Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Use of Continuous Exponential Families to Link Forms via Anchor Tests. Research Report. ETS RR-11-11

ERIC Educational Resources Information Center

Haberman, Shelby J.; Yan, Duanli

2011-01-01

Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…

A quantitative description of normal AV nodal conduction curve in man.

PubMed

Teague, S; Collins, S; Wu, D; Denes, P; Rosen, K; Arzbaecher, R

1976-01-01

The AV nodal conduction curve generated by the atrial extrastimulus technique has been described only qualitatively in man, making clinical comparison of known normal curves with those of suspected AV nodal dysfunction difficult. Also, the effects of physiological and pharmacological interventions have not been quantifiable. In 50 patients with normal AV conduction as defined by normal AH (less than 130 ms), normal AV nodal effective and functional refractory periods (less than 380 and less than 500 ms), and absence of demonstrable dual AV nodal pathways, we found that conduction curves (at sinus rhythm or longest paced cycle length) can be described by an exponential equation of the form delta = Ae-Bx. In this equation, delta is the increase in AV nodal conduction time of an extrastimulus compared to that of a regular beat and x is extrastimulus interval. The natural logarithm of this equation is linear in the semilogarithmic plane, thus permitting the constants A and B to be easily determined by a least-squares regression analysis with a hand calculator.

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Determination of relationship between sensory viscosity rating and instrumental flow behaviour of soluble dietary fibers.

PubMed

Arora, Simran Kaur; Patel, A A; Kumar, Naveen; Chauhan, O P

2016-04-01

The shear-thinning low, medium and high-viscosity fiber preparations (0.15-1.05 % psyllium husk, 0.07-0.6 % guar gum, 0.15-1.20 % gum tragacanth, 0.1-0.8 % gum karaya, 0.15-1.05 % high-viscosity Carboxy Methyl Cellulose and 0.1-0.7 % xanthan gum) showed that the consistency coefficient (k) was a function of concentration, the relationship being exponential (R(2), 0.87-0.96; P < 0.01). The flow behaviour index (n) (except for gum karaya and CMC) was exponentially related to concentration (R(2), 0.61-0.98). The relationship between k and sensory viscosity rating (SVR) was essentially linear in nearly all cases. The SVR could be predicted from the consistency coefficient using the regression equations developed. Also, the relationship of k with fiber concentration would make it possible to identify the concentration of a particular gum required to have desired consistency in terms of SVR.

Using Differentials to Differentiate Trigonometric and Exponential Functions

ERIC Educational Resources Information Center

Dray, Tevian

2013-01-01

Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

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.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

NASA Astrophysics Data System (ADS)

Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md

2017-12-01

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Gauge equivalence of the Gross Pitaevskii equation and the equivalent Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Radha, R.; Kumar, V. Ramesh

2007-11-01

In this paper, we construct an equivalent spin chain for the Gross-Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S3 and S-. We find that the spin solitons for S3 and S- can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.

Nonlinear stability of the 1D Boltzmann equation in a periodic box

NASA Astrophysics Data System (ADS)

Wu, Kung-Chien

2018-05-01

We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

The mechanism of double-exponential growth in hyper-inflation

NASA Astrophysics Data System (ADS)

Mizuno, T.; Takayasu, M.; Takayasu, H.

2002-05-01

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers’ actions in open markets, we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

On the performance of exponential integrators for problems in magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Einkemmer, Lukas; Tokman, Mayya; Loffeld, John

2017-02-01

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Attractors of three-dimensional fast-rotating Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Trahe, Markus

The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.

Exponential propagators for the Schrödinger equation with a time-dependent potential.

PubMed

Bader, Philipp; Blanes, Sergio; Kopylov, Nikita

2018-06-28

We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of the said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similar to the well-known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Effect of algae and water on water color shift

NASA Astrophysics Data System (ADS)

Yang, Shengguang; Xia, Daying; Yang, Xiaolong; Zhao, Jun

1991-03-01

This study showed that the combined effect of absorption of planktonic algae and water on water color shift can be simulated approximately by the exponential function: Log( E {100cm/ W }+ E {100cm/ Xch1})=0.002λ-2.5 where E {100/cm W }, E {100cm/ Xchl} are, respectively, extinction coefficients of seawater and chlorophyll—a (concentration is equal to X mg/m3), and λ (nm) is wavelength. This empirical regression equation is very useful for forecasting the relation between water color and biomass in water not affected by terrigenous material. The main factor affecting water color shift in the ocean should be the absorption of blue light by planktonic algae.

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Flows in a tube structure: Equation on the graph

NASA Astrophysics Data System (ADS)

Panasenko, Grigory; Pileckas, Konstantin

2014-08-01

The steady-state Navier-Stokes equations in thin structures lead to some elliptic second order equation for the macroscopic pressure on a graph. At the nodes of the graph the pressure satisfies Kirchoff-type junction conditions. In the non-steady case the problem for the macroscopic pressure on the graph becomes nonlocal in time. In the paper we study the existence and uniqueness of a solution to such one-dimensional model on the graph for a pipe-wise network. We also prove the exponential decay of the solution with respect to the time variable in the case when the data decay exponentially with respect to time.

Regression relation for pure quantum states and its implications for efficient computing.

PubMed

Elsayed, Tarek A; Fine, Boris V

2013-02-15

We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schrödinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

Biomass expansion factor and root-to-shoot ratio for Pinus in Brazil.

PubMed

Sanquetta, Carlos R; Corte, Ana Pd; da Silva, Fernando

2011-09-24

The Biomass Expansion Factor (BEF) and the Root-to-Shoot Ratio (R) are variables used to quantify carbon stock in forests. They are often considered as constant or species/area specific values in most studies. This study aimed at showing tree size and age dependence upon BEF and R and proposed equations to improve forest biomass and carbon stock. Data from 70 sample Pinus spp. grown in southern Brazil trees in different diameter classes and ages were used to demonstrate the correlation between BEF and R, and forest inventory data, such as DBH, tree height and age. Total dry biomass, carbon stock and CO2 equivalent were simulated using the IPCC default values of BEF and R, corresponding average calculated from data used in this study, as well as the values estimated by regression equations. The mean values of BEF and R calculated in this study were 1.47 and 0.17, respectively. The relationship between BEF and R and the tree measurement variables were inversely related with negative exponential behavior. Simulations indicated that use of fixed values of BEF and R, either IPCC default or current average data, may lead to unreliable estimates of carbon stock inventories and CDM projects. It was concluded that accounting for the variations in BEF and R and using regression equations to relate them to DBH, tree height and age, is fundamental in obtaining reliable estimates of forest tree biomass, carbon sink and CO2 equivalent.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Exponentially varying viscosity of magnetohydrodynamic mixed convection Eyring-Powell nanofluid flow over an inclined surface

NASA Astrophysics Data System (ADS)

Khan, Imad; Fatima, Sumreen; Malik, M. Y.; Salahuddin, T.

2018-03-01

This paper explores the theoretical study of the steady incompressible two dimensional MHD boundary layer flow of Eyring-Powell nanofluid over an inclined surface. The fluid is considered to be electrically conducting and the viscosity of the fluid is assumed to be varying exponentially. The governing partial differential equations (PDE's) are reduced into ordinary differential equations (ODE's) by applying similarity approach. The resulting ordinary differential equations are solved successfully by using Homotopy analysis method. The impact of pertinent parameters on velocity, concentration and temperature profiles are examined through graphs and tables. Also coefficient of skin friction, Sherwood and Nusselt numbers are illustrated in tabular and graphical form.

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

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

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

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

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

A Landsat study of water quality in Lake Okeechobee

NASA Technical Reports Server (NTRS)

Gervin, J. C.; Marshall, M. L.

1976-01-01

This paper uses multiple regression techniques to investigate the relationship between Landsat radiance values and water quality measurements. For a period of over one year, the Central and Southern Florida Flood Control District sampled the water of Lake Okeechobee for chlorophyll, carotenoids, turbidity, and various nutrients at the time of Landsat overpasses. Using an overlay map of the sampling stations, Landsat radiance values were measured from computer compatible tapes using a GE image 100 and averaging over a 22-acre area at each station. These radiance values in four bands were used to form a number of functions (powers, logarithms, exponentials, and ratios), which were then compared with the ground measurements using multiple linear regression techniques. Several dates were used to provide generality and to study possible seasonal variations. Individual correlations were presented for the various water quality parameters and best fit equations were examined for chlorophyll and turbidity. The results and their relationship to past hydrological research were discussed.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Concept of the Exponential Law Prior to 1900

ERIC Educational Resources Information Center

Curtis, Lorenzo J.

1978-01-01

Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

We establish a pointwise stability estimate for the Thomas-Fermi-von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

PubMed

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Slip Effects On MHD Three Dimensional Flow Of Casson Fluid Over An Exponentially Stretching Surface

NASA Astrophysics Data System (ADS)

Madhusudhana Rao, B.; Krishna Murthy, M.; Sivakumar, N.; Rushi Kumar, B.; Raju, C. S. K.

2018-04-01

Heat and mass transfer effects on MHD three dimensional flow of Casson fluid over an exponentially stretching surface with slip conditions is examined. The similarity transformations are used to convert the governing equations into a set of nonlinear ordinary differential equations and are solved numerically using fourth order Runge-Kutta method along with shooting technique. The effects of Casson parameter, Hartmann number, heat source/sink,chemical reaction and slip factors on velocity, temperature and concentration are shown graphically. The skin friction coefficient and the Nusselt number are examined numerically.

Hypersurface Homogeneous Cosmological Model in Modified Theory of Gravitation

NASA Astrophysics Data System (ADS)

Katore, S. D.; Hatkar, S. P.; Baxi, R. J.

2016-12-01

We study a hypersurface homogeneous space-time in the framework of the f (R, T) theory of gravitation in the presence of a perfect fluid. Exact solutions of field equations are obtained for exponential and power law volumetric expansions. We also solve the field equations by assuming the proportionality relation between the shear scalar (σ ) and the expansion scalar (θ ). It is observed that in the exponential model, the universe approaches isotropy at large time (late universe). The investigated model is notably accelerating and expanding. The physical and geometrical properties of the investigated model are also discussed.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

NASA Technical Reports Server (NTRS)

Pratt, D. T.; Radhakrishnan, K.

1986-01-01

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Exponential asymptotics of homoclinic snaking

NASA Astrophysics Data System (ADS)

Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

2011-12-01

We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

Dichotomies for generalized ordinary differential equations and applications

NASA Astrophysics Data System (ADS)

Bonotto, E. M.; Federson, M.; Santos, F. L.

