Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

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.

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Time-dependent buoyant puff model for explosive sources

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

Kansa, E.J.

1997-01-01

Several models exist to predict the time dependent behavior of bouyant puffs that result from explosions. This paper presents a new model that is derived from the strong conservative form of the conservation partial differential equations that are integrated over space to yield a coupled system of time dependent nonlinear ordinary differential equations. This model permits the cloud to evolve from an intial spherical shape not an ellipsoidal shape. It ignores the Boussinesq approximation, and treats the turbulence that is generated by the puff itself and the ambient atmospheric tubulence as separate mechanisms in determining the puff history. The puffmore » cloud rise history was found to depend no only on the mass and initial temperature of the explosion, but also upon the stability conditions of the ambient atmosphere. This model was calibrated by comparison with the Roller Coaster experiments.« less

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

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

PubMed

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

2010-04-01

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

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

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

Mundt, Michael; Kuemmel, Stephan

2006-08-15

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential ismore » analyzed.« less

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.

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1991-01-01

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

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 $T$.

The evolution of continental roots in numerical thermo-chemical mantle convection models including differentiation by partial melting

NASA Astrophysics Data System (ADS)

de Smet, J. H.; van den Berg, A. P.; Vlaar, N. J.

1999-09-01

Incorporating upper mantle differentiation through decompression melting in a numerical mantle convection model, we demonstrate that a compositionally distinct root consisting of depleted peridotite can grow and remain stable during a long period of secular cooling. Our modeling results show that in a hot convecting mantle partial melting will produce a compositional layering in a relatively short time of about 50 Ma. Due to secular cooling mantle differentiation finally stops before 1 Ga. The resulting continental root remains stable on a billion year time scale due to the combined effects of its intrinsically lower density and temperature-dependent rheology. Two different parameterizations of the melting phase-diagram are used in the models. The results indicate that during the Archaean melting occurred on a significant scale in the deep regions of the upper mantle, at pressures in excess of 15 GPa. The compositional depths of continental roots extend to 400 km depending on the potential temperature and the type of phase-diagram parameterization used in the model. The results reveal a strong correlation between lateral variations of temperature and the thickness of the continental root. This shows that cold regions in cratons are stabilized by a thick depleted root.

Exact time-dependent solutions for a self-regulating gene.

PubMed

Ramos, A F; Innocentini, G C P; Hornos, J E M

2011-06-01

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

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.

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.

Carpet: Adaptive Mesh Refinement for the Cactus Framework

NASA Astrophysics Data System (ADS)

Schnetter, Erik; Hawley, Scott; Hawke, Ian

2016-11-01

Carpet is an adaptive mesh refinement and multi-patch driver for the Cactus Framework (ascl:1102.013). Cactus is a software framework for solving time-dependent partial differential equations on block-structured grids, and Carpet acts as driver layer providing adaptive mesh refinement, multi-patch capability, as well as parallelization and efficient I/O.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

NASA Astrophysics Data System (ADS)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 122 907 No. of bytes in distributed program, including test data, etc.: 609 662 Distribution format: tar.gz Programming language: FORTRAN 77 and Fortran 90/95 Computer: PC Operating system: Linux, Unix RAM: 1 GByte (i, iv, v), 2 GByte (ii, vi, vii, x, xi), 4 GByte (iii, viii, xii), 8 GByte (ix) Classification: 2.9, 4.3, 4.12 Nature of problem: These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Solution method: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems. Additional comments: This package consists of 12 programs, see "Program title", above. FORTRAN77 versions are provided for each of the 12 and, in addition, Fortran 90/95 versions are included for ii, iii, vi, viii, ix, xii. For the particular purpose of each program please see the below. Running time: Minutes on a medium PC (i, iv, v, vii, x, xi), a few hours on a medium PC (ii, vi, viii, xii), days on a medium PC (iii, ix). Program summary (1)Title of program: imagtime1d.F Title of electronic file: imagtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (2)Title of program: imagtimecir.F Title of electronic file: imagtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (3)Title of program: imagtimesph.F Title of electronic file: imagtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (4)Title of program: realtime1d.F Title of electronic file: realtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (5)Title of program: realtimecir.F Title of electronic file: realtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (6)Title of program: realtimesph.F Title of electronic file: realtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (7)Title of programs: imagtimeaxial.F and imagtimeaxial.f90 Title of electronic file: imagtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (8)Title of program: imagtime2d.F and imagtime2d.f90 Title of electronic file: imagtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (9)Title of program: realtimeaxial.F and realtimeaxial.f90 Title of electronic file: realtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (10)Title of program: realtime2d.F and realtime2d.f90 Title of electronic file: realtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (11)Title of program: imagtime3d.F and imagtime3d.f90 Title of electronic file: imagtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (12)Title of program: realtime3d.F and realtime3d.f90 Title of electronic file: realtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum Ram Memory: 8 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems.

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Stencil computations for PDE-based applications with examples from DUNE and hypre

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

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Isostable reduction with applications to time-dependent partial differential equations.

PubMed

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

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.

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

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

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.

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.

Theory of Metastable State Relaxation for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander; Myerson, Allan S.

1993-01-01

A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

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

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.

Investigating the principles of recrystallization from glyceride melts.

PubMed

Windbergs, Maike; Strachan, Clare J; Kleinebudde, Peter

2009-01-01

Different lipids were melted and resolidified as model systems to gain deeper insight into the principles of recrystallization processes in lipid-based dosage forms. Solid-state characterization was performed on the samples with differential scanning calorimetry and X-ray powder diffraction. Several recrystallization processes could be identified during storage of the lipid layers. Pure triglycerides that generally crystallize to the metastable alpha-form from the melt followed by a recrystallization process to the stable beta-form with time showed a chain-length-dependent behavior during storage. With increasing chain length, the recrystallization to the stable beta-form was decelerated. Partial glycerides exhibited a more complex recrystallization behavior due to the fact that these substances are less homogenous. Mixtures of a long-chain triglyceride and a partial glyceride showed evidence of some interaction between the two components as the partial glyceride hindered the recrystallization of the triglyceride to the stable beta-form. In addition, the extent of this phenomenon depended on the amount of partial glyceride in the mixture. Based on these results, changes in solid dosage forms based on glycerides during processing and storage can be better understood.

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.

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

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.

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).

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

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

PubMed

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

2006-08-01

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

Partial Thermalization of Correlations in pA and AA collisionss

NASA Astrophysics Data System (ADS)

Gavin, Sean; Moschelli, George; Zin, Christopher

2017-09-01

Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting with Israel-Stewart hydrodynamics and Boltzmann-like kinetic theory in the presence of dynamic Langevin noise, we derive new partial differential equations for two-particle correlation functions. To illustrate how these equations can be used, we study the effect of thermalization on long range correlations. We show quite generally that two particle correlations at early times depend on S, the average probability that a parton suffers no interactions. We extract S from transverse momentum fluctuations measured in Pb+Pb collisions and predict the degree of partial thermalization in pA experiments. NSF-PHY-1207687.

TRUMP. Transient & S-State Temperature Distribution

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

Elrod, D.C.; Turner, W.D.

1992-03-03

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

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

Elrod, D.C.; Turner, W.D.

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

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

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

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

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

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

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.

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.

Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk

PubMed Central

2014-01-01

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail. PMID:24835274

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1972-01-01

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

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.

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

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.

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.

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.

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.

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.

Atmospheres of partially differentiated super-Earth exoplanets

NASA Astrophysics Data System (ADS)

Schaefer, Laura; Sasselov, Dimitar

2015-11-01

Terrestrial exoplanets have been discovered in a range of sizes, densities and orbital locations that defy our expectations based upon the Solar System. Planets discovered to date with radii less than ~1.5-1.6 Earth radii all seem to fall on an iso-density curve with the Earth [1]. However, mass and radius determinations, which depend on the known properties of the host star, are not accurate enough to distinguish between a fully differentiated three-layer planet (core, mantle, ocean/atmosphere) and an incompletely differentiated planet [2]. Full differentiation of a planet will depend upon the conditions at the time of accretion, including the abundance of short-lived radioisotopes, which will vary from system to system, as well as the number of giant impacts the planet experiences. Furthermore, separation of metal and silicates at the much larger pressures found inside super-Earths will depend on how the chemistry of these materials change at high pressures. There are therefore hints emerging that not all super-Earths will be fully differentiated. Incomplete differentiation will result in a more reduced mantle oxidation state and may have implications for the composition of an outgassed atmosphere. Here we will present the first results from a chemical equilibrium model of the composition of such an outgassed atmosphere and discuss the possibility of distinguishing between fully and incompletely differentiated planets through atmospheric observations.[1] Rogers, L. 2015. ApJ, 801, 41. [2] Zeng, L. & Sasselov, D. 2013. PASP, 125, 227.

Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations

NASA Astrophysics Data System (ADS)

Cosso, Andrea; Russo, Francesco

2016-11-01

Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.

An implicit fast Fourier transform method for integration of the time dependent Schrodinger equation

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

Riley, M.E.; Ritchie, A.B.

1997-12-31

One finds that the conventional exponentiated split operator procedure is subject to difficulties when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. The authors report investigations of this novel implicit split operator procedure. The results look promising for a purely numerical approach to certain electron quantum mechanical problems. A charge exchange calculation is presented as anmore » example of the power of the method.« less

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-06-01

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems.

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

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

On several aspects and applications of the multigrid method for solving partial differential equations

NASA Technical Reports Server (NTRS)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984

DTIC Science & Technology

1985-02-01

0 Here Q denotes the midplane of the plate ?assumed to be a Lipschitzian) with a smooth boundary ", and H (Q) and H (Q) are the Hilbert spaces of...using a reproducing kernel Hilbert space approach, Weinert [8,9] et al, developed a structural correspondence between spline interpolation and linear...597 A Mesh Moving Technique for Time Dependent Partial Differential Equations in Two Space Dimensions David C. Arney and Joseph

Topographic Effects on Geologic Mass Movements

NASA Technical Reports Server (NTRS)

Baloga, Stephen M.; Frey, Herbert (Technical Monitor)

2000-01-01

This report describes research directed toward understanding the response of volcanic lahars and lava flows to changes in the topography along the path of the flow. We have used a variety of steady-state and time-dependent models of lahars and lava flows to calculate the changes in flow dynamics due to variable topography. These models are based on first-order partial differential equations for the local conservation of volume. A global volume conservation requirement is also imposed to determine the extent of the flow as a function of time and the advance rate. Simulated DEMs have been used in this report.

Adaptive mesh strategies for the spectral element method

NASA Technical Reports Server (NTRS)

Mavriplis, Catherine

1992-01-01

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Stability and growth of continental shields in mantle convection models including recurrent melt production

NASA Astrophysics Data System (ADS)

de Smet, J. H.; van den Berg, A. P.; Vlaar, N. J.

1998-10-01

The long-term growth and stability of compositionally layered continental upper mantle has been investigated by numerical modelling. We present the first numerical model of a convecting mantle including differentiation through partial melting resulting in a stable compositionally layered continental upper mantle structure. This structure includes a continental root extending to a depth of about 200 km. The model covers the upper mantle including the crust and incorporates physical features important for the study of the continental upper mantle during secular cooling of the Earth since the Archaean. Among these features are: a partial melt generation mechanism allowing consistent recurrent melting, time-dependent non-uniform radiogenic heat production, and a temperature- and pressure-dependent rheology. The numerical results reveal a long-term growth mechanism of the continental compositional root. This mechanism operates through episodical injection of small diapiric upwellings from the deep layer of undepleted mantle into the continental root which consists of compositionally distinct depleted mantle material. Our modelling results show the layered continental structure to remain stable during at least 1.5 Ga. After this period mantle differentiation through partial melting ceases due to the prolonged secular cooling and small-scale instabilities set in through continental delamination. This stable period of 1.5 Ga is related to a number of limitations in our model. By improving on these limitations in the future this stable period will be extended to more realistic values.

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.

Analysis of differential and active charging phenomena on ATS-5 and ATS-6

NASA Technical Reports Server (NTRS)

Olsen, R. C.; Whipple, E. C., Jr.

1980-01-01

Spacecraft charging on the differential charging and artificial particle emission experiments on ATS 5 and ATS 6 were studied. Differential charging of spacecraft surfaces generated large electrostatic barriers to spacecraft generated electrons, from photoemission, secondary emission, and thermal emitters. The electron emitter could partially or totally discharge the satellite, but the mainframe recharged negatively in a few 10's of seconds. The time dependence of the charging behavior was explained by the relatively large capacitance for differential charging in comparison to the small spacecraft to space capacitance. A daylight charging event on ATS 6 was shown to have a charging behavior suggesting the dominance of differential charging on the absolute potential of the mainframe. Ion engine operations and plasma emission experiments on ATS 6 were shown to be an effective means of controlling the spacecraft potential in eclipse and sunlight. Elimination of barrier effects around the detectors and improving the quality of the particle data are discussed.

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

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

A Double-Blinded, Randomized Comparison of Medetomidine-Tiletamine-Zolazepam and Dexmedetomidine-Tiletamine-Zolazepam Anesthesia in Free-Ranging Brown Bears (Ursus Arctos)

PubMed Central

Cattet, Marc; Zedrosser, Andreas; Stenhouse, Gordon B.; Küker, Susanne; Evans, Alina L.; Arnemo, Jon M.

2017-01-01

We compared anesthetic features, blood parameters, and physiological responses to either medetomidine-tiletamine-zolazepam or dexmedetomidine-tiletamine-zolazepam using a double-blinded, randomized experimental design during 40 anesthetic events of free-ranging brown bears (Ursus arctos) either captured by helicopter in Sweden or by culvert trap in Canada. Induction was smooth and predictable with both anesthetic protocols. Induction time, the need for supplemental drugs to sustain anesthesia, and capture-related stress were analyzed using generalized linear models, but anesthetic protocol did not differentially affect these variables. Arterial blood gases and acid-base status, and physiological responses were examined using linear mixed models. We documented acidemia (pH of arterial blood < 7.35), hypoxemia (partial pressure of arterial oxygen < 80 mmHg), and hypercapnia (partial pressure of arterial carbon dioxide ≥ 45 mmHg) with both protocols. Arterial pH and oxygen partial pressure were similar between groups with the latter improving markedly after oxygen supplementation (p < 0.001). We documented dose-dependent effects of both anesthetic protocols on induction time and arterial oxygen partial pressure. The partial pressure of arterial carbon dioxide increased as respiratory rate increased with medetomidine-tiletamine-zolazepam, but not with dexmedetomidine-tiletamine-zolazepam, demonstrating a differential drug effect. Differences in heart rate, respiratory rate, and rectal temperature among bears could not be attributed to the anesthetic protocol. Heart rate increased with increasing rectal temperature (p < 0.001) and ordinal day of capture (p = 0.002). Respiratory rate was significantly higher in bears captured by helicopter in Sweden than in bears captured by culvert trap in Canada (p < 0.001). Rectal temperature significantly decreased over time (p ≤ 0.05). Overall, we did not find any benefit of using dexmedetomidine-tiletamine-zolazepam instead of medetomidine-tiletamine-zolazepam in the anesthesia of brown bears. Both drug combinations appeared to be safe and reliable for the anesthesia of free-ranging brown bears captured by helicopter or by culvert trap. PMID:28118413

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.

Engineering applications and analysis of vibratory motion fourth order fluid film over the time dependent heated flat plate

NASA Astrophysics Data System (ADS)

Mohmand, Muhammad Ismail; Mamat, Mustafa Bin; Shah, Qayyum

2017-07-01

This article deals with the time dependent analysis of thermally conducting and Magneto-hydrodynamic (MHD) liquid film flow of a fourth order fluid past a vertical and vibratory plate. In this article have been developed for higher order complex nature fluids. The governing-equations have been modeled in the terms of nonlinear partial differential equations with the help of physical boundary circumstances. Two different analytical approaches i.e. Adomian decomposition method (ADM) and the optimal homotopy asymptotic method (OHAM), have been used for discoveryof the series clarification of the problems. Solutions obtained via two diversemethods have been compared using the graphs, tables and found an excellent contract. Variants of the embedded flow parameters in the solution have been analysed through the graphical diagrams.

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.

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.

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.

The Modelling of Axially Translating Flexible Beams

NASA Astrophysics Data System (ADS)

Theodore, R. J.; Arakeri, J. H.; Ghosal, A.

1996-04-01

The axially translating flexible beam with a prismatic joint can be modelled by using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, a non-dimensional form of the Euler Bernoulli beam equation is presented, obtained by using the concept of group velocity, and also the conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions leads to a time-dependent frequency equation for the translating flexible beam. A novel method is presented for solving this time dependent frequency equation by using a differential form of the frequency equation. The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. It is shown by using Lyapunov's first method that the dynamic responses of flexural modal variables become unstable during retraction of the flexible beam, which the dynamic response during extension of the beam is stable. Numerical simulation results are presented for the uniform axial motion induced transverse vibration for a typical flexible beam.

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

PubMed

Gottlieb, Daniel A

2006-03-01

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

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.

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.

Neurotoxicity of "ecstasy" and its metabolites in human dopaminergic differentiated SH-SY5Y cells.

PubMed

Ferreira, Patrícia Silva; Nogueira, Tiago Bernandes; Costa, Vera Marisa; Branco, Paula Sério; Ferreira, Luísa Maria; Fernandes, Eduarda; Bastos, Maria Lourdes; Meisel, Andreas; Carvalho, Félix; Capela, João Paulo

2013-02-04

"Ecstasy" (3,4-methylenedioxymethamphetamine or MDMA) is a widely abused recreational drug, reported to produce neurotoxic effects, both in laboratory animals and in humans. MDMA metabolites can be major contributors for MDMA neurotoxicity. This work studied the neurotoxicity of MDMA and its catechol metabolites, α-methyldopamine (α-MeDA) and N-methyl-α-methyldopamine (N-Me-α-MeDA) in human dopaminergic SH-SY5Y cells differentiated with retinoic acid and 12-O-tetradecanoyl-phorbol-13-acetate. Differentiation led to SH-SY5Y neurons with higher ability to accumulate dopamine and higher resistance towards dopamine neurotoxicity. MDMA catechol metabolites were neurotoxic to SH-SY5Y neurons, leading to caspase 3-independent cell death in a concentration- and time-dependent manner. MDMA did not show a concentration- and time-dependent death. Pre-treatment with the antioxidant and glutathione precursor, N-acetylcysteine (NAC), resulted in strong protection against the MDMA metabolites' neurotoxicity. Neither the superoxide radical scavenger, tiron, nor the inhibitor of the dopamine (DA) transporter, GBR 12909, prevented the metabolites' toxicity. Cells exposed to α-MeDA showed an increase in intracellular glutathione (GSH) levels, which, at the 48 h time-point, was not dependent in the activity increase of γ-glutamylcysteine synthetase (γ-GCS), revealing a possible transient effect. Importantly, pre-treatment with buthionine sulfoximine (BSO), an inhibitor of γ-GCS, prevented α-MeDA induced increase in GSH levels, but did not augment this metabolite cytotoxicity. Even so, BSO pre-treatment abolished NAC protective effects against α-MeDA neurotoxicity, which were, at least partially, due to GSH de novo synthesis. Inversely, pre-treatment of cells with BSO augmented N-Me-α-MeDA-induced neurotoxicity, but only slightly affected NAC neuroprotection. In conclusion, MDMA catechol metabolites promote differential toxic effects to differentiated dopaminergic human SH-SY5Y cells. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Aripiprazole and Haloperidol Activate GSK3β-Dependent Signalling Pathway Differentially in Various Brain Regions of Rats.

PubMed

Pan, Bo; Huang, Xu-Feng; Deng, Chao

2016-03-28

Aripiprazole, a dopamine D₂ receptor (D₂R) partial agonist, possesses a unique clinical profile. Glycogen synthase kinase 3β (GSK3β)-dependent signalling pathways have been implicated in the pathophysiology of schizophrenia and antipsychotic drug actions. The present study examined whether aripiprazole differentially affects the GSK3β-dependent signalling pathways in the prefrontal cortex (PFC), nucleus accumbens (NAc), and caudate putamen (CPu), in comparison with haloperidol (a D₂R antagonist) and bifeprunox (a D₂R partial agonist). Rats were orally administrated aripiprazole (0.75 mg/kg), bifeprunox (0.8 mg/kg), haloperidol (0.1 mg/kg) or vehicle three times per day for one week. The levels of protein kinase B (Akt), p-Akt, GSK3β, p-GSK3β, dishevelled (Dvl)-3, and β-catenin were measured by Western Blots. Aripiprazole increased GSK3β phosphorylation in the PFC and NAc, respectively, while haloperidol elevated it in the NAc only. However, Akt activity was not changed by any of these drugs. Additionally, both aripiprazole and haloperidol, but not bifeprunox, increased the expression of Dvl-3 and β-catenin in the NAc. The present study suggests that activation of GSK3β phosphorylation in the PFC and NAc may be involved in the clinical profile of aripiprazole; additionally, aripiprazole can increase GSK3β phosphorylation via the Dvl-GSK3β-β-catenin signalling pathway in the NAc, probably due to its relatively low intrinsic activity at D₂Rs.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

NASA Astrophysics Data System (ADS)

Barker, T.; Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

PubMed Central

Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-01-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities. PMID:28588402

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology.

PubMed

Barker, T; Schaeffer, D G; Shearer, M; Gray, J M N T

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.

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.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Spatial and temporal accuracy of asynchrony-tolerant finite difference schemes for partial differential equations at extreme scales

NASA Astrophysics Data System (ADS)

Kumari, Komal; Donzis, Diego

2017-11-01

Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.

Model selection for pion photoproduction

DOE PAGES

Landay, J.; Doring, M.; Fernandez-Ramirez, C.; ...

2017-01-12

Partial-wave analysis of meson and photon-induced reactions is needed to enable the comparison of many theoretical approaches to data. In both energy-dependent and independent parametrizations of partial waves, the selection of the model amplitude is crucial. Principles of the S matrix are implemented to a different degree in different approaches; but a many times overlooked aspect concerns the selection of undetermined coefficients and functional forms for fitting, leading to a minimal yet sufficient parametrization. We present an analysis of low-energy neutral pion photoproduction using the least absolute shrinkage and selection operator (LASSO) in combination with criteria from information theory andmore » K-fold cross validation. These methods are not yet widely known in the analysis of excited hadrons but will become relevant in the era of precision spectroscopy. As a result, the principle is first illustrated with synthetic data; then, its feasibility for real data is demonstrated by analyzing the latest available measurements of differential cross sections (dσ/dΩ), photon-beam asymmetries (Σ), and target asymmetry differential cross sections (dσ T/d≡Tdσ/dΩ) in the low-energy regime.« less

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.

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.

Bropirimine inhibits osteoclast differentiation through production of interferon-β

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

Suzuki, Hiroaki; Mochizuki, Ayako; Yoshimura, Kentaro

Bropirimine is a synthetic agonist for toll-like receptor 7 (TLR7). In this study, we investigated the effects of bropirimine on differentiation and bone-resorbing activity of osteoclasts in vitro. Bropirimine inhibited osteoclast differentiation of mouse bone marrow-derived macrophages (BMMs) induced by receptor activator of nuclear factor κB ligand (RANKL) in a concentration-dependent manner. Furthermore, it suppressed the mRNA expression of nuclear factor of activated T-cells, cytoplasmic, calcineurin-dependent 1 (NFATc1), a master transcription factor for osteoclast differentiation, without affecting BMM viability. Bropirimine also inhibited osteoclast differentiation induced in co-cultures of mouse bone marrow cells (BMCs) and mouse osteoblastic UAMS-32 cells in the presencemore » of activated vitamin D{sub 3}. Bropirimine partially suppressed the expression of RANKL mRNA in UAMS-32 cells induced by activated vitamin D{sub 3}. Finally, the anti-interferon-β (IFN-β) antibody restored RANKL-dependent differentiation of BMMs into osteoclasts suppressed by bropirimine. These results suggest that bropirimine inhibits differentiation of osteoclast precursor cells into osteoclasts via TLR7-mediated production of IFN-β.« less

Age-dependent epigenetic control of differentiation inhibitors is critical for remyelination efficiency

PubMed Central

Shen, Siming; Sandoval, Juan; Swiss, Victoria A; Li, Jiadong; Dupree, Jeff; Franklin, Robin J M; Casaccia-Bonnefil, Patrizia

2009-01-01

The efficiency of remyelination decreases with age, but the molecular mechanisms responsible for this decline remain only partially understood. In this study, we show that remyelination is regulated by age-dependent epigenetic control of gene expression. In demyelinated young brains, new myelin synthesis is preceded by downregulation of oligodendrocyte differentiation inhibitors and neural stem cell markers, and this is associated with recruitment of histone deacetylases (HDACs) to promoter regions. In demyelinated old brains, HDAC recruitment is inefficient, and this allows the accumulation of transcriptional inhibitors and prevents the subsequent surge in myelin gene expression. Defective remyelination can be recapitulated in vivo in mice receiving systemic administration of pharmacological HDAC inhibitors during cuprizone treatment and is consistent with in vitro results showing defective differentiation of oligodendrocyte progenitors after silencing specific HDAC isoforms. Thus, we suggest that inefficient epigenetic modulation of the oligodendrocyte differentiation program contributes to the age-dependent decline in remyelination efficiency. PMID:19160500

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.

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.

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.

Electrostatic interactions guide the active site face of a structure-specific ribonuclease to its RNA substrate.

PubMed

Plantinga, Matthew J; Korennykh, Alexei V; Piccirilli, Joseph A; Correll, Carl C

2008-08-26

Restrictocin, a member of the alpha-sarcin family of site-specific endoribonucleases, uses electrostatic interactions to bind to the ribosome and to RNA oligonucleotides, including the minimal specific substrate, the sarcin/ricin loop (SRL) of 23S-28S rRNA. Restrictocin binds to the SRL by forming a ground-state E:S complex that is stabilized predominantly by Coulomb interactions and depends on neither the sequence nor structure of the RNA, suggesting a nonspecific complex. The 22 cationic residues of restrictocin are dispersed throughout this protein surface, complicating a priori identification of a Coulomb interacting surface. Structural studies have identified an enzyme-substrate interface, which is expected to overlap with the electrostatic E:S interface. Here, we identified restrictocin residues that contribute to binding in the E:S complex by determining the salt dependence [partial differential log(k 2/ K 1/2)/ partial differential log[KCl

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

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.

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.

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.

Aripiprazole and Haloperidol Activate GSK3β-Dependent Signalling Pathway Differentially in Various Brain Regions of Rats

PubMed Central

Pan, Bo; Huang, Xu-Feng; Deng, Chao

2016-01-01

Aripiprazole, a dopamine D2 receptor (D2R) partial agonist, possesses a unique clinical profile. Glycogen synthase kinase 3β (GSK3β)-dependent signalling pathways have been implicated in the pathophysiology of schizophrenia and antipsychotic drug actions. The present study examined whether aripiprazole differentially affects the GSK3β-dependent signalling pathways in the prefrontal cortex (PFC), nucleus accumbens (NAc), and caudate putamen (CPu), in comparison with haloperidol (a D2R antagonist) and bifeprunox (a D2R partial agonist). Rats were orally administrated aripiprazole (0.75 mg/kg), bifeprunox (0.8 mg/kg), haloperidol (0.1 mg/kg) or vehicle three times per day for one week. The levels of protein kinase B (Akt), p-Akt, GSK3β, p-GSK3β, dishevelled (Dvl)-3, and β-catenin were measured by Western Blots. Aripiprazole increased GSK3β phosphorylation in the PFC and NAc, respectively, while haloperidol elevated it in the NAc only. However, Akt activity was not changed by any of these drugs. Additionally, both aripiprazole and haloperidol, but not bifeprunox, increased the expression of Dvl-3 and β-catenin in the NAc. The present study suggests that activation of GSK3β phosphorylation in the PFC and NAc may be involved in the clinical profile of aripiprazole; additionally, aripiprazole can increase GSK3β phosphorylation via the Dvl-GSK3β-β-catenin signalling pathway in the NAc, probably due to its relatively low intrinsic activity at D2Rs. PMID:27043526

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.

