Direct Shear Failure in Reinforced Concrete Beams under Impulsive Loading

DTIC Science & Technology

1983-09-01

115 References ............... ............................. 119 Tables . ............................. 124 Figures ............ 1..............30...8217. : = differentiable functions of time 1 = elastic modulus enhancement function 4) 41’ = constants for a given mode W’, = frequency w tfirst thickness-shear...are defined by linear partial differential equations. The analytic results are compared to data gathered on one-way slabs loaded with impulsive blast

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Changes in Gene Expression of Arabidopsis Thaliana Cell Cultures Upon Exposure to Real and Simulated Partial- g Forces

NASA Astrophysics Data System (ADS)

Fengler, Svenja; Spirer, Ina; Neef, Maren; Ecke, Margret; Hauslage, Jens; Hampp, Rüdiger

2016-06-01

Cell cultures of the plant model organism Arabidopsis thaliana were exposed to partial- g forces during parabolic flight and clinostat experiments (0.16 g, 0.38 g and 0.5 g were tested). In order to investigate gravity-dependent alterations in gene expression, samples were metabolically quenched by the fixative RNA later Ⓡ to stabilize nucleic acids and used for whole-genome microarray analysis. An attempt to identify the potential threshold acceleration for the gravity-dependent response showed that the smaller the experienced g-force, the greater was the susceptibility of the cell cultures. Compared to short-term μ g during a parabolic flight, the number of differentially expressed genes under partial- g was lower. In addition, the effect on the alteration of amounts of transcripts decreased during partial- g parabolic flight due to the sequence of the different parabolas (0.38 g, 0.16 g and μ g). A time-dependent analysis under simulated 0.5 g indicates that adaptation occurs within minutes. Differentially expressed genes (at least 2-fold up- or down-regulated in expression) under real flight conditions were to some extent identical with those affected by clinorotation. The highest number of homologuous genes was detected within seconds of exposure to 0.38 g (both flight and clinorotation). To a considerable part, these genes deal with cell wall properties. Additionally, responses specific for clinorotation were observed.

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

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

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

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.

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

DOE PAGES

Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; ...

2013-01-01

We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

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…

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.

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

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

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

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Mean field games with congestion

NASA Astrophysics Data System (ADS)

Achdou, Yves; Porretta, Alessio

2018-03-01

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both posed in $(0,T)\\times (\\mathbb{R}^N /\\mathbb{Z}^N)$. Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to $+\\infty$ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon $T$.

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.

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).

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

PubMed

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

2001-08-01

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

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

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

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

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

Smoking bans and the secondhand smoking problem: an economic analysis.

PubMed

Hofmann, Annette; Nell, Martin

2012-06-01

Smoking bans are gaining widespread support in the European Union and other countries. The vast majority of these bans are partial bans given that smoking is still permitted in certain places. This article investigates the role of partial smoking bans in coping with externalities caused by the secondhand smoking problem. Although it is widely known that Pigouvian taxation is superior to a perfect ban, this result does not necessarily carry over to a partial ban because taxes cannot (easily) be differentiated according to location. We show that under an easy and intuitive condition, (1) enacting a partial smoking ban alone always improves social welfare (a) in an unregulated society and (b) even in a regulated society if externalities can be eliminated, and (2) it is ensured that a combination of Pigouvian tax and a partial smoking ban leads to a higher social optimum than implementing corrective Pigouvian taxation alone.

Open Competition or Balkanized Coexistence? the Effects of Market Segments on Toronto Private Schools

ERIC Educational Resources Information Center

Pizarro Milian, Roger; Davies, Scott

2017-01-01

For over 25 years, school choice advocates have argued that market competition drives educational organizations to become more differentiated and technically-oriented. However, empirical research has only partially supported this view, observing such outcomes only under certain conditions. To better understand the contingent nature of market…

Discretization-dependent model for weakly connected excitable media

NASA Astrophysics Data System (ADS)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

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

2006-06-01

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

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

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

Improved Sensitivity Relations in State Constrained Optimal Control

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

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

2015-04-15

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

Effects of oxygen partial pressure on Li-air battery performance

NASA Astrophysics Data System (ADS)

Kwon, Hyuk Jae; Lee, Heung Chan; Ko, Jeongsik; Jung, In Sun; Lee, Hyun Chul; Lee, Hyunpyo; Kim, Mokwon; Lee, Dong Joon; Kim, Hyunjin; Kim, Tae Young; Im, Dongmin

2017-10-01

For application in electric vehicles (EVs), the Li-air battery system needs an air intake system to supply dry oxygen at controlled concentration and feeding rate as the cathode active material. To facilitate the design of such air intake systems, we have investigated the effects of oxygen partial pressure (≤1 atm) on the performance of the Li-air cell, which has not been systematically examined. The amounts of consumed O2 and evolved CO2 from the Li-air cell are measured with a custom in situ differential electrochemical gas chromatography-mass spectrometry (DEGC-MS). The amounts of consumed O2 suggest that the oxygen partial pressure does not affect the reaction mechanism during discharge, and the two-electron reaction occurs under all test conditions. On the other hand, the charging behavior varies by the oxygen partial pressure. The highest O2 evolution ratio is attained under 70% O2, along with the lowest CO2 evolution. The cell cycle life also peaks at 70% O2 condition. Overall, an oxygen partial pressure of about 0.5-0.7 atm maximizes the Li-air cell capacity and stability at 1 atm condition. The findings here indicate that the appropriate oxygen partial pressure can be a key factor when developing practical Li-air battery systems.

Genomic regions with a history of divergent selection affect fitness of hybrids between two butterfly species.

PubMed

Gompert, Zachariah; Lucas, Lauren K; Nice, Chris C; Fordyce, James A; Forister, Matthew L; Buerkle, C Alex

2012-07-01

Speciation is the process by which reproductively isolated lineages arise, and is one of the fundamental means by which the diversity of life increases. Whereas numerous studies have documented an association between ecological divergence and reproductive isolation, relatively little is known about the role of natural selection in genome divergence during the process of speciation. Here, we use genome-wide DNA sequences and Bayesian models to test the hypothesis that loci under divergent selection between two butterfly species (Lycaeides idas and L. melissa) also affect fitness in an admixed population. Locus-specific measures of genetic differentiation between L. idas and L. melissa and genomic introgression in hybrids varied across the genome. The most differentiated genetic regions were characterized by elevated L. idas ancestry in the admixed population, which occurs in L. idas-like habitat, consistent with the hypothesis that local adaptation contributes to speciation. Moreover, locus-specific measures of genetic differentiation (a metric of divergent selection) were positively associated with extreme genomic introgression (a metric of hybrid fitness). Interestingly, concordance of differentiation and introgression was only partial. We discuss multiple, complementary explanations for this partial concordance. © 2012 The Author(s).

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

On the motion of classical three-body system with consideration of quantum fluctuations

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

Asteroid differentiation - Pyroclastic volcanism to magma oceans

NASA Technical Reports Server (NTRS)

Taylor, G. J.; Keil, Klaus; Mccoy, Timothy; Haack, Henning; Scott, Edward R. D.

1993-01-01

A summary is presented of theoretical and speculative research on the physics of igneous processes involved in asteroid differentiation. Partial melting processes, melt migration, and their products are discussed and explosive volcanism is described. Evidence for the existence of asteroidal magma oceans is considered and processes which may have occurred in these oceans are examined. Synthesis and inferences of asteroid heat sources are discussed under the assumption that asteroids are heated mainly by internal processes and that the role of impact heating is small. Inferences of these results for earth-forming planetesimals are suggested.

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.

Are impulsive adolescents differentially influenced by the good and bad of neighborhood and family?

PubMed

Barker, Edward D; Trentacosta, Christopher J; Salekin, Randall T

2011-11-01

Using the differential susceptibility perspective (Belsky & Pluess, 2009) as a guiding frame-work, age 12 neighborhood disadvantage (ND) and family characteristics (parental knowledge) were examined as moderators of the relations between age 12 youth impulsivity and the development (ages 13, 14, and 15) of positive (community activities) and negative (antisocial behavior; ASB) adolescent behavior. An interaction between ND and youth impulsivity (age 12) operated with differential susceptibility, but only for female community activities at age 13: under low levels of ND, impulsive adolescent females engaged in the highest levels of community activities, whereas under high ND, they engaged in the lowest levels. Exploratory analysis showed the association between community activities and ND to be partially related to parents' or adults' engagement in informal social controls (e.g., alerting the police with misbehavior in the neighborhood). Differential susceptibility effects were not identified for: (i) parental knowledge and impulsivity; (ii) ASB (ages 13, 14 or 15); or (iii) community involvement at ages 14 and 15. Findings provide limited evidence for impulsivity as a differential susceptibility phenotype.

Electrical treeing behaviors in silicone rubber under an impulse voltage considering high temperature

NASA Astrophysics Data System (ADS)

Yunxiao, ZHANG; Yuanxiang, ZHOU; Ling, ZHANG; Zhen, LIN; Jie, LIU; Zhongliu, ZHOU

2018-05-01

In this paper, work was conducted to reveal electrical tree behaviors (initiation and propagation) of silicone rubber (SIR) under an impulse voltage with high temperature. Impulse frequencies ranging from 10 Hz to 1 kHz were applied and the temperature was controlled between 30 °C and 90 °C. Experimental results show that tree initiation voltage decreases with increasing pulse frequency, and the descending amplitude is different in different frequency bands. As the pulse frequency increases, more frequent partial discharges occur in the channel, increasing the tree growth rate and the final shape intensity. As for temperature, the initiation voltage decreases and the tree shape becomes denser as the temperature gets higher. Based on differential scanning calorimetry results, we believe that partial segment relaxation of SIR at high temperature leads to a decrease in the initiation voltage. However, the tree growth rate decreases with increasing temperature. Carbonization deposition in the channel under high temperature was observed under microscope and proven by Raman analysis. Different tree growth models considering tree channel characteristics are proposed. It is believed that increasing the conductivity in the tree channel restrains the partial discharge, holding back the tree growth at high temperature.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Proceedings of the 6th annual Speakeasy conference. [Chicago, August 17-18, 1978

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

Not Available

1978-01-01

This meeting on the Speakeasy programming language and its applications included papers on the following subjects: graphics (graphics under Speakeasy, Speakeasy on a mini, color graphics), time series (OASIS - a user-oriented system at USDA, writing input-burdened linkules), applications (weather and crop yield analysis system, property investment analysis system), data bases under Speakeasy (relational data base, applications of relational data bases), survey analysis (survey analysis package from Liege, sic and its future under Speakeasy), and new features in Speakeasy (partial differential equations, the Speakeasy compiler and optimization). (RWR)

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 .

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

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

Melikyan, Arik; Bernhard, Pierre

2005-06-15

We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs' equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approachmore » and one with a tangential approach.« less

Validity of GNRB® arthrometer compared to Telos™ in the assessment of partial anterior cruciate ligament tears.

PubMed

Lefevre, N; Bohu, Y; Naouri, J F; Klouche, S; Herman, S

2014-02-01

The main goal of this study was to compare the results of the GNRB(®) arthrometer to those of Telos™ in the diagnosis of partial thickness tears of the anterior cruciate ligament (ACL). A prospective study performed January-December 2011 included all patients presenting with a partial or full-thickness ACL tears without ACL reconstruction and with a healthy contralateral knee. Anterior laxity was measured in all patients by the Telos™ and GNRB(®) devices. This series included 139 patients, mean age 30.7 ± 9.3 years. Arthroscopic reconstruction was performed in 109 patients, 97 for complete tears and 12 single bundle reconstructions for partial thickness tears. Conservative treatment was proposed in 30 patients with a partial thickness tear. The correlation between the two devices was evaluated by the Spearman coefficient. The optimal laxity thresholds were determined with ROC curves, and the diagnostic value of the tests was assessed by the area under the curve (AUC). The differential laxities of full and partial thickness tears were significantly different with the two tests. The correlation between the results of laxity measurement with the two devices was fair, with the strongest correlation between Telos™ 250 N and GNRB(®) 250 N (r = 0.46, p = 0.00001). Evaluation of the AUC showed that the informative value of all tests was fair with the best results with the GNRB(®) 250 N: AUC = 0.89 [95 % CI 0.83-0.94]. The optimal differential laxity threshold with the GNRB(®) 250 N was 2.5 mm (Se = 84 %, Sp = 81 %). The diagnostic value of GNRB(®) was better than Telos™ for ACL partial thickness tears.

The differentiation directions of the bone marrow stromal cells under modeling microgravity

NASA Astrophysics Data System (ADS)

Nesterenko, Olga; Rodionova, Natalia; Katkova, Olena

Within experiments on rats simulating microgravity by base load remove from back limbs (duration of the experiment 1,5 months) on marrow stromal cells cultures (ex vivo, in vitro) comprising osteogenic cells-predecessors, extracted from femurs, studied their peculiarities of the colony formation ablity, the cell structure, some cytological and ultra-structural characteristics and differentiation direction. It was found that that under microgravity conditions there is a decline of the stromal cells colony formation intensity, decrease of the colonies size and cells mitotic activity that indicates decrease of their growth potential. Both in control and in experiment the colonies were presented by population of low-differentiated cells, differentiated cells and mature cells. The comparative cytological and morphometric analysis have shown that the studied stromal cells in colonies have the smaller sizes, more elongated shape, and higher nucleocytoplasmic ratio. Cells composition in the experiment colonies is reliably different by the ratio of the low-differentiating to being differentiated cells; a ratio of low-differentiated to already differentiated cells; ratio of differentiated cells to total number of all cells. In comparison with control group, amount of the cells passed trough a differentiation stage and mature cells in colonies is decreased by 3 to 4 times. Among the differentiated stromal cells in colonies increasing amount of adipocytes was revealed. The analysis of electron microscope microphotographs showed that in osteogenic cells differentiated under microgravity conditions, there is a reduction of the specific volume of a granular endoplasmic reticulum, Golgi's complex and quantity of nuclei reduction that indicates depression of the specific biosyntheses process intensity in cells. The increase of lysosomes and myelinic structures quantity is linked to organelles partial reduction. Consolidation of mitochondrias is an evidence of the cells’ energy metabolism disorder. In differentiated cells, disorganization and a cytoskeleton destruction was observed. Results showed that under microgravity conditions proliferative and differentiation (including osteogenic) potentialities of low-differentiated marrow stromal cells decreased, induction of their adipocytic differentiation was observes as well. Obtained results make a new contribution into gravitation sensitivity mechanisms understanding for stromal cells of the bone marrow which contain osteogenic cells- predecessors, features of the osteoporosis development.

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

Deformation of a plate with periodically changing parameters

NASA Astrophysics Data System (ADS)

Naumova, Natalia V.; Ivanov, Denis; Voloshinova, Tatiana

2018-05-01

Deformation of reinforced square plate under external pressure is considered. The averaged fourth-order partial differential equation for the plate deflection w is obtained. The new mathematical model of the plate is offered. Asymptotic averaging and Finite Elements Method (ANSYS) are used to get the values of normal deflections of the plate surface. The comparison of numerical and asymptotic results is performed.

Lunar and Planetary Science XXXV: Terrestrial Planets: Building Blocks and Differentiation

NASA Technical Reports Server (NTRS)

2004-01-01

The session "Terrestrial Planets: Building Blocks and Differentiation: included the following topics:Magnesium Isotopes in the Earth, Moon, Mars, and Pallasite Parent Body: High-Precision Analysis of Olivine by Laser-Ablation Multi-Collector ICPMS; Meteoritic Constraints on Collision Rates in the Primordial Asteroid Belt and Its Origin; New Constraints on the Origin of the Highly Siderophile Elements in the Earth's Upper Mantle; Further Lu-Hf and Sm-Nd Isotopic Data on Planetary Materials and Consequences for Planetary Differentiation; A Deep Lunar Magma Ocean Based on Neodymium, Strontium and Hafnium Isotope Mass Balance Partial Resetting on Hf-W System by Giant Impacts; On the Problem of Metal-Silicate Equilibration During Planet Formation: Significance for Hf-W Chronometry ; Solid Metal-Liquid Metal Partitioning of Pt, Re, and Os: The Effect of Carbon; Siderophile Element Abundances in Fe-S-Ni-O Melts Segregated from Partially Molten Ordinary Chondrite Under Dynamic Conditions; Activity Coefficients of Silicon in Iron-Nickel Alloys: Experimental Determination and Relevance for Planetary Differentiation; Reinvestigation of the Ni and Co Metal-Silicate Partitioning; Metal/Silicate Paritioning of P, Ga, and W at High Pressures and Temperatures: Dependence on Silicate Melt Composition; and Closure of the Fe-S-Si Liquid Miscibility Gap at High Pressure and Its Implications for Planetary Core Formation.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

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

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.

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

Numerical analysis of MHD Carreau fluid flow over a stretching cylinder with homogenous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif

2018-06-01

The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

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…

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.

Etiolation Symptoms in Sunflower (Helianthus annuus) Cotyledons Partially Covered by the Pericarp of the Achene

PubMed Central

Solymosi, Katalin; Vitányi, Beáta; Hideg, Éva; Böddi, Béla

2007-01-01

Background and Aims Etiolation symptoms and the greening process are usually studied on dark-germinated seedlings and this raises the question – can these results be generalized for plants growing under field conditions? This work examines various aspects of the plastid differentiation under the covering of the achene wall, which often remains attached to the cotyledons of sunflower (Helianthus annuus) seedlings grown under light. Methods Cotyledons of 7- to 10-d-old sunflower seedlings grown in the dark and on light were examined. The partially covered cotyledons were sectioned into light-exposed, covered and transition zones. Pigment contents, 77 K fluorescence spectroscopy, electron microscopy and fluorescence imaging, along with fluorescence kinetic methods, were used. Key Results The light-exposed zone of the partially covered cotyledons was similar to cotyledons developed without achene covering. However, some of the plastids had prolamellar bodies among the granal thylakoid membranes; despite this no protochlorophyllide was detected. The fully covered, yellowish sections contained protochlorophyllide forms emitting at 633 and 655 nm and well-developed prolamellar bodies, similar to those of etiolated cotyledons. In addition, reduced amounts of chlorophyll a, chlorophyll b and stacked thylakoid membrane pairs were found in this region. The transitional sections showed a mixture of the characteristics of the covered and exposed sections. Various, but significantly different values of the photosynthetic activity parameters were found in each sector of the partially covered cotyledons. Conclusions The partial covering of the achene wall shades the cotyledon tissues effectively, enough to provoke the appearance of etiolation phenomena, i.e. the permanent presence of flash-photoactive protochlorophyllide complexes and prolamellar bodies (with or without protochlorophyllide), which proves that these phenomena may appear under natural illumination conditions. PMID:17452377

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

Rajalin, Ann-Marie; Pollock, Hanna; Aarnisalo, Piia, E-mail: piia.aarnisalo@helsinki.fi

The orphan nuclear receptor estrogen-related receptor-{alpha} (ERR{alpha}) has been reported to have both a positive and a negative regulatory role in osteoblastic and adipocytic differentiation. We have studied the role of ERR{alpha} in osteoblastic and adipogenic differentiation of mesenchymal stem cells. Bone marrow mesenchymal stem cells were isolated from ERR{alpha} deficient mice and their differentiation capacities were compared to that of the wild-type cells. ERR{alpha} deficient cultures displayed reduced cellular proliferation, osteoblastic differentiation, and mineralization. In the complementary experiment, overexpression of ERR{alpha} in MC3T3-E1 cells increased the expression of osteoblastic markers and mineralization. Alterations in the expression of bone sialoproteinmore » (BSP) may at least partially explain the effects on mineralization as BSP expression was reduced in ERR{alpha} deficient MSCs and enhanced upon ERR{alpha} overexpression in MC3T3-E1 cells. Furthermore, a luciferase reporter construct driven by the BSP promoter was efficiently transactivated by ERR{alpha}. Under adipogenic conditions, ERR{alpha} deficient cultures displayed reduced adipocytic differentiation. Our data thus propose a positive role for ERR{alpha} in osteoblastic and adipocytic differentiation. The variability in the results yielded in the different studies implies that ERR{alpha} may play different roles in bone under different physiological conditions.« less

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

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…

Comparison of transcript profiles in different life stages of the nematode Globodera pallida under different host potato genotypes.

PubMed

Palomares-Rius, Juan E; Hedley, Pete E; Cock, Peter J A; Morris, Jenny A; Jones, John T; Vovlas, Nikos; Blok, Vivian

2012-12-01

The potato cyst nematodes (PCNs) Globodera pallida and Globodera rostochiensis are important parasites of potato. PCNs undergo complex biotrophic interactions with their hosts that involve gene expression changes in both the nematode and the host plant. The aim of this study was to determine key genes that are differentially expressed in Globodera pallida life cycle stages and during the initiation of the feeding site in susceptible and partially resistant potato genotypes. For this purpose, two microarray experiments were designed: (i) a comparison of eggs, infective second-stage juveniles (J2s) and sedentary parasitic-stage J2s (SJ2); (ii) a comparison of SJ2s at 8 days after inoculation (DAI) in the susceptible cultivar (Desirée) and two partially resistant lines. The results showed differential expression of G. pallida genes during the stages studied, including previously characterized effectors. In addition, a large number of genes changed their expression between SJ2s in the susceptible cultivar and those infecting partially resistant lines; the number of genes with modified expression was lower when the two partially resistant lines were compared. Moreover, a histopathological study was performed at several time points (7, 14 and 30 DAI) and showed the similarities between both partially resistant lines with a delay and degeneration in the formation of the syncytia in comparison with the susceptible cultivar. Females at 30 DAI in partially resistant lines showed a delay in their development in comparison with those in the susceptible cultivar. © 2012 THE AUTHORS. MOLECULAR PLANT PATHOLOGY © 2012 BSPP AND BLACKWELL PUBLISHING LTD.

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

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

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

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

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

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

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

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

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

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Partial least squares based gene expression analysis in estrogen receptor positive and negative breast tumors.

PubMed

Ma, W; Zhang, T-F; Lu, P; Lu, S H

2014-01-01

Breast cancer is categorized into two broad groups: estrogen receptor positive (ER+) and ER negative (ER-) groups. Previous study proposed that under trastuzumab-based neoadjuvant chemotherapy, tumor initiating cell (TIC) featured ER- tumors response better than ER+ tumors. Exploration of the molecular difference of these two groups may help developing new therapeutic strategies, especially for ER- patients. With gene expression profile from the Gene Expression Omnibus (GEO) database, we performed partial least squares (PLS) based analysis, which is more sensitive than common variance/regression analysis. We acquired 512 differentially expressed genes. Four pathways were found to be enriched with differentially expressed genes, involving immune system, metabolism and genetic information processing process. Network analysis identified five hub genes with degrees higher than 10, including APP, ESR1, SMAD3, HDAC2, and PRKAA1. Our findings provide new understanding for the molecular difference between TIC featured ER- and ER+ breast tumors with the hope offer supports for therapeutic studies.

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

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.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

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

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

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

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.

Differential invariants in nonclassical models of hydrodynamics

NASA Astrophysics Data System (ADS)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with analytical methods makes it possible to make the results of mathematical modeling more accurate and reliable.

Peridynamic Multiscale Finite Element Methods

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

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

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

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

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

On implicit abstract neutral nonlinear differential equations

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

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

2016-04-15

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

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

PubMed

Li, Wei Nian; Sheng, Weihong

2016-01-01

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

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.

SIADH and partial hypopituitarism in a patient with intravascular large B-cell lymphoma: a rare cause of a common presentation

PubMed Central

Akhtar, Simeen; Cheesman, Edmund; Jude, Edward B

2013-01-01

Hyponatraemia is a very common electrolyte abnormality with varied presenting features depending on the underlying cause. The authors report the case of a 75-year-old, previously fit, gentleman who presented with weight loss, lethargy and blackouts. He required four admissions to the hospital over an 8-month period. Investigations revealed persistent hyponatraemia consistent with a diagnosis of syndrome of inappropriate antidiuretic hormone secretion, macrocytic anaemia and partial hypopituitarism. Unfortunately, all other investigations that were performed failed to identify the underlying cause and a diagnosis of intravascular large B-cell lymphoma was only confirmed following postmortem studies. The authors recommend that endocrinologists should be involved at the outset in the management of patients with persistent hyponatraemia and that intravascular large B-cell lymphoma should be considered in the differential diagnosis of hyponatraemia. PMID:23362070

The Mediated MIMIC Model for Understanding the Underlying Mechanism of DIF.

PubMed

Cheng, Ying; Shao, Can; Lathrop, Quinn N

2016-02-01

Due to its flexibility, the multiple-indicator, multiple-causes (MIMIC) model has become an increasingly popular method for the detection of differential item functioning (DIF). In this article, we propose the mediated MIMIC model method to uncover the underlying mechanism of DIF. This method extends the usual MIMIC model by including one variable or multiple variables that may completely or partially mediate the DIF effect. If complete mediation effect is found, the DIF effect is fully accounted for. Through our simulation study, we find that the mediated MIMIC model is very successful in detecting the mediation effect that completely or partially accounts for DIF, while keeping the Type I error rate well controlled for both balanced and unbalanced sample sizes between focal and reference groups. Because it is successful in detecting such mediation effects, the mediated MIMIC model may help explain DIF and give guidance in the revision of a DIF item.

The Mediated MIMIC Model for Understanding the Underlying Mechanism of DIF

PubMed Central

Cheng, Ying; Shao, Can; Lathrop, Quinn N.

