatly increased with a small amount of multi-wall carbon nanotubes, MWCNT, loading in PET electrospun, ES, fibers. A general model is given for polymer ES fibers with MWCNTs: the addition of MWCNTs causes polymer chains in the ES fibers to become more extended, (ie, more stretched), resulting in more confinement of PET chains and an increase in the RAF.

Parareal algorithms with local time-integrators for time fractional differential equations

NASA Astrophysics Data System (ADS)

Wu, Shu-Lin; Zhou, Tao

2018-04-01

It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal method to such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions.

Approximations of e and ?: An Exploration

ERIC Educational Resources Information Center

Brown, Philip R.

2017-01-01

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

A technique for production of nanocrystalline cellulose with a narrow size distribution

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

Bai, Wen; Holbery, James D.; Li, Kaichang

2009-02-01

Nanocrystalline cellulose (NCC) was prepared by sulfuric acid hydrolysis of microcrystalline cellulose. A differential centrifugation technique was studied to obtain NCC whiskers with a narrow size distribution. It was shown that the volume of NCC in different fractions had an inverse relationship with relative centrifugal force (RCF). The length of NCC whiskers was also fractionized by differential RCF. The aspect ratio of NCC in different fractions had a relatively narrow range. This technique provides an easy way of producing NCC whiskers with a narrow size distribution.

Raman spectroscopy for the characterization of different fractions of hemp essential oil extracted at 130 °C using steam distillation method

NASA Astrophysics Data System (ADS)

Hanif, Muhammad Asif; Nawaz, Haq; Naz, Saima; Mukhtar, Rubina; Rashid, Nosheen; Bhatti, Ijaz Ahmad; Saleem, Muhammad

2017-07-01

In this study, Raman spectroscopy along with Principal Component Analysis (PCA) is used for the characterization of pure essential oil (pure EO) isolated from the leaves of the Hemp (Cannabis sativa L.,) as well as its different fractions obtained by fractional distillation process. Raman spectra of pure Hemp essential oil and its different fractions show characteristic key bands of main volatile terpenes and terpenoids, which significantly differentiate them from each other. These bands provide information about the chemical composition of sample under investigation and hence can be used as Raman spectral markers for the qualitative monitoring of the pure EO and different fractions containing different active compounds. PCA differentiates the Raman spectral data into different clusters and loadings of the PCA further confirm the biological origin of the different fractions of the essential oil.

The Axum-Adwa basalt-trachyte complex: a late magmatic activity at the periphery of the Afar plume

NASA Astrophysics Data System (ADS)

Natali, C.; Beccaluva, L.; Bianchini, G.; Siena, F.

2013-08-01

The Axum-Adwa igneous complex consists of a basalt-trachyte (syenite) suite emplaced at the northern periphery of the Ethiopian plateau, after the paroxysmal eruption of the Oligocene (ca 30 Ma) continental flood basalts (CFB), which is related to the Afar plume activity. 40Ar/39Ar and K-Ar ages, carried out for the first time on felsic and basaltic rocks, constrain the magmatic age of the greater part of the complex around Axum to 19-15 Ma, whereas trachytic lavas from volcanic centres NE of Adwa are dated ca 27 Ma. The felsic compositions straddle the critical SiO2-saturation boundary, ranging from normative quartz trachyte lavas east of Adwa to normative (and modal) nepheline syenite subvolcanic domes (the obelisks stones of ancient axumites) around Axum. Petrogenetic modelling based on rock chemical data and phase equilibria calculations by PELE (Boudreau 1999) shows that low-pressure fractional crystallization processes, starting from mildly alkaline- and alkaline basalts comparable to those present in the complex, could generate SiO2-saturated trachytes and SiO2-undersaturated syenites, respectively, which correspond to residual liquid fractions of 17 and 10 %. The observed differentiation processes are consistent with the development of rifting events and formation of shallow magma chambers plausibly located between displaced (tilted) crustal blocks that favoured trapping of basaltic parental magmas and their fractionation to felsic differentiates. In syenitic domes, late- to post-magmatic processes are sometimes evidenced by secondary mineral associations (e.g. Bete Giorgis dome) which overprint the magmatic parageneses, and mainly induce additional nepheline and sodic pyroxene neo-crystallization. These metasomatic reactions were promoted by the circulation of Na-Cl-rich deuteric fluids (600-400 °C), as indicated by mineral and bulk rock chemical budgets as well as by δ18O analyses on mineral separates. The occurrence of this magmatism post-dating the CFB event, characterized by comparatively lower volume of more alkaline products, conforms to the progressive vanishing of the Afar plume thermal effects and the parallel decrease of the partial melting degrees of the related mantle sources. This evolution is also concomitant with the variation of the tectono-magmatic regime from regional lithospheric extension (CFB eruption) to localized rifting processes that favoured magmatic differentiation.

Early mantle heterogeneities in the Réunion hotspot source inferred from highly siderophile elements in cumulate xenoliths

NASA Astrophysics Data System (ADS)

Peters, Bradley J.; Day, James M. D.; Taylor, Lawrence A.

2016-08-01

Ultramafic cumulate rocks form during intrusive crystallization of high-MgO magmas, incorporating relatively high abundances of compatible elements, including Cr and Ni, and high abundances of the highly siderophile elements (HSE: Os, Ir, Ru, Pt, Pd, Re). Here, we utilize a suite of cumulate xenoliths from Piton de la Fournaise, La Réunion (Indian Ocean), to examine the mantle source composition of the Réunion hotspot using HSE abundances and Os isotopes. Dunite and wherlite xenoliths and associated lavas from the Piton de la Fournaise volcanic complex span a range of MgO contents (46 to 7 wt.%), yet exhibit remarkably homogeneous 187Os/188Os (0.1324 ± 0.0014, 2σ), representing the Os-isotopic composition of Réunion hotspot primary melts. A significant fraction of the xenoliths also have primitive upper-mantle (PUM) normalized HSE patterns with elevated Ru and Pd (PUM-normalized Ru/Ir and Pd/Ir of 0.8-6.3 and 0.2-7.2, respectively). These patterns are not artifacts of alteration, fractional crystallization, or partial melting processes, but rather require a primary magma with similar relative enrichments. Some highly olivine-phyric (>40 modal percent olivine) Piton de la Fournaise lavas also preserve these relative Ru and Pd enrichments, while others preserve a pattern that is likely related to sulfur saturation in evolved melts. The estimate of HSE abundances in PUM indicates high Ru/Ir and Pd/Pt values relative to carbonaceous, ordinary and enstatite chondrite meteorite groups. Thus, the existence of cumulate rocks with even more fractionated HSE patterns relative to PUM suggests that the Réunion hotspot samples a yet unrecognized mantle source. The origin of fractionated HSE patterns in Réunion melts may arise from sampling of a mantle source that experienced limited late accretion (<0.2% by mass) compared with PUM (0.5-0.8%), possibly involving impactors that were distinct from present-day chondrites, or limited core-mantle interactions. Given the remarkably homogeneous Os, Pb, and noble-gas isotopic signatures of Réunion, which plot near the convergence point of isotopic data for many hotspots, such a conclusion provides evidence for an early differentiated and subsequently isolated mantle domain that may be partially sampled by some ocean island basalts.

Crystal fractionation in the SNC meteorites: Implications for sample selection

NASA Technical Reports Server (NTRS)

Treiman, Allan H.

1988-01-01

Almost all rock types in the SNC meteorites are cumulates, products of magma differentiation by crystal fractionation (addition or removal of crystals). If the SNC meteorites are from the surface of Mars or near subsurface, then most of the igneous units on Mars are differentiated. Basaltic units probably experienced minor to moderate differientation, but ultrabasic units probably experienced extreme differentiation. Products of this differentiation may include Fe-rich gabbro, pyroxenite, periodotite (and thus serpentine), and possibly massive sulfides. The SNC meteorites include ten lithologies (three in EETA79001), eight of which are crystal cumulates. The other lithologies, EETA79001 A and B are subophitic basalts.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

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.

Stochasticity and Spatial Interaction Govern Stem Cell Differentiation Dynamics

NASA Astrophysics Data System (ADS)

Smith, Quinton; Stukalin, Evgeny; Kusuma, Sravanti; Gerecht, Sharon; Sun, Sean X.

2015-07-01

Stem cell differentiation underlies many fundamental processes such as development, tissue growth and regeneration, as well as disease progression. Understanding how stem cell differentiation is controlled in mixed cell populations is an important step in developing quantitative models of cell population dynamics. Here we focus on quantifying the role of cell-cell interactions in determining stem cell fate. Toward this, we monitor stem cell differentiation in adherent cultures on micropatterns and collect statistical cell fate data. Results show high cell fate variability and a bimodal probability distribution of stem cell fraction on small (80-140 μm diameter) micropatterns. On larger (225-500 μm diameter) micropatterns, the variability is also high but the distribution of the stem cell fraction becomes unimodal. Using a stochastic model, we analyze the differentiation dynamics and quantitatively determine the differentiation probability as a function of stem cell fraction. Results indicate that stem cells can interact and sense cellular composition in their immediate neighborhood and adjust their differentiation probability accordingly. Blocking epithelial cadherin (E-cadherin) can diminish this cell-cell contact mediated sensing. For larger micropatterns, cell motility adds a spatial dimension to the picture. Taken together, we find stochasticity and cell-cell interactions are important factors in determining cell fate in mixed cell populations.

Association of Rpn10 with high molecular weight complex is enhanced during retinoic acid-induced differentiation of neuroblastoma cells.

PubMed

Tayama, Yoko; Kawahara, Hiroyuki; Minami, Ryosuke; Shimada, Masumi; Yokosawa, Hideyoshi

2007-12-01

The ubiquitin-binding Rpn10 protein serves as an ubiquitin receptor that delivers client proteins to the 26S proteasome, the protein degradation complex. It has been suggested that the ubiquitin-dependent protein degradation is critical for neuronal differentiation and for preventing neurodegenerative diseases. Our previous study indicated the importance of Rpn10 in control of cellular differentiation (Shimada et al., Mol Biol Cell 17:5356-5371, 2006), though the functional relevance of Rpn10 in neuronal cell differentiation remains a mystery to be uncovered. In the present study, we have examined the level of Rpn10 in a proteasome-containing high molecular weight (HMW) protein fraction prepared from the mouse neuroblastoma cell line Neuro2a. We here report that the protein level of Rpn10 in HMW fraction from un-differentiated Neuro2a cells was significantly lower than that of other cultured cell lines. We have found that retinoic acid-induced neural differentiation of Neuro2a cells significantly stimulates the incorporation of Rpn10 into HMW fractions, although the amounts of 26S proteasome subunits were not changed. Our findings provide the first evidence that the modulation of Rpn10 is linked to the control of retinoic acid-induced differentiation of neuroblastoma cells.

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.

A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

NASA Astrophysics Data System (ADS)

Abro, Kashif Ali; Memon, Anwar Ahmed; Uqaili, Muhammad Aslam

2018-03-01

This research article is analyzed for the comparative study of RL and RC electrical circuits by employing newly presented Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. The governing ordinary differential equations of RL and RC electrical circuits have been fractionalized in terms of fractional operators in the range of 0 ≤ ξ ≤ 1 and 0 ≤ η ≤ 1. The analytic solutions of fractional differential equations for RL and RC electrical circuits have been solved by using the Laplace transform with its inversions. General solutions have been investigated for periodic and exponential sources by implementing the Atangana-Baleanu and Caputo-Fabrizio fractional operators separately. The investigated solutions have been expressed in terms of simple elementary functions with convolution product. On the basis of newly fractional derivatives with and without singular kernel, the voltage and current have interesting behavior with several similarities and differences for the periodic and exponential sources.

Fluorescence analysis of humic and fulvic acids from two Brazilian oxisols as affected by biosolid amendment.

PubMed

Bertoncini, E I; D'Orazio, V; Senesi, N; Mattiazzo, M E

2005-03-01

Conventional monodimensional fluorescence spectroscopy in the emission, excitation, and synchronous-scan modes and total luminescence spectroscopy have proven to be sensitive techniques for characterization and differentiation of humic acid (HA) and fulvic acid (FA) fractions isolated from an aerobically and anaerobically digested and limed biosolid, two layers of a sandy and a clayey Brazilian oxisol, and the corresponding biosolid-amended soils. The spectral patterns and the relative fluorescence intensities suggest greater molecular heterogeneity, less aromatic polycondensation, and less humification of biosolid HA and FA compared with soil HA and FA. However, the differences are smaller for the FA fractions than for the HA fractions. Fluorescence properties of soil HA and FA differ slightly as a function of soil type and soil layer. Biosolid application causes a shift to shorter wavelengths of the main fluorescence peaks and marked variation of the relative fluorescence intensities of HA and FA isolated from amended soils. These results suggest that molecular components of relatively small molecular size, with a low level of aromatic polycondensation, and low degree of humification present in biosolid HA and FA are partially and variously incorporated into amended soil HA and FA. In general, these modifications seem to be smaller in HA and FA from the clayey soil layers than in those from the sandy soil layers, possibly because of protective effects exerted by clay minerals of native soil HA and FA against disturbances caused by biosolid application.

Identification of Centella asiatica's Effective Ingredients for Inducing the Neuronal Differentiation.

PubMed

Jiang, Hui; Zheng, Guoshuai; Lv, Junwei; Chen, Heyu; Lin, Jinjin; Li, Yiyang; Fan, Guorong; Ding, Xianting

2016-01-01

Centella asiatica, commonly known as Gotu kola, has been widely used as a traditional herb for decades. Yet, the study on which compounds or compound combinations actually lead to its brain benefits remains scarce. To study the neuroprotection effects of Centella asiatica, neuronal differentiation of PC12 cells was applied. In our pilot study, we isolated 45 Centella asiatica fractions and tested their abilities for inducing neuronal differentiation on PC12 cells. The most effective fraction showed robust induction in neurite outgrowth and neurofilament expression. LC-MS fingerprint analysis of this fraction revealed asiatic acid and madecassic acid as the dominant components. A further investigation on the pure combination of these two compounds indicated that the combination of these two compounds extensively promoted nerve differentiation in vitro. Application of PD98059, a protein MEK inhibitor, attenuated combination-induced neurofilament expression, indicating the combination-induced nerve differentiation through activation of MEK signaling pathway. Our results support the use of combination of asiatic acid and madecassic acid as an effective mean to intervene neurodegenerative diseases in which neurotrophin deficiency is involved.