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.

1993-01-01

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).

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.

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.

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

Theoretical predictions of latitude dependencies in the solar wind

NASA Technical Reports Server (NTRS)

Winge, C. R., Jr.; Coleman, P. J., Jr.

1974-01-01

Results are presented which were obtained with the Winge-Coleman model for theoretical predictions of latitudinal dependencies in the solar wind. A first-order expansion is described which allows analysis of first-order latitudinal variations in the coronal boundary conditions and results in a second-order partial differential equation for the perturbation stream function. Latitudinal dependencies are analytically separated out in the form of Legendre polynomials and their derivative, and are reduced to the solution of radial differential equations. This analysis is shown to supply an estimate of how large the coronal variation in latitude must be to produce an 11 km/sec/deg gradient in the radial velocity of the solar wind, assuming steady-state processes.

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.

Exciting Quantized Vortex Rings in a Superfluid Unitary Fermi Gas

NASA Astrophysics Data System (ADS)

Bulgac, Aurel

2014-03-01

In a recent article, Yefsah et al., Nature 499, 426 (2013) report the observation of an unusual quantum excitation mode in an elongated harmonically trapped unitary Fermi gas. After phase imprinting a domain wall, they observe collective oscillations of the superfluid atomic cloud with a period almost an order of magnitude larger than that predicted by any theory of domain walls, which they interpret as a possible new quantum phenomenon dubbed ``a heavy soliton'' with an inertial mass some 50 times larger than one expected for a domain wall. We present compelling evidence that this ``heavy soliton'' is instead a quantized vortex ring by showing that the main aspects of the experiment can be naturally explained within an extension of the time-dependent density functional theory (TDDFT) to superfluid systems. The numerical simulations required the solution of some 260,000 nonlinear coupled time-dependent 3-dimensional partial differential equations and was implemented on 2048 GPUs on the Cray XK7 supercomputer Titan of the Oak Ridge Leadership Computing Facility.

A framework for simultaneous aerodynamic design optimization in the presence of chaos

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

Günther, Stefanie, E-mail: stefanie.guenther@scicomp.uni-kl.de; Gauger, Nicolas R.; Wang, Qiqi

Integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward-in-time information propagation of classical time-stepping methods. This paper applies the simultaneous single-step one-shot optimization method to a reformulated unsteady constraint that allows for both forward- and backward-in-time information propagation. Especially in the presence of chaotic and turbulent flow, solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length. The new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations. This enables efficient one-shot optimizationmore » that is independent of the time domain length, even in the presence of chaos.« less

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.

Rapid differentiation in a sill-like magma reservoir: a case study from the campi flegrei caldera.

PubMed

Pappalardo, Lucia; Mastrolorenzo, Giuseppe

2012-01-01

In recent decades, geophysical investigations have detected wide magma reservoirs beneath quiescent calderas. However, the discovery of partially melted horizons inside the crust is not sufficient to put constraints on capability of reservoirs to supply cataclysmic eruptions, which strictly depends on the chemical-physical properties of magmas (composition, viscosity, gas content etc.), and thus on their differentiation histories. In this study, by using geochemical, isotopic and textural records of rocks erupted from the high-risk Campi Flegrei caldera, we show that the alkaline magmas have evolved toward a critical state of explosive behaviour over a time span shorter than the repose time of most volcanic systems and that these magmas have risen rapidly toward the surface. Moreover, similar results on the depth and timescale of magma storage were previously obtained for the neighbouring Somma-Vesuvius volcano. This consistency suggests that there might be a unique long-lived magma pool beneath the whole Neapolitan area.

Rapid differentiation in a sill-like magma reservoir: a case study from the campi flegrei caldera

PubMed Central

Pappalardo, Lucia; Mastrolorenzo, Giuseppe

2012-01-01

In recent decades, geophysical investigations have detected wide magma reservoirs beneath quiescent calderas. However, the discovery of partially melted horizons inside the crust is not sufficient to put constraints on capability of reservoirs to supply cataclysmic eruptions, which strictly depends on the chemical-physical properties of magmas (composition, viscosity, gas content etc.), and thus on their differentiation histories. In this study, by using geochemical, isotopic and textural records of rocks erupted from the high-risk Campi Flegrei caldera, we show that the alkaline magmas have evolved toward a critical state of explosive behaviour over a time span shorter than the repose time of most volcanic systems and that these magmas have risen rapidly toward the surface. Moreover, similar results on the depth and timescale of magma storage were previously obtained for the neighbouring Somma-Vesuvius volcano. This consistency suggests that there might be a unique long-lived magma pool beneath the whole Neapolitan area. PMID:23050096

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

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.

Functional differentiability in time-dependent quantum mechanics.

PubMed

Penz, Markus; Ruggenthaler, Michael

2015-03-28

In this work, we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave functions, Fréchet differentiability is proven. From this follows an estimate for the difference of two solutions to the time-dependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the one-particle density and to bounded operators, and present a rigorous formulation of non-equilibrium linear-response theory where the usual Lehmann representation of the linear-response kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of time-dependent density-functional theory.

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 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.

A theory of post-stall transients in axial compression systems. I - Development of equations

NASA Technical Reports Server (NTRS)

Moore, F. K.; Greitzer, E. M.

1985-01-01

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

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.

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1976-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitational and rotational terms in the equations are of first order in the space variables, the pressure-gradient terms are of second order, and the turbulent-viscosity term is of third order. The presence of turbulent viscosity ensures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial flow is always inward and allows collapse to occur (axially) even when the rotation is large. An approximate solution of the governing partial differential equations is also given in order to study the spatial distributions of the density and velocity.

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1975-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the intial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given, in order to study the spacial distributions of the density and velocity.

Exponential growth and Gaussian—like fluctuations of solutions of stochastic differential equations with maximum functionals

NASA Astrophysics Data System (ADS)

Appleby, J. A. D.; Wu, H.

2008-11-01

In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1975-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given; the equations are used to study the spacial distributions of the density and velocity.

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.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Queues on a Dynamically Evolving Graph

NASA Astrophysics Data System (ADS)

Mandjes, Michel; Starreveld, Nicos J.; Bekker, René

2018-04-01

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between `up' and `down'. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues' time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links' outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

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.

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

NASA Astrophysics Data System (ADS)

Kumar, Rakesh; Sood, Shilpa; Shehzad, Sabir Ali; Sheikholeslami, Mohsen

A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables.

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.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Kreider, K. L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

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.

Functional requirements of a mathematical model of the heart.

PubMed

Palladino, Joseph L; Noordergraaf, Abraham

2009-01-01

Functional descriptions of the heart, especially the left ventricle, are often based on the measured variables pressure and ventricular outflow, embodied as a time-varying elastance. The fundamental difficulty of describing the mechanical properties of the heart with a time-varying elastance function that is set a priori is described. As an alternative, a new functional model of the heart is presented, which characterizes the ventricle's contractile state with parameters, rather than variables. Each chamber is treated as a pressure generator that is time and volume dependent. The heart's complex dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds. This equation permits the calculation of ventricular elastance via E(v) = partial differentialp(v)/ partial differentialV(v). This heart model is defined independently from load properties, and ventricular elastance is dynamic and reflects changing numbers of crossbridge bonds. In this paper, the functionality of this new heart model is presented via computed work loops that demonstrate the Frank-Starling mechanism and the effects of preload, the effects of afterload, inotropic changes, and varied heart rate, as well as the interdependence of these effects. Results suggest the origin of the equivalent of Hill's force-velocity relation in the ventricle.

On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation

PubMed Central

Wahle, Chris W.; Ross, David S.; Thurston, George M.

2012-01-01

We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)10.1063/1.2937902], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures. PMID:22830693

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.

Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment

NASA Astrophysics Data System (ADS)

Liang, Feng; Yang, Xiao-Dong; Zhang, Wei; Qian, Ying-Jing

2018-03-01

In this paper, a dynamical model of simply-supported spinning pipes conveying fluid with axial deployment is proposed and the transverse free vibration and stability for such a doubly gyroscopic system involving time-dependent parameters are investigated. The partial differential equations of motion are derived by the extended Hamilton principle and then truncated by the Galerkin technique. The time-variant frequencies, mode shapes and responses to initial conditions are comprehensively investigated to reveal the dynamical essence of the system. It is indicated that the qualitative stability evolution of the system mainly depends on the effect of fluid-structure interaction (FSI), while the spinning motion will enhance the pipe rigidity and eliminate the buckling instability. The dynamical evolution of a retracting pipe is almost inverse to that of the deploying one. The pipe possesses different mode configurations of spatial curves as the pipe length increases and some modal and response characteristics of the present system are found rather distinct from those of deploying cantilevered structures.

A mathematical model of intestinal oedema formation.

PubMed

Young, Jennifer; Rivière, Béatrice; Cox, Charles S; Uray, Karen

2014-03-01

Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.

Miscibility, Crystallization, and Rheological Behavior of Solution Casting Poly(3-hydroxybutyrate)/poly(ethylene succinate) Blends Probed by Differential Scanning Calorimetry, Rheology, and Optical Microscope Techniques

NASA Astrophysics Data System (ADS)

Sun, Wei-hua; Qiao, Xiao-ping; Cao, Qi-kun; Liu, Jie-ping

2010-02-01

The miscibility and crystallization of solution casting biodegradable poly(3-hydroxybutyrate)/poly(ethylene succinate) (PHB/PES) blends was investigated by differential scanning calorimetry, rheology, and optical microscopy. The blends showed two glass transition temperatures and a depression of melting temperature of PHB with compositions in phase diagram, which indicated that the blend was partially miscible. The morphology observation supported this result. It was found that the PHB and PES can crystallize simultaneously or upon stepwise depending on the crystallization temperatures and compositions. The spherulite growth rate of PHB increased with increasing of PES content. The influence of compositions on the spherulitic growth rate for the partially miscible polymer blends was discussed.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

On a `time' reparametrization in relativistic electrodynamics with travelling waves

NASA Astrophysics Data System (ADS)

Fiore, Gaetano

2018-01-01

We briefly report on our method [23] of simplifying the equations of motion of charged particles in an electromagnetic (EM) field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent variables and the independent one (light-like coordinate ξ instead of time t). We sketch its application to a few cases of extreme laser-induced accelerations, both in vacuum and in plane problems at the vacuum-plasma interface, where we are able to reduce the system of the (Lorentz-Maxwell and continuity) partial differential equations into a family of decoupled systems of Hamilton equations in 1 dimension. Since Fourier analysis plays no role, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulses".

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…

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

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

Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads

NASA Astrophysics Data System (ADS)

Stepanov, Alexey B.; Antman, Stuart S.

2017-12-01

This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.

The APC/C Coordinates Retinal Differentiation with G1 Arrest through the Nek2-Dependent Modulation of Wingless Signaling.

PubMed

Martins, Torcato; Meghini, Francesco; Florio, Francesca; Kimata, Yuu

2017-01-09

The cell cycle is coordinated with differentiation during animal development. Here we report a cell-cycle-independent developmental role for a master cell-cycle regulator, the anaphase-promoting complex or cyclosome (APC/C), in the regulation of cell fate through modulation of Wingless (Wg) signaling. The APC/C controls both cell-cycle progression and postmitotic processes through ubiquitin-dependent proteolysis. Through an RNAi screen in the developing Drosophila eye, we found that partial APC/C inactivation severely inhibits retinal differentiation independently of cell-cycle defects. The differentiation inhibition coincides with hyperactivation of Wg signaling caused by the accumulation of a Wg modulator, Drosophila Nek2 (dNek2). The APC/C degrades dNek2 upon synchronous G1 arrest prior to differentiation, which allows retinal differentiation through local suppression of Wg signaling. We also provide evidence that decapentaplegic signaling may posttranslationally regulate this APC/C function. Thus, the APC/C coordinates cell-fate determination with the cell cycle through the modulation of developmental signaling pathways. Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

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

PubMed

Lenarda, P; Paggi, M

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

TRUMP; transient and steady state temperature distribution. [IBM360,370; CDC7600; FORTRAN IV (95%) and BAL (5%) (IBM); FORTRAN IV (CDC)

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

Elrod, D.C.; Turner, W.D.

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables--temperature, pressure, or field strength. Initial conditions may vary with spatial position, andmore » among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.IBM360,370;CDC7600; FORTRAN IV (95%) and BAL (5%) (IBM); FORTRAN IV (CDC); OS/360 (IBM360), OS/370 (IBM370), SCOPE 2.1.5 (CDC7600); As dimensioned, the program requires 400K bytes of storage on an IBM370 and 145,100 (octal) words on a CDC7600.« less

On the Importance of the Dynamics of Discretizations

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)

1995-01-01

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

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.

A Numerical Study of Three Moving-Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines

NASA Astrophysics Data System (ADS)

Furzeland, R. M.; Verwer, J. G.; Zegeling, P. A.

1990-08-01

In recent years, several sophisticated packages based on the method of lines (MOL) have been developed for the automatic numerical integration of time-dependent problems in partial differential equations (PDEs), notably for problems in one space dimension. These packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers. However, from the PDE point of view, they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes, but use just a fixed space grid, chosen a priori, for the entire calculation. For solutions possessing sharp spatial transitions that move, e.g., travelling wave fronts or emerging boundary and interior layers, a grid held fixed for the entire calculation is computationally inefficient, since for a good solution this grid often must contain a very large number of nodes. In such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity. Methods and codes that operate this way belong to the realm of adaptive or moving-grid methods. Following the MOL approach, this paper is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of three moving-grid methods for 1D problems, viz., the finite-element method of Miller and co-workers, the method published by Petzold, and a method based on ideas adopted from Dorfi and Drury. Our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness, and efficiency of the conventional MOL approach. Therefore, considerable attention is paid to the temporal performance of the methods.

(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.

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.

Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

n-Alkanols potentiate sodium channel inactivation in squid giant axons.

PubMed Central

Oxford, G S; Swenson, R P

1979-01-01

The effects of n-octanol and n-decanol on nerve membrane sodium channels were examined in internally perfused, voltage-clamped squid giant axons. Both n-octanol and n-decanol almost completely eliminated the residual sodium conductance at the end of 8-ms voltage steps. In contrast, peak sodium conductance was only partially reduced. This block of peak and residual sodium conductance was very reversible and seen with both internal and external alkanol application. The differential sensitivity of peak and residual conductance to alkanol treatment was eliminated after internal pronase treatment, suggesting that n-octanol and n-decanol enhance the normal inactivation mechanism rather than directly blocking channels in a time-dependent manner. PMID:233577

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Differential effects of lipid depletion on membrane sodium-plus-potassium ion-dependent adenosine triphosphatase and potassium ion-dependent phosphatase.

PubMed Central

Wheeler, K P; Walker, J A

1975-01-01

The phospholipid-dependence of the (Na-++K-+)-dependent ATPase (adenosine triphosphatase) (EC 3.6.1.3) and associated K-+-dependent phosphatase activity (EC 3.6.1.7) have been compared. Unlike the (Na-++K-+)-dependent ATPase activities, the K-+-dependent phosphatase activities of a number of different preparations were not closely correlated with their total phospholipid contents. After partial lipid depletion with a single extraction in Lubrol W the residual ATPase and phosphatase activities were correlated, but their magnitudes were quite different: on average only about 5% of the former remained compared with 50% of the latter. A similar differential effect on these activities was found after extraction with deoxycholate. In contrast with the ATPase, consistent restoration of the phosphatase activity of Lubrol-extracted enzymes by added exogenous phospholipids was not observed. We conclude that, although the K-+-dependent phosphatase may be lipid-dependent, the lipid requirement must be different from that of the complete ATPase system, and this difference should help investigations of their relationship. PMID:167727

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

Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Thrombocytopenia induced by the histone deacetylase inhibitor abexinostat involves p53-dependent and -independent mechanisms.

PubMed

Ali, A; Bluteau, O; Messaoudi, K; Palazzo, A; Boukour, S; Lordier, L; Lecluse, Y; Rameau, P; Kraus-Berthier, L; Jacquet-Bescond, A; Lelièvre, H; Depil, S; Dessen, P; Solary, E; Raslova, H; Vainchenker, W; Plo, I; Debili, N

2013-07-25

Abexinostat is a pan histone deacetylase inhibitor (HDACi) that demonstrates efficacy in malignancy treatment. Like other HDACi, this drug induces a profound thrombocytopenia whose mechanism is only partially understood. We have analyzed its effect at doses reached in patient plasma on in vitro megakaryopoiesis derived from human CD34(+) cells. When added at day 0 in culture, abexinostat inhibited CFU-MK growth, megakaryocyte (MK) proliferation and differentiation. These effects required only a short incubation period. Decreased proliferation was due to induction of apoptosis and was not related to a defect in TPO/MPL/JAK2/STAT signaling. When added later (day 8), the compound induced a dose-dependent decrease (up to 10-fold) in proplatelet (PPT) formation. Gene profiling from MK revealed a silencing in the expression of DNA repair genes with a marked RAD51 decrease at protein level. DNA double-strand breaks were increased as attested by elevated γH2AX phosphorylation level. Moreover, ATM was phosphorylated leading to p53 stabilization and increased BAX and p21 expression. The use of a p53 shRNA rescued apoptosis, and only partially the defect in PPT formation. These results suggest that HDACi induces a thrombocytopenia by a p53-dependent mechanism along MK differentiation and a p53-dependent and -independent mechanism for PPT formation.

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.

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.

Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

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).

Local bifurcations in differential equations with state-dependent delay.

PubMed

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics.

PubMed

Xia, Yingcun; Bjørnstad, Ottar N; Grenfell, Bryan T

2004-08-01

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.

Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface

NASA Astrophysics Data System (ADS)

Zaigham Zia, Q. M.; Ullah, Ikram; Waqas, M.; Alsaedi, A.; Hayat, T.

2018-03-01

This research intends to elaborate Soret-Dufour characteristics in mixed convective radiated Casson liquid flow by exponentially heated surface. Novel features of exponential space dependent heat source are introduced. Appropriate variables are implemented for conversion of partial differential frameworks into a sets of ordinary differential expressions. Homotopic scheme is employed for construction of analytic solutions. Behavior of various embedding variables on velocity, temperature and concentration distributions are plotted graphically and analyzed in detail. Besides, skin friction coefficients and heat and mass transfer rates are also computed and interpreted. The results signify the pronounced characteristics of temperature corresponding to convective and radiation variables. Concentration bears opposite response for Soret and Dufour variables.

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

Plant family identity distinguishes patterns of carbon and nitrogen stable isotope abundance and nitrogen concentration in mycoheterotrophic plants associated with ectomycorrhizal fungi

PubMed Central

Hynson, Nicole A.; Schiebold, Julienne M.-I.; Gebauer, Gerhard

2016-01-01

Background and Aims Mycoheterotrophy entails plants meeting all or a portion of their carbon (C) demands via symbiotic interactions with root-inhabiting mycorrhizal fungi. Ecophysiological traits of mycoheterotrophs, such as their C stable isotope abundances, strongly correlate with the degree of species’ dependency on fungal C gains relative to C gains via photosynthesis. Less explored is the relationship between plant evolutionary history and mycoheterotrophic plant ecophysiology. We hypothesized that the C and nitrogen (N) stable isotope compositions, and N concentrations of fully and partially mycoheterotrophic species differentiate them from autotrophs, and that plant family identity would be an additional and significant explanatory factor for differences in these traits among species. We focused on mycoheterotrophic species that associate with ectomycorrhizal fungi from plant families Ericaceae and Orchidaceae. Methods Published and unpublished data were compiled on the N concentrations, C and N stable isotope abundances (δ13C and δ15N) of fully (n = 18) and partially (n = 22) mycoheterotrophic species from each plant family as well as corresponding autotrophic reference species (n = 156). These data were used to calculate site-independent C and N stable isotope enrichment factors (ε). Then we tested for differences in N concentration, 13C and 15N enrichment among plant families and trophic strategies. Key Results We found that in addition to differentiating partially and fully mycoheterotrophic species from each other and from autotrophs, C and N stable isotope enrichment also differentiates plant species based on familial identity. Differences in N concentrations clustered at the plant family level rather than the degree of dependency on mycoheterotrophy. Conclusions We posit that differences in stable isotope composition and N concentrations are related to plant family-specific physiological interactions with fungi and their environments. PMID:27451987

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

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.

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

Timed Knickkopf function is essential for wing cuticle formation in Drosophila melanogaster.

PubMed

Li, Kaixia; Zhang, Xubo; Zuo, Ying; Liu, Weimin; Zhang, Jianzhen; Moussian, Bernard

2017-10-01

The insect cuticle is an extracellular matrix that consists of the polysaccharide chitin, proteins, lipids and organic molecules that are arranged in distinct horizontal layers. In Drosophila melanogaster, these layers are not formed sequentially, but, at least partially, at the same time. Timing of the underlying molecular mechanisms is conceivably crucial for cuticle formation. To study this issue, we determined the time period during which the function of Knickkopf (Knk), a key factor of chitin organization, is required for wing cuticle differentiation in D. melanogaster. Although knk is expressed throughout metamorphosis, we demonstrate that its expression 30 h prior and 48 h after pupariation is essential for correct wing cuticle formation. In other words, expression beyond this period is futile. Importantly, manipulation of Knk expression during this time causes wing bending suggesting an effect of Knk amounts on the physical properties of the wing cuticle. Manipulation of Knk expression also interferes with the structure and function of the cuticle surface. First, we show that the shape of surface nano-structures depends on the expression levels of knk. Second, we find that cuticle impermeability is compromised in wings with reduced knk expression. In summary, despite the extended supply of Knk during metamorphosis, controlled amounts of Knk are important for correct wing cuticle differentiation and function in a concise period of time. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

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

Acoustic wave simulation using an overset grid for the global monitoring system

NASA Astrophysics Data System (ADS)

Kushida, N.; Le Bras, R.

2017-12-01

The International Monitoring System of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) has been monitoring hydro-acoustic and infrasound waves over the globe. Because of the complex natures of the oceans and the atmosphere, computer simulation can play an important role in understanding the observed signals. In this regard, methods which depend on partial differential equations and require minimum modelling, are preferable. So far, to our best knowledge, acoustic wave propagation simulations based on partial differential equations on such a large scale have not been performed (pp 147 - 161 of ref [1], [2]). The main difficulties in building such simulation codes are: (1) considering the inhomogeneity of medium including background flows, (2) high aspect ratio of computational domain, (3) stability during long time integration. To overcome these difficulties, we employ a two-dimensional finite different (FDM) scheme on spherical coordinates with the Yin-Yang overset grid[3] solving the governing equation of acoustic waves introduces by Ostashev et. al.[4]. The comparison with real recording examples in hydro-acoustic will be presented at the conference. [1] Paul C. Etter: Underwater Acoustic Modeling and Simulation, Fourth Edition, CRC Press, 2013. [2] LIAN WANG et. al.: REVIEW OF UNDERWATER ACOUSTIC PROPAGATION MODELS, NPL Report AC 12, 2014. [3] A. Kageyama and T. Sato: "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005, 2004. [4] Vladimir E. Ostashev et. al: Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation, Acoustical Society of America. DOI: 10.1121/1.1841531, 2005.

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.

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.

Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

DOE PAGES

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

2017-09-04

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support ourmore » construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

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

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numericalmore » experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.« less

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Remote sensing applied to numerical modelling. [water resources pollution

NASA Technical Reports Server (NTRS)

Sengupta, S.; Lee, S. S.; Veziroglu, T. N.; Bland, R.

1975-01-01

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

PubMed Central

2014-01-01

Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be “well balanced” and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments. PMID:24563581

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

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

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

Automatic differentiation evaluated as a tool for rotorcraft design and optimization

NASA Technical Reports Server (NTRS)

Walsh, Joanne L.; Young, Katherine C.

1995-01-01

This paper investigates the use of automatic differentiation (AD) as a means for generating sensitivity analyses in rotorcraft design and optimization. This technique transforms an existing computer program into a new program that performs sensitivity analysis in addition to the original analysis. The original FORTRAN program calculates a set of dependent (output) variables from a set of independent (input) variables, the new FORTRAN program calculates the partial derivatives of the dependent variables with respect to the independent variables. The AD technique is a systematic implementation of the chain rule of differentiation, this method produces derivatives to machine accuracy at a cost that is comparable with that of finite-differencing methods. For this study, an analysis code that consists of the Langley-developed hover analysis HOVT, the comprehensive rotor analysis CAMRAD/JA, and associated preprocessors is processed through the AD preprocessor ADIFOR 2.0. The resulting derivatives are compared with derivatives obtained from finite-differencing techniques. The derivatives obtained with ADIFOR 2.0 are exact within machine accuracy and do not depend on the selection of step-size, as are the derivatives obtained with finite-differencing techniques.

Energy use in repairs by cover concrete replacement or silane treatment for extending service life of chloride-exposed concrete structures

NASA Astrophysics Data System (ADS)

Petcherdchoo, A.

2018-05-01

In this study, the service life of repaired concrete structures under chloride environment is predicted. This prediction is performed by considering the mechanism of chloride ion diffusion using the partial differential equation (PDE) of the Fick’s second law. The one-dimensional PDE cannot simply be solved, when concrete structures are cyclically repaired with cover concrete replacement or silane treatment. The difficulty is encountered in solving position-dependent chloride profile and diffusion coefficient after repairs. In order to remedy the difficulty, the finite difference method is used. By virtue of numerical computation, the position-dependent chloride profile can be treated position by position. And, based on the Crank-Nicolson scheme, a proper formulation embedded with position-dependent diffusion coefficient can be derived. By using the aforementioned idea, position- and time-dependent chloride ion concentration profiles for concrete structures with repairs can be calculated and shown, and their service life can be predicted. Moreover, the use of energy in different repair actions is also considered for comparison. From the study, it is found that repairs can control rebar corrosion and/or concrete cracking depending on repair actions.

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Green's Functions in Space and Time.

ERIC Educational Resources Information Center

Rowe, E. G. Peter

1979-01-01

Gives a sketch of some topics in distribution theory that is technically simple, yet provides techniques for handling the partial differential equations satisfied by the most important Green's functions in physics. (Author/GA)

Modelling Solar Energetic Particle Propagation in Realistic Heliospheric Solar Wind Conditions Using a Combined MHD and Stochastic Differential Equation Approach

NASA Astrophysics Data System (ADS)

Wijsen, N.; Poedts, S.; Pomoell, J.

2017-12-01

Solar energetic particles (SEPs) are high energy particles originating from solar eruptive events. These particles can be energised at solar flare sites during magnetic reconnection events, or in shock waves propagating in front of coronal mass ejections (CMEs). These CME-driven shocks are in particular believed to act as powerful accelerators of charged particles throughout their propagation in the solar corona. After escaping from their acceleration site, SEPs propagate through the heliosphere and may eventually reach our planet where they can disrupt the microelectronics on satellites in orbit and endanger astronauts among other effects. Therefore it is of vital importance to understand and thereby build models capable of predicting the characteristics of SEP events. The propagation of SEPs in the heliosphere can be described by the time-dependent focused transport equation. This five-dimensional parabolic partial differential equation can be solved using e.g., a finite difference method or by integrating a set of corresponding first order stochastic differential equations. In this work we take the latter approach to model SEP events under different solar wind and scattering conditions. The background solar wind in which the energetic particles propagate is computed using a magnetohydrodynamic model. This allows us to study the influence of different realistic heliospheric configurations on SEP transport. In particular, in this study we focus on exploring the influence of high speed solar wind streams originating from coronal holes that are located close to the eruption source region on the resulting particle characteristics at Earth. Finally, we discuss our upcoming efforts towards integrating our particle propagation model with time-dependent heliospheric MHD space weather modelling.

Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls

NASA Astrophysics Data System (ADS)

Dauenhauer, Eric C.; Majdalani, Joseph

2003-06-01

This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Fast neural solution of a nonlinear wave equation

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad; Barhen, Jacob

1992-01-01

A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

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

Pabst, M., E-mail: M.Pabst@fz-juelich.de

2014-06-14

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximatedmore » by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.« less

Noise exposure of immature rats can induce different age-dependent extra-auditory alterations that can be partially restored by rearing animals in an enriched environment.

PubMed

Molina, S J; Capani, F; Guelman, L R

2016-04-01

It has been previously shown that different extra-auditory alterations can be induced in animals exposed to noise at 15 days. However, data regarding exposure of younger animals, that do not have a functional auditory system, have not been obtained yet. Besides, the possibility to find a helpful strategy to restore these changes has not been explored so far. Therefore, the aims of the present work were to test age-related differences in diverse hippocampal-dependent behavioral measurements that might be affected in noise-exposed rats, as well as to evaluate the effectiveness of a potential neuroprotective strategy, the enriched environment (EE), on noise-induced behavioral alterations. Male Wistar rats of 7 and 15 days were exposed to moderate levels of noise for two hours. At weaning, animals were separated and reared either in standard or in EE cages for one week. At 28 days of age, different hippocampal-dependent behavioral assessments were performed. Results show that rats exposed to noise at 7 and 15 days were differentially affected. Moreover, EE was effective in restoring all altered variables when animals were exposed at 7 days, while a few were restored in rats exposed at 15 days. The present findings suggest that noise exposure was capable to trigger significant hippocampal-related behavioral alterations that were differentially affected, depending on the age of exposure. In addition, it could be proposed that hearing structures did not seem to be necessarily involved in the generation of noise-induced hippocampal-related behaviors, as they were observed even in animals with an immature auditory pathway. Finally, it could be hypothesized that the differential restoration achieved by EE rearing might also depend on the degree of maturation at the time of exposure and the variable evaluated, being younger animals more susceptible to environmental manipulations. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

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.

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

The Effect of Quercetin on the Osteogenesic Differentiation and Angiogenic Factor Expression of Bone Marrow-Derived Mesenchymal Stem Cells

PubMed Central

Zhou, Yuning; Wu, Yuqiong; Jiang, Xinquan; Zhang, Xiuli; Xia, Lunguo; Lin, Kaili; Xu, Yuanjin

2015-01-01

Bone marrow-derived mesenchymal stem cells (BMSCs) are widely used in regenerative medicine in light of their ability to differentiate along the chondrogenic and osteogenic lineages. As a type of traditional Chinese medicine, quercetin has been preliminarily reported to promote osteogenic differentiation in osteoblasts. In the present study, the effects of quercetin on the proliferation, viability, cellular morphology, osteogenic differentiation and angiogenic factor secretion of rat BMSCs (rBMSCs) were examined by MTT assay, fluorescence activated cell sorter (FACS) analysis, real-time quantitative PCR (RT-PCR) analysis, alkaline phosphatase (ALP) activity and calcium deposition assays, and Enzyme-linked immunosorbent assay (ELISA). Moreover, whether mitogen-activated protein kinase (MAPK) signaling pathways were involved in these processes was also explored. The results showed that quercetin significantly enhanced the cell proliferation, osteogenic differentiation and angiogenic factor secretion of rBMSCs in a dose-dependent manner, with a concentration of 2 μM achieving the greatest stimulatory effect. Moreover, the activation of the extracellular signal-regulated protein kinases (ERK) and p38 pathways was observed in quercetin-treated rBMSCs. Furthermore, these induction effects could be repressed by either the ERK inhibitor PD98059 or the p38 inhibitor SB202190, respectively. These data indicated that quercetin could promote the proliferation, osteogenic differentiation and angiogenic factor secretion of rBMSCs in vitro, partially through the ERK and p38 signaling pathways. PMID:26053266

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

NASA Astrophysics Data System (ADS)

Warnez, M. T.; Johnsen, E.

2015-06-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.

Stock-specific migration timing of adult spring-summer Chinook salmon in the Columbia River basin

USGS Publications Warehouse

Keefer, M.L.; Peery, C.A.; Jepson, M.A.; Tolotti, K.R.; Bjornn, T.C.; Stuehrenberg, L.C.

2004-01-01

An understanding of the migration timing patterns of Pacific salmon Oncorhynchus spp. and steelhead O. mykiss is important for managing complex mixed-stock fisheries and preserving genetic and life history diversity. We examined adult return timing for 3,317 radio-tagged fish from 38 stocks of Columbia River basin spring-summer Chinook salmon O. tshawytscha over 5 years. Stock composition varied widely within and between years depending on the strength of influential populations. Most individual stocks migrated at similar times each year relative to overall runs, supporting the hypotheses that run timing is predictable, is at least partially due to genetic adaptation, and can be used to differentiate between some conspecific populations. Arrival timing of both aggregated radio-tagged stocks and annual runs was strongly correlated with river discharge; stocks arrived earlier at Bonneville Dam and at upstream dams in years with low discharge. Migration timing analyses identified many between-stock and between-year differences in anadromous salmonid return behavior and should and managers interested in protection and recovery of evolutionary significant populations.

Surface topography during neural stem cell differentiation regulates cell migration and cell morphology.

PubMed

Czeisler, Catherine; Short, Aaron; Nelson, Tyler; Gygli, Patrick; Ortiz, Cristina; Catacutan, Fay Patsy; Stocker, Ben; Cronin, James; Lannutti, John; Winter, Jessica; Otero, José Javier

2016-12-01

We sought to determine the contribution of scaffold topography to the migration and morphology of neural stem cells by mimicking anatomical features of scaffolds found in vivo. We mimicked two types of central nervous system scaffolds encountered by neural stem cells during development in vitro by constructing different diameter electrospun polycaprolactone (PCL) fiber mats, a substrate that we have shown to be topographically similar to brain scaffolds. We compared the effects of large fibers (made to mimic blood vessel topography) with those of small-diameter fibers (made to mimic radial glial process topography) on the migration and differentiation of neural stem cells. Neural stem cells showed differential migratory and morphological reactions with laminin in different topographical contexts. We demonstrate, for the first time, that neural stem cell biological responses to laminin are dependent on topographical context. Large-fiber topography without laminin prevented cell migration, which was partially reversed by treatment with rock inhibitor. Cell morphology complexity assayed by fractal dimension was inhibited in nocodazole- and cytochalasin-D-treated neural precursor cells in large-fiber topography, but was not changed in small-fiber topography with these inhibitors. These data indicate that cell morphology has different requirements on cytoskeletal proteins dependent on the topographical environment encountered by the cell. We propose that the physical structure of distinct scaffolds induces unique signaling cascades that regulate migration and morphology in embryonic neural precursor cells. J. Comp. Neurol. 524:3485-3502, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Pathophysiology of immobilization osteoporosis

NASA Technical Reports Server (NTRS)

Doty, S. B.; DiCarlo, E. F.

1995-01-01

The reduction of gravity-related forces on the skeleton creates a type of osteoporosis that is unique because its severity is dependent on the mechanical stress bearing function of the skeleton as well as the length of time that the forces are absent or reduced. Bones that bear weight under normal conditions are more affected than bones that normally do not bear weight. The cytokine environment and the cells in the affected bones are altered in time so that stem cells produce fewer new cells and the differentiated cells tend to be less active. These alterations in the local environment of the affected parts appear to resemble those of age- and disease-associated systemic forms of osteoporosis. The osteoporosis produced as a result of the loss of normal activity however, appears to be at least partially reversible through remobilization, strenuous exercise, and--possibly in the future--cytokine therapy.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

NASA Astrophysics Data System (ADS)

Husa, Sascha; Hinder, Ian; Lechner, Christiane

2006-06-01

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations. Program summaryTitle of program: Kranc Catalogue identifier: ADXS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under Linux Programming language used: Mathematica, C, Fortran 90 Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KB Has the code been vectorized or parallelized: The code is parallelized based on the Cactus framework. Number of bytes in distributed program, including test data, etc.: 1 578 142 Number of lines in distributed program, including test data, etc.: 11 711 Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations. Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface. Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500 3. Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor. Unusual features of the program: based on Mathematica and Cactus

Further Results on Finite-Time Partial Stability and Stabilization. Applications to Nonlinear Control Systems

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

Jammazi, Chaker

2009-03-05

The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.

Evidence for greater cue reactivity among low-dependent vs. high-dependent smokers.

PubMed

Watson, Noreen L; Carpenter, Matthew J; Saladin, Michael E; Gray, Kevin M; Upadhyaya, Himanshu P

2010-07-01

Cue reactivity paradigms are well-established laboratory procedures used to examine subjective craving in response to substance-related cues. For smokers, the relationship between nicotine dependence and cue reactivity has not been clearly established. The main aim of the present study was to further examine this relationship. Participants (N=90) were between the ages 18-40 and smoked > or =10 cigarettes per day. Average nicotine dependence (Fagerström Test for Nicotine Dependence; FTND) at baseline was 4.9 (SD=2.1). Participants completed four cue reactivity sessions consisting of two in vivo cues (smoking and neutral) and two affective imagery cues (stressful and relaxed), all counterbalanced. Craving in response to cues was assessed following each cue exposure using the Questionnaire of Smoking Urges-Brief (QSU-B). Differential cue reactivity was operationally defined as the difference in QSU scores between the smoking and neutral cues, and between the stressful and relaxed cues. Nicotine dependence was significantly and negatively associated with differential cue reactivity scores in regard to hedonic craving (QSU factor 1) for both in vivo and imagery cues, such that those who had low FTND scores demonstrated greater differential cue reactivity than those with higher FTND scores (beta=-.082; p=.037; beta=-.101; p=.023, respectively). Similar trends were found for the Total QSU and for negative reinforcement craving (QSU factor 2), but did not reach statistical significance. Under partially sated conditions, less dependent smokers may be more differentially cue reactive to smoking cues as compared to heavily dependent smokers. These findings offer methodological and interpretative implications for cue reactivity studies. 2010 Elsevier Ltd. All rights reserved.

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

PubMed Central

Zhao, Xiaofeng; McGough, Robert J.

2016-01-01

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

D-region differential-phase measurements and ionization variability studies

NASA Technical Reports Server (NTRS)

Weiland, R. M.; Bowhill, S. A.

1978-01-01

Measurements of electron densities in the D region are made by the partial-reflection differential-absorption and differential-phase techniques. The differential-phase data are obtained by a hard-wired phase-measuring system. Electron-sensity profiles obtained by the two techniques on six occasions are plotted and compared. Electron-density profiles obtained at the same time on 30 occasions during the years 1975 through 1977 are averaged to form a single profile for each technique. The effect of varying the assumed collision-frequency profile on these averaged profiles is studied. Time series of D-region electron-sensity data obtained by 3.4 minute intervals on six days during the summer of 1977 are examined for wave-like disturbances and tidal oscillations.

Internal state of Lutetia as a function of the macroporosity

NASA Astrophysics Data System (ADS)

Neumann, W.; Breuer, D.; Spohn, T.

2014-07-01

The asteroid (21) Lutetia appears to be an intermediate object between the small near-primordial asteroids and a fully differentiated dwarf planet (4) Vesta. Understanding its evolution is crucial for the understanding of the accretion chain from km-sized planetesimals to full-sized planets and of the possible origin of both differentiated and undifferentiated meteorites. Remarkable is the bulk density value of 3400 kg m^{-3} obtained by the Rosetta flyby in July 2010 [1]. It indicates a relatively high intrinsic density, because the heavily cratered surface suggests a certain macroporosity of this body. Thereby, the macroporosity ϕ_{m} remains an uncertainty. We adopted the numerical model from [2] to consider an enstatite chondritic composition suggested by the spectrum [3], and supplemented it with a radiation boundary condition. Thereby, the nebula temperature is variable in order to simulate the cooling of the protoplanetary nebula with time and the migration of Lutetia from the inner Solar System (where it could have formed) to its present orbit. Assuming a value of ϕ_{m} in the range of 0-25 %, we calculate the intrinsic material properties, such as the density, composition, and radiogenic heat-source abundance. Subsequently, we simulate the accretion of Lutetia from the protoplanetary dust as a porous aggregate. Upon radiogenic heating by the short-lived radionuclides ^{26}Al and ^{60}Fe, compaction of the interior to the consolidated state by hot pressing is modeled using a creep-law-related approach. In the frame of a complex numerical model, a variety of physical processes is taken into account, like the calculation of melting, latent heat consumption and release, magmatic heat transport, melt segregation by porous flow, and the associated approach on differentiation modelling. The equations describing the physical processes like simultaneous growth due to the accretion, shrinkage due to the compaction, and differentiation, are solved simultaneously. The goal is to constrain the present-day macroporosity of the asteroid and its possible internal structure (porous/compacted/differentiated), starting with accretion from a highly porous building material. The evolution scenarios arising from assumptions on the macroporosity ϕ_{m} are examined to derive implications on the compaction of an initially highly porous material and (partial) differentiation. The calculated final structures are compared with the observations of Rosetta in order to derive bounds on the present-day macroporosity and internal structure of Lutetia. We obtain a number of possible compaction and differentiation scenarios consistent with the properties of the present-day Lutetia. The most probable macroporosity for a Lutetia-like body with the observed bulk density of 3400 kg m^{-3} is ϕ_{m} ≥ 0.04. Small changes can be expected if an error of ± 300 kg m^{-3} in the bulk density is considered. Depending on the adopted value of ϕ_{m}, Lutetia may have formed contemporaneously with the calcium-aluminium-rich inclusions (ϕ_{m} = 0.04) or up to 8 Ma later (ϕ_{m}= 0.25). The degree of differentiation varies significantly and the most evolved structure consists of an iron core and a silicate mantle that are covered by an undifferentiated but sintered layer and an undifferentiated and unsintered regolith. We find a differentiated interior, i.e., an iron-rich core and a silicate mantle, only for a rather narrow interval between 0.04 ≤ ϕ_{m} < 0.06 with the formation times between 0 Ma and 1.8 Ma after the CAIs. Regardless of melting and partial differentiation, no melt extrusion through the porous layer is likely -- a finding that is consistent with the lack of basalt at the surface of Lutetia. Thus, although the outside is primordial, it could still have experienced substantial melting, have an iron core and a hidden igneous activity in the past. For ϕ_{m} ≥ 0.6, an iron-silicate differentiation is not possible, but the interior is compacted due to sintering below a porous outer layer. Our results [4] confirm the idea raised theoretically in [2,5] that a small asteroid like Lutetia can be a parent body of undifferentiated (chondritic), partially differentiated (primitive achondritic), and differentiated (achondritic) meteorites. Thus, enstatite chondritic, iron, and primitive achondritic meteorites can, in principle, originate from Lutetia, because it may be partially differentiated and was clearly disturbed by several major impacts. Furthermore, the timing of the occurrence of thermal convection in the metallic core suggests the possibility of an internal dynamo on Lutetia. This could explain the remanent magnetization found in undifferentiated chondritic meteorites.

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.

Cytokine Response of Cultured Skeletal Muscle Cells Stimulated with Proinflammatory Factors Depends on Differentiation Stage

PubMed Central

Podbregar, Matej; Lainscak, Mitja; Prelovsek, Oja; Mars, Tomaz

2013-01-01

Myoblast proliferation and myotube formation are critical early events in skeletal muscle regeneration. The attending inflammation and cytokine signaling are involved in regulation of skeletal muscle cell proliferation and differentiation. Secretion of muscle-derived cytokines upon exposure to inflammatory factors may depend on the differentiation stage of regenerating muscle cells. Cultured human myoblasts and myotubes were exposed to 24-hour treatment with tumor necrosis factor (TNF)-α or lipopolysaccharide (LPS). Secretion of interleukin 6 (IL-6), a major muscle-derived cytokine, and interleukin 1 (IL-1), an important regulator of inflammatory response, was measured 24 hours after termination of TNF-α or LPS treatment. Myoblasts pretreated with TNF-α or LPS displayed robustly increased IL-6 secretion during the 24-hour period after removal of treatments, while IL-1 secretion remained unaltered. IL-6 secretion was also increased in myotubes, but the response was less pronounced compared with myoblasts. In contrast to myoblasts, IL-1 secretion was markedly stimulated in LPS-pretreated myotubes. We demonstrate that preceding exposure to inflammatory factors stimulates a prolonged upregulation of muscle-derived IL-6 and/or IL-1 in cultured skeletal muscle cells. Our findings also indicate that cytokine response to inflammatory factors in regenerating skeletal muscle partially depends on the differentiation stage of myogenic cells. PMID:23509435

The Proteasome Inhibitor Bortezomib Enhances ATRA-Induced Differentiation of Neuroblastoma Cells via the JNK Mitogen-Activated Protein Kinase Pathway

PubMed Central

Luo, Peihua; Lin, Meili; Li, Lin; Yang, Bo; He, Qiaojun

2011-01-01

Neuroblastoma (NB) is the most common extracranial solid tumor in childhood. Differentiated human NBs are associated with better outcome and lower stage; induction of differentiation is considered to be therapeutically advantageous. All-trans retinoic acid (ATRA) has been shown to induce the differentiation of neuroblastoma (NB) cell lines. The proteasome inhibitor bortezomib inhibits cell growth and angiogenesis in NBs. Here, we investigated the synergistic effect between bortezomib and ATRA in inducing NB cell differentiation in different NB cell lines. Bortezomib combined with ATRA had a significantly enhanced antiproliferative effect. This inhibition was characterized by a synergistic increase in neuronal differentiation. At the same time, the combination therapy showed little neuronal toxicity which was assessed in primary cultures of rat cerebellar granule cells by the MTT assay, PI staining. The combination of bortezomib and ATRA triggered increased differentiation through the activation of proteins, including RARα, RARβ, RARγ, p-JNK and p21, compared with ATRA treatment alone. Using JNK inhibitor SP600125 to block JNK-dependent activity, the combination therapy-induced neuronal differentiation was partially attenuated. In addition, p21 shRNA had no effect on the combination therapy-induced neuronal differentiation. The in vivo antitumor activities were examined in human NB cell xenografts and GFP-labeled human NB cell xenografts. Treatment of human NB cell CHP126-bearing nude mice with ATRA plus bortezomib resulted in more significant tumor growth inhibition than mice treated with either drug alone. These findings provide the rationale for the development of a new therapeutic strategy for NB based on the pharmacological combination of ATRA and bortezomib. PMID:22087283

Depolarization of the Electrogenic Transmembrane Electropotential of Zea mays L. by Bipolaris (Helminthosporium) maydis Race T Toxin, Azide, Cyanide, Dodecyl Succinic Acid, or Cold Temperature 1

PubMed Central

Mertz, Stuart M.; Arntzen, Charles J.

1978-01-01

The transmembrane electrical potential of root cells of Zea mays L. cv. W64A in a modified 1× Higinbotham solution was partially depolarized by semipurified toxin obtained from Bipolaris (Helminthosporium) maydis race T. At a given toxin concentration depolarization of Texas cytoplasm cells was much greater than for normal cytoplasm cells. This observation correlated directly to the differential host susceptibility to the fungus. The time course and magnitude of depolarization were dependent on toxin concentration; at high concentration the electropotential difference change was rapid. Cortex cells depolarized more slowly than epidermal cells indicating that the toxin slowly permeated intercellular regions. Toxin concentrations which affected electropotential difference were of the same magnitude as those required to inhibit root growth, ion uptake, and mitochondrial processes. Azide, cyanide, and cold temperature (5 C) gave the same partial depolarization as did the toxin. Dodecyl succinic acid caused complete depolarization. These and other data indicate that one of the primary actions of the toxin is to inhibit electrogenic ion pumps in the plasmalemma. PMID:16660605

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

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 partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

PubMed

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

Presymplectic current and the inverse problem of the calculus of variations

NASA Astrophysics Data System (ADS)

Khavkine, Igor

2013-11-01

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159-178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45-64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.

Modelling of subsonic COIL with an arbitrary magnetic modulation

NASA Astrophysics Data System (ADS)

Beránek, Jaroslav; Rohlena, Karel

2007-05-01

The concept of 1D subsonic COIL model with a mixing length was generalized to include the influence of a variable magnetic field on the stimulated emission cross-section. Equations describing the chemical kinetics were solved taking into account together with the gas temperature also a simplified mixing model of oxygen and iodine molecules. With the external time variable magnetic field the model is no longer stationary. A transformation in the system moving with the mixture reduces partial differential equations to ordinary equations in time with initial conditions given either by the stationary flow at the moment when the magnetic field is switched on combined with the boundary conditions at the injector. Advantage of this procedure is a possibility to consider an arbitrary temporal dependence of the imposed magnetic field and to calculate directly the response of the laser output. The method was applied to model the experimental data measured with the subsonic version of the COIL device in the Institute of Physics, Prague, where the applied magnetic field had a saw-tooth dependence. We found that various values characterizing the laser performance, such as the power density distribution over the active zone cross-section, may have a fairly complicated structure given by combined effects of the delayed reaction to the magnetic switching and the flow velocity. This is necessarily translated in a time dependent spatial inhomogeneity of output beam intensity profile.

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

NASA Astrophysics Data System (ADS)

Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang

2018-01-01

We consider a class of time-dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker-Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.

First-passage times for pattern formation in nonlocal partial differential equations

NASA Astrophysics Data System (ADS)

Cáceres, Manuel O.; Fuentes, Miguel A.

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

First-passage times for pattern formation in nonlocal partial differential equations.

PubMed

Cáceres, Manuel O; Fuentes, Miguel A

2015-10-01

We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.

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 .

A consistent modelling methodology for secondary settling tanks: a reliable numerical method.

PubMed

Bürger, Raimund; Diehl, Stefan; Farås, Sebastian; Nopens, Ingmar; Torfs, Elena

2013-01-01

The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection-diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.

Time-evolution of grain size distributions in random nucleation and growth crystallization processes

NASA Astrophysics Data System (ADS)

Teran, Anthony V.; Bill, Andreas; Bergmann, Ralf B.

2010-02-01

We study the time dependence of the grain size distribution N(r,t) during crystallization of a d -dimensional solid. A partial differential equation, including a source term for nuclei and a growth law for grains, is solved analytically for any dimension d . We discuss solutions obtained for processes described by the Kolmogorov-Avrami-Mehl-Johnson model for random nucleation and growth (RNG). Nucleation and growth are set on the same footing, which leads to a time-dependent decay of both effective rates. We analyze in detail how model parameters, the dimensionality of the crystallization process, and time influence the shape of the distribution. The calculations show that the dynamics of the effective nucleation and effective growth rates play an essential role in determining the final form of the distribution obtained at full crystallization. We demonstrate that for one class of nucleation and growth rates, the distribution evolves in time into the logarithmic-normal (lognormal) form discussed earlier by Bergmann and Bill [J. Cryst. Growth 310, 3135 (2008)]. We also obtain an analytical expression for the finite maximal grain size at all times. The theory allows for the description of a variety of RNG crystallization processes in thin films and bulk materials. Expressions useful for experimental data analysis are presented for the grain size distribution and the moments in terms of fundamental and measurable parameters of the model.

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.

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

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

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

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki

2016-01-01

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Fibronectin is a survival factor for differentiated osteoblasts

NASA Technical Reports Server (NTRS)

Globus, R. K.; Doty, S. B.; Lull, J. C.; Holmuhamedov, E.; Humphries, M. J.; Damsky, C. H.

1998-01-01

The skeletal extracellular matrix produced by osteoblasts contains the glycoprotein fibronectin, which regulates the adhesion, differentiation and function of various adherent cells. Interactions with fibronectin are required for osteoblast differentiation in vitro, since fibronectin antagonists added to cultures of immature fetal calvarial osteoblasts inhibit their progressive differentiation. To determine if fibronectin plays a unique role in fully differentiated osteoblasts, cultures that had already formed mineralized nodules in vitro were treated with fibronectin antagonists. Fibronectin antibodies caused >95% of the cells in the mature cultures to display characteristic features of apoptosis (nuclear condensation, apoptotic body formation, DNA laddering) within 24 hours. Cells appeared to acquire sensitivity to fibronectin antibody-induced apoptosis as a consequence of differentiation, since antibodies failed to kill immature cells and the first cells killed were those associated with mature nodules. Intact plasma fibronectin, as well as fragments corresponding to the amino-terminal, cell-binding, and carboxy-terminal domains of fibronectin, independently induced apoptosis of mature (day-13), but not immature (day-4), osteoblasts. Finally, transforming growth factor-beta1 partially protected cells from the apoptotic effects of fibronectin antagonists. Thus, in the course of maturation cultured osteoblasts switch from depending on fibronectin for differentiation to depending on fibronectin for survival. These data suggest that fibronectin, together with transforming growth factor-beta1, may affect bone formation, in part by regulating the survival of osteoblasts.

Extending compile-time reverse mode and exploiting partial separability in ADIFOR

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

Bischof, C.H.; El-Khadiri, M.

1992-10-01

The numerical methods employed in the solution of many scientific computing problems require the computation of the gradient of a function f: R[sup n] [yields] R. ADIFOR is a source translator that, given a collection of subroutines to compute f, generates Fortran 77 code for computing the derivative of this function. Using the so-called torsion problem from the MINPACK-2 test collection as an example, this paper explores two issues in automatic differentiation: the efficient computation of derivatives for partial separable functions and the use of the compile-time reverse mode for the generation of derivatives. We show that orders of magnitudesmore » of improvement are possible when exploiting partial separability and maximizing use of the reverse mode.« less

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

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

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

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.

Plant family identity distinguishes patterns of carbon and nitrogen stable isotope abundance and nitrogen concentration in mycoheterotrophic plants associated with ectomycorrhizal fungi.

PubMed

Hynson, Nicole A; Schiebold, Julienne M-I; Gebauer, Gerhard

2016-09-01

Mycoheterotrophy entails plants meeting all or a portion of their carbon (C) demands via symbiotic interactions with root-inhabiting mycorrhizal fungi. Ecophysiological traits of mycoheterotrophs, such as their C stable isotope abundances, strongly correlate with the degree of species' dependency on fungal C gains relative to C gains via photosynthesis. Less explored is the relationship between plant evolutionary history and mycoheterotrophic plant ecophysiology. We hypothesized that the C and nitrogen (N) stable isotope compositions, and N concentrations of fully and partially mycoheterotrophic species differentiate them from autotrophs, and that plant family identity would be an additional and significant explanatory factor for differences in these traits among species. We focused on mycoheterotrophic species that associate with ectomycorrhizal fungi from plant families Ericaceae and Orchidaceae. Published and unpublished data were compiled on the N concentrations, C and N stable isotope abundances (δ(13)C and δ(15)N) of fully (n = 18) and partially (n = 22) mycoheterotrophic species from each plant family as well as corresponding autotrophic reference species (n = 156). These data were used to calculate site-independent C and N stable isotope enrichment factors (ε). Then we tested for differences in N concentration, (13)C and (15)N enrichment among plant families and trophic strategies. We found that in addition to differentiating partially and fully mycoheterotrophic species from each other and from autotrophs, C and N stable isotope enrichment also differentiates plant species based on familial identity. Differences in N concentrations clustered at the plant family level rather than the degree of dependency on mycoheterotrophy. We posit that differences in stable isotope composition and N concentrations are related to plant family-specific physiological interactions with fungi and their environments. © The Author 2016. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

PubMed Central

Eisenberg, Bob; Hyon, YunKyong; Liu, Chun

2010-01-01

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton’s least action and Rayleigh’s dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an “extra layer” of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler–Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler–Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler–Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson–Nernst–Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary “binding” in the channel, and the eventual accumulation of salts in “unstirred layers” near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions. PMID:20849161

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

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.