2015-01-01

Due to its flexibility, the multiple-indicator, multiple-causes (MIMIC) model has become an increasingly popular method for the detection of differential item functioning (DIF). In this article, we propose the mediated MIMIC model method to uncover the underlying mechanism of DIF. This method extends the usual MIMIC model by including one variable or multiple variables that may completely or partially mediate the DIF effect. If complete mediation effect is found, the DIF effect is fully accounted for. Through our simulation study, we find that the mediated MIMIC model is very successful in detecting the mediation effect that completely or partially accounts for DIF, while keeping the Type I error rate well controlled for both balanced and unbalanced sample sizes between focal and reference groups. Because it is successful in detecting such mediation effects, the mediated MIMIC model may help explain DIF and give guidance in the revision of a DIF item.

Influence of Partial O₂ Pressure on the Adhesion, Proliferation, and Osteogenic Differentiation of Human Dental Pulp Stem Cells on β-Tricalcium Phosphate Scaffold.

PubMed

Viña-Almunia, Jose; Mas-Bargues, Cristina; Borras, Consuelo; Gambini, Juan; El Alami, Marya; Sanz-Ros, Jorge; Peñarrocha, Miguel; Vina, Jose

To analyze, in vitro, the influence of O₂ pressure on the adhesion, proliferation, and osteogenic differentiation of human dental pulp stem cells (DPSC) on β-tricalcium phosphate (β-TCP) scaffold. DPSC, positive for the molecular markers CD133, Oct4, Nestin, Stro-1, and CD34, and negative for CD45, were isolated from extracted third molars. Experiments were started by seeding 200,000 cells on β-TCP cultured under 3% or 21% O₂ pressure. No osteogenic medium was used. Eight different cultures were performed at each time point under each O₂ pressure condition. Cell adhesion, proliferation, and differentiation over the biomaterial were evaluated at 7, 13, 18, and 23 days of culture. Cell adhesion was determined by light microscopy, proliferation by DNA quantification, and osteogenic differentiation by alkaline phosphatase (ALP) activity analysis. DPSC adhered to β-TCP with both O₂ conditions. Cell proliferation was found from day 7 of culture. Higher values were recorded at 3% O₂ in each time point. Statistically significant differences were recorded at 23 days of culture (P = .033). ALP activity was not detectable at 7 days. There was, however, an increase in ALP activity over time in both groups. At 13, 18, and 23 days of culture, higher ALP activity was recorded under 3% O₂ pressure. Statistical differences were found at day 23 (P = .014). DPSC display capacity of adhering to β-TCP under 3% or 21% O₂ pressure conditions. Cell proliferation on β-TCP phosphate is significantly higher at 3% than at 21% O₂ pressure, the most frequently used O₂ tension. β-TCP can itself promote osteogenic differentiation of DPSC and is enhanced under 3% O₂ compared with 21%.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Coculture with endothelial cells enhances osteogenic differentiation of periodontal ligament stem cells via cyclooxygenase-2/prostaglandin E2/vascular endothelial growth factor signaling under hypoxia.

PubMed

Zhao, Lixing; Wu, Yeke; Tan, Lijun; Xu, Zhenrui; Wang, Jun; Zhao, Zhihe; Li, Xiaoyu; Li, Yu; Yang, Pu; Tang, Tian

2013-12-01

During periodontitis and orthodontic tooth movement, periodontal vasculature is severely impaired, leading to a hypoxic microenvironment of periodontal cells. However, the impact of hypoxia on periodontal cells is poorly defined. The present study investigates responses of cocultured endothelial cells (ECs) and periodontal ligament stem cells (PDLSCs) to hypoxia. Osteogenic differentiation, molecular characterization, and various behaviors of PDLSCs and human umbilical venous ECs under hypoxia were assessed by quantitative real-time reverse-transcription polymerase chain reaction, Western blot, and enzyme-linked immunosorbent assay. Moreover, the effect of ECs on PDLSC osteogenic differentiation was tested using NS398 (cyclooxygenase 2 blocker), SU5416 (vascular endothelial growth factor [VEGF] receptor inhibitor), AH6809, L-798106, and L-161982 (EP1/2/3/4 antagonists). First, hypoxia promoted osteogenic differentiation in PDLSCs and enhanced EC migration, whereas PD98059 (extracellular signal-regulated protein kinase [ERK] inhibitor) blocked, and cocultured ECs further enhanced, hypoxia-induced osteogenic differentiation. Second, NS398 impaired EC migration and prostaglandin E2 (PGE2)/VEGF release, whereas cocultured PDLSCs and exogenous PGE2 partially reversed it. Third, NS398 (pretreated ECs) decreased PGE2/VEGF concentrations. NS398-treated ECs and AH6809/SU5416-treated PDLSCs impaired cocultured EC-induced enhancement of PDLSC osteogenic differentiation. Hypoxia enhances ERK-mediated osteogenic differentiation in PDLSCs. Coculture with EC further augments PDLSC osteogenic differentiation via cyclooxygenase-2/PGE2/VEGF signaling.

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.

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

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).

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.

Analytical study on the thermal performance of a partially wet constructal T-shaped fin

NASA Astrophysics Data System (ADS)

Hazarika, Saheera Azmi; Zeeshan, Mohd; Bhanja, Dipankar; Nath, Sujit

2017-07-01

The present paper addresses the thermal analysis of a T-shaped fin under partially wet condition by adopting a cubic variation of the humidity ratio of saturated air with the corresponding fin surface temperature. The point separating the dry and wet parts may lie either in the flange or stem part of the fin and so, two different cases having different governing equations and boundary conditions are analyzed in this paper. Since the governing equations are highly non-linear, they are solved by using an analytical technique called the Differential Transform Method and subsequently, the dry fin length, temperature distribution and fin performances are evaluated and analyzed for a wide range of the various psychometric, geometric and thermo-physical parameters. Finally, it can be highlighted that relative humidity has a pronounced effect on the performance parameters when the fin surface is partially wet whereas this effect is marginally small for fully wet surface.

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.

Operation of mixed conducting metal oxide membrane systems under transient conditions

DOEpatents

Carolan, Michael Francis [Allentown, PA

2008-12-23

Method of operating an oxygen-permeable mixed conducting membrane having an oxidant feed side, an oxidant feed surface, a permeate side, and a permeate surface, which method comprises controlling the differential strain between the permeate surface and the oxidant feed surface at a value below a selected maximum value by varying the oxygen partial pressure on either or both of the oxidant feed side and the permeate side of the membrane.

Self-Similar Compressible Free Vortices

NASA Technical Reports Server (NTRS)

vonEllenrieder, Karl

1998-01-01

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

Symmetry analysis of a model for the exercise of a barrier option

NASA Astrophysics Data System (ADS)

O'Hara, J. G.; Sophocleous, C.; Leach, P. G. L.

2013-09-01

A barrier option takes into account the possibility of an unacceptable change in the price of the underlying stock. Such a change could carry considerable financial loss. We examine one model based upon the Black-Scholes-Merton Equation and determine the functional forms of the barrier function and rebate function which are consistent with a solution of the underlying evolution partial differential equation using the Lie Theory of Extended Groups. The solution is consistent with the possibility of no rebate and the barrier function is very similar to one adopted on an heuristic basis.

Biological effects of weightlessness and clinostatic conditions registered in cells of root meristem and cap of higher plants

NASA Astrophysics Data System (ADS)

Sytnik, K. M.; Kordyum, E. L.; Belyavskaya, N. A.; Nedukha, E. M.; Tarasenko, V. A.

Research in cellular reproduction, differentiation and vital activity, i.e. processes underlying the development and functioning of organisms, plants included, is essential for solving fundamental and applied problems of space biology. Detailed anatomical analysis of roots of higher plants grown on board the Salyut 6 orbital research station show that under conditions of weightlessness for defined duration mitosis, cytokinesis and tissue differentiation in plant vegetative organs occur essentially normally. At the same time, certain rearrangements in the structural organization of cellular organelles - mainly the plastid apparatus, mitochondria, Golgi apparatus and nucleus - are established in the root meristem and cap of the experimental plants. This is evidence for considerable changes in cellular metabolism. The structural changes in the subcellular level arising under spaceflight conditions are partially absent in clinostat experiments designed to simulate weightlessness. Various clinostatic conditions have different influences on the cell structural and functional organization than does space flight. It is suggested that alterations of cellular metabolism under weightlessness and clinostatic conditions occur within existing genetic programs.

Similarity transformation for equilibrium boundary layers, including effects of blowing and suction

NASA Astrophysics Data System (ADS)

Chen, Xi; Hussain, Fazle

2017-03-01

We present a similarity transformation for the mean velocity profiles in sink flow turbulent boundary layers, including effects of blowing and suction. It is based on symmetry analysis which transforms the governing partial differential equations (for mean mass and momentum) into an ordinary differential equation and yields a new result including an exact, linear relation between the mean normal (V ) and streamwise (U ) velocities. A characteristic length function is further introduced which, under a first order expansion (whose coefficient is η ) in wall blowing and suction velocity, leads to the similarity transformation for U with the value of η ≈-1 /9 . This transformation is shown to be a group invariant and maps different U profiles under different blowing and suction conditions into a (universal) profile for no blowing or suction. Its inverse transformation enables predictions of all mean quantities in the mean mass and momentum equations, in good agreement with DNS data.

Neonatal testosterone partially organizes sex differences in stress-induced emotionality in mice.

PubMed

Seney, Marianne L; Walsh, Christopher; Stolakis, Ryan; Sibille, Etienne

2012-05-01

Major depressive disorder (MDD) is a debilitating disorder of altered mood regulation. Despite well established sex differences in MDD prevalence, the mechanism underlying the increased female vulnerability remains unknown. Although evidence suggests an influence of adult circulating hormone levels on mood (i.e. activational effects of hormones), MDD prevalence is consistently higher in women across life stages (and therefore hormonal states), suggesting that additional underlying structural or biological differences place women at higher risk. Studies in human subjects and in rodent models suggest a developmental origin for mood disorders, and interestingly, a developmental process also establishes sex differences in the brain. Hence, based on these parallel developmental trajectories, we hypothesized that a proportion of the female higher vulnerability to MDD may originate from the differential organization of mood regulatory neural networks early in life (i.e. organizational effects of hormones). To test this hypothesis in a rodent system, we took advantage of a well-established technique used in the field of sexual differentiation (neonatal injection with testosterone) to masculinize sexually dimorphic brain regions in female mice. We then investigated adult behavioral consequences relating to emotionality by comparing neonatal testosterone-treated females to normal males and females. Under baseline/trait conditions, neonatal testosterone treatment of female mice did not influence adult emotionality, but masculinized adult locomotor activity, as revealed by the activational actions of hormones. Conversely, the increased vulnerability of female mice to develop high emotionality following unpredictable chronic mild stress (UCMS) was partially masculinized by neonatal testosterone exposure, with no effect on post-UCMS locomotion. The elevated female UCMS-induced vulnerability did not differ between adult hormone treated groups. These results demonstrate that sex differences in adult emotionality in mice are partially caused by the organizational effects of sex hormones during development, hence supporting a developmental hypothesis of the human adult female prevalence of MDD. Copyright © 2012 Elsevier Inc. All rights reserved.

Neonatal testosterone partially organizes sex differences in stress-induced emotionality in mice

PubMed Central

Seney, Marianne L.; Walsh, Christopher; Stolakis, Ryan; Sibille, Etienne

2012-01-01

Major depressive disorder (MDD) is a debilitating disorder of altered mood regulation. Despite well established sex differences in MDD prevalence, the mechanism underlying the increased female vulnerability remains unknown. Although evidence suggests an influence of adult circulating hormone levels on mood (i.e. activational effects of hormones), MDD prevalence is consistently higher in women across life stages (and therefore hormonal states), suggesting that additional underlying structural or biological differences place women at higher risk. Studies in human subjects and in rodent models suggest a developmental origin for mood disorders, and interestingly, a developmental process also establishes sex differences in the brain. Hence, based on these parallel developmental trajectories, we hypothesized that a proportion of the female higher vulnerability to MDD may originate from the differential organization of mood regulatory neural networks early in life (i.e. organizational effects of hormones). To test this hypothesis in a rodent system, we took advantage of a well-established technique used in the field of sexual differentiation (neonatal injection with testosterone) to masculinize sexually dimorphic brain regions in female mice. We then investigated adult behavioral consequences relating to emotionality by comparing neonatal testosterone-treated females to normal males and females. Under baseline/trait conditions, neonatal testosterone treatment of female mice did not influence adult emotionality, but masculinized adult locomotor activity, as revealed by the activational actions of hormones. Conversely, the increased vulnerability of female mice to develop high emotionality following unpredictable chronic mild stress (UCMS) was partially masculinized by neonatal testosterone exposure, with no effect on post-UCMS locomotion. The elevated female UCMS-induced vulnerability did not differ between adult hormone treated groups. These results demonstrate that sex differences in adult emotionality in mice are partially caused by the organizational effects of sex hormones during development, hence supporting a developmental hypothesis of the human adult female prevalence of MDD. PMID:22394611

Glucose availability controls adipogenesis in mouse 3T3-L1 adipocytes via up-regulation of nicotinamide metabolism.

PubMed

Jackson, Robert M; Griesel, Beth A; Gurley, Jami M; Szweda, Luke I; Olson, Ann Louise

2017-11-10

Expansion of adipose tissue in response to a positive energy balance underlies obesity and occurs through both hypertrophy of existing cells and increased differentiation of adipocyte precursors (hyperplasia). To better understand the nutrient signals that promote adipocyte differentiation, we investigated the role of glucose availability in regulating adipocyte differentiation and maturation. 3T3-L1 preadipocytes were grown and differentiated in medium containing a standard differentiation hormone mixture and either 4 or 25 mm glucose. Adipocyte maturation at day 9 post-differentiation was determined by key adipocyte markers, including glucose transporter 4 (GLUT4) and adiponectin expression and Oil Red O staining of neutral lipids. We found that adipocyte differentiation and maturation required a pulse of 25 mm glucose only during the first 3 days of differentiation. Importantly, fatty acids were unable to substitute for the 25 mm glucose pulse during this period. The 25 mm glucose pulse increased adiponectin and GLUT4 expression and accumulation of neutral lipids via distinct mechanisms. Adiponectin expression and other early markers of differentiation required an increase in the intracellular pool of total NAD/P. In contrast, GLUT4 protein expression was only partially restored by increased NAD/P levels. Furthermore, GLUT4 mRNA expression was mediated by glucose-dependent activation of GLUT4 gene transcription through the cis-acting GLUT4-liver X receptor element (LXRE) promoter element. In summary, this study supports the conclusion that high glucose promotes adipocyte differentiation via distinct metabolic pathways and independently of fatty acids. This may partly explain the mechanism underlying adipocyte hyperplasia that occurs much later than adipocyte hypertrophy in the development of obesity. © 2017 by The American Society for Biochemistry and Molecular Biology, Inc.

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...

Impact of parenchymal loss on renal function after laparoscopic partial nephrectomy under warm ischemia.

PubMed

Bagheri, Fariborz; Pusztai, Csaba; Farkas, László; Kallidonis, Panagiotis; Buzogány, István; Szabó, Zsuzsanna; Lantos, János; Imre, Marianna; Farkas, Nelli; Szántó, Árpád

2016-12-01

To elucidate the impact of renal parenchymal loss and the ischemic reperfusion injury (RI) on the renal function after laparoscopic partial nephrectomy (LPN) under warm ischemia (WI). Thirty-five patients with a single polar renal mass ≤4 cm and normal contralateral kidney underwent LPN. Transperitoneal LPN with WI using en bloc hilar occlusion was performed. The total differential renal function (T-DRF) using 99m Tc-dimercaptosuccinic acid was evaluated preoperatively and postoperatively over a period of 1 year. A special region of interest (ROI) was selected on the non-tumorous pole of the involved kidney, and was compared with the same ROI in the contralateral kidney. The latter comparison was defined as partial differential renal function (P-DRF). Any postoperative decline in the P-DRF of the operated kidney was attributed to the RI. Subtraction of the P-DRF decline from the T-DRF decline was attributed to the parenchymal loss caused by the resection of the tumor and suturing of the normal parenchyma. The mean WI time was 22 min, and the mean weight of resected specimen was 18 g. The mean postoperative eGFR declined to 87 ml/min/1.73 m 2 from its baseline mean value of 97 ml/min/1.73 m 2 (p value = 0.075). Mean postoperative T-DRF and P-DRF of the operated kidney declined by 7 and 3 %, respectively. After LPN of small renal mass, decline in renal function is primarily attributed to parenchymal loss caused by tumor resection and suturing of the normal parenchyma rather than the RI.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

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

PubMed Central

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

2012-01-01

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

Differential Curing In Fiber/Resin Laminates

NASA Technical Reports Server (NTRS)

Webster, Charles N.

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

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

Computational Methods for Control in Partial Differential Equations

DTIC Science & Technology

1998-07-13

supported in part under this grant are C. Musante (Ph.D. thesis completed in May, 1998), M. Buksas (Ph.D. thesis to be completed in August, 1998) and M...continuing initial promising simulation findings. A summary of theoretical and numerical results to date is given in the Ph.D. thesis of Musante [4]. II... Musante and Buksas in visits to Brooks Air Force Base. The collaborations intensified during 1997 with the following visits: 1. June 15-August 30

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

18F-FDG PET-CT pattern in idiopathic normal pressure hydrocephalus.

PubMed

Townley, Ryan A; Botha, Hugo; Graff-Radford, Jonathan; Boeve, Bradley F; Petersen, Ronald C; Senjem, Matthew L; Knopman, David S; Lowe, Val; Jack, Clifford R; Jones, David T

2018-01-01

Idiopathic normal pressure hydrocephalus (iNPH) is an important and treatable cause of neurologic impairment. Diagnosis is complicated due to symptoms overlapping with other age related disorders. The pathophysiology underlying iNPH is not well understood. We explored FDG-PET abnormalities in iNPH patients in order to determine if FDG-PET may serve as a biomarker to differentiate iNPH from common neurodegenerative disorders. We retrospectively compared 18 F-FDG PET-CT imaging patterns from seven iNPH patients (mean age 74 ± 6 years) to age and sex matched controls, as well as patients diagnosed with clinical Alzheimer's disease dementia (AD), Dementia with Lewy Bodies (DLB) and Parkinson's Disease Dementia (PDD), and behavioral variant frontotemporal dementia (bvFTD). Partial volume corrected and uncorrected images were reviewed separately. Patients with iNPH, when compared to controls, AD, DLB/PDD, and bvFTD, had significant regional hypometabolism in the dorsal striatum, involving the caudate and putamen bilaterally. These results remained highly significant after partial volume correction. In this study, we report a FDG-PET pattern of hypometabolism in iNPH involving the caudate and putamen with preserved cortical metabolism. This pattern may differentiate iNPH from degenerative diseases and has the potential to serve as a biomarker for iNPH in future studies. These findings also further our understanding of the pathophysiology underlying the iNPH clinical presentation.

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

ERIC Educational Resources Information Center

Gomez, Rapson

2012-01-01

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

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

USGS Publications Warehouse

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

1982-01-01

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

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

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

2014-01-01

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

Distributional fold change test – a statistical approach for detecting differential expression in microarray experiments

PubMed Central

2012-01-01

Background Because of the large volume of data and the intrinsic variation of data intensity observed in microarray experiments, different statistical methods have been used to systematically extract biological information and to quantify the associated uncertainty. The simplest method to identify differentially expressed genes is to evaluate the ratio of average intensities in two different conditions and consider all genes that differ by more than an arbitrary cut-off value to be differentially expressed. This filtering approach is not a statistical test and there is no associated value that can indicate the level of confidence in the designation of genes as differentially expressed or not differentially expressed. At the same time the fold change by itself provide valuable information and it is important to find unambiguous ways of using this information in expression data treatment. Results A new method of finding differentially expressed genes, called distributional fold change (DFC) test is introduced. The method is based on an analysis of the intensity distribution of all microarray probe sets mapped to a three dimensional feature space composed of average expression level, average difference of gene expression and total variance. The proposed method allows one to rank each feature based on the signal-to-noise ratio and to ascertain for each feature the confidence level and power for being differentially expressed. The performance of the new method was evaluated using the total and partial area under receiver operating curves and tested on 11 data sets from Gene Omnibus Database with independently verified differentially expressed genes and compared with the t-test and shrinkage t-test. Overall the DFC test performed the best – on average it had higher sensitivity and partial AUC and its elevation was most prominent in the low range of differentially expressed features, typical for formalin-fixed paraffin-embedded sample sets. Conclusions The distributional fold change test is an effective method for finding and ranking differentially expressed probesets on microarrays. The application of this test is advantageous to data sets using formalin-fixed paraffin-embedded samples or other systems where degradation effects diminish the applicability of correlation adjusted methods to the whole feature set. PMID:23122055

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

NASA Astrophysics Data System (ADS)

Ganesh Kumar, K.; Rudraswamy, N. G.; Gireesha, B. J.; Krishnamurthy, M. R.

2017-09-01

Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

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

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

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

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

PubMed

Zhukovsky, K

2014-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

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

Lorentz force effect on mixed convection micropolar flow in a vertical conduit

NASA Astrophysics Data System (ADS)

Abdel-wahed, Mohamed S.

2017-05-01

The present work provides a simulation of control and filtration process of hydromagnetic blood flow with Hall current under the effect of heat source or sink through a vertical conduit (pipe). This work meets other engineering applications, such as nuclear reactors cooled during emergency shutdown, geophysical transport in electrically conducting and heat exchangers at low velocity conditions. The problem is modeled by a system of partial differential equations taking the effect of viscous dissipation, and these equations are simplified and solved analytically as a series solution using the Differential Transformation Method (DTM). The velocities and temperature profiles of the flow are plotted and discussed. Moreover, the conduit wall shear stress and heat flux are deduced and explained.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

[Role of CD2-associated protein in podocyte differentiation.].

PubMed

Jiang, Hua-Jun; Chang, Ying; Zhu, Zhong-Hua; Liu, Jian-She; Deng, An-Guo; Zhang, Chun

2008-02-25

To study the cellular changes and the potential role of CD2-associated protein (CD2AP) in podocyte differentiation, conditionally immortalized murine podocyte cell line was cultured in RPMI 1640 medium under permissive condition at 33 °C. After transfection with CD2AP small interfering RNA (siRNA) the cells were shifted to non-permissive condition at 37 °C. Simultaneously, untransfected cells were taken as differentiation control. The podocyte proliferation rate was determined by MTT method. The expressions of CD2AP, WT1, synaptopodin and nephrin mRNAs were examined by RT-PCR. CD2AP, WT1 and nephrin protein expressions were examined by Western blot. The distribution of CD2AP, nephrin, F-actin and tubulin in differentiated and undifferentiated podocytes was detected by laser scanning confocal microscopy. The results showed: (1) CD2AP, WT1 and nephrin were stably expressed in differentiated and undifferentiated podocytes while synaptopodin was only expressed in differentiated podocytes. (2) CD2AP and nephrin mRNA and protein expressions were up-regulated during podocyte differentiation (P<0.05). (3) CD2AP and tubulin were distributed in the cytoplasm and perinulcear region in undifferentiated podocytes, and F-actin was predominantly localized to a cortical belt and paralleled to the cell axis. Under differentiation condition, CD2AP distribution profile was presented as peripheral accumulation, tubulin took on fascicular style and F-actin extended into foot processes in podocytes. CD2AP colocalized with nephrin and F-actin in undifferentiated podocytes. (4) After transfection with CD2AP siRNA, the expression of CD2AP was partially inhibited and cell growth was arrested; Synaptopodin, the differentiation podocyte marker, was apparently down-regulated; The differentiation of podocytes was delayed. The results demonstrate that podocyte differentiation is accompanied by cytoskeleton rearrangement and cell morphology change. CD2AP might play an essential role in podocyte differentiation.

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.

A therapy inactivating the tumor angiogenic factors.

PubMed

Morales-Rodrigo, Cristian

2013-02-01

This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.

Effect of epidemic spreading on species coexistence in spatial rock-paper-scissors games.

PubMed

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2010-04-01

A fundamental question in nonlinear science and evolutionary biology is how epidemic spreading may affect coexistence. We address this question in the framework of mobile species under cyclic competitions by investigating the roles of both intra- and interspecies spreading. A surprising finding is that intraspecies infection can strongly promote coexistence while interspecies spreading cannot. These results are quantified and a theoretical paradigm based on nonlinear partial differential equations is derived to explain the numerical results.

Control of vibrations of a moving beam

NASA Astrophysics Data System (ADS)

Banichuk, N. V.; Ivanova, S. Yu; Makeev, E. V.; Sinitsyn, A. V.

2018-04-01

The translational motion of a thermoelastic beam under transverse vibrations caused by initial perturbations is considered. It is assumed that a beam moving at a constant translational speed is described by a model of a thermoelastic panel supported at the edges of the considered span. The problem of optimal suppression of vibrations is formulated when applying active transverse influences to the panel. To solve the optimization problem, modern methods developed in the theory of control of systems with distributed parameters described by partial differential equations are used.

A Maple package for computing Gröbner bases for linear recurrence relations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Robertz, Daniel

2006-04-01

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type.

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

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

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

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

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

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

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

Effect of evaporative surface cooling on thermographic assessment of burn depth

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

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

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.