2018-03-01

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments

NASA Astrophysics Data System (ADS)

Ben Shabat, Yael; Shitzer, Avraham

2012-07-01

Facial heat exchange convection coefficients were estimated from experimental data in cold and windy ambient conditions applicable to wind chill calculations. Measured facial temperature datasets, that were made available to this study, originated from 3 separate studies involving 18 male and 6 female subjects. Most of these data were for a -10°C ambient environment and wind speeds in the range of 0.2 to 6 m s-1. Additional single experiments were for -5°C, 0°C and 10°C environments and wind speeds in the same range. Convection coefficients were estimated for all these conditions by means of a numerical facial heat exchange model, applying properties of biological tissues and a typical facial diameter of 0.18 m. Estimation was performed by adjusting the guessed convection coefficients in the computed facial temperatures, while comparing them to measured data, to obtain a satisfactory fit ( r 2 > 0.98, in most cases). In one of the studies, heat flux meters were additionally used. Convection coefficients derived from these meters closely approached the estimated values for only the male subjects. They differed significantly, by about 50%, when compared to the estimated female subjects' data. Regression analysis was performed for just the -10°C ambient temperature, and the range of experimental wind speeds, due to the limited availability of data for other ambient temperatures. The regressed equation was assumed in the form of the equation underlying the "new" wind chill chart. Regressed convection coefficients, which closely duplicated the measured data, were consistently higher than those calculated by this equation, except for one single case. The estimated and currently used convection coefficients are shown to diverge exponentially from each other, as wind speed increases. This finding casts considerable doubts on the validity of the convection coefficients that are used in the computation of the "new" wind chill chart and their applicability to humans in cold and windy environments.

Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments.

PubMed

Ben Shabat, Yael; Shitzer, Avraham

2012-07-01

Facial heat exchange convection coefficients were estimated from experimental data in cold and windy ambient conditions applicable to wind chill calculations. Measured facial temperature datasets, that were made available to this study, originated from 3 separate studies involving 18 male and 6 female subjects. Most of these data were for a -10°C ambient environment and wind speeds in the range of 0.2 to 6 m s(-1). Additional single experiments were for -5°C, 0°C and 10°C environments and wind speeds in the same range. Convection coefficients were estimated for all these conditions by means of a numerical facial heat exchange model, applying properties of biological tissues and a typical facial diameter of 0.18 m. Estimation was performed by adjusting the guessed convection coefficients in the computed facial temperatures, while comparing them to measured data, to obtain a satisfactory fit (r(2) > 0.98, in most cases). In one of the studies, heat flux meters were additionally used. Convection coefficients derived from these meters closely approached the estimated values for only the male subjects. They differed significantly, by about 50%, when compared to the estimated female subjects' data. Regression analysis was performed for just the -10°C ambient temperature, and the range of experimental wind speeds, due to the limited availability of data for other ambient temperatures. The regressed equation was assumed in the form of the equation underlying the "new" wind chill chart. Regressed convection coefficients, which closely duplicated the measured data, were consistently higher than those calculated by this equation, except for one single case. The estimated and currently used convection coefficients are shown to diverge exponentially from each other, as wind speed increases. This finding casts considerable doubts on the validity of the convection coefficients that are used in the computation of the "new" wind chill chart and their applicability to humans in cold and windy environments.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Regional height-diameter equations for major tree species of southwest Oregon.

Treesearch

H. Temesgen; D.W. Hann; V.J. Monleon

2006-01-01

Selected tree height and diameter functions were evaluated for their predictive abilities for major tree species of southwest Oregon. The equations included tree diameter alone, or diameter plus alternative measures of stand density and relative position. Two of the base equations were asymptotic functions, and two were exponential functional forms. The inclusion of...

Modeling of thermal degradation kinetics of the C-glucosyl xanthone mangiferin in an aqueous model solution as a function of pH and temperature and protective effect of honeybush extract matrix.

PubMed

Beelders, Theresa; de Beer, Dalene; Kidd, Martin; Joubert, Elizabeth

2018-01-01

Mangiferin, a C-glucosyl xanthone, abundant in mango and honeybush, is increasingly targeted for its bioactive properties and thus to enhance functional properties of food. The thermal degradation kinetics of mangiferin at pH3, 4, 5, 6 and 7 were each modeled at five temperatures ranging between 60 and 140°C. First-order reaction models were fitted to the data using non-linear regression to determine the reaction rate constant at each pH-temperature combination. The reaction rate constant increased with increasing temperature and pH. Comparison of the reaction rate constants at 100°C revealed an exponential relationship between the reaction rate constant and pH. The data for each pH were also modeled with the Arrhenius equation using non-linear and linear regression to determine the activation energy and pre-exponential factor. Activation energies decreased slightly with increasing pH. Finally, a multi-linear model taking into account both temperature and pH was developed for mangiferin degradation. Sterilization (121°C for 4min) of honeybush extracts dissolved at pH4, 5 and 7 did not cause noticeable degradation of mangiferin, although the multi-linear model predicted 34% degradation at pH7. The extract matrix is postulated to exert a protective effect as changes in potential precursor content could not fully explain the stability of mangiferin. Copyright © 2017 Elsevier Ltd. All rights reserved.

A demographic study of the exponential distribution applied to uneven-aged forests

Treesearch

Jeffrey H. Gove

2016-01-01

A demographic approach based on a size-structured version of the McKendrick-Von Foerster equation is used to demonstrate a theoretical link between the population size distribution and the underlying vital rates (recruitment, mortality and diameter growth) for the population of individuals whose diameter distribution is negative exponential. This model supports the...

The Study on Grinding Ratio in Form Grinding with White Fused Alumina (WA) Grinding Wheels

NASA Astrophysics Data System (ADS)

Junming, Wang; Jiong, Wang; Deyuan, Lou

2018-03-01

The study is carried out based on an experiment of form grinding spur rack with white fused alumina (WA) grinding wheels. In the experiment, SOV-3020A type tri-axial image mapper is utilized to measure the profile of the tooth space in the rack, and the curve equations between the sectional area of the tooth space and the tooth sequence under different grinding depths are established by nonlinear curve regress using software of origin8.0. Then, it deduces the prediction equations for current grinding ratio and cumulative grinding ratio under different grinding depths. The result shows that the grinding ratio is exponential decline relationship with the increase of the number of the tooth to be ground under the same grinding depth, and the decline speed is fast in the initial stage. With the increase of grinding depth, the grinding ratio increases gradually. The cumulative grinding ratio is about twice as high as the current grinding ratio. Thus, large grinding depth is generally used in rough grinding to improve grinding efficiency.

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

A nonperturbative light-front coupled-cluster method

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2012-10-01

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Study of effect of magnetohydrodynamics and couple stress on steady and dynamic characteristics of porous exponential slider bearings

NASA Astrophysics Data System (ADS)

Hanumagowda, B. N.; Gonchigara, Thippeswamy; Santhosh Kumar, J.; MShiva Kumar, H.

2018-04-01

Exponential slider bearings with porous facing is analysed in this article. The modified Reynolds equation is derived for the Exponential porous slider bearing with MHD and couple stress fluid. Computed values of Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient are presented in graphical form. The Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient decreases with increasing values of permeability parameter and increases with increasing values of couplestress parameter and Hartmann number.

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

NASA Technical Reports Server (NTRS)

Walker, K. P.; Freed, A. D.

1991-01-01

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Use of the Priestley-Taylor evaporation equation for soil water limited conditions in a small forest clearcut

USGS Publications Warehouse

Flint, A.L.; Childs, S.W.

1991-01-01

The Priestley-Taylor equation, a simplification of the Penman equation, was used to allow calculations of evapotranspiration under conditions where soil water supply limits evapotranspiration. The Priestley-Taylor coefficient, ??, was calculated to incorporate an exponential decrease in evapotranspiration as soil water content decreases. The method is appropriate for use when detailed meteorological measurements are not available. The data required to determine the parameter for the ?? coefficient are net radiation, soil heat flux, average air temperature, and soil water content. These values can be obtained from measurements or models. The dataset used in this report pertains to a partially vegetated clearcut forest site in southwest Oregon with soil depths ranging from 0.48 to 0.70 m and weathered bedrock below that. Evapotranspiration was estimated using the Bowen ratio method, and the calculated Priestley-Taylor coefficient was fitted to these estimates by nonlinear regression. The calculated Priestley-Taylor coefficient (?????) was found to be approximately 0.9 when the soil was near field capacity (0.225 cm3 cm-3). It was not until soil water content was less than 0.14 cm3 cm-3 that soil water supply limited evapotranspiration. The soil reached a final residual water content near 0.05 cm3 cm-3 at the end of the growing season. ?? 1991.

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

NASA Astrophysics Data System (ADS)

Chen, Dongxiang; Wang, Yuxi; Zhang, Zhifei

2018-05-01

By using the paralinearization technique, we prove the well-posedness of the Prandtl equation for monotonic data in anisotropic Sobolev space with exponential weight and low regularity. The proof is very elementary, thus is expected to provide a new possible way for the zero-viscosity limit problem of the Navier-Stokes equations with the non-slip boundary condition.

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen

2018-06-01

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

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

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

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

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Study of velocity and temperature distributions in boundary layer flow of fourth grade fluid over an exponential stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Najeeb Alam; Saeed, Umair Bin; Sultan, Faqiha; Ullah, Saif; Rehman, Abdul

2018-02-01

This study deals with the investigation of boundary layer flow of a fourth grade fluid and heat transfer over an exponential stretching sheet. For analyzing two heating processes, namely, (i) prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF), the temperature distribution in a fluid has been considered. The suitable transformations associated with the velocity components and temperature, have been employed for reducing the nonlinear model equation to a system of ordinary differential equations. The flow and temperature fields are revealed by solving these reduced nonlinear equations through an effective analytical method. The important findings in this analysis are to observe the effects of viscoelastic, cross-viscous, third grade fluid, and fourth grade fluid parameters on the constructed analytical expression for velocity profile. Likewise, the heat transfer properties are studied for Prandtl and Eckert numbers.

Unstable Mode Solutions to the Klein-Gordon Equation in Kerr-anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Dold, Dominic

2017-03-01

For any cosmological constant {Λ = -3/ℓ2 < 0} and any {α < 9/4}, we find a Kerr-AdS spacetime {({M}, g_{KAdS})}, in which the Klein-Gordon equation {Box_{g_{KAdS}}ψ + α/ℓ2ψ = 0} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound {r+2 > |a|ℓ}. We obtain an analogous result for Neumann boundary conditions if {5/4 < α < 9/4}. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses {α} such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in (Commun. Math. Phys. 329:859-891, 2014) and provides the first rigorous construction of a superradiant instability for negative cosmological constant.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes.

PubMed

Bačová, P; Košovan, P; Uhlík, F; Kuldová, J; Limpouchová, Z; Procházka, K

2012-06-01

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

Exponential Decay of Dispersion-Managed Solitons for General Dispersion Profiles

NASA Astrophysics Data System (ADS)

Green, William R.; Hundertmark, Dirk

2016-02-01

We show that any weak solution of the dispersion management equation describing dispersion-managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdoğan, Hundertmark, and Lee in two directions, to arbitrary non-negative average dispersion and, more importantly, to rather general dispersion profiles, which cover most, if not all, physically relevant cases.

Exponential integration algorithms applied to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.

Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.

Methods for estimating the magnitude and frequency of peak streamflows at ungaged sites in and near the Oklahoma Panhandle

USGS Publications Warehouse

Smith, S. Jerrod; Lewis, Jason M.; Graves, Grant M.