Identification of Centella asiatica's Effective Ingredients for Inducing the Neuronal Differentiation

PubMed Central

Jiang, Hui; Zheng, Guoshuai; Lv, Junwei; Chen, Heyu; Lin, Jinjin; Li, Yiyang; Fan, Guorong

2016-01-01

Centella asiatica, commonly known as Gotu kola, has been widely used as a traditional herb for decades. Yet, the study on which compounds or compound combinations actually lead to its brain benefits remains scarce. To study the neuroprotection effects of Centella asiatica, neuronal differentiation of PC12 cells was applied. In our pilot study, we isolated 45 Centella asiatica fractions and tested their abilities for inducing neuronal differentiation on PC12 cells. The most effective fraction showed robust induction in neurite outgrowth and neurofilament expression. LC-MS fingerprint analysis of this fraction revealed asiatic acid and madecassic acid as the dominant components. A further investigation on the pure combination of these two compounds indicated that the combination of these two compounds extensively promoted nerve differentiation in vitro. Application of PD98059, a protein MEK inhibitor, attenuated combination-induced neurofilament expression, indicating the combination-induced nerve differentiation through activation of MEK signaling pathway. Our results support the use of combination of asiatic acid and madecassic acid as an effective mean to intervene neurodegenerative diseases in which neurotrophin deficiency is involved. PMID:27446228

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Calcium Isotopic Compositions of Normal Mid-Ocean Ridge Basalts From the Southern Juan de Fuca Ridge

NASA Astrophysics Data System (ADS)

Zhu, Hongli; Liu, Fang; Li, Xin; Wang, Guiqin; Zhang, Zhaofeng; Sun, Weidong

2018-02-01

Mantle peridotites show that Ca is isotopically heterogeneous in Earth's mantle, but the mechanism for such heterogeneity remains obscure. To investigate the effect of partial melting on Ca isotopic fractionation and the mechanism for Ca isotopic heterogeneity in the mantle, we report high-precision Ca isotopic compositions of the normal Mid-Ocean Ridge Basalts (N-MORB) from the southern Juan de Fuca Ridge. δ44/40Ca of these N-MORB samples display a small variation ranging from 0.75 ± 0.05 to 0.86 ± 0.03‰ (relative to NIST SRM 915a, a standard reference material produced by the National Institute of Standards and Technology), which are slightly lower than the estimated Upper Mantle value of 1.05 ± 0.04‰ and the Bulk Silicate Earth (BSE) value of 0.94 ± 0.05‰. This phenomenon cannot be explained by fractional crystallization, because olivine and orthopyroxene fractional crystallization has limited influence on δ44/40Ca of N-MORB due to their low CaO contents, while plagioclase fractional crystallization cannot lead to light Ca isotopic compositions of the residue magma. Instead, the lower δ44/40Ca of N-MORB samples compared to their mantle source is most likely caused by partial melting. The offset in δ44/40Ca between N-MORB and BSE indicates that at least 0.1-0.2‰ fractionation would occur during partial melting and light Ca isotopes are preferred to be enriched in magma melt, which is in accordance with the fact that δ44/40Ca of melt-depleted peridotites are higher than fertile peridotites in literature. Therefore, partial melting is an important process that can decrease δ44/40Ca in basalts and induce Ca isotopic heterogeneity in Earth's mantle.

Phase equilibria constraints on models of subduction zone magmatism

NASA Astrophysics Data System (ADS)

Myers, James D.; Johnston, Dana A.

Petrologic models of subduction zone magmatism can be grouped into three broad classes: (1) predominantly slab-derived, (2) mainly mantle-derived, and (3) multi-source. Slab-derived models assume high-alumina basalt (HAB) approximates primary magma and is derived by partial fusion of the subducting slab. Such melts must, therefore, be saturated with some combination of eclogite phases, e.g. cpx, garnet, qtz, at the pressures, temperatures and water contents of magma generation. In contrast, mantle-dominated models suggest partial melting of the mantle wedge produces primary high-magnesia basalts (HMB) which fractionate to yield derivative HAB magmas. In this context, HMB melts should be saturated with a combination of peridotite phases, i.e. ol, cpx and opx, and have liquid-lines-of-descent that produce high-alumina basalts. HAB generated in this manner must be saturated with a mafic phase assemblage at the intensive conditions of fractionation. Multi-source models combine slab and mantle components in varying proportions to generate the four main lava types (HMB, HAB, high-magnesia andesites (HMA) and evolved lavas) characteristic of subduction zones. The mechanism of mass transfer from slab to wedge as well as the nature and fate of primary magmas vary considerably among these models. Because of their complexity, these models imply a wide range of phase equilibria. Although the experiments conducted on calc-alkaline lavas are limited, they place the following limitations on arc petrologic models: (1) HAB cannot be derived from HMB by crystal fractionation at the intensive conditions thus far investigated, (2) HAB could be produced by anhydrous partial fusion of eclogite at high pressure, (3) HMB liquids can be produced by peridotite partial fusion 50-60 km above the slab-mantle interface, (4) HMA cannot be primary magmas derived by partial melting of the subducted slab, but could have formed by slab melt-peridotite interaction, and (5) many evolved calc-alkaline lavas could have been formed by crystal fractionation at a range of crustal pressures.

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.

MitoTracker Green labeling of mitochondrial proteins and their subsequent analysis by capillary electrophoresis with laser-induced fluorescence detection.

PubMed

Presley, Andrew D; Fuller, Kathryn M; Arriaga, Edgar A

2003-08-05

MitoTracker Green (MTG) is a mitochondrial-selective fluorescent label commonly used in confocal microscopy and flow cytometry. It is expected that this dye selectively accumulates in the mitochondrial matrix where it covalently binds to mitochondrial proteins by reacting with free thiol groups of cysteine residues. Here we demonstrate that MTG can be used as a protein labeling reagent that is compatible with a subsequent analysis by capillary electrophoresis with laser-induced fluorescence detection (CE-LIF). Although the MTG-labeled proteins and MTG do not seem to electrophoretically separate, an enhancement in fluorescence intensity of the product indicates that only proteins with free thiol groups are capable of reacting with MTG. In addition we propose that MTG is a partially selective label towards some mitochondrial proteins. This selectivity stems from the high MTG concentration in the mitochondrial matrix that favors alkylation of the available thiol groups in this subcellular compartment. To that effect we treated mitochondria-enriched fractions that had been prepared by differential centrifugation of an NS-1 cell lysate. This fraction was solubilized with an SDS-containing buffer and analyzed by CE-LIF. The presence of a band with fluorescence stronger than MTG alone also indicated the presence of an MTG-protein product. Confirming that MTG is labeling mitochondrial proteins was done by treating the solubilized mitochondrial fraction with 5-furoylquinoline-3-carboxaldehyde (FQ), a fluorogenic reagent that reacts with primary amino groups, and analysis by CE-LIF using two separate detection channels: 520 nm for MTG-labeled species and 635 nm for FQ-labeled species. In addition, these results indicate that MTG labels only a subset of proteins in the mitochondria-enriched fraction.

Soil organic matter composition from correlated thermal analysis and nuclear magnetic resonance data in Australian national inventory of agricultural soils

NASA Astrophysics Data System (ADS)

Moore, T. S.; Sanderman, J.; Baldock, J.; Plante, A. F.

2016-12-01

National-scale inventories typically include soil organic carbon (SOC) content, but not chemical composition or biogeochemical stability. Australia's Soil Carbon Research Programme (SCaRP) represents a national inventory of SOC content and composition in agricultural systems. The program used physical fractionation followed by 13C nuclear magnetic resonance (NMR) spectroscopy. While these techniques are highly effective, they are typically too expensive and time consuming for use in large-scale SOC monitoring. We seek to understand if analytical thermal analysis is a viable alternative. Coupled differential scanning calorimetry (DSC) and evolved gas analysis (CO2- and H2O-EGA) yields valuable data on SOC composition and stability via ramped combustion. The technique requires little training to use, and does not require fractionation or other sample pre-treatment. We analyzed 300 agricultural samples collected by SCaRP, divided into four fractions: whole soil, coarse particulates (POM), untreated mineral associated (HUM), and hydrofluoric acid (HF)-treated HUM. All samples were analyzed by DSC-EGA, but only the POM and HF-HUM fractions were analyzed by NMR. Multivariate statistical analyses were used to explore natural clustering in SOC composition and stability based on DSC-EGA data. A partial least-squares regression (PLSR) model was used to explore correlations among the NMR and DSC-EGA data. Correlations demonstrated regions of combustion attributable to specific functional groups, which may relate to SOC stability. We are increasingly challenged with developing an efficient technique to assess SOC composition and stability at large spatial and temporal scales. Correlations between NMR and DSC-EGA may demonstrate the viability of using thermal analysis in lieu of more demanding methods in future large-scale surveys, and may provide data that goes beyond chemical composition to better approach quantification of biogeochemical stability.

Thermodynamic properties and energy characteristics of water+1-propanol

NASA Astrophysics Data System (ADS)

Alhasov, A. B.; Bazaev, A. R.; Bazaev, E. A.; Osmanova, B. K.

2017-11-01

By using own precise experimental data on p,ρ,T,x- relations differential and integral thermodynamic properties of water+1-propanol homogeneous binary mixtures (0.2, 0.5, and 0.8 mole fractions of 1-propanol) were obtained in one phase (liquid, vapor) region, along coexistence curve phase, at critical and supercritical regions of parameters of state. These values were obtained in the regions of temperatures 373.15 - 673.15 K, densities 3 - 820 kg/m3 and pressures up to 50 MPa. It is found that shape of p,ρ,T,- dependences of water+1-propanol mixtures in investigated range of temperatures is the same with those of pure liquid, but the pressure of the mixture is higher than those of pure water or 1-propanol. The critical line of water+1-propanol binary mixtures as opposed to those of water+methanol and water+ethanol mixtures has convex shape. It is ascertained that using water+1-propanol mixture (0.2 mol.fraction of 1-propanol) instead of pure water allows to decrease lower limit of operating temperatures to 50 K, to increase effective coefficient of efficiency and partially unify thermal mechanical equipment of power plant. Our comparative energy analysis of cycles of steam-turbine plant on water and water+1- propanol mixtures, carried out at the same thermobaric conditionsand showed that thermal coefficient of efficiencyofcycle of steam-turbine plant onwater+1-propanol mixture (0.2 mol.fraction of 1-propanol) is higher than those of pure water.Thus and so we made a conclusion about usability of water+1-propanol mixture (0.2 mole fraction of 1-propanol) as a working substance of steam-turbine plant cycle.

X-ray Microtomography of Intermittency in Multiphase Flow at Steady State Using a Differential Imaging Method

NASA Astrophysics Data System (ADS)

Gao, Ying; Lin, Qingyang; Bijeljic, Branko; Blunt, Martin J.

2017-12-01

We imaged the steady state flow of brine and decane in Bentheimer sandstone. We devised an experimental method based on differential imaging to examine how flow rate impacts impact the pore-scale distribution of fluids during coinjection. This allows us to elucidate flow regimes (connected, or breakup of the nonwetting phase pathways) for a range of fractional flows at two capillary numbers, Ca, namely 3.0 × 10-7 and 7.5 × 10-6. At the lower Ca, for a fixed fractional flow, the two phases appear to flow in connected unchanging subnetworks of the pore space, consistent with conventional theory. At the higher Ca, we observed that a significant fraction of the pore space contained sometimes oil and sometimes brine during the 1 h scan: this intermittent occupancy, which was interpreted as regions of the pore space that contained both fluid phases for some time, is necessary to explain the flow and dynamic connectivity of the oil phase; pathways of always oil-filled portions of the void space did not span the core. This phase was segmented from the differential image between the 30 wt % KI brine image and the scans taken at each fractional flow. Using the grey scale histogram distribution of the raw images, the oil proportion in the intermittent phase was calculated. The pressure drops at each fractional flow at low and high flow rates were measured by high-precision differential pressure sensors. The relative permeabilities and fractional flow obtained by our experiment at the mm-scale compare well with data from the literature on cm-scale samples.

Liquid fractionation. Part I: Basic principles and experimental simulations

NASA Astrophysics Data System (ADS)

McBirney, Alexander R.; Baker, Brian H.; Nilson, Robert H.

1985-03-01

A possible explanation for the closely associated magmas of contrasting compositions erupted from many mature volcanic centers can be found in the large differences of density produced by relatively small compositional variations in liquids that evolve by crystallization or melting at the walls of shallow magma chambers. A mechanism of liquid fractionation in which differentiated liquids segragate gravitationally to form compositionally graded columns of magma may surmount the long-standing problem of explaining large volumes of highly evolved liquids that reach advanced degrees of differentiation in times that are too short to be consistent with conventional models of crystal fractionation based on crystal settling. In those types of magmas that decrease in density as they differentiate, a fractionated liquid next to a wall may form a buoyant compositional boundary layer that flows up the wall and accumulates as a separate zone in the upper levels of the reservoir. Magmas that increase in density as they differentiate will have the opposite behavior; they descend along the wall and pond on the floor. Both types of systems can be modeled using simple aqueous solutions and techniques similar to those developed by Chen and Turner (1980). The insights gained through experiments of this kind suggest a number of processes that may be responsible for common types of volcanic behavior and patterns of differentiation in shallow plutons.

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.

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

In vivo label-free lymphangiography of cutaneous lymphatic vessels in human burn scars using optical coherence tomography

PubMed Central

Gong, Peijun; Es’haghian, Shaghayegh; Harms, Karl-Anton; Murray, Alexandra; Rea, Suzanne; Wood, Fiona M.; Sampson, David D.; McLaughlin, Robert A.

2016-01-01

We present an automated, label-free method for lymphangiography of cutaneous lymphatic vessels in humans in vivo using optical coherence tomography (OCT). This method corrects for the variation in OCT signal due to the confocal function and sensitivity fall-off of a spectral-domain OCT system and utilizes a single-scattering model to compensate for A-scan signal attenuation to enable reliable thresholding of lymphatic vessels. A segment-joining algorithm is then incorporated into the method to mitigate partial-volume effects with small vessels. The lymphatic vessel images are augmented with images of the blood vessel network, acquired from the speckle decorrelation with additional weighting to differentiate blood vessels from the observed high decorrelation in lymphatic vessels. We demonstrate the method with longitudinal scans of human burn scar patients undergoing ablative fractional laser treatment, showing the visualization of the cutaneous lymphatic and blood vessel networks. PMID:28018713

Stability toward High Energy Radiation of Non-Proteinogenic Amino Acids: Implications for the Origins of Life

PubMed Central

Cataldo, Franco; Iglesias-Groth, Susana; Angelini, Giancarlo; Hafez, Yaser

2013-01-01

A series of non-proteinogenic amino acids, most of them found quite commonly in the meteorites known as carbonaceous chondrites, were subjected to solid state radiolysis in vacuum to a total radiation dose of 3.2 MGy corresponding to 23% of the total dose expected to be taken by organic molecules buried in asteroids and meteorites since the beginning of the solar system 4.6 × 109 years ago. The radiolyzed amino acids were studied by FT-IR spectroscopy, Differential Scanning Calorimetry (DSC) and by polarimety and Optical Rotatory Dispersion (ORD). It is shown that an important fraction of each amino acid is able to “survive” the massive dose of radiation, while the enantiomeric excess is partially preserved. Based on the results obtained, it is concluded that it is unsurprising to find amino acids even in enantiomeric excess in carbonaceous chondrites. PMID:25369815

Unsteady free convection flow past a semi-infinite vertical plate with constant heat flux in water based nanofluids

NASA Astrophysics Data System (ADS)

Narahari, Marneni

2018-04-01

The unsteady free convective flow of nanofluids past a semi-infinite vertical plate with uniform heat flux has been investigated numerically. An implicit finite difference technique of Crank-Nicolson scheme has been employed to solve the governing partial differential equations. Five different types of water based nanofluids containing Cu, Ag, Al2O3, CuO and TiO2 nanoparticles are considered to study the fluid flow characteristics with various time and solid volume fraction parameters. It is found that the local as well as the average Nusselt number for nanofluids is higher than the pure fluid (water). The local skin-friction is higher for pure fluid as compared to the nanofluids. The present numerical results obtained for local Nusselt number are validated with the previously published correlation results for a limiting case and it is found that the results are in good agreement.

Mixed convective stagnation point flow of nanofluid with Darcy-Fochheimer relation and partial slip

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Ijaz, Misbah; Qayyum, Sumaira; Ayub, Muhammad; Alsaedi, Ahmed

2018-06-01

Here axisymmetric mixed convective, stagnation point flow of electrically conducting nanofluid by a permeable cylinder is examined. Magnetic field in transverse direction is applied. The Darcy-Forchheimer relation is accounted to specify the flow nature in porous medium. Formulation of mathematical model is given by using Tiwari-Das nanofluid model. The velocity and thermal slip conditions.are taken. This whole communication comprises water as a base fluid with nano-sized particles (Aluminum oxide, Copper and Titanium Oxide). The nonlinear coupled ordinary differential equations are obtained after using appropriate transformations. The convergent series solution of nonlinear system is accomplished by homotopic approach. The nondimensional velocity and temperature curve are examined under the impact of physical parameters like the nanoparticle volume fraction, permeability parameter, curvature parameter, the magnetic parameter and the mixed convection parameter. Numeric values of coefficient of skin friction and Nusselt number are analyzed.