A similarity solution of time dependent MHD liquid film flow over stretching sheet with variable physical properties

NASA Astrophysics Data System (ADS)

Idrees, M.; Rehman, Sajid; Shah, Rehan Ali; Ullah, M.; Abbas, Tariq

2018-03-01

An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM) while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″ (0) , Nusselt number (heat flux) -θ‧ (0) and free surface temperature θ (1) are presented graphically and in tabular form.

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.

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.

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

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

Messina, Riccardo; Vasile, Ruggero; Passante, Roberto

2010-12-15

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behavior of the time-dependent force on an initially partially dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

PubMed

Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

2016-04-01

Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it possible to distinguish cancerous cells from normal cells. A typical example of liver distinguished from gray matter, white matter and kidney is demonstrated. Bessel functions and properties are specifically needed to show the direct effect of the instantaneous velocity on the NMR signal originating from normal and abnormal tissues.

Presymplectic current and the inverse problem of the calculus of variations

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

Khavkine, Igor, E-mail: i.khavkine@uu.nl

2013-11-15

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159–178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45–64 (1982)]more » from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.« less

On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

NASA Astrophysics Data System (ADS)

Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

2012-04-01

The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

CTCF orchestrates the germinal centre transcriptional program and prevents premature plasma cell differentiation

PubMed Central

Pérez-García, Arantxa; Marina-Zárate, Ester; Álvarez-Prado, Ángel F.; Ligos, Jose M.; Galjart, Niels; Ramiro, Almudena R.

2017-01-01

In germinal centres (GC) mature B cells undergo intense proliferation and immunoglobulin gene modification before they differentiate into memory B cells or long-lived plasma cells (PC). GC B-cell-to-PC transition involves a major transcriptional switch that promotes a halt in cell proliferation and the production of secreted immunoglobulins. Here we show that the CCCTC-binding factor (CTCF) is required for the GC reaction in vivo, whereas in vitro the requirement for CTCF is not universal and instead depends on the pathways used for B-cell activation. CTCF maintains the GC transcriptional programme, allows a high proliferation rate, and represses the expression of Blimp-1, the master regulator of PC differentiation. Restoration of Blimp-1 levels partially rescues the proliferation defect of CTCF-deficient B cells. Thus, our data reveal an essential function of CTCF in maintaining the GC transcriptional programme and preventing premature PC differentiation. PMID:28677680

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Effects of sodium phenylbutyrate on differentiation and induction of the P21WAF1/CIP1 anti-oncogene in human liver carcinoma cell lines.

PubMed

Meng, Mei; Jiang, Jun Mei; Liu, Hui; In, Cheng Yong; Zhu, Ju Ren

2005-01-01

To explore the effects of sodium phenylbutyrate on the proliferation, differentiation, cell cycle arrest and induction of the P(21WAF1/CIP1) anti-oncogene in human liver carcinoma cell lines Bel-7402 and HepG2. Bel-7402 and HepG2 human liver carcinoma cells were treated with sodium phenylbutyrate at different concentrations. Light microscopy was used to observe morphological changes in the carcinoma cells. Effects on the cell cycle were detected by using flow cytometry. P(21WAF1/CIP1) expression was determined by both reverse transcription-polymerase chain reaction and western blotting. Statistical analysis was performed by using one-way anova and Student's t-test. Sodium phenylbutyrate treatment caused time- and dose-dependent growth inhibition of Bel-7402 and HepG2 cells. This treatment also caused a decline in the proportion of S-phase cells and an increase in the proportion of G(0)/G(1) cells. Sodium phenylbutyrate increased the expression of P(21WAF1/CIP1). Sodium phenylbutyrate inhibits the proliferation of human liver carcinoma cells Bel-7402 and HepG2, induces partial differentiation, and increases the expression of P(21WAF1/CIP1).

Complex Conjugated certificateless-based signcryption with differential integrated factor for secured message communication in mobile network

PubMed Central

Rajagopalan, S. P.

2017-01-01

Certificateless-based signcryption overcomes inherent shortcomings in traditional Public Key Infrastructure (PKI) and Key Escrow problem. It imparts efficient methods to design PKIs with public verifiability and cipher text authenticity with minimum dependency. As a classic primitive in public key cryptography, signcryption performs validity of cipher text without decryption by combining authentication, confidentiality, public verifiability and cipher text authenticity much more efficiently than the traditional approach. In this paper, we first define a security model for certificateless-based signcryption called, Complex Conjugate Differential Integrated Factor (CC-DIF) scheme by introducing complex conjugates through introduction of the security parameter and improving secured message distribution rate. However, both partial private key and secret value changes with respect to time. To overcome this weakness, a new certificateless-based signcryption scheme is proposed by setting the private key through Differential (Diff) Equation using an Integration Factor (DiffEIF), minimizing computational cost and communication overhead. The scheme is therefore said to be proven secure (i.e. improving the secured message distributing rate) against certificateless access control and signcryption-based scheme. In addition, compared with the three other existing schemes, the CC-DIF scheme has the least computational cost and communication overhead for secured message communication in mobile network. PMID:29040290

Complex Conjugated certificateless-based signcryption with differential integrated factor for secured message communication in mobile network.

PubMed

Alagarsamy, Sumithra; Rajagopalan, S P

2017-01-01

Certificateless-based signcryption overcomes inherent shortcomings in traditional Public Key Infrastructure (PKI) and Key Escrow problem. It imparts efficient methods to design PKIs with public verifiability and cipher text authenticity with minimum dependency. As a classic primitive in public key cryptography, signcryption performs validity of cipher text without decryption by combining authentication, confidentiality, public verifiability and cipher text authenticity much more efficiently than the traditional approach. In this paper, we first define a security model for certificateless-based signcryption called, Complex Conjugate Differential Integrated Factor (CC-DIF) scheme by introducing complex conjugates through introduction of the security parameter and improving secured message distribution rate. However, both partial private key and secret value changes with respect to time. To overcome this weakness, a new certificateless-based signcryption scheme is proposed by setting the private key through Differential (Diff) Equation using an Integration Factor (DiffEIF), minimizing computational cost and communication overhead. The scheme is therefore said to be proven secure (i.e. improving the secured message distributing rate) against certificateless access control and signcryption-based scheme. In addition, compared with the three other existing schemes, the CC-DIF scheme has the least computational cost and communication overhead for secured message communication in mobile network.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

PubMed Central

Warnez, M. T.; Johnsen, E.

2015-01-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller–Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin–Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time. PMID:26130967

Optimal Harvesting in an Age-Structured Predator-Prey Model

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

Fister, K. Renee; Lenhart, Suzanne

2006-06-15

We investigate optimal harvesting control in a predator-prey model in which the prey population is represented by a first-order partial differential equation with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established.

Extending compile-time reverse mode and exploiting partial separability in ADIFOR. ADIFOR Working Note No. 7

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

Bischof, C.H.; El-Khadiri, M.

1992-10-01

The numerical methods employed in the solution of many scientific computing problems require the computation of the gradient of a function f: R{sup n} {yields} R. ADIFOR is a source translator that, given a collection of subroutines to compute f, generates Fortran 77 code for computing the derivative of this function. Using the so-called torsion problem from the MINPACK-2 test collection as an example, this paper explores two issues in automatic differentiation: the efficient computation of derivatives for partial separable functions and the use of the compile-time reverse mode for the generation of derivatives. We show that orders of magnitudesmore » of improvement are possible when exploiting partial separability and maximizing use of the reverse mode.« less

A negative feedback mechanism for the long-term stabilization of the earth's surface temperature

NASA Technical Reports Server (NTRS)

Walker, J. C. G.; Hays, P. B.; Kasting, J. F.

1981-01-01

It is suggested that the partial pressure of carbon dioxide in the atmosphere is buffered, over geological time scales, by a negative feedback mechanism, in which the rate of weathering of silicate minerals (followed by deposition of carbonate minerals) depends on surface temperature, which in turn depends on the carbon dioxide partial pressure through the greenhouse effect. Although the quantitative details of this mechanism are speculative, it appears able to partially stabilize the earth's surface temperature against the steady increase of solar luminosity, believed to have occurred since the origin of the solar system.

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Robust analysis of semiparametric renewal process models

PubMed Central

Lin, Feng-Chang; Truong, Young K.; Fine, Jason P.

2013-01-01

Summary A rate model is proposed for a modulated renewal process comprising a single long sequence, where the covariate process may not capture the dependencies in the sequence as in standard intensity models. We consider partial likelihood-based inferences under a semiparametric multiplicative rate model, which has been widely studied in the context of independent and identical data. Under an intensity model, gap times in a single long sequence may be used naively in the partial likelihood with variance estimation utilizing the observed information matrix. Under a rate model, the gap times cannot be treated as independent and studying the partial likelihood is much more challenging. We employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality. The estimator's variance is quite complicated owing to the unknown gap times dependence structure. We adapt block bootstrapping and cluster variance estimators to the partial likelihood. Simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach. PMID:24550568

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

X-ray Absorption Spectroscopy Combined with Time-Dependent Density Functional Theory Elucidates Differential Substitution Pathways of Au(I) and Au(III) with Zinc Fingers.

PubMed

Abbehausen, Camilla; de Paiva, Raphael Enoque Ferraz; Bjornsson, Ragnar; Gomes, Saulo Quintana; Du, Zhifeng; Corbi, Pedro Paulo; Lima, Frederico Alves; Farrell, Nicholas

2018-01-02

A combination of two elements' (Au, Zn) X-ray absorption spectroscopy (XAS) and time-dependent density functional theory (TD-DFT) allowed the elucidation of differential substitution pathways of Au(I) and Au(III) compounds reacting with biologically relevant zinc fingers (ZnFs). Gold L 3 -edge XAS probed the interaction of gold and the C-terminal Cys 2 HisCys finger of the HIV-1 nucleocapsid protein NCp7, and the Cys 2 His 2 human transcription factor Sp1. The use of model compounds helped assign oxidation states and the identity of the gold-bound ligands. The computational studies accurately reproduced the experimental XAS spectra and allowed the proposition of structural models for the interaction products at early time points. The direct electrophilic attack on the ZnF by the highly thiophilic Au(I) resulted in a linear P-Au-Cys coordination sphere after zinc ejection whereas for the Sp1, loss of PEt 3 results in linear Cys-Au-Cys or Cys-Au-His arrangements. Reactions with Au(III) compounds, on the other hand, showed multiple binding modes. Prompt reaction between [AuCl(dien)] 2+ and [Au(dien)(DMAP)] 3+ with Sp1 showed a partially reduced Au center and a final linear His-Au-His coordination. Differently, in the presence of NCp7, [AuCl(dien)] 2+ readily reduces to Au(I) and changes from square-planar to linear geometry with Cys-Au-His coordination, while [Au(dien)(DMAP)] 3+ initially maintains its Au(III) oxidation state and square-planar geometry and the same first coordination sphere. The latter is the first observation of a "noncovalent" interaction of a Au(III) complex with a zinc finger and confirms early hypotheses that stabilization of Au(III) occurs with N-donor ligands. Modification of the zinc coordination sphere, suggesting full or partial zinc ejection, is observed in all cases, and for [Au(dien)(DMAP)] 3+ this represents a novel mechanism for nucleocapsid inactivation. The combination of XAS and TD-DFT presents the first direct experimental observation that not only compound reactivity, but also ZnF core specificity, can be modulated on the basis of the coordination sphere of Au(III) compounds.

Separation of Time-Based and Trial-Based Accounts of the Partial Reinforcement Extinction Effect

PubMed Central

Bouton, Mark E.; Woods, Amanda M.; Todd, Travis P.

2013-01-01

Two appetitive conditioning experiments with rats examined time-based and trial-based accounts of the partial reinforcement extinction effect (PREE). In the PREE, the loss of responding that occurs in extinction is slower when the conditioned stimulus (CS) has been paired with a reinforcer on some of its presentations (partially reinforced) instead of every presentation (continuously reinforced). According to a time-based or “time-accumulation” view (e.g., Gallistel & Gibbon, 2000), the PREE occurs because the organism has learned in partial reinforcement to expect the reinforcer after a larger amount of time has accumulated in the CS over trials. In contrast, according to a trial-based view (e.g., Capaldi, 1967), the PREE occurs because the organism has learned in partial reinforcement to expect the reinforcer after a larger number of CS presentations. Experiment 1 used a procedure that equated partially- and continuously-reinforced groups on their expected times to reinforcement during conditioning. A PREE was still observed. Experiment 2 then used an extinction procedure that allowed time in the CS and the number of trials to accumulate differentially through extinction. The PREE was still evident when responding was examined as a function of expected time units to the reinforcer, but was eliminated when responding was examined as a function of expected trial units to the reinforcer. There was no evidence that the animal responded according to the ratio of time accumulated during the CS in extinction over the time in the CS expected before the reinforcer. The results thus favor a trial-based account over a time-based account of extinction and the PREE. PMID:23962669

Separation of time-based and trial-based accounts of the partial reinforcement extinction effect.

PubMed

Bouton, Mark E; Woods, Amanda M; Todd, Travis P

2014-01-01

Two appetitive conditioning experiments with rats examined time-based and trial-based accounts of the partial reinforcement extinction effect (PREE). In the PREE, the loss of responding that occurs in extinction is slower when the conditioned stimulus (CS) has been paired with a reinforcer on some of its presentations (partially reinforced) instead of every presentation (continuously reinforced). According to a time-based or "time-accumulation" view (e.g., Gallistel and Gibbon, 2000), the PREE occurs because the organism has learned in partial reinforcement to expect the reinforcer after a larger amount of time has accumulated in the CS over trials. In contrast, according to a trial-based view (e.g., Capaldi, 1967), the PREE occurs because the organism has learned in partial reinforcement to expect the reinforcer after a larger number of CS presentations. Experiment 1 used a procedure that equated partially and continuously reinforced groups on their expected times to reinforcement during conditioning. A PREE was still observed. Experiment 2 then used an extinction procedure that allowed time in the CS and the number of trials to accumulate differentially through extinction. The PREE was still evident when responding was examined as a function of expected time units to the reinforcer, but was eliminated when responding was examined as a function of expected trial units to the reinforcer. There was no evidence that the animal responded according to the ratio of time accumulated during the CS in extinction over the time in the CS expected before the reinforcer. The results thus favor a trial-based account over a time-based account of extinction and the PREE. This article is part of a Special Issue entitled: Associative and Temporal Learning. Copyright © 2013 Elsevier B.V. All rights reserved.

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

PubMed Central

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

2011-01-01

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

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Direct Determinations of the πNN Coupling Constants

NASA Astrophysics Data System (ADS)

Ericson, T. E. O.; Loiseau, B.

1998-11-01

A novel extrapolation method has been used to deduce directly the charged πN N coupling constant from backward np differential scattering cross sections. The extracted value, g2c = 14.52(0.26) is higher than the indirectly deduced values obtained in nucleon-nucleon energy-dependent partial-wave analyses. Our preliminary direct value from a reanalysis of the GMO sum-rule points to an intermediate value of g2c about 13.97(30).

An economic order quantity model with nonlinear holding cost, partial backlogging and ramp-type demand

NASA Astrophysics Data System (ADS)

San-José, Luis A.; Sicilia, Joaquín; González-de-la-Rosa, Manuel; Febles-Acosta, Jaime

2018-07-01

In this article, a deterministic inventory model with a ramp-type demand depending on price and time is developed. The cumulative holding cost is assumed to be a nonlinear function of time. Shortages are allowed and are partially backlogged. Thus, the fraction of backlogged demand depends on the waiting time and on the stock-out period. The aim is to maximize the total profit per unit time. To do this, a procedure that determines the economic lot size, the optimal inventory cycle and the maximum profit is presented. The inventory system studied here extends diverse inventory models proposed in the literature. Finally, some numerical examples are provided to illustrate the theoretical results previously propounded.

Finding higher symmetries of differential equations using the MAPLE package DESOLVII

NASA Astrophysics Data System (ADS)

Vu, K. T.; Jefferson, G. F.; Carminati, J.

2012-04-01

We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. Catalogue identifier: ADYZ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYZ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 858 No. of bytes in distributed program, including test data, etc.: 112 515 Distribution format: tar.gz Programming language: MAPLE internal language Computer: PCs and workstations Operating system: Linux, Windows XP and Windows 7 RAM: Depends on the type of problem and the complexity of the system (small ≈ MB, large ≈ GB) Classification: 4.3, 5 Catalogue identifier of previous version: ADYZ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 682 Does the new version supersede the previous version?: Yes Nature of problem: There are a number of approaches one may use to find solutions to systems of differential equations. These include numerical, perturbative, and algebraic methods. Unfortunately, approximate or numerical solution methods may be inappropriate in many cases or even impossible due to the nature of the system and hence exact methods are important. In their own right, exact solutions are valuable not only as a yardstick for approximate/numerical solutions but also as a means of elucidating the physical meaning of fundamental quantities in systems. One particular method of finding special exact solutions is afforded by the work of Sophus Lie and the use of continuous transformation groups. The power of Lie's group theoretic method lies in its ability to unify a number of ad hoc integration methods through the use of symmetries, that is, continuous groups of transformations which leave the differential system “unchanged”. These symmetry groups may then be used to find special solutions. Solutions found in this manner are called similarity or invariant solutions. The method of finding symmetry transformations initially requires the generation of a large overdetermined system of linear, homogeneous, coupled PDEs. The integration of this system is usually reasonably straightforward requiring the (often elementary) integration of equations by splitting the system according to dependency on different orders and degrees of the dependent variable/s. Unfortunately, in the case of contact and Lie-Bäcklund symmetries, the integration of the determining system becomes increasingly more difficult as the order of the symmetry is increased. This is because the symmetry generating functions become dependent on higher orders of the derivatives of the dependent variables and this diminishes the overall resulting “separable” differential conditions derived from the main determining system. Furthermore, typical determining systems consist of tens to hundreds of equations and this, combined with standard mechanical solution methods, makes the process well suited to automation using computer algebra systems. The new MAPLE package DESOLVII, which is a major upgrade of DESOLV, now includes routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. In addition, significant improvements have been implemented to the algorithm for PDE solution. Finally, we have made some improvements in the overall automated process so as to improve user friendliness by reducing user intervention where possible. Solution method: See “Nature of problem” above. Reasons for new version: New and improved functionality. New functionality - can now compute generalised symmetries. Much improved efficiency (speed and memory use) of existing routines. Restrictions: Sufficient memory may be required for complex systems. Running time: Depends on the type of problem and the complexity of the system (small ≈ seconds, large ≈ hours).

A Walsh Function Module Users' Manual

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2014-01-01

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

First passage times for multiple particles with reversible target-binding kinetics

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.

2017-10-01

We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles. We compute analytically the mean first passage time (MFPT) for two independent particles by mapping the original problem to higher-dimensional surface-mediated diffusion and solving the coupled partial differential equations. The respective effects of the adsorption and desorption rates on the MFPT are revealed and discussed.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology. PMID:26356082

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.

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.

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

PubMed

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

2008-01-28

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

Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls

NASA Astrophysics Data System (ADS)

Iglesias, Marco; Sawlan, Zaid; Scavino, Marco; Tempone, Raúl; Wood, Christopher

2018-07-01

In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach (Ruggeri et al 2017 Bayesian Anal. 12 407–33, Iglesias et al 2018 Int. J. Heat Mass Transfer 116 417–31), for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified ensemble Kalman filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.

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.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

[Penetration of external thermal perturbations into homeothermic organisms, part I (author's transl)].

PubMed

Theves, B

1978-03-20

The general importance of the mean surface curvature for heat conduction problems is explained and a special symmetry with constant mean curvature on the isothermal surfaces is defined. The applicability for the body shapes of homeothermic organisms is demonstrated and the partial differential equation of heat conduction for this case is derived. The definition: heat release = real heat production + convective pseudoproduction eliminates the term of convective heat transfer through the blood stream and allows the reduction to a mere heat conduction problem. Formulas for the heat loss to the environment and for steady state temperature profiles are given. In case of sudden change of heat loss the partial differential equation is solved and a formula is derived, using dimensionless coordinates of time and distance. The mean surface curvature has strongest influence to the interior temperature field. The solution shows clearly the importance of thermal inertia of the homeothermic organism, for the external temperature wave penetrates into the body with a long phase displacement in time.

Time as an Observable in Nonrelativistic Quantum Mechanics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2003-01-01

The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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…

Sparse dynamics for partial differential equations

PubMed Central

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D.; Osher, Stanley

2013-01-01

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms. PMID:23533273

Sparse dynamics for partial differential equations.

PubMed

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

2013-04-23

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Differentiated protection method in passive optical networks based on OPEX

NASA Astrophysics Data System (ADS)

Zhang, Zhicheng; Guo, Wei; Jin, Yaohui; Sun, Weiqiang; Hu, Weisheng

2011-12-01

Reliable service delivery becomes more significant due to increased dependency on electronic services all over society and the growing importance of reliable service delivery. As the capability of PON increasing, both residential and business customers may be included in a PON. Meanwhile, OPEX have been proven to be a very important factor of the total cost for a telecommunication operator. Thus, in this paper, we present the partial protection PON architecture and compare the operational expenditures (OPEX) of fully duplicated protection and partly duplicated protection for ONUs with different distributed fiber length, reliability requirement and penalty cost per hour. At last, we propose a differentiated protection method to minimize OPEX.

A lysigenic programmed cell death-dependent process shapes schizogenously formed aerenchyma in the stems of the waterweed Egeria densa

PubMed Central

Bartoli, G.; Forino, L. M. C.; Durante, M.; Tagliasacchi, A. M.

2015-01-01

Background and Aims Plant adaptation to submergence can include the formation of prominent aerenchyma to facilitate gas exchange. The aim of this study was to characterize the differentiation of the constitutive aerenchyma in the stem of the aquatic macrophyte Egeria densa (Hydrocharitaceae) and to verify if any form of cell death might be involved. Methods Plants were collected from a pool in a botanical garden. Aerenchyma differentiation and apoptotic hallmarks were investigated by light microscopy and terminal deoxynucleotidyl transferase-mediated dUTP nick-end labelling (TUNEL) assay coupled with genomic DNA extraction and gel electrophoresis (DNA laddering assay). Cell viability and the occurrence of peroxides and nitric oxide (NO) were determined histochemically using specific fluorogenic probes. Key Results Aerenchyma differentiation started from a hexagonally packed pre-aerenchymatic tissue and, following a basipetal and centripetal developmental pattern, produced a honeycomb arrangement. After an early schizogenous differentiation process, a late lysigenous programmed cell death- (PCD) dependent mechanism occurred. This was characterized by a number of typical apoptotic hallmarks, including DNA fragmentation, chromatin condensation, apoptotic-like bodies, partial cell wall lysis and plasmolysis. In addition, local increases in H2O2 and NO were observed and quantified. Conclusions The differentiation of cortical aerenchyma in the stem of E. densa is a complex process, consisting of a combination of an early schizogenous differentiation mechanism and a late lysigenous PCD-dependent process. The PCD remodels the architecture of the gas spaces previously formed schizogenously, and also results in a reduction of O2-consuming cells and in recycling of material derived from the lysigenic dismantling of the cells. PMID:26002256

A lysigenic programmed cell death-dependent process shapes schizogenously formed aerenchyma in the stems of the waterweed Egeria densa.

PubMed

Bartoli, G; Forino, L M C; Durante, M; Tagliasacchi, A M

2015-07-01

Plant adaptation to submergence can include the formation of prominent aerenchyma to facilitate gas exchange. The aim of this study was to characterize the differentiation of the constitutive aerenchyma in the stem of the aquatic macrophyte Egeria densa (Hydrocharitaceae) and to verify if any form of cell death might be involved. Plants were collected from a pool in a botanical garden. Aerenchyma differentiation and apoptotic hallmarks were investigated by light microscopy and terminal deoxynucleotidyl transferase-mediated dUTP nick-end labelling (TUNEL) assay coupled with genomic DNA extraction and gel electrophoresis (DNA laddering assay). Cell viability and the occurrence of peroxides and nitric oxide (NO) were determined histochemically using specific fluorogenic probes. Aerenchyma differentiation started from a hexagonally packed pre-aerenchymatic tissue and, following a basipetal and centripetal developmental pattern, produced a honeycomb arrangement. After an early schizogenous differentiation process, a late lysigenous programmed cell death- (PCD) dependent mechanism occurred. This was characterized by a number of typical apoptotic hallmarks, including DNA fragmentation, chromatin condensation, apoptotic-like bodies, partial cell wall lysis and plasmolysis. In addition, local increases in H2O2 and NO were observed and quantified. The differentiation of cortical aerenchyma in the stem of E. densa is a complex process, consisting of a combination of an early schizogenous differentiation mechanism and a late lysigenous PCD-dependent process. The PCD remodels the architecture of the gas spaces previously formed schizogenously, and also results in a reduction of O2-consuming cells and in recycling of material derived from the lysigenic dismantling of the cells. © The Author 2015. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

PubMed Central

Kaikina, Elena I.

2013-01-01

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185

Non-invasive Differentiation of Kidney Stone Types using X-ray Dark-Field Radiography

PubMed Central

Scherer, Kai; Braig, Eva; Willer, Konstantin; Willner, Marian; Fingerle, Alexander A.; Chabior, Michael; Herzen, Julia; Eiber, Matthias; Haller, Bernhard; Straub, Michael; Schneider, Heike; Rummeny, Ernst J.; Noël, Peter B.; Pfeiffer, Franz

2015-01-01

Treatment of renal calculi is highly dependent on the chemical composition of the stone in question, which is difficult to determine using standard imaging techniques. The objective of this study is to evaluate the potential of scatter-sensitive X-ray dark-field radiography to differentiate between the most common types of kidney stones in clinical practice. Here, we examine the absorption-to-scattering ratio of 118 extracted kidney stones with a laboratory Talbot-Lau Interferometer. Depending on their chemical composition, microscopic growth structure and morphology the various types of kidney stones show strongly varying, partially opposite contrasts in absorption and dark-field imaging. By assessing the microscopic calculi morphology with high resolution micro-computed tomography measurements, we illustrate the dependence of dark-field signal strength on the respective stone type. Finally, we utilize X-ray dark-field radiography as a non-invasive, highly sensitive (100%) and specific (97%) tool for the differentiation of calcium oxalate, uric acid and mixed types of stones, while additionally improving the detectability of radio-lucent calculi. We prove clinical feasibility of the here proposed method by accurately classifying renal stones, embedded within a fresh pig kidney, using dose-compatible measurements and a quick and simple visual inspection. PMID:25873414

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.

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

Sensitivity analysis of dynamic biological systems with time-delays.

PubMed

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2010-10-15

Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential equation (DDE) models. Numerical sensitivity analysis of a DDE model by the direct method requires the solutions of model and sensitivity equations with time-delays. The major effort is the computation of Jacobian matrix when computing the solution of sensitivity equations. The computation of partial derivatives of complex equations either by the analytic method or by symbolic manipulation is time consuming, inconvenient, and prone to introduce human errors. To address this problem, an automatic approach to obtain the derivatives of complex functions efficiently and accurately is necessary. We have proposed an efficient algorithm with an adaptive step size control to compute the solution and dynamic sensitivities of biological systems described by ordinal differential equations (ODEs). The adaptive direct-decoupled algorithm is extended to solve the solution and dynamic sensitivities of time-delay systems describing by DDEs. To save the human effort and avoid the human errors in the computation of partial derivatives, an automatic differentiation technique is embedded in the extended algorithm to evaluate the Jacobian matrix. The extended algorithm is implemented and applied to two realistic models with time-delays: the cardiovascular control system and the TNF-α signal transduction network. The results show that the extended algorithm is a good tool for dynamic sensitivity analysis on DDE models with less user intervention. By comparing with direct-coupled methods in theory, the extended algorithm is efficient, accurate, and easy to use for end users without programming background to do dynamic sensitivity analysis on complex biological systems with time-delays.