2015-09-28

Generalized-least-squares multiple-linear regression analysis was used to formulate regression relations between peak-streamflow frequency statistics and basin characteristics. Contributing drainage area was the only basin characteristic determined to be statistically significant for all percentage of annual exceedance probabilities and was the only basin characteristic used in regional regression equations for estimating peak-streamflow frequency statistics on unregulated streams in and near the Oklahoma Panhandle. The regression model pseudo-coefficient of determination, converted to percent, for the Oklahoma Panhandle regional regression equations ranged from about 38 to 63 percent. The standard errors of prediction and the standard model errors for the Oklahoma Panhandle regional regression equations ranged from about 84 to 148 percent and from about 76 to 138 percent, respectively. These errors were comparable to those reported for regional peak-streamflow frequency regression equations for the High Plains areas of Texas and Colorado. The root mean square errors for the Oklahoma Panhandle regional regression equations (ranging from 3,170 to 92,000 cubic feet per second) were less than the root mean square errors for the Oklahoma statewide regression equations (ranging from 18,900 to 412,000 cubic feet per second); therefore, the Oklahoma Panhandle regional regression equations produce more accurate peak-streamflow statistic estimates for the irrigated period of record in the Oklahoma Panhandle than do the Oklahoma statewide regression equations. The regression equations developed in this report are applicable to streams that are not substantially affected by regulation, impoundment, or surface-water withdrawals. These regression equations are intended for use for stream sites with contributing drainage areas less than or equal to about 2,060 square miles, the maximum value for the independent variable used in the regression analysis.

A mathematical model for evolution and SETI.

PubMed

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

Modelling Evolution and SETI Mathematically

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2012-05-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factor increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions constrained between the time axis and the exponential growth curve. Finally, since each lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A Mathematical Model for Evolution and SETI

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-12-01

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

NASA Astrophysics Data System (ADS)

Dalkilic, Turkan Erbay; Apaydin, Aysen

2009-11-01

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+[epsilon]. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the [`]switching regression model' and it is expressed with . Here li indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665-685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363-399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306-310]. In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

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

Diwaker, E-mail: diwakerphysics@gmail.com; Chakraborty, Aniruddha

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

Erosion over time on severely disturbed granitic soils: a model

Treesearch

W. F. Megahan

1974-01-01

A negative exponential equation containing three parameters was derived to describe time trends in surface erosion on severely disturbed soils. Data from four different studies of surface erosion on roads constructed from the granitic materials found in the Idaho Batholith were used to develop equation parameters. The evidence suggests that surface "armoring...

Introduction of the Notion of Differential Equations by Modelling Based Teaching

ERIC Educational Resources Information Center

Budinski, Natalija; Takaci, Djurdjica

2011-01-01

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Modelling of capital asset pricing by considering the lagged effects

NASA Astrophysics Data System (ADS)

Sukono; Hidayat, Y.; Bon, A. Talib bin; Supian, S.

2017-01-01

In this paper the problem of modelling the Capital Asset Pricing Model (CAPM) with the effect of the lagged is discussed. It is assumed that asset returns are analysed influenced by the market return and the return of risk-free assets. To analyse the relationship between asset returns, the market return, and the return of risk-free assets, it is conducted by using a regression equation of CAPM, and regression equation of lagged distributed CAPM. Associated with the regression equation lagged CAPM distributed, this paper also developed a regression equation of Koyck transformation CAPM. Results of development show that the regression equation of Koyck transformation CAPM has advantages, namely simple as it only requires three parameters, compared with regression equation of lagged distributed CAPM.

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

NASA Technical Reports Server (NTRS)

Ito, K.

1984-01-01

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

NASA Technical Reports Server (NTRS)

Revenaugh, Justin; Parsons, Barry

1987-01-01

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Power law incidence rate in epidemic models. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Allen, Linda J. S.

2016-09-01

Dr. Chowell and colleagues emphasize the importance of considering a variety of modeling approaches to characterize the growth of an epidemic during the early stages [1]. A fit of data from the 2009 H1N1 influenza pandemic and the 2014-2015 Ebola outbreak to models indicates sub-exponential growth, in contrast to the classic, homogeneous-mixing SIR model with exponential growth. With incidence rate βSI / N and S approximately equal to the total population size N, the number of new infections in an SIR epidemic model grows exponentially as in the differential equation,

Methane exchange at the peatland forest floor - automatic chamber system exposes the dynamics of small fluxes

NASA Astrophysics Data System (ADS)

Korkiakoski, Mika; Tuovinen, Juha-Pekka; Aurela, Mika; Koskinen, Markku; Minkkinen, Kari; Ojanen, Paavo; Penttilä, Timo; Rainne, Juuso; Laurila, Tuomas; Lohila, Annalea

2017-04-01

We measured methane (CH4) exchange rates with automatic chambers at the forest floor of a nutrient-rich drained peatland in 2011-2013. The fen, located in southern Finland, was drained for forestry in 1969 and the tree stand is now a mixture of Scots pine, Norway spruce, and pubescent birch. Our measurement system consisted of six transparent chambers and stainless steel frames, positioned on a number of different field and moss layer compositions. Gas concentrations were measured with an online cavity ring-down spectroscopy gas analyzer. Fluxes were calculated with both linear and exponential regression. The use of linear regression resulted in systematically smaller CH4 fluxes by 10-45 % as compared to exponential regression. However, the use of exponential regression with small fluxes ( < 2.5 µg CH4 m-2 h-1) typically resulted in anomalously large absolute fluxes and high hour-to-hour deviations. Therefore, we recommend that fluxes are initially calculated with linear regression to determine the threshold for low fluxes and that higher fluxes are then recalculated using exponential regression. The exponential flux was clearly affected by the length of the fitting period when this period was < 190 s, but stabilized with longer periods. Thus, we also recommend the use of a fitting period of several minutes to stabilize the results and decrease the flux detection limit. There were clear seasonal dynamics in the CH4 flux: the forest floor acted as a CH4 sink particularly from early summer until the end of the year, while in late winter the flux was very small and fluctuated around zero. However, the magnitude of fluxes was relatively small throughout the year, ranging mainly from -130 to +100 µg CH4 m-2 h-1. CH4 emission peaks were observed occasionally, mostly in summer during heavy rainfall events. Diurnal variation, showing a lower CH4 uptake rate during the daytime, was observed in all of the chambers, mainly in the summer and late spring, particularly in dry conditions. It was attributed more to changes in wind speed than air or soil temperature, which suggest that physical rather than biological phenomena are responsible for the observed variation. The annual net CH4 exchange varied from -104 ± 30 to -505 ± 39 mg CH4 m-2 yr-1 among the six chambers, with an average of -219 mg CH4 m-2 yr-1 over the 2-year measurement period.

Using Regression Equations Built from Summary Data in the Psychological Assessment of the Individual Case: Extension to Multiple Regression

ERIC Educational Resources Information Center

Crawford, John R.; Garthwaite, Paul H.; Denham, Annie K.; Chelune, Gordon J.

2012-01-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…

Isometric Arm Strength and Subjective Rating of Upper Limb Fatigue in Two-Handed Carrying Tasks

PubMed Central

Li, Kai Way; Chiu, Wen-Sheng

2015-01-01

Sustained carrying could result in muscular fatigue of the upper limb. Ten male and ten female subjects were recruited for measurements of isometric arm strength before and during carrying a load for a period of 4 minutes. Two levels of load of carrying were tested for each of the male and female subjects. Exponential function based predictive equations for the isometric arm strength were established. The mean absolute deviations of these models in predicting the isometric arm strength were in the range of 3.24 to 17.34 N. Regression analyses between the subjective ratings of upper limb fatigue and force change index (FCI) for the carrying were also performed. The results indicated that the subjective rating of muscular fatigue may be estimated by multiplying the FCI with a constant. The FCI may, therefore, be adopted as an index to assess muscular fatigue for two-handed carrying tasks. PMID:25794159

Isometric arm strength and subjective rating of upper limb fatigue in two-handed carrying tasks.

PubMed

Li, Kai Way; Chiu, Wen-Sheng

2015-01-01

Sustained carrying could result in muscular fatigue of the upper limb. Ten male and ten female subjects were recruited for measurements of isometric arm strength before and during carrying a load for a period of 4 minutes. Two levels of load of carrying were tested for each of the male and female subjects. Exponential function based predictive equations for the isometric arm strength were established. The mean absolute deviations of these models in predicting the isometric arm strength were in the range of 3.24 to 17.34 N. Regression analyses between the subjective ratings of upper limb fatigue and force change index (FCI) for the carrying were also performed. The results indicated that the subjective rating of muscular fatigue may be estimated by multiplying the FCI with a constant. The FCI may, therefore, be adopted as an index to assess muscular fatigue for two-handed carrying tasks.

`Un-Darkening' the Cosmos: New laws of physics for an expanding universe

NASA Astrophysics Data System (ADS)

George, William

2017-11-01

Dark matter is believed to exist because Newton's Laws are inconsistent with the visible matter in galaxies. Dark energy is necessary to explain the universe expansion. (also available from www.turbulence-online.com) suggested that the equations themselves might be in error because they implicitly assume that time is measured in linear increments. This presentation couples the possible non-linearity of time with an expanding universe. Maxwell's equations for an expanding universe with constant speed of light are shown to be invariant only if time itself is non-linear. Both linear and exponential expansion rates are considered. A linearly expanding universe corresponds to logarithmic time, while exponential expansion corresponds to exponentially varying time. Revised Newton's laws using either leads to different definitions of mass and kinetic energy, both of which appear time-dependent if expressed in linear time. And provide the possibility of explaining the astronomical observations without either dark matter or dark energy. We would have never noticed the differences on earth, since the leading term in both expansions is linear in δ /to where to is the current age.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

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

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay

NASA Astrophysics Data System (ADS)

Dai, Qiuyi; Yang, Zhifeng

2014-10-01

In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).

Two-time scale subordination in physical processes with long-term memory

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2008-03-01

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.

Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Shateyi, Stanford; Marewo, Gerald T.

2018-05-01

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

NASA Astrophysics Data System (ADS)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

Adjustment of regional regression equations for urban storm-runoff quality using at-site data

USGS Publications Warehouse

Barks, C.S.

1996-01-01

Regional regression equations have been developed to estimate urban storm-runoff loads and mean concentrations using a national data base. Four statistical methods using at-site data to adjust the regional equation predictions were developed to provide better local estimates. The four adjustment procedures are a single-factor adjustment, a regression of the observed data against the predicted values, a regression of the observed values against the predicted values and additional local independent variables, and a weighted combination of a local regression with the regional prediction. Data collected at five representative storm-runoff sites during 22 storms in Little Rock, Arkansas, were used to verify, and, when appropriate, adjust the regional regression equation predictions. Comparison of observed values of stormrunoff loads and mean concentrations to the predicted values from the regional regression equations for nine constituents (chemical oxygen demand, suspended solids, total nitrogen as N, total ammonia plus organic nitrogen as N, total phosphorus as P, dissolved phosphorus as P, total recoverable copper, total recoverable lead, and total recoverable zinc) showed large prediction errors ranging from 63 percent to more than several thousand percent. Prediction errors for 6 of the 18 regional regression equations were less than 100 percent and could be considered reasonable for water-quality prediction equations. The regression adjustment procedure was used to adjust five of the regional equation predictions to improve the predictive accuracy. For seven of the regional equations the observed and the predicted values are not significantly correlated. Thus neither the unadjusted regional equations nor any of the adjustments were appropriate. The mean of the observed values was used as a simple estimator when the regional equation predictions and adjusted predictions were not appropriate.