Potential for improving fiber digestion in the rumen of cattle (Bos taurus) through microbial inoculation from bison (Bison bison): In situ fiber degradation.

PubMed

Griffith, C; Ribeiro, G O; Oba, M; McAllister, T A; Beauchemin, K A

2017-05-01

The objective of this experiment was to determine if partial replacement of cattle rumen contents with those from bison would increase in situ ruminal fiber degradation of various forages. The second objective was to examine individual variation among cattle in their ability to degrade forage and their responses to inoculation. In situ degradation of barley straw, canola straw, alfalfa hay, and timothy hay was measured in 16 ruminally cannulated heifers fed a barley straw-based diet before and after inoculation with combined rumen contents from 32 bison (performed twice, 14 d apart). Each feed was incubated in the rumen of each heifer for 0, 4, 8, 12, 24, 48, 96, and 120 h, and the degradation parameters were determined as washout fraction (), potentially degradable fraction (), rate of digestion of fraction (), and total potentially degradable fraction (). The of barley straw decreased ( = 0.04) after inoculation, whereas fraction of NDF increased ( = 0.03) and fraction of NDF and ADF decreased ( ≤ 0.02) by inoculation. In contrast, of alfalfa hay NDF and ADF decreased ( = 0.002) after inoculation, but fraction of NDF and ADF ( ≤ 0.02) increased. There were no major effects ( > 0.06) of inoculation on the fiber degradation of timothy hay or canola straw. The differential response between barley straw and alfalfa hay may have occurred because the cattle were previously adapted to a barley straw diet, whereas the bison were fed barley silage and oats. Some animals consistently ranked higher or lower for or across at least 3 of the 4 feeds incubated, but the rankings changed after inoculation. In conclusion, inoculation of cattle with bison rumen contents failed to improve degradation of fiber from barley straw, canola straw, or timothy hay in cattle well adapted to a barley straw diet, although there were small improvements in the extent of degradation of fiber from alfalfa hay. Cattle varied both in their ability to degrade various forages and in their responses to inoculation with bison rumen contents.

Developing Systems of Notation as a Trace of Reasoning

ERIC Educational Resources Information Center

Tillema, Erik; Hackenberg, Amy

2011-01-01

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in…

Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics

NASA Astrophysics Data System (ADS)

Baskin, E.; Iomin, A.

2011-12-01

We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation. The method is based on fractional calculus and permits to obtain analytical expressions for the electric-field enhancement.

Growth-suppressing and algicidal properties of an extract from Arundo donax, an invasive riparian plant, against Prymnesium parvum, an invasive harmful alga.

PubMed

Patiño, Reynaldo; Rashel, Rakib H; Rubio, Amede; Longing, Scott

2018-01-01

This study examined the ability of acidic and neutral/alkaline fractions of a methanolic extract from giant reed (Arundo donax) and of two of its constituents, gramine and skatole, to inhibit growth of the ichthyotoxic golden alga (Prymnesium parvum) in batch culture. For this study, growth suppression was defined as inhibition of maximum cell density, algicidal activity as early occurrence of negative growth, and algistatic activity as lack of net growth. The acidic fraction did not affect algal growth. The neutral/alkaline fraction showed growth-suppressing and algicidal activities but no signs of algistatic activity - namely, cells in cultures surviving a partial-algicidal exposure concentration (causing transient negative growth) were later able to initiate positive growth but at higher concentrations, algicidal activity was full and irreversible. Gramine suppressed growth more effectively than skatole and at the highest concentration tested, gramine also showed partial-algicidal and algistatic activity. While the partial-algicidal activities of the neutral/alkaline fraction and of gramine were short-lived (≤6days) and thus may share similar mechanisms, algistatic activity was unique to gramine and persisted for >3 weeks. Given gramine's reported concentration in the neutral/alkaline fraction, its corresponding level of algicidal activity is much lower than the fraction's suggesting the latter contains additional potent algicides. Inhibition of maximum cell density by all test compounds was associated with reductions in exponential growth rate, and in the case of the neutral/alkaline fraction and gramine also reductions in early (pre-exponential) growth. These results indicate that giant reed is a potential source of natural products to control golden alga blooms. Giant reed is an invasive species in North America, thus also providing incentive for research into strategies to couple management efforts for both species. Published by Elsevier B.V.

Summary Report: NMSBA CY 2016 - AEgis Technologies Group Inc. #12458.

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

Bellum, John Curtis; Field, Ella Suzanne

2016-12-01

AEgis requires large area partial mirror optics consisting of partially reflecting optical coatings on large dimension substrates for high energy laser (HEL) applications. The partial mirrors should transmit nearly the same small fraction of HEL radiation incident from a wide range of angles of incidence (AOIs), and the laser-induced damage threshold (LIDT) of the coatings should be high enough for them to be able to withstand direct exposure to near infrared CW HEL radiation at multi-kilowatt/cm2 power levels. The transmitted fraction of incident HEL radiation should reach an array of detectors at power levels high enough for reliable detection butmore » low enough to not damage the detectors. The reflected fraction of incident HEL radiation should scatter into a divergent pattern so as to be eye safe at a distance of ~ 200 m from the mirror in the case of 100 kilowatt incident laser power. The detector array together with the partial mirror optic and possible additional optics that provide divergent scattering of reflected HEL radiation constitute what AEgis refers to as a target board. The target board use environment may vary from benign, indoor laboratory conditions to harsh, outdoor conditions in tests on the ground as well as in air. Under this NMSBA project, Sandia agreed to apply its extensive expertise and capability in the design and production of high LIDT coatings on large dimension optics for high power pulsed laser radiation to advise and assist AEgis in the design and development of high LIDT coatings for the partial mirror optic. Sandia and AEgis met several times to discuss the partial mirror and target board requirements, and Sandia was guided in its work by these discussions as well as by the partial mirror and target board requirement summaries of Tables 1 and 2, respectively, that were provided by AEgis.« less

Induction and repair of radiation-induced DNA double-strand breaks in human fibroblasts are not affected by terminal differentiation.

PubMed

Brammer, Ingo; Herskind, Carsten; Haase, Oliver; Rodemann, H Peter; Dikomey, Ekkehard

2004-02-03

It was studied for human skin fibroblasts, whether the induction or repair of DNA double-strand breaks (dsb) depend on the differentiation status. These studies were performed (a) with a fibroblast strain (HSF1) kept in progenitor state (mitotic fibroblasts, MF) or triggered to premature terminal differentiation (postmitotic fibrocytes, PMF) by exposure to mitomycin C or (b) with 20 fibroblast strains differing intrinsically in their differentiation status. The differentiation status was quantified by determining the fraction of postmitotic fibrocytes by light microscopy. DNA dsb were measured by constant-field gel electrophoresis, and the fraction of apoptotic cells by comet assay. MF and PMF cultures of HSF1 cells were irradiated with X-ray doses up to 160 Gy, and dsb were measured either immediately after irradiation or after a repair incubation of 4 or 24 h. There were a difference neither in the number of initial nor residual dsb. PMF cultures, however, showed a slightly higher number of dsb already present in non-irradiated cells, which was measured to result from a small fraction of 5% apoptotic cells. The 20 analysed fibroblast strains showed a substantial variation in the fraction of postmitotic fibrocytes (9-51%) as well as in the number of dsb remaining at 24 h after irradiation (1.9-4.9%), but there was no correlation between these two parameters. These data demonstrate that for fibroblasts the terminal differentiation has an effect neither on the induction nor the repair of radiation-induced dsb. This result indicates that the variation in dsb-repair capacity previously observed for fibroblast strains and which was considered to be the main cause for the variation in the cellular radiosensitivity, cannot be ascribed to differences in the differentiation status.

Counter-current carbon dioxide purification of partially deacylated sunflower oil

USDA-ARS?s Scientific Manuscript database

High oleic sunflower oil was partially deacylated by propanolysis to produce a mixture of diglycerides and triglycerides. To remove by-product fatty acid propyl esters (FAPEs) from this reaction mixture, a liquid carbon dioxide (L-CO2) counter-current fractionation method was developed. The fracti...

Prevalence of pure versus mixed snow cover pixels across spatial resolutions in alpine environments: implications for binary and fractional remote sensing approaches

USGS Publications Warehouse

Selkowitz, David J.; Forster, Richard; Caldwell, Megan K.

2014-01-01

Remote sensing of snow-covered area (SCA) can be binary (indicating the presence/absence of snow cover at each pixel) or fractional (indicating the fraction of each pixel covered by snow). Fractional SCA mapping provides more information than binary SCA, but is more difficult to implement and may not be feasible with all types of remote sensing data. The utility of fractional SCA mapping relative to binary SCA mapping varies with the intended application as well as by spatial resolution, temporal resolution and period of interest, and climate. We quantified the frequency of occurrence of partially snow-covered (mixed) pixels at spatial resolutions between 1 m and 500 m over five dates at two study areas in the western U.S., using 0.5 m binary SCA maps derived from high spatial resolution imagery aggregated to fractional SCA at coarser spatial resolutions. In addition, we used in situ monitoring to estimate the frequency of partially snow-covered conditions for the period September 2013–August 2014 at 10 60-m grid cell footprints at two study areas with continental snow climates. Results from the image analysis indicate that at 40 m, slightly above the nominal spatial resolution of Landsat, mixed pixels accounted for 25%–93% of total pixels, while at 500 m, the nominal spatial resolution of MODIS bands used for snow cover mapping, mixed pixels accounted for 67%–100% of total pixels. Mixed pixels occurred more commonly at the continental snow climate site than at the maritime snow climate site. The in situ data indicate that some snow cover was present between 186 and 303 days, and partial snow cover conditions occurred on 10%–98% of days with snow cover. Four sites remained partially snow-free throughout most of the winter and spring, while six sites were entirely snow covered throughout most or all of the winter and spring. Within 60 m grid cells, the late spring/summer transition from snow-covered to snow-free conditions lasted 17–56 days and averaged 37 days. Our results suggest that mixed snow-covered snow-free pixels are common at the spatial resolutions imaged by both the Landsat and MODIS sensors. This highlights the additional information available from fractional SCA products and suggests fractional SCA can provide a major advantage for hydrological and climatological monitoring and modeling, particularly when accurate representation of the spatial distribution of snow cover is critical.

Experimental evidence for the absence of iron isotope fractionation between metal and silicate liquids at 1 GPa and 1250-1300 °C and its cosmochemical consequences

NASA Astrophysics Data System (ADS)

Hin, Remco C.; Schmidt, Max W.; Bourdon, Bernard

2012-09-01

Iron isotope fractionation during metal-silicate differentiation has been proposed as a cause for differences in iron isotope compositions of chondrites, iron meteorites and the bulk silicate Earth. Stable isotope fractionation, however, rapidly decreases with increasing temperature. We have thus performed liquid metal-liquid silicate equilibration experiments at 1250-1300 °C and 1 GPa to address whether Fe isotope fractionation is resolvable at the lowest possible temperatures for magmatic metal-silicate differentiation. A centrifuging piston cylinder apparatus enabled quantitative metal-silicate segregation. Elemental tin or sulphur was used in the synthetic metal-oxide mixtures to lower the melting temperature of the metal. The analyses demonstrate that eight of the 10 experimental systems equilibrated in a closed isotopic system, as was assessed by varying run durations and starting Fe isotope compositions. Statistically significant iron isotope fractionation between quenched metals and silicates was absent in nine of the 10 experiments and all 10 experiments yield an average metal-silicate fractionation factor of 0.01 ± 0.04‰, independent of whether graphite or silica glass capsules were used. This implies that Fe isotopes do not fractionate during low pressure metal-silicate segregation under magmatic conditions. In large bodies such as the Earth, fractionation between metal and high pressure (>20 GPa) silicate phases may still be a possible process for equilibrium fractionation during metal-silicate differentiation. However, the 0.07 ± 0.02‰ heavier composition of bulk magmatic iron meteorites relative to the average of bulk ordinary/carbonaceous chondrites cannot result from equilibrium Fe isotope fractionation during core segregation. The up to 0.5‰ lighter sulphide than metal fraction in iron meteorites and in one ordinary chondrite can only be explained by fractionation during subsolidus processes.

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.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

PubMed

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

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.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

Analysis of differential detergent fractions of an AtT-20 cellular homogenate using one- and two-dimensional capillary electrophoresis.

PubMed

Fazal, Md Abul; Palmer, Vanessa R; Dovichi, Norman J

2006-10-20

Differential detergent fractionation was used to sequentially extract cytosolic, membrane, nuclear, and cytoskeletal fractions from AtT-20 cells. Extracted components were denatured by sodium dodecyl sulfate (SDS) and then labeled with the fluorogenic reagent 3-(2-furoyl) quinoline-1-carboxaldehyde. Both capillary sieving electrophoresis (CSE) and micellar electrokinetic capillary chromatography (MECC) were used to separate labeled components by one-dimensional (1D) electrophoresis. Labeled components were also separated by two-dimensional (2D) capillary electrophoresis; CSE was employed in the first dimension and MECC in the second dimension. Roughly 150 fractions were transferred from the first to the second capillary for this comprehensive analysis in 2.5 h.

Absolute measurement of hadronic branching fractions of the Ds+ meson.

PubMed

Alexander, J P; Berkelman, K; Cassel, D G; Duboscq, J E; Ehrlich, R; Fields, L; Gibbons, L; Gray, R; Gray, S W; Hartill, D L; Heltsley, B K; Hertz, D; Jones, C D; Kandaswamy, J; Kreinick, D L; Kuznetsov, V E; Mahlke-Krüger, H; Mohapatra, D; Onyisi, P U E; Patterson, J R; Peterson, D; Riley, D; Ryd, A; Sadoff, A J; Shi, X; Stroiney, S; Sun, W M; Wilksen, T; Athar, S B; Patel, R; Yelton, J; Rubin, P; Eisenstein, B I; Karliner, I; Mehrabyan, S; Lowrey, N; Selen, M; White, E J; Wiss, J; Mitchell, R E; Shepherd, M R; Besson, D; Pedlar, T K; Cronin-Hennessy, D; Gao, K Y; Hietala, J; Kubota, Y; Klein, T; Lang, B W; Poling, R; Scott, A W; Zweber, P; Dobbs, S; Metreveli, Z; Seth, K K; Tomaradze, A; Libby, J; Powell, A; Wilkinson, G; Ecklund, K M; Love, W; Savinov, V; Lopez, A; Mendez, H; Ramirez, J; Ge, J Y; Miller, D H; Sanghi, B; Shipsey, I P J; Xin, B; Adams, G S; Anderson, M; Cummings, J P; Danko, I; Hu, D; Moziak, B; Napolitano, J; He, Q; Insler, J; Muramatsu, H; Park, C S; Thorndike, E H; Yang, F; Artuso, M; Blusk, S; Khalil, S; Li, J; Mountain, R; Nisar, S; Randrianarivony, K; Sultana, N; Skwarnicki, T; Stone, S; Wang, J C; Zhang, L M; Bonvicini, G; Cinabro, D; Dubrovin, M; Lincoln, A; Rademacker, J; Asner, D M; Edwards, K W; Naik, P; Briere, R A; Ferguson, T; Tatishvili, G; Vogel, H; Watkins, M E; Rosner, J L

2008-04-25

The branching fractions of D(s)(+/-) meson decays serve to normalize many measurements of processes involving charm quarks. Using 298 pb(-1) of e(+)e(-) collisions recorded at a center of mass energy of 4.17 GeV, we determine absolute branching fractions for eight D(s)(+/-) decays with a double tag technique. In particular we determine the branching fraction B(D(s)(+)-->K(-)K(+}pi(+))=(5.50+/-0.23+/-0.16)%, where the uncertainties are statistical and systematic, respectively. We also provide partial branching fractions for kinematic subsets of the K(-)K(+)pi(+) decay mode.