Comparative Transcriptomic Analysis in Paddy Rice under Storage and Identification of Differentially Regulated Genes in Response to High Temperature and Humidity.

PubMed

Zhao, Chanjuan; Xie, Junqi; Li, Li; Cao, Chongjiang

2017-09-20

The transcriptomes of paddy rice in response to high temperature and humidity were studied using a high-throughput RNA sequencing approach. Effects of high temperature and humidity on the sucrose and starch contents and α/β-amylase activity were also investigated. Results showed that 6876 differentially expressed genes (DEGs) were identified in paddy rice under high temperature and humidity storage. Importantly, 12 DEGs that were downregulated fell into the "starch and sucrose pathway". The quantitative real-time polymerase chain reaction assays indicated that expression of these 12 DEGs was significantly decreased, which was in parallel with the reduced level of enzyme activities and the contents of sucrose and starch in paddy rice stored at high temperature and humidity conditions compared to the control group. Taken together, high temperature and humidity influence the quality of paddy rice at least partially by downregulating the expression of genes encoding sucrose transferases and hydrolases, which might result in the decrease of starch and sucrose contents.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

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

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

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

Context-Dependent Modulation of GABAAR-Mediated Tonic Currents.

PubMed

Patel, Bijal; Bright, Damian P; Mortensen, Martin; Frølund, Bente; Smart, Trevor G

2016-01-13

Tonic GABA currents mediated by high-affinity extrasynaptic GABAA receptors, are increasingly recognized as important regulators of cell and neuronal network excitability. Dysfunctional GABAA receptor signaling that results in modified tonic GABA currents is associated with a number of neurological disorders. Consequently, developing compounds to selectively modulate the activity of extrasynaptic GABAA receptors underlying tonic inhibition is likely to prove therapeutically useful. Here, we examine the GABAA receptor subtype selectivity of the weak partial agonist, 5-(4-piperidyl)isoxazol-3-ol (4-PIOL), as a potential mechanism for modulating extrasynaptic GABAA receptor-mediated tonic currents. By using recombinant GABAA receptors expressed in HEK293 cells, and native GABAA receptors of cerebellar granule cells, hippocampal neurons, and thalamic relay neurons, 4-PIOL evidently displayed differential agonist and antagonist-type profiles, depending on the extrasynaptic GABAA receptor isoforms targeted. For neurons, this resulted in differential modulation of GABA tonic currents, depending on the cell type studied, their respective GABAA receptor subunit compositions, and critically, on the ambient GABA levels. Unexpectedly, 4-PIOL revealed a significant population of relatively low-affinity γ2 subunit-containing GABAA receptors in the thalamus, which can contribute to tonic inhibition under specific conditions when GABA levels are raised. Together, these data indicate that partial agonists, such as 4-PIOL, may be useful for modulating GABAA receptor-mediated tonic currents, but the direction and extent of this modulation is strongly dependent on relative expression levels of different extrasynaptic GABAA receptor subtypes, and on the ambient GABA levels. A background level of inhibition (tonic) is important in the brain for controlling neuronal excitability. Increased levels of tonic inhibition are associated with some neurological disorders but there are no specific ligands capable of selectively reducing tonic inhibition. Here we explore the use of a GABA partial agonist as a selective chemical tool in three different brain regions. We discover that the activity of a partial agonist is heavily dependent upon the GABAA receptor subunit composition underpinning tonic inhibition, and on the ambient levels of GABA in the brain. Copyright © 2016 Patel et al.

Context-Dependent Modulation of GABAAR-Mediated Tonic Currents

PubMed Central

Patel, Bijal; Bright, Damian P.; Mortensen, Martin; Frølund, Bente

2016-01-01

Tonic GABA currents mediated by high-affinity extrasynaptic GABAA receptors, are increasingly recognized as important regulators of cell and neuronal network excitability. Dysfunctional GABAA receptor signaling that results in modified tonic GABA currents is associated with a number of neurological disorders. Consequently, developing compounds to selectively modulate the activity of extrasynaptic GABAA receptors underlying tonic inhibition is likely to prove therapeutically useful. Here, we examine the GABAA receptor subtype selectivity of the weak partial agonist, 5-(4-piperidyl)isoxazol-3-ol (4-PIOL), as a potential mechanism for modulating extrasynaptic GABAA receptor-mediated tonic currents. By using recombinant GABAA receptors expressed in HEK293 cells, and native GABAA receptors of cerebellar granule cells, hippocampal neurons, and thalamic relay neurons, 4-PIOL evidently displayed differential agonist and antagonist-type profiles, depending on the extrasynaptic GABAA receptor isoforms targeted. For neurons, this resulted in differential modulation of GABA tonic currents, depending on the cell type studied, their respective GABAA receptor subunit compositions, and critically, on the ambient GABA levels. Unexpectedly, 4-PIOL revealed a significant population of relatively low-affinity γ2 subunit-containing GABAA receptors in the thalamus, which can contribute to tonic inhibition under specific conditions when GABA levels are raised. Together, these data indicate that partial agonists, such as 4-PIOL, may be useful for modulating GABAA receptor-mediated tonic currents, but the direction and extent of this modulation is strongly dependent on relative expression levels of different extrasynaptic GABAA receptor subtypes, and on the ambient GABA levels. SIGNIFICANCE STATEMENT A background level of inhibition (tonic) is important in the brain for controlling neuronal excitability. Increased levels of tonic inhibition are associated with some neurological disorders but there are no specific ligands capable of selectively reducing tonic inhibition. Here we explore the use of a GABA partial agonist as a selective chemical tool in three different brain regions. We discover that the activity of a partial agonist is heavily dependent upon the GABAA receptor subunit composition underpinning tonic inhibition, and on the ambient levels of GABA in the brain. PMID:26758848

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

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

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

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

Research on Nonlinear Dynamical Systems.

DTIC Science & Technology

1983-01-10

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

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

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

Stability of gradient semigroups under perturbations

NASA Astrophysics Data System (ADS)

Aragão-Costa, E. R.; Caraballo, T.; Carvalho, A. N.; Langa, J. A.

2011-07-01

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

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...

Classical Affine W-Superalgebras via Generalized Drinfeld-Sokolov Reductions and Related Integrable Systems

NASA Astrophysics Data System (ADS)

Suh, Uhi Rinn

2018-02-01

The purpose of this article is to investigate relations between W-superalgebras and integrable super-Hamiltonian systems. To this end, we introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie superalgebra g and its even nilpotent element f, and we find a new definition of the classical affine W-superalgebra W(g,f,k) via the D-S reduction. This new construction allows us to find free generators of W(g,f,k), as a differential superalgebra, and two independent Lie brackets on W(g,f,k)/partial W(g,f,k). Moreover, we describe super-Hamiltonian systems with the Poisson vertex algebras theory. A W-superalgebra with certain properties can be understood as an underlying differential superalgebra of a series of integrable super-Hamiltonian systems.

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

NASA Technical Reports Server (NTRS)

Streett, C. L.

1987-01-01

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

Electron beam enhanced surface modification for making highly resolved structures

DOEpatents

Pitts, John R.

1986-01-01

A method for forming high resolution submicron structures on a substrate is provided by direct writing with a submicron electron beam in a partial pressure of a selected gas phase characterized by the ability to dissociate under the beam into a stable gaseous leaving group and a reactant fragment that combines with the substrate material under beam energy to form at least a surface compound. Variations of the method provide semiconductor device regions on doped silicon substrates, interconnect lines between active sites, three dimensional electronic chip structures, electron beam and optical read mass storage devices that may include color differentiated data areas, and resist areas for use with selective etching techniques.

Electron beam enhanced surface modification for making highly resolved structures

DOEpatents

Pitts, J.R.

1984-10-10

A method for forming high resolution submicron structures on a substrate is provided by direct writing with a submicron electron beam in a partial pressure of a selected gas phase characterized by the ability to dissociate under the beam into a stable gaseous leaving group and a reactant fragment that combines with the substrate material under beam energy to form at least a surface compound. Variations of the method provide semiconductor device regions on doped silicon substrates, interconnect lines between active sites, three dimensional electronic chip structures, electron beam and optical read mass storage devices that may include color differentiated data areas, and resist areas for use with selective etching techniques.

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.

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

PubMed Central

Mitchell, William F.

1998-01-01

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

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

PubMed

Mitchell, William F

1998-01-01

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

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

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

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

PubMed

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

2015-07-01

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

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

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

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

A convex penalty for switching control of partial differential equations

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

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

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

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

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

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

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

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

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

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

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

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

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

2016-05-25

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

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

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

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)

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Salt-water-freshwater transient upconing - An implicit boundary-element solution

USGS Publications Warehouse

Kemblowski, M.

1985-01-01

The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.

Human mesenchymal stem cells inhibit osteoclastogenesis through osteoprotegerin production.

PubMed

Oshita, Koichi; Yamaoka, Kunihiro; Udagawa, Nobuyuki; Fukuyo, Shunsuke; Sonomoto, Koshiro; Maeshima, Keisuke; Kurihara, Ryuji; Nakano, Kazuhisa; Saito, Kazuyoshi; Okada, Yosuke; Chiba, Kenji; Tanaka, Yoshiya

2011-06-01

Mesenchymal stem cells (MSCs) have been proposed to be a useful tool for treatment of rheumatoid arthritis (RA), not only because of their multipotency but also because of their immunosuppressive effect on lymphocytes, dendritic cells, and other proinflammatory cells. Since bone destruction caused by activated osteoclasts occurs in RA, we undertook the present study to investigate the effect of MSCs on osteoclast function and differentiation in order to evaluate their potential use in RA therapy. Human MSCs and peripheral blood mononuclear cells were cultured under cell-cell contact-free conditions with osteoclast induction medium. Differentiation into osteoclast-like cells was determined by tartrate-resistant acid phosphatase staining and expression of osteoclast differentiation markers. The number of osteoclast-like cells was decreased and expression of cathepsin K and nuclear factor of activated T cells c1 (NF-ATc1) was down-regulated by the addition of either MSCs or a conditioned medium obtained from MSCs. Osteoprotegerin (OPG) was constitutively produced by MSCs and inhibited osteoclastogenesis. However, osteoclast differentiation was not fully recovered upon treatment with either anti-OPG antibody or OPG small interfering RNA, suggesting that OPG had only a partial role in the inhibitory effect of MSCs. Moreover, bone-resorbing activity of osteoclast-like cells was partially recovered by addition of anti-OPG antibody into the conditioned medium. The present results indicate that human MSCs constitutively produce OPG, resulting in inhibition of osteoclastogenesis and expression of NF-ATc1 and cathepsin K in the absence of cell-cell contact. Therefore, we conclude that human MSCs exert a suppressive effect on osteoclastogenesis, which may be beneficial in inhibition of joint damage in RA. Copyright © 2011 by the American College of Rheumatology.

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

Investigation of magneto-hemodynamic flow in a semi-porous channel using orthonormal Bernstein polynomials

NASA Astrophysics Data System (ADS)

Hosseini, E.; Loghmani, G. B.; Heydari, M.; Rashidi, M. M.

2017-07-01

In this paper, the problem of the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field is investigated numerically. Using a Berman's similarity transformation, the two-dimensional momentum conservation partial differential equations can be written as a system of nonlinear ordinary differential equations incorporating Lorentizian magneto-hydrodynamic body force terms. A new computational method based on the operational matrix of derivative of orthonormal Bernstein polynomials for solving the resulting differential systems is introduced. Moreover, by using the residual correction process, two types of error estimates are provided and reported to show the strength of the proposed method. Graphical and tabular results are presented to investigate the influence of the Hartmann number ( Ha) and the transpiration Reynolds number ( Re on velocity profiles in the channel. The results are compared with those obtained by previous works to confirm the accuracy and efficiency of the proposed scheme.

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

NASA Astrophysics Data System (ADS)

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

2002-03-01

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

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

PubMed

Murase, Kenya

2016-01-01

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

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

PubMed Central

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

2015-01-01

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

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.

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.

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.

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2009-01-01

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

A role for the Swe1 checkpoint kinase during filamentous growth of Saccharomyces cerevisiae.

PubMed Central

La Valle, R; Wittenberg, C

2001-01-01

In this study we show that inactivation of Hsl1 or Hsl7, negative regulators of the Swe1 kinase, enhances the invasive behavior of haploid and diploid cells. The enhancement of filamentous growth caused by inactivation of both genes is mediated via the Swe1 protein kinase. Whereas Swe1 contributes noticeably to the effectiveness of haploid invasive growth under all conditions tested, its contribution to pseudohyphal growth is limited to the morphological response under standard assay conditions. However, Swe1 is essential for pseudohyphal differentiation under a number of nonstandard assay conditions including altered temperature and increased nitrogen. Swe1 is also required for pseudohyphal growth in the absence of Tec1 and for the induction of filamentation by butanol, a related phenomenon. Although inactivation of Hsl1 is sufficient to suppress the defect in filamentous growth caused by inactivation of Tec1 or Flo8, it is insufficient to promote filamentous growth in the absence of both factors. Moreover, inactivation of Hsl1 will not bypass the requirement for nitrogen starvation or growth on solid medium for pseudohyphal differentiation. We conclude that the Swe1 kinase modulates filamentous development under a broad spectrum of conditions and that its role is partially redundant with the Tec1 and Flo8 transcription factors. PMID:11404321

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…

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.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

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

DTIC Science & Technology

1971-06-01

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

A partial differential equation for pseudocontact shift.

PubMed

Charnock, G T P; Kuprov, Ilya

2014-10-07

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

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

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

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

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

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

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

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

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

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

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

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

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

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

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.

Creating Weather System Ensembles Through Synergistic Process Modeling and Machine Learning

NASA Astrophysics Data System (ADS)

Chen, B.; Posselt, D. J.; Nguyen, H.; Wu, L.; Su, H.; Braverman, A. J.

2017-12-01

Earth's weather and climate are sensitive to a variety of control factors (e.g., initial state, forcing functions, etc). Characterizing the response of the atmosphere to a change in initial conditions or model forcing is critical for weather forecasting (ensemble prediction) and climate change assessment. Input - response relationships can be quantified by generating an ensemble of multiple (100s to 1000s) realistic realizations of weather and climate states. Atmospheric numerical models generate simulated data through discretized numerical approximation of the partial differential equations (PDEs) governing the underlying physics. However, the computational expense of running high resolution atmospheric state models makes generation of more than a few simulations infeasible. Here, we discuss an experiment wherein we approximate the numerical PDE solver within the Weather Research and Forecasting (WRF) Model using neural networks trained on a subset of model run outputs. Once trained, these neural nets can produce large number of realization of weather states from a small number of deterministic simulations with speeds that are orders of magnitude faster than the underlying PDE solver. Our neural network architecture is inspired by the governing partial differential equations. These equations are location-invariant, and consist of first and second derivations. As such, we use a 3x3 lon-lat grid of atmospheric profiles as the predictor in the neural net to provide the network the information necessary to compute the first and second moments. Results indicate that the neural network algorithm can approximate the PDE outputs with high degree of accuracy (less than 1% error), and that this error increases as a function of the prediction time lag.

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.

Oxygen interaction with hexagonal OsB 2 at high temperature

DOE PAGES

Xie, Zhilin; Blair, Richard G.; Orlovskaya, Nina; ...

2016-08-10

The stability of ReB 2-type hexagonal OsB 2 powder at high temperature with oxygen presence has been studied by thermogravimetric analysis, differential scanning calorimetry, SEM, EDS, and high-temperature scanning transmission electron microscopy and XRD. Results of the study revealed that OsB 2 ceramics interact readily with oxygen present in reducing atmosphere, especially at high temperature and produces boric acid, which decomposes on the surface of the powder resulting in the formation of boron vacancies in the hexagonal OsB 2 lattice as well as changes in the stoichiometry of the compound. It was also found that under low oxygen partial pressure,more » sintering of OsB 2 powders occurred at a relatively low temperature (900°C). Finally, hexagonal OsB 2 ceramic is prone to oxidation and it is very sensitive to oxygen partial pressures, especially at high temperatures.« less

Oxygen interaction with hexagonal OsB 2 at high temperature

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

Xie, Zhilin; Blair, Richard G.; Orlovskaya, Nina

The stability of ReB 2-type hexagonal OsB 2 powder at high temperature with oxygen presence has been studied by thermogravimetric analysis, differential scanning calorimetry, SEM, EDS, and high-temperature scanning transmission electron microscopy and XRD. Results of the study revealed that OsB 2 ceramics interact readily with oxygen present in reducing atmosphere, especially at high temperature and produces boric acid, which decomposes on the surface of the powder resulting in the formation of boron vacancies in the hexagonal OsB 2 lattice as well as changes in the stoichiometry of the compound. It was also found that under low oxygen partial pressure,more » sintering of OsB 2 powders occurred at a relatively low temperature (900°C). Finally, hexagonal OsB 2 ceramic is prone to oxidation and it is very sensitive to oxygen partial pressures, especially at high temperatures.« less

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

Variation in migratory behavior influences regional genetic diversity and structure among American kestrel populations (Falco sparverius) in North America

USGS Publications Warehouse

Miller, Mark P.; Mullins, Thomas D.; Parrish, John G.; Walters, Jeffrey R.; Haig, Susan M.

2012-01-01

Birds employ numerous strategies to cope with seasonal fluctuations in high-quality habitat availability. Long distance migration is a common tactic; however, partial migration is especially common among broadly distributed species. Under partial migration systems, a portion of a species migrates, whereas the remainder inhabits breeding grounds year round. In this study, we identified effects of migratory behavior variation on genetic structure and diversity of American Kestrels (Falco sparverius), a widespread partial migrant in North America. American Kestrels generally migrate; however, a resident group inhabits the southeastern United States year round. The southeastern group is designated as a separate subspecies (F. s. paulus) from the migratory group (F. s. sparverius). Using mitochondrial DNA and microsatellites from 183 and 211 individuals, respectively, we illustrate that genetic structure is stronger among nonmigratory populations, with differentiation measures ranging from 0.060 to 0.189 depending on genetic marker and analysis approach. In contrast, measures from western North American populations ranged from 0 to 0.032. These findings suggest that seasonal migratory behavior is also associated with natal and breeding dispersal tendencies. We likewise detected significantly lower genetic diversity within nonmigratory populations, reflecting the greater influence of genetic drift in small populations. We identified the signal of population expansion among nonmigratory populations, consistent with the recent establishment of higher latitude breeding locations following Pleistocene glacial retreat. Differentiation of F. s. paulus and F. s. sparverius reflected subtle differences in allele frequencies. Because migratory behavior can evolve quickly, our analyses suggest recent origins of migratory American Kestrel populations in North America.

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

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

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

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

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

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

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

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

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

Hyperforin inhibits cell proliferation and differentiation in mouse embryonic stem cells.

PubMed

Nakamura, K; Aizawa, K; Yamauchi, J; Tanoue, A

2013-10-01

Hyperforin, a phloroglucinol derivative of St. John's Wort, has been identified as the major molecule responsible for this plant's products anti-depressant effects. It can be expected that exposure to St. John's Wort during pregnancy occurs with some frequency although embryotoxic or teratogenic effects of St. John's Wort and hyperforin have not yet been experimentally examined in detail. In this study, to determine any embryotoxic effects of hyperforin, we have attempted to determine whether hyperforin affects growth and survival processes of employing mouse embryonic stem (mES) cells (representing embryonic tissue) and fibroblasts (representing adult tissues). We used a modified embryonic stem cell test, which has been validated as an in vitro developmental toxicity protocol, mES cells, to assess embryotoxic potential of chemicals under investigation. We have identified that high concentrations of hyperforin inhibited mouse ES cell population growth and induced apoptosis in fibroblasts. Under our cell culture conditions, ES cells mainly differentiated into cardiomyocytes, although various other cell types were also produced. In this condition, hyperforin affected ES cell differentiation into cardiomyocytes in a dose-dependent manner. Analysis of tissue-specific marker expression also revealed that hyperforin at high concentrations partially inhibited ES cell differentiation into mesodermal and endodermal lineages. Hyperforin is currently used in the clinic as a safe and effective antidepressant. Our data indicate that at typical dosages it has only a low risk of embryotoxicity; ingestion of large amounts of hyperforin by pregnant women, however, may pose embryotoxic and teratogenic risks. © 2013 John Wiley & Sons Ltd.

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies

NASA Astrophysics Data System (ADS)

Ilssar, Dotan; Bucher, Izhak

2015-10-01

This paper introduces a simplified analytical model describing the governing dynamics of near-field acoustically levitated objects. The simplification converts the equation of motion coupled with the partial differential equation of a compressible fluid, into a compact, second order ordinary differential equation, where the local stiffness and damping are transparent. The simplified model allows one to more easily analyse and design near-field acoustic levitation based systems, and it also helps to devise closed-loop controller algorithms for such systems. Near-field acoustic levitation employs fast ultrasonic vibrations of a driving surface and exploits the viscosity and the compressibility of a gaseous medium to achieve average, load carrying pressure. It is demonstrated that the slow dynamics dominates the transient behaviour, while the time-scale associated with the fast, ultrasonic excitation has a small presence in the oscillations of the levitated object. Indeed, the present paper formulates the slow dynamics under an ultrasonic excitation without the need to explicitly consider the latter. The simplified model is compared with a numerical scheme based on Reynolds equation and with experiments, both showing reasonably good results.

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

PubMed Central

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2005-09-01

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

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

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

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

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

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

1988-12-31

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

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Raman spectroscopic analysis of gunshot residue offering great potential for caliber differentiation.

PubMed

Bueno, Justin; Sikirzhytski, Vitali; Lednev, Igor K

2012-05-15

Near-infrared (NIR) Raman microspectroscopy combined with advanced statistics was used to differentiate gunshot residue (GSR) particles originating from different caliber ammunition. The firearm discharge process is analogous to a complex chemical reaction. The reagents of this process are represented by the chemical composition of the ammunition, firearm, and cartridge case. The specific firearm parameters determine the conditions of the reaction and thus the subsequent product, GSR. We found that Raman spectra collected from these products are characteristic for different caliber ammunition. GSR particles from 9 mm and 0.38 caliber ammunition, collected under identical discharge conditions, were used to demonstrate the capability of confocal Raman microspectroscopy for the discrimination and identification of GSR particles. The caliber differentiation algorithm is based on support vector machines (SVM) and partial least squares (PLS) discriminant analyses, validated by a leave-one-out cross-validation method. This study demonstrates for the first time that NIR Raman microspectroscopy has the potential for the reagentless differentiation of GSR based upon forensically relevant parameters, such as caliber size. When fully developed, this method should have a significant impact on the efficiency of crime scene investigations.

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

PubMed

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

2006-02-24

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

Function of FEZF1 during early neural differentiation of human embryonic stem cells.

PubMed

Liu, Xin; Su, Pei; Lu, Lisha; Feng, Zicen; Wang, Hongtao; Zhou, Jiaxi

2018-01-01

The understanding of the mechanism underlying human neural development has been hampered due to lack of a cellular system and complicated ethical issues. Human embryonic stem cells (hESCs) provide an invaluable model for dissecting human development because of unlimited self-renewal and the capacity to differentiate into nearly all cell types in the human body. In this study, using a chemical defined neural induction protocol and molecular profiling, we identified Fez family zinc finger 1 (FEZF1) as a potential regulator of early human neural development. FEZF1 is rapidly up-regulated during neural differentiation in hESCs and expressed before PAX6, a well-established marker of early human neural induction. We generated FEZF1-knockout H1 hESC lines using CRISPR-CAS9 technology and found that depletion of FEZF1 abrogates neural differentiation of hESCs. Moreover, loss of FEZF1 impairs the pluripotency exit of hESCs during neural specification, which partially explains the neural induction defect caused by FEZF1 deletion. However, enforced expression of FEZF1 itself fails to drive neural differentiation in hESCs, suggesting that FEZF1 is necessary but not sufficient for neural differentiation from hESCs. Taken together, our findings identify one of the earliest regulators expressed upon neural induction and provide insight into early neural development in human.

The Effects of Topographical Patterns and Sizes on Neural Stem Cell Behavior

PubMed Central

Qi, Lin; Li, Ning; Huang, Rong; Song, Qin; Wang, Long; Zhang, Qi; Su, Ruigong; Kong, Tao; Tang, Mingliang; Cheng, Guosheng

2013-01-01

Engineered topographical manipulation, a paralleling approach with conventional biochemical cues, has recently attracted the growing interests in utilizations to control stem cell fate. In this study, effects of topological parameters, pattern and size are emphasized on the proliferation and differentiation of adult neural stem cells (ANSCs). We fabricate micro-scale topographical Si wafers with two different feature sizes. These topographical patterns present linear micro-pattern (LMP), circular micro-pattern (CMP) and dot micro-pattern (DMP). The results show that the three topography substrates are suitable for ANSC growth, while they all depress ANSC proliferation when compared to non-patterned substrates (control). Meanwhile, LMP and CMP with two feature sizes can both significantly enhance ANSC differentiation to neurons compared to control. The smaller the feature size is, the better upregulation applies to ANSC for the differentiated neurons. The underlying mechanisms of topography-enhanced neuronal differentiation are further revealed by directing suppression of mitogen-activated protein kinase/extracellular signaling-regulated kinase (MAPK/Erk) signaling pathway in ANSC using U0126, known to inhibit the activation of Erk. The statistical results suggest MAPK/Erk pathway is partially involved in topography-induced differentiation. These observations provide a better understanding on the different roles of topographical cues on stem cell behavior, especially on the selective differentiation, and facilitate to advance the field of stem cell therapy. PMID:23527077

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

PubMed

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

2016-09-01

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

Continuation of probability density functions using a generalized Lyapunov approach

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

Baars, S., E-mail: s.baars@rug.nl; Viebahn, J.P., E-mail: viebahn@cwi.nl; Mulder, T.E., E-mail: t.e.mulder@uu.nl

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

Numerical Algorithms Based on Biorthogonal Wavelets

NASA Technical Reports Server (NTRS)

Ponenti, Pj.; Liandrat, J.