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

NASA Astrophysics Data System (ADS)

Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

2018-05-01

In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Ultrastable light sources in the crossover from superradiance to lasing

NASA Astrophysics Data System (ADS)

Xu, Minghui; Tieri, David; Holland, Murray

2013-05-01

We theoretically investigate the crossover from steady-state superradiance to optical lasing. An exact solution of the quantum master equation is difficult to obtain due to the exponential scaling of the Hilbert space dimension with system size. However, since Lindblad operators in the master equation are invariant under SU(4) transformations, we are able to reduce the exponential scaling of the problem to cubic by expanding the density matrix in terms of an SU(4) basis. In this way, we obtain exact quantum solutions of the superradiance-laser crossover. We use this theory to investigate the potential for ultrastable lasers in the millihertz linewidth regime, and find the behavior of important observables, such as intensity, linewidth, spin-correlation, and entanglement. This work was supported by the DARPA QUASAR program and NSF.

Transient photoresponse in amorphous In-Ga-Zn-O thin films under stretched exponential analysis

NASA Astrophysics Data System (ADS)

Luo, Jiajun; Adler, Alexander U.; Mason, Thomas O.; Bruce Buchholz, D.; Chang, R. P. H.; Grayson, M.

2013-04-01

We investigated transient photoresponse and Hall effect in amorphous In-Ga-Zn-O thin films and observed a stretched exponential response which allows characterization of the activation energy spectrum with only three fit parameters. Measurements of as-grown films and 350 K annealed films were conducted at room temperature by recording conductivity, carrier density, and mobility over day-long time scales, both under illumination and in the dark. Hall measurements verify approximately constant mobility, even as the photoinduced carrier density changes by orders of magnitude. The transient photoconductivity data fit well to a stretched exponential during both illumination and dark relaxation, but with slower response in the dark. The inverse Laplace transforms of these stretched exponentials yield the density of activation energies responsible for transient photoconductivity. An empirical equation is introduced, which determines the linewidth of the activation energy band from the stretched exponential parameter β. Dry annealing at 350 K is observed to slow the transient photoresponse.

The many faces of the quantum Liouville exponentials

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup; Schnittger, Jens

1994-01-01

First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.

Motion of the two-control airplane in rectilinear flight after initial disturbances with introduction of controls following an exponential law

NASA Technical Reports Server (NTRS)

Klemin, Alexander

1937-01-01

An airplane in steady rectilinear flight was assumed to experience an initial disturbance in rolling or yawing velocity. The equations of motion were solved to see if it was possible to hasten recovery of a stable airplane or to secure recovery of an unstable airplane by the application of a single lateral control following an exponential law. The sample computations indicate that, for initial disturbances complex in character, it would be difficult to secure correlation with any type of exponential control. The possibility is visualized that the two-control operation may seriously impair the ability to hasten recovery or counteract instability.

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Using a Physics Experiment in a Lecture Setting to Engage Biology Students with the Concepts of Poiseuille's Law

ERIC Educational Resources Information Center

Breckler, Jennifer L.; Christensen, Tina; Sun, Wendy

2013-01-01

Biology students enrolled in a typical undergraduate physiology course encounter Poiseuille's law, a physics equation that describes the properties governing the flow of blood through the circulation. According to the equation, a small change in vessel radius has an exponential effect on resistance, resulting in a larger than expected change in…

A mathematical approach for evaluating nickel-hydrogen cells

NASA Technical Reports Server (NTRS)

Leibecki, H. F.

1986-01-01

A mathematical equation is presented which gives a quantitative relationship between time-voltage discharge curves, when a cell's ampere-hour capacity is determined at a constant discharge current. In particular the equation quantifies the initial exponential voltage decay; the rate of voltage decay; the overall voltage shift of the curve and the total capacity of the cell at the given discharge current. The results of 12 nickel-hydrogen boiler plate cells cycled to 80 percent depth-of-discharge (DOD) are discussed in association with these equations.

Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

USGS Publications Warehouse

Asquith, William H.; Thompson, David B.

2008-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

When growth models are not universal: evidence from marine invertebrates

PubMed Central

Hirst, Andrew G.; Forster, Jack

2013-01-01

The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

Year-round measurements of CH4 exchange in a forested drained peatland using automated chambers

NASA Astrophysics Data System (ADS)

Korkiakoski, Mika; Koskinen, Markku; Penttilä, Timo; Arffman, Pentti; Ojanen, Paavo; Minkkinen, Kari; Laurila, Tuomas; Lohila, Annalea

2016-04-01

Pristine peatlands are usually carbon accumulating ecosystems and sources of methane (CH4). Draining peatlands for forestry increases the thickness of the oxic layer, thus enhancing CH4 oxidation which leads to decreased CH4 emissions. Closed chambers are commonly used in estimating the greenhouse gas exchange between the soil and the atmosphere. However, the closed chamber technique alters the gas concentration gradient making the concentration development against time non-linear. Selecting the correct fitting method is important as it can be the largest source of uncertainty in flux calculation. We measured CH4 exchange rates and their diurnal and seasonal variations in a nutrient-rich drained peatland located in southern Finland. The original fen was drained for forestry in 1970s and now the tree stand is a mixture of Scots pine, Norway spruce and Downy birch. Our system consisted of six transparent polycarbonate chambers and stainless steel frames, positioned on different types of field and moss layer. During winter, the frame was raised above the snowpack with extension collars and the height of the snowpack inside the chamber was measured regularly. The chambers were closed hourly and the sample gas was sucked into a cavity ring-down spectrometer and analysed for CH4, CO2 and H2O concentration with 5 second time resolution. The concentration change in time in the beginning of a closure was determined with linear and exponential fits. The results show that linear regression systematically underestimated the CH4 flux when compared to exponential regression by 20-50 %. On the other hand, the exponential regression seemed not to work reliably with small fluxes (< 3.5 μg CH4 m-2 h-1): using exponential regression in such cases typically resulted in anomalously large fluxes and high deviation. Due to these facts, we recommend first calculating the flux with the linear regression and, if the flux is high enough, calculate the flux again using the exponential regression and use this value in later analysis. The forest floor at the site (including the ground vegetation) acted as a CH4 sink most of the time. CH4 emission peaks were occasionally observed, particularly in spring during the snow melt, and during rainfall events in summer. Diurnal variation was observed mainly in summer. The net CH4 exchange for the two year measurement period in the six chambers varied from -31 to -155 mg CH4 m-2 yr-1, the average being -67 mg CH4 m-2 yr-1. However, this does not include the ditches which typically act as a significant source for CH4.

Dry season mean monthly flow and harmonic mean flow regression equations for selected ungaged basins in Arkansas

USGS Publications Warehouse

Breaker, Brian K.

2015-01-01

Equations for two regions were found to be statistically significant for developing regression equations for estimating harmonic mean flows at ungaged basins; thus, equations are applicable only to streams in those respective regions in Arkansas. Regression equations for dry season mean monthly flows are applicable only to streams located throughout Arkansas. All regression equations are applicable only to unaltered streams where flows were not significantly affected by regulation, diversion, or urbanization. The median number of years used for dry season mean monthly flow calculation was 43, and the median number of years used for harmonic mean flow calculations was 34 for region 1 and 43 for region 2.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process.

PubMed

Wang, Gang; Yuan, Jianli; Wang, Xizhi; Xiao, Sa; Huang, Wenbing

2004-11-01

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

NASA Astrophysics Data System (ADS)

Samanta, G. C.; Myrzakulov, R.

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter ωv. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface.

PubMed

Ahmad Khan, Junaid; Mustafa, M; Hayat, T; Alsaedi, A

2015-01-01

This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. Similarity approach is utilized to normalize the governing boundary layer equations. Local similarity solutions are achieved by shooting approach together with fourth-fifth-order Runge-Kutta integration technique and Newton's method. Our computations reveal that fluid temperature has inverse relationship with the thermal relaxation time. Further the fluid velocity is a decreasing function of the fluid relaxation time. A comparison of Fourier's law and the Cattaneo-Christov's law is also presented. Present attempt even in the case of Newtonian fluid is not yet available in the literature.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Investigation of hyperelastic models for nonlinear elastic behavior of demineralized and deproteinized bovine cortical femur bone.

PubMed

Hosseinzadeh, M; Ghoreishi, M; Narooei, K

2016-06-01

In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Low-flow, base-flow, and mean-flow regression equations for Pennsylvania streams

USGS Publications Warehouse

Stuckey, Marla H.

2006-01-01

Low-flow, base-flow, and mean-flow characteristics are an important part of assessing water resources in a watershed. These streamflow characteristics can be used by watershed planners and regulators to determine water availability, water-use allocations, assimilative capacities of streams, and aquatic-habitat needs. Streamflow characteristics are commonly predicted by use of regression equations when a nearby streamflow-gaging station is not available. Regression equations for predicting low-flow, base-flow, and mean-flow characteristics for Pennsylvania streams were developed from data collected at 293 continuous- and partial-record streamflow-gaging stations with flow unaffected by upstream regulation, diversion, or mining. Continuous-record stations used in the regression analysis had 9 years or more of data, and partial-record stations used had seven or more measurements collected during base-flow conditions. The state was divided into five low-flow regions and regional regression equations were developed for the 7-day, 10-year; 7-day, 2-year; 30-day, 10-year; 30-day, 2-year; and 90-day, 10-year low flows using generalized least-squares regression. Statewide regression equations were developed for the 10-year, 25-year, and 50-year base flows using generalized least-squares regression. Statewide regression equations were developed for harmonic mean and mean annual flow using weighted least-squares regression. Basin characteristics found to be significant explanatory variables at the 95-percent confidence level for one or more regression equations were drainage area, basin slope, thickness of soil, stream density, mean annual precipitation, mean elevation, and the percentage of glaciation, carbonate bedrock, forested area, and urban area within a basin. Standard errors of prediction ranged from 33 to 66 percent for the n-day, T-year low flows; 21 to 23 percent for the base flows; and 12 to 38 percent for the mean annual flow and harmonic mean, respectively. The regression equations are not valid in watersheds with upstream regulation, diversions, or mining activities. Watersheds with karst features need close examination as to the applicability of the regression-equation results.

Hypersonic Flight Mechanics. [for atmospheric entry trajectories

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented.

Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

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

Peng, Bo; Kowalski, Karol

In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CCmore » self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.« less

Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies

PubMed Central

Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.