Absolute Measurement of Hadronic Branching Fractions of the Ds+ Meson

NASA Astrophysics Data System (ADS)

Alexander, J. P.; Berkelman, K.; Cassel, D. G.; Duboscq, J. E.; Ehrlich, R.; Fields, L.; Gibbons, L.; Gray, R.; Gray, S. W.; Hartill, D. L.; Heltsley, B. K.; Hertz, D.; Jones, C. D.; Kandaswamy, J.; Kreinick, D. L.; Kuznetsov, V. E.; Mahlke-Krüger, H.; Mohapatra, D.; Onyisi, P. U. E.; Patterson, J. R.; Peterson, D.; Riley, D.; Ryd, A.; Sadoff, A. J.; Shi, X.; Stroiney, S.; Sun, W. M.; Wilksen, T.; Athar, S. B.; Patel, R.; Yelton, J.; Rubin, P.; Eisenstein, B. I.; Karliner, I.; Mehrabyan, S.; Lowrey, N.; Selen, M.; White, E. J.; Wiss, J.; Mitchell, R. E.; Shepherd, M. R.; Besson, D.; Pedlar, T. K.; Cronin-Hennessy, D.; Gao, K. Y.; Hietala, J.; Kubota, Y.; Klein, T.; Lang, B. W.; Poling, R.; Scott, A. W.; Zweber, P.; Dobbs, S.; Metreveli, Z.; Seth, K. K.; Tomaradze, A.; Libby, J.; Powell, A.; Wilkinson, G.; Ecklund, K. M.; Love, W.; Savinov, V.; Lopez, A.; Mendez, H.; Ramirez, J.; Ge, J. Y.; Miller, D. H.; Sanghi, B.; Shipsey, I. P. J.; Xin, B.; Adams, G. S.; Anderson, M.; Cummings, J. P.; Danko, I.; Hu, D.; Moziak, B.; Napolitano, J.; He, Q.; Insler, J.; Muramatsu, H.; Park, C. S.; Thorndike, E. H.; Yang, F.; Artuso, M.; Blusk, S.; Khalil, S.; Li, J.; Mountain, R.; Nisar, S.; Randrianarivony, K.; Sultana, N.; Skwarnicki, T.; Stone, S.; Wang, J. C.; Zhang, L. M.; Bonvicini, G.; Cinabro, D.; Dubrovin, M.; Lincoln, A.; Rademacker, J.; Asner, D. M.; Edwards, K. W.; Naik, P.; Briere, R. A.; Ferguson, T.; Tatishvili, G.; Vogel, H.; Watkins, M. E.; Rosner, J. L.

2008-04-01

The branching fractions of Ds± meson decays serve to normalize many measurements of processes involving charm quarks. Using 298pb-1 of e+e- collisions recorded at a center of mass energy of 4.17 GeV, we determine absolute branching fractions for eight Ds± decays with a double tag technique. In particular we determine the branching fraction B(Ds+→K-K+π+)=(5.50±0.23±0.16)%, where the uncertainties are statistical and systematic, respectively. We also provide partial branching fractions for kinematic subsets of the K-K+π+ decay mode.

Predicting the Sources and Formation Mechanisms of Evolved Lunar Crust by Linking K/Ca Ratios of Lunar Granites to Analogous Terrestrial Igneous Rocks

NASA Technical Reports Server (NTRS)

Mills, R. D.; Simon, J. I.

2012-01-01

Although silicic rocks (i.e. granites and rhyolites) comprise a minor component of the sampled portion of the lunar crust, recent remote sensing studies [e.g., 1-4] indicate that several un-sampled regions of the Moon have significantly higher concentrations of silicic material (also high in [K], [U], and [Th]) than sampled regions. Within these areas are morphological features that are best explained by the existence of chemically evolved volcanic rocks. Observations of silicic domes [e.g., 1-5] suggest that sizable networks of silicic melt were present during crust formation. Isotopic data indicate that silicic melts were generated over a prolonged timespan from 4.3 to 3.9 Ga [e.g., 6-8]. The protracted age range and broad distribution of silicic rocks on the Moon indicate that their petrogenesis was an important mechanism for secondary crust formation. Understanding the origin and evolution of such silicic magmas is critical to determining the composition of the lunar crustal highlands and will help to distinguish between opposing ideas for the Moon's bulk composition and differentiation. The two main hypotheses for generating silicic melts on Earth are fractional crystallization or partial melting. On the Moon silicic melts are thought to have been generated during extreme fractional crystallization involving end-stage silicate liquid immiscibility (SLI) [e.g. 9, 10]. However, SLI cannot account for the production of significant volumes of silicic melt and its wide distribution, as reported by the remote global surveys [1, 2, 3]. In addition, experimental and natural products of SLI show that U and Th, which are abundant in the lunar granites and seen in the remote sensing data of the domes, are preferentially partitioned into the depolymerized ferrobasaltic magma and not the silicic portion [11, 12]. If SLI is not the mechanism that generated silicic magmas on the Moon then alternative processes such as fractional crystallization (only crystal-liquid separation) or partial melting should be considered as viable possibilities to be tested.

Characterization of the Tissue and Stromal Cell Components of Micro-Superficial Enhanced Fluid Fat Injection (Micro-SEFFI) for Facial Aging Treatment.

PubMed

Rossi, Martina; Roda, Barbara; Zia, Silvia; Vigliotta, Ilaria; Zannini, Chiara; Alviano, Francesco; Bonsi, Laura; Zattoni, Andrea; Reschiglian, Pierluigi; Gennai, Alessandro

2018-06-14

New microfat preparations provide material suitable for use as a regenerative filler for different facial areas. To support the development of new robust techniques for regenerative purposes, the cellular content of the sample should be considered. To evaluate the stromal vascular fraction (SVF) cell components of micro-superficial enhanced fluid fat injection (SEFFI) samples via a technique to harvest re-injectable tissue with minimum manipulation. The results were compared to those obtained from SEFFI samples. Microscopy analysis was performed to visualize the tissue structure. Micro-SEFFI samples were also fractionated using Celector ®, an innovative non-invasive separation technique, to provide an initial evaluation of sample fluidity and composition. SVFs obtained from SEFFI and micro-SEFFI were studied. Adipose stromal cells (ASCs) were isolated and characterized by proliferation and differentiation capacity assays. Microscopic and quality analyses of micro-SEFFI samples by Celector® confirmed the high fluidity and sample cellular composition in terms of red blood cell contamination, the presence of cell aggregates and extracellular matrix fragments. ASCs were isolated from adipose tissue harvested using SEFFI and micro-SEFFI systems. These cells were demonstrated to have a good proliferation rate and differentiation potential towards mesenchymal lineages. Despite the small sizes and low cellularity observed in micro-SEFFI-derived tissue, we were able to isolate stem cells. This result partially explains the regenerative potential of autologous micro-SEFFI tissue grafts. In addition, using this novel Celector® technology, tissues used for aging treatment were characterized analytically, and the adipose tissue composition was evaluated with no need for extra sample processing.

Modelling the balance between quiescence and cell death in normal and tumour cell populations.

PubMed

Spinelli, Lorenzo; Torricelli, Alessandro; Ubezio, Paolo; Basse, Britta

2006-08-01

When considering either human adult tissues (in vivo) or cell cultures (in vitro), cell number is regulated by the relationship between quiescent cells, proliferating cells, cell death and other controls of cell cycle duration. By formulating a mathematical description we see that even small alterations of this relationship may cause a non-growing population to start growing with doubling times characteristic of human tumours. Our model consists of two age structured partial differential equations for the proliferating and quiescent cell compartments. Model parameters are death rates from and transition rates between these compartments. The partial differential equations can be solved for the steady-age distributions, giving the distribution of the cells through the cell cycle, dependent on specific model parameter values. Appropriate formulas can then be derived for various population characteristic quantities such as labelling index, proliferation fraction, doubling time and potential doubling time of the cell population. Such characteristic quantities can be estimated experimentally, although with decreasing precision from in vitro, to in vivo experimental systems and to the clinic. The model can be used to investigate the effects of a single alteration of either quiescence or cell death control on the growth of the whole population and the non-trivial dependence of the doubling time and other observable quantities on particular underlying cell cycle scenarios of death and quiescence. The model indicates that tumour evolution in vivo is a sequence of steady-states, each characterised by particular death and quiescence rate functions. We suggest that a key passage of carcinogenesis is a loss of the communication between quiescence, death and cell cycle machineries, causing a defect in their precise, cell cycle dependent relationship.

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...

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.

Hydrous partial melting in the sheeted dike complex at fast spreading ridges: experimental and natural observations

NASA Astrophysics Data System (ADS)

France, Lydéric; Koepke, Juergen; Ildefonse, Benoit; Cichy, Sarah B.; Deschamps, Fabien

2010-11-01

In ophiolites and in present-day oceanic crust formed at fast spreading ridges, oceanic plagiogranites are commonly observed at, or close to the base of the sheeted dike complex. They can be produced either by differentiation of mafic melts, or by hydrous partial melting of the hydrothermally altered sheeted dikes. In addition, the hydrothermally altered base of the sheeted dike complex, which is often infiltrated by plagiogranitic veins, is usually recrystallized into granoblastic dikes that are commonly interpreted as a result of prograde granulitic metamorphism. To test the anatectic origin of oceanic plagiogranites, we performed melting experiments on a natural hydrothermally altered dike, under conditions that match those prevailing at the base of the sheeted dike complex. All generated melts are water saturated, transitional between tholeiitic and calc-alkaline, and match the compositions of oceanic plagiogranites observed close to the base of the sheeted dike complex. Newly crystallized clinopyroxene and plagioclase have compositions that are characteristic of the same minerals in granoblastic dikes. Published silicic melt compositions obtained in classical MORB fractionation experiments also broadly match the compositions of oceanic plagiogranites; however, the compositions of the coexisting experimental minerals significantly deviate from those of the granoblastic dikes. Our results demonstrate that hydrous partial melting is a likely common process in the root zone of the sheeted dike complex, starting at temperatures exceeding 850°C. The newly formed melt can either crystallize to form oceanic plagiogranites or may be recycled within the melt lens resulting in hybridized and contaminated MORB melts. It represents the main MORB crustal contamination process. The residue after the partial melting event is represented by the granoblastic dikes. Our results support a model with a dynamic melt lens that has the potential to trigger hydrous partial melting reactions in the previously hydrothermally altered sheeted dikes. A new thermometer using the Al content of clinopyroxene is also elaborated.

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.

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.

Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Baleanu, Dumitru

2018-03-01

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Extremely low order time-fractional differential equation and application in combustion process

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Xu, Yufeng

2018-11-01

Fractional blow-up model, especially which is of very low order of fractional derivative, plays a significant role in combustion process. The order of time-fractional derivative in diffusion model essentially distinguishes the super-diffusion and sub-diffusion processes when it is relatively high or low accordingly. In this paper, the blow-up phenomenon and condition of its appearance are theoretically proved. The blow-up moment is estimated by using differential inequalities. To numerically study the behavior around blow-up point, a mixed numerical method based on adaptive finite difference on temporal direction and highly effective discontinuous Galerkin method on spatial direction is proposed. The time of blow-up is calculated accurately. In simulation, we analyze the dynamics of fractional blow-up model under different orders of fractional derivative. It is found that the lower the order, the earlier the blow-up comes, by fixing the other parameters in the model. Our results confirm the physical truth that a combustor for explosion cannot be too small.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Investigation of solubility of carbon dioxide in anhydrous milk fat by lab-scale manometric method.

PubMed

Truong, Tuyen; Palmer, Martin; Bansal, Nidhi; Bhandari, Bhesh

2017-12-15

This study aims to examine the solubility of CO 2 in anhydrous milk fat (AMF) as functions of partial pressure, temperature, chemical composition and physical state of AMF. AMF was fractionated at 21°C to obtain stearin and olein fractions. The CO 2 solubility was measured using a home-made experimental apparatus based on changes of CO 2 partial pressures. The apparatus was found to be reliable as the measured and theoretical values based on the ideal gas law were comparable. The dissolved CO 2 concentration in AMF increased with an increase in CO 2 partial pressure (0-101kPa). The apparent CO 2 solubility coefficients (molkg -1 Pa -1 ) in the AMF were 5.75±0.16×10 -7 , 3.9±0.19×10 -7 and 1.19±0.14×10 -7 at 35, 24 and 4°C, respectively. Higher liquid oil proportions resulted in higher CO 2 solubility in the AMF. There was insignificant difference in the dissolved CO 2 concentration among the AMF, stearin and olein fractions in their liquid state at 40°C. Copyright © 2017 Elsevier Ltd. All rights reserved.

Method for hydrocracking a heavy polynuclear hydrocarbonaceous feedstock in the presence of a molten metal halide catalyst

DOEpatents

Gorin, Everett

1981-01-01

A method for hydrocracking a heavy polynuclear hydrocarbonaceous feedstock to produce lighter hydrocarbon fuels by contacting the feedstock with hydrogen in the presence of a molten metal halide catalyst, the method comprising: mixing the feedstock with a heavy naphtha fraction which has an initial boiling point from about 100.degree. to about 160.degree. C. with a boiling point difference between the initial boiling point and the final boiling point of no more than about 50.degree. C. to produce a mixture; thereafter contacting the mixture with partially spent molten metal halide and hydrogen under temperature and pressure conditions so that the temperature is near the critical temperature of the heavy naphtha fraction; separating at least a portion of the heavy naphtha fraction and lighter hydrocarbon fuels from the partially spent molten metal halide, unreacted feedstock and reaction products; thereafter contacting the partially spent molten metal halide, unreacted feedstock and reaction products with hydrogen and fresh molten metal halide in a hydrocracking zone to produce additional lighter hydrocarbon fuels and separating at least a major portion of the lighter hydrocarbon fuels from the spent molten metal halide.

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

Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle

USGS Publications Warehouse

Teng, F.-Z.; Wadhwa, M.; Helz, R.T.

2007-01-01

To investigate whether magnesium isotopes are fractionated during basalt differentiation, we have performed high-precision Mg isotopic analyses by multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) on a set of well-characterized samples from Kilauea Iki lava lake, Hawaii, USA. Samples from the Kilauea Iki lava lake, produced by closed-system crystal-melt fractionation, range from olivine-rich cumulates to highly differentiated basalts with MgO content ranging from 2.37 to 26.87??wt.%. Our results demonstrate that although these basalts have diverse chemical compositions, mineralogies, crystallization temperatures and degrees of differentiation, their Mg isotopic compositions display no measurable variation within the limits of our external precision (average ??26Mg = - 0.36 ?? 0.10 and ??25Mg = - 0.20 ?? 0.07; uncertainties are 2SD). This indicates that Mg isotopic fractionation during crystal-melt fractionation at temperatures of ??? 1055????C is undetectable at the level of precision of the current investigation. Calculations based on our data suggest that at near-magmatic temperatures the maximum fractionation in the 26Mg/24Mg ratio between olivine and melt is 0.07???. Two additional oceanic basalts, two continental basalts (BCR-1 and BCR-2), and two primitive carbonaceous chondrites (Allende and Murchison) analyzed in this study have Mg isotopic compositions similar to the Kilauea Iki lava lake samples. In contrast to a recent report [U. Wiechert, A.N. Halliday, Non-chondritic magnesium and the origins of the inner terrestrial planets, Earth and Planetary Science Letters 256 (2007) 360-371], the results presented here suggest that the Bulk Silicate Earth has a chondritic Mg isotopic composition. ?? 2007.

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.