1996-01-01

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Placental mesenchymal dysplasia complicated by hydrops fetalis and fetal death: a case report.

PubMed

Akbarzadeh-Jahromi, Mojgan; Sari Aslani, Fatemeh; Parvari, Shams

2013-09-01

Placental mesenchymal dysplasia is a rare condition of the placenta and its true incidence and underlying cause has remained unknown till now due to its rarity. Its accurate diagnosis is essential, because placental mesenchymal dysplasia is usually compatible with a good fetal and maternal outcome. A precise ultrasonographic evaluation can contribute to the identification of characteristic features, particularly to discriminate it from partial hydatidiform mole, its main differential diagnosis. We report an early third-trimester pathologically- diagnosed case of placental mesenchymal dysplasia. It was complicated by fetal hydrops and death. 

Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Morozov, Oleg I.

2018-06-01

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.

Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Symbolic computer vector analysis

NASA Technical Reports Server (NTRS)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Sudbury project (University of Muenster-Ontario Geological Survey): Isotope systematics support the impact origin

NASA Technical Reports Server (NTRS)

Deutsch, A.; Buhl, D.; Brockmeyer, P.; Lakomy, R.; Flucks, M.

1992-01-01

Within the framework of the Sudbury project a considerable number of Sr-Nd isotope analyses were carried out on petrographically well-defined samples of different breccia units. Together with isotope data from the literature these data are reviewed under the aspect of a self-consistent impact model. The crucial point of this model is that the Sudbury Igneous Complex (SIC) is interpreted as a differentiated impact melt sheet without any need for an endogenic 'magmatic' component such as 'impact-triggered' magmatism or 'partial' impact melting of the crust and mixing with a mantle-derived magma.

Symmetric linear systems - An application of algebraic systems theory

NASA Technical Reports Server (NTRS)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

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

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

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

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

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

2017-07-01

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

Diagnostic power of optic disc morphology, peripapillary retinal nerve fiber layer thickness, and macular inner retinal layer thickness in glaucoma diagnosis with fourier-domain optical coherence tomography.

PubMed

Huang, Jehn-Yu; Pekmezci, Melike; Mesiwala, Nisreen; Kao, Andrew; Lin, Shan

2011-02-01

To evaluate the capability of the optic disc, peripapillary retinal nerve fiber layer (P-RNFL), macular inner retinal layer (M-IRL) parameters, and their combination obtained by Fourier-domain optical coherent tomography (OCT) in differentiating a glaucoma suspect from perimetric glaucoma. Two hundred and twenty eyes from 220 patients were enrolled in this study. The optic disc morphology, P-RNFL, and M-IRL were assessed by the Fourier-domain OCT (RTVue OCT, Model RT100, Optovue, Fremont, CA). A linear discriminant function was generated by stepwise linear discriminant analysis on the basis of OCT parameters and demographic factors. The diagnostic power of these parameters was evaluated with receiver operating characteristic (ROC) curve analysis. The diagnostic power in the clinically relevant range (specificity ≥ 80%) was presented as the partial area under the ROC curve (partial AROC). The individual OCT parameter with the largest AROC and partial AROC in the high specificity (≥ 80%) range were cup/disc vertical ratio (AROC = 0.854 and partial AROC = 0.142) for the optic disc parameters, average thickness (AROC = 0.919 and partial AROC = 0.147) for P-RNFL parameters, inferior hemisphere thickness (AROC = 0.871 and partial AROC = 0.138) for M-IRL parameters, respectively. The linear discriminant function further enhanced the ability in detecting perimetric glaucoma (AROC = 0.970 and partial AROC = 0.172). Average P-RNFL thickness is the optimal individual OCT parameter to detect perimetric glaucoma. Simultaneous evaluation on disc morphology, P-RNFL, and M-IRL thickness can improve the diagnostic accuracy in diagnosing glaucoma.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

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

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

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

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

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

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

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

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

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

Partial differential equation models in macroeconomics.

PubMed

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

2014-11-13

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

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

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

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

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

PubMed

Kumar, Gautam; Kothare, Mayuresh V

2013-12-01

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

Resonant tunnelling in a quantum oxide superlattice

DOE PAGES

Choi, Woo Seok; Lee, Sang A.; You, Jeong Ho; ...

2015-06-24

Resonant tunneling is a quantum mechanical process that has long been attracting both scientific and technological attention owing to its intriguing underlying physics and unique applications for high-speed electronics. The materials system exhibiting resonant tunneling, however, has been largely limited to the conventional semiconductors, partially due to their excellent crystalline quality. Here we show that a deliberately designed transition metal oxide superlattice exhibits a resonant tunneling behaviour with a clear negative differential resistance. The tunneling occurred through an atomically thin, lanthanum δ- doped SrTiO 3 layer, and the negative differential resistance was realized on top of the bi-polar resistance switchingmore » typically observed for perovskite oxide junctions. This combined process resulted in an extremely large resistance ratio (~10 5) between the high and low resistance states. Lastly, the unprecedentedly large control found in atomically thin δ-doped oxide superlattices can open a door to novel oxide-based high-frequency logic devices.« less

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

Heat generation/absorption and nonlinear radiation effects on stagnation point flow of nanofluid along a moving surface

NASA Astrophysics Data System (ADS)

Soomro, Feroz Ahmed; Haq, Rizwan Ul; Al-Mdallal, Qasem M.; Zhang, Qiang

2018-03-01

In this study, heat generation/absorption effects are studied in the presence of nonlinear thermal radiation along a moving slip surface. Uniform magnetic field and convective condition along the stretching surface are adjusted to deal the slip mechanisms in term of Brownian motion and thermophoresis for nanofluid. The mathematical model is constructed in the form of coupled partial differential equations. By introducing the suitable similarity transformation, system of coupled nonlinear ordinary differential equations are obtained. Finite difference approach is implemented to obtain the unknown functions of velocity, temperature, nanoparticle concentration. To deduct the effects at the surface, physical quantities of interest are computed under the effects of controlled physical parameters. Present numerical solutions are validated via numerical comparison with existing published work for limiting cases. Present study indicates that due to increase in both Brownian motion and thermophoresis, the Nusselt number decreases while Sherwood number shows the gradual increase.

A computational study of entropy generation in magnetohydrodynamic flow and heat transfer over an unsteady stretching permeable sheet

NASA Astrophysics Data System (ADS)

Saeed Butt, Adnan; Ali, Asif

2014-01-01

The present article aims to investigate the entropy effects in magnetohydrodynamic flow and heat transfer over an unsteady permeable stretching surface. The time-dependent partial differential equations are converted into non-linear ordinary differential equations by suitable similarity transformations. The solutions of these equations are computed analytically by the Homotopy Analysis Method (HAM) then solved numerically by the MATLAB built-in routine. Comparison of the obtained results is made with the existing literature under limiting cases to validate our study. The effects of unsteadiness parameter, magnetic field parameter, suction/injection parameter, Prandtl number, group parameter and Reynolds number on flow and heat transfer characteristics are checked and analysed with the aid of graphs and tables. Moreover, the effects of these parameters on entropy generation number and Bejan number are also shown graphically. It is examined that the unsteadiness and presence of magnetic field augments the entropy production.

Alpha-lipoic acid supplementation protects enzymes from damage by nitrosative and oxidative stress.

PubMed

Hiller, Sylvia; DeKroon, Robert; Hamlett, Eric D; Xu, Longquan; Osorio, Cristina; Robinette, Jennifer; Winnik, Witold; Simington, Stephen; Maeda, Nobuyo; Alzate, Oscar; Yi, Xianwen

2016-01-01

S-nitrosylation of mitochondrial enzymes involved in energy transfer under nitrosative stress may result in ATP deficiency. We investigated whether α-lipoic acid, a powerful antioxidant, could alleviate nitrosative stress by regulating S-nitrosylation, which could result in retaining the mitochondrial enzyme activity. In this study, we have identified the S-nitrosylated forms of subunit 1 of dihydrolipoyllysine succinyltransferase (complex III), and subunit 2 of the α-ketoglutarate dehydrogenase complex by implementing a fluorescence-based differential quantitative proteomics method. We found that the activities of these two mitochondrial enzymes were partially but reversibly inhibited by S-nitrosylation in cultured endothelial cells, and that their activities were partially restored by supplementation of α-lipoic acid. We show that protein S-nitrosylation affects the activity of mitochondrial enzymes that are central to energy supply, and that α-lipoic acid protects mitochondrial enzymes by altering S-nitrosylation levels. Inhibiting protein S-nitrosylation with α-lipoic acid seems to be a protective mechanism against nitrosative stress. Identification and characterization of these new protein targets should contribute to expanding the therapeutic power of α-lipoic acid and to a better understanding of the underlying antioxidant mechanisms.

Great influence of geographic isolation on the genetic differentiation of Myriophyllum spicatum under a steep environmental gradient

PubMed Central

Wu, Zhigang; Yu, Dan; Wang, Zhong; Li, Xing; Xu, Xinwei

2015-01-01

Understanding how natural processes affect population genetic structures is an important issue in evolutionary biology. One effective method is to assess the relative importance of environmental and geographical factors in the genetic structure of populations. In this study, we examined the spatial genetic variation of thirteen Myriophyllum spicatum populations from the Qinghai-Tibetan Plateau (QTP) and adjacent highlands (Yunnan-Guizhou Plateau, YGP) by using microsatellite loci and environmental and geographical factors. Bioclim layers, hydrological properties and elevation were considered as environmental variables and reduced by principal component analysis. The genetic isolation by geographic distance (IBD) was tested by Mantel tests and the relative importance of environmental variables on population genetic differentiation was determined by a partial Mantel test and multiple matrix regression with randomization (MMRR). Two genetic clusters corresponding to the QTP and YGP were identified. Both tests and MMRR revealed a significant and strong correlation between genetic divergence and geographic isolation under the influence of environmental heterogeneity at the overall and finer spatial scales. Our findings suggested the dominant role of geography on the evolution of M. spicatum under a steep environmental gradient in the alpine landscape as a result of dispersal limitation and genetic drift. PMID:26494202

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

HEPATOCYTE GROWTH FACTOR ACTS AS A MITOGEN AND CHEMOATTRACTANT FOR POSTNATAL SUBVENTRICULAR ZONE-OLFACTORY BULB NEUROGENESIS

PubMed Central

Wang, Tsu-Wei; Zhang, Huailin; Gyetko, Margaret R.; Parent, Jack M.

2011-01-01

Neural progenitor cells persist throughout life in the forebrain subventricular zone (SVZ). They generate neuroblasts that migrate to the olfactory bulb and differentiate into interneurons, but mechanisms underlying these processes are poorly understood. Hepatocyte growth factor/scatter factor (HGF/SF) is a pleiotropic factor that influences cell motility, proliferation and morphogenesis in neural and non-neural tissues. HGF and its receptor, c-Met, are present in the rodent SVZ-olfactory bulb pathway. Using in vitro neurogenesis assays and in vivo studies of partially HGF-deficient mice, we find that HGF promotes SVZ cell proliferation and progenitor cell maintenance, while slowing differentiation and possibly altering cell fate choices. HGF also acts as a chemoattractant for SVZ neuroblasts in co-culture assays. Decreased HGF signaling induces ectopic SVZ neuroblast migration and alters the timing of migration to the olfactory bulb. These results suggest that HGF influences multiple steps in postnatal forebrain neurogenesis. HGF is a mitogen for SVZ neural progenitors, and regulates their differentiation and olfactory bulb migration. PMID:21683144

Flap-lag-torsional dynamics of helicopter rotor blades in forward flight

NASA Technical Reports Server (NTRS)

Crespodasilva, M. R. M.

1986-01-01

A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented.

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

PubMed Central

Gazizov, R. K.

2017-01-01

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

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

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

MicroRNAs regulate the main events in rice drought stress response by manipulating the water supply to shoots.

PubMed

Fard, Ehsan Mohseni; Bakhshi, Behnam; Farsi, Mohammad; Kakhki, Amin Mirshamsi; Nikpay, Nava; Ebrahimi, Mohammad Ali; Mardi, Mohsen; Salekdeh, Ghasem Hosseini

2017-10-24

MicroRNAs (miRNAs) are small endogenous regulatory RNAs that are involved in a variety of biological processes related to proliferation, development, and response to biotic and abiotic stresses. miRNA profiles of rice (Oryza sativa L. cv. IR64.) leaves in a partial root zone drying (PRD) system were analysed using a high-throughput sequencing approach to identify miRNAs associated with drought signalling. The treatments performed in this study were as follows: well-watered ("wet" roots, WW), wherein both halves of the pot were watered daily; drought ("dry" roots, DD), wherein water was withheld from both halves of the pot; and well-watered/drought ("wet" and "dry" roots, WD), wherein one half of each pot was watered daily, the same as in WW, and water was withheld from the other part, the same as in DD. High-throughput sequencing enabled us to detect novel miRNAs and study the differential expression of known miRNAs. A total of 209 novel miRNAs were detected in this study. Differential miRNA profiling of the DD, WD and WW conditions showed differential expression of 159 miRNAs, among which 83, 44 and 32 miRNAs showed differential expression under both DD and WD conditions. The detection of putative targets of the differentially expressed miRNAs and investigation of their functions showed that most of these genes encode transcription factors involved in growth and development, leaf morphology, regulation of hormonal homeostasis, and stress response. The most important differences between the DD and WD conditions involved regulation of the levels of hormones such as auxin, cytokinin, abscisic acid, and jasmonic acid and also regulation of phosphor homeostasis. Overall, differentially expressed miRNAs under WD conditions were found to differ from those under DD conditions, with such differences playing a role in adaptation and inducing the normal condition. The mechanisms involved in regulating hormonal homeostasis and involved in energy production and consumption were found to be the most important regulatory pathways distinguishing the DD and WD conditions.

Physically-enhanced data visualisation: towards real time solution of Partial Differential Equations in 3D domains

NASA Astrophysics Data System (ADS)

Zlotnik, Sergio

2017-04-01

Information provided by visualisation environments can be largely increased if the data shown is combined with some relevant physical processes and the used is allowed to interact with those processes. This is particularly interesting in VR environments where the user has a deep interplay with the data. For example, a geological seismic line in a 3D "cave" shows information of the geological structure of the subsoil. The available information could be enhanced with the thermal state of the region under study, with water-flow patterns in porous rocks or with rock displacements under some stress conditions. The information added by the physical processes is usually the output of some numerical technique applied to solve a Partial Differential Equation (PDE) that describes the underlying physics. Many techniques are available to obtain numerical solutions of PDE (e.g. Finite Elements, Finite Volumes, Finite Differences, etc). Although, all these traditional techniques require very large computational resources (particularly in 3D), making them useless in a real time visualization environment -such as VR- because the time required to compute a solution is measured in minutes or even in hours. We present here a novel alternative for the resolution of PDE-based problems that is able to provide a 3D solutions for a very large family of problems in real time. That is, the solution is evaluated in a one thousands of a second, making the solver ideal to be embedded into VR environments. Based on Model Order Reduction ideas, the proposed technique divides the computational work in to a computationally intensive "offline" phase, that is run only once in a life time, and an "online" phase that allow the real time evaluation of any solution within a family of problems. Preliminary examples of real time solutions of complex PDE-based problems will be presented, including thermal problems, flow problems, wave problems and some simple coupled problems.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

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

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

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

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

Non-specific sex-differential effect of DTP vaccination may partially explain the excess girl child mortality in Ballabgarh, India.

PubMed

Krishnan, A; Srivastava, R; Dwivedi, P; Ng, N; Byass, P; Pandav, C S

2013-11-01

To test the hypothesis that a gender differential exists in the effect on child mortality of BCG, DTP, measles vaccine as administered under programme conditions in Ballabgarh HDSS area. All live births in 28 villages of Ballabgarh block in North India from 2006 to 2011 were followed until 31 December 2011 or 36 months of age whichever was earlier. The period of analysis was divided into four time periods based on eligibility for vaccines under the national immunisation schedule (BCG for tuberculosis, primary and booster doses of diphtheria-tetanus-pertussis and measles). Cox proportional hazards regression was used to assess the association between sex and risk of mortality by vaccination status using age as the timescale in survival analysis and adjusting for wealth index, access to health care, the presence of a health facility in the village, parental education, type of family, birth order of the child and year of birth. 702 deaths (332 boys and 370 girls) occurred among 12,142 children in the cohort in the 3 years of follow-up giving a cumulative mortality rate of 57.5 per 1000 live births with 35% excess girl child mortality. Age at vaccination for the four vaccines did not differ by sex. There was significant excess mortality among girls after immunisation with DTP, for both primary (HR 1.65; 95% CI:1.17-2.32) and DTPb (2.21; 1.24-3.93) vaccinations. No significant excess morality among girls was noted after exposure to BCG 1.06 (0.67-1.67) or measles 1.34 (0.85-2.12) vaccine. This study supports the contention that DTP vaccination is partially responsible for higher mortality among girls in this study population. © 2013 John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

NASA Astrophysics Data System (ADS)

Abd Elazem, Nader Y.; Ebaid, Abdelhalim

2017-12-01

In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

A Model for Siderophile Element Distribution in Planetary Differentiation

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

Temporal expression profiles indicate a primary function for microRNA during the peak of DNA replication after rat partial hepatectomy.

PubMed

Raschzok, Nathanael; Werner, Wiebke; Sallmon, Hannes; Billecke, Nils; Dame, Christof; Neuhaus, Peter; Sauer, Igor M

2011-06-01

The liver has the unique capacity to regenerate after surgical resection. However, the regulation of liver regeneration is not completely understood. Recent reports indicate an essential role for small noncoding microRNAs (miRNAs) in the regulation of hepatic development, carcinogenesis, and early regeneration. We hypothesized that miRNAs are critically involved in all phases of liver regeneration after partial hepatectomy. We performed miRNA microarray analyses after 70% partial hepatectomy in rats under isoflurane anesthesia at different time points (0 h to 5 days) and after sham laparotomy. Putative targets of differentially expressed miRNAs were determined using a bioinformatic approach. Two-dimensional (2D)-PAGE proteomic analyses and protein identification were performed on specimens at 0 and 24 h after resection. The temporal dynamics of liver regeneration were characterized by 5-bromo- 2-deoxyuridine, proliferating cell nuclear antigen, IL-6, and hepatocyte growth factor. We demonstrate that miRNA expression patterns changed during liver regeneration and that these changes were most evident during the peak of DNA replication at 24 h after resection. Expression of 13 miRNAs was significantly reduced 12-48 h after resection (>25% change), out of which downreguation was confirmed in isolated hepatocytes for 6 miRNAs at 24 h, whereas three miRNAs were significantly upregulated. Proteomic analysis revealed 65 upregulated proteins; among them, 23 represent putative targets of the differentially expressed miRNAs. We provide a temporal miRNA expression and proteomic dataset of the regenerating rat liver, which indicates a primary function for miRNA during the peak of DNA replication. These data will assist further functional studies on the role of miRNAs during liver regeneration.

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

USGS Publications Warehouse

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

2002-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Discussion summary: Fictitious domain methods

NASA Technical Reports Server (NTRS)

Glowinski, Rowland; Rodrigue, Garry

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

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

PubMed

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

2002-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

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

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

2005-08-10

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

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

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

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

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

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

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

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

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

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

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

Liquid spreading under partial wetting conditions

NASA Astrophysics Data System (ADS)

Chen, M.; Pahlavan, A. A.; Cueto-Felgueroso, L.; McKinley, G. H.; Juanes, R.

2013-12-01

Traditional mathematical descriptions of multiphase flow in porous media rely on a multiphase extension of Darcy's law, and lead to nonlinear second-order (advection-diffusion) partial differential equations for fluid saturations. Here, we study horizontal redistribution of immiscible fluids. The traditional Darcy-flow model predicts that the spreading of a finite amount of liquid in a horizontal porous medium never stops; a prediction that is not substantiated by observation. To help guide the development of new models of multiphase flow in porous media [1], we draw an analogy with the flow of thin films. The flow of thin films over flat surfaces has been the subject of much theoretical, experimental and computational research [2]. Under the lubrication approximation, the classical mathematical model for these flows takes the form of a nonlinear fourth-order PDE, where the fourth-order term models the effect of surface tension [3]. This classical model, however, effectively assumes that the film is perfectly wetting to the substrate and, therefore, does not capture the partial wetting regime. Partial wetting is responsible for stopping the spread of a liquid puddle. Here, we present experiments of (large-volume) liquid spreading over a flat horizontal substrate in the partial wetting regime, and characterize the four spreading regimes that we observe. We extend our previous theoretical work of two-phase flow in a capillary tube [4], and develop a macroscopic phase-field modeling of thin-film flows with partial wetting. Our model naturally accounts for the dynamic contact angle at the contact line, and therefore permits modeling thin-film flows without invoking a precursor film, leading to compactly-supported solutions that reproduce the spreading dynamics and the static equilibrium configuration observed in the experiments. We anticipate that this modeling approach will provide a natural mathematical framework to describe spreading and redistribution of immiscible fluids in porous media. [1] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008). [2] D. Bonn et al., Rev. Mod. Phys. 81, 739-805 (2009). [3] H. E. Huppert, Nature 300, 427-429 (1982). [4] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 108, 144502 (2012).

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

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…

The distinguishing motor features of cataplexy: a study from video-recorded attacks.

PubMed

Pizza, Fabio; Antelmi, Elena; Vandi, Stefano; Meletti, Stefano; Erro, Roberto; Baumann, Christian R; Bhatia, Kailash P; Dauvilliers, Yves; Edwards, Mark J; Iranzo, Alex; Overeem, Sebastiaan; Tinazzi, Michele; Liguori, Rocco; Plazzi, Giuseppe

2018-05-01

To describe the motor pattern of cataplexy and to determine its phenomenological differences from pseudocataplexy in the differential diagnosis of episodic falls. We selected 30 video-recorded cataplexy and 21 pseudocataplexy attacks in 17 and 10 patients evaluated for suspected narcolepsy and with final diagnosis of narcolepsy type 1 and conversion disorder, respectively, together with self-reported attacks features, and asked expert neurologists to blindly evaluate the motor features of the attacks. Video documented and self-reported attack features of cataplexy and pseudocataplexy were contrasted. Video-recorded cataplexy can be positively differentiated from pseudocataplexy by the occurrence of facial hypotonia (ptosis, mouth opening, tongue protrusion) intermingled by jerks and grimaces abruptly interrupting laughter behavior (i.e. smile, facial expression) and postural control (head drops, trunk fall) under clear emotional trigger. Facial involvement is present in both partial and generalized cataplexy. Conversely, generalized pseudocataplexy is associated with persistence of deep tendon reflexes during the attack. Self-reported features confirmed the important role of positive emotions (laughter, telling a joke) in triggering the attacks, as well as the more frequent occurrence of partial body involvement in cataplexy compared with pseudocataplexy. Cataplexy is characterized by abrupt facial involvement during laughter behavior. Video recording of suspected cataplexy attacks allows the identification of positive clinical signs useful for diagnosis and, possibly in the future, for severity assessment.

Describing the geographic spread of dengue disease by traveling waves.

PubMed

Maidana, Norberto Aníbal; Yang, Hyun Mo

2008-09-01

Dengue is a human disease transmitted by the mosquito Aedes aegypti. For this reason geographical regions infested by this mosquito species are under the risk of dengue outbreaks. In this work, we propose a mathematical model to study the spatial dissemination of dengue using a system of partial differential reaction-diffusion equations. With respect to the human and mosquito populations, we take into account their respective subclasses of infected and uninfected individuals. The dynamics of the mosquito population considers only two subpopulations: the winged form (mature female mosquitoes), and an aquatic population (comprising eggs, larvae and pupae). We disregard the long-distance movement by transportation facilities, for which reason the diffusion is considered restricted only to the winged form. The human population is considered homogeneously distributed in space, in order to describe localized dengue dissemination during a short period of epidemics. The cross-infection is modeled by the law of mass action. A threshold value as a function of the model's parameters is obtained, which determines the rate of dengue dissemination and the risk of dengue outbreaks. Assuming that an area was previously colonized by the mosquitoes, the rate of disease dissemination is determined as a function of the model's parameters. This rate of dissemination of dengue disease is determined by applying the traveling wave solutions to the corresponding system of partial differential equations.

Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

NASA Astrophysics Data System (ADS)

Becker, Roland; Vexler, Boris

2005-06-01

We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.

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

PubMed

Chirikjian; Wang

2000-07-01

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

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

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

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

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

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

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

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

1988-03-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

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

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

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

Evidence that differentiation-inducing factor-1 controls chemotaxis and cell differentiation, at least in part, via mitochondria in D. discoideum.