2016-01-01

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Regional Regression Equations to Estimate Flow-Duration Statistics at Ungaged Stream Sites in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2010-01-01

Multiple linear regression equations for determining flow-duration statistics were developed to estimate select flow exceedances ranging from 25- to 99-percent for six 'bioperiods'-Salmonid Spawning (November), Overwinter (December-February), Habitat Forming (March-April), Clupeid Spawning (May), Resident Spawning (June), and Rearing and Growth (July-October)-in Connecticut. Regression equations also were developed to estimate the 25- and 99-percent flow exceedances without reference to a bioperiod. In total, 32 equations were developed. The predictive equations were based on regression analyses relating flow statistics from streamgages to GIS-determined basin and climatic characteristics for the drainage areas of those streamgages. Thirty-nine streamgages (and an additional 6 short-term streamgages and 28 partial-record sites for the non-bioperiod 99-percent exceedance) in Connecticut and adjacent areas of neighboring States were used in the regression analysis. Weighted least squares regression analysis was used to determine the predictive equations; weights were assigned based on record length. The basin characteristics-drainage area, percentage of area with coarse-grained stratified deposits, percentage of area with wetlands, mean monthly precipitation (November), mean seasonal precipitation (December, January, and February), and mean basin elevation-are used as explanatory variables in the equations. Standard errors of estimate of the 32 equations ranged from 10.7 to 156 percent with medians of 19.2 and 55.4 percent to predict the 25- and 99-percent exceedances, respectively. Regression equations to estimate high and median flows (25- to 75-percent exceedances) are better predictors (smaller variability of the residual values around the regression line) than the equations to estimate low flows (less than 75-percent exceedance). The Habitat Forming (March-April) bioperiod had the smallest standard errors of estimate, ranging from 10.7 to 20.9 percent. In contrast, the Rearing and Growth (July-October) bioperiod had the largest standard errors, ranging from 30.9 to 156 percent. The adjusted coefficient of determination of the equations ranged from 77.5 to 99.4 percent with medians of 98.5 and 90.6 percent to predict the 25- and 99-percent exceedances, respectively. Descriptive information on the streamgages used in the regression, measured basin and climatic characteristics, and estimated flow-duration statistics are provided in this report. Flow-duration statistics and the 32 regression equations for estimating flow-duration statistics in Connecticut are stored on the U.S. Geological Survey World Wide Web application ?StreamStats? (http://water.usgs.gov/osw/streamstats/index.html). The regression equations developed in this report can be used to produce unbiased estimates of select flow exceedances statewide.

Nationwide summary of US Geological Survey regional regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993

USGS Publications Warehouse

Jennings, M.E.; Thomas, W.O.; Riggs, H.C.

1994-01-01

For many years, the U.S. Geological Survey (USGS) has been involved in the development of regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally these equations have been developed on a statewide or metropolitan area basis as part of cooperative study programs with specific State Departments of Transportation or specific cities. The USGS, in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency, has compiled all the current (as of September 1993) statewide and metropolitan area regression equations into a micro-computer program titled the National Flood Frequency Program.This program includes regression equations for estimating flood-peak discharges and techniques for estimating a typical flood hydrograph for a given recurrence interval peak discharge for unregulated rural and urban watersheds. These techniques should be useful to engineers and hydrologists for planning and design applications. This report summarizes the statewide regression equations for rural watersheds in each State, summarizes the applicable metropolitan area or statewide regression equations for urban watersheds, describes the National Flood Frequency Program for making these computations, and provides much of the reference information on the extrapolation variables needed to run the program.

Model equations for the Eiffel Tower profile: historical perspective and new results

NASA Astrophysics Data System (ADS)

Weidman, Patrick; Pinelis, Iosif

2004-07-01

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, "in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind". An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).

An exponential time-integrator scheme for steady and unsteady inviscid flows

NASA Astrophysics Data System (ADS)

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

2018-07-01

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows.

Stability of post-fertilization traveling waves

NASA Astrophysics Data System (ADS)

Flores, Gilberto; Plaza, Ramón G.

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.

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.

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routine

NASA Astrophysics Data System (ADS)

Wang, Jun; Endreny, Theodore A.; Hassett, James M.

2006-11-01

TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4.8 cm h-1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright

A Question of Interest

ERIC Educational Resources Information Center

Holley, Ann D.

1978-01-01

Formulas are developed which answer installment-buying questions without the use of amortization, sinking funds, or annuity tables. Applications for geometric progressions, proof by induction, solution of exponential equations, and the notion of recursive functions are displayed. (MN)

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Hathwar, Raghuraj; Saraniti, Marco; Goodnick, Stephen M.

2016-07-01

We report on a new numerical approach for multi-band drift within the context of full band Monte Carlo (FBMC) simulation and apply this to Si and InAs nanowires. The approach is based on the solution of the Krieger and Iafrate (KI) equations [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)], which gives the probability of carriers undergoing interband transitions subject to an applied electric field. The KI equations are based on the solution of the time-dependent Schrödinger equation, and previous solutions of these equations have used Runge-Kutta (RK) methods to numerically solve the KI equations. This approach made the solution of the KI equations numerically expensive and was therefore only applied to a small part of the Brillouin zone (BZ). Here we discuss an alternate approach to the solution of the KI equations using the Magnus expansion (also known as "exponential perturbation theory"). This method is more accurate than the RK method as the solution lies on the exponential map and shares important qualitative properties with the exact solution such as the preservation of the unitary character of the time evolution operator. The solution of the KI equations is then incorporated through a modified FBMC free-flight drift routine and applied throughout the nanowire BZ. The importance of the multi-band drift model is then demonstrated for the case of Si and InAs nanowires by simulating a uniform field FBMC and analyzing the average carrier energies and carrier populations under high electric fields. Numerical simulations show that the average energy of the carriers under high electric field is significantly higher when multi-band drift is taken into consideration, due to the interband transitions allowing carriers to achieve higher energies.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Regression of altitude-produced cardiac hypertrophy.

NASA Technical Reports Server (NTRS)

Sizemore, D. A.; Mcintyre, T. W.; Van Liere, E. J.; Wilson , M. F.

1973-01-01

The rate of regression of cardiac hypertrophy with time has been determined in adult male albino rats. The hypertrophy was induced by intermittent exposure to simulated high altitude. The percentage hypertrophy was much greater (46%) in the right ventricle than in the left (16%). The regression could be adequately fitted to a single exponential function with a half-time of 6.73 plus or minus 0.71 days (90% CI). There was no significant difference in the rates of regression for the two ventricles.

Methods for estimating selected spring and fall low-flow frequency statistics for ungaged stream sites in Iowa, based on data through June 2014

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.; O'Shea, Padraic S.

2016-09-19

A statewide study was led to develop regression equations for estimating three selected spring and three selected fall low-flow frequency statistics for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include spring (April through June) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and fall (October through December) 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years. Estimates of the three selected spring statistics are provided for 241 U.S. Geological Survey continuous-record streamgages, and estimates of the three selected fall statistics are provided for 238 of these streamgages, using data through June 2014. Because only 9 years of fall streamflow record were available, three streamgages included in the development of the spring regression equations were not included in the development of the fall regression equations. Because of regulation, diversion, or urbanization, 30 of the 241 streamgages were not included in the development of the regression equations. The study area includes Iowa and adjacent areas within 50 miles of the Iowa border. Because trend analyses indicated statistically significant positive trends when considering the period of record for most of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. Geographic information system software was used to measure 63 selected basin characteristics for each of the 211streamgages used to develop the regional regression equations. The study area was divided into three low-flow regions that were defined in a previous study for the development of regional regression equations.Because several streamgages included in the development of regional regression equations have estimates of zero flow calculated from observed streamflow for selected spring and fall low-flow frequency statistics, the final equations for the three low-flow regions were developed using two types of regression analyses—left-censored and generalized-least-squares regression analyses. A total of 211 streamgages were included in the development of nine spring regression equations—three equations for each of the three low-flow regions. A total of 208 streamgages were included in the development of nine fall regression equations—three equations for each of the three low-flow regions. A censoring threshold was used to develop 15 left-censored regression equations to estimate the three fall low-flow frequency statistics for each of the three low-flow regions and to estimate the three spring low-flow frequency statistics for the southern and northwest regions. For the northeast region, generalized-least-squares regression was used to develop three equations to estimate the three spring low-flow frequency statistics. For the northeast region, average standard errors of prediction range from 32.4 to 48.4 percent for the spring equations and average standard errors of estimate range from 56.4 to 73.8 percent for the fall equations. For the northwest region, average standard errors of estimate range from 58.9 to 62.1 percent for the spring equations and from 83.2 to 109.4 percent for the fall equations. For the southern region, average standard errors of estimate range from 43.2 to 64.0 percent for the spring equations and from 78.1 to 78.7 percent for the fall equations.The regression equations are applicable only to stream sites in Iowa with low flows not substantially affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. The regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system application. StreamStats allows users to click on any ungaged stream site and compute estimates of the six selected spring and fall low-flow statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged site are provided. StreamStats also allows users to click on any Iowa streamgage to obtain computed estimates for the six selected spring and fall low-flow statistics.

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

PubMed

Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

2015-01-01

In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

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

PubMed

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

2013-05-13

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

Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Kang, Moon-Jin; Morales, Javier

2018-03-01

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

Solution of the equation of heat conduction with time dependent sources: Programmed application to planetary thermal history

NASA Technical Reports Server (NTRS)

Conel, J. E.

1975-01-01

A computer program (Program SPHERE) solving the inhomogeneous equation of heat conduction with radiation boundary condition on a thermally homogeneous sphere is described. The source terms are taken to be exponential functions of the time. Thermal properties are independent of temperature. The solutions are appropriate to studying certain classes of planetary thermal history. Special application to the moon is discussed.

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

NASA Technical Reports Server (NTRS)

Kousen, Kenneth A.

1999-01-01

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

Environmental factors controlling spatial variation in sediment yield in a central Andean mountain area

NASA Astrophysics Data System (ADS)

Molina, Armando; Govers, Gerard; Poesen, Jean; Van Hemelryck, Hendrik; De Bièvre, Bert; Vanacker, Veerle

2008-06-01

A large spatial variability in sediment yield was observed from small streams in the Ecuadorian Andes. The objective of this study was to analyze the environmental factors controlling these variations in sediment yield in the Paute basin, Ecuador. Sediment yield data were calculated based on sediment volumes accumulated behind checkdams for 37 small catchments. Mean annual specific sediment yield (SSY) shows a large spatial variability and ranges between 26 and 15,100 Mg km - 2 year - 1 . Mean vegetation cover (C, fraction) in the catchment, i.e. the plant cover at or near the surface, exerts a first order control on sediment yield. The fractional vegetation cover alone explains 57% of the observed variance in ln(SSY). The negative exponential relation (SSY = a × e- b C) which was found between vegetation cover and sediment yield at the catchment scale (10 3-10 9 m 2), is very similar to the equations derived from splash, interrill and rill erosion experiments at the plot scale (1-10 3 m 2). This affirms the general character of an exponential decrease of sediment yield with increasing vegetation cover at a wide range of spatial scales, provided the distribution of cover can be considered to be essentially random. Lithology also significantly affects the sediment yield, and explains an additional 23% of the observed variance in ln(SSY). Based on these two catchment parameters, a multiple regression model was built. This empirical regression model already explains more than 75% of the total variance in the mean annual sediment yield. These results highlight the large potential of revegetation programs for controlling sediment yield. They show that a slight increase in the overall fractional vegetation cover of degraded land is likely to have a large effect on sediment production and delivery. Moreover, they point to the importance of detailed surface vegetation data for predicting and modeling sediment production rates.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Tempered fractional calculus

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

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Breathers in a locally resonant granular chain with precompression

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-01

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computedmore » exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.« less

Initial conditions and degrees of freedom of non-local gravity

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe

2018-05-01

We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.