Anatomical gradients in proliferation and differentiation of embryonic rat CNS accessed by buoyant density fractionation: alpha 3, beta 3 and gamma 2 GABAA receptor subunit co-expression by post-mitotic neocortical neurons correlates directly with cell buoyancy.

PubMed

Maric, D; Maric, I; Ma, W; Lahojuji, F; Somogyi, R; Wen, X; Sieghart, W; Fritschy, J M; Barker, J L

1997-03-01

Development of the CNS occurs as a complex cascade of pre-programmed events involving distinct phases of cell proliferation and differentiation. Here we show these phases correlate with cells of specific buoyant densities which can be readily accessed by density gradient fractionation. Sprague-Dawley dams were pulse-labelled with bromodeoxyuridine (BrdU) and selected regions of embryonic (E) CNS tissues at E11-22 dissociated with papain into single-cell suspensions. Proliferative cell populations were assessed by anti-BrdU and propidium iodide staining using flow cytometry. Cell differentiation was evaluated using molecular and immunocytochemical probes against mRNAs and antigens differentiating the neuroepithelial, neuronal and glial cell lineages. The results show the emergence of distinctive spatiotemporal changes in BrdU+ populations throughout the CNS during embryonic development, which were followed by corresponding changes in the cellular distributions of antigens distinguishing specific cell types. Fractionation of neocortical cells using discontinuous Percoll gradients revealed that an increasing number of cells increase their buoyancy during corticogenesis. Immunocytochemical and molecular characterization showed that the proliferative and progenitor cell populations are for the most part associated with lower buoyancy or higher specific buoyant densities (> 1.056 g/ml) whereas the post-mitotic, differentiated neurons generally separated into fractions of higher buoyancy or lower specific buoyant densities (< 1.043 g/ml). Immunostaining with antibodies against several GABAA receptor subunits (alpha 3, beta 3, gamma 2) revealed that the highest percent (70-90%) of immunopositive cells could be identified in the most buoyant, differentiating neurons found in the cortical plate/subplate regions, with the lowest percent of the immunopositive cells found in the least buoyant, proliferative and progenitor cell populations originating from the ventricular/subventricular zones. Taken together, these results indicate that buoyant density is a distinguishing characteristic of embryonic CNS cells transforming from primarily proliferative to mainly differentiating, and that fractionation of these cells according to their buoyant densities provides rapid access to the properties of specific cell lineages during the prenatal period of CNS development.

Enzymatic activity and partial purification of solanapyrone synthase: first enzyme catalyzing Diels-Alder reaction.

PubMed

Katayama, K; Kobayashi, T; Oikawa, H; Honma, M; Ichihara, A

1998-05-19

In cell-free extracts of Alternaria solani, an enzymatic activity converting prosolanapyrone II to solanapyrones A and D via oxidation and subsequent Diels-Alder reaction has been found. Chromatography with DEAE-Sepharose provided two active fractions, pools 1 and 2. The former fraction converted prosolanapyrone II to solanapyrones A and D in a ratio of 2.2:1 with optical purities of 99% and 45% ee, respectively. The latter fraction did so in a ratio of 7.6:1 with 99% and nearly 0% ee, respectively. The enzyme partially purified from pool 2 native molecular weight of 40-62 kD and a pl of 4.25. The high reactivity of prosolanapyrone III in aqueous solution and the chromatographic behavior of the enzyme in pool 2 suggest that a single enzyme catalyzes both the oxidation and Diels-Alder reaction.

Experimental determination of U and Th partitioning between clinopyroxene and natural and synthetic basaltic liquid

NASA Technical Reports Server (NTRS)

Latourrette, T. Z.; Burnett, D. S.

1992-01-01

Experimental measurements of U and the partition coefficients between clinopyroxene and synthetic and natural basaltic liquid are presented. The results demonstrate that crystal-liquid U-Th fractionation is fO2-dependent and that U in terrestrial magmas is not entirely tetravalent. During partial melting, the liquid will have a Th/U ratio less than the clinopyroxene in the source. The observed U-238 - Th-230 disequilibrium in MORB requires that the partial melt should have a U/Th ratio greater than the bulk source and therefore cannot result from clinopyroxene-liquid partitioning. Further, the magnitudes of the measured partition coefficients are too small to generate significant U-Th fractionation in either direction. Assuming that clinopyroxene contains the bulk of the U and Th in the MORB source, the results indicate that U-238 - Th-230 disequilibrium in MORB may not be caused by partial melting at all.

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...

Limited Knowledge of Fraction Representations Differentiates Middle School Students with Mathematics Learning Disability (Dyscalculia) versus Low Mathematics Achievement

ERIC Educational Resources Information Center

Mazzocco, Michele M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

2013-01-01

Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions…

Mass dependent fractionation of stable chromium isotopes in mare basalts: Implications for the formation and the differentiation of the Moon

NASA Astrophysics Data System (ADS)

Bonnand, Pierre; Parkinson, Ian J.; Anand, Mahesh

2016-02-01

We present the first stable chromium isotopic data from mare basalts in order to investigate the similarity between the Moon and the Earth's mantle. A double spike technique coupled with MC-ICP-MS measurements was used to analyse 19 mare basalts, comprising high-Ti, low-Ti and KREEP-rich varieties. Chromium isotope ratios (δ53Cr) for mare basalts are positively correlated with indices of magmatic differentiation such as Mg# and Cr concentration which suggests that Cr isotopes were fractionated during magmatic differentiation. Modelling of the results provides evidence that spinel and pyroxene are the main phases controlling the Cr isotopic composition during fractional crystallisation. The most evolved samples have the lightest isotopic compositions, complemented by cumulates that are isotopically heavy. Two hypotheses are proposed to explain this fractionation: (i) equilibrium fractionation where heavy isotopes are preferentially incorporated into the spinel lattice and (ii) a difference in isotopic composition between Cr2+ and Cr3+ in the melt. However, both processes require magmatic temperatures below 1200 °C for appreciable Cr3+ to be present at the low oxygen fugacities found in the Moon (IW -1 to -2 log units). There is no isotopic difference between the most primitive high-Ti, low-Ti and KREEP basalts, which suggest that the sources of these basalts were homogeneous in terms of stable Cr isotopes. The least differentiated sample in our sample set is the low-Ti basalt 12016, characterised by a Cr isotopic composition of -0.222 ± 0.025‰, which is within error of the current BSE value (-0.124 ± 0.101‰). The similarity between the mantles of the Moon and Earth is consistent with a terrestrial origin for a major fraction of the lunar Cr. This similarity also suggests that Cr isotopes were not fractionated by core formation on the Moon.

Fractional power-law spatial dispersion in electrodynamics

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru; Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife; Trujillo, Juan J., E-mail: jtrujill@ullmat.es

2013-07-15

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s lawmore » and Debye’s screening for the media.« less

New insights into the origin of the bimodal volcanism in the middle Okinawa Trough: not a basalt-rhyolite differentiation process

NASA Astrophysics Data System (ADS)

Zhang, Yuxiang; Zeng, Zhigang; Chen, Shuai; Wang, Xiaoyuan; Yin, Xuebo

2018-06-01

In the middle Okinawa Trough (MOT), rhyolites have been typically considered as products of crystallization differentiation of basaltic magma as a feature of bimodal volcanism. However, the evidence is insufficient. This paper compared chemical trends of volcanic rocks from the MOT with fractional crystallization simulation models and experimental results and utilized trace element modeling combined with Rayleigh fractionation calculations to re-examine fractional crystallization processes in generating rhyolites. Both qualitative and quantitative studies indicate that andesites, rather than rhyolites, originate by fractional crystallization from basalts in the MOT. Furthermore, we established two batch-melting models for the MOT rhyolites and proposed that type 1 rhyolites are produced by remelting of andesites with amphiboles in the residue, while type 2 rhyolites are derived from remelting of andesites without residual amphiboles. It is difficult to produce melts with a SiO2 content ranging from 62% to 68% either by magmatic differentiation from basalts or by remelting of andesites, and this difficulty might help account for the compositional gap (Daly gap) for bimodal volcanism in the Okinawa Trough.

Modes of planetary-scale Fe isotope fractionation

NASA Astrophysics Data System (ADS)

Schoenberg, Ronny; von Blanckenburg, Friedhelm

2006-12-01

A comprehensive set of high-precision Fe isotope data for the principle meteorite types and silicate reservoirs of the Earth is used to investigate iron isotope fractionation at inter- and intra-planetary scales. 14 chondrite analyses yield a homogeneous Fe isotope composition with an average δ56Fe/ 54Fe value of - 0.015 ± 0.020‰ (2 SE) relative to the international iron standard IRMM-014. Eight non-cumulate and polymict eucrite meteorites that sample the silicate portion of the HED (howardite-eucrite-diogenite) parent body yield an average δ56Fe/ 54Fe value of - 0.001 ± 0.017‰, indistinguishable to the chondritic Fe isotope composition. Fe isotope ratios that are indistinguishable to the chondritic value have also been published for SNC meteorites. This inner-solar system homogeneity in Fe isotopes suggests that planetary accretion itself did not significantly fractionate iron. Nine mantle xenoliths yield a 2 σ envelope of - 0.13‰ to + 0.09‰ in δ56Fe/ 54Fe. Using this range as proxy for the bulk silicate Earth in a mass balance model places the Fe isotope composition of the outer liquid core that contains ca. 83% of Earth's total iron to within ± 0.020‰ of the chondritic δ56Fe/ 54Fe value. These calculations allow to interprete magmatic iron meteorites ( δ56Fe/ 54Fe = + 0.047 ± 0.016‰; N = 8) to be representative for the Earth's inner metallic core. Eight terrestrial basalt samples yield a homogeneous Fe isotope composition with an average δ56Fe/ 54Fe value of + 0.072 ± 0.016‰. The observation that terrestrial basalts appear to be slightly heavier than mantle xenoliths and that thus partial mantle melting preferentially transfers heavy iron into the melt [S. Weyer, A.D. Anbar, G.P. Brey, C. Munker, K. Mezger and A.B. Woodland, Iron isotope fractionation during planetary differentiation, Earth and Planetary Science Letters 240(2), 251-264, 2005.] is intriguing, but also raises some important questions: first it is questionable whether the Fe isotope composition of lithospheric mantle xenoliths are representative for an undisturbed melt source, and second, HED and SNC meteorites, representing melting products of 4Vesta and Mars silicate mantles would be expected to show a similar fractionation towards heavy isotope compositions. This is not observed. Four international granitoid standards with SiO 2 contents between 60 and 70 wt.% yield δ56Fe/ 54Fe values between 0.118‰ and 0.132‰. An investigation of the alpine Bergell igneous rock suite revealed a positive correlation between Fe isotope compositions and SiO 2 contents — from gabbros and tonalites ( δ56Fe/ 54Fe ≈ 0.03 to 0.09‰) to granodiorites and silicic dykes ( δ56Fe/ 54Fe ≈ 0.14 to 0.23‰). Although in this suite δ56Fe/ 54Fe correlates with δ18O values and radiogenic isotopes, open-system behavior to explain the heavy iron is not undisputed. This is because an obvious assimilant with the required heavy Fe isotope composition has so far not been identified. Alternatively, the relatively heavy granite compositions might be obtained by fractional crystallisation of the melt. Ultimately, further detailed studies on natural rocks and the experimental determination of mineral/melt fractionation factors at magmatic conditions are required to unravel whether or not iron isotope fractionation takes place during partial mantle melting and crystal fractionation.

Fractional Order Spatiotemporal Chaos with Delay in Spatial Nonlinear Coupling

NASA Astrophysics Data System (ADS)

Zhang, Yingqian; Wang, Xingyuan; Liu, Liyan; Liu, Jia

We investigate the spatiotemporal dynamics with fractional order differential logistic map with delay under nonlinear chaotic maps for spatial coupling connections. Here, the coupling methods between lattices are the nonlinear chaotic map coupling of lattices. The fractional order differential logistic map with delay breaks the limits of the range of parameter μ ∈ [3.75, 4] in the classical logistic map for chaotic states. The Kolmogorov-Sinai entropy density and universality, and bifurcation diagrams are employed to investigate the chaotic behaviors of the proposed model in this paper. The proposed model can also be applied for cryptography, which is verified in a color image encryption scheme in this paper.

A class of fractional differential hemivariational inequalities with application to contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Liu, Zhenhai; Migorski, Stanislaw

2018-04-01

In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.

Hydration of alcohol clusters in 1-propanol-water mixture studied by quasielastic neutron scattering and an interpretation of anomalous excess partial molar volume.

PubMed

Misawa, M; Inamura, Y; Hosaka, D; Yamamuro, O

2006-08-21

Quasielastic neutron scattering measurements have been made for 1-propanol-water mixtures in a range of alcohol concentration from 0.0 to 0.167 in mole fraction at 25 degrees C. Fraction alpha of water molecules hydrated to fractal surface of alcohol clusters in 1-propanol-water mixture was obtained as a function of alcohol concentration. Average hydration number N(ws) of 1-propanol molecule is derived from the value of alpha as a function of alcohol concentration. By extrapolating N(ws) to infinite dilution, we obtain values of 12-13 as hydration number of isolated 1-propanol molecule. A simple interpretation of structural origin of anomalous excess partial molar volume of water is proposed and as a result a simple equation for the excess partial molar volume is deduced in terms of alpha. Calculated values of the excess partial molar volumes of water and 1-propanol and the excess molar volume of the mixture are in good agreement with experimental values.

Xanthophyll esterification accompanying carotenoid overaccumulation in chromoplast of Capsicum annuum ripening fruits is a constitutive process and useful for ripeness index.

PubMed

Hornero-Méndez, D; Mínguez-Mosquera, M I

2000-05-01

Changes in xanthophyll esterification degree during pepper fruit ripening have been studied in five cultivars (Numex, Mana, Belrubi, Delfin, and Negral). Esterification of xanthophylls with fatty acids is seen to be a process that is contemporary with and directly linked to the transformation of chloroplast (present in the green fruit) into chromoplast (present in the red fruit). Changes in the fractions of free and partially and totally esterified carotenoids are similar between varieties, reflecting the constitutive nature of esterification as part of the ripening process and being controlled by it. From the first stages of ripening, the fraction of totally esterified pigments (zeaxanthin diester, beta-cryptoxanthin diester, capsanthin diester, and capsorubin diester) makes up almost 50% of the total carotenoid content. The proportion of the partially esterified pigment fraction (zeaxanthin monoester, capsanthin monoester, and capsorubin monoester) in the total carotenoid content increases, with a gradual decrease in the fraction of free pigments (beta-cryptoxanthin, beta-carotene, zeaxanthin, capsanthin, and capsorubin). In the fully ripe stage, a balance is reached between the three esterification fractions (free, partially esterified, and totally esterified), with mean values of 24.17 +/- 4.06, 31.48 +/- 4. 61, and 44.36 +/- 5.05, respectively, which seems to be largely independent of variety. This suggests a marked control of the carotenoid composition of the totally developed chromoplast, indicating its use as an index of ripeness. The inclusion in the present study of a variety (Negral) that retains chlorophylls when ripening, and which shows the same esterification behavior, supports the idea that carotenogenesis is normal and independent of chlorophyll catabolism.

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.

Existence and uniqueness theorems for impulsive fractional differential equations with the two-point and integral boundary conditions.

PubMed

Mardanov, M J; Mahmudov, N I; Sharifov, Y A

2014-01-01

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

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.