PubMed

Kubohara, Yuzuru; Kikuchi, Haruhisa; Nguyen, Van Hai; Kuwayama, Hidekazu; Oshima, Yoshiteru

2017-06-15

Differentiation-inducing factor-1 [1-(3,5-dichloro-2,6-dihydroxy-4-methoxyphenyl)hexan-1-one (DIF-1)] is an important regulator of cell differentiation and chemotaxis in the development of the cellular slime mold Dictyostelium discoideum However, the entire signaling pathways downstream of DIF-1 remain to be elucidated. To characterize DIF-1 and its potential receptor(s), we synthesized two fluorescent derivatives of DIF-1, boron-dipyrromethene (BODIPY)-conjugated DIF-1 (DIF-1-BODIPY) and nitrobenzoxadiazole (NBD)-conjugated DIF-1 (DIF-1-NBD), and investigated their biological activities and cellular localization. DIF-1-BODIPY (5 µM) and DIF-1 (2 nM) induced stalk cell differentiation in the DIF-deficient strain HM44 in the presence of cyclic adenosine monosphosphate (cAMP), whereas DIF-1-NBD (5 µM) hardly induced stalk cell differentiation under the same conditions. Microscopic analyses revealed that the biologically active derivative, DIF-1-BODIPY, was incorporated by stalk cells at late stages of differentiation and was localized to mitochondria. The mitochondrial uncouplers carbonyl cyanide m -chlorophenylhydrazone (CCCP), at 25-50 nM, and dinitrophenol (DNP), at 2.5-5 µM, induced partial stalk cell differentiation in HM44 in the presence of cAMP. DIF-1-BODIPY (1-2 µM) and DIF-1 (10 nM), as well as CCCP and DNP, suppressed chemotaxis in the wild-type strain Ax2 in shallow cAMP gradients. These results suggest that DIF-1-BODIPY and DIF-1 induce stalk cell differentiation and modulate chemotaxis, at least in part, by disturbing mitochondrial activity. © 2017. Published by The Company of Biologists Ltd.

Evidence that differentiation-inducing factor-1 controls chemotaxis and cell differentiation, at least in part, via mitochondria in D. discoideum

PubMed Central

Kikuchi, Haruhisa; Nguyen, Van Hai; Kuwayama, Hidekazu; Oshima, Yoshiteru

2017-01-01

ABSTRACT Differentiation-inducing factor-1 [1-(3,5-dichloro-2,6-dihydroxy-4-methoxyphenyl)hexan-1-one (DIF-1)] is an important regulator of cell differentiation and chemotaxis in the development of the cellular slime mold Dictyostelium discoideum. However, the entire signaling pathways downstream of DIF-1 remain to be elucidated. To characterize DIF-1 and its potential receptor(s), we synthesized two fluorescent derivatives of DIF-1, boron-dipyrromethene (BODIPY)-conjugated DIF-1 (DIF-1-BODIPY) and nitrobenzoxadiazole (NBD)-conjugated DIF-1 (DIF-1-NBD), and investigated their biological activities and cellular localization. DIF-1-BODIPY (5 µM) and DIF-1 (2 nM) induced stalk cell differentiation in the DIF-deficient strain HM44 in the presence of cyclic adenosine monosphosphate (cAMP), whereas DIF-1-NBD (5 µM) hardly induced stalk cell differentiation under the same conditions. Microscopic analyses revealed that the biologically active derivative, DIF-1-BODIPY, was incorporated by stalk cells at late stages of differentiation and was localized to mitochondria. The mitochondrial uncouplers carbonyl cyanide m-chlorophenylhydrazone (CCCP), at 25–50 nM, and dinitrophenol (DNP), at 2.5–5 µM, induced partial stalk cell differentiation in HM44 in the presence of cAMP. DIF-1-BODIPY (1–2 µM) and DIF-1 (10 nM), as well as CCCP and DNP, suppressed chemotaxis in the wild-type strain Ax2 in shallow cAMP gradients. These results suggest that DIF-1-BODIPY and DIF-1 induce stalk cell differentiation and modulate chemotaxis, at least in part, by disturbing mitochondrial activity. PMID:28619991

Differential interactions between Curtobacterium flaccumfaciens pv. flaccumfaciens and common bean.

PubMed

Valdo, S C D; Wendland, A; Araújo, L G; Melo, L C; Pereira, H S; Melo, P G; Faria, L C

2016-11-21

Bacterial wilt of common bean caused by Curtobacterium flaccumfaciens pv. flaccumfaciens is an important disease in terms of economic importance. It reduces grain yield by colonizing xylem vessels, subsequently impeding the translocation of water and nutrients to the superior plant parts. The existence of physiological races in C. flaccumfaciens pv. flaccumfaciens has not so far been reported. The objective of the present investigation was to identify physiological races, evaluate differential interaction, and select resistant genotypes of common bean. Initially, 30 genotypes of common bean were inoculated with eight isolates exhibiting different levels of aggressiveness, under controlled greenhouse conditions. Disease was assessed 15 days after inoculation. The existence of differential interactions between C. flaccumfaciens pv. flaccumfaciens isolates and common bean genotypes were identified by utilizing partial diallel analysis. The most aggressive isolates were BRM 14939 and BRM 14942 and the least aggressive isolates were BRM 14941 and BRM 14946. The genotypes IPA 9, Ouro Branco, and Michelite were selected as more resistant among the test isolates. The genotypes IAC Carioca Akytã, BRS Notável, Pérola, IAC Carioca Aruã, and Coquinho contributed more to the isolate x genotype interaction according to the ecovalence method of estimation, and were, therefore, indicated as differentials. Based on these results, it was possible to conclude that physiological races of the pathogen exist, to select resistant genotypes, and to propose a set of differentials.

Brain Natriuretic Peptide Stimulates Lipid Metabolism through Its Receptor NPR1 and the Glycerolipid Metabolism Pathway in Chicken Adipocytes.

PubMed

Huang, H Y; Zhao, G P; Liu, R R; Li, Q H; Zheng, M Q; Li, S F; Liang, Z; Zhao, Z H; Wen, J

2015-11-03

Brain natriuretic peptide (BNP) is related to lipid metabolism in mammals, but its effect and the molecular mechanisms underlying it in chickens are incompletely understood. We found that the level of natriuretic peptide precursor B (NPPB, which encodes BNP) mRNA expression in high-abdominal-fat chicken groups was significantly higher than that of low-abdominal-fat groups. Partial correlations indicated that changes in the weight of abdominal fat were positively correlated with NPPB mRNA expression level. In vitro, compared with the control group, preadipocytes with NPPB interference showed reduced levels of proliferation, differentiation, and glycerin in media. Treatments of cells with BNP led to enhanced proliferation and differentiation of cells and glycerin concentration, and mRNA expression of its receptor natriuretic peptide receptor 1 (NPR1) was upregulated significantly. In cells exposed to BNP, 482 differentially expressed genes were identified compared with controls without BNP. Four genes known to be related to lipid metabolism (diacylglycerol kinase; lipase, endothelial; 1-acylglycerol-3-phosphate O-acyltransferase 1; and 1-acylglycerol-3-phosphate O-acyltransferase 2) were enriched in the glycerolipid metabolism pathway and expressed differentially. In conclusion, BNP stimulates the proliferation, differentiation, and lipolysis of preadipocytes through upregulation of the levels of expression of its receptor NPR1 and key genes enriched in the glycerolipid metabolic pathway.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

High oxygen condition facilitates the differentiation of mouse and human pluripotent stem cells into pancreatic progenitors and insulin-producing cells.

PubMed

Hakim, Farzana; Kaitsuka, Taku; Raeed, Jamiruddin Mohd; Wei, Fan-Yan; Shiraki, Nobuaki; Akagi, Tadayuki; Yokota, Takashi; Kume, Shoen; Tomizawa, Kazuhito

2014-04-04

Pluripotent stem cells have potential applications in regenerative medicine for diabetes. Differentiation of stem cells into insulin-producing cells has been achieved using various protocols. However, both the efficiency of the method and potency of differentiated cells are insufficient. Oxygen tension, the partial pressure of oxygen, has been shown to regulate the embryonic development of several organs, including pancreatic β-cells. In this study, we tried to establish an effective method for the differentiation of induced pluripotent stem cells (iPSCs) into insulin-producing cells by culturing under high oxygen (O2) conditions. Treatment with a high O2 condition in the early stage of differentiation increased insulin-positive cells at the terminus of differentiation. We found that a high O2 condition repressed Notch-dependent gene Hes1 expression and increased Ngn3 expression at the stage of pancreatic progenitors. This effect was caused by inhibition of hypoxia-inducible factor-1α protein level. Moreover, a high O2 condition activated Wnt signaling. Optimal stage-specific treatment with a high O2 condition resulted in a significant increase in insulin production in both mouse embryonic stem cells and human iPSCs and yielded populations containing up to 10% C-peptide-positive cells in human iPSCs. These results suggest that culturing in a high O2 condition at a specific stage is useful for the efficient generation of insulin-producing cells.

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

PubMed

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

2017-08-01

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

Incomplete response to artificial tears is associated with features of neuropathic ocular pain.

PubMed

Galor, Anat; Batawi, Hatim; Felix, Elizabeth R; Margolis, Todd P; Sarantopoulos, Konstantinos D; Martin, Eden R; Levitt, Roy C

2016-06-01

Artificial tears are first-line therapy for patients with dry eye symptoms. It is not known, however, which patient factors associate with a positive response to therapy. The purpose of this study was to evaluate whether certain ocular and systemic findings are associated with a differential subjective response to artificial tears. Cross-sectional study of 118 individuals reporting artificial tears use (hypromellose 0.4%) to treat dry eye-associated ocular pain. An evaluation was performed to assess dry eye symptoms (via the dry eye questionnaire 5 and ocular surface disease index), ocular and systemic (non-ocular) pain complaints and ocular signs (tear osmolarity, tear breakup time, corneal staining, Schirmer testing with anaesthesia, and eyelid and meibomian gland assessment). The main outcome measures were factors associated with differential subjective response to artificial tears. By self-report, 23 patients reported no improvement, 73 partial improvement and 22 complete improvement in ocular pain with artificial tears. Patients who reported no or partial improvement in pain with artificial tears reported higher levels of hot-burning ocular pain and sensitivity to wind compared with those with complete improvement. Patients were also asked to rate the intensity of systemic pain elsewhere in the body (other than the eye). Patients who reported no or incomplete improvement with artificial tears had higher systemic pain scores compared with those with complete improvement. Both ocular and systemic (non-ocular) pain complaints are associated with a differential subjective response to artificial tears. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

The opioid receptor pharmacology of GSK1521498 compared to other ligands with differential effects on compulsive reward-related behaviours.

PubMed

Kelly, Eamonn; Mundell, Stuart J; Sava, Anna; Roth, Adelheid L; Felici, Antonio; Maltby, Kay; Nathan, Pradeep J; Bullmore, Edward T; Henderson, Graeme

2015-01-01

The novel opioid receptor antagonist, GSK1421498, has been shown to attenuate reward-driven compulsive behaviours, such as stimulant drug seeking or binge eating, in animals and humans. Here, we report new data on the receptor pharmacology of GSK121498, in comparison to naltrexone, naloxone, 6-β-naltrexol and nalmefene. To determine whether the novel opioid antagonist, GSK1521498, is an orthosteric or allosteric antagonist at the μ opioid receptor (MOPr) and whether it has neutral antagonist or inverse agonist properties. A combination of radioligand binding assays and [(35)S]GTPγS binding assays was employed. GSK1521498 completely displaced [(3)H]naloxone binding to MOPr and did not alter the rate of [(3)H]naloxone dissociation from MOPr observations compatible with it binding to the orthosteric site on MOPr. GSK1521498 exhibited inverse agonism when MOPr was overexpressed but not when the level of MOPr expression was low. In parallel studies under conditions of high receptor expression density, naloxone, naltrexone, 6-β-naltrexol and nalmefene exhibited partial agonism, not inverse agonism as has been reported previously for naloxone and naltrexone. In brain tissue from mice receiving a prolonged morphine pre-treatment, GSK1521498 exhibited slight inverse agonism. Differences between GSK1521498 and naltrexone in their effects on compulsive reward seeking are arguably linked to the more selective and complete MOPr antagonism of GSK1521498 versus the partial MOPr agonism of naltrexone. GSK1521498 is also pharmacologically differentiated by its inverse agonist efficacy at high levels of MOPr expression, but this may be less likely to contribute to behavioural differentiation at patho-physiological levels of expression.

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

ERIC Educational Resources Information Center

Cornelius, Tara L.; Owen-DeSchryver, Jamie

2008-01-01

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

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

NASA Astrophysics Data System (ADS)

Khan, Noor Saeed

2018-04-01

The bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. A real-life system evolves under the flow and various taxis. The study is initially proposed in the context of gyrotactic system, which is used as a key element for the description of complex bioconvection patterns and dynamics in such systems. The governing partial differential equations are transformed into a system of ordinary ones through the similarity variables and solved analytically via homotopy analysis method (HAM). The solution is expressed through graphs and illustrated which show the influences of all the parameters.

Bioconvection in Second Grade Nanofluid Flow Containing Nanoparticles and Gyrotactic Microorganisms

NASA Astrophysics Data System (ADS)

Khan, Noor Saeed

2018-06-01

The bioconvection in steady second grade nanofluid thin film flow containing nanoparticles and gyrotactic microorganisms is considered using passively controlled nanofluid model boundary conditions. A real-life system evolves under the flow and various taxis. The study is initially proposed in the context of gyrotactic system, which is used as a key element for the description of complex bioconvection patterns and dynamics in such systems. The governing partial differential equations are transformed into a system of ordinary ones through the similarity variables and solved analytically via homotopy analysis method (HAM). The solution is expressed through graphs and illustrated which show the influences of all the parameters.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

PubMed

Sheng, Yin; Zhang, Hao; Zeng, Zhigang

2017-10-01

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Differential Diptera succession patterns onto partially burned and unburned pig carrion in southeastern Brazil.

PubMed

Oliveira-Costa, J; Lamego, C M D; Couri, M S; Mello-Patiu, C A

2014-11-01

In the present contribution we compared the entomological succession pattern of a burned carcass with that of an unburned one. For that, we used domestic pig carcasses and focused on Calliphoridae, Muscidae and Sarcophagidae flies, because they are the ones most commonly used in Postmortem Interval estimates. Adult and immature flies were collected daily. A total of 27 species and 2,498 specimens were collected, 1,295 specimens of 26 species from the partially burned carcass and 1,203 specimens of 22 species from the control carcass (unburned). The species composition in the two samples differed, and the results of the similarity measures were 0.875 by Sorensen and 0.756 by Bray-Curtis index. The results obtained for both carcasses also differ with respect to the decomposition process, indicating that the post mortem interval would be underestimated if the entomological succession pattern observed for a carcass under normal conditions was applied to a carbonized carcass.

Chromatin Switches during Neural Cell Differentiation and Their Dysregulation by Prenatal Alcohol Exposure.

PubMed

Gavin, David P; Grayson, Dennis R; Varghese, Sajoy P; Guizzetti, Marina

2017-05-11

Prenatal alcohol exposure causes persistent neuropsychiatric deficits included under the term fetal alcohol spectrum disorders (FASD). Cellular identity emerges from a cascade of intrinsic and extrinsic (involving cell-cell interactions and signaling) processes that are partially initiated and maintained through changes in chromatin structure. Prenatal alcohol exposure influences neuronal and astrocyte development, permanently altering brain connectivity. Prenatal alcohol exposure also alters chromatin structure through histone and DNA modifications. However, the data linking alcohol-induced differentiation changes with developmental alterations in chromatin structure remain to be elucidated. In the first part of this review, we discuss the sequence of chromatin structural changes involved in neural cell differentiation during normal development. We then discuss the effects of prenatal alcohol on developmental histone modifications and DNA methylation in the context of neurogenesis and astrogliogenesis. We attempt to synthesize the developmental literature with the FASD literature, proposing that alcohol-induced changes to chromatin structure account for altered neurogenesis and astrogliogenesis as well as altered neuron and astrocyte differentiation. Together these changes may contribute to the cognitive and behavioral abnormalities in FASD. Future studies using standardized alcohol exposure paradigms at specific developmental stages will advance the understanding of how chromatin structural changes impact neural cell fate and maturation in FASD.

Chromatin Switches during Neural Cell Differentiation and Their Dysregulation by Prenatal Alcohol Exposure

PubMed Central

Gavin, David P.; Grayson, Dennis R.; Varghese, Sajoy P.; Guizzetti, Marina

2017-01-01

Prenatal alcohol exposure causes persistent neuropsychiatric deficits included under the term fetal alcohol spectrum disorders (FASD). Cellular identity emerges from a cascade of intrinsic and extrinsic (involving cell-cell interactions and signaling) processes that are partially initiated and maintained through changes in chromatin structure. Prenatal alcohol exposure influences neuronal and astrocyte development, permanently altering brain connectivity. Prenatal alcohol exposure also alters chromatin structure through histone and DNA modifications. However, the data linking alcohol-induced differentiation changes with developmental alterations in chromatin structure remain to be elucidated. In the first part of this review, we discuss the sequence of chromatin structural changes involved in neural cell differentiation during normal development. We then discuss the effects of prenatal alcohol on developmental histone modifications and DNA methylation in the context of neurogenesis and astrogliogenesis. We attempt to synthesize the developmental literature with the FASD literature, proposing that alcohol-induced changes to chromatin structure account for altered neurogenesis and astrogliogenesis as well as altered neuron and astrocyte differentiation. Together these changes may contribute to the cognitive and behavioral abnormalities in FASD. Future studies using standardized alcohol exposure paradigms at specific developmental stages will advance the understanding of how chromatin structural changes impact neural cell fate and maturation in FASD. PMID:28492482

Glial kon/NG2 gene network for central nervous system repair.

PubMed

Losada-Perez, Maria; Harrison, Neale; Hidalgo, Alicia

2017-01-01

The glial regenerative response to central nervous system (CNS) injury, although limited, can be harnessed to promote regeneration and repair. Injury provokes the proliferation of ensheathing glial cells, which can differentiate to remyelinate axons, and partially restore function. This response is evolutionarily conserved, strongly implying an underlying genetic mechanism. In mammals, it is elicited by NG2 glia, but most often newly generated cells fail to differentiate. Thus an important goal had been to find out how to promote glial differentiation following the proliferative response. A gene network involving Notch and prospero (pros) controls the balance between glial proliferation and differentiation in flies and mice, and promotes CNS repair at least in fruit-flies. A key missing link had been how to relate the function of NG2 to this gene network. Recent findings by Losada-Perez et al., published in JCB, demonstrated that the Drosophila NG2 homologue kon-tiki (kon) is functionally linked to Notch and pros in glia. By engaging in two feedback loops with Notch and Pros, in response to injury, Kon can regulate both glial cell number and glial shape homeostasis, essential for repair. Drosophila offers powerful genetics to unravel the control of stem and progenitor cells for regeneration and repair.

The impact of Wnt signalling and hypoxia on osteogenic and cementogenic differentiation in human periodontal ligament cells

PubMed Central

Li, Shuigen; Shao, Jin; Zhou, Yinghong; Friis, Thor; Yao, Jiangwu; Shi, Bin; Xiao, Yin

2016-01-01

Cementum is a periodontal support tissue that is directly connected to the periodontal ligament. It shares common traits with bone tissues, however, unlike bone, the cementum has a limited capacity for regeneration. As a result, following damage the cementum rarely, if ever, regenerates. Periodontal ligament cells (PDLCs) are able to differentiate into osteoblastic and cementogenic lineages according to specific local environmental conditions, including hypoxia, which is induced by inflammation or activation of the Wnt signalling pathway by local loading. The interactions between the Wnt signalling pathway and hypoxia during cementogenesis are of particular interest to improve the understanding of periodontal tissue regeneration. In the present study, osteogenic and cementogenic differentiation of PDLCs was investigated under hypoxic conditions in the presence and absence of Wnt pathway activation. Protein and gene expression of the osteogenic markers type 1 collagen (COL1) and runt-related transcription factor 2 (RUNX2), and cementum protein 1 (CEMP1) were used as markers for osteogenic and cementogenic differentiation, respectively. Wnt signalling activation inhibited cementogenesis, whereas hypoxia alone did not affect PDLC differentiation. However, hypoxia reversed the inhibition of cementogenesis that resulted from overexpression of Wnt signalling. Cross-talk between hypoxia and Wnt signalling pathways was, therefore, demonstrated to be involved in the differentiation of PDLCs to the osteogenic and cementogenic lineages. In summary, the present study suggests that the differentiation of PDLCs into osteogenic and cementogenic lineages is partially regulated by the Wnt signalling pathway and that hypoxia is also involved in this process. PMID:27840938

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

PubMed

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

2012-09-01

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

Local algebraic analysis of differential systems

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2015-06-01

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

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

PubMed

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

2015-06-01

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

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

PubMed

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

2009-11-01

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

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

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

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

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

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

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

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

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

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

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

NASA Astrophysics Data System (ADS)

de la Madrid, Rafael

2015-08-01

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

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

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

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

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

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

Patterns of differentiation among endangered pondberry populations

Treesearch

Craig S Echt; Dennis Deemer; Danny Gustafson

2011-01-01

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

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

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

2006-05-01

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

Partial differential equation models in the socio-economic sciences.

PubMed

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

2014-11-13

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

Estimating varying coefficients for partial differential equation models.

PubMed

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

2017-09-01

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

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

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

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

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

NASA Technical Reports Server (NTRS)

Chang, S. C.

1984-01-01

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

Solution of partial differential equations on vector and parallel computers

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Analytical solutions for systems of partial differential-algebraic equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

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

Time-partitioning simulation models for calculation on parallel computers

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Inheritance of partial resistance against Colletotrichum lindemuthianum in Phaseolus vulgaris and co-localization of quantitative trait loci with genes involved in specific resistance.

PubMed

Geffroy, V; Sévignac, M; De Oliveira, J C; Fouilloux, G; Skroch, P; Thoquet, P; Gepts, P; Langin, T; Dron, M

2000-03-01

Anthracnose, one of the most important diseases of common bean (Phaseolus vulgaris), is caused by the fungus Colletotrichum lindemuthianum. A "candidate gene" approach was used to map anthracnose resistance quantitative trait loci (QTL). Candidate genes included genes for both pathogen recognition (resistance genes and resistance gene analogs [RGAs]) and general plant defense (defense response genes). Two strains of C. lindemuthianum, identified in a world collection of 177 strains, displayed a reproducible and differential aggressiveness toward BAT93 and JaloEEP558, two parental lines of P. vulgaris representing the two major gene pools of this crop. A reliable test was developed to score partial resistance in aerial organs of the plant (stem, leaf, petiole) under controlled growth chamber conditions. BAT93 was more resistant than JaloEEP558 regardless of the organ or strain tested. With a recombinant inbred line (RIL) population derived from a cross between these two parental lines, 10 QTL were located on a genetic map harboring 143 markers, including known defense response genes, anthracnose-specific resistance genes, and RGAs. Eight of the QTL displayed isolate specificity. Two were co-localized with known defense genes (phenylalanine ammonia-lyase and hydroxyproline-rich glycoprotein) and three with anthracnose-specific resistance genes and/or RGAs. Interestingly, two QTL, with different allelic contribution, mapped on linkage group B4 in a 5.0 cM interval containing Andean and Mesoamerican specific resistance genes against C. lindemuthianum and 11 polymorphic fragments revealed with a RGA probe. The possible relationship between genes underlying specific and partial resistance is discussed.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

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

PubMed

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

2017-04-01

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

Epidermal differentiation during ontogeny and after hatching in the snake Liasis fuscus (Pythonidae, Serpentes, Reptilia), with emphasis on the formation of the shedding complex.

PubMed

Alibardi, L; Thompson, M B

2003-04-01

Differentiation and localization of keratin in the epidermis during embryonic development and up to 3 months posthatching in the Australian water python, Liasis fuscus, was studied by ultrastructural and immunocytochemical methods. Scales arise from dome-like folds in the skin that produce tightly imbricating scales. The dermis of these scales is completely differentiated before any epidermal differentiation begins, with a loose dermis made of mesenchymal cells beneath the differentiating outer scale surface. At this stage (33) the embryo is still unpigmented and two layers of suprabasal cells contain abundant glycogen. At Stage 34 (beginning of pigmentation) the first layers of cells beneath the bilayered periderm (presumptive clear and oberhautchen layers) have not yet formed a shedding complex, within which prehatching shedding takes place. At Stage 35 the shedding complex, consisting of the clear and oberhautchen layers, is discernible. The clear layer contains a fine fibrous network that faces the underlying oberhautchen, where the spinulae initially contain a core of fibrous material and small beta-keratin packets. Differentiation continues at Stage 36 when the beta-layer forms and beta-keratin packets are deposited both on the fibrous core of the oberhautchen and within beta-cells. Mesos cells are produced from the germinal layer but remain undifferentiated. At Stage 37, before hatching, the beta-layer is compact, the mesos layer contains mesos granules, and cells of the alpha-layer are present but are not yet keratinized. They are still only partially differentiated a few hours after hatching, when a new shedding complex is forming underneath. Using antibodies against chick scale beta-keratin resolved at high magnification with immunofluorescent or immunogold conjugates, we offer the first molecular confirmation that in snakes only the oberhautchen component of the shedding complex and the underlying beta cells contain beta-keratin. Initially, there is little immunoreactivity in the small beta-packets of the oberhautchen, but it increases after fusion with the underlying cells to produce the syncytial beta layer. The beta-keratin packets coalesce with the tonofilaments, including those attached to desmosomes, which rapidly disappear in both oberhautchen and beta-cells as differentiation progresses. The labeling is low to absent in forming mesos-cells beneath the beta-layer. This study further supports the hypothesis that the shedding complex in lepidosaurian reptiles evolved after there was a segregation between alpha-keratogenic cells from beta-keratogenic cells during epidermal renewal. Copyright 2003 Wiley-Liss, Inc.