Peak flow regression equations For small, ungaged streams in Maine: Comparing map-based to field-based variables

USGS Publications Warehouse

Lombard, Pamela J.; Hodgkins, Glenn A.

2015-01-01

Regression equations to estimate peak streamflows with 1- to 500-year recurrence intervals (annual exceedance probabilities from 99 to 0.2 percent, respectively) were developed for small, ungaged streams in Maine. Equations presented here are the best available equations for estimating peak flows at ungaged basins in Maine with drainage areas from 0.3 to 12 square miles (mi2). Previously developed equations continue to be the best available equations for estimating peak flows for basin areas greater than 12 mi2. New equations presented here are based on streamflow records at 40 U.S. Geological Survey streamgages with a minimum of 10 years of recorded peak flows between 1963 and 2012. Ordinary least-squares regression techniques were used to determine the best explanatory variables for the regression equations. Traditional map-based explanatory variables were compared to variables requiring field measurements. Two field-based variables—culvert rust lines and bankfull channel widths—either were not commonly found or did not explain enough of the variability in the peak flows to warrant inclusion in the equations. The best explanatory variables were drainage area and percent basin wetlands; values for these variables were determined with a geographic information system. Generalized least-squares regression was used with these two variables to determine the equation coefficients and estimates of accuracy for the final equations.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Propagating Qualitative Values Through Quantitative Equations

NASA Technical Reports Server (NTRS)

Kulkarni, Deepak

1992-01-01

In most practical problems where traditional numeric simulation is not adequate, one need to reason about a system with both qualitative and quantitative equations. In this paper, we address the problem of propagating qualitative values represented as interval values through quantitative equations. Previous research has produced exponential-time algorithms for approximate solution of the problem. These may not meet the stringent requirements of many real time applications. This paper advances the state of art by producing a linear-time algorithm that can propagate a qualitative value through a class of complex quantitative equations exactly and through arbitrary algebraic expressions approximately. The algorithm was found applicable to Space Shuttle Reaction Control System model.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Methods for estimating the magnitude and frequency of peak streamflows for unregulated streams in Oklahoma

USGS Publications Warehouse

Lewis, Jason M.

2010-01-01

Peak-streamflow regression equations were determined for estimating flows with exceedance probabilities from 50 to 0.2 percent for the state of Oklahoma. These regression equations incorporate basin characteristics to estimate peak-streamflow magnitude and frequency throughout the state by use of a generalized least squares regression analysis. The most statistically significant independent variables required to estimate peak-streamflow magnitude and frequency for unregulated streams in Oklahoma are contributing drainage area, mean-annual precipitation, and main-channel slope. The regression equations are applicable for watershed basins with drainage areas less than 2,510 square miles that are not affected by regulation. The resulting regression equations had a standard model error ranging from 31 to 46 percent. Annual-maximum peak flows observed at 231 streamflow-gaging stations through water year 2008 were used for the regression analysis. Gage peak-streamflow estimates were used from previous work unless 2008 gaging-station data were available, in which new peak-streamflow estimates were calculated. The U.S. Geological Survey StreamStats web application was used to obtain the independent variables required for the peak-streamflow regression equations. Limitations on the use of the regression equations and the reliability of regression estimates for natural unregulated streams are described. Log-Pearson Type III analysis information, basin and climate characteristics, and the peak-streamflow frequency estimates for the 231 gaging stations in and near Oklahoma are listed. Methodologies are presented to estimate peak streamflows at ungaged sites by using estimates from gaging stations on unregulated streams. For ungaged sites on urban streams and streams regulated by small floodwater retarding structures, an adjustment of the statewide regression equations for natural unregulated streams can be used to estimate peak-streamflow magnitude and frequency.

A method of examining the structure and topological properties of public-transport networks

NASA Astrophysics Data System (ADS)

Dimitrov, Stavri Dimitri; Ceder, Avishai (Avi)

2016-06-01

This work presents a new method of examining the structure of public-transport networks (PTNs) and analyzes their topological properties through a combination of computer programming, statistical data and large-network analyses. In order to automate the extraction, processing and exporting of data, a software program was developed allowing to extract the needed data from General Transit Feed Specification, thus overcoming difficulties occurring in accessing and collecting data. The proposed method was applied to a real-life PTN in Auckland, New Zealand, with the purpose of examining whether it showed characteristics of scale-free networks and exhibited features of ;small-world; networks. As a result, new regression equations were derived analytically describing observed, strong, non-linear relationships among the probabilities of randomly chosen stops in the PTN to be serviced by a given number of routes. The established dependence is best fitted by an exponential rather than a power-law function, showing that the PTN examined is neither random nor scale-free, but a mixture of the two. This finding explains the presence of hubs that are not typical of exponential networks and simultaneously not highly connected to the other nodes as is the case with scale-free networks. On the other hand, the observed values of the topological properties of the network show that although it is highly clustered, owing to its representation as a directed graph, it differs slightly from ;small-world; networks, which are characterized by strong clustering and a short average path length.

Assessment on spatiotemporal relationship between rainfall and cloud top temperature from new generation weather satellite imagery

NASA Astrophysics Data System (ADS)

Wei, Chiang; Yeh, Hui-Chung; Chen, Yen-Chang

2017-04-01

This study addressed the relationship between rainfall and cloud top temperature (CCT) from new generation satellite Himawari-8 imagery at different spatiotemporal scale. This satellite provides higher band, more bits for data format, spatial and temporal resolution compared with previous GMS series. The multi-infrared channels with 10-minute and 1-2 km resolution make it possible for rainfall estimating/forecasting in small/medium watershed. The preliminary result investigated at Chenyulan watershed (443.6 square kilometer) of Central Taiwan in 2016 Typhoon Megi shows the regression coefficient fitted by negative exponential equation of largest rainfall vs. CCT (B8 band) at pixel scale increases as time scales enlarges and reach 0.462 for 120-minute accumulative rainfall; the value (CTT of B15 band) decreases from 0.635 for 10-minute to 0.423 for 120-minute accumulative rainfall at basin-wide scale. More rainfall events for different regime are yet to evaluate to get solid results.

Effects of Economy Type and Nicotine on the Essential Value of Food in Rats

PubMed Central

Cassidy, Rachel N; Dallery, Jesse

2012-01-01

The exponential demand equation proposed by Hursh and Silberberg (2008) provides an estimate of the essential value of a good as a function of price. The model predicts that essential value should remain constant across changes in the magnitude of a reinforcer, but may change as a function of motivational operations. In Experiment 1, rats' demand for food across a sequence of fixed-ratio schedules was assessed during open and closed economy conditions and across one- and two-pellet per reinforcer delivery conditions. The exponential equation was fitted to the relation between fixed-ratio size and the logarithm of the absolute number of reinforcers. Estimates of the rate of change in elasticity of food, the proposed measure of essential value, were compared across conditions. Essential value was equivalent across magnitudes during the closed economy, but showed a slight decrease across magnitudes during the open economy. Experiment 2 explored the behavioral mechanisms of nicotine's effects on consumption with the results from Experiment 1 serving as a within-subject frame of reference. The same subjects were administered nicotine via subcutaneously implanted osmotic minipumps at a dose of 3 mg/kg/day and exposed to both the one- and two-pellet conditions under a closed economy. Although nicotine produced large decreases in demand, essential value was not significantly changed. The data from the present experiments provide further evidence for the adequacy of the exponential demand equation as a tool for quantifying the rate of change in elasticity of a good and for assessing behavioral mechanisms of drug action. PMID:22389525

Effects of economy type and nicotine on the essential value of food in rats.

PubMed

Cassidy, Rachel N; Dallery, Jesse

2012-03-01

The exponential demand equation proposed by Hursh and Silberberg (2008) provides an estimate of the essential value of a good as a function of price. The model predicts that essential value should remain constant across changes in the magnitude of a reinforcer, but may change as a function of motivational operations. In Experiment 1, rats' demand for food across a sequence of fixed-ratio schedules was assessed during open and closed economy conditions and across one- and two-pellet per reinforcer delivery conditions. The exponential equation was fitted to the relation between fixed-ratio size and the logarithm of the absolute number of reinforcers. Estimates of the rate of change in elasticity of food, the proposed measure of essential value, were compared across conditions. Essential value was equivalent across magnitudes during the closed economy, but showed a slight decrease across magnitudes during the open economy. Experiment 2 explored the behavioral mechanisms of nicotine's effects on consumption with the results from Experiment 1 serving as a within-subject frame of reference. The same subjects were administered nicotine via subcutaneously implanted osmotic minipumps at a dose of 3 mg/kg/day and exposed to both the one- and two-pellet conditions under a closed economy. Although nicotine produced large decreases in demand, essential value was not significantly changed. The data from the present experiments provide further evidence for the adequacy of the exponential demand equation as a tool for quantifying the rate of change in elasticity of a good and for assessing behavioral mechanisms of drug action.

Asymmetrical flow field-flow fractionation coupled with multiple detections: A complementary approach in the characterization of egg yolk plasma.

PubMed

Dou, Haiyang; Li, Yueqiu; Choi, Jaeyeong; Huo, Shuying; Ding, Liang; Shen, Shigang; Lee, Seungho

2016-09-23

The capability of asymmetrical flow field-flow fractionation (AF4) coupled with UV/VIS, multiangle light scattering (MALS) and quasi-elastic light scattering (QELS) (AF4-UV-MALS-QELS) for separation and characterization of egg yolk plasma was evaluated. The accuracy of hydrodynamic radius (Rh) obtained from QELS and AF4 theory (using both simplified and full expression of AF4 retention equations) was discussed. The conformation of low density lipoprotein (LDL) and its aggregates in egg yolk plasma was discussed based on the ratio of radius of gyration (Rg) to Rh together with the results from bio-transmission electron microscopy (Bio-TEM). The results indicate that the full retention equation is more relevant than simplified version for the Rh determination at high cross flow rate. The Rh from online QELS is reliable only at a specific range of sample concentration. The effect of programmed cross flow rate (linear and exponential decay) on the analysis of egg yolk plasma was also investigated. It was found that the use of an exponentially decaying cross flow rate not only reduces the AF4 analysis time of the egg yolk plasma, but also provides better resolution than the use of either a constant or linearly decaying cross flow rate. A combination of an exponentially decaying cross flow AF4-UV-MALS-QELS and the utilization of full retention equation was proved to be a useful method for the separation and characterization of egg yolk plasma. Copyright © 2016 Elsevier B.V. All rights reserved.