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

Permeability and 3-Dimensional Melt Distribution in Partially Molten Rocks

NASA Astrophysics Data System (ADS)

Zhu, Wen-Lu; Gaetani, Glenn; Fusseis, Florian

2010-05-01

Quantitative knowledge of the distribution of small amounts of silicate melt in peridotite and of its influence on permeability are critical to our understanding of melt migration and segregation processes in the upper mantle, as well as interpretations of the geochemical and geophysical observations at ocean ridges. For a system containing a single solid phase of isotropic interfacial energy, chemical and mechanical equilibrium requires a constant mean curvature of solid-melt interfaces and a single dihedral angle. Under these conditions, a simple power-law relationship between permeability, grain size and melt fraction, has been derived [e.g., von Bargen and Waff, 1986]. However, microstructural observations on texturally equilibrated, partially molten rocks reveal that the melt distribution is more complex than predicted by the isotropic model. Several factors, such as non-hydrostatic stress, anisotropic interfacial energy, or the presence of a second solid phase, will alter the power-law relationship. Better estimates for the permeability of partially molten rock require an accurate assessment of 3-dimensional melt distribution at the grain-scale. Existing studies of melt distribution, carried out on 2-D slices through experimental charges, have produced divergent models for melt distribution at small melt fractions. While some studies conclude that small amounts of melt are distributed primarily along 3-grain junctions [e.g., Wark et al., 2003], others predict an important role for melt distribution along grain boundaries at low melt fractions [e.g., Faul 1997]. Using X-ray synchrotron microtomography, we have carried out the first high quality non-destructive imaging of 3-dimensional melt distribution in experimentally equilibrated olivine-basalt aggregates [Zhu et al., 2009]. Microtomographic images of melt distribution were obtained on 1 mm cylindrical cores with melt fractions of 0.2, 0.1, and 0.02, at a spatial resolution of 0.7 microns. Textual information such as melt channel size and channel connectivity was determined using AVIZO and MATLAB. Our data indicate that as melt fraction decreases from 0.2 to 0.02, grain size increases slightly whereas melt interconnectivity decreases. Network modeling and the Lattice Boltzmann method provide a quantitative link between the macroscale transport properties and microscale melt distribtution. Incorporating our quantitative 3-D melt distribution data into these models allow us to simulate melt transport and, thereby, calculate the permeability and electrical conductivity of partially molten peridotite, especially at low melt fractions.

Iron Isotopic Fractionation in Igneous Systems: Looking for Anharmonicity

NASA Astrophysics Data System (ADS)

Dauphas, N.; Roskosz, M.; Hu, M. Y.; Neuville, D. R.; Alp, E. E.; Hu, J.; Heard, A.; Zhao, J.

2017-12-01

Igneous rocks display variations in their Fe isotopic compositions that can be used to trace partial melting, magma differentiation, the origin of mineral zoning, and metasomatic processes. While tremendous progress has been made in our understanding of how iron isotopes can be fractionated at equilibrium or during diffusion, significant work remains to be done to establish equilibrium fractionation factors between phases relevant to igneous petrology. A virtue of iron isotope systematics is that iron possesses a Mössbauer isotope, 57Fe, and one can use the method of NRIXS to measure the force constant of iron bonds, from which beta-factors can be calculated. These measurements are done at a few synchrotron beamlines around the world, such as sector 3ID of the APS (Argonne). Tremendous insights have already been gained by applying this technique to Earth science materials. It was shown for instance that significant equilibrium fractionation exists between Fe2+ and Fe3+ at magmatic temperature, that the iron isotopic fractionation resulting from core formation must be small, and that iron isotopic fractionation is influenced by the polymerization of the melt. Combining NRIXS and ab initio studies, there are approximately 130 geologically-relevant solids and aqueous species for which beta-factors have been reported. A potential limitation of applying published NRIXS data to igneous petrology is that all the force constants have been measured at room temperature and the beta-factors are extrapolated to magmatic temperatures assuming that the systems are harmonic, which has never been demonstrated. One way to test this critical assumption is to measure the apparent force constant of iron bonds at various temperatures, so that the interatomic potential of iron bonds can be probed. A further virtue of NRIXS is that the data also allows us to derive the mean square displacement. If significant anharmonicity is present, it should be manifested as a decrease in the apparent force constant with increasing temperature and increasing mean square displacement. We have measured the Fe force constant of basalt glass and olivine using a wire furnace. At the conference, we will report on these experiments and will discuss some implications for igneous petrology.

Electrical conductivity of partially-molten olivine aggregate and melt interconnectivity in the oceanic upper mantle

NASA Astrophysics Data System (ADS)

Laumonier, Mickael; Frost, Dan; Farla, Robert; Katsura, Tomoo; Marquardt, Katharina

2016-04-01

A consistent explanation for mantle geophysical anomalies such as the Lithosphere-Astenosphere Boundary (LAB) relies on the existence of little amount of melt trapped in the solid peridotite. Mathematical models have been used to assess the melt fraction possibly lying at mantle depths, but they have not been experimentally checked at low melt fraction (< 2 vol. %). To fill this gap, we performed in situ electrical conductivity (EC) measurement on a partially-molten olivine aggregate (Fo92-olivine from a natural peridotite of Lanzarote, Canary Islands, Spain) containing various amount of basaltic (MORB-like composition) melt (0 to 100%) at upper mantle conditions. We used the MAVO 6-ram press (BGI) combined with a Solartron gain phase analyser to acquire the electrical resistance of the sample at pressure of 1.5 GPa and temperature up to 1400°C. The results show the increase of the electrical conductivity with the temperature following an Arrhenius law, and with the melt fraction, but the effect of pressure between 1.5 and 3.0 GPa was found negligible at a melt fraction of 0.5 vol.%. The conductivity of a partially molten aggregate fits the modified Archie's law from 0.5 to 100 vol.%. At melt fractions of 0.25, 0.15 and 0.0 vol.%, the EC value deviates from the trend previously defined, suggesting that the melt is no longer fully interconnected through the sample, also supported by chemical mapping. Our results extend the previous results obtained on mixed system between 1 and 10% of melt. Since the melt appears fully interconnected down to very low melt fraction (0.5 vol.%), we conclude that (i) only 0.5 to 1 vol.% of melt is enough to explain the LAB EC anomaly, lower than previously determined; and (ii) deformation is not mandatory to enhance electrical conductivity of melt-bearing mantle rocks.

Growth-suppressing and algicidal properties of an extract from Arundo donax, an invasive riparian plant, against Prymnesium parvum, an invasive harmful alga

USGS Publications Warehouse

Patino, Reynaldo; Rashel, Rakib H.; Rubio, Amede; Longing, Scott

2018-01-01

This study examined the ability of acidic and neutral/alkaline fractions of a methanolic extract from giant reed (Arundo donax) and of two of its constituents, gramine and skatole, to inhibit growth of the ichthyotoxic golden alga (Prymnesium parvum) in batch culture. For this study, growth suppression was defined as inhibition of maximum cell density, algicidal activity as early occurrence of negative growth, and algistatic activity as lack of net growth. The acidic fraction did not affect algal growth. The neutral/alkaline fraction showed growth-suppressing and algicidal activities but no signs of algistatic activity – namely, cells in cultures surviving a partial-algicidal exposure concentration (causing transient negative growth) were later able to initiate positive growth but at higher concentrations, algicidal activity was full and irreversible. Gramine suppressed growth more effectively than skatole and at the highest concentration tested, gramine also showed partial-algicidal and algistatic activity. While the partial-algicidal activities of the neutral/alkaline fraction and of gramine were short-lived (≤6 days) and thus may share similar mechanisms, algistatic activity was unique to gramine and persisted for >3 weeks. Given gramine’s reported concentration in the neutral/alkaline fraction, its corresponding level of algicidal activity is much lower than the fraction’s suggesting the latter contains additional potent algicides. Inhibition of maximum cell density by all test compounds was associated with reductions in exponential growth rate, and in the case of the neutral/alkaline fraction and gramine also reductions in early (pre-exponential) growth. These results indicate that giant reed is a potential source of natural products to control golden alga blooms. Giant reed is an invasive species in North America, thus also providing incentive for research into strategies to couple management efforts for both species.

Gamma-H2AX-based dose estimation for whole and partial body radiation exposure.

PubMed

Horn, Simon; Barnard, Stephen; Rothkamm, Kai

2011-01-01

Most human exposures to ionising radiation are partial body exposures. However, to date only limited tools are available for rapid and accurate estimation of the dose distribution and the extent of the body spared from the exposure. These parameters are of great importance for emergency triage and clinical management of exposed individuals. Here, measurements of γ-H2AX immunofluorescence by microscopy and flow cytometry were compared as rapid biodosimetric tools for whole and partial body exposures. Ex vivo uniformly X-irradiated blood lymphocytes from one donor were used to generate a universal biexponential calibration function for γ-H2AX foci/intensity yields per unit dose for time points up to 96 hours post exposure. Foci--but not intensity--levels remained significantly above background for 96 hours for doses of 0.5 Gy or more. Foci-based dose estimates for ex vivo X-irradiated blood samples from 13 volunteers were in excellent agreement with the actual dose delivered to the targeted samples. Flow cytometric dose estimates for X-irradiated blood samples from 8 volunteers were in excellent agreement with the actual dose delivered at 1 hour post exposure but less so at 24 hours post exposure. In partial body exposures, simulated by mixing ex vivo irradiated and unirradiated lymphocytes, foci/intensity distributions were significantly over-dispersed compared to uniformly irradiated lymphocytes. For both methods and in all cases the estimated fraction of irradiated lymphocytes and dose to that fraction, calculated using the zero contaminated Poisson test and γ-H2AX calibration function, were in good agreement with the actual mixing ratios and doses delivered to the samples. In conclusion, γ-H2AX analysis of irradiated lymphocytes enables rapid and accurate assessment of whole body doses while dispersion analysis of foci or intensity distributions helps determine partial body doses and the irradiated fraction size in cases of partial body exposures.

Experimentally determined sulfur isotope fractionation between metal and silicate and implications for planetary differentiation

NASA Astrophysics Data System (ADS)

Labidi, J.; Shahar, A.; Le Losq, C.; Hillgren, V. J.; Mysen, B. O.; Farquhar, J.

2016-02-01

The Earth's mantle displays a subchondritic 34S/32S ratio. Sulfur is a moderately siderophile element (i.e. iron-loving), and its partitioning into the Earth's core may have left such a distinctive isotope composition on the terrestrial mantle. In order to constrain the sulfur isotope fractionation occurring during core-mantle differentiation, high-pressure and temperature experiments were conducted with synthetic mixtures of metal and silicate melts. With the purpose to identify the mechanism(s) responsible for the S isotope fractionations, we performed our experiments in different capsules - namely, graphite and boron nitride capsules - and thus at different fO2, with varying major element chemistry of the silicate and metal fractions. The S isotope fractionations Δ34Smetal-silicate of equilibrated metal alloys versus silicate melts is +0.2 ± 0.1‰ in a boron-free and aluminum-poor system quenched at 1-1.5 GPa and 1650 °C. The isotope fractionation increases linearly with increasing boron and aluminum content, up to +1.4 ± 0.2‰, and is observed to be independent of the silicon abundance as well as of the fO2 over ∼3.5 log units of variations explored here. The isotope fractionations are also independent of the graphite or nitride saturation of the metal. Only the melt structural changes associated with aluminum and boron concentration in silicate melts have been observed to affect the strength of sulfur bonding. These results establish that the structure of silicate melts has a direct influence on the S2- average bonding strengths. These results can be interpreted in the context of planetary differentiation. Indeed, the structural environments of silicate evolve strongly with pressure. For example, the aluminum, iron or silicon coordination numbers increase under the effect of pressure. Consequently, based on our observations, the sulfur-bonding environment is likely to be affected. In this scheme, we tentatively hypothesize that S isotope fractionations between the silicate mantle and metallic core of terrestrial planetary bodies would depend on the average pressure at which their core-mantle differentiation occurred.

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.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Numerical study of entropy generation in MHD water-based carbon nanotubes along an inclined permeable surface

NASA Astrophysics Data System (ADS)

Soomro, Feroz Ahmed; Rizwan-ul-Haq; Khan, Z. H.; Zhang, Qiang

2017-10-01

Main theme of the article is to examine the entropy generation analysis for the magneto-hydrodynamic mixed convection flow of water functionalized carbon nanotubes along an inclined stretching surface. Thermophysical properties of both particles and working fluid are incorporated in the system of governing partial differential equations. Rehabilitation of nonlinear system of equations is obtained via similarity transformations. Moreover, solutions of these equations are further utilized to determine the volumetric entropy and characteristic entropy generation. Solutions of governing boundary layer equations are obtained numerically using the finite difference method. Effects of two types of carbon nanotubes, namely, single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) with water as base fluid have been analyzed over the physical quantities of interest, namely, surface skin friction, heat transfer rate and entropy generation coefficients. Influential results of velocities, temperature, entropy generation and isotherms are plotted against the emerging parameter, namely, nanoparticle fraction 0≤φ ≤ 0.2, thermal convective parameter 0≤ λ ≤ 5, Hartmann number 0≤ M≤ 2, suction/injection parameter -1≤ S≤ 1, and Eckert number 0≤ Ec ≤ 2. It is finally concluded that skin friction increases due to the increase in the magnetic parameter, suction/injection and nanoparticle volume fraction, whereas the Nusselt number shows an increasing trend due to the increase in the suction parameter, mixed convection parameter and nanoparticle volume fraction. Similarly, entropy generation shows an opposite behavior for the Hartmann number and mixed convection parameter for both single-wall and multi-wall carbon nanotubes.

Increasing the predictive accuracy of amyloid-β blood-borne biomarkers in Alzheimer's disease.

PubMed

Watt, Andrew D; Perez, Keyla A; Faux, Noel G; Pike, Kerryn E; Rowe, Christopher C; Bourgeat, Pierrick; Salvado, Olivier; Masters, Colin L; Villemagne, Victor L; Barnham, Kevin J

2011-01-01

Diagnostic measures for Alzheimer's disease (AD) commonly rely on evaluating the levels of amyloid-β (Aβ) peptides within the cerebrospinal fluid (CSF) of affected individuals. These levels are often combined with levels of an additional non-Aβ marker to increase predictive accuracy. Recent efforts to overcome the invasive nature of CSF collection led to the observation of Aβ species within the blood cellular fraction, however, little is known of what additional biomarkers may be found in this membranous fraction. The current study aimed to undertake a discovery-based proteomic investigation of the blood cellular fraction from AD patients (n = 18) and healthy controls (HC; n = 15) using copper immobilized metal affinity capture and Surface Enhanced Laser Desorption/Ionisation Time-Of-Flight Mass Spectrometry. Three candidate biomarkers were observed which could differentiate AD patients from HC (ROC AUC > 0.8). Bivariate pairwise comparisons revealed significant correlations between these markers and measures of AD severity including; MMSE, composite memory, brain amyloid burden, and hippocampal volume. A partial least squares regression model was generated using the three candidate markers along with blood levels of Aβ. This model was able to distinguish AD from HC with high specificity (90%) and sensitivity (77%) and was able to separate individuals with mild cognitive impairment (MCI) who converted to AD from MCI non-converters. While requiring further characterization, these candidate biomarkers reaffirm the potential efficacy of blood-based investigations into neurodegenerative conditions. Furthermore, the findings indicate that the incorporation of non-amyloid markers into predictive models, function to increase the accuracy of the diagnostic potential of Aβ.

The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate

NASA Astrophysics Data System (ADS)

Xiao, Weilin; Zhang, Weiguo; Zhang, Xili; Chen, Xiaoyan

2014-01-01

Motivated by the empirical evidence of long range dependence in short-term interest rates and considering the long maturities of equity warrants, we propose the fractional Vasicek model to describe the dynamics of the short rate in the pricing environment of equity warrants. Using the partial differential equation approach, we present a valuation model for equity warrants under the assumption that the short rate follows the fractional Vasicek process. After identifying the pricing model for equity warrants, we provide the parameter estimation procedure for the proposed pricing model. Since obtaining the values of equity warrants from the proposed model needs to solve a nonlinear equation, we employ a hybrid intelligent algorithm to get around this optimization problem. Furthermore, to illustrate the practicality of our proposed model, we conduct an empirical study to ascertain the performance of our proposed model using the data from China’s warrant market and the China Foreign Exchange Trade System. The comparison of traditional models (such as the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model) with our proposed model is also presented. The empirical results show that the mean absolute percentage error of our pricing model is 10.30%. By contrast, the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model applied to the same warrant produce mean absolute errors of 35.26%, 37.67%, 33.40%, 32.81%, respectively. Thus the long memory property in stochastic interest rates cannot be ignored in determining the valuation of equity warrants.