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization.

PubMed

Fujarewicz, Krzysztof; Lakomiec, Krzysztof

2016-12-01

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

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.

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Small, Des; Wiggins, Stephen

2006-12-01

In the past 15 years the framework and ideas from dynamical systems theory have been applied to a variety of transport and mixing problems in oceanic flows. The motivation for this approach comes directly from advances in observational capabilities in oceanography (e.g., drifter deployments, remote sensing capabilities, satellite imagery, etc.) which reveal space-time structures that are highly suggestive of the structures one visualizes in the global, geometrical study of dynamical systems theory. In this tutorial, we motivate this approach by showing the relationship between fluid transport in two-dimensional time-periodic incompressible flows and the geometrical structures that exist for two-dimensional area-preserving maps, such as hyperbolic periodic orbits, their stable and unstable manifolds and KAM (Kolmogorov-Arnold-Moser) tori. This serves to set the stage for the attempt to “transfer” this approach to more realistic flows modelling the ocean. However, in order to accomplish this several difficulties must be overcome. The first difficulty that confronts us that any attempt to carry out a dynamical systems approach to transport requires us to obtain the appropriate “dynamical system”, which is the velocity field describing the fluid flow. In general, adequate model velocity fields are obtained by numerical solution of appropriate partial differential equations describing the dynamical evolution of the velocity field. Numerical solution of the partial differential equations can only be done for a finite time interval, and since the ocean is generally not time-periodic, this leads to a new type of dynamical system: a finite-time, aperiodically time-dependent velocity field defined as a data set on a space-time grid. The global, geometrical analysis of transport in such dynamical systems requires both new concepts and new analytical and computational tools, as well as the necessity to discard some of the standard ideas and results from dynamical systems theory. The purpose of this tutorial is to describe these new concepts and analytical tools first using simple dynamical systems where quantities can be computed exactly. We then discuss their computational implications and implementation in the context of a model geophysical flow: a turbulent wind-driven double-gyre in the quasigeostrophic approximation.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

The hedgehog system machinery controls transforming growth factor-β-dependent myofibroblastic differentiation in humans: involvement in idiopathic pulmonary fibrosis.

PubMed

Cigna, Natacha; Farrokhi Moshai, Elika; Brayer, Stéphanie; Marchal-Somme, Joëlle; Wémeau-Stervinou, Lidwine; Fabre, Aurélie; Mal, Hervé; Lesèche, Guy; Dehoux, Monique; Soler, Paul; Crestani, Bruno; Mailleux, Arnaud A

2012-12-01

Idiopathic pulmonary fibrosis (IPF) is a devastating disease of unknown cause. Key signaling developmental pathways are aberrantly expressed in IPF. The hedgehog pathway plays a key role during fetal lung development and may be involved in lung fibrogenesis. We determined the expression pattern of several Sonic hedgehog (SHH) pathway members in normal and IPF human lung biopsies and primary fibroblasts. The effect of hedgehog pathway inhibition was assayed by lung fibroblast proliferation and differentiation with and without transforming growth factor (TGF)-β1. We showed that the hedgehog pathway was reactivated in the IPF lung. Importantly, we deciphered the cross talk between the hedgehog and TGF-β pathway in human lung fibroblasts. TGF-β1 modulated the expression of key components of the hedgehog pathway independent of Smoothened, the obligatory signal transducer of the pathway. Smoothened was required for TGF-β1-induced myofibroblastic differentiation of control fibroblasts, but differentiation of IPF fibroblasts was partially resistant to Smoothened inhibition. Furthermore, functional hedgehog pathway machinery from the primary cilium, as well as GLI-dependent transcription in the nucleus, was required for the TGF-β1 effects on normal and IPF fibroblasts during myofibroblastic differentiation. These data identify the GLI transcription factors as potential therapeutic targets in lung fibrosis. Copyright © 2012 American Society for Investigative Pathology. Published by Elsevier Inc. All rights reserved.

A time- and matrix-dependent TGFBR3–JUND–KRT5 regulatory circuit in single breast epithelial cells and basal-like premalignancies

PubMed Central

Wang, Chun-Chao; Bajikar, Sameer S.; Jamal, Leen; Atkins, Kristen A.; Janes, Kevin A.

2014-01-01

Basal-like breast carcinoma is characterized by poor prognosis and high intratumor heterogeneity. In an immortalized basal-like breast epithelial cell line, we identified two anti-correlated gene-expression programs that arise among single extracellular matrix (ECM)-attached cells during organotypic 3D culture. The first contains multiple TGFβ-related genes including TGFBR3, whereas the second contains JUND and the basal-like marker, KRT5. TGFBR3 and JUND interconnect through four negative-feedback loops to form a circuit that exhibits spontaneous damped oscillations in 3D culture. The TGFBR3–JUND circuit appears conserved in some premalignant lesions that heterogeneously express KRT5. The circuit depends on ECM engagement, as detachment causes a rewiring that is triggered by RPS6 dephosphorylation and maintained by juxtacrine tenascin C, which is critical for intraductal colonization of basal-like breast cancer cells in vivo. Intratumor heterogeneity need not stem from partial differentiation and could instead reflect dynamic toggling of cells between expression states that are not cell autonomous. PMID:24658685

Finite-difference model to simulate the areal flow of saltwater and fresh water separated by an interface

USGS Publications Warehouse

Mercer, James W.; Larson, S.P.; Faust, Charles R.

1980-01-01

Model documentation is presented for a two-dimensional (areal) model capable of simulating ground-water flow of salt water and fresh water separated by an interface. The partial differential equations are integrated over the thicknesses of fresh water and salt water resulting in two equations describing the flow characteristics in the areal domain. These equations are approximated using finite-difference techniques and the resulting algebraic equations are solved for the dependent variables, fresh water head and salt water head. An iterative solution method was found to be most appropriate. The program is designed to simulate time-dependent problems such as those associated with the development of coastal aquifers, and can treat water-table conditions or confined conditions with steady-state leakage of fresh water. The program will generally be most applicable to the analysis of regional aquifer problems in which the zone between salt water and fresh water can be considered a surface (sharp interface). Example problems and a listing of the computer code are included. (USGS).

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

The extimated presence of differentiated higly explosive magmas beneath Vesuvius and Campi Flegrei: evidence from geochemical and textural studies.

NASA Astrophysics Data System (ADS)

Pappalardo, Lucia; Mastrolorenzo, Giuseppe

2010-05-01

Highly catastrophic explosive eruptions are supplied by Si-rich magmas, generated at shallower level in crust by the evolution of mantle liquids. The timescale of these evolution processes is a crucial factor, because of its control on the length of volcano repose interval leading to high explosive events. Campi Flegrei and Somma-Vesuvius alkaline volcanic systems, located respectively at few kilometers west and east of Neapolitan metropolitan area, produced a variety of eruptions ranging from not explosive lava flows and domes to highly destructive eruptions. Both these high risk volcanoes are in repose time since the last eruption occurred in the 1538 and 1944 BP, respectively. Since that time, the volcanoes experienced fumarolic activity, low level of seismicity with rare earthquakes swarms, as well as two bradyseismic crisis (1969-1972 and 1982-1984) localized in the center of Campi Flegrei caldera, that generated a net uplift of 3.5 m around the town of Pozzuoli. A wide low velocity layer interpreted as an extended magmatic body has been detected at 8-10 km depth beneath these volcanoes by seismic data. The capability of this reservoir to erupt explosively again strongly depends on magma differentiation degree, therefore the knowledge of the time lapse necessary at not explosive mafic liquids to differentiate toward explosive magmas is very crucial to predict the size of a possible short-term future eruption in Campanian area. Our petrologic data indicate that a multi-depth supply system was active under the Campanian Plain since 39 ka. Fractional crystallization during magma cooling associated with upward migration of less dense evolved liquids appears to be the prevalent differentiation process. Our results indicate that huge steam exolution occurred during the late stage of trachyte and phonolite crystallization thus accounting for the high Volcanic Explosivity Index (VEI) of eruptions supplied by these melts. Moreover our CSD data on phenocrysts reveal rapid crystallization and differentiation time for alkaline Campanian magmas (in the order of decades to few centuries). This evidence implies that the 400 km2 partial melting zone detected by tomography study at 8-10 km depth beneath Vesuvius and Campi Flegrei, should consist of differentiated magma already capable to produce also large scale (plinian) explosive events in case of renewal of the activity from the present closed-conduit state.

ICASE Semiannual Report. April 1, 1993 through September 30, 1993

DTIC Science & Technology

1993-12-01

scientists from universities and industry who have resident appointments for limited periods of time as well as by visiting and resident consultants... time integration. One of these is the time advancement of systems of hyperbolic partial differential equations via high order Runge- Kutta algorithms...Typically if the R-K methods is of, say, fourth order accuracy then there will be four intermediate steps between time level t = n6 and t + 6 = (n + 1)b

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

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

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…

Cell shape, cytoskeletal mechanics, and cell cycle control in angiogenesis

NASA Technical Reports Server (NTRS)

Ingber, D. E.; Prusty, D.; Sun, Z.; Betensky, H.; Wang, N.

1995-01-01

Capillary endothelial cells can be switched between growth and differentiation by altering cell-extracellular matrix interactions and thereby, modulating cell shape. Studies were carried out to determine when cell shape exerts its growth-regulatory influence during cell cycle progression and to explore the role of cytoskeletal structure and mechanics in this control mechanism. When G0-synchronized cells were cultured in basic fibroblast growth factor (FGF)-containing defined medium on dishes coated with increasing densities of fibronectin or a synthetic integrin ligand (RGD-containing peptide), cell spreading, nuclear extension, and DNA synthesis all increased in parallel. To determine the minimum time cells must be adherent and spread on extracellular matrix (ECM) to gain entry into S phase, cells were removed with trypsin or induced to retract using cytochalasin D at different times after plating. Both approaches revealed that cells must remain extended for approximately 12-15 h and hence, most of G1, in order to enter S phase. After this restriction point was passed, normally 'anchorage-dependent' endothelial cells turned on DNA synthesis even when round and in suspension. The importance of actin-containing microfilaments in shape-dependent growth control was confirmed by culturing cells in the presence of cytochalasin D (25-1000 ng ml-1): dose-dependent inhibition of cell spreading, nuclear extension, and DNA synthesis resulted. In contrast, induction of microtubule disassembly using nocodazole had little effect on cell or nuclear spreading and only partially inhibited DNA synthesis. Interestingly, combination of nocodazole with a suboptimal dose of cytochalasin D (100 ng ml-1) resulted in potent inhibition of both spreading and growth, suggesting that microtubules are redundant structural elements which can provide critical load-bearing functions when microfilaments are partially compromised. Similar synergism between nocodazole and cytochalasin D was observed when cytoskeletal stiffness was measured directly in living cells using magnetic twisting cytometry. These results emphasize the importance of matrix-dependent changes in cell and nuclear shape as well as higher order structural interactions between different cytoskeletal filament systems for control of capillary cell growth during angiogenesis.

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.

Solving Partial Differential Equations on Overlapping Grids

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

Henshaw, W D

2008-09-22

We discuss the solution of partial differential equations (PDEs) on overlapping grids. This is a powerful technique for efficiently solving problems in complex, possibly moving, geometry. An overlapping grid consists of a set of structured grids that overlap and cover the computational domain. By allowing the grids to overlap, grids for complex geometries can be more easily constructed. The overlapping grid approach can also be used to remove coordinate singularities by, for example, covering a sphere with two or more patches. We describe the application of the overlapping grid approach to a variety of different problems. These include the solutionmore » of incompressible fluid flows with moving and deforming geometry, the solution of high-speed compressible reactive flow with rigid bodies using adaptive mesh refinement (AMR), and the solution of the time-domain Maxwell's equations of electromagnetism.« less

Vildagliptin Stimulates Endothelial Cell Network Formation and Ischemia-induced Revascularization via an Endothelial Nitric-oxide Synthase-dependent Mechanism*

PubMed Central

Ishii, Masakazu; Shibata, Rei; Kondo, Kazuhisa; Kambara, Takahiro; Shimizu, Yuuki; Tanigawa, Tohru; Bando, Yasuko K.; Nishimura, Masahiro; Ouchi, Noriyuki; Murohara, Toyoaki

2014-01-01

Dipeptidyl peptidase-4 inhibitors are known to lower glucose levels and are also beneficial in the management of cardiovascular disease. Here, we investigated whether a dipeptidyl peptidase-4 inhibitor, vildagliptin, modulates endothelial cell network formation and revascularization processes in vitro and in vivo. Treatment with vildagliptin enhanced blood flow recovery and capillary density in the ischemic limbs of wild-type mice, with accompanying increases in phosphorylation of Akt and endothelial nitric-oxide synthase (eNOS). In contrast to wild-type mice, treatment with vildagliptin did not improve blood flow in ischemic muscles of eNOS-deficient mice. Treatment with vildagliptin increased the levels of glucagon-like peptide-1 (GLP-1) and adiponectin, which have protective effects on the vasculature. Both vildagliptin and GLP-1 increased the differentiation of cultured human umbilical vein endothelial cells (HUVECs) into vascular-like structures, although vildagliptin was less effective than GLP-1. GLP-1 and vildagliptin also stimulated the phosphorylation of Akt and eNOS in HUVECs. Pretreatment with a PI3 kinase or NOS inhibitor blocked the stimulatory effects of both vildagliptin and GLP-1 on HUVEC differentiation. Furthermore, treatment with vildagliptin only partially increased the limb flow of ischemic muscle in adiponectin-deficient mice in vivo. GLP-1, but not vildagliptin, significantly increased adiponectin expression in differentiated 3T3-L1 adipocytes in vitro. These data indicate that vildagliptin promotes endothelial cell function via eNOS signaling, an effect that may be mediated by both GLP-1-dependent and GLP-1-independent mechanisms. The beneficial activity of GLP-1 for revascularization may also be partially mediated by its ability to increase adiponectin production. PMID:25100725

Vildagliptin stimulates endothelial cell network formation and ischemia-induced revascularization via an endothelial nitric-oxide synthase-dependent mechanism.

PubMed

Ishii, Masakazu; Shibata, Rei; Kondo, Kazuhisa; Kambara, Takahiro; Shimizu, Yuuki; Tanigawa, Tohru; Bando, Yasuko K; Nishimura, Masahiro; Ouchi, Noriyuki; Murohara, Toyoaki

2014-09-26

Dipeptidyl peptidase-4 inhibitors are known to lower glucose levels and are also beneficial in the management of cardiovascular disease. Here, we investigated whether a dipeptidyl peptidase-4 inhibitor, vildagliptin, modulates endothelial cell network formation and revascularization processes in vitro and in vivo. Treatment with vildagliptin enhanced blood flow recovery and capillary density in the ischemic limbs of wild-type mice, with accompanying increases in phosphorylation of Akt and endothelial nitric-oxide synthase (eNOS). In contrast to wild-type mice, treatment with vildagliptin did not improve blood flow in ischemic muscles of eNOS-deficient mice. Treatment with vildagliptin increased the levels of glucagon-like peptide-1 (GLP-1) and adiponectin, which have protective effects on the vasculature. Both vildagliptin and GLP-1 increased the differentiation of cultured human umbilical vein endothelial cells (HUVECs) into vascular-like structures, although vildagliptin was less effective than GLP-1. GLP-1 and vildagliptin also stimulated the phosphorylation of Akt and eNOS in HUVECs. Pretreatment with a PI3 kinase or NOS inhibitor blocked the stimulatory effects of both vildagliptin and GLP-1 on HUVEC differentiation. Furthermore, treatment with vildagliptin only partially increased the limb flow of ischemic muscle in adiponectin-deficient mice in vivo. GLP-1, but not vildagliptin, significantly increased adiponectin expression in differentiated 3T3-L1 adipocytes in vitro. These data indicate that vildagliptin promotes endothelial cell function via eNOS signaling, an effect that may be mediated by both GLP-1-dependent and GLP-1-independent mechanisms. The beneficial activity of GLP-1 for revascularization may also be partially mediated by its ability to increase adiponectin production. © 2014 by The American Society for Biochemistry and Molecular Biology, Inc.

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.

Molecular mechanism of G1 arrest and cellular senescence induced by LEE011, a novel CDK4/CDK6 inhibitor, in leukemia cells.

PubMed

Tao, Yan-Fang; Wang, Na-Na; Xu, Li-Xiao; Li, Zhi-Heng; Li, Xiao-Lu; Xu, Yun-Yun; Fang, Fang; Li, Mei; Qian, Guang-Hui; Li, Yan-Hong; Li, Yi-Ping; Wu, Yi; Ren, Jun-Li; Du, Wei-Wei; Lu, Jun; Feng, Xing; Wang, Jian; He, Wei-Qi; Hu, Shao-Yan; Pan, Jian

2017-01-01

Overexpression of cyclin D1 dependent kinases 4 and 6 (CDK4/6) is a common feature of many human cancers including leukemia. LEE011 is a novel inhibitor of both CDK4 and 6. To date, the molecular function of LEE011 in leukemia remains unclear. Leukemia cell growth and apoptosis following LEE011 treatment was assessed through CCK-8 and annexin V/propidium iodide staining assays. Cell senescence was assessed by β-galactosidase staining and p16 INK4a expression analysis. Gene expression profiles of LEE011 treated HL-60 cells were investigated using an Arraystar Human LncRNA array. Gene ontology and KEGG pathway analysis were then used to analyze the differentially expressed genes from the cluster analysis. Our studies demonstrated that LEE011 inhibited proliferation of leukemia cells and could induce apoptosis. Hoechst 33,342 staining analysis showed DNA fragmentation and distortion of nuclear structures following LEE011 treatment. Cell cycle analysis showed LEE011 significantly induced cell cycle G 1 arrest in seven of eight acute leukemia cells lines, the exception being THP-1 cells. β-Galactosidase staining analysis and p16 INK4a expression analysis showed that LEE011 treatment can induce cell senescence of leukemia cells. LncRNA microarray analysis showed 2083 differentially expressed mRNAs and 3224 differentially expressed lncRNAs in LEE011-treated HL-60 cells compared with controls. Molecular function analysis showed that LEE011 induced senescence in leukemia cells partially through downregulation of the transcriptional expression of MYBL2. We demonstrate for the first time that LEE011 treatment results in inhibition of cell proliferation and induction of G 1 arrest and cellular senescence in leukemia cells. LncRNA microarray analysis showed differentially expressed mRNAs and lncRNAs in LEE011-treated HL-60 cells and we demonstrated that LEE011 induces cellular senescence partially through downregulation of the expression of MYBL2. These results may open new lines of investigation regarding the molecular mechanism of LEE011 induced cellular senescence.

Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

PubMed Central

Gupta, Diksha; Singh, Bani

2014-01-01

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310

Dynamics of column stability with partial end restraints

NASA Technical Reports Server (NTRS)

Gregory, Peyton B.

1990-01-01

The dynamic behavior of columns with partial end restraints and loads consisting of a dead load and a pulsating load are investigated. The differential equation is solved using a lumped impulse recurrence formula relative to time coupled with a finite difference discretization along the member length. A computer program is written from which the first critical frequencies are found as a function of end stiffness. The case of a pinned ended column compares very well with the exact solution. Also, the natural frequency and buckling load formulas are derived for equal and unequal end restraints.

Analysis of forced convective modified Burgers liquid flow considering Cattaneo-Christov double diffusion

NASA Astrophysics Data System (ADS)

Waqas, M.; Hayat, T.; Shehzad, S. A.; Alsaedi, A.

2018-03-01

A mathematical model is formulated to characterize the non-Fourier and Fick's double diffusive models of heat and mass in moving flow of modified Burger's liquid. Temperature-dependent conductivity of liquid is taken into account. The concept of stratification is utilized to govern the equations of energy and mass species. The idea of boundary layer theory is employed to obtain the mathematical model of considered physical problem. The obtained partial differential system is converted into ordinary ones with the help of relevant variables. The homotopic concept lead to the convergent solutions of governing expressions. Convergence is attained and acceptable values are certified by expressing the so called ℏ -curves and numerical benchmark. Several graphs are made for different values of physical constraints to explore the mechanism of heat and mass transportation. We explored that the liquid temperature and concentration are retard for the larger thermal/concentration relaxation time constraint.

Statistics of Experiments on Cluster Formation and Transport in a Gravitational Field

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.

1993-01-01

Metastable state relaxation in a gravitational field is investigated in the case of non-critical binary solutions. A relaxation description is presented in terms of the time-dependent Ginzburg-Landau formalism for a non-conserved order parameter. A new ansatz for solution of the corresponding partial nonlinear stochastic differential equation is discussed. It is proved that, for the supersaturated solution under consideration, the metastable state relaxation in a gravitational field leads to formation of solute concentration gradients due to the sedimentation of subcritical solute clusters. The pure discussion of the possible methods to compare theoretical results and experimental data related to solute sedimentation in a gravitational field is presented. It is shown that in order to describe these experiments it is necessary to deal both with the value of the solute concentration gradient and with its formation rate. The stochastic nature of the sedimentation process is shown.

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.

Development of a distributed-parameter mathematical model for simulation of cryogenic wind tunnels

NASA Technical Reports Server (NTRS)

Tripp, J. S.

1983-01-01

A one-dimensional distributed-parameter dynamic model of a cryogenic wind tunnel was developed which accounts for internal and external heat transfer, viscous momentum losses, and slotted-test-section dynamics. Boundary conditions imposed by liquid-nitrogen injection, gas venting, and the tunnel fan were included. A time-dependent numerical solution to the resultant set of partial differential equations was obtained on a CDC CYBER 203 vector-processing digital computer at a usable computational rate. Preliminary computational studies were performed by using parameters of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Studies were performed by using parameters from the National Transonic Facility (NTF). The NTF wind-tunnel model was used in the design of control loops for Mach number, total temperature, and total pressure and for determining interactions between the control loops. It was employed in the application of optimal linear-regulator theory and eigenvalue-placement techniques to develop Mach number control laws.

Investigation for all polarization conversions of the guided-modes in a bending waveguide

NASA Astrophysics Data System (ADS)

Shi, Yunjie; Shang, Hongpeng; Sun, DeGui

2018-03-01

In this work, a new solution to the partial differential Maxwell equations is first derived to investigate all polarization conversions of the transverse and the longitudinal components of guided-modes in a bending waveguide. Then, for the silica-waveguides, the polarization conversion efficiencies are numerical calculated and a significant finding is that the transverse-longitudinal polarization conversion efficiency is much higher than that of transverse-transverse polarization conversion. Furthermore, the dependences of all the conversion efficiencies on waveguide parameters are found. The agreeable results between the numerical calculation and the finite difference time-domain (FDTD) simulation show that for two 100 μm long bending waveguides of 0.75 and 1.50% index contrasts, the amplitude conversion efficiencies from ∼10-3 to ∼10-2 can be realized for the transverse-transverse polarization components and that of ∼10-1 can be realized for the transverse-longitudinal polarization components.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

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

A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives with Target Redemption Features

NASA Astrophysics Data System (ADS)

Christara, Christina C.; Minh Dang, Duy; Jackson, Kenneth R.; Lakhany, Asif

2010-09-01

We propose a general framework for efficient pricing via a partial differential equation (PDE) approach for exotic cross-currency interest rate (IR) derivatives, with strong emphasis on long-dated foreign exchange (FX) IR hybrids, namely Power Reverse Dual Currency (PRDC) swaps with a FX Target Redemption (FX-TARN) provision. The FX-TARN provision provides a cap on the FX-linked PRDC coupon amounts, and once the accumulated coupon amount reaches this cap, the underlying PRDC swap terminates. Our PDE pricing framework is based on an auxiliary state variable to keep track of the total accumulated PRDC coupon amount. Finite differences on uniform grids and the Alternating Direction Implicit (ADI) method are used for the spatial and time discretizations, respectively, of the model-dependent PDE corresponding to each discretized value of the auxiliary variable. Numerical examples illustrating the convergence properties of the numerical methods are provided.

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

Partial wetting gas-liquid segmented flow microreactor.

PubMed

Kazemi Oskooei, S Ali; Sinton, David

2010-07-07

A microfluidic reactor strategy for reducing plug-to-plug transport in gas-liquid segmented flow microfluidic reactors is presented. The segmented flow is generated in a wetting portion of the chip that transitions downstream to a partially wetting reaction channel that serves to disconnect the liquid plugs. The resulting residence time distributions show little dependence on channel length, and over 60% narrowing in residence time distribution as compared to an otherwise similar reactor. This partial wetting strategy mitigates a central limitation (plug-to-plug dispersion) while preserving the many attractive features of gas-liquid segmented flow reactors.

WE-AB-204-07: Spatiotemporal Distribution of the FDG PET Tracer in Solid Tumors: Contributions of Diffusion and Convection Mechanisms

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

Soltani, M; Sefidgar, M; Bazmara, H

2015-06-15

Purpose: In this study, a mathematical model is utilized to simulate FDG distribution in tumor tissue. In contrast to conventional compartmental modeling, tracer distributions across space and time are directly linked together (i.e. moving beyond ordinary differential equations (ODEs) to utilizing partial differential equations (PDEs) coupling space and time). The diffusion and convection transport mechanisms are both incorporated to model tracer distribution. We aimed to investigate the contributions of these two mechanisms on FDG distribution for various tumor geometries obtained from PET/CT images. Methods: FDG transport was simulated via a spatiotemporal distribution model (SDM). The model is based on amore » 5K compartmental model. We model the fact that tracer concentration in the second compartment (extracellular space) is modulated via convection and diffusion. Data from n=45 patients with pancreatic tumors as imaged using clinical FDG PET/CT imaging were analyzed, and geometrical information from the tumors including size, shape, and aspect ratios were classified. Tumors with varying shapes and sizes were assessed in order to investigate the effects of convection and diffusion mechanisms on FDG transport. Numerical methods simulating interstitial flow and solute transport in tissue were utilized. Results: We have shown the convection mechanism to depend on the shape and size of tumors whereas diffusion mechanism is seen to exhibit low dependency on shape and size. Results show that concentration distribution of FDG is relatively similar for the considered tumors; and that the diffusion mechanism of FDG transport significantly dominates the convection mechanism. The Peclet number which shows the ratio of convection to diffusion rates was shown to be of the order of 10−{sup 3} for all considered tumors. Conclusion: We have demonstrated that even though convection leads to varying tracer distribution profiles depending on tumor shape and size, the domination of the diffusion phenomenon prevents these factors from modulating FDG distribution.« less

Transcription factors ETF, E2F, and SP-1 are involved in cytokine-independent proliferation of murine hepatocytes.

PubMed

Zellmer, Sebastian; Schmidt-Heck, Wolfgang; Godoy, Patricio; Weng, Honglei; Meyer, Christoph; Lehmann, Thomas; Sparna, Titus; Schormann, Wiebke; Hammad, Seddik; Kreutz, Clemens; Timmer, Jens; von Weizsäcker, Fritz; Thürmann, Petra A; Merfort, Irmgard; Guthke, Reinhard; Dooley, Steven; Hengstler, Jan G; Gebhardt, Rolf

2010-12-01

The cellular basis of liver regeneration has been intensely investigated for many years. However, the mechanisms initiating hepatocyte "plasticity" and priming for proliferation are not yet fully clear. We investigated alterations in gene expression patterns during the first 72 hours of C57BL/6N mouse hepatocyte culture on collagen monolayers (CM), which display a high basal frequency of proliferation in the absence of cytokines. Although many metabolic genes were down-regulated, genes related to mitogen-activated protein kinase (MAPK) signaling and cell cycle were up-regulated. The latter genes showed an overrepresentation of transcription factor binding sites (TFBS) for ETF (TEA domain family member 2), E2F1 (E2F transcription factor 1), and SP-1 (Sp1 transcription factor) (P < 0.001), all depending on MAPK signaling. Time-dependent increase of ERK1/2 phosphorylation occurred during the first 48 hours (and beyond) in the absence of cytokines, accompanied by an enhanced bromodeoxyuridine labeling index of 20%. The MEK inhibitor PD98059 blunted these effects indicating MAPK signaling as major trigger for this cytokine-independent proliferative response. In line with these in vitro findings, liver tissue of mice challenged with CCl(4) displayed hepatocytes with intense p-ERK1/2 staining and nuclear SP-1 and E2F1 expression. Furthermore, differentially expressed genes in mice after partial hepatectomy contained overrepresented TFBS for ETF, E2F1, and SP-1 and displayed increased expression of E2F1. Cultivation of murine hepatocytes on CM primes cells for proliferation through cytokine-independent activation of MAPK signaling. The transcription factors ETF, E2F1, and SP-1 seem to play a pronounced role in mediating proliferation-dependent differential gene expression. Similar events, but on a shorter time-scale, occur very early after liver damage in vivo. Copyright © 2010 American Association for the Study of Liver Diseases.