Combining Relevance Vector Machines and exponential regression for bearing residual life estimation

NASA Astrophysics Data System (ADS)

Di Maio, Francesco; Tsui, Kwok Leung; Zio, Enrico

2012-08-01

In this paper we present a new procedure for estimating the bearing Residual Useful Life (RUL) by combining data-driven and model-based techniques. Respectively, we resort to (i) Relevance Vector Machines (RVMs) for selecting a low number of significant basis functions, called Relevant Vectors (RVs), and (ii) exponential regression to compute and continuously update residual life estimations. The combination of these techniques is developed with reference to partially degraded thrust ball bearings and tested on real world vibration-based degradation data. On the case study considered, the proposed procedure outperforms other model-based methods, with the added value of an adequate representation of the uncertainty associated to the estimates of the quantification of the credibility of the results by the Prognostic Horizon (PH) metric.

Regression Equations for Estimating Flood Flows at Selected Recurrence Intervals for Ungaged Streams in Pennsylvania

USGS Publications Warehouse

Roland, Mark A.; Stuckey, Marla H.

2008-01-01

Regression equations were developed for estimating flood flows at selected recurrence intervals for ungaged streams in Pennsylvania with drainage areas less than 2,000 square miles. These equations were developed utilizing peak-flow data from 322 streamflow-gaging stations within Pennsylvania and surrounding states. All stations used in the development of the equations had 10 or more years of record and included active and discontinued continuous-record as well as crest-stage partial-record stations. The state was divided into four regions, and regional regression equations were developed to estimate the 2-, 5-, 10-, 50-, 100-, and 500-year recurrence-interval flood flows. The equations were developed by means of a regression analysis that utilized basin characteristics and flow data associated with the stations. Significant explanatory variables at the 95-percent confidence level for one or more regression equations included the following basin characteristics: drainage area; mean basin elevation; and the percentages of carbonate bedrock, urban area, and storage within a basin. The regression equations can be used to predict the magnitude of flood flows for specified recurrence intervals for most streams in the state; however, they are not valid for streams with drainage areas generally greater than 2,000 square miles or with substantial regulation, diversion, or mining activity within the basin. Estimates of flood-flow magnitude and frequency for streamflow-gaging stations substantially affected by upstream regulation are also presented.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

An exponential model equation for thiamin loss in irradiated ground pork as a function of dose and temperature of irradiation

NASA Astrophysics Data System (ADS)

Fox, J. B.; Thayer, D. W.; Phillips, J. G.

The effect of low dose γ-irradiation on the thiamin content of ground pork was studied in the range of 0-14 kGy at 2°C and at radiation doses from 0.5 to 7 kGy at temperatures -20, 10, 0, 10 and 20°C. The detailed study at 2°C showed that loss of thiamin was exponential down to 0kGy. An exponential expression was derived for the effect of radiation dose and temperature of irradiation on thiamin loss, and compared with a previously derived general linear expression. Both models were accurate depictions of the data, but the exponential expression showed a significant decrease in the rate of loss between 0 and -10°C. This is the range over which water in meat freezes, the decrease being due to the immobolization of reactive radiolytic products of water in ice crystals.

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.

Use and interpretation of logistic regression in habitat-selection studies

USGS Publications Warehouse

Keating, Kim A.; Cherry, Steve

2004-01-01

 Logistic regression is an important tool for wildlife habitat-selection studies, but the method frequently has been misapplied due to an inadequate understanding of the logistic model, its interpretation, and the influence of sampling design. To promote better use of this method, we review its application and interpretation under 3 sampling designs: random, case-control, and use-availability. Logistic regression is appropriate for habitat use-nonuse studies employing random sampling and can be used to directly model the conditional probability of use in such cases. Logistic regression also is appropriate for studies employing case-control sampling designs, but careful attention is required to interpret results correctly. Unless bias can be estimated or probability of use is small for all habitats, results of case-control studies should be interpreted as odds ratios, rather than probability of use or relative probability of use. When data are gathered under a use-availability design, logistic regression can be used to estimate approximate odds ratios if probability of use is small, at least on average. More generally, however, logistic regression is inappropriate for modeling habitat selection in use-availability studies. In particular, using logistic regression to fit the exponential model of Manly et al. (2002:100) does not guarantee maximum-likelihood estimates, valid probabilities, or valid likelihoods. We show that the resource selection function (RSF) commonly used for the exponential model is proportional to a logistic discriminant function. Thus, it may be used to rank habitats with respect to probability of use and to identify important habitat characteristics or their surrogates, but it is not guaranteed to be proportional to probability of use. Other problems associated with the exponential model also are discussed. We describe an alternative model based on Lancaster and Imbens (1996) that offers a method for estimating conditional probability of use in use-availability studies. Although promising, this model fails to converge to a unique solution in some important situations. Further work is needed to obtain a robust method that is broadly applicable to use-availability studies.

On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Arnold, Anton; Einav, Amit; Wöhrer, Tobias

2018-06-01

We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in time. The novelty of our study lies in the amalgamation of spectral theory and a quantitative non-symmetric hypercontractivity result, as opposed to the usual approach of the entropy method.

On the renewal risk model under a threshold strategy

NASA Astrophysics Data System (ADS)

Dong, Yinghui; Wang, Guojing; Yuen, Kam C.

2009-08-01

In this paper, we consider the renewal risk process under a threshold dividend payment strategy. For this model, the expected discounted dividend payments and the Gerber-Shiu expected discounted penalty function are investigated. Integral equations, integro-differential equations and some closed form expressions for them are derived. When the claims are exponentially distributed, it is verified that the expected penalty of the deficit at ruin is proportional to the ruin probability.

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

NASA Astrophysics Data System (ADS)

Mestel, B. D.; Osbaldestin, A. H.

2004-10-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

Baecklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation

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

Qu Qixing; Sun Kun; Jiang Yan

2011-01-15

By using Bell polynomials and symbolic computation, we investigate the Caudrey-Dodd-Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Baecklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

Reformulating the Schrödinger equation as a Shabat-Zakharov system

NASA Astrophysics Data System (ADS)

Boonserm, Petarpa; Visser, Matt

2010-02-01

We reformulate the second-order Schrödinger equation as a set of two coupled first-order differential equations, a so-called "Shabat-Zakharov system" (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasize the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrödinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ordinary differential equation.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

Regression equations to estimate seasonal flow duration, n-day high-flow frequency, and n-day low-flow frequency at sites in North Dakota using data through water year 2009

USGS Publications Warehouse

Williams-Sether, Tara; Gross, Tara A.

2016-02-09

Seasonal mean daily flow data from 119 U.S. Geological Survey streamflow-gaging stations in North Dakota; the surrounding states of Montana, Minnesota, and South Dakota; and the Canadian provinces of Manitoba and Saskatchewan with 10 or more years of unregulated flow record were used to develop regression equations for flow duration, n-day high flow and n-day low flow using ordinary least-squares and Tobit regression techniques. Regression equations were developed for seasonal flow durations at the 10th, 25th, 50th, 75th, and 90th percent exceedances; the 1-, 7-, and 30-day seasonal mean high flows for the 10-, 25-, and 50-year recurrence intervals; and the 1-, 7-, and 30-day seasonal mean low flows for the 2-, 5-, and 10-year recurrence intervals. Basin and climatic characteristics determined to be significant explanatory variables in one or more regression equations included drainage area, percentage of basin drainage area that drains to isolated lakes and ponds, ruggedness number, stream length, basin compactness ratio, minimum basin elevation, precipitation, slope ratio, stream slope, and soil permeability. The adjusted coefficient of determination for the n-day high-flow regression equations ranged from 55.87 to 94.53 percent. The Chi2 values for the duration regression equations ranged from 13.49 to 117.94, whereas the Chi2 values for the n-day low-flow regression equations ranged from 4.20 to 49.68.

An efficient technique for higher order fractional differential equation.

PubMed

Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

2016-01-01

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St Clair River system (Michigan, USA)

USGS Publications Warehouse

Craig, J.M.; Thomas, M.V.; Nichols, S.J.

2005-01-01

Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May-September, 1997-2002. Analysis of covariance found no difference in the length-weight relationship between sampling gear or sex. Least-squares regression of log10W ?? log10TL produced the overall equation logW = 3.365logTL - 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn - W/[(4.786 ?? 10-10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes. ?? 2005 Blackwell Verlag, Berlin.

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St. Clair River system (Michigan, USA)

USGS Publications Warehouse

Craig, Jaquelyn M.; Thomas, Michael V.; Nichols, S. Jerrine

2005-01-01

Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length-weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May-September, 1997-2002. Analysis of covariance found no difference in the length-weight relationship between sampling gear or sex. Least-squares regression of log10W x log10TL produced the overall equation logW = 3.365logTL - 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn = W/ [(4.786 x 10-10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes.

Further Improvement in 3DGRAPE

NASA Technical Reports Server (NTRS)

Alter, Stephen

2004-01-01

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Razumikhin-Type Stability Criteria for Differential Equations with Delayed Impulses.

PubMed

Wang, Qing; Zhu, Quanxin

2013-01-01

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

[Ultrasonic measurements of fetal thalamus, caudate nucleus and lenticular nucleus in prenatal diagnosis].

PubMed

Yang, Ruiqi; Wang, Fei; Zhang, Jialing; Zhu, Chonglei; Fan, Limei

2015-05-19

To establish the reference values of thalamus, caudate nucleus and lenticular nucleus diameters through fetal thalamic transverse section. A total of 265 fetuses at our hospital were randomly selected from November 2012 to August 2014. And the transverse and length diameters of thalamus, caudate nucleus and lenticular nucleus were measured. SPSS 19.0 statistical software was used to calculate the regression curve of fetal diameter changes and gestational weeks of pregnancy. P < 0.05 was considered as having statistical significance. The linear regression equation of fetal thalamic length diameter and gestational week was: Y = 0.051X+0.201, R = 0.876, linear regression equation of thalamic transverse diameter and fetal gestational week was: Y = 0.031X+0.229, R = 0.817, linear regression equation of fetal head of caudate nucleus length diameter and gestational age was: Y = 0.033X+0.101, R = 0.722, linear regression equation of fetal head of caudate nucleus transverse diameter and gestational week was: R = 0.025 - 0.046, R = 0.711, linear regression equation of fetal lentiform nucleus length diameter and gestational week was: Y = 0.046+0.229, R = 0.765, linear regression equation of fetal lentiform nucleus diameter and gestational week was: Y = 0.025 - 0.05, R = 0.772. Ultrasonic measurement of diameter of fetal thalamus caudate nucleus, and lenticular nucleus through thalamic transverse section is simple and convenient. And measurements increase with fetal gestational weeks and there is linear regression relationship between them.

Stochastic processes in cosmology

NASA Astrophysics Data System (ADS)

Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.

1987-08-01

The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

NASA Technical Reports Server (NTRS)

Rodriguez, Pedro I.

1986-01-01

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Ion transfer through solvent polymeric membranes driven by an exponential current flux.