Turbulent piloted partially-premixed flames with varying levels of O2/N2: stability limits and PDF calculations

NASA Astrophysics Data System (ADS)

Juddoo, Mrinal; Masri, Assaad R.; Pope, Stephen B.

2011-12-01

This paper reports measured stability limits and PDF calculations of piloted, turbulent flames of compressed natural gas (CNG) partially-premixed with either pure oxygen, or with varying levels of O2/N2. Stability limits are presented for flames of CNG fuel premixed with up to 20% oxygen as well as CNG-O2-N2 fuel where the O2 content is varied from 8 to 22% by volume. Calculations are presented for (i) Sydney flame B [Masri et al. 1988] which uses pure CNG as well as flames B15 to B25 where the CNG is partially-premixed with 15-25% oxygen by volume, respectively and (ii) Sandia methane-air (1:3 by volume) flame E [Barlow et al. 2005] as well as new flames E15 and E25 that are partially-premixed with 'reconstituted air' where the O2 content in nitrogen is 15 and 25% by volume, respectively. The calculations solve a transported PDF of composition using a particle-based Monte Carlo method and employ the EMST mixing model as well as detailed chemical kinetics. The addition of oxygen to the fuel increases stability, shortens the flames, broadens the reaction zone, and shifts the stoichiometric mixture fraction towards the inner side of the jet. It is found that for pure CNG flames where the reaction zone is narrow (∼0.1 in mixture fraction space), the PDF calculations fail to reproduce the correct level of local extinction on approach to blow-off. A broadening in the reaction zone up to about 0.25 in mixture fraction space is needed for the PDF/EMST approach to be able to capture these finite-rate chemistry effects. It is also found that for the same level of partial premixing, increasing the O2/N2 ratio increases the maximum levels of CO and NO but shifts the peak to richer mixture fractions. Over the range of oxygenation investigated here, stability limits have shown to improve almost linearly with increasing oxygen levels in the fuel and with increasing the contribution of release rate from the pilot.

A SELDI mass spectrometry study of experimental autoimmune encephalomyelitis: sample preparation, reproducibility, and differential protein expression patterns.

PubMed

Azzam, Sausan; Broadwater, Laurie; Li, Shuo; Freeman, Ernest J; McDonough, Jennifer; Gregory, Roger B

2013-05-01

Experimental autoimmune encephalomyelitis (EAE) is an autoimmune, inflammatory disease of the central nervous system that is widely used as a model of multiple sclerosis (MS). Mitochondrial dysfunction appears to play a role in the development of neuropathology in MS and may also play a role in disease pathology in EAE. Here, surface enhanced laser desorption ionization mass spectrometry (SELDI-MS) has been employed to obtain protein expression profiles from mitochondrially enriched fractions derived from EAE and control mouse brain. To gain insight into experimental variation, the reproducibility of sub-cellular fractionation, anion exchange fractionation as well as spot-to-spot and chip-to-chip variation using pooled samples from brain tissue was examined. Variability of SELDI mass spectral peak intensities indicates a coefficient of variation (CV) of 15.6% and 17.6% between spots on a given chip and between different chips, respectively. Thinly slicing tissue prior to homogenization with a rotor homogenizer showed better reproducibility (CV = 17.0%) than homogenization of blocks of brain tissue with a Teflon® pestle (CV = 27.0%). Fractionation of proteins with anion exchange beads prior to SELDI-MS analysis gave overall CV values from 16.1% to 18.6%. SELDI mass spectra of mitochondrial fractions obtained from brain tissue from EAE mice and controls displayed 39 differentially expressed proteins (p≤ 0.05) out of a total of 241 protein peaks observed in anion exchange fractions. Hierarchical clustering analysis showed that protein fractions from EAE animals with severe disability clearly segregated from controls. Several components of electron transport chain complexes (cytochrome c oxidase subunit 6b1, subunit 6C, and subunit 4; NADH dehydrogenase flavoprotein 3, alpha subcomplex subunit 2, Fe-S protein 4, and Fe-S protein 6; and ATP synthase subunit e) were identified as possible differentially expressed proteins. Myelin Basic Protein isoform 8 (MBP8) (14.2 kDa) levels were lower in EAE samples with advanced disease relative to controls, while an MBP fragment (12. 4kDa), likely due to calpain digestion, was increased in EAE relative to controls. The appearance of MBP in mitochondrially enriched fractions is due to tissue freezing and storage, as MBP was not found associated with mitochondria obtained from fresh tissue. SELDI mass spectrometry can be employed to explore the proteome of a complex tissue (brain) and obtain protein profiles of differentially expressed proteins from protein fractions. Appropriate homogenization protocols and protein fractionation using anion exchange beads can be employed to reduce sample complexity without introducing significant additional variation into the SELDI mass spectra beyond that inherent in the SELDI- MS method itself. SELDI-MS coupled with principal component analysis and hierarchical cluster analysis provides protein patterns that can clearly distinguish the disease state from controls. However, identification of individual differentially expressed proteins requires a separate purification of the proteins of interest by polyacrylamide electrophoresis prior to trypsin digestion and peptide mass fingerprint analysis, and unambiguous identification of differentially expressed proteins can be difficult if protein bands consist of several proteins with similar molecular weights.

A SELDI mass spectrometry study of experimental autoimmune encephalomyelitis: sample preparation, reproducibility, and differential protein expression patterns

PubMed Central

2013-01-01

Background Experimental autoimmune encephalomyelitis (EAE) is an autoimmune, inflammatory disease of the central nervous system that is widely used as a model of multiple sclerosis (MS). Mitochondrial dysfunction appears to play a role in the development of neuropathology in MS and may also play a role in disease pathology in EAE. Here, surface enhanced laser desorption ionization mass spectrometry (SELDI-MS) has been employed to obtain protein expression profiles from mitochondrially enriched fractions derived from EAE and control mouse brain. To gain insight into experimental variation, the reproducibility of sub-cellular fractionation, anion exchange fractionation as well as spot-to-spot and chip-to-chip variation using pooled samples from brain tissue was examined. Results Variability of SELDI mass spectral peak intensities indicates a coefficient of variation (CV) of 15.6% and 17.6% between spots on a given chip and between different chips, respectively. Thinly slicing tissue prior to homogenization with a rotor homogenizer showed better reproducibility (CV = 17.0%) than homogenization of blocks of brain tissue with a Teflon® pestle (CV = 27.0%). Fractionation of proteins with anion exchange beads prior to SELDI-MS analysis gave overall CV values from 16.1% to 18.6%. SELDI mass spectra of mitochondrial fractions obtained from brain tissue from EAE mice and controls displayed 39 differentially expressed proteins (p≤ 0.05) out of a total of 241 protein peaks observed in anion exchange fractions. Hierarchical clustering analysis showed that protein fractions from EAE animals with severe disability clearly segregated from controls. Several components of electron transport chain complexes (cytochrome c oxidase subunit 6b1, subunit 6C, and subunit 4; NADH dehydrogenase flavoprotein 3, alpha subcomplex subunit 2, Fe-S protein 4, and Fe-S protein 6; and ATP synthase subunit e) were identified as possible differentially expressed proteins. Myelin Basic Protein isoform 8 (MBP8) (14.2 kDa) levels were lower in EAE samples with advanced disease relative to controls, while an MBP fragment (12. 4kDa), likely due to calpain digestion, was increased in EAE relative to controls. The appearance of MBP in mitochondrially enriched fractions is due to tissue freezing and storage, as MBP was not found associated with mitochondria obtained from fresh tissue. Conclusions SELDI mass spectrometry can be employed to explore the proteome of a complex tissue (brain) and obtain protein profiles of differentially expressed proteins from protein fractions. Appropriate homogenization protocols and protein fractionation using anion exchange beads can be employed to reduce sample complexity without introducing significant additional variation into the SELDI mass spectra beyond that inherent in the SELDI- MS method itself. SELDI-MS coupled with principal component analysis and hierarchical cluster analysis provides protein patterns that can clearly distinguish the disease state from controls. However, identification of individual differentially expressed proteins requires a separate purification of the proteins of interest by polyacrylamide electrophoresis prior to trypsin digestion and peptide mass fingerprint analysis, and unambiguous identification of differentially expressed proteins can be difficult if protein bands consist of several proteins with similar molecular weights. PMID:23635033

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

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.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

An experimental method for directly determining the interconnectivity of melt in a partially molten system

NASA Technical Reports Server (NTRS)

Daines, Martha J.; Richter, Frank M.

1988-01-01

An experimental method for directly determining the degree of interconnectivity of melt in a partially molten system is discussed using an olivine-basalt system as an example. Samarium 151 is allowed time to diffuse through mixtures of olivine and basalt powder which have texturally equilibrated at 1350 C and 13 to 15 kbars. The final distribution of samarium is determined through examination of developed radiographs of the samples. Results suggest an interconnected melt network is established at melt fractions at least as low as 1 wt pct and all melt is completely interconnected at melt fractions at least as low as 2 wt pct for the system examined.

PHAGE FORMATION IN STAPHYLOCOCCUS MUSCAE CULTURES

PubMed Central

Price, Winston H.

1949-01-01

1. A non-dialyzable fraction from fresh bakers' yeast stimulates the formation of S. muscae virus in cells in synthetic medium in the log phase of multiplication. 2. A similar fraction was not found in calf thymus, pancreas, or liver. 3. The active substance in this fraction has been partially purified. 4. This substance is taken up by the cells. In the absence of virus the added substance is metabolized to a form no longer available for virus formation. 5. A purified yeast fraction, which stimulates adaptive enzyme formation in yeast, has been found to stimulate virus formation in the S. muscae system. 6. The similarities between the yeast fraction that stimulates adaptive enzyme formation and the yeast fraction that stimulates virus formation are discussed. PMID:18123312

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

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

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.

A dual mode breath sampler for the collection of the end-tidal and dead space fractions.

PubMed

Salvo, P; Ferrari, C; Persia, R; Ghimenti, S; Lomonaco, T; Bellagambi, F; Di Francesco, F

2015-06-01

This work presents a breath sampler prototype automatically collecting end-tidal (single and multiple breaths) or dead space air fractions (multiple breaths). This result is achieved by real time measurements of the CO2 partial pressure and airflow during the expiratory and inspiratory phases. Suitable algorithms, used to control a solenoid valve, guarantee that a Nalophan(®) bag is filled with the selected breath fraction even if the subject under test hyperventilates. The breath sampler has low pressure drop (<0.5 kPa) and uses inert or disposable components to avoid bacteriological risk for the patients and contamination of the breath samples. A fully customisable software interface allows a real time control of the hardware and software status. The performances of the breath sampler were evaluated by comparing (a) the CO2 partial pressure calculated during the sampling with the CO2 pressure measured off-line within the Nalophan(®) bag; (b) the concentrations of four selected volatile organic compounds in dead space, end-tidal and mixed breath fractions. Results showed negligible deviations between calculated and off-line CO2 pressure values and the distributions of the selected compounds into dead space, end-tidal and mixed breath fractions were in agreement with their chemical-physical properties. Copyright © 2015. Published by Elsevier Ltd.

Purified polysaccharides of Geoffroea spinosa barks have anticoagulant and antithrombotic activities devoid of hemorrhagic risks.

PubMed

Souza, Racquel O S; Assreuy, Ana M S; Madeira, Juliana C; Chagas, Francisco D S; Parreiras, Luane A; Santos, Gustavo R C; Mourão, Paulo A S; Pereira, Maria G

2015-06-25

Polysaccharides were extracted from the barks of Geoffroea spinosa, purified using anion exchange chromatography and characterized by chemical and methylation analysis, complemented by infrared and NMR spectroscopies. These polysaccharides were tested for their anticoagulant, antithrombotic and antiplatelet activities and also for their effects on bleeding. Unfractionated polysaccharide contains low levels of protein and high levels of carbohydrate (including hexuronic acid). The purified polysaccharides (fractions FII and FIII) are composed of arabinose (Ara), rhamnose (Rha), hexuronic acid, small amounts of galactose, but no sulfate ester. They have highly complex structure, which was partially characterized. NMR and methylation analysis indicate that the polysaccharides have a core of α-Rhap and branches of 5-linked α-Araf. Residues of 4-linked α-GalpA are also found in the structure. The unfractionated (TPL) and fraction FIII, but not fractions FI and FII, prolonged the activated partial thromboplastin time (aPTT). TPL, FII and FIII inhibited the platelet aggregation induced by ADP. More significantly, both unfractionated and purified fractions exhibited potent antithrombotic effect (31-60%) and the fractions did not modify the bleeding tendency. These plant polysaccharides could be alternative source of new anticoagulant, antiplatelet and antithrombotic compounds devoid of the undesirable risk of hemorrhage. Copyright © 2015 Elsevier Ltd. All rights reserved.

Partially deuterated potassium dihydrogen phosphate optimized for ultra-broadband optical parametric amplification

NASA Astrophysics Data System (ADS)

Fujioka, K.; Fujimoto, Y.; Tsubakimoto, K.; Kawanaka, J.; Shoji, I.; Miyanaga, N.

2015-03-01

The refractive index of a potassium dihydrogen phosphate (KDP) crystal strongly depends on the deuteration fraction of the crystal. The wavelength dependence of the phase-matching angle in the near-infrared optical parametric process shows convex and concave characteristics for pure KDP and pure deuterated KDP (DKDP), respectively, when pumped by the second harmonic of Nd- or Yb-doped solid state lasers. Using these characteristics, ultra-broadband phase matching can be realized by optimization of the deuteration fraction. The refractive index of DKDP that was grown with a different deuteration fraction (known as partially deuterated KDP or pDKDP) was measured over a wide wavelength range of 0.4-1.5 μm by the minimum deviation method. The wavelength dispersions of the measured refractive indices were fitted using a modified Sellmeier equation, and the deuteration fraction dependence was analyzed using the Lorentz-Lorenz equation. The wavelength-dependent phase-matching angle for an arbitrary deuteration fraction was then calculated for optical parametric amplification with pumping at a wavelength of 526.5 nm. The results revealed that a refractive index database with precision of more than 2 × 10-5 was necessary for exact evaluation of the phase-matching condition. An ultra-broad gain bandwidth of up to 490 nm will be feasible when using the 68% pDKDP crystal.

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.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

NASA Astrophysics Data System (ADS)

Khan, W. A.; Khan, Z. H.; Rahi, M.

2014-06-01

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Utilization of the computational technique to improve the thermophysical performance in the transportation of an electrically conducting Al2O3 - Ag/H2O hybrid nanofluid

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Azhar, Ehtsham; Maraj, E. N.

2017-12-01

In this study, we analyzed the induced magnetic field effect on stagnation-point flow of a Al2O3-Ag/water hybrid nanofluid over a stretching sheet. Hybrid nanofluid, a new type of conventional fluid has been used for enhancement of heat transfer within boundary layer flow. It is notable here that only 1% to 5% contribution of nanoparticles enhance thermal conductivity of water. Nonlinear governing equations are simplified into boundary layer equations under boundary layer approximation assumption. A coupled system of nonlinear partial differential equation is transformed into a nonlinear system of ordinary differential equation by implementing suitable similarity conversions. Numerical analysis is performed by means of Keller box scheme. Effects of different non-dimensional governing parameters on velocity, induced magnetic field and temperature profiles, along with skinfriction coefficient and local Nusselt number, are discussed and presented through graphs and tables. Hybrid nanofluid is considered by keeping the 0.1% volumetric fraction of silver. From this study it is observed that the heat transfer rate of hybrid nanofluid (Al2O3-Ag/water) is higher than nanofluid (Ag/water). Novel results computed are useful in academic studies of hybrid nanofluids in engineering and industry.