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

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

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

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

A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Farajpour, A.

2018-03-01

In this study, the buckling behavior of a three-layered composite nanoplate reinforced with shape memory alloy (SMA) nanowires is examined. Whereas the upper and lower layers are reinforced with typical nanowires, SMA nanoscale wires are used to strengthen the middle layer of the system. The composite nanoplate is assumed to be under the action of biaxial compressive loading. A scale-dependent mathematical model is presented with the consideration of size effects within the context of the Eringen’s nonlocal continuum mechanics. Using the one-dimensional Brinson’s theory and the Kirchhoff theory of plates, the governing partial differential equations of SMA nanowire-reinforced hybrid nanoplates are derived. Both lateral and longitudinal deflections are taken into consideration in the theoretical formulation and method of solution. In order to reduce the governing differential equations to their corresponding algebraic equations, a discretization approach based on the differential quadrature method is employed. The critical buckling loads of the hybrid nanosystem with various boundary conditions are obtained with the use of a standard eigenvalue solver. It is found that the stability response of SMA composite nanoplates is strongly sensitive to the small scale effect.

Cytochrome b based genetic differentiation of Indian wild pig (Sus scrofa cristatus) and domestic pig (Sus scrofa domestica) and its use in wildlife forensics.

PubMed

Gupta, Sandeep Kumar; Kumar, Ajit; Hussain, Syed Ainul; Vipin; Singh, Lalji

2013-06-01

The Indian wild pig (Sus scrofa cristatus) is a protected species and listed in the Indian Wildlife (Protection) Act, 1972. The wild pig is often hunted illegally and sold in market as meat warranting punishment under law. To avoid confusion in identification of these two subspecies during wildlife forensic examinations, we describe genetic differentiation of Indian wild and domestic pigs using a molecular technique. Analysis of sequence generated from the partial fragment (421bp) of mitochondrial DNA (mtDNA) cytochrome b (Cyt b) gene exhibited unambiguous (>3%) genetic variation between Indian wild and domestic pigs. We observed nine forensically informative nucleotide sequence (FINS) variations between Indian wild and domestic pigs. The overall genetic variation described in this study is helpful in forensic identification of the biological samples of wild and domestic pigs. It also helped in differentiating the Indian wild pig from other wild pig races. This study indicates that domestic pigs in India are not descendent of the Indian wild pig, however; they are closer to the other wild pig races found in Asia and Europe. Copyright © 2012 Forensic Science Society. Published by Elsevier Ireland Ltd. All rights reserved.

Organization of the cytokeratin network in an epithelial cell.

PubMed

Portet, Stéphanie; Arino, Ovide; Vassy, Jany; Schoëvaërt, Damien

2003-08-07

The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.

Response of rice genotypes to weed competition in dry direct-seeded rice in India.

PubMed

Mahajan, Gulshan; Ramesha, Mugalodi S; Chauhan, Bhagirath S

2014-01-01

The differential weed-competitive abilities of eight rice genotypes and the traits that may confer such attributes were investigated under partial weedy and weed-free conditions in naturally occurring weed flora in dry direct-seeded rice during the rainy seasons of 2011 and 2012 at Ludhiana, Punjab, India. The results showed genotypic differences in competitiveness against weeds. In weed-free plots, grain yield varied from 6.6 to 8.9 t ha(-1) across different genotypes; it was lowest for PR-115 and highest for the hybrid H-97158. In partial weedy plots, grain yield and weed biomass at flowering varied from 3.6 to 6.7 t ha(-1) and from 174 to 419 g m(-2), respectively. In partial weedy plots, grain yield was lowest for PR-115 and highest for PR-120. Average yield loss due to weed competition ranged from 21 to 46% in different rice genotypes. The study showed that early canopy closure, high leaf area index at early stage, and high root biomass and volume correlated positively with competitiveness. This study suggests that some traits (root biomass, leaf area index, and shoot biomass at the early stage) could play an important role in conferring weed competitiveness and these traits can be explored for dry-seeded rice.

Response of Rice Genotypes to Weed Competition in Dry Direct-Seeded Rice in India

PubMed Central

Mahajan, Gulshan; Ramesha, Mugalodi S.; Chauhan, Bhagirath S.

2014-01-01

The differential weed-competitive abilities of eight rice genotypes and the traits that may confer such attributes were investigated under partial weedy and weed-free conditions in naturally occurring weed flora in dry direct-seeded rice during the rainy seasons of 2011 and 2012 at Ludhiana, Punjab, India. The results showed genotypic differences in competitiveness against weeds. In weed-free plots, grain yield varied from 6.6 to 8.9 t ha−1 across different genotypes; it was lowest for PR-115 and highest for the hybrid H-97158. In partial weedy plots, grain yield and weed biomass at flowering varied from 3.6 to 6.7 t ha−1 and from 174 to 419 g m−2, respectively. In partial weedy plots, grain yield was lowest for PR-115 and highest for PR-120. Average yield loss due to weed competition ranged from 21 to 46% in different rice genotypes. The study showed that early canopy closure, high leaf area index at early stage, and high root biomass and volume correlated positively with competitiveness. This study suggests that some traits (root biomass, leaf area index, and shoot biomass at the early stage) could play an important role in conferring weed competitiveness and these traits can be explored for dry-seeded rice. PMID:25093205

Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

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

Mixed convection flow of a nanofluid containing gyrotactic microorganisms over a stretching/shrinking sheet in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Aman, Fazlina; Mohamad Khazim, Wan Nor Hafizah Wan; Mansur, Syahira

2017-09-01

Interaction of motile microorganisms and nanoparticles along with buoyancy forces will produce nanofluid bioconvection. Bioconvection happened because of the microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend. In this paper, we investigated the problem of mixed convection flow of a nanofluid combined with gyrotactic microorganisms over a stretching/shrinking sheet under the influence of magnetic field. The nonlinear partial differential equations are transformed into a set of five similarities nonlinear ordinary differential equations by using similarity transformation, before being solved numerically. Some of the governing parameters involve in this problem are magnetic parameter, stretching/shrinking parameter, Brownian motion parameter, thermophoresis parameter and Prandtl number. Using tables and graphs, the consequences of numerous parameters on the flow and heat transfer features are examined and discussed. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms are strongly affected by the governing parameters.

Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nanoparticles

NASA Astrophysics Data System (ADS)

Raju, C. S. K.; Sekhar, K. R.; Ibrahim, S. M.; Lorenzini, G.; Viswanatha Reddy, G.; Lorenzini, E.

2017-05-01

In this study, we proposed a theoretical investigation on the temperature-dependent viscosity effect on magnetohydrodynamic dissipative nanofluid over a truncated cone with heat source/sink. The involving set of nonlinear partial differential equations is transforming to set of nonlinear ordinary differential equations by using self-similarity solutions. The transformed governing equations are solved numerically using Runge-Kutta-based Newton's technique. The effects of various dimensionless parameters on the skin friction coefficient and the local Nusselt number profiles are discussed and presented with the support of graphs. We also obtained the validation of the current solutions with existing solution under some special cases. The water-based titanium alloy has a lesser friction factor coefficient as compared with kerosene-based titanium alloy, whereas the rate of heat transfer is higher in water-based titanium alloy compared with kerosene-based titanium alloy. From this we can highlight that depending on the industrial needs cooling/heating chooses the water- or kerosene-based titanium alloys.

An approach to get thermodynamic properties from speed of sound

NASA Astrophysics Data System (ADS)

Núñez, M. A.; Medina, L. A.

2017-01-01

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

MHD Effect on Unsteady Mixed Convection Boundary Layer Flow past a Circular Cylinder with Constant Wall Temperature

NASA Astrophysics Data System (ADS)

Ismail, M. A.; Mohamad, N. F.; Ilias, M. R.; Shafie, S.

2017-09-01

Magnetohydrodynamic (MHD) effect is a study on motion of electrical-conducting fluid under magnetic fields. This effect has great intention due to its applications such as design of heat exchanger and nuclear reactor. In the problem in fluid motion, flow of separation can reduced the effectiveness of the system as well as can increased the energy lost. This study will present the results on reducing the flow separation by considering magnetic effect. In this study, unsteady mixed convection boundary layer flow past a circular cylinder is given attention. Focus of study is on the separation times that affected by the magnetic fields. The mathematical models in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effect of magnetic parameter on velocity and temperature profiles as well as skin friction and Nusselt number are studied.

Aeroelastic Analysis of Helicopter Rotor Blades Incorporating Anisotropic Piezoelectric Twist Actuation

NASA Technical Reports Server (NTRS)

Wilkie, W. Keats; Belvin, W. Keith; Park, K. C.

1996-01-01

A simple aeroelastic analysis of a helicopter rotor blade incorporating embedded piezoelectric fiber composite, interdigitated electrode blade twist actuators is described. The analysis consists of a linear torsion and flapwise bending model coupled with a nonlinear ONERA based unsteady aerodynamics model. A modified Galerkin procedure is performed upon the rotor blade partial differential equations of motion to develop a system of ordinary differential equations suitable for dynamics simulation using numerical integration. The twist actuation responses for three conceptual fullscale blade designs with realistic constraints on blade mass are numerically evaluated using the analysis. Numerical results indicate that useful amplitudes of nonresonant elastic twist, on the order of one to two degrees, are achievable under one-g hovering flight conditions for interdigitated electrode poling configurations. Twist actuation for the interdigitated electrode blades is also compared with the twist actuation of a conventionally poled piezoelectric fiber composite blade. Elastic twist produced using the interdigitated electrode actuators was found to be four to five times larger than that obtained with the conventionally poled actuators.

An aeroelastic analysis of helicopter rotor blades incorporating piezoelectric fiber composite twist actuation

NASA Technical Reports Server (NTRS)

Wilkie, W. Keats; Park, K. C.

1996-01-01

A simple aeroelastic analysis of a helicopter rotor blade incorporating embedded piezoelectric fiber composite, interdigitated electrode blade twist actuators is described. The analysis consist of a linear torsion and flapwise bending model coupled with a nonlinear ONERA based unsteady aerodynamics model. A modified Galerkin procedure is performed upon the rotor blade partial differential equations of motion to develop a system of ordinary differential equations suitable for numerical integration. The twist actuation responses for three conceptual full-scale blade designs with realistic constraints on blade mass are numerically evaluated using the analysis. Numerical results indicate that useful amplitudes of nonresonant elastic twist, on the order of one to two degrees, are achievable under one-g hovering flight conditions for interdigitated electrode poling configurations. Twist actuation for the interdigitated electrode blades is also compared with the twist actuation of a conventionally poled piezoelectric fiber composite blade. Elastic twist produced using the interdigitated electrode actuators was found to be four to five times larger than that obtained with the conventionally poled actuators.

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

PubMed

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

2007-10-20

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

PubMed Central

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

2008-01-01

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

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

PubMed

Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

2013-10-01

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

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

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

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

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

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

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

Constraints on the rheology of the partially molten mantle from numerical models of laboratory experiments

NASA Astrophysics Data System (ADS)

Rudge, J. F.; Alisic Jewell, L.; Rhebergen, S.; Katz, R. F.; Wells, G. N.

2015-12-01

One of the fundamental components in any dynamical model of melt transport is the rheology of partially molten rock. This rheology is poorly understood, and one way in which a better understanding can be obtained is by comparing the results of laboratory deformation experiments to numerical models. Here we present a comparison between numerical models and the laboratory setup of Qi et al. 2013 (EPSL), where a cylinder of partially molten rock containing rigid spherical inclusions was placed under torsion. We have replicated this setup in a finite element model which solves the partial differential equations describing the mechanical process of compaction. These computationally-demanding 3D simulations are only possible due to the recent development of a new preconditioning method for the equations of magma dynamics. The experiments show a distinct pattern of melt-rich and melt-depleted regions around the inclusions. In our numerical models, the pattern of melt varies with key rheological parameters, such as the ratio of bulk to shear viscosity, and the porosity- and strain-rate-dependence of the shear viscosity. These observed melt patterns therefore have the potential to constrain rheological properties. While there are many similarities between the experiments and the numerical models, there are also important differences, which highlight the need for better models of the physics of two-phase mantle/magma dynamics. In particular, the laboratory experiments display more pervasive melt-rich bands than is seen in our numerics.

Apolipoprotein E promotes lipid accumulation and differentiation in human adipocytes

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

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

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

Temperature gradient affects differentiation of gene expression and SNP allele frequencies in the dominant Lake Baikal zooplankton species.

PubMed

Bowman, Larry L; Kondrateva, Elizaveta S; Timofeyev, Maxim A; Yampolsky, Lev Y

2018-06-01

Local adaptation and phenotypic plasticity are main mechanisms of organisms' resilience in changing environments. Both are affected by gene flow and are expected to be weak in zooplankton populations inhabiting large continuous water bodies and strongly affected by currents. Lake Baikal, the deepest and one of the coldest lakes on Earth, experienced epilimnion temperature increase during the last 100 years, exposing Baikal's zooplankton to novel selective pressures. We obtained a partial transcriptome of Epischura baikalensis (Copepoda: Calanoida), the dominant component of Baikal's zooplankton, and estimated SNP allele frequencies and transcript abundances in samples from regions of Baikal that differ in multiyear average surface temperatures. The strongest signal in both SNP and transcript abundance differentiation is the SW-NE gradient along the 600+ km long axis of the lake, suggesting isolation by distance. SNP differentiation is stronger for nonsynonymous than synonymous SNPs and is paralleled by differential survival during a laboratory exposure to increased temperature, indicating directional selection operating on the temperature gradient. Transcript abundance, generally collinear with the SNP differentiation, shows samples from the warmest, less deep location clustering together with the southernmost samples. Differential expression is more frequent among transcripts orthologous to candidate thermal response genes previously identified in model arthropods, including genes encoding cytoskeleton proteins, heat-shock proteins, proteases, enzymes of central energy metabolism, lipid and antioxidant pathways. We conclude that the pivotal endemic zooplankton species in Lake Baikal exists under temperature-mediated selection and possesses both genetic variation and plasticity to respond to novel temperature-related environmental pressures. © 2018 John Wiley & Sons Ltd.

Animal tracking meets migration genomics: transcriptomic analysis of a partially migratory bird species.

PubMed

Franchini, Paolo; Irisarri, Iker; Fudickar, Adam; Schmidt, Andreas; Meyer, Axel; Wikelski, Martin; Partecke, Jesko

2017-06-01

Seasonal migration is a widespread phenomenon, which is found in many different lineages of animals. This spectacular behaviour allows animals to avoid seasonally adverse environmental conditions to exploit more favourable habitats. Migration has been intensively studied in birds, which display astonishing variation in migration strategies, thus providing a powerful system for studying the ecological and evolutionary processes that shape migratory behaviour. Despite intensive research, the genetic basis of migration remains largely unknown. Here, we used state-of-the-art radio-tracking technology to characterize the migratory behaviour of a partially migratory population of European blackbirds (Turdus merula) in southern Germany. We compared gene expression of resident and migrant individuals using high-throughput transcriptomics in blood samples. Analyses of sequence variation revealed a nonsignificant genetic structure between blackbirds differing by their migratory phenotype. We detected only four differentially expressed genes between migrants and residents, which might be associated with hyperphagia, moulting and enhanced DNA replication and transcription. The most pronounced changes in gene expression occurred between migratory birds depending on when, in relation to their date of departure, blood was collected. Overall, the differentially expressed genes detected in this analysis may play crucial roles in determining the decision to migrate, or in controlling the physiological processes required for the onset of migration. These results provide new insights into, and testable hypotheses for, the molecular mechanisms controlling the migratory phenotype and its underlying physiological mechanisms in blackbirds and other migratory bird species. © 2017 John Wiley & Sons Ltd.

Proteomic analysis of stress-related proteins and metabolic pathways in Picea asperata somatic embryos during partial desiccation.

PubMed

Jing, Danlong; Zhang, Jianwei; Xia, Yan; Kong, Lisheng; OuYang, Fangqun; Zhang, Shougong; Zhang, Hanguo; Wang, Junhui

2017-01-01

Partial desiccation treatment (PDT) stimulates germination and enhances the conversion of conifer somatic embryos. To better understand the mechanisms underlying the responses of somatic embryos to PDT, we used proteomic and physiological analyses to investigate these responses during PDT in Picea asperata. Comparative proteomic analysis revealed that, during PDT, stress-related proteins were mainly involved in osmosis, endogenous hormones, antioxidative proteins, molecular chaperones and defence-related proteins. Compared with those in cotyledonary embryos before PDT, these stress-related proteins remained at high levels on days 7 (D7) and 14 (D14) of PDT. The proteins that differentially accumulated in the somatic embryos on D7 were mapped to stress and/or stimuli. They may also be involved in the glyoxylate cycle and the chitin metabolic process. The most significant difference in the differentially accumulated proteins occurred in the metabolic pathways of photosynthesis on D14. Furthermore, in accordance with the changes in stress-related proteins, analyses of changes in water content, abscisic acid, indoleacetic acid and H 2 O 2 levels in the embryos indicated that PDT is involved in water-deficit tolerance and affects endogenous hormones. Our results provide insight into the mechanisms responsible for the transition from morphologically mature to physiologically mature somatic embryos during the PDT process in P. asperata. © 2016 The Authors. Plant Biotechnology Journal published by Society for Experimental Biology and The Association of Applied Biologists and John Wiley & Sons Ltd.

In vitro effect of mineralized and demineralized bone allografts on proliferation and differentiation of MG-63 osteoblast-like cells.

PubMed

Lafzi, Ardeshir; Vahabi, Surena; Ghods, Shadab; Torshabi, Maryam

2016-03-01

Due to the extensive use of bone allografts in bone reconstruction and periodontal therapy as suitable alternatives to autografts, they are now marketed under different commercial brands. Considering the controversial reports regarding the osteoinductive properties of bone allografts, this study sought to assess the effect of type (mineralized/demineralized), amount and particle size of several allografts on the proliferation and differentiation of MG-63 osteoblast-like cells. MG-63 cells (24-h culture) were exposed to 20 and 40 mg amounts of nine different commercially available freeze-dried bone allografts. After 24 and 72 h of incubation, the effect of water-soluble allograft released materials on cell viability and proliferation was assessed using methyl thiazol tetrazolium (MTT) assay after 24 and 72 h of exposure. Cell differentiation and mineralization was assessed by real-time quantitative reverse transcription PCR and alizarin red staining after 72 h of exposure. The amount and particle size of understudy allografts had significant effects on cell viability after 24 h of exposure (in contrast to 72 h). Higher rate of proliferation was seen in non-differentiated or slow-differentiated groups. The amount and particle size factors had no significant effect on the amount of calcified nodules or the expression of osteogenic marker genes in most groups. Faster and more distinct differentiation and mineralization was noted in mineralized compared to demineralized groups during the 3-day study period. Based on the results, the understudy mineralized (non-demineralized) bone allografts had greater effect on osteogenic differentiation of the MG-63 cells and showed more in vitro osteoinductive activity compared to partially demineralized and fully demineralized types.

Identifying States along the Hematopoietic Stem Cell Differentiation Hierarchy with Single Cell Specificity via Raman Spectroscopy.

PubMed

Ilin, Yelena; Choi, Ji Sun; Harley, Brendan A C; Kraft, Mary L

2015-11-17

A major challenge for expanding specific types of hematopoietic cells ex vivo for the treatment of blood cell pathologies is identifying the combinations of cellular and matrix cues that direct hematopoietic stem cells (HSC) to self-renew or differentiate into cell populations ex vivo. Microscale screening platforms enable minimizing the number of rare HSCs required to screen the effects of numerous cues on HSC fate decisions. These platforms create a strong demand for label-free methods that accurately identify the fate decisions of individual hematopoietic cells at specific locations on the platform. We demonstrate the capacity to identify discrete cells along the HSC differentiation hierarchy via multivariate analysis of Raman spectra. Notably, cell state identification is accurate for individual cells and independent of the biophysical properties of the functionalized polyacrylamide gels upon which these cells are cultured. We report partial least-squares discriminant analysis (PLS-DA) models of single cell Raman spectra enable identifying four dissimilar hematopoietic cell populations across the HSC lineage specification. Successful discrimination was obtained for a population enriched for long-term repopulating HSCs (LT-HSCs) versus their more differentiated progeny, including closely related short-term repopulating HSCs (ST-HSCs) and fully differentiated lymphoid (B cells) and myeloid (granulocytes) cells. The lineage-specific differentiation states of cells from these four subpopulations were accurately identified independent of the stiffness of the underlying biomaterial substrate, indicating subtle spectral variations that discriminated these populations were not masked by features from the culture substrate. This approach enables identifying the lineage-specific differentiation stages of hematopoietic cells on biomaterial substrates of differing composition and may facilitate correlating hematopoietic cell fate decisions with the extrinsic cues that elicited them.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Three-dimensional control of crystal growth using magnetic fields

NASA Astrophysics Data System (ADS)

Dulikravich, George S.; Ahuja, Vineet; Lee, Seungsoo

1993-07-01

Two coupled systems of partial differential equations governing three-dimensional laminar viscous flow undergoing solidification or melting under the influence of arbitrarily oriented externally applied magnetic fields have been formulated. The model accounts for arbitrary temperature dependence of physical properties including latent heat release, effects of Joule heating, magnetic field forces, and mushy region existence. On the basis of this model a numerical algorithm has been developed and implemented using central differencing on a curvilinear boundary-conforming grid and Runge-Kutta explicit time-stepping. The numerical results clearly demonstrate possibilities for active and practically instantaneous control of melt/solid interface shape, the solidification/melting front propagation speed, and the amount and location of solid accrued.

Fem Formulation for Heat and Mass Transfer in Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

PIFEX: An advanced programmable pipelined-image processor

NASA Technical Reports Server (NTRS)

Gennery, D. B.; Wilcox, B.

1985-01-01

PIFEX is a pipelined-image processor being built in the JPL Robotics Lab. It will operate on digitized raster-scanned images (at 60 frames per second for images up to about 300 by 400 and at lesser rates for larger images), performing a variety of operations simultaneously under program control. It thus is a powerful, flexible tool for image processing and low-level computer vision. It also has applications in other two-dimensional problems such as route planning for obstacle avoidance and the numerical solution of two-dimensional partial differential equations (although its low numerical precision limits its use in the latter field). The concept and design of PIFEX are described herein, and some examples of its use are given.

Partial differential equations of 3D boundary layer and their numerical solutions in turbomachinery

NASA Astrophysics Data System (ADS)

Zhang, Guoqing; Hua, Yaonan; Wu, Chung-Hua

1991-08-01

This paper studies the 3D boundary layer equations (3DBLE) and their numerical solutions in turbomachinery: (1) the general form of 3DBLE in turbomachines with rotational and curvature effects are derived under the semiorthogonal coordinate system, in which the normal pressure gradient is not equal to zero; (2) the method of solution of the 3DBLE is discussed; (3) the 3D boundary layers on the rotating blade surface, IGV endwall, rotor endwall (with a relatively moving boundary) are numerically solved, and the predicted data correlates well with the measured data; and (4) the comparison is made between the numerical results of 3DBLE with and without normal pressure gradient.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

PubMed

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.

Thermodynamic investigations on the growth of CuAlO2 delafossite crystals

NASA Astrophysics Data System (ADS)

Wolff, Nora; Klimm, Detlef; Siche, Dietmar

2018-02-01

Simultaneous differential thermal analysis (DTA) and thermogravimetric (TG) measurements with copper oxide/aluminum oxide mixtures were performed in atmospheres with varying oxygen partial pressures and with crucibles made of different materials. Only sapphire and platinum crucibles proved to be stable under conditions that are useful for the growth of CuAlO2 delafossite single crystals. Then the ternary phase diagram Al2O3-CuO-Cu and its isopleth section Cu2O-Al2O3 were redetermined. Millimeter sized crystals could be obtained from copper oxide melts with 1-2 mol% addition of aluminum oxide that are stable in platinum crucibles held in oxidizing atmosphere containing 15-21% oxygen.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

[Correlation between gaseous exchange rate, body temperature, and mitochondrial protein content in the liver of mice].

PubMed

Muradian, Kh K; Utko, N O; Mozzhukhina, T H; Pishel', I M; Litoshenko, O Ia; Bezrukov, V V; Fraĭfel'd, V E

2002-01-01

Correlative and regressive relations between the gaseous exchange, thermoregulation and mitochondrial protein content were analyzed by two- and three-dimensional statistics in mice. It has been shown that the pair wise linear methods of analysis did not reveal any significant correlation between the parameters under exploration. However, it became evident at three-dimensional and non-linear plotting for which the coefficients of multivariable correlation reached and even exceeded 0.7-0.8. The calculations based on partial differentiation of the multivariable regression equations allow to conclude that at certain values of VO2, VCO2 and body temperature negative relations between the systems of gaseous exchange and thermoregulation become dominating.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

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

2010-11-01

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

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

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

Intuitive Understanding of Solutions of Partially Differential Equations

ERIC Educational Resources Information Center

Kobayashi, Y.