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.

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

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Curve and Polygon Evolution Techniques for Image Processing

DTIC Science & Technology

2002-01-01

iterative image registration technique with an application to stereo vision. IJCAI, pages 674–679, 1981. 127 [93] R . Malladi , J.A. Sethian, and B.C...Notation A digital image to be processed is a 2-Dimensional (2-D) function denoted by I , I : ! R , where R2 is the domain of the function. Processing a...function Io(x; y), which depends on two spatial variables, x 2 R , and y 2 R , via a partial differential equation (PDE) takes the form; It = A(I; Ix

Measurement of the absolute differential cross section of proton–proton elastic scattering at small angles

DOE PAGES

Mchedlishvili, D.; Chiladze, D.; Dymov, S.; ...

2016-02-03

The differential cross section for proton-proton elastic scattering has been measured at a beam kinetic energy of 1.0 GeV and in 200 MeV steps from 1.6 to 2.8 GeV for centre-of-mass angles in the range from 12°-16° to 25°-30°, depending on the energy. A precision in the overall normalisation of typically 3% was achieved by studying the energy losses of the circulating beam of the COSY storage ring as it passed repeatedly through the windowless hydrogen target of the ANKE magnetic spectrometer. It is shown that the data have a significant impact upon the results of a partial wave analysis.more » Furthermore, after extrapolating the differential cross sections to the forward direction, the results are broadly compatible with the predictions of forward dispersion relations.« less

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.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

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

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Carleton, O.

1972-01-01

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

High-Throughput Screening Enhances Kidney Organoid Differentiation from Human Pluripotent Stem Cells and Enables Automated Multidimensional Phenotyping.

PubMed

Czerniecki, Stefan M; Cruz, Nelly M; Harder, Jennifer L; Menon, Rajasree; Annis, James; Otto, Edgar A; Gulieva, Ramila E; Islas, Laura V; Kim, Yong Kyun; Tran, Linh M; Martins, Timothy J; Pippin, Jeffrey W; Fu, Hongxia; Kretzler, Matthias; Shankland, Stuart J; Himmelfarb, Jonathan; Moon, Randall T; Paragas, Neal; Freedman, Benjamin S

2018-05-15

Organoids derived from human pluripotent stem cells are a potentially powerful tool for high-throughput screening (HTS), but the complexity of organoid cultures poses a significant challenge for miniaturization and automation. Here, we present a fully automated, HTS-compatible platform for enhanced differentiation and phenotyping of human kidney organoids. The entire 21-day protocol, from plating to differentiation to analysis, can be performed automatically by liquid-handling robots, or alternatively by manual pipetting. High-content imaging analysis reveals both dose-dependent and threshold effects during organoid differentiation. Immunofluorescence and single-cell RNA sequencing identify previously undetected parietal, interstitial, and partially differentiated compartments within organoids and define conditions that greatly expand the vascular endothelium. Chemical modulation of toxicity and disease phenotypes can be quantified for safety and efficacy prediction. Screening in gene-edited organoids in this system reveals an unexpected role for myosin in polycystic kidney disease. Organoids in HTS formats thus establish an attractive platform for multidimensional phenotypic screening. Copyright © 2018 Elsevier Inc. All rights reserved.

Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer.

PubMed

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes.

COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY.

PubMed

Feng, Zhilan; Han, Qing; Qiu, Zhipeng; Hill, Andrew N; Glasser, John W

2016-03-01

For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.

Mixed Convection Flow of Viscoelastic Fluid by a Stretching Cylinder with Heat Transfer

PubMed Central

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes. PMID:25775032

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

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

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

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.

Eroding dipoles and vorticity growth for Euler flows in {{{R}}}^{3}: the hairpin geometry as a model for finite-time blowup

NASA Astrophysics Data System (ADS)

Childress, Stephen; Gilbert, Andrew D.

2018-02-01

A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as realized in the eroding hairpin excludes a finite time blowup for the corresponding Navier-Stokes model.

Measurement of time-dependent CP asymmetries and constraints on sin(2beta+gamma) with partial reconstruction of B0-->D*-/+pi+/- decays.

PubMed

Aubert, B; Barate, R; Boutigny, D; Couderc, F; Gaillard, J-M; Hicheur, A; Karyotakis, Y; Lees, J P; Robbe, P; Tisserand, V; Zghiche, A; Palano, A; Pompili, A; Chen, J C; Qi, N D; Rong, G; Wang, P; Zhu, Y S; Eigen, G; Ofte, I; Stugu, B; Abrams, G S; Borgland, A W; Breon, A B; Brown, D N; Button-Shafer, J; Cahn, R N; Charles, E; Day, C T; Gill, M S; Gritsan, A V; Groysman, Y; Jacobsen, R G; Kadel, R W; Kadyk, J; Kerth, L T; Kolomensky, Yu G; Kukartsev, G; LeClerc, C; Levi, M E; Lynch, G; Mir, L M; Oddone, P J; Orimoto, T J; Pripstein, M; Roe, N A; Romosan, A; Ronan, M T; Shelkov, V G; Telnov, A V; Wenzel, W A; Ford, K; Harrison, T J; Hawkes, C M; Knowles, D J; Morgan, S E; Penny, R C; Watson, A T; Watson, N K; Goetzen, K; Held, T; Koch, H; Lewandowski, B; Pelizaeus, M; Peters, K; Schmuecker, H; Steinke, M; Boyd, J T; Chevalier, N; Cottingham, W N; Kelly, M P; Latham, T E; Mackay, C; Wilson, F F; Abe, K; Cuhadar-Donszelmann, T; Hearty, C; Mattison, T S; McKenna, J A; Thiessen, D; Kyberd, P; McKemey, A K; Teodorescu, L; Blinov, V E; Bukin, A D; Golubev, V B; Ivanchenko, V N; Kravchenko, E A; Onuchin, A P; Serednyakov, S I; Skovpen, Yu I; Solodov, E P; Yushkov, A N; Best, D; Bruinsma, M; Chao, M; Kirkby, D; Lankford, A J; Mandelkern, M; Mommsen, R K; Roethel, W; Stoker, D P; Buchanan, C; Hartfiel, B L; Gary, J W; Layter, J; Shen, B C; Wang, K; del Re, D; Hadavand, H K; Hill, E J; MacFarlane, D B; Paar, H P; Rahatlou, Sh; Sharma, V; Berryhill, J W; Campagnari, C; Dahmes, B; Levy, S L; Long, O; Lu, A; Mazur, M A; Richman, J D; Verkerke, W; Beck, T W; Beringer, J; Eisner, A M; Heusch, C A; Lockman, W S; Schalk, T; Schmitz, R E; Schumm, B A; Seiden, A; Spradlin, P; Turri, M; Walkowiak, W; Williams, D C; Wilson, M G; Albert, J; Chen, E; Dubois-Felsmann, G P; Dvoretskii, A; Erwin, R J; Hitlin, D G; Narsky, I; Piatenko, T; Porter, F C; Ryd, A; Samuel, A; Yang, S; Jayatilleke, S; Mancinelli, G; Meadows, B T; Sokoloff, M D; Abe, T; Blanc, F; Bloom, P; Chen, S; Clark, P J; Ford, W T; Nauenberg, U; Olivas, A; Rankin, P; Roy, J; Smith, J G; van Hoek, W C; Zhang, L; Harton, J L; Hu, T; Soffer, A; Toki, W H; Wilson, R J; Zhang, J; Altenburg, D; Brandt, T; Brose, J; Colberg, T; Dickopp, M; Dubitzky, R S; Hauke, A; Lacker, H M; Maly, E; Müller-Pfefferkorn, R; Nogowski, R; Otto, S; Schubert, J; Schubert, K R; Schwierz, R; Spaan, B; Wilden, L; Bernard, D; Bonneaud, G R; Brochard, F; Cohen-Tanugi, J; Grenier, P; Thiebaux, Ch; Vasileiadis, G; Verderi, M; Khan, A; Lavin, D; Muheim, F; Playfer, S; Swain, J E; Andreotti, M; Azzolini, V; Bettoni, D; Bozzi, C; Calabrese, R; Cibinetto, G; Luppi, E; Negrini, M; Piemontese, L; Sarti, A; Treadwell, E; Baldini-Ferroli, R; Calcaterra, A; de Sangro, R; Falciai, D; Finocchiaro, G; Patteri, P; Piccolo, M; Zallo, A; Buzzo, A; Capra, R; Contri, R; Crosetti, G; Lo Vetere, M; Macri, M; Monge, M R; Passaggio, S; Patrignani, C; Robutti, E; Santroni, A; Tosi, S; Bailey, S; Morii, M; Won, E; Bhimji, W; Bowerman, D A; Dauncey, P D; Egede, U; Eschrich, I; Gaillard, J R; Morton, G W; Nash, J A; Taylor, G P; Grenier, G J; Lee, S-J; Mallik, U; Cochran, J; Crawley, H B; Lamsa, J; Meyer, W T; Prell, S; Rosenberg, E I; Yi, J; Davier, M; Grosdidier, G; Höcker, A; Laplace, S; Diberder, F Le; Lepeltier, V; Lutz, A M; Petersen, T C; Plaszczynski, S; Schune, M H; Tantot, L; Wormser, G; Brigljević, V; Cheng, C H; Lange, D J; Simani, M C; Wright, D M; Bevan, A J; Coleman, J P; Fry, J R; Gabathuler, E; Gamet, R; Kay, M; Parry, R J; Payne, D J; Sloane, R J; Touramanis, C; Back, J J; Harrison, P F; Shorthouse, H W; Vidal, P B; Brown, C L; Cowan, G; Flack, R L; Flaecher, H U; George, S; Green, M G; Kurup, A; Marker, C E; McMahon, T R; Ricciardi, S; Salvatore, F; Vaitsas, G; Winter, M A; Brown, D; Davis, C L; Allison, J; Barlow, N R; Barlow, R J; Hart, P A; Hodgkinson, M C; Jackson, F; Lafferty, G D; Lyon, A J; Weatherall, J H; Williams, J C; Farbin, A; Jawahery, A; Kovalskyi, D; Lae, C K; Lillard, V; Roberts, D A; Blaylock, G; Dallapiccola, C; Flood, K T; Hertzbach, S S; Kofler, R; Koptchev, V B; Moore, T B; Saremi, S; Staengle, H; Willocq, S; Cowan, R; Sciolla, G; Taylor, F; Yamamoto, R K; Mangeol, D J J; Patel, P M; Robertson, S H; Lazzaro, A; Palombo, F; Bauer, J M; Cremaldi, L; Eschenburg, V; Godang, R; Kroeger, R; Reidy, J; Sanders, D A; Summers, D J; Zhao, H W; Brunet, S; Cote-Ahern, D; Taras, P; Nicholson, H; Cartaro, C; Cavallo, N; De Nardo, G; Fabozzi, F; Gatto, C; Lista, L; Paolucci, P; Piccolo, D; Sciacca, C; Baak, M A; Raven, G; LoSecco, J M; Gabriel, T A; Brau, B; Gan, K K; Honscheid, K; Hufnagel, D; Kagan, H; Kass, R; Pulliam, T; Wong, Q K; Brau, J; Frey, R; Igonkina, O; Potter, C T; Sinev, N B; Strom, D; Torrence, E; Colecchia, F; Dorigo, A; Galeazzi, F; Margoni, M; Morandin, M; Posocco, M; Rotondo, M; Simonetto, F; Stroili, R; Tiozzo, G; Voci, C; Benayoun, M; Briand, H; Chauveau, J; David, P; de la Vaissière, Ch; Del Buono, L; Hamon, O; John, M J J; Leruste, Ph; Ocariz, J; Pivk, M; Roos, L; Stark, J; T'Jampens, S; Therin, G; Manfredi, P F; Re, V; Behera, P K; Gladney, L; Guo, Q H; Panetta, J; Anulli, F; Biasini, M; Peruzzi, I M; Pioppi, M; Angelini, C; Batignani, G; Bettarini, S; Bondioli, M; Bucci, F; Calderini, G; Carpinelli, M; Del Gamba, V; Forti, F; Giorgi, M A; Lusiani, A; Marchiori, G; Martinez-Vidal, F; Morganti, M; Neri, N; Paoloni, E; Rama, M; Rizzo, G; Sandrelli, F; Walsh, J; Haire, M; Judd, D; Paick, K; Wagoner, D E; Danielson, N; Elmer, P; Lu, C; Miftakov, V; Olsen, J; Smith, A J S; Tanaka, H A; Varnes, E W; Bellini, F; Cavoto, G; Faccini, R; Ferrarotto, F; Ferroni, F; Gaspero, M; Mazzoni, M A; Morganti, S; Pierini, M; Piredda, G; SafaiTehrani, F; Voena, C; Christ, S; Wagner, G; Waldi, R; Adye, T; De Groot, N; Franek, B; Geddes, N I; Gopal, G P; Olaiya, E O; Xella, S M; Aleksan, R; Emery, S; Gaidot, A; Ganzhur, S F; Giraud, P-F; Hamel de Monchenault, G; Kozanecki, W; Langer, M; Legendre, M; London, G W; Mayer, B; Schott, G; Vasseur, G; Yeche, Ch; Zito, M; Purohit, M V; Weidemann, A W; Yumiceva, F X; Aston, D; Bartoldus, R; Berger, N; Boyarski, A M; Buchmueller, O L; Convery, M R; Cristinziani, M; Dong, D; Dorfan, J; Dujmic, D; Dunwoodie, W; Elsen, E E; Field, R C; Glanzman, T; Gowdy, S J; Grauges-Pous, E; Hadig, T; Halyo, V; Hryn'ova, T; Innes, W R; Jessop, C P; Kelsey, M H; Kim, P; Kocian, M L; Langenegger, U; Leith, D W G S; Libby, J; Luitz, S; Luth, V; Lynch, H L; Marsiske, H; Messner, R; Muller, D R; O'Grady, C P; Ozcan, V E; Perazzo, A; Perl, M; Petrak, S; Ratcliff, B N; Roodman, A; Salnikov, A A; Schindler, R H; Schwiening, J; Simi, G; Snyder, A; Soha, A; Stelzer, J; Su, D; Sullivan, M K; Va'vra, J; Wagner, S R; Weaver, M; Weinstein, A J R; Wisniewski, W J; Wright, D H; Young, C C; Burchat, P R; Edwards, A J; Meyer, T I; Petersen, B A; Roat, C; Ahmed, M; Ahmed, S; Alam, M S; Ernst, J A; Saeed, M A; Saleem, M; Wappler, F R; Bugg, W; Krishnamurthy, M; Spanier, S M; Eckmann, R; Kim, H; Ritchie, J L; Schwitters, R F; Izen, J M; Kitayama, I; Lou, X C; Ye, S; Bianchi, F; Bona, M; Gallo, F; Gamba, D; Borean, C; Bosisio, L; Della Ricca, G; Dittongo, S; Grancagnolo, S; Lanceri, L; Poropat, P; Vitale, L; Vuagnin, G; Panvini, R S; Banerjee, Sw; Brown, C M; Fortin, D; Jackson, P D; Kowalewski, R; Roney, J M; Band, H R; Dasu, S; Datta, M; Eichenbaum, A M; Johnson, J R; Kutter, P E; Li, H; Liu, R; Di Lodovico, F; Mihalyi, A; Mohapatra, A K; Pan, Y; Prepost, R; Sekula, S J; von Wimmersperg-Toeller, J H; Wu, J; Wu, S L; Yu, Z; Neal, H

2004-06-25

We present a measurement of time-dependent CP-violating asymmetries in decays of neutral B mesons to the final states D(*-/+)pi(+/-), using approximately 82x10(6) BBmacr; events recorded by the BABAR experiment at the PEP-II e(+)e(-) storage ring. Events containing these decays are selected with a partial reconstruction technique, in which only the high-momentum pi(+/-) from the B decay and the low-momentum pi(-/+) from the D(*-/+) decay are used. We measure the amplitude of the asymmetry to be -0.063+/-0.024(stat)+/-0.014(syst) and compute bounds on |sin((2beta+gamma)|.

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.

Non-linear dynamics of compound sawteeth in tokamaks

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

Ahn, J.-H., E-mail: jae-heon.ahn@polytechnique.edu; Garbet, X.; Sabot, R.

2016-05-15

Compound sawteeth is studied with the XTOR-2F code. Non-linear full 3D magnetohydrodynamic simulations show that the plasma hot core is radially displaced and rotates during the partial crash, but is not fully expelled out of the q = 1 surface. Partial crashes occur when the radius of the q = 1 surface exceeds a critical value, at fixed poloidal beta. This critical value depends on the plasma elongation. The partial crash time is larger than the collapse time of an ordinary sawtooth, likely due to a weaker diamagnetic stabilization. This suggests that partial crashes result from a competition between destabilizing effects such as themore » q = 1 radius and diamagnetic stabilization.« less

Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation

NASA Astrophysics Data System (ADS)

Palanivel, M.; Uthayakumar, R.

2015-07-01

This paper deals with an economic order quantity (EOQ) model for non-instantaneous deteriorating items with price and advertisement dependent demand pattern under the effect of inflation and time value of money over a finite planning horizon. In this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This paper aids the retailer in minimising the total inventory cost by finding the optimal interval and the optimal order quantity. An algorithm is designed to find the optimum solution of the proposed model. Numerical examples are given to demonstrate the results. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented and the implications are discussed in detail.

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

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.

Cystic fibrosis airway secretions exhibit mucin hyperconcentration and increased osmotic pressure

PubMed Central

Henderson, Ashley G.; Ehre, Camille; Button, Brian; Abdullah, Lubna H.; Cai, Li-Heng; Leigh, Margaret W.; DeMaria, Genevieve C.; Matsui, Hiro; Donaldson, Scott H.; Davis, C. William; Sheehan, John K.; Boucher, Richard C.; Kesimer, Mehmet

2014-01-01

The pathogenesis of mucoinfective lung disease in cystic fibrosis (CF) patients likely involves poor mucus clearance. A recent model of mucus clearance predicts that mucus flow depends on the relative mucin concentration of the mucus layer compared with that of the periciliary layer; however, mucin concentrations have been difficult to measure in CF secretions. Here, we have shown that the concentration of mucin in CF sputum is low when measured by immunologically based techniques, and mass spectrometric analyses of CF mucins revealed mucin cleavage at antibody recognition sites. Using physical size exclusion chromatography/differential refractometry (SEC/dRI) techniques, we determined that mucin concentrations in CF secretions were higher than those in normal secretions. Measurements of partial osmotic pressures revealed that the partial osmotic pressure of CF sputum and the retained mucus in excised CF lungs were substantially greater than the partial osmotic pressure of normal secretions. Our data reveal that mucin concentration cannot be accurately measured immunologically in proteolytically active CF secretions; mucins are hyperconcentrated in CF secretions; and CF secretion osmotic pressures predict mucus layer–dependent osmotic compression of the periciliary liquid layer in CF lungs. Consequently, mucin hypersecretion likely produces mucus stasis, which contributes to key infectious and inflammatory components of CF lung disease. PMID:24892808

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

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

A Methodology to Determine Self-Similarity, Illustrated by Example: Transient Heat Transfer with Constant Flux

ERIC Educational Resources Information Center

Monroe, Charles; Newman, John

2005-01-01

This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations. A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from…

Activity-Dependent Bidirectional Regulation of GAD Expression in a Homeostatic Fashion Is Mediated by BDNF-Dependent and Independent Pathways

PubMed Central

Hanno-Iijima, Yoko; Tanaka, Masami; Iijima, Takatoshi

2015-01-01

Homeostatic synaptic plasticity, or synaptic scaling, is a mechanism that tunes neuronal transmission to compensate for prolonged, excessive changes in neuronal activity. Both excitatory and inhibitory neurons undergo homeostatic changes based on synaptic transmission strength, which could effectively contribute to a fine-tuning of circuit activity. However, gene regulation that underlies homeostatic synaptic plasticity in GABAergic (GABA, gamma aminobutyric) neurons is still poorly understood. The present study demonstrated activity-dependent dynamic scaling in which NMDA-R (N-methyl-D-aspartic acid receptor) activity regulated the expression of GABA synthetic enzymes: glutamic acid decarboxylase 65 and 67 (GAD65 and GAD67). Results revealed that activity-regulated BDNF (brain-derived neurotrophic factor) release is necessary, but not sufficient, for activity-dependent up-scaling of these GAD isoforms. Bidirectional forms of activity-dependent GAD expression require both BDNF-dependent and BDNF-independent pathways, both triggered by NMDA-R activity. Additional results indicated that these two GAD genes differ in their responsiveness to chronic changes in neuronal activity, which could be partially caused by differential dependence on BDNF. In parallel to activity-dependent bidirectional scaling in GAD expression, the present study further observed that a chronic change in neuronal activity leads to an alteration in neurotransmitter release from GABAergic neurons in a homeostatic, bidirectional fashion. Therefore, the differential expression of GAD65 and 67 during prolonged changes in neuronal activity may be implicated in some aspects of bidirectional homeostatic plasticity within mature GABAergic presynapses. PMID:26241953

Activity-Dependent Bidirectional Regulation of GAD Expression in a Homeostatic Fashion Is Mediated by BDNF-Dependent and Independent Pathways.

PubMed

Hanno-Iijima, Yoko; Tanaka, Masami; Iijima, Takatoshi

2015-01-01

Homeostatic synaptic plasticity, or synaptic scaling, is a mechanism that tunes neuronal transmission to compensate for prolonged, excessive changes in neuronal activity. Both excitatory and inhibitory neurons undergo homeostatic changes based on synaptic transmission strength, which could effectively contribute to a fine-tuning of circuit activity. However, gene regulation that underlies homeostatic synaptic plasticity in GABAergic (GABA, gamma aminobutyric) neurons is still poorly understood. The present study demonstrated activity-dependent dynamic scaling in which NMDA-R (N-methyl-D-aspartic acid receptor) activity regulated the expression of GABA synthetic enzymes: glutamic acid decarboxylase 65 and 67 (GAD65 and GAD67). Results revealed that activity-regulated BDNF (brain-derived neurotrophic factor) release is necessary, but not sufficient, for activity-dependent up-scaling of these GAD isoforms. Bidirectional forms of activity-dependent GAD expression require both BDNF-dependent and BDNF-independent pathways, both triggered by NMDA-R activity. Additional results indicated that these two GAD genes differ in their responsiveness to chronic changes in neuronal activity, which could be partially caused by differential dependence on BDNF. In parallel to activity-dependent bidirectional scaling in GAD expression, the present study further observed that a chronic change in neuronal activity leads to an alteration in neurotransmitter release from GABAergic neurons in a homeostatic, bidirectional fashion. Therefore, the differential expression of GAD65 and 67 during prolonged changes in neuronal activity may be implicated in some aspects of bidirectional homeostatic plasticity within mature GABAergic presynapses.

Solving differential equations with unknown constitutive relations as recurrent neural networks

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

Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.

We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learningmore » literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.« less

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

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.

Differential Equations Models to Study Quorum Sensing.

PubMed

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

A new computational method for reacting hypersonic flows

NASA Astrophysics Data System (ADS)

Niculescu, M. L.; Cojocaru, M. G.; Pricop, M. V.; Fadgyas, M. C.; Pepelea, D.; Stoican, M. G.

2017-07-01

Hypersonic gas dynamics computations are challenging due to the difficulties to have reliable and robust chemistry models that are usually added to Navier-Stokes equations. From the numerical point of view, it is very difficult to integrate together Navier-Stokes equations and chemistry model equations because these partial differential equations have different specific time scales. For these reasons, almost all known finite volume methods fail shortly to solve this second order partial differential system. Unfortunately, the heating of Earth reentry vehicles such as space shuttles and capsules is very close linked to endothermic chemical reactions. A better prediction of wall heat flux leads to smaller safety coefficient for thermal shield of space reentry vehicle; therefore, the size of thermal shield decreases and the payload increases. For these reasons, the present paper proposes a new computational method based on chemical equilibrium, which gives accurate prediction of hypersonic heating in order to support the Earth reentry capsule design.

An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising.

PubMed

Khanian, Maryam; Feizi, Awat; Davari, Ali

2014-01-01

Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient stopping criterion is presented. In this regard, the current paper introduces two strategies: utilizing the efficient explicit method due to its advantages with presenting impressive software technique to effectively solve the anisotropic diffusion filter which is mathematically unstable, proposing an automatic stopping criterion, that takes into consideration just input image, as opposed to other stopping criteria, besides the quality of denoised image, easiness and time. Various medical images are examined to confirm the claim.

Global collocation methods for approximation and the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Solomonoff, A.; Turkel, E.

1986-01-01

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Wavelets and distributed approximating functionals

NASA Astrophysics Data System (ADS)

Wei, G. W.; Kouri, D. J.; Hoffman, D. K.

1998-07-01

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

Exposure to low-dose bisphenol A impairs meiosis in the rat seminiferous tubule culture model: a physiotoxicogenomic approach.

PubMed

Ali, Sazan; Steinmetz, Gérard; Montillet, Guillaume; Perrard, Marie-Hélène; Loundou, Anderson; Durand, Philippe; Guichaoua, Marie-Roberte; Prat, Odette

2014-01-01

Bisphenol A (BPA) is one of the most widespread chemicals in the world and is suspected of being responsible for male reproductive impairments. Nevertheless, its molecular mode of action on spermatogenesis is unclear. This work combines physiology and toxicogenomics to identify mechanisms by which BPA affects the timing of meiosis and induces germ-cell abnormalities. We used a rat seminiferous tubule culture model mimicking the in vivo adult rat situation. BPA (1 nM and 10 nM) was added to the culture medium. Transcriptomic and meiotic studies were performed on the same cultures at the same exposure times (days 8, 14, and 21). Transcriptomics was performed using pangenomic rat microarrays. Immunocytochemistry was conducted with an anti-SCP3 antibody. The gene expression analysis showed that the total number of differentially expressed transcripts was time but not dose dependent. We focused on 120 genes directly involved in the first meiotic prophase, sustaining immunocytochemistry. Sixty-two genes were directly involved in pairing and recombination, some of them with high fold changes. Immunocytochemistry indicated alteration of meiotic progression in the presence of BPA, with increased leptotene and decreased diplotene spermatocyte percentages and partial meiotic arrest at the pachytene checkpoint. Morphological abnormalities were observed at all stages of the meiotic prophase. The prevalent abnormalities were total asynapsis and apoptosis. Transcriptomic analysis sustained immunocytological observations. We showed that low doses of BPA alter numerous genes expression, especially those involved in the reproductive system, and severely impair crucial events of the meiotic prophase leading to partial arrest of meiosis in rat seminiferous tubule cultures.