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2017-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2018-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2}. An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

PubMed

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

SU-F-T-01: Optimization of the Accelerated Partial Breast Brachytherapy Fractionation with Consideration of Physical Doses to Tumor and Organ at Risk

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

Fu, W; Huq, M

2016-06-15

Purpose: The accelerated partial breast irradiation (APBI) with brachytherapy prescribes 34Gy to be delivered in 10 fractions over 5 consecutive working days without considering the physical dose to the target and organs at risk (OARs) for an individual patient. The purpose of this study is to optimize the fractionation scheme by evaluating the radiation effect on tumor and OARs with a modified linear-quadratic (LQ) model based on dose-volume histograms (DVHs). Methods: Five breast patients treated with multilumen balloon brachytherapy were selected. The minimum skin and rib spacing were ranged from 2.5mm to 14.3mm and from 1.0mm to 25.0mm, respectively. Themore » LQ model parameters were set as: (1) breast: α=0.08, β=0.028, doubling time Tpot=14.4 days, and starting time Tk=21days; (2) skin: acute reaction α=0.101, β=0.009; late reaction α=0.064, β=0.029; (3) rib: α=0.3, β=0.12. Boundary dose Dt was 6 Gy for both target and OARs. The relation between radiation effects on the tumor (ET) and OARs (EOAR) were plotted for fraction number from 1 to 20. Results: The value of radiation effect from routine 3.4Gyx10 fractions was used as reference, ETref and EOARref. If set ET=ETref, the fractionation that results in minimum EOAR values correspond to the optimal fractionation. For these patients, the optimal numbers are 10 fractions for skin acute reaction, 18 fractions for skin and rib late reaction while the doses per fraction are 3.4Gy and 2.05–2.10Gy, respectively. If set EOAR=EOARref, the fractionation that results in a maximum ET value corresponds to the optimal fractionation. The optimal fractionation is 3.4Gyx10 fractions for skin acute reaction, and 2.10–2.25Gyx18 fractions for skin late reaction and rib. Conclusion: For APBI brachytherapy, the routine 3.4Gyx10 fractions is optimal fractionation for skin acute reaction, while 2.05–2.25Gyx18 fractions is optimal fractionation for late reaction of skin and rib.« less

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…

Zinc isotope fractionation during magmatic differentiation and the isotopic composition of the bulk Earth

USGS Publications Warehouse

Chen, Heng; Savage, Paul S.; Teng, Fang-Zehn; Helz, Rosalind T.; Moynier, Frédéric

2013-01-01

he zinc stable isotope system has been successfully applied to many and varied fields in geochemistry, but to date it is still not completely clear how this isotope system is affected by igneous processes. In order to evaluate the potential application of Zn isotopes as a proxy for planetary differentiation and volatile history, it is important to constrain the magnitude of Zn isotopic fractionation induced by magmatic differentiation. In this study we present high-precision Zn isotope analyses of two sets of chemically diverse, cogenetic samples from Kilauea Iki lava lake, Hawaii, and Hekla volcano, Iceland, which both show clear evidence of having undergone variable and significant degrees of magmatic differentiation. The Kilauea Iki samples display small but resolvable variations in Zn isotope composition (0.26‰66Zn66Zn defined as the per mille deviation of a sample's 66Zn/64Zn compositional ratio from the JMC-Lyon standard), with the most differentiated lithologies exhibiting more positive δ66Zn values. This fractionation is likely a result of the crystallization of olivine and/or Fe–Ti oxides, which can both host Zn in their crystal structures. Samples from Hekla have a similar range of isotopic variation (0.22‰66Zn66Zn=0.28±0.05‰ (2s.d.).

Mango (Mangifera indica L.) peel extract fractions from different cultivars differentially affect lipid accumulation in 3T3-L1 adipocyte cells.

PubMed

Taing, Meng-Wong; Pierson, Jean-Thomas; Shaw, Paul N; Dietzgen, Ralf G; Roberts-Thomson, Sarah J; Gidley, Michael J; Monteith, Gregory R

2013-02-26

Plant phytochemicals are increasingly recognised as sources of bioactive molecules which may have potential benefit in many health conditions. In mangoes, peel extracts from different cultivars exhibit varying effects on adipogenesis in the 3T3-L1 adipocyte cell line. In this study, the effects of preparative HPLC fractions of methanol peel extracts from Irwin, Nam Doc Mai and Kensington Pride mangoes were evaluated. Fraction 1 contained the most hydrophilic components while subsequent fractions contained increasingly more hydrophobic components. High content imaging was used to assess mango peel fraction effects on lipid accumulation, nuclei count and nuclear area in differentiating 3T3-L1 cells. For all three mango cultivars, the more hydrophilic peel fractions 1-3 inhibited lipid accumulation with greater potency than the more hydrophobic peel fractions 4. For all three cultivars, the more lipophilic fraction 4 had concentrations that enhanced lipid accumulation greater than fractions 1-3 as assessed by lipid droplet integrated intensity. The potency of this fraction 4 varied significantly between cultivars. Using mass spectrometry, five long chain free fatty acids were detected in fraction 4; these were not present in any other peel extract fractions. Total levels varied between cultivars, with Irwin fraction 4 containing the highest levels of these free fatty acids. Lipophilic components appear to be responsible for the lipid accumulation promoting effects of some mango extracts and are the likely cause of the diverse effects of peel extracts from different mango cultivars on lipid accumulation.

Angular analysis of the decay $$ \\mathrm{ B^0 \\to K^{*0} \\mu^{+} \\mu^{-} }$$ from pp collisions at $$\\sqrt{s}= $$ 8 TeV

DOE PAGES

Khachatryan, Vardan

2015-12-11

The angular distributions and the differential branching fraction of the decay B 0→K*(892) 0μ +μ - are studied using data corresponding to an integrated luminosity of 20.5 fb -1 collected with the CMS detector at the LHC in pp collisions at √s = 8 TeV. Additionally, from 1430 signal decays, the forward–backward asymmetry of the muons, the K*(892) 0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the dimuon invariant mass squared. Our measurements are among the most precise to date and are in good agreement with standard model predictions.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Early Earth differentiation [rapid communication

NASA Astrophysics Data System (ADS)

Walter, Michael J.; Trønnes, Reidar G.

2004-09-01

The birth and infancy of Earth was a time of profound differentiation involving massive internal reorganization into core, mantle and proto-crust, all within a few hundred million years of solar system formation ( t0). Physical and isotopic evidence indicate that the formation of iron-rich cores generally occurred very early in planetesimals, the building blocks of proto-Earth, within about 3 million years of t0. The final stages of terrestrial planetary accretion involved violent and tremendously energetic giant impacts among core-segregated Mercury- to Mars-sized objects and planetary embryos. As a consequence of impact heating, the early Earth was at times partially or wholly molten, increasing the likelihood for high-pressure and high-temperature equilibration among core- and mantle-forming materials. The Earth's silicate mantle harmoniously possesses abundance levels of the siderophile elements Ni and Co that can be reconciled by equilibration between iron alloy and silicate at conditions comparable to those expected for a deep magma ocean. Solidification of a deep magma ocean possibly involved crystal-melt segregation at high pressures, but subsequent convective stirring of the mantle could have largely erased nascent layering. However, primitive upper mantle rocks apparently have some nonchondritic major and trace element refractory lithophile element ratios that can be plausibly linked to early mantle differentiation of ultra-high-pressure mantle phases. The geochemical effects of crystal fractionation in a deep magma ocean are partly constrained by high-pressure experimentation. Comparison between compositional models for the primitive convecting mantle and bulk silicate Earth generally allows, and possibly favors, 10-15% total fractionation of a deep mantle assemblage comprised predominantly of Mg-perovskite and with minor but geochemically important amounts of Ca-perovskite and ferropericlase. Long-term isolation of such a crystal pile is generally consistent with isotopic constraints for time-integrated Sm/Nd and Lu/Hf ratios in the modern upper mantle and might account for the characteristics of some mantle isotope reservoirs. Although much remains to be learned about the earliest formative period in the Earth's development, a convergence of theoretical, physical, isotopic and geochemical arguments is beginning to yield a self-consistent portrait of the infant Earth.

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.

Origin of the X-ray Spectral Variation and Seemingly Broad Iron Line Strucuture in the Seyfert Galaxies

NASA Astrophysics Data System (ADS)

Ebisawa, Ken; Naoki, Iso

2012-07-01

X-ray intensities and spectra of the Seyfert galaxies are known to be variable. Some of the sources have characteristic seemingly broad iron line structure, and their spectral variations are small in the iron line energy band. MCG-6-30-15 is such an archetypal source, and Miyakawa (2011) proposed a "Variable Partial Covering (VPC)" model to explain its continuum spectral variation, seemingly broad iron line structure, and small spectral variation in the iron energy band simultaneously, only due to variation of a single parameter. That single parameter is the "partial covering fraction" to describe the geometrical fraction of the X-ray emitting area covered by the ionized absorbers in the line of sight. The intrinsic X-ray luminosity is hardly variable in this model. We have applied the VPC model to the 27 Seyfert galaxies observed with Suzaku, and found that spectral variations of the 22 sources are successfully explained by this model only varying the partial covering fraction. Intrinsic X-ray luminosities of Seyfert galaxies are not variable, as opposed to what they apparently seem, and gravitationally red-shifted iron line is not necessary. Those ionized absorbing clouds are most likely to be Broad Line Region (BLR) clouds, and we will be able to constrain the BLR structure from X-ray observations.

Fractional Bateman—Feshbach Tikochinsky Oscillator

NASA Astrophysics Data System (ADS)

Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

2014-02-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

Isotopomers as a method for differentiating between bacterial and fungal production of nitrous oxide

NASA Astrophysics Data System (ADS)

Sutka, R. L.; Adams, G.; Ostrom, N.; Ostrom, P.

2007-12-01

In order to study the importance of fungi to nitrous oxide (N2O) production in the environment it is critical to have a non-intrusive method for differentiating between fungal and bacterial N2O production. Site preference (SP), the difference in d15N between the central and outer N atoms in N2O, has been used to differentiate between bacterial nitrification and denitrification. In this study we compare the SP, d15N and d18O of N2O produced by the two best-studied fungal denitrifiers, Fusarium oxysporum and Cylindrocarpon tonkinense, to data from our previous bacterial studies. Both d18O and SP values remained fairly constant during the course of nitrite reduction which likely reflects isotopic exchange with water in the case of d18O and conservative behavior in SP that has been observed previously (Sutka et al., 2006). We observed a wide range of fractionation factors for fungal denitrification, -74.7 to -6.6 ‰, and non-linear behavior indicating that fractionation was controlled by more than one step. We interpret the small degree of fractionation as reflecting fractionation during diffusion and the more negative values as being controlled by enzymatic fractionation. Data from this and our previous study of bacterial production (Sutka et al., 2006) reveals that N2O produced via nitrification by fungi can be differentiated from N2O produced by bacterial denitrification primarily on the basis of d18O. The site preference of N2O produced by F. oxysporum and C. tonkinense was 37.1 ± 2.5 ‰ and 36.9 ± 2.8 ‰, respectively. These results indicate that isotopomers can be used as a basis for differentiating bacterial and fungal denitrification. Our work further reveals the role that fungal and bacterial nitric oxide reductases have in determining site preference during N2O production.

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

Magnesium isotope evidence that accretional vapour loss shapes planetary compositions

PubMed Central

Hin, Remco C.; Coath, Christopher D.; Carter, Philip J.; Nimmo, Francis; Lai, Yi-Jen; Pogge von Strandmann, Philip A.E.; Willbold, Matthias; Leinhardt, Zoë M.; Walter, Michael J.; Elliott, Tim

2017-01-01

It has long been recognised that Earth and other differentiated planetary bodies are chemically fractionated compared to primitive, chondritic meteorites and by inference the primordial disk from which they formed. An important question has been whether the notable volatile depletions of planetary bodies are a consequence of accretion1, or inherited from prior nebular fractionation2. The isotopic compositions of the main constituents of planetary bodies can contribute to this debate3–6. Using a new analytical approach to address key issues of accuracy inherent in conventional methods, we show that all differentiated bodies have isotopically heavier magnesium compositions than chondritic meteorites. We argue that possible magnesium isotope fractionation during condensation of the solar nebula, core formation and silicate differentiation cannot explain these observations. However, isotopic fractionation between liquid and vapour followed by vapour escape during accretionary growth of planetesimals generates appropriate residual compositions. Our modelling implies that the isotopic compositions of Mg, Si and Fe and the relative abundances of the major elements of Earth, and other planetary bodies, are a natural consequence of substantial (~40% by mass) vapour loss from growing planetesimals by this mechanism. PMID:28959965

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

NASA Astrophysics Data System (ADS)

Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

2009-10-01

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

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.

A differential protein solubility approach for the depletion of highly abundant proteins in plasma using ammonium sulfate.

PubMed

Bollineni, Ravi Chand; Guldvik, Ingrid J; Grönberg, Henrik; Wiklund, Fredrik; Mills, Ian G; Thiede, Bernd

2015-12-21

Depletion of highly abundant proteins is an approved step in blood plasma analysis by mass spectrometry (MS). In this study, we explored a precipitation and differential protein solubility approach as a fractionation strategy for abundant protein removal from plasma. Total proteins from plasma were precipitated with 90% saturated ammonium sulfate, followed by differential solubilization in 55% and 35% saturated ammonium sulfate solutions. Using a four hour liquid chromatography (LC) gradient and an LTQ-Orbitrap XL mass spectrometer, a total of 167 and 224 proteins were identified from the 55% and 35% ammonium sulfate fractions, whereas 235 proteins were found in the remaining protein fractions with at least two unique peptides. SDS-PAGE and exclusive total spectrum counts from LC-MS/MS analyses clearly showed that majority of the abundant plasma proteins were solubilized in 55% and 35% ammonium sulfate solutions, indicating that the remaining protein fraction is of potential interest for identification of less abundant plasma proteins. Serum albumin, serotransferrin, alpha-1-antitrypsin and transthyretin were the abundant proteins that were highly enriched in 55% ammonium sulfate fractions. Immunoglobulins, complement system proteins, and apolipoproteins were among other abundant plasma proteins that were enriched in 35% ammonium sulfate fractions. In the remaining protein fractions a total of 40 unique proteins were identified of which, 32 proteins were identified with at least 10 exclusive spectrum counts. According to PeptideAtlas, 9 of these 32 proteins were estimated to be present at low μg ml(-1) (0.12-1.9 μg ml(-1)) concentrations in the plasma, and 17 at low ng ml(-1) (0.1-55 ng ml(-1)) range.

Fractional flow in fractured chalk; a flow and tracer test revisited.

PubMed

Odling, N E; West, L J; Hartmann, S; Kilpatrick, A

2013-04-01

A multi-borehole pumping and tracer test in fractured chalk is revisited and reinterpreted in the light of fractional flow. Pumping test data analyzed using a fractional flow model gives sub-spherical flow dimensions of 2.2-2.4 which are interpreted as due to the partially penetrating nature of the pumped borehole. The fractional flow model offers greater versatility than classical methods for interpreting pumping tests in fractured aquifers but its use has been hampered because the hydraulic parameters derived are hard to interpret. A method is developed to convert apparent transmissivity and storativity (L(4-n)/T and S(2-n)) to conventional transmissivity and storativity (L2/T and dimensionless) for the case where flow dimension, 2

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

PubMed

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.