2008-01-01

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

Partial wave analysis for folded differential cross sections

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

PubMed

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

2009-01-01

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

Modeling of magnetic particle orientation in magnetic powder injection molding

NASA Astrophysics Data System (ADS)

Doo Jung, Im; Kang, Tae Gon; Seul Shin, Da; Park, Seong Jin

2018-03-01

The magnetic micro powder orientation under viscous shear flow has been analytically understood and characterized into a new analytical orientation model for a powder injection molding process. The effects of hydrodynamic force from the viscous flow, external magnetic force and internal dipole-dipole interaction were considered to predict the orientation under given process conditions. Comparative studies with a finite element method proved the calculation validity with a partial differential form of the model. The angular motion, agglomeration and magnetic chain formation have been simulated, which shows that the effect of dipole-dipole interaction among powders on the orientation state becomes negligible at a high Mason number condition and at a low λ condition (the ratio of external magnetic field strength and internal magnetic moment of powder). Our developed model can be very usefully employed in the process analysis and design of magnetic powder injection molding.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Traction patterns of tumor cells.

PubMed

Ambrosi, D; Duperray, A; Peschetola, V; Verdier, C

2009-01-01

The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.

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

NASA Astrophysics Data System (ADS)

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

2007-02-01

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

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

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

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek

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

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

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

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

PubMed

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

2017-04-01

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

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

DOE PAGES

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

2016-01-26

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

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

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

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

Separation of Variables and Superintegrability; The symmetry of solvable systems

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

PubMed

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

2008-10-01

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

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

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

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

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

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

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

1992-09-01

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

Differential formulation of the gyrokinetic Landau operator

DOE PAGES

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

2017-01-05

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

Complex partial status epilepticus: a recurrent problem.

PubMed Central

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

1994-01-01

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

Dynamic Decision Making under Uncertainty and Partial Information

DTIC Science & Technology

2017-01-30

order to address these problems, we investigated efficient computational methodologies for dynamic decision making under uncertainty and partial...information. In the course of this research, we developed and studied efficient simulation-based methodologies for dynamic decision making under...uncertainty and partial information; (ii) studied the application of these decision making models and methodologies to practical problems, such as those

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

PubMed

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

2008-01-01

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

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.

Regulation of Viable and Optimal Cohorts

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

Aubin, Jean-Pierre, E-mail: aubin.jp@gmail.com

This study deals with the evolution of (scalar) attributes (resources or income in evolutionary demography or economics, position in traffic management, etc.) of a population of “mobiles” (economic agents, vehicles, etc.). The set of mobiles sharing the same attributes is regarded as an instantaneous cohort described by the number of its elements. The union of instantaneous cohorts during a mobile window between two attributes is a cohort. Given a measure defining the number of instantaneous cohorts, the accumulation of the mobile attributes on a evolving mobile window is the measure of the cohort on this temporal mobile window. Imposing accumulationmore » constraints and departure conditions, this study is devoted to the regulation of the evolutions of the attributes which are1.viable in the sense that the accumulations constraints are satisfied at each instant;2.and, among them, optimal, in the sense that both the duration of the temporal mobile window is maximum and that the accumulation on this temporal mobile window is the largest viable one. This value is the “accumulation valuation” function. Viable and optimal evolutions under accumulation constraints are regulated by an “implicit Volterra integro-differential inclusion” built from the accumulation valuation function, solution to an Hamilton–Jacobi–Bellman partial differential equation under constraints which is constructed for this purpose.« less

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

PubMed

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

2005-12-01

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

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

PubMed Central

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

2005-01-01

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

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

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

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

USDA-ARS?s Scientific Manuscript database

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

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

USDA-ARS?s Scientific Manuscript database

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

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

PubMed

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

2017-09-01

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

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

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

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

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

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

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

PubMed

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

2011-01-01

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

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

PubMed Central

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

2011-01-01

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

Electron-pair-production cross section in the tip region of the positron spectrum

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

Sud, K.K.; Sharma, D.K.

1984-11-01

The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

DOE PAGES

Kouri, Drew Philip

2017-12-19

In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

Use of Partial Least Squares improves the efficacy of removing unwanted variability in differential expression analyses based on RNA-Seq data.

PubMed

Chakraborty, Sutirtha

2018-05-26

RNA-Seq technology has revolutionized the face of gene expression profiling by generating read count data measuring the transcript abundances for each queried gene on multiple experimental subjects. But on the downside, the underlying technical artefacts and hidden biological profiles of the samples generate a wide variety of latent effects that may potentially distort the actual transcript/gene expression signals. Standard normalization techniques fail to correct for these hidden variables and lead to flawed downstream analyses. In this work I demonstrate the use of Partial Least Squares (built as an R package 'SVAPLSseq') to correct for the traces of extraneous variability in RNA-Seq data. A novel and thorough comparative analysis of the PLS based method is presented along with some of the other popularly used approaches for latent variable correction in RNA-Seq. Overall, the method is found to achieve a substantially improved estimation of the hidden effect signatures in the RNA-Seq transcriptome expression landscape compared to other available techniques. Copyright © 2017. Published by Elsevier Inc.

Silk fibroin scaffolds enhance cell commitment of adult rat cardiac progenitor cells.

PubMed

Di Felice, Valentina; Serradifalco, Claudia; Rizzuto, Luigi; De Luca, Angela; Rappa, Francesca; Barone, Rosario; Di Marco, Patrizia; Cassata, Giovanni; Puleio, Roberto; Verin, Lucia; Motta, Antonella; Migliaresi, Claudio; Guercio, Annalisa; Zummo, Giovanni

2015-11-01

The use of three-dimensional (3D) cultures may induce cardiac progenitor cells to synthesize their own extracellular matrix (ECM) and sarcomeric proteins to initiate cardiac differentiation. 3D cultures grown on synthetic scaffolds may favour the implantation and survival of stem cells for cell therapy when pharmacological therapies are not efficient in curing cardiovascular diseases and when organ transplantation remains the only treatment able to rescue the patient's life. Silk fibroin-based scaffolds may be used to increase cell affinity to biomaterials and may be chemically modified to improve cell adhesion. In the present study, porous, partially orientated and electrospun nanometric nets were used. Cardiac progenitor cells isolated from adult rats were seeded by capillarity in the 3D structures and cultured inside inserts for 21 days. Under this condition, the cells expressed a high level of sarcomeric and cardiac proteins and synthesized a great quantity of ECM. In particular, partially orientated scaffolds induced the synthesis of titin, which is a fundamental protein in sarcomere assembly. Copyright © 2013 John Wiley & Sons, Ltd.

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

PubMed Central

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

2012-01-01

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

Unravelling the genetic differentiation among varieties of the Neotropical savanna tree Hancornia speciosa Gomes.

PubMed

Collevatti, Rosane G; Rodrigues, Eduardo E; Vitorino, Luciana C; Lima-Ribeiro, Matheus S; Chaves, Lázaro J; Telles, Mariana P C

2018-04-20

Spatial distribution of species genetic diversity is often driven by geographical distance (isolation by distance) or environmental conditions (isolation by environment), especially under climate change scenarios such as Quaternary glaciations. Here, we used coalescent analyses coupled with ecological niche modelling (ENM), spatially explicit quantile regression analyses and the multiple matrix regression with randomization (MMRR) approach to unravel the patterns of genetic differentiation in the widely distributed Neotropical savanna tree, Hancornia speciosa (Apocynaceae). Due to its high morphological differentiation, the species was originally classified into six botanical varieties by Monachino, and has recently been recognized as only two varieties by Flora do Brasil 2020. Thus, H. speciosa is a good biological model for learning about evolution of phenotypic plasticity under genetic and ecological effects, and predicting their responses to changing environmental conditions. We sampled 28 populations (777 individuals) of Monachino's four varieties of H. speciosa and used seven microsatellite loci to genotype them. Bayesian clustering showed five distinct genetic groups (K = 5) with high admixture among Monachino's varieties, mainly among populations in the central area of the species geographical range. Genetic differentiation among Monachino's varieties was lower than the genetic differentiation among populations within varieties, with higher within-population inbreeding. A high historical connectivity among populations of the central Cerrado shown by coalescent analyses may explain the high admixture among varieties. In addition, areas of higher climatic suitability also presented higher genetic diversity in such a way that the wide historical refugium across central Brazil might have promoted the long-term connectivity among populations. Yet, FST was significantly related to geographic distances, but not to environmental distances, and coalescent analyses and ENM predicted a demographical scenario of quasi-stability through time. Our findings show that demographical history and isolation by distance, but not isolation by environment, drove genetic differentiation of populations. Finally, the genetic clusters do not support the two recently recognized botanical varieties of H. speciosa, but partially support Monachino's classification at least for the four sampled varieties, similar to morphological variation.

Human Enteroids as a Model of Upper Small Intestinal Ion Transport Physiology and Pathophysiology.

PubMed

Foulke-Abel, Jennifer; In, Julie; Yin, Jianyi; Zachos, Nicholas C; Kovbasnjuk, Olga; Estes, Mary K; de Jonge, Hugo; Donowitz, Mark

2016-03-01

Human intestinal crypt-derived enteroids are a model of intestinal ion transport that require validation by comparison with cell culture and animal models. We used human small intestinal enteroids to study neutral Na(+) absorption and stimulated fluid and anion secretion under basal and regulated conditions in undifferentiated and differentiated cultures to show their functional relevance to ion transport physiology and pathophysiology. Human intestinal tissue specimens were obtained from an endoscopic biopsy or surgical resections performed at Johns Hopkins Hospital. Crypts were isolated, enteroids were propagated in culture, induced to undergo differentiation, and transduced with lentiviral vectors. Crypt markers, surface cell enzymes, and membrane ion transporters were characterized using quantitative reverse-transcription polymerase chain reaction, immunoblot, or immunofluorescence analyses. We used multiphoton and time-lapse confocal microscopy to monitor intracellular pH and luminal dilatation in enteroids under basal and regulated conditions. Enteroids differentiated upon withdrawal of WNT3A, yielding decreased crypt markers and increased villus-like characteristics. Na(+)/H(+) exchanger 3 activity was similar in undifferentiated and differentiated enteroids, and was affected by known inhibitors, second messengers, and bacterial enterotoxins. Forskolin-induced swelling was completely dependent on cystic fibrosis transmembrane conductance regulator and partially dependent on Na(+)/H(+) exchanger 3 and Na(+)/K(+)/2Cl(-) cotransporter 1 inhibition in undifferentiated and differentiated enteroids. Increases in cyclic adenosine monophosphate with forskolin caused enteroid intracellular acidification in HCO3(-)-free buffer. Cyclic adenosine monophosphate-induced enteroid intracellular pH acidification as part of duodenal HCO3(-) secretion appears to require cystic fibrosis transmembrane conductance regulator and electrogenic Na(+)/HCO3(-) cotransporter 1. Undifferentiated or crypt-like, and differentiated or villus-like, human enteroids represent distinct points along the crypt-villus axis; they can be used to characterize electrolyte transport processes along the vertical axis of the small intestine. The duodenal enteroid model showed that electrogenic Na(+)/HCO3(-) cotransporter 1 might be a target in the intestinal mucosa for treatment of secretory diarrheas. Copyright © 2016 AGA Institute. Published by Elsevier Inc. All rights reserved.

Experimental ductile reactivation of pseudotachylyte-bearing faults.

NASA Astrophysics Data System (ADS)

Tielke, J.; Di Toro, G.; Passelegue, F. X.; Mecklenburgh, J.

2017-12-01

In most large earthquakes, afterslip is primarily accommodated by ductile deformation in the deep crust and upper mantle. In the last decades, field and experimental studies highlighted that seismic rupture can induce frictional meltin. The product of frictional melting, called pseudotachylyte, is considered the best signature of seismic rupture in exposed sections of rocks. Deformation of pseudotachylyte in the deep crust may explain the observed reduction of the strength after earthquakes, providing an explanation for the large afterslip or creep phenomena. In addition, the observation of natural mylonitized pseudotachylytes confirms the hypothesis of ductile reactivations. In this study, we conducted experiments under deep crust PT conditions on natural pseudotachylyte and tonalite from the Gole Larghe fault zone. Deformation experiments were carried out using a gas-medium apparatus at temperatures of 700° to 900°C, a confining pressure of 300 MPa, differential stresses stages of 5 to 400 MPa resulting in different strain rates. Mechanical data were used to derive flow law parameters. The intact tonalite present the largest strength of the rocks tested. The deformation mechanisms remain mostly brittle even at 900°C, and experiments finished by the brittle failure of the rock specimens. In pseudotachylyte-bearing tonalite, strain is strongly localized within pseudotachylyte-rich regions. While the rocks samples remain strong at 700°C , weakening initiates at 800°C. The dependence of strain rate on stress follows a power-law relationship with a stress exponent (n) of 1 at low differential stress, and 3 at high differential stress. At 900°C, the strength of the pseudotachylyte vein samples drastically weakens and values of n of 3 are observed even at low differential stress. Microstructural analyses demonstrate that strain localization in pseudotachylite-bearing rocks corresponds with the initiation of partial melting at 800°C. In contrast, tonalite that is free of pseudotachylite only exhibits brittle processes. Evidence of the initiation of mylonitization is observed at low strain conditions. Our results suggest that the presence of pseudotachylyte in crustal rocks drastically reduces the strength of the system when the temperature allows for initiation of partial melting.

Population response of the northern red-backed vole (Clethrionomys rutilus) to differentially cut white spruce forest.

Treesearch

Stephen D. West; R. Glenn Ford; John C. Zasada

1980-01-01

The population response of the northern red-backed vole (Clethrionomys rutilus) to a differentially cut white spruce (Picea glauca) forest 30 km southwest of Fairbanks, Alaska, was monitored by simultaneous livetrapping in a clearcut, in a partially cut or shelterwood area, and in an area of uncut forest. During the first...

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory

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

Gruen, Christine, E-mail: christine.gruen@univ-brest.fr

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.

Effects of partial interlaminar bonding on impact resistance and loaded-hole behavior of graphite/epoxy quasi-isotropic laminates

NASA Technical Reports Server (NTRS)

Illg, W.

1986-01-01

A partial-bonding interlaminar toughening concept was evaluated for resistance to impact and for behavior of a loaded hole. Perforated Mylar sheets were interleaved between all 24 plies of a graphite/epoxy quasi-isotropic lay-up. Specimens were impacted by aluminum spheres while under tensile or compressive loads. Impact-failure thresholds and residual strengths were obtained. Loaded-hole specimens were tested in three configurations that were critical in bearing, shear, or tension. Partial bonding reduced the tensile and compressive strengths of undamaged specimens by about one-third. For impact, partial bonding did not change the threshold for impact failure under tensile preload. However, under compressive preload, partial bonding caused serious degradation of impact resistance. Partial bonding reduced the maximum load-carrying capacity of all three types of loaded-hole specimens. Overall, partial bonding degraded both impact resistance and bearing strength of holes.

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.

Characterization of stem-like cells in a new astroblastoma cell line

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

Coban, Esra Aydemir; Kasikci, Ezgi; Karatas, Omer Faruk

Cell lines established from tumors are the most commonly used models in cancer research, and their use in recent years has enabled a greater understanding of the biology of cancer and the means to develop effective treatment strategies. Astroblastomas are uncommon neuroepithelial tumors of glial origin, predominantly affecting young people, mainly teenagers and children, predominantly females. To date, only a single study has reported that astroblastomas contain a large number of neural stem-like cells, which had only a partial proliferation capacity and differentiation. Our objective was to establish an astroblastoma cell line to investigate the presence of astroblastic cells andmore » cancer stem-like cells. The migratory and invasion abilities of the cells were quantified with invasion and migration assays and compared to a glioblastoma cell line. The presence of stem cells was detected with surface-marker analysis by using flow cytometry, and measuring the differentiation ability with a differentiation assay and the self-renewal capacity with a sphere-forming assay. These characteristics may determine whether this novel cell line is a model for astroblastomas that may have stem-cell characteristics. With this novel cell line, scientists can investigate the molecular pathways underlying astroblastomas and develop new therapeutic strategies for patients with these tumors. - Highlights: • An establishment of a novel astroblastoma cell line was proposed. • The presence of astroblastic cells and cancer stem-like cells was investigated. • The molecular pathways underlying astroblastomas may be investigated. • New therapeutic strategies for patients with astroblastoma may be developed.« less

Role of differential physical properties in the collective mechanics and dynamics of tissues

NASA Astrophysics Data System (ADS)

Das, Moumita

Living cells and tissues are highly mechanically sensitive and active. Mechanical stimuli influence the shape, motility, and functions of cells, modulate the behavior of tissues, and play a key role in several diseases. In this talk I will discuss how collective biophysical properties of tissues emerge from the interplay between differential mechanical properties and statistical physics of underlying components, focusing on two complementary tissue types whose properties are primarily determined by (1) the extracellular matrix (ECM), and (2) individual and collective cell properties. I will start with the structure-mechanics-function relationships in articular cartilage (AC), a soft tissue that has very few cells, and its mechanical response is primarily due to its ECM. AC is a remarkable tissue: it can support loads exceeding ten times our body weight and bear 60+ years of daily mechanical loading despite having minimal regenerative capacity. I will discuss the biophysical principles underlying this exceptional mechanical response using the framework of rigidity percolation theory, and compare our predictions with experiments done by our collaborators. Next I will discuss ongoing theoretical work on how the differences in cell mechanics, motility, adhesion, and proliferation in a co-culture of breast cancer cells and healthy breast epithelial cells may modulate experimentally observed differential migration and segregation. Our results may provide insights into the mechanobiology of tissues with cell populations with different physical properties present together such as during the formation of embryos or the initiation of tumors. This work was partially supported by a Cottrell College Science Award.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Multigrid Methods

NASA Technical Reports Server (NTRS)

1981-01-01

Developments in numerical solution of certain types of partial differential equations by rapidly converging sequences of operations on supporting grids that range from very fine to very coarse are presented.

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1982-01-01

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Naik, Vijay K.

1988-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, J. H.; Naik, V. K.

1985-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

DOE PAGES

Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; ...

2012-01-01

A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertaintymore » quantification results for a 3D PDE application.« less

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Proceedings of the Dundee Conference (10th) Held in Dundee, Scotland on July 1988. Ordinary and Partial Differential Equations. Volume 2

DTIC Science & Technology

1988-07-01

a priori inequalities with applications to R J Knops boundary value problems 40 Singular systems of differential equations V G Sigiilito S L...Stochastic functional differential equations S E A Mohammed 100 Optimal control of variational inequalities 125 Ennio de Giorgi Colloquium V Barbu P Kr e...location of the period-doubled bifurcation point varies slightly with Zc [ 3 ]. In addition, no significant effect is found if a smoother functional

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

Isa, Sharena Mohamad; Ali, Anati

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating.

PubMed

Qasim, Muhammad; Khan, Ilyas; Shafie, Sharidan

2013-01-01

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involved parameters on dimensionless velocity, microrotation and temperature is examined. An excellent agreement is found between the present and previous limiting results.

Examining sex differentials in the uptake and process of HIV testing in three high prevalence districts of India.

PubMed

Joseph, Saju; Kielmann, Karina; Kudale, Abhay; Sheikh, Kabir; Shinde, Swati; Porter, John; Rangan, Sheela

2010-03-01

Sex differentials in the uptake of HIV testing have been reported in a range of settings, however, men's and women's testing patterns are not consistent across these settings, suggesting the need to set sex differentials against gender norms in patient testing behaviour and provider practices. A community-based, cross-sectional survey among 347 people living with HIV in three HIV high prevalence districts of India examined reasons for undergoing an HIV test, location of testing and conditions under which individuals were tested. HIV testing was almost always provider-initiated for men. Men were more likely to be advised to test by a private practitioner and to test in the private sector. Women were more likely to be advised to test by a family member, and to test in the public sector. Men were more likely to receive pre-test information than women, when tested in the private sector. Men were also more likely to receive direct disclosure of their HIV positive status by a health provider, regardless of the sector in which they tested. More women than men were repeatedly tested for HIV, regardless of sector. These sex differentials in the uptake and process of HIV testing are partially explained through differences in public and private sector testing practices. However, they also reflect women's lack of awareness and agency in HIV care seeking and differential treatment by providers. Examining gender dynamics that underpin sex differentials in HIV testing patterns and practices is essential for a realistic assessment of the challenges and implications of scaling-up HIV testing and mainstreaming gender in HIV/AIDS programmes.

Cooperation between both Wnt/β-catenin and PTEN/PI3K/Akt signaling promotes primitive hematopoietic stem cell self-renewal and expansion

PubMed Central

Perry, John M.; He, Xi C.; Sugimura, Ryohichi; Grindley, Justin C.; Haug, Jeffrey S.; Ding, Sheng; Li, Linheng

2011-01-01

Although self-renewal is the central property of stem cells, the underlying mechanism remains inadequately defined. Using a hematopoietic stem and progenitor cell (HSPC)-specific conditional induction line, we generated a compound genetic model bearing both Pten deletion and β-catenin activation. These double mutant mice exhibit a novel phenotype, including expansion of phenotypic long-term hematopoietic stem cells (LT-HSCs) without extensive differentiation. Unexpectedly, constitutive activation of β-catenin alone results in apoptosis of HSCs. However, together, the Wnt/β-catenin and PTEN/PI3k/Akt pathways interact to drive phenotypic LT-HSC expansion by inducing proliferation while simultaneously inhibiting apoptosis and blocking differentiation, demonstrating the necessity of complementary cooperation between the two pathways in promoting self-renewal. Mechanistically, β-catenin activation reduces multiple differentiation-inducing transcription factors, blocking differentiation partially through up-regulation of Inhibitor of differentiation 2 (Id2). In double mutants, loss of Pten enhances the HSC anti-apoptotic factor Mcl-1. All of these contribute in a complementary way to HSC self-renewal and expansion. While permanent, genetic alteration of both pathways in double mutant mice leads to expansion of phenotypic HSCs, these HSCs cannot function due to blocked differentiation. We developed a pharmacological approach to expand normal, functional HSCs in culture using factors that reversibly activate both Wnt/β-catenin and PI3K/Akt signaling simultaneously. We show for the first time that activation of either single pathway is insufficient to expand primitive HSCs, but in combination, both pathways drive self-renewal and expansion of HSCs with long-term functional capacity. PMID:21890648

Prostate cancer cells induce osteoblastic differentiation via semaphorin 3A.

PubMed

Liu, Fuzhou; Shen, Weiwei; Qiu, Hao; Hu, Xu; Zhang, Chao; Chu, Tongwei

2015-03-01

Prostate cancer metastasis to bone is the second most commonly diagnosed malignant disease among men worldwide. Such metastatic disease is characterized by the presence of osteoblastic bone lesions, and is associated with high rates of mortality. However, the various mechanisms involved in prostate cancer-induced osteoblastic differentiation have not been fully explored. Semaphorin 3A (Sema 3A) is a newly identified regulator of bone metabolism which stimulates differentiation of pre-osteoblastic cells under physiological conditions. We investigated in this study whether prostate cancer cells can mediate osteoblastic activity through Sema 3A. We cultured osteoprogenitor MC3T3-E1 cells in prostate cancer-conditioned medium, and analyzed levels of Sema 3A protein in diverse prostate cancer cell lines to identify cell lines in which Sema 3A production showed a positive correlation with osteo-stimulation. C4-2 cells were stably transfected with Sema 3A short hairpin RNA to further determine whether Sema 3A contributes to the ability of C4-2 cells to induce osteoblastic differentiation. Down-regulation of Sema 3A expression decreased indicators of C4-2 CM-induced osteoblastic differentiation, including alkaline phosphatase production and mineralization. Additionally, silencing or neutralizing Sema 3A in C4-2 cells resulted in diminished β-catenin expression in osteogenitor MC3T3-E1 cells. Our results suggest that prostate cancer-induced osteoblastic differentiation is at least partially mediated by Sema 3A, and may be regulated by the β-catenin signalling pathway. Sema 3A may represent a novel target for treatment of prostate cancer-induced osteoblastic lesions. © 2014 Wiley Periodicals, Inc.

[Differential diagnosis of chronic myeloic leucemia in infancy (author's transl)].

PubMed

Binder, C; Pichler, E; Radaskiewicz, T; Scheibenreiter, S

1976-01-01

A 3 months old girl presented with significant enlargement of liver, spleen and lymphnodes, with moderate anemia, thrombopenia and leucocytosis. In the differential count there was a shift to the left and an increase of monocyte-like cells (35%). Differential diagnosis included leucemoid reaction, infectious mononucleosis, myelo-proliferative disorder with a missing C chromosome and chronic myeloid leucemia. Clinical symptoms, cytochemistry and caryotype of bone marrow cells suggested infantile chronic myeloic leucemia and normal ALP index and possibly normal HbF. Treatment with 6-mercaptopurine was followed by partial remission. The therapeutic consequences of exact differential diagnosis are discussed.

The evolution of the moon and the terrestrial planets

NASA Technical Reports Server (NTRS)

Toksoez, M. N.; Johnston, D. H.

1974-01-01

The thermal evolutions of the Moon, Mars, Venus and Mercury are calculated theoretically starting from cosmochemical condensation models. An assortment of geological, geochemical and geophysical data are used to constrain both the present day temperatures and the thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. The moon, smallest in size, is characterized as a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. Mars, intermediate in size, is assumed to have differentiated an Fe-FeS core. Venus is characterized as a planet not unlike the earth in many respects. Core formation has occurred probably during the first billion years after the formation. Mercury, which probably has a large core, may have a 500 km thick solid lithosphere and a partially molten core if it is assumed that some heat sources exist in the core.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

Pharmacological inhibition of DNA methylation attenuates pressure overload-induced cardiac hypertrophy in rats.