A new approach to treat discontinuities in multi-layered soils

NASA Astrophysics Data System (ADS)

Berardi, Marco; Difonzo, Fabio; Caputo, Maria; Vurro, Michele; Lopez, Luciano

2017-04-01

The water infiltration into two (or more) layered soils can give rise to preferential flow paths at the interface between different soils. The deep understanding of this phenomenon can be of great interest in modeling different environmental problems in geosciences and hydrology. Flow through layered soils arises naturally in agriculture, and layered soils are also engineered as cover liners for landfills. In particular, the treatment of the soil discontinuity is of great interest from the modeling and the numerical point of view, and is still an open problem.% (see, for example, te{Matthews_et_al,Zha_vzj_2013,DeLuca_Cepeda_ASCE_2016}). Assuming to approximate the soils with different porous media, the governing equation for this phenomenon is Richards' equation, in the following form: {eq:different_Richards_1} C_1(ψ) partial ψ/partial t = partial /partial z [ K_1(ψ) ( partial ψ/partial z - 1 ) ], \\quad if \\quad z < \\overline{z}, C_2(ψ) partial ψ/partial t = partial /partial z [ K_2(ψ) ( partial ψ/partial z - 1 ) ], \\quad if \\quad z > \\overline{z}, where \\overline{z} is the spatial threshold that identifies the change in soil structure, and C1 C_2, K_1, K_2, the hydraulic functions that describe the upper and the lower soil, respectively. The ψ-based form is used, in this work. Here we have used the Filippov's theory in order to deal with discontinuous differential systems, and we handled opportunely the numerical discretization in order to treat the abovementioned system by means of this theory, letting the discontinuity depend on the state variable. The advantage of this technique is a better insight on the solution behavior on the discontinuity surface, and the no-need to average the hydraulic conductivity field on the threshold itself, as in the existing literature.

Higher-order hybrid implicit/explicit FDTD time-stepping

NASA Astrophysics Data System (ADS)

Tierens, W.

2016-12-01

Both partially implicit FDTD methods, and symplectic FDTD methods of high temporal accuracy (3rd or 4th order), are well documented in the literature. In this paper we combine them: we construct a conservative FDTD method which is fourth order accurate in time and is partially implicit. We show that the stability condition for this method depends exclusively on the explicit part, which makes it suitable for use in e.g. modelling wave propagation in plasmas.

Effect of phase and orbital wave parameter choices on CS and IOS degeneracy averaged differential cross sections

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

Khare, V.; Fitz, D.E.; Kouri, D.J.

1980-09-15

The effect of phase choice and partial wave parameter choice on CS and IOS inelastic degeneracy averaged differential cross sections is studied. An approximate simplified CS scattering amplitude for l-bar=1/2(l'+l) is derived and is shown to have a form which closely resembles the McGuire--Kouri scattering amplitude for odd ..delta..j transitions and reduces to it for even ..delta..j transitions. The choice of phase in the CS wave function is shown to result in different approximations which yield significantly different shapes for the degeneracy averaged differential cross section. Time reversal symmetry arguments are employed to select the proper phase choice. IOS calculationsmore » of the degeneracy averaged differential cross sections of He--CO, He--Cl and Ne--HD using l-bar=1/2(l+l') and the phase choice which ensures proper time reversal symmetry are found to correct the phase disagreement which was previously noted for odd ..delta..j transitions using l-bar=l or l' and either the time reversal phase or other phase choices.« less

Value of Nephrometry Score Constituents on Perioperative Outcomes and Split Renal Function in Patients Undergoing Minimally Invasive Partial Nephrectomy.

PubMed

Watts, Kara L; Ghosh, Propa; Stein, Solomon; Ghavamian, Reza

2017-01-01

To assess the relationship between individual nephrometry score (NS) constituents (RENAL) on perioperative outcomes and renal function of the surgical kidney in patients undergoing laparoscopic partial nephrectomy or robotic-assisted partial nephrectomy. Two hundred forty-five patients who underwent laparoscopic partial nephrectomy or robotic-assisted partial nephrectomy between 2005 and 2014 were retrospectively reviewed. Each renal mass' NS was calculated from preoperative computed tomography imaging. Multivariate regression analysis was used to evaluate the effect of NS variables on perioperative outcomes and change in overall renal function (as estimated by glomerular filtration rate) from preoperative to 1-year postoperative. A cohort analysis assessed the effect of NS variables on change in split renal function of the surgical kidney from pre- to postoperative based on nuclear medicine renal scintigraphy. Tumor radius (R), endophytic nature (E), and nearness to collecting system (N) variables significantly and incrementally predicted a longer operative time and warm ischemia time. Overall renal function based on glomerular filtration rate was not affected by any NS variable. However, percent function of the surgical kidney by renal scintigraphy significantly decreased postoperatively as R and E values increased. R, E, and N were associated with significant changes in warm ischemia time and operative time. R and E were associated with a significant decrease in split renal function of the surgical kidney at 1 year after surgery but not with overall renal function. R, E, and N are the NS constituents most relevant to perioperative outcomes and postoperative differential renal function after partial nephrectomy. Copyright © 2016. Published by Elsevier Inc.

Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

USGS Publications Warehouse

Rubin, Jacob

1983-01-01

Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

Phenolic Analysis and Theoretic Design for Chinese Commercial Wines' Authentication.

PubMed

Li, Si-Yu; Zhu, Bao-Qing; Reeves, Malcolm J; Duan, Chang-Qing

2018-01-01

To develop a robust tool for Chinese commercial wines' varietal, regional, and vintage authentication, phenolic compounds in 121 Chinese commercial dry red wines were detected and quantified by using high-performance liquid chromatography triple-quadrupole mass spectrometry (HPLC-QqQ-MS/MS), and differentiation abilities of principal component analysis (PCA), partial least squares discriminant analysis (PLS-DA), and orthogonal partial least squares discriminant analysis (OPLS-DA) were compared. Better than PCA and PLS-DA, OPLS-DA models used to differentiate wines according to their varieties (Cabernet Sauvignon or other varieties), regions (east or west Cabernet Sauvignon wines), and vintages (young or old Cabernet Sauvignon wines) were ideally established. The S-plot provided in OPLS-DA models showed the key phenolic compounds which were both statistically and biochemically significant in sample differentiation. Besides, the potential of the OPLS-DA models in deeper sample differentiating of more detailed regional and vintage information of wines was proved optimistic. On the basis of our results, a promising theoretic design for wine authentication was further proposed for the first time, which might be helpful in practical authentication of more commercial wines. The phenolic data of 121 Chinese commercial dry red wines was processed with different statistical tools for varietal, regional, and vintage differentiation. A promising theoretical design was summarized, which might be helpful for wine authentication in practical situation. © 2017 Institute of Food Technologists®.

Time multiplexing for increased FOV and resolution in virtual reality

NASA Astrophysics Data System (ADS)

Miñano, Juan C.; Benitez, Pablo; Grabovičkić, Dejan; Zamora, Pablo; Buljan, Marina; Narasimhan, Bharathwaj

2017-06-01

We introduce a time multiplexing strategy to increase the total pixel count of the virtual image seen in a VR headset. This translates into an improvement of the pixel density or the Field of View FOV (or both) A given virtual image is displayed by generating a succession of partial real images, each representing part of the virtual image and together representing the virtual image. Each partial real image uses the full set of physical pixels available in the display. The partial real images are successively formed and combine spatially and temporally to form a virtual image viewable from the eye position. Partial real images are imaged through different optical channels depending of its time slot. Shutters or other schemes are used to avoid that a partial real image be imaged through the wrong optical channels or at the wrong time slot. This time multiplexing strategy needs real images be shown at high frame rates (>120fps). Available display and shutters technologies are discussed. Several optical designs for achieving this time multiplexing scheme in a compact format are shown. This time multiplexing scheme allows increasing the resolution/FOV of the virtual image not only by increasing the physical pixel density but also by decreasing the pixels switching time, a feature that may be simpler to achieve in certain circumstances.

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

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

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

Highly Scalable Asynchronous Computing Method for Partial Differential Equations: A Path Towards Exascale

NASA Astrophysics Data System (ADS)

Konduri, Aditya

Many natural and engineering systems are governed by nonlinear partial differential equations (PDEs) which result in a multiscale phenomena, e.g. turbulent flows. Numerical simulations of these problems are computationally very expensive and demand for extreme levels of parallelism. At realistic conditions, simulations are being carried out on massively parallel computers with hundreds of thousands of processing elements (PEs). It has been observed that communication between PEs as well as their synchronization at these extreme scales take up a significant portion of the total simulation time and result in poor scalability of codes. This issue is likely to pose a bottleneck in scalability of codes on future Exascale systems. In this work, we propose an asynchronous computing algorithm based on widely used finite difference methods to solve PDEs in which synchronization between PEs due to communication is relaxed at a mathematical level. We show that while stability is conserved when schemes are used asynchronously, accuracy is greatly degraded. Since message arrivals at PEs are random processes, so is the behavior of the error. We propose a new statistical framework in which we show that average errors drop always to first-order regardless of the original scheme. We propose new asynchrony-tolerant schemes that maintain accuracy when synchronization is relaxed. The quality of the solution is shown to depend, not only on the physical phenomena and numerical schemes, but also on the characteristics of the computing machine. A novel algorithm using remote memory access communications has been developed to demonstrate excellent scalability of the method for large-scale computing. Finally, we present a path to extend this method in solving complex multi-scale problems on Exascale machines.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

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

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

Solidification of a binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.

1982-01-01

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

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

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

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

Sloshing dynamics on rotating helium dewar tank

NASA Technical Reports Server (NTRS)

Hung, R. J.

1993-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

Numerical studies of the surface tension effect of cryogenic liquid helium

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.

An extinction/reignition dynamic method for turbulent combustion

NASA Astrophysics Data System (ADS)

Knaus, Robert; Pantano, Carlos

2011-11-01

Quasi-randomly distributed locations of high strain in turbulent combustion can cause a nonpremixed or partially premixed flame to develop local regions of extinction called ``flame holes''. The presence and extent of these holes can increase certain pollutants and reduce the amount of fuel burned. Accurately modeling the dynamics of these interacting regions can improve the accuracy of combustion simulations by effectively incorporating finite-rate chemistry effects. In the proposed method, the flame hole state is characterized by a progress variable that nominally exists on the stoichiometric surface. The evolution of this field is governed by a partial-differential equation embedded in the time-dependent two-manifold of the flame surface. This equation includes advection, propagation, and flame hole formation (flame hole healing or collapse is accounted by propagation naturally). We present a computational algorithm that solves this equation by embedding it in the usual three-dimensional space. A piece-wise parabolic WENO scheme combined with a compression algorithm are used to evolve the flame hole progress variable. A key aspect of the method is the extension of the surface data to the three-dimensional space in an efficient manner. We present results of this method applied to canonical turbulent combusting flows where the flame holes interact and describe their statistics.

Water-Rock Differentiation on Ceres as Derived From Numerical Studies: Late Water Separation and Thick Undifferentiated Crust

NASA Astrophysics Data System (ADS)

Neumann, Wladimir Otto; Breuer, Doris; Spohn, Tilman

2016-10-01

Water-rock separation is a major factor in discriminating between models of Ceres' present-day state. We calculate differentiation models of Ceres to investigate how water-rock separation and convection influence its evolution. We expand on the presence of liquids and the possibility of cryovolcanism in order to explain surface features observed by Dawn[1,2].The model[3] includes accretion, reduction of the dust porosity, latent heat of ice melting, compaction driven water-rock separation, accretional heating, hydrothermal circulation, solid-state convection of ice, and convection in a water ocean.Accretion times considered cover 1-10 Ma rel. to CAIs. Compaction of the dust pores starts with ice at T≈180-240 K and proceeds with rock minerals at temperatures of up to 730 K. Sub-surface remains too cold to close these pores. The water-rock separation proceeds by water percolation in a rock matrix. Differentiation timing depends on the matrix deformation and no differentiation occurs in layers with leftover dust porosity. Compaction takes several hundred million years due to a slow temperature increase. The differentiation is extended according to this time scale even though liquid water is produced early. While the radionuclides are concentrated in the core no heat is produced in the ocean. If convection is neglected, the ocean is heated by the core and cooled through the crust, and remains totally liquid until the present day. Convection keeps the ocean cold and results in a colder present-day crust. Only a thin basal part of the ocean remains liquid, while the upper part freezes.In our models, a water ocean starts forming within 10 Ma after CAIs, but its completion is retarded relative to the melting of ice by up to O(0.1 Ga). The differentiation is partial and a porous outer layer is retained. Present-day temperatures calculated indicate that hydrated salts can be mobile at a depth of ≥1.5-5 km implying buoyancy of ice and salt-enriched crustal reservoirs. The impacts Haulani, Ikapati and Occator may have cut into these reservoirs triggering the mobility that formed cryovolcanic features[1,2].[1] Jaumann R et al. (2016) LPSC XLVII [2] Krohn K et al. (2016) LPSC XLVII. [3] Neumann W et al. (2015) A&A 584: A117.

Protein tyrosine phosphatase of liver regeneration-1 is required for normal timing of cell cycle progression during liver regeneration

PubMed Central

Jiao, Yang; Ye, Diana Z.; Li, Zhaoyu; Teta-Bissett, Monica; Peng, Yong; Taub, Rebecca; Greenbaum, Linda E.

2014-01-01

Protein tyrosine phosphatase of liver regeneration-1 (Prl-1) is an immediate-early gene that is significantly induced during liver regeneration. Several in vitro studies have suggested that Prl-1 is important for the regulation of cell cycle progression. To evaluate its function in liver regeneration, we ablated the Prl-1 gene specifically in mouse hepatocytes using the Cre-loxP system. Prl-1 mutant mice (Prl-1loxP/loxP;AlfpCre) appeared normal and fertile. Liver size and metabolic function in Prl-1 mutants were comparable to controls, indicating that Prl-1 is dispensable for liver development, postnatal growth, and hepatocyte differentiation. Mutant mice demonstrated a delay in DNA synthesis after 70% partial hepatectomy, although ultimate liver mass restoration was not affected. At 40 h posthepatectomy, reduced protein levels of the cell cycle regulators cyclin E, cyclin A2, cyclin B1, and cyclin-dependent kinase 1 were observed in Prl-1 mutant liver. Investigation of the major signaling pathways involved in liver regeneration demonstrated that phosphorylation of protein kinase B (AKT) and signal transducer and activator of transcription (STAT) 3 were significantly reduced at 40 h posthepatectomy in Prl-1 mutants. Taken together, this study provides evidence that Prl-1 is required for proper timing of liver regeneration after partial hepatectomy. Prl-1 promotes G1/S progression via modulating expression of several cell cycle regulators through activation of the AKT and STAT3 signaling pathway. PMID:25377314

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.

Direct imaging of small scatterers using reduced time dependent data

NASA Astrophysics Data System (ADS)

Cakoni, Fioralba; Rezac, Jacob D.

2017-06-01

We introduce qualitative methods for locating small objects using time dependent acoustic near field waves. These methods have reduced data collection requirements compared to typical qualitative imaging techniques. In particular, we only collect scattered field data in a small region surrounding the location from which an incident field was transmitted. The new methods are partially theoretically justified and numerical simulations demonstrate their efficacy. We show that these reduced data techniques give comparable results to methods which require full multistatic data and that these time dependent methods require less scattered field data than their time harmonic analogs.

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

Zhang, Long; Shi, Songting; Zhang, Juan

Highlights: Black-Right-Pointing-Pointer Expression of Id3 but not Id1 is induced by Wnt3a stimulation in C2C12 cells. Black-Right-Pointing-Pointer Wnt3a induces Id3 expression via canonical Wnt/{beta}-catenin pathway. Black-Right-Pointing-Pointer Wnt3a-induced Id3 expression does not depend on BMP signaling activation. Black-Right-Pointing-Pointer Induction of Id3 expression is critical determinant in Wnt3a-induced cell proliferation and differentiation. -- Abstract: Canonical Wnt signaling plays important roles in regulating cell proliferation and differentiation. In this study, we report that inhibitor of differentiation (Id)3 is a Wnt-inducible gene in mouse C2C12 myoblasts. Wnt3a induced Id3 expression in a {beta}-catenin-dependent manner. Bone morphogenetic protein (BMP) also potently induced Id3 expression. However,more » Wnt-induced Id3 expression occurred independent of the BMP/Smad pathway. Functional studies showed that Id3 depletion in C2C12 cells impaired Wnt3a-induced cell proliferation and alkaline phosphatase activity, an early marker of osteoblast cells. Id3 depletion elevated myogenin induction during myogenic differentiation and partially impaired Wnt3a suppressed myogenin expression in C2C12 cells. These results suggest that Id3 is an important Wnt/{beta}-catenin induced gene in myoblast cell fate determination.« less

Characteristic time scales for diffusion processes through layers and across interfaces

NASA Astrophysics Data System (ADS)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces.

PubMed

Carr, Elliot J

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

A complete and partial integrability technique of the Lorenz system

NASA Astrophysics Data System (ADS)

Bougoffa, Lazhar; Al-Awfi, Saud; Bougouffa, Smail

2018-06-01

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage to the Lorenz system. Furthermore, we show that the reduction to the third order non linear equation can be performed. Therefore, the obtained differential equation can be analytically solved in some special cases and transformed to Abel, Dufing, Painlevé and generalized Emden-Fowler equations. So, a motivating technique that permitted a complete and partial integrability of the Lorenz system is presented.

Modelling atmospheric flows with adaptive moving meshes

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas

2012-04-01

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) - employed in the integration of the underlying anelastic PDEs - that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.

Dynamics of BMP signaling in limb bud mesenchyme and polydactyly.

PubMed

Norrie, Jacqueline L; Lewandowski, Jordan P; Bouldin, Cortney M; Amarnath, Smita; Li, Qiang; Vokes, Martha S; Ehrlich, Lauren I R; Harfe, Brian D; Vokes, Steven A

2014-09-15

Mutations in the Bone Morphogenetic Protein (BMP) pathway are associated with a range of defects in skeletal formation. Genetic analysis of BMP signaling requirements is complicated by the presence of three partially redundant BMPs that are required for multiple stages of limb development. We generated an inducible allele of a BMP inhibitor, Gremlin, which reduces BMP signaling. We show that BMPs act in a dose and time dependent manner in which early reduction of BMPs result in digit loss, while inhibiting overall BMP signaling between E10.5 and E11.5 allows polydactylous digit formation. During this period, inhibiting BMPs extends the duration of FGF signaling. Sox9 is initially expressed in normal digit ray domains but at reduced levels that correlate with the reduction in BMP signaling. The persistence of elevated FGF signaling likely promotes cell proliferation and survival, inhibiting the activation of Sox9 and secondarily, inhibiting the differentiation of Sox9-expressing chondrocytes. Our results provide new insights into the timing and clarify the mechanisms underlying BMP signaling during digit morphogenesis. Copyright © 2014 Elsevier Inc. All rights reserved.

Modal Structures in flow past a cylinder

NASA Astrophysics Data System (ADS)

Murshed, Mohammad

2017-11-01

With the advent of data, there have been opportunities to apply formalism to detect patterns or simple relations. For instance, a phenomenon can be defined through a partial differential equation which may not be very useful right away, whereas a formula for the evolution of a primary variable may be interpreted quite easily. Having access to data is not enough to move on since doing advanced linear algebra can put strain on the way computations are being done. A canonical problem in the field of aerodynamics is the transient flow past a cylinder where the viscosity can be adjusted to set the Reynolds number (Re). We observe the effect of the critical Re on the certain modes of behavior in time scale. A 2D-velocity field works as an input to analyze the modal structure of the flow using the Proper Orthogonal Decomposition and Koopman Mode/Dynamic Mode Decomposition. This will enable prediction of the solution further in time (taking into account the dependence on Re) and help us evaluate and discuss the associated error in the mechanism.

Measurements of angular flux on surface of Li/sub 2/O slab assemblies and their analysis by a direct integration transport code ''BERMUDA''

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

Maekawa, H.; Oyama, Y.

1983-09-01

Angle-dependent neutron leakage spectra above 0.5 MeV from Li/sub 2/O slab assemblies were measured accurately by the time-of-flight method. The measured angles were 0/sup 0/, 12.2/sup 0/, 24.9/sup 0/, 41.8/sup 0/ and 66.8/sup 0/. The sizes of Li/sub 2/O assemblies were 31.4 cm in equivalent radius and 5.06, 20.24 and 40.48 cm in thickness. The data were analyzed by a new transport code ''BERMUDA-2DN''. Time-independent transport equation is solved for two-dimensional, cylindrical, multi-regional geometry using the direct integration method in a multi-group model. The group transfer kernels are accurately obtained from the double-differential cross section data without using Legendre expansion.more » The results were compared absolutely. While there exist discrepancies partially, the calculational spectra agree well with the experimental ones as a whole. The BERMUDA code was demonstrated to be useful for the analyses of the fusion neutronics and shielding.« less

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.

Copeptin in the diagnosis of vasopressin-dependent disorders of fluid homeostasis.

PubMed

Christ-Crain, Mirjam; Fenske, Wiebke

2016-03-01

Copeptin and arginine vasopressin (AVP) are derived from a common precursor molecule and have equimolar secretion and response to osmotic, haemodynamic and stress-related stimuli. Plasma concentrations of copeptin and AVP in relation to serum osmolality are highly correlated. The physiological functions of AVP with respect to homeostasis of fluid balance, vascular tonus and regulation of the endocrine stress response are well known, but the exact function of copeptin is undetermined. Quantification of AVP can be difficult, but copeptin is stable in plasma and can be easily measured with a sandwich immunoassay. For this reason, copeptin has emerged as a promising marker for the diagnosis of AVP-dependent fluid disorders. Copeptin measurements can enable differentiation between various conditions within the polyuria-polydipsia syndrome. In the absence of prior fluid deprivation, baseline copeptin levels >20 pmol/l identify patients with nephrogenic diabetes insipidus. Conversely, copeptin levels measured upon osmotic stimulation differentiate primary polydipsia from partial central diabetes insipidus. In patients with hyponatraemia, low levels of copeptin together with low urine osmolality identify patients with primary polydipsia, and the ratio of copeptin to urinary sodium can distinguish the syndrome of inappropriate antidiuretic hormone secretion from other AVP-dependent forms of hyponatraemia.

Coalescence with Background and Balancing Selection in Systems with Bi- and Uniparental Reproduction: Contrasting Partial Asexuality and Selfing

PubMed Central

Agrawal, Aneil F.; Hartfield, Matthew

2016-01-01

Uniparental reproduction in diploids, via asexual reproduction or selfing, reduces the independence with which separate loci are transmitted across generations. This is expected to increase the extent to which a neutral marker is affected by selection elsewhere in the genome. Such effects have previously been quantified in coalescent models involving selfing. Here we examine the effects of background selection and balancing selection in diploids capable of both sexual and asexual reproduction (i.e., partial asexuality). We find that the effect of background selection on reducing coalescent time (and effective population size) can be orders of magnitude greater when rates of sex are low than when sex is common. This is because asexuality enhances the effects of background selection through both a recombination effect and a segregation effect. We show that there are several reasons that the strength of background selection differs between systems with partial asexuality and those with comparable levels of uniparental reproduction via selfing. Expectations for reductions in Ne via background selection have been verified using stochastic simulations. In contrast to background selection, balancing selection increases the coalescence time for a linked neutral site. With partial asexuality, the effect of balancing selection is somewhat dependent upon the mode of selection (e.g., heterozygote advantage vs. negative frequency-dependent selection) in a manner that does not apply to selfing. This is because the frequency of heterozygotes, which are required for recombination onto alternative genetic backgrounds, is more dependent on the pattern of selection with partial asexuality than with selfing. PMID:26584901

Coalescence with Background and Balancing Selection in Systems with Bi- and Uniparental Reproduction: Contrasting Partial Asexuality and Selfing.

PubMed

Agrawal, Aneil F; Hartfield, Matthew

2016-01-01

Uniparental reproduction in diploids, via asexual reproduction or selfing, reduces the independence with which separate loci are transmitted across generations. This is expected to increase the extent to which a neutral marker is affected by selection elsewhere in the genome. Such effects have previously been quantified in coalescent models involving selfing. Here we examine the effects of background selection and balancing selection in diploids capable of both sexual and asexual reproduction (i.e., partial asexuality). We find that the effect of background selection on reducing coalescent time (and effective population size) can be orders of magnitude greater when rates of sex are low than when sex is common. This is because asexuality enhances the effects of background selection through both a recombination effect and a segregation effect. We show that there are several reasons that the strength of background selection differs between systems with partial asexuality and those with comparable levels of uniparental reproduction via selfing. Expectations for reductions in Ne via background selection have been verified using stochastic simulations. In contrast to background selection, balancing selection increases the coalescence time for a linked neutral site. With partial asexuality, the effect of balancing selection is somewhat dependent upon the mode of selection (e.g., heterozygote advantage vs. negative frequency-dependent selection) in a manner that does not apply to selfing. This is because the frequency of heterozygotes, which are required for recombination onto alternative genetic backgrounds, is more dependent on the pattern of selection with partial asexuality than with selfing. Copyright © 2016 by the Genetics Society of America.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

PubMed

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

The numerical modelling of mixing phenomena of nanofluids in passive micromixers

NASA Astrophysics Data System (ADS)

Milotin, R.; Lelea, D.

2018-01-01

The paper deals with the rapid mixing phenomena in micro-mixing devices with four tangential injections and converging tube, considering nanoparticles and water as the base fluid. Several parameters like Reynolds number (Re = 6 - 284) or fluid temperature are considered in order to optimize the process and obtain fundamental insight in mixing phenomena. The set of partial differential equations is considered based on conservation of momentum and species. Commercial package software Ansys-Fluent is used for solution of differential equations, based on a finite volume method. The results reveal that mixing index and mixing process is strongly dependent both on Reynolds number and heat flux. Moreover there is a certain Reynolds number when flow instabilities are generated that intensify the mixing process due to the tangential injections of the fluids.

Study of Falling Roof Vibrations in a Production Face at Roof Support Resistance in the Form of Concentrated Force

NASA Astrophysics Data System (ADS)

Buyalich, G. D.; Buyalich, K. G.; Umrikhina, V. Yu

2016-08-01

One of the main reasons of roof support failures in production faces is mismatch of their parameters and parameters of dynamic impact on the metal structure from the falling roof during its secondary convergences. To assess the parameters of vibrational interaction of roof support with the roof, it was suggested to use computational models of forces application and a partial differential equation of fourth order describing this process, its numerical solution allowed to assess frequency, amplitude and speed of roof strata movement depending on physical and mechanical properties of the roof strata as well as on load bearing and geometry parameters of the roof support. To simplify solving of the differential equation, roof support response was taken as the concentrated force.

Trajectory-based modeling of fluid transport in a medium with smoothly varying heterogeneity

DOE PAGES

Vasco, D. W.; Pride, Steven R.; Commer, Michael

2016-03-04

Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In anmore » application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. In conclusion, the arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.« less

Differential Aging in Place and Depressive Symptoms: Interplay Among Time, Income, and Senior Housing.

PubMed

Park, Sojung; Kim, BoRin; Han, Yoonsun

2018-03-01

We examined cumulative and differential experiences of aging in place. Data came from the 2002 and 2010 wave of the Health Retirement Study. We modeled the trajectory of later-life depressive symptoms, and how senior-housing environments moderate the negative association between economic disadvantages and depressive symptoms. At baseline, economically disadvantaged older adults were more likely to exhibit depressive symptoms. However, detrimental effects of income group (non-low income vs. moderate income; non-low income vs. low income) on depressive symptoms did not significantly change over time. The age-leveler hypothesis may account for nonsignificant effects of disadvantaged income groups over time. Findings suggest that moderate-income seniors may experience positive differentials if they age in place in a supportive senior-housing environment. Moderate-income seniors may have broader opportunities in senior housing compared to private-home peers. Senior housing might partially counter risks such as low mental health, emerging from life-course disadvantage.

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...

Chronic Ethanol Exposure Produces Time- and Brain Region-Dependent Changes in Gene Coexpression Networks

PubMed Central

Osterndorff-Kahanek, Elizabeth A.; Becker, Howard C.; Lopez, Marcelo F.; Farris, Sean P.; Tiwari, Gayatri R.; Nunez, Yury O.; Harris, R. Adron; Mayfield, R. Dayne

2015-01-01

Repeated ethanol exposure and withdrawal in mice increases voluntary drinking and represents an animal model of physical dependence. We examined time- and brain region-dependent changes in gene coexpression networks in amygdala (AMY), nucleus accumbens (NAC), prefrontal cortex (PFC), and liver after four weekly cycles of chronic intermittent ethanol (CIE) vapor exposure in C57BL/6J mice. Microarrays were used to compare gene expression profiles at 0-, 8-, and 120-hours following the last ethanol exposure. Each brain region exhibited a large number of differentially expressed genes (2,000-3,000) at the 0- and 8-hour time points, but fewer changes were detected at the 120-hour time point (400-600). Within each region, there was little gene overlap across time (~20%). All brain regions were significantly enriched with differentially expressed immune-related genes at the 8-hour time point. Weighted gene correlation network analysis identified modules that were highly enriched with differentially expressed genes at the 0- and 8-hour time points with virtually no enrichment at 120 hours. Modules enriched for both ethanol-responsive and cell-specific genes were identified in each brain region. These results indicate that chronic alcohol exposure causes global ‘rewiring‘ of coexpression systems involving glial and immune signaling as well as neuronal genes. PMID:25803291

Theories of time-dependent and time-independent nearside-farside reactive scattering dynamics

NASA Astrophysics Data System (ADS)

Monks, Phillip David Durrant

The first application of nearside-farside (NF) theory is made to the time-dependent partial wave series (PWS) representation of the scattering amplitude for the reaction H + D[2](v = 0,j = 0, m = 0) → HD(v' = 3,j' = 0, m'= 0) + D. Time-dependent NF angular distributions and time-dependent NF local angular momenta (LAMs) are defined and used to analyse the dynamics in terms of time- direct and time-delayed reaction mechanisms. The concept of a cumulative time-evolving differential cross section (DCS) is introduced and used to provide a new method for visualising the time evolution of a chemical reaction. Time-independent NF DCS and LAM analyses of the H + D[2] reaction are presented, highlighting a distinctive "trench-ridge" feature present in the full and N LAMs. It is used to define a cut line which separates the energy-analogs of the two time- distinct reaction mechanisms. This trench-ridge feature is shown to be an interference between the time-direct (backward-scattered) and time-delayed (forward-scattered) reaction mechanisms. Resummation PWS theory is used to "clean" plots of the NF DCSs and LAMs of unphysical effects. A limitation of the resummation theory is described, whereby unphysical behaviour is sometimes introduced into the N and F subamplitudes. A technique for predicting and avoiding these undesired effects is used to further improve the usefulness of the resummation technique. The fundamental identity for NF local angular momenta is stated and derived by two methods. This identity gives rise to a CLAM plot (where CLAM denotes Cross section x LAM), which provides insight into the empirical obsei'vation that DCS and LAM analyses give consistent, yet complementary, information on the reaction dynamics. Applications are reported for the H + D[2] reaction, as well as for F + H[2](v = 0,j=0, m = 0)→ FH(v' = 3,j' = 3, m' = 0) + H. The angular time-delay for a state-to-state reactive collision often displays complicated behaviour. It is shown for the H + D[2] and F + H[2] reactions that this behaviour is caused by NF interference. The fundamental identity for NF angular time-delays is stated, and CATD (Cross section x Angular Time-Delay) results are reported, which provide further insight into the properties of the angular time-delay.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Endometrial vessel maturation in women exposed to levonorgestrel-releasing intrauterine system for a short or prolonged period of time.

PubMed

Stéphanie, Ravet; Labied, Soraya; Blacher, Silvia; Frankenne, Francis; Munaut, Carine; Fridman, Viviana; Beliard, Aude; Foidart, Jean-Michel; Nisolle, Michelle

2007-12-01

Levonorgestrel-releasing intrauterine system (LNG-IUS), although inserted to reduce heavy menstruation, causes irregular early transient bleeding. The objective of the study was to document quantitative changes in endometrial vessels of short- (< or =3 months) and long-term (> or =12 months) LNG users. The area, density and maturation of endometrial vessels were quantified in 19 endometrial biopsies of women with LNG-IUS and in 10 normally ovulating patients during mid-luteal phase. Vessel maturation was evaluated by double immunostaining using anti-von Willebrand factor (endothelial cell marker) and anti-alpha Smooth Muscle Actin (vascular smooth muscle cells) antibodies. Vessel area, number and density were quantified with a novel computer-assisted image analysis system. Endometrium exposed to LNG-IUS for 1-3 months displayed a 11.5-fold increase in small naked vessel number. The partially mature vessel (alphaSMA partially positive) number increased six times. After long-term LNG-IUS treatment, the immature and partially mature vessel number remained four times higher than in the control group. Vessel area and density also increased dramatically in a time-dependent pattern with LNG-IUS use. Levonorgestrel affects blood vessel number, area, density and maturation in a time-dependent pattern that may explain the early transient increase in breakthrough bleeding with the LNG-IUS.

Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

PubMed Central

Lin, S. H.; Eyring, H.

1971-01-01

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898

Control of amplitude chimeras by time delay in oscillator networks

NASA Astrophysics Data System (ADS)

Gjurchinovski, Aleksandar; Schöll, Eckehard; Zakharova, Anna

2017-04-01

We investigate the influence of time-delayed coupling in a ring network of nonlocally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras, which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and we show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant coupling delay, for time-varying delay, and for distributed-delay coupling, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.

Hippocampus-dependent spatial memory impairment due to molar tooth loss is ameliorated by an enriched environment.

PubMed

Kondo, Hiroko; Kurahashi, Minori; Mori, Daisuke; Iinuma, Mitsuo; Tamura, Yasuo; Mizutani, Kenmei; Shimpo, Kan; Sonoda, Shigeru; Azuma, Kagaku; Kubo, Kin-ya

2016-01-01

Teeth are crucial, not only for mastication, but for overall nutrition and general health, including cognitive function. Aged mice with chronic stress due to tooth loss exhibit impaired hippocampus-dependent learning and memory. Exposure to an enriched environment restores the reduced hippocampal function. Here, we explored the effects of an enriched environment on learning deficits and hippocampal morphologic changes in aged senescence-accelerated mouse strain P8 (SAMP8) mice with tooth loss. Eight-month-old male aged SAMP8 mice with molar intact or with molars removed were housed in either a standard environment or enriched environment for 3 weeks. The Morris water maze was performed for spatial memory test. The newborn cell proliferation, survival, and differentiation in the hippocampus were analyzed using 5-Bromodeoxyuridine (BrdU) immunohistochemical method. The hippocampal brain-derived neurotrophic factor (BDNF) levels were also measured. Mice with upper molars removed (molarless) exhibited a significant decline in the proliferation and survival of newborn cells in the dentate gyrus (DG) as well as in hippocampal BDNF levels. In addition, neuronal differentiation of newly generated cells was suppressed and hippocampus-dependent spatial memory was impaired. Exposure of molarless mice to an enriched environment attenuated the reductions in the hippocampal BDNF levels and neuronal differentiation, and partially improved the proliferation and survival of newborn cells, as well as the spatial memory ability. These findings indicated that an enriched environment could ameliorate the hippocampus-dependent spatial memory impairment induced by molar tooth loss. Copyright © 2015 Elsevier Ltd. All rights reserved.

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

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

NASA Astrophysics Data System (ADS)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

Solitary Waves, Periodic Peakons and Pseudo-Peakons of the Nonlinear Acoustic Wave Model in Rotating Magnetized Plasma

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions.

Periodic Peakons, Pseudo-Peakons and Compactons of Ion-Acoustic Wave Model in Electronegative Plasmas with Electrons Featuring Tsallis Distribution

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear ion-acoustic oscillations is governed by a partial differential equation system. Its traveling system is just a singular traveling wave system of first class depending on four parameters. By using the method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions.

Spatial Characteristics of F/A-18 Vertical Tail Buffet Pressures Measured in Flight

NASA Technical Reports Server (NTRS)

Moses, Robert W.; Shah, Gautam H.

1998-01-01

Buffeting is an aeroelastic phenomenon which plagues high performance aircraft, especially those with twin vertical tails, at high angles of attack. Previous wind-tunnel and flight tests were conducted to characterize the buffet loads on the vertical tails by measuring surface pressures, bending moments, and accelerations. Following these tests, buffeting estimates were computed using the measured buffet pressures and compared to the measured responses. The estimates did not match the measured data because the assumed spatial correlation of the buffet pressures was not correct. A better understanding of the partial (spatial) correlation of the differential buffet pressures on the tail was necessary to improve the buffeting estimates. Several wind-tunnel investigations were conducted for this purpose. When combined and compared, the results of these tests show that the partial correlation depends on and scales with flight conditions. One of the remaining questions is whether the windtunnel data is consistent with flight data. Presented herein, cross-spectra and coherence functions calculated from pressures that were measured on the high alpha research vehicle (HARV) indicate that the partial correlation of the buffet pressures in flight agrees with the partial correlation observed in the wind tunnel.

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

Run-time scheduling and execution of loops on message passing machines

NASA Technical Reports Server (NTRS)

Crowley, Kay; Saltz, Joel; Mirchandaney, Ravi; Berryman, Harry

1989-01-01

Sparse system solvers and general purpose codes for solving partial differential equations are examples of the many types of problems whose irregularity can result in poor performance on distributed memory machines. Often, the data structures used in these problems are very flexible. Crucial details concerning loop dependences are encoded in these structures rather than being explicitly represented in the program. Good methods for parallelizing and partitioning these types of problems require assignment of computations in rather arbitrary ways. Naive implementations of programs on distributed memory machines requiring general loop partitions can be extremely inefficient. Instead, the scheduling mechanism needs to capture the data reference patterns of the loops in order to partition the problem. First, the indices assigned to each processor must be locally numbered. Next, it is necessary to precompute what information is needed by each processor at various points in the computation. The precomputed information is then used to generate an execution template designed to carry out the computation, communication, and partitioning of data, in an optimized manner. The design is presented for a general preprocessor and schedule executer, the structures of which do not vary, even though the details of the computation and of the type of information are problem dependent.

Run-time scheduling and execution of loops on message passing machines

NASA Technical Reports Server (NTRS)

Saltz, Joel; Crowley, Kathleen; Mirchandaney, Ravi; Berryman, Harry

1990-01-01

Sparse system solvers and general purpose codes for solving partial differential equations are examples of the many types of problems whose irregularity can result in poor performance on distributed memory machines. Often, the data structures used in these problems are very flexible. Crucial details concerning loop dependences are encoded in these structures rather than being explicitly represented in the program. Good methods for parallelizing and partitioning these types of problems require assignment of computations in rather arbitrary ways. Naive implementations of programs on distributed memory machines requiring general loop partitions can be extremely inefficient. Instead, the scheduling mechanism needs to capture the data reference patterns of the loops in order to partition the problem. First, the indices assigned to each processor must be locally numbered. Next, it is necessary to precompute what information is needed by each processor at various points in the computation. The precomputed information is then used to generate an execution template designed to carry out the computation, communication, and partitioning of data, in an optimized manner. The design is presented for a general preprocessor and schedule executer, the structures of which do not vary, even though the details of the computation and of the type of information are problem dependent.

14-3-3 proteins regulate desmosomal adhesion via plakophilins.

PubMed

Rietscher, Katrin; Keil, René; Jordan, Annemarie; Hatzfeld, Mechthild

2018-05-22

Desmosomes are essential for strong intercellular adhesion and are abundant in tissues exposed to mechanical strain. At the same time, desmosomes need to be dynamic to allow for remodeling of epithelia during differentiation or wound healing. Phosphorylation of desmosomal plaque proteins appears to be essential for desmosome dynamics. However, the mechanisms of how context-dependent post-translational modifications regulate desmosome formation, dynamics or stability are incompletely understood. Here, we show that growth factor signaling regulates the phosphorylation-dependent association of plakophilins 1 and 3 (PKP1 and PKP3) with 14-3-3 protein isoforms, and uncover unique and partially antagonistic functions of members of the 14-3-3 family in the regulation of desmosomes. 14-3-3γ associated primarily with cytoplasmic PKP1 phosphorylated at S155 and destabilized intercellular cohesion of keratinocytes by reducing its incorporation into desmosomes. In contrast, 14-3-3σ (also known as stratifin, encoded by SFN ) interacted preferentially with S285-phosphorylated PKP3 to promote its accumulation at tricellular contact sites, leading to stable desmosomes. Taken together, our study identifies a new layer of regulation of intercellular adhesion by 14-3-3 proteins. © 2018. Published by The Company of Biologists Ltd.

16S rRNA partial gene sequencing for the differentiation and molecular subtyping of Listeria species.

PubMed

Hellberg, Rosalee S; Martin, Keely G; Keys, Ashley L; Haney, Christopher J; Shen, Yuelian; Smiley, R Derike

2013-12-01

Use of 16S rRNA partial gene sequencing within the regulatory workflow could greatly reduce the time and labor needed for confirmation and subtyping of Listeria monocytogenes. The goal of this study was to build a 16S rRNA partial gene reference library for Listeria spp. and investigate the potential for 16S rRNA molecular subtyping. A total of 86 isolates of Listeria representing L. innocua, L. seeligeri, L. welshimeri, and L. monocytogenes were obtained for use in building the custom library. Seven non-Listeria species and three additional strains of Listeria were obtained for use in exclusivity and food spiking tests. Isolates were sequenced for the partial 16S rRNA gene using the MicroSeq ID 500 Bacterial Identification Kit (Applied Biosystems). High-quality sequences were obtained for 84 of the custom library isolates and 23 unique 16S sequence types were discovered for use in molecular subtyping. All of the exclusivity strains were negative for Listeria and the three Listeria strains used in food spiking were consistently recovered and correctly identified at the species level. The spiking results also allowed for differentiation beyond the species level, as 87% of replicates for one strain and 100% of replicates for the other two strains consistently matched the same 16S type. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

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.

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Partial dust obscuration in active galactic nuclei as a cause of broad-line profile and lag variability, and apparent accretion disc inhomogeneities

NASA Astrophysics Data System (ADS)

Gaskell, C. Martin; Harrington, Peter Z.

2018-04-01

The profiles of the broad emission lines of active galactic nuclei (AGNs) and the time delays in their response to changes in the ionizing continuum ("lags") give information about the structure and kinematics of the inner regions of AGNs. Line profiles are also our main way of estimating the masses of the supermassive black holes (SMBHs). However, the profiles often show ill-understood, asymmetric structure and velocity-dependent lags vary with time. Here we show that partial obscuration of the broad-line region (BLR) by outflowing, compact, dusty clumps produces asymmetries and velocity-dependent lags similar to those observed. Our model explains previously inexplicable changes in the ratios of the hydrogen lines with time and velocity, the lack of correlation of changes in line profiles with variability of the central engine, the velocity dependence of lags, and the change of lags with time. We propose that changes on timescales longer than the light-crossing time do not come from dynamical changes in the BLR, but are a natural result of the effect of outflowing dusty clumps driven by radiation pressure acting on the dust. The motion of these clumps offers an explanation of long-term changes in polarization. The effects of the dust complicate the study of the structure and kinematics of the BLR and the search for sub-parsec SMBH binaries. Partial obscuration of the accretion disc can also provide the local fluctuations in luminosity that can explain sizes deduced from microlensing.

Hamstring strain - aftercare

MedlinePlus

Pulled hamstring muscle; Sprain - hamstring ... There are 3 levels of hamstring strains: Grade 1 -- mild muscle strain or pull Grade 2 -- partial muscle tear Grade 3 -- complete muscle tear Recovery time depends ...

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Self similar solution of superradiant amplification of ultrashort laser pulses in plasma

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

Moghadasin, H.; Niknam, A. R., E-mail: a-niknam@sbu.ac.ir; Shokri, B.

2015-05-15

Based on the self-similar method, superradiant amplification of ultrashort laser pulses by the counterpropagating pump in a plasma is investigated. Here, we present a governing system of partial differential equations for the signal pulse and the motion of the electrons. These equations are transformed to ordinary differential equations by the self-similar method and numerically solved. It is found that the increase of the signal intensity is proportional to the square of the propagation distance and the signal frequency has a red shift. Also, depending on the pulse width, the signal breaks up into a train of short pulses or itsmore » duration decreases with the inverse square root of the distance. Moreover, we identified two distinct categories of the electrons by the phase space analysis. In the beginning, one of them is trapped in the ponderomotive potential well and oscillates while the other is untrapped. Over time, electrons of the second kind also join to the trapped electrons. In the potential well, the electrons are bunched to form an electron density grating which reflects the pump pulse into the signal pulse. It is shown that the backscattered intensity is enhanced with the increase of the electron bunching parameter which leads to the enhanced efficiency of superradiant amplification.« less

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…

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

PubMed

Tyagi, Aruna; Chandra, Arti

2006-08-01

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

The role of Coulomb collisions in limiting differential flow and temperature differences in the solar wind

NASA Technical Reports Server (NTRS)

Neugebauer, M.

1976-01-01

Data obtained by OGO 5 are used to confirm IMP 6 observations of an inverse dependence of the helium-to-hydrogen temperature ratio in the solar wind on the ratio of solar-wind expansion time to the Coulomb-collision equipartition time. The analysis is then extended to determine the relation of the difference between the hydrogen and helium bulk velocities (the differential flow vector) with the ratio between the solar-wind expansion time and the time required for Coulomb collisions to slow down a beam of ions passing through a plasma. It is found that the magnitude of the differential flow vector varies inversely with the time ratio when the latter is small and approaches zero when it is large. These results are shown to suggest a model of continuous preferential heating and acceleration of helium (or cooling and deceleration of hydrogen), which is cancelled or limited by Coulomb collisions by the time the plasma has reached 1 AU. Since the average dependence of the differential flow vector on the time ratio cannot explain all the systematic variations of the vector observed in corotating high-velocity streams, it is concluded that additional helium acceleration probably occurs on the leading edge of such streams.

Low dose reconstruction algorithm for differential phase contrast imaging.

PubMed

Wang, Zhentian; Huang, Zhifeng; Zhang, Li; Chen, Zhiqiang; Kang, Kejun; Yin, Hongxia; Wang, Zhenchang; Marco, Stampanoni

2011-01-01

Differential phase contrast imaging computed tomography (DPCI-CT) is a novel x-ray inspection method to reconstruct the distribution of refraction index rather than the attenuation coefficient in weakly absorbing samples. In this paper, we propose an iterative reconstruction algorithm for DPCI-CT which benefits from the new compressed sensing theory. We first realize a differential algebraic reconstruction technique (DART) by discretizing the projection process of the differential phase contrast imaging into a linear partial derivative matrix. In this way the compressed sensing reconstruction problem of DPCI reconstruction can be transformed to a resolved problem in the transmission imaging CT. Our algorithm has the potential to reconstruct the refraction index distribution of the sample from highly undersampled projection data. Thus it can significantly reduce the dose and inspection time. The proposed algorithm has been validated by numerical simulations and actual experiments.

Samples from Differentiated Asteroids; Regolithic Achondrites

NASA Technical Reports Server (NTRS)

Herrin J. S.; Ross, A. J.; Cartwright, J. A.; Ross, D. K.; Zolensky, Michael E.; Jenniskens, P.

2011-01-01

Differentiated and partially differentiated asteroids preserve a glimpse of planet formation frozen in time from the early solar system and thus are attractive targets for future exploration. Samples of such asteroids arrive to Earth in the form of achondrite meteorites. Many achondrites, particularly those thought to be most representative of asteroidal regolith, contain a diverse assortment of materials both indigenous and exogenous to the original igneous parent body intermixed at microscopic scales. Remote sensing spacecraft and landers would have difficulty deciphering individual components at these spatial scales, potentially leading to confusing results. Sample return would thus be much more informative than a robotic probe. In this and a companion abstract [1] we consider two regolithic achondrite types, howardites and (polymict) ureilites, in order to evaluate what materials might occur in samples returned from surfaces of differentiated asteroids and what sampling strategies might be prudent.

Acoustic imaging of a duct spinning mode by the use of an in-duct circular microphone array.

PubMed

Wei, Qingkai; Huang, Xun; Peers, Edward

2013-06-01

An imaging method of acoustic spinning modes propagating within a circular duct simply with surface pressure information is introduced in this paper. The proposed method is developed in a theoretical way and is demonstrated by a numerical simulation case. Nowadays, the measurements within a duct have to be conducted using in-duct microphone array, which is unable to provide information of complete acoustic solutions across the test section. The proposed method can estimate immeasurable information by forming a so-called observer. The fundamental idea behind the testing method was originally developed in control theory for ordinary differential equations. Spinning mode propagation, however, is formulated in partial differential equations. A finite difference technique is used to reduce the associated partial differential equations to a classical form in control. The observer method can thereafter be applied straightforwardly. The algorithm is recursive and, thus, could be operated in real-time. A numerical simulation for a straight circular duct is conducted. The acoustic solutions on the test section can be reconstructed with good agreement to analytical solutions. The results suggest the potential and applications of the proposed method.

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.

Native low-density lipoprotein uptake by macrophage colony-stimulating factor-differentiated human macrophages is mediated by macropinocytosis and micropinocytosis.

PubMed

Anzinger, Joshua J; Chang, Janet; Xu, Qing; Buono, Chiara; Li, Yifu; Leyva, Francisco J; Park, Bum-Chan; Greene, Lois E; Kruth, Howard S

2010-10-01

To examine the pinocytotic pathways mediating native low-density lipoprotein (LDL) uptake by human macrophage colony-stimulating factor-differentiated macrophages (the predominant macrophage phenotype in human atherosclerotic plaques). We identified the kinase inhibitor SU6656 and the Rho GTPase inhibitor toxin B as inhibitors of macrophage fluid-phase pinocytosis of LDL. Assessment of macropinocytosis by time-lapse microscopy revealed that both drugs almost completely inhibited macropinocytosis, although LDL uptake and cholesterol accumulation by macrophages were only partially inhibited (approximately 40%) by these agents. Therefore, we investigated the role of micropinocytosis in mediating LDL uptake in macrophages and identified bafilomycin A1 as an additional partial inhibitor (approximately 40%) of macrophage LDL uptake that targeted micropinocytosis. When macrophages were incubated with both bafilomycin A1 and SU6656, inhibition of LDL uptake was additive (reaching 80%), showing that these inhibitors target different pathways. Microscopic analysis of fluid-phase uptake pathways in these macrophages confirmed that LDL uptake occurs through both macropinocytosis and micropinocytosis. Our findings show that human macrophage colony-stimulating factor-differentiated macrophages take up native LDL by macropinocytosis and micropinocytosis, underscoring the importance of both pathways in mediating LDL uptake by these cells.

Osteogenesis of human adipose-derived stem cells on hydroxyapatite-mineralized poly(lactic acid) nanofiber sheets.

PubMed

Kung, Fu-Chen; Lin, Chi-Chang; Lai, Wen-Fu T

2014-12-01

Electrospun fiber sheets with various orientations (random, partially aligned, and aligned) and smooth and roughened casted membranes were prepared. Hydroxyapatite (HA) crystals were in situ formed on these material surfaces via immersion in 10× simulated body fluid solution. The size and morphology of the resulting fibers were examined using scanning electron microscopy. The average diameter of the fibers ranged from 225±25 to 1050±150 nm depending on the electrospinning parameters. Biological experiment results show that human adipose-derived stem cells exhibit different adhesion and osteogenic differentiation on the three types of fiber. The cell proliferation and osteogenic differentiation were best on the aligned fibers. Similar results were found for phosphorylated focal adhesion kinase expression. Electrospun poly(lactic acid) aligned fibers mineralized with HA crystals provide a good environment for cell growth and osteogenic differentiation and thus have great potential in the tissue engineering field. Copyright © 2014 Elsevier B.V. All rights reserved.

Runge-Kutta Methods for Linear Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Nuclear spin dependence of time reversal invariance violating effects in neutron scattering

NASA Astrophysics Data System (ADS)

Gudkov, Vladimir; Shimizu, Hirohiko M.

2018-06-01

The spin structure of parity violating and time reversal invariance violating effects in neutron scattering is discussed. The explicit relations between these effects are presented in terms of functions nuclear spins and neutron partial widths of p -wave resonances.

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

SAGUARO: a finite-element computer program for partially saturated porous flow problems

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

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Does the type of CIA policy significantly affect bar and restaurant employment in Minnesota cities?

PubMed Central

Klein, Elizabeth G.; Forster, Jean L.; Erickson, Darin J.; Lytle, Leslie A.; Schillo, Barbara

2009-01-01

Background Clean indoor air (CIA) policies that include free-standing bars and restaurants have been adopted by communities to protect employees in all workplaces from exposure to environmental tobacco smoke, most notably employees working in restaurants and free-standing bars. However, due to the perception of negative economic effects on alcohol-licensed hospitality businesses, partial CIA policies (those that provide an exemption for free-standing bars) have been proposed as a means to reduce the risk of economic effects of comprehensive CIA policies applied to all worksites. Objective To determine if partial CIA produce differential economic effects compared to comprehensive CIA policies using bar and restaurant employment per capita. Design, setting, and subjects Ten cities in the state of Minnesota were studied from 2003 to 2006. Economic data were drawn from monthly employment in bars and restaurants, and a pooled time-series was completed to evaluate three types of local CIA policies: Comprehensive, partial, or none beyond the state law. Results Communities with a comprehensive CIA policy had a decrease of 9 employees per 10,000 residents compared with communities with a partial CIA policies (p=0.10). Communities with any type of CIA policy (partial or comprehensive) had an increase of 3 employees per 10,000 residents compared to communities without any CIA policies (p=0.36). Conclusion There were no significant differential economic effects by CIA policy type in Minnesota cities. These findings support the adoption of comprehensive CIA policies to provide all employees protection from environmental tobacco smoke exposure. PMID:19184432

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

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

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

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

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

2016-08-15

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

Dynamic system classifier.

PubMed

Pumpe, Daniel; Greiner, Maksim; Müller, Ewald; Enßlin, Torsten A

2016-07-01

Stochastic differential equations describe well many physical, biological, and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time-dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of the DSC to oscillation processes with a time-dependent frequency ω(t) and damping factor γ(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The ω and γ time lines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.

Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

PubMed

Bai, Shirong; Skodje, Rex T

2017-08-17

A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

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.

Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

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.

Numerical simulation of the interaction between a flowfield and chemical reaction on premixed pulsed jet combustion

NASA Astrophysics Data System (ADS)

Hishida, Manabu; Hayashi, A. Koichi

1992-12-01

Pulsed Jet Combustion (PJC) is numerically simulated using time-dependent, axisymmetric, full Navier-Stokes equations with the mass, momentum, energy, and species conservation equations for a hydrogen-air mixture. A hydrogen-air reaction mechanism is modeled by nine species and nineteen elementary forward and backward reactions to evaluate the effect of the chemical reactions accurately. A point implicit method with the Harten and Yee's non-MUSCL (Monotone Upstream-centerd Schemes for Conservation Laws) modified-flux type TVD (Total Variation Diminishing) scheme is applied to deal with the stiff partial differential equations. Furthermore, a zonal method making use of the Fortified Solution Algorithm (FSA) is applied to simulate the phenomena in the complicated shape of the sub-chamber. The numerical result shows that flames propagating in the sub-chamber interact with pressure waves and are deformed to be wrinkled like a 'tulip' flame and a jet passed through the orifice changes its mass flux quasi-periodically.