PubMed

Stenzig, Justus; Schneeberger, Yvonne; Löser, Alexandra; Peters, Barbara S; Schaefer, Andreas; Zhao, Rong-Rong; Ng, Shi Ling; Höppner, Grit; Geertz, Birgit; Hirt, Marc N; Tan, Wilson; Wong, Eleanor; Reichenspurner, Hermann; Foo, Roger S-Y; Eschenhagen, Thomas

2018-07-01

Heart failure is associated with altered gene expression and DNA methylation. De novo DNA methylation is associated with gene silencing, but its role in cardiac pathology remains incompletely understood. We hypothesized that inhibition of DNA methyltransferases (DNMT) might prevent the deregulation of gene expression and the deterioration of cardiac function under pressure overload (PO). To test this hypothesis, we evaluated a DNMT inhibitor in PO in rats and analysed DNA methylation in cardiomyocytes. Young male Wistar rats were subjected to PO by transverse aortic constriction (TAC) or to sham surgery. Rats from both groups received solvent or 12.5 mg/kg body weight of the non-nucleosidic DNMT inhibitor RG108, initiated on the day of the intervention. After 4 weeks, we analysed cardiac function by MRI, fibrosis with Sirius Red staining, gene expression by RNA sequencing and qPCR, and DNA methylation by reduced representation bisulphite sequencing (RRBS). RG108 attenuated the ~70% increase in heart weight/body weight ratio of TAC over sham to 47% over sham, partially rescued reduced contractility, diminished the fibrotic response and the downregulation of a set of genes including Atp2a2 (SERCA2a) and Adrb1 (beta1-adrenoceptor). RG108 was associated with significantly lower global DNA methylation in cardiomyocytes by ~2%. The differentially methylated pathways were "cardiac hypertrophy", "cell death" and "xenobiotic metabolism signalling". Among these, "cardiac hypertrophy" was associated with significant methylation differences in the group comparison sham vs. TAC, but not significant between sham+RG108 and TAC+RG108 treatment, suggesting that RG108 partially prevented differential methylation. However, when comparing TAC and TAC+RG108, the pathway cardiac hypertrophy was not significantly differentially methylated. DNMT inhibitor treatment is associated with attenuation of cardiac hypertrophy and moderate changes in cardiomyocyte DNA methylation. The potential mechanistic link between these two effects and the role of non-myocytes need further clarification. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Mortality Divide in India: The Differential Contributions of Gender, Caste, and Standard of Living Across the Life Course

PubMed Central

Subramanian, S.V.; Nandy, Shailen; Irving, Michelle; Gordon, Dave; Lambert, Helen; Davey Smith, George

2006-01-01

Objectives. We investigated the contributions of gender, caste, and standard of living to inequalities in mortality across the life course in India. Methods. We conducted a multilevel cross-sectional analysis of individual mortality, using the 1998–1999 Indian National Family Health Survey data for 529321 individuals from 26 states. Results. Substantial mortality differentials were observed between the lowest and highest standard-of-living quintiles across all age groups, ranging from an odds ratio (OR) of 4.61 (95% confidence interval [CI]=2.98, 7.13) in the age group 2 to 5 years to an OR of 1.97 (95% CI=1.68, 2.32) in the age group 45 to 64 years. Excess mortality for girls was evident only for the age group 2 to 5 years (OR=1.33, 95% CI=1.13, 1.58). Substantial caste differentials were observed at the beginning and end stages of life. Area variation in mortality is partially a result of the compositional effects of household standard of living and caste. Conclusions. The mortality burden, across the life course in India, falls disproportionately on economically disadvantaged and lower-caste groups. Residual state-level variation in mortality suggests an underlying ecology to the mortality divide in India. PMID:16571702

Minimum time search in uncertain dynamic domains with complex sensorial platforms.

PubMed

Lanillos, Pablo; Besada-Portas, Eva; Lopez-Orozco, Jose Antonio; de la Cruz, Jesus Manuel

2014-08-04

The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous/discontinuous differentiable/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models.

The mortality divide in India: the differential contributions of gender, caste, and standard of living across the life course.

PubMed

Subramanian, S V; Nandy, Shailen; Irving, Michelle; Gordon, Dave; Lambert, Helen; Davey Smith, George

2006-05-01

We investigated the contributions of gender, caste, and standard of living to inequalities in mortality across the life course in India. We conducted a multilevel cross-sectional analysis of individual mortality, using the 1998-1999 Indian National Family Health Survey data for 529321 individuals from 26 states. Substantial mortality differentials were observed between the lowest and highest standard-of-living quintiles across all age groups, ranging from an odds ratio (OR) of 4.61 (95% confidence interval [CI]=2.98, 7.13) in the age group 2 to 5 years to an OR of 1.97 (95% CI=1.68, 2.32) in the age group 45 to 64 years. Excess mortality for girls was evident only for the age group 2 to 5 years (OR=1.33, 95% CI=1.13, 1.58). Substantial caste differentials were observed at the beginning and end stages of life. Area variation in mortality is partially a result of the compositional effects of household standard of living and caste. The mortality burden, across the life course in India, falls disproportionately on economically disadvantaged and lower-caste groups. Residual state-level variation in mortality suggests an underlying ecology to the mortality divide in India.

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

PubMed Central

Lanillos, Pablo; Besada-Portas, Eva; Lopez-Orozco, Jose Antonio; de la Cruz, Jesus Manuel

2014-01-01

The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous/discontinuous differentiable/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models. PMID:25093345

The Serum Analysis of Dampness Syndrome in Patients with Coronary Heart Disease and Chronic Renal Failure Based on the Theory of "Same Syndromes in Different Diseases".

PubMed

Hao, Yiming; Yuan, Xue; Qian, Peng; Bai, Guanfeng; Wang, Yiqin

2017-01-01

To analyze the serum metabolites in patients with coronary heart disease (CHD) showing dampness syndrome and patients with chronic renal failure (CRF) showing dampness syndrome and to seek the substance that serves as the underlying basis of dampness syndrome in "same syndromes in different diseases." Methods . Metabolic spectrum by GC-MS was performed using serum samples from 29 patients with CHD showing dampness syndrome and 32 patients with CRF showing dampness syndrome. The principal component analysis and statistical analysis of partial least squares were performed to detect the metabolites with different levels of expression in patients with CHD and CRF. Furthermore, by comparing the VIP value and data mining in METLIN and HMDB, we identified the common metabolites in both patient groups. (1) Ten differential metabolites were found in patients with CHD showing dampness syndrome when compared to healthy subjects. Meanwhile, nine differential metabolites were found in patients with CRF showing dampness syndrome when compared to healthy subjects. (2) There were 9 differential metabolites identified when the serum metabolites of the CHD patients with dampness syndrome were compared to those of CRF patients with dampness syndrome. There were 4 common metabolites found in the serums of both patient groups.

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

Sun, Pei; Fang, Z. Zak; Koopman, Mark

Hydrogen has been investigated for decades as a temporary alloying element to refine the microstructure of Ti-6Al-4V, and is now being used in a novel powder metallurgy method known as "hydrogen sintering and phase transformation". Pseudo-binary phase diagrams of (Ti-6Al-4V)-xH have been studied and developed, but are not well established due to methodological limitations. In this paper, in situ studies of phase transformations during hydrogenation and dehydrogenation of (Ti-6Al-4V)-xH alloys were conducted using high-energy synchrotron X-ray diffraction (XRD), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The eutectoid phase transformation of β ↔ α + δ was observed in themore » (Ti-6Al-4V)-xH alloy via in situ synchrotron XRD at 211 °C with a hydrogen concentration of 37.5 at.% (measured using TGA-DSC). The relationships of hydrogen composition to partial pressure and temperature were investigated in the temperature range 450-900°C. Based on these results, a partial pseudo-binary phase diagram of (Ti-6Al-4V)-xH is proposed for hydrogen compositions up to 60 at.% in the temperature range 100-900°C. Using the data collected in real time under controlled parameters of temperature, composition and hydrogen partial pressure, this work characterizes relevant phase transformations and microstructural evolution for practical titanium-hydrogen technologies of Ti-6Al-4V.« less

Experimental confirmation of a PDE-based approach to design of feedback controls

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.; Brown, D. E.; Silcox, R. J.; Metcalf, Vern L.

1995-01-01

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

LANDSAT imagery of the Venetian Lagoon: A multitemporal analysis

NASA Technical Reports Server (NTRS)

Alberotanza, L.; Zandonella, A. (Principal Investigator)

1980-01-01

The use of LANDSAT multispectral scanner images from 1975 to 1979 to determine pollution dispersion in the central basin of the lagoon under varying tidal conditions is described. Images taken during the late spring and representing both short and long range tidal dynamics were processed for partial haze removal and removal of residual striping. Selected spectral bands were correlated to different types of turbid water. The multitemporal data was calibrated, classified considering sea truth data, and evaluated. The classification differentiated tide diffusion, algae belts, and industrial, agricultural, and urban turbidity distributions. Pollution concentration is derived during the short time interval between inflow and outflow and from the distance between the two lagoon inlets and the industrial zones. Increasing pollution of the lagoon is indicated.

The Elasto-Plastic Stability of Plates

NASA Technical Reports Server (NTRS)

Ilyushin, A. A.

1947-01-01

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type

NASA Astrophysics Data System (ADS)

Scarpa, Luca

2017-08-01

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form dXt - div γ (∇Xt) dt + β (Xt) dt ∋ B (t ,Xt) dWt, where γ and β are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on Rd and R respectively, and W is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray-Lions conditions on γ and with no restrictive smoothness or growth assumptions on β. The operator B is assumed to be Hilbert-Schmidt and to satisfy some classical Lipschitz conditions in the second variable.

Suddenly included: cultural differences in experiencing re-inclusion.

PubMed

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

2015-03-01

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

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

DNA–PKcs–SIN1 complexation mediates low-dose X-ray irradiation (LDI)-induced Akt activation and osteoblast differentiation

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

Xu, Yong; Fang, Shi-ji; Zhu, Li-juan

Highlights: • LDI increases ALP activity, promotes type I collagen (Col I)/Runx2 mRNA expression. • LDI induces DNA–PKcs activation, which is required for osteoblast differentiation. • Akt activation mediates LDI-induced ALP activity and Col I/Runx2 mRNA increase. • DNA–PKcs–SIN1 complexation mediates LDI-induced Akt Ser-473 phosphorylation. • DNA–PKcs–SIN1 complexation is important for osteoblast differentiation. - Abstract: Low-dose irradiation (LDI) induces osteoblast differentiation, however the underlying mechanisms are not fully understood. In this study, we explored the potential role of DNA-dependent protein kinase catalytic subunit (DNA–PKcs)–Akt signaling in LDI-induced osteoblast differentiation. We confirmed that LDI promoted mouse calvarial osteoblast differentiation, which wasmore » detected by increased alkaline phosphatase (ALP) activity as well as mRNA expression of type I collagen (Col I) and runt-related transcription factor 2 (Runx2). In mouse osteoblasts, LDI (1 Gy) induced phosphorylation of DNA–PKcs and Akt (mainly at Ser-473). The kinase inhibitors against DNA–PKcs (NU-7026 and NU-7441) or Akt (LY294002, perifosine and MK-2206), as well as partial depletion of DNA–PKcs or Akt1 by targeted-shRNA, dramatically inhibited LDI-induced Akt activation and mouse osteoblast differentiation. Further, siRNA-knockdown of SIN1, a key component of mTOR complex 2 (mTORC2), also inhibited LDI-induced Akt Ser-473 phosphorylation as well as ALP activity increase and Col I/Runx2 expression in mouse osteoblasts. Co-immunoprecipitation (Co-IP) assay results demonstrated that LDI-induced DNA–PKcs–SIN1 complexation, which was inhibited by NU-7441 or SIN1 siRNA-knockdown in mouse osteoblasts. In summary, our data suggest that DNA–PKcs–SIN1 complexation-mediated Akt activation (Ser-473 phosphorylation) is required for mouse osteoblast differentiation.« less

Polytomous Differential Item Functioning and Violations of Ordering of the Expected Latent Trait by the Raw Score

ERIC Educational Resources Information Center

DeMars, Christine E.

2008-01-01

The graded response (GR) and generalized partial credit (GPC) models do not imply that examinees ordered by raw observed score will necessarily be ordered on the expected value of the latent trait (OEL). Factors were manipulated to assess whether increased violations of OEL also produced increased Type I error rates in differential item…

Early differentiation of the Moon: Experimental and modeling studies

NASA Technical Reports Server (NTRS)

Longhi, J.

1986-01-01

Major accomplishments include the mapping out of liquidus boundaries of lunar and meteoritic basalts at low pressure; the refinement of computer models that simulate low pressure fractional crystallization; the development of a computer model to calculate high pressure partial melting of the lunar and Martian interiors; and the proposal of a hypothesis of early lunar differentiation based upon terrestrial analogs.

On the Well-Definedness of the Order of an Ordinary Differential Equation

ERIC Educational Resources Information Center

Dobbs, David E.

2006-01-01

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

Portent of Heine's Reciprocal Square Root Identity

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

Cohl, H W

Precise efforts in theoretical astrophysics are needed to fully understand the mechanisms that govern the structure, stability, dynamics, formation, and evolution of differentially rotating stars. Direct computation of the physical attributes of a star can be facilitated by the use of highly compact azimuthal and separation angle Fourier formulations of the Green's functions for the linear partial differential equations of mathematical physics.

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Multilevel Mediation: Cumulative Contextual Risk, Maternal Differential Treatment, and Children's Behavior within Families

ERIC Educational Resources Information Center

Meunier, Jean Christophe; Boyle, Michael; O'Connor, Thomas G.; Jenkins, Jennifer M.

2013-01-01

This study tests the hypothesis that links between contextual risk and children's outcomes are partially explained by differential parenting. Using multi-informant measurement and including up to four children per family (M[subscript age] = 3.51, SD = 2.38) in a sample of 397 families, indirect effects (through maternal differential…

Bmi1 regulates murine intestinal stem cell proliferation and self-renewal downstream of Notch.

PubMed

López-Arribillaga, Erika; Rodilla, Verónica; Pellegrinet, Luca; Guiu, Jordi; Iglesias, Mar; Roman, Angel Carlos; Gutarra, Susana; González, Susana; Muñoz-Cánoves, Pura; Fernández-Salguero, Pedro; Radtke, Freddy; Bigas, Anna; Espinosa, Lluís

2015-01-01

Genetic data indicate that abrogation of Notch-Rbpj or Wnt-β-catenin pathways results in the loss of the intestinal stem cells (ISCs). However, whether the effect of Notch is direct or due to the aberrant differentiation of the transit-amplifying cells into post-mitotic goblet cells is unknown. To address this issue, we have generated composite tamoxifen-inducible intestine-specific genetic mouse models and analyzed the expression of intestinal differentiation markers. Importantly, we found that activation of β-catenin partially rescues the differentiation phenotype of Rbpj deletion mutants, but not the loss of the ISC compartment. Moreover, we identified Bmi1, which is expressed in the ISC and progenitor compartments, as a gene that is co-regulated by Notch and β-catenin. Loss of Bmi1 resulted in reduced proliferation in the ISC compartment accompanied by p16(INK4a) and p19(ARF) (splice variants of Cdkn2a) accumulation, and increased differentiation to the post-mitotic goblet cell lineage that partially mimics Notch loss-of-function defects. Finally, we provide evidence that Bmi1 contributes to ISC self-renewal. © 2015. Published by The Company of Biologists Ltd.

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

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

The histone demethylase KDM5A is a key factor for the resistance to temozolomide in glioblastoma.

PubMed

Banelli, Barbara; Carra, Elisa; Barbieri, Federica; Würth, Roberto; Parodi, Federica; Pattarozzi, Alessandra; Carosio, Roberta; Forlani, Alessandra; Allemanni, Giorgio; Marubbi, Daniela; Florio, Tullio; Daga, Antonio; Romani, Massimo

2015-01-01

Notwithstanding current multimodal treatment, including surgery, radiotherapy and chemotherapy with temozolomide (TMZ), median survival of glioblastoma (GBM) patients is about 14 months, due to the rapid emergence of cell clones resistant to treatment. Therefore, understanding the mechanisms underlying chemoresistance is mandatory to improve treatments' outcome. We generated TMZ resistant cells (TMZ-R) from a GBM cell line and from cancer stem cell-enriched cultures isolated from human GBMs. We demonstrated that TMZ resistance is partially reverted by "drug wash-out" suggesting the contribution of epigenetic mechanisms in drug resistance and supporting the possibility of TMZ rechallenge in GBM patients after prior drug exposure. The expression of histone lysine demethylase genes (KDMs) was increased in TMZ-R cells compared to parental cells, and TMZ resistance or restored sensitivity was mimicked by over-expressing or inactivating KDM5A. Methylation and expression of O6-methylguanine-DNA methyltransferase (MGMT) and drug efflux mechanisms were not altered in TMZ-R cells compared to parental TMZ sensitive cells. TMZ-R cells transiently acquired morphologic and molecular characteristics of differentiated tumor cells, features that were lost after drug wash-out. In conclusion, we demonstrated that treatment-induced TMZ resistance in GBM involves epigenetic mechanisms in a subset of slow-cycling and transiently partially differentiated cells that escape drug cytotoxicity, overcome G2 checkpoint and sustain clonal growth. We found that TMZ-R cells are sensitive to histone deacethylase inhibitors (HDACi) that synergize with TMZ. This strong synergism could be exploited to develop novel combined adjuvant therapies for this rapidly progressing and invariably lethal cancer.

Quercetin Exerts Differential Neuroprotective Effects Against H2O2 and Aβ Aggregates in Hippocampal Neurons: the Role of Mitochondria.

PubMed

Godoy, Juan A; Lindsay, Carolina B; Quintanilla, Rodrigo A; Carvajal, Francisco J; Cerpa, Waldo; Inestrosa, Nibaldo C

2017-11-01

Amyloid-β peptide (Aβ) is one of the major players in the pathogenesis of Alzheimer's disease (AD). Despite numerous studies, the mechanisms by which Aβ induces neurodegeneration are not completely understood. Oxidative stress is considered a major contributor to the pathogenesis of AD, and accumulating evidence indicates that high levels of reactive oxygen species (ROS) are involved in Aβ-induced neurodegeneration. Moreover, Aβ can induce the deregulation of calcium homeostasis, which also affects mitochondrial function and triggers neuronal cell death. In the present study, we analyzed the effects of quercetin, a plant flavonoid with antioxidant properties, on oxidative stress- and Aβ-induced degeneration. Our results indicate that quercetin efficiently protected against H 2 O 2 -induced neuronal toxicity; however, this protection was only partial in rat hippocampal neurons that were treated with Aβ. Treatment with quercetin decreased ROS levels, recovered the normal morphology of mitochondria, and prevented mitochondrial dysfunction in neurons that were treated with H 2 O 2 . By contrast, quercetin treatment partially rescued hippocampal neurons from Aβ-induced mitochondrial injury. Most importantly, quercetin treatment prevented the toxic effects that are induced by H 2 O 2 in hippocampal neurons and, to a lesser extent, the Aβ-induced toxicity that is associated with the superoxide anion, which is a precursor of ROS production in mitochondria. Collectively, these results indicate that quercetin exerts differential effects on the prevention of H 2 O 2 - and Aβ-induced neurotoxicity in hippocampal neurons and may be a powerful tool for dissecting the molecular mechanisms underlying Aβ neurotoxicity.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

A systematic literature review of Burgers' equation with recent advances

NASA Astrophysics Data System (ADS)

Bonkile, Mayur P.; Awasthi, Ashish; Lakshmi, C.; Mukundan, Vijitha; Aswin, V. S.

2018-06-01

Even if numerical simulation of the Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers' equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective-diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers' equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers' equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers' equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers' equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Incorporating Conservation Zone Effectiveness for Protecting Biodiversity in Marine Planning

PubMed Central

Makino, Azusa; Klein, Carissa J.; Beger, Maria; Jupiter, Stacy D.; Possingham, Hugh P.

2013-01-01

Establishing different types of conservation zones is becoming commonplace. However, spatial prioritization methods that can accommodate multiple zones are poorly understood in theory and application. It is typically assumed that management regulations across zones have differential levels of effectiveness (“zone effectiveness”) for biodiversity protection, but the influence of zone effectiveness on achieving conservation targets has not yet been explored. Here, we consider the zone effectiveness of three zones: permanent closure, partial protection, and open, for planning for the protection of five different marine habitats in the Vatu-i-Ra Seascape, Fiji. We explore the impact of differential zone effectiveness on the location and costs of conservation priorities. We assume that permanent closure zones are fully effective at protecting all habitats, open zones do not contribute towards the conservation targets and partial protection zones lie between these two extremes. We use four different estimates for zone effectiveness and three different estimates for zone cost of the partial protection zone. To enhance the practical utility of the approach, we also explore how much of each traditional fishing ground can remain open for fishing while still achieving conservation targets. Our results show that all of the high priority areas for permanent closure zones would not be a high priority when the zone effectiveness of the partial protection zone is equal to that of permanent closure zones. When differential zone effectiveness and costs are considered, the resulting marine protected area network consequently increases in size, with more area allocated to permanent closure zones to meet conservation targets. By distributing the loss of fishing opportunity equitably among local communities, we find that 84–88% of each traditional fishing ground can be left open while still meeting conservation targets. Finally, we summarize the steps for developing marine zoning that accounts for zone effectiveness. PMID:24223870

Computation of partially invariant solutions for the Einstein Walker manifolds' identifying equations

NASA Astrophysics Data System (ADS)

Nadjafikhah, Mehdi; Jafari, Mehdi

2013-12-01

In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential equations (PDEs) and can be regarded as the generalization of the similarity reduction method. For this purpose, those cases of PISs which have the defect structure δ=1 and are resulted from two-dimensional subalgebras are considered in the present paper. Also it is shown that the obtained PISs are distinct from the invariant solutions that obtained by similarity reduction method.

Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation: A Comparative Study

NASA Astrophysics Data System (ADS)

Sagheer, M.; Bilal, M.; Hussain, S.; Ahmed, R. N.

2018-03-01

This article examines a mathematical model to analyze the rotating flow of three-dimensional water based nanofluid over a convectively heated exponentially stretching sheet in the presence of transverse magnetic field with additional effects of thermal radiation, Joule heating and viscous dissipation. Silver (Ag), copper (Cu), copper oxide (CuO), aluminum oxide (Al 2 O 3 ) and titanium dioxide (TiO 2 ) have been taken under consideration as the nanoparticles and water (H 2 O) as the base fluid. Using suitable similarity transformations, the governing partial differential equations (PDEs) of the modeled problem are transformed to the ordinary differential equations (ODEs). These ODEs are then solved numerically by applying the shooting method. For the particular situation, the results are compared with the available literature. The effects of different nanoparticles on the temperature distribution are also discussed graphically and numerically. It is witnessed that the skin friction coefficient is maximum for silver based nanofluid. Also, the velocity profile is found to diminish for the increasing values of the magnetic parameter.

Parametric instability analysis of truncated conical shells using the Haar wavelet method

NASA Astrophysics Data System (ADS)

Dai, Qiyi; Cao, Qingjie

2018-05-01

In this paper, the Haar wavelet method is employed to analyze the parametric instability of truncated conical shells under static and time dependent periodic axial loads. The present work is based on the Love first-approximation theory for classical thin shells. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. Then the partial differential equations are reduced into a system of coupled Mathieu-type ordinary differential equations describing dynamic instability behavior of the shell. Using Bolotin's method, the first-order and second-order approximations of principal instability regions are determined. The correctness of present method is examined by comparing the results with those in the literature and very good agreement is observed. The difference between the first-order and second-order approximations of principal instability regions for tensile and compressive loads is also investigated. Finally, numerical results are presented to bring out the influences of various parameters like static load factors, boundary conditions and shell geometrical characteristics on the domains of parametric instability of conical shells.

Defective Number Sense or Impaired Access? Differential Impairments in Different Subgroups of Children With Mathematics Difficulties.

PubMed

Wong, Terry T-Y; Ho, Connie S-H; Tang, Joey

2017-01-01

Developmental dyscalculia (DD) is a specific learning disability in mathematics that affects around 6% of the population. Currently, the core deficit of DD remains unknown. While the number sense deficit hypothesis suggests that the core deficit of DD lies in the inability to represent nonsymbolic numerosity, the access deficit hypothesis suggests that the origin of this disability lies in the inability to associate numbers with the underlying magnitude representation. The present study compared the performance of DDs with their low-achieving (LA) and normally achieving peers in nonsymbolic numerosity processing and number-magnitude mapping over 1 year (from kindergarten to 1st grade). The results demonstrated differential impairments in different subgroups of children with mathematics difficulties. While DDs showed deficits in both nonsymbolic numerosity processing and number-magnitude mapping, LAs showed deficit only in the number-magnitude mapping. Furthermore, the deficit in number-magnitude mapping among the DD group was partially explained by their number sense deficit. The number sense deficit hypothesis is supported. Theoretical and practical implications are discussed. © Hammill Institute on Disabilities 2015.