PubMed

Molina, A; Torralba, E; González, J; Serna, C; Ortuño, J A

2011-03-21

General analytical equations which govern ion transfer through liquid membranes with one and two polarized interfaces driven by an exponential current flux are derived. Expressions for the transient and stationary E-t, dt/dE-E and dI/dE-E curves are obtained, and the evolution from transient to steady behaviour has been analyzed in depth. We have also shown mathematically that the voltammetric and stationary chronopotentiometric I(N)-E curves are identical (with E being the applied potential for voltammetric techniques and the measured potential for chronopotentiometric techniques), and hence, their derivatives provide identical information.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Estimating design-flood discharges for streams in Iowa using drainage-basin and channel-geometry characteristics

USGS Publications Warehouse

Eash, D.A.

1993-01-01

Procedures provided for applying the drainage-basin and channel-geometry regression equations depend on whether the design-flood discharge estimate is for a site on an ungaged stream, an ungaged site on a gaged stream, or a gaged site. When both a drainage-basin and a channel-geometry regression-equation estimate are available for a stream site, a procedure is presented for determining a weighted average of the two flood estimates. The drainage-basin regression equations are applicable to unregulated rural drainage areas less than 1,060 square miles, and the channel-geometry regression equations are applicable to unregulated rural streams in Iowa with stabilized channels.

Regression Simulation Model. Appendix X. Users Manual,

DTIC Science & Technology

1981-03-01

change as the prediction equations become refined. Whereas no notice will be provided when the changes are made, the programs will be modified such that...NATIONAL BUREAU Of STANDARDS 1963 A ___,_ __ _ __ _ . APPENDIX X ( R4/ EGRESSION IMULATION ’jDEL. Ape’A ’) 7 USERS MANUA submitted to The Great River...regression analysis and to establish a prediction equation (model). The prediction equation contains the partial regression coefficients (B-weights) which

Is it growing exponentially fast? -- Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics.

PubMed

Chowell, Gerardo; Viboud, Cécile

2016-10-01

The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.

Force on a storage ring vacuum chamber after sudden turn-off of a magnet power supply

NASA Astrophysics Data System (ADS)

Sinha, Gautam; Prabhu, S. S.

2011-10-01

We are commissioning a 2.5 GeV synchrotron radiation source (SRS) where electrons travel in high vacuum inside the vacuum chambers made of aluminum alloys. These chambers are kept between the pole gaps of magnets and are made to facilitate the radiation coming out of the storage ring to the experimental station. These chambers are connected by metallic bellows. During the commissioning phase of the SRS, the metallic bellows became ruptured due to the frequent tripping of the dipole magnet power supply. The machine was down for quite some time. In the case of a power supply trip, the current in the magnets decays exponentially. It was observed experimentally that the fast B field decay generates a large eddy current in the chambers and consequently the chambers are subjected to a huge Lorentz force. This motivated us to develop a theoretical model to study the force acting on a metallic plate when exposed to an exponentially decaying field and then to extend it for a rectangular vacuum chamber. The problem is formulated using Maxwell’s equations and converted to the inhomogeneous Helmholtz equation. After taking the Laplace transform, the equation is solved with appropriate boundary conditions. Final results are obtained after taking the appropriate inverse Laplace transform. The expressions for eddy current contour and magnetic field produced by the eddy current are also derived. Variations of the force on chambers of different wall thickness due to spatially varying and exponentially time decaying field are presented. The result is a general theory which can be applied to different geometries and calculation of power loss as well. Comparisons are made with results obtained by simulation using a finite element based code, for quick verification of the theoretical model.

A new concept for stainless steels ranking upon the resistance to cavitation erosion

NASA Astrophysics Data System (ADS)

Bordeasu, I.; Popoviciu, M. O.; Salcianu, L. C.; Ghera, C.; Micu, L. M.; Badarau, R.; Iosif, A.; Pirvulescu, L. D.; Podoleanu, C. E.

2017-01-01

In present, the ranking of materials as their resistance to cavitation erosion is obtained by using laboratory tests finalized with the characteristic curves mean depth erosion against time MDE(t) and mean depth erosion rate against time MDER(t). In some previous papers, Bordeasu and co-workers give procedures to establish exponential equation representing the curves, with minimum scatter of the experimental obtained results. For a given material, both exponential equations MDE(t) and MDER(t) have the same values for the parameters of scale and for the shape one. For the ranking of materials is sometimes important to establish single figure. Till now in Timisoara Polytechnic University Cavitation Laboratory were used three such numbers: the stable value of the curve MDER(t), the resistance to cavitation erosion (Rcav ≡ 1/MDERstable) and the normalized cavitation resistance Rns which is the rate between vs = MDERstable for the analyzed material and vse= MDERse the mean depth erosion rate for the steel OH12NDL (Rns = vs/vse ). OH12NDL is a material used for manufacturing the blades of numerous Kaplan turbines in Romania for which both cavitation erosion laboratory tests and field measurements of cavitation erosions are available. In the present paper we recommend a new method for ranking the materials upon cavitation erosion resistance. This method uses the scale and shape parameters of the exponential equations which represents the characteristic cavitation erosion curves. Till now the method was applied only for stainless steels. The experimental results show that the scale parameter represents an excellent method for ranking the stainless steels. In the future this kind of ranking will be tested also for other materials especially for bronzes used for manufacturing ship propellers.

Contribution to modeling the viscosity Arrhenius-type equation for saturated pure fluids

NASA Astrophysics Data System (ADS)

Tian, Jianxiang; Zhang, Laibin

2016-09-01

Recently, Haj-Kacem et al. proposed an equation modeling the relationship between the two parameters of viscosity Arrhenius-type equations [Fluid Phase Equilibria 383, 11 (2014)]. The authors found that the two parameters are dependent upon each other in an exponential function form. In this paper, we reconsidered their ideas and calculated the two parameter values for 49 saturated pure fluids by using the experimental data in the NIST WebBook. Our conclusion is different with the ones of Haj-Kacem et al. We found that (the linearity shown by) the Arrhenius equation stands strongly only in low temperature range and that the two parameters of the Arrhenius equation are independent upon each other in the whole temperature range from the triple point to the critical point.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Growth and mortality of larval sunfish in backwaters of the upper Mississippi River

USGS Publications Warehouse

Zigler, S.J.; Jennings, C.A.

1993-01-01

The authors estimated the growth and mortality of larval sunfish Lepomis spp. in backwater habitats of the upper Mississippi River with an otolith-based method and a length-based method. Fish were sampled with plankton nets at one station in Navigation Pools 8 and 14 in 1989 and at two stations in Pool 8 in 1990. For both methods, growth was modeled with an exponential equation, and instantaneous mortality was estimated by regressing the natural logarithm of fish catch for each 1-mm size-group against the estimated age of the group, which was derived from the growth equations. At two of the stations, the otolith-based method provided more precise estimates of sunfish growth than the length-based method. We were able to compare length-based and otolith-based estimates of sunfish mortality only at the two stations where we caught the largest numbers of sunfish. Estimates of mortality were similar for both methods in Pool 14, where catches were higher, but the length-based method gave significantly higher estimates in Pool 8, where the catches were lower. The otolith- based method required more laboratory analysis, but provided better estimates of the growth and mortality than the length-based method when catches were low. However, the length-based method was more cost- effective for estimating growth and mortality when catches were large.

Methods for estimating selected low-flow frequency statistics and harmonic mean flows for streams in Iowa

USGS Publications Warehouse

Eash, David A.; Barnes, Kimberlee K.

2017-01-01

A statewide study was conducted to develop regression equations for estimating six selected low-flow frequency statistics and harmonic mean flows for ungaged stream sites in Iowa. The estimation equations developed for the six low-flow frequency statistics include: the annual 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years, the annual 30-day mean low flow for a recurrence interval of 5 years, and the seasonal (October 1 through December 31) 1- and 7-day mean low flows for a recurrence interval of 10 years. Estimation equations also were developed for the harmonic-mean-flow statistic. Estimates of these seven selected statistics are provided for 208 U.S. Geological Survey continuous-record streamgages using data through September 30, 2006. The study area comprises streamgages located within Iowa and 50 miles beyond the State's borders. Because trend analyses indicated statistically significant positive trends when considering the entire period of record for the majority of the streamgages, the longest, most recent period of record without a significant trend was determined for each streamgage for use in the study. The median number of years of record used to compute each of these seven selected statistics was 35. Geographic information system software was used to measure 54 selected basin characteristics for each streamgage. Following the removal of two streamgages from the initial data set, data collected for 206 streamgages were compiled to investigate three approaches for regionalization of the seven selected statistics. Regionalization, a process using statistical regression analysis, provides a relation for efficiently transferring information from a group of streamgages in a region to ungaged sites in the region. The three regionalization approaches tested included statewide, regional, and region-of-influence regressions. For the regional regression, the study area was divided into three low-flow regions on the basis of hydrologic characteristics, landform regions, and soil regions. A comparison of root mean square errors and average standard errors of prediction for the statewide, regional, and region-of-influence regressions determined that the regional regression provided the best estimates of the seven selected statistics at ungaged sites in Iowa. Because a significant number of streams in Iowa reach zero flow as their minimum flow during low-flow years, four different types of regression analyses were used: left-censored, logistic, generalized-least-squares, and weighted-least-squares regression. A total of 192 streamgages were included in the development of 27 regression equations for the three low-flow regions. For the northeast and northwest regions, a censoring threshold was used to develop 12 left-censored regression equations to estimate the 6 low-flow frequency statistics for each region. For the southern region a total of 12 regression equations were developed; 6 logistic regression equations were developed to estimate the probability of zero flow for the 6 low-flow frequency statistics and 6 generalized least-squares regression equations were developed to estimate the 6 low-flow frequency statistics, if nonzero flow is estimated first by use of the logistic equations. A weighted-least-squares regression equation was developed for each region to estimate the harmonic-mean-flow statistic. Average standard errors of estimate for the left-censored equations for the northeast region range from 64.7 to 88.1 percent and for the northwest region range from 85.8 to 111.8 percent. Misclassification percentages for the logistic equations for the southern region range from 5.6 to 14.0 percent. Average standard errors of prediction for generalized least-squares equations for the southern region range from 71.7 to 98.9 percent and pseudo coefficients of determination for the generalized-least-squares equations range from 87.7 to 91.8 percent. Average standard errors of prediction for weighted-least-squares equations developed for estimating the harmonic-mean-flow statistic for each of the three regions range from 66.4 to 80.4 percent. The regression equations are applicable only to stream sites in Iowa with low flows not significantly affected by regulation, diversion, or urbanization and with basin characteristics within the range of those used to develop the equations. If the equations are used at ungaged sites on regulated streams, or on streams affected by water-supply and agricultural withdrawals, then the estimates will need to be adjusted by the amount of regulation or withdrawal to estimate the actual flow conditions if that is of interest. Caution is advised when applying the equations for basins with characteristics near the applicable limits of the equations and for basins located in karst topography. A test of two drainage-area ratio methods using 31 pairs of streamgages, for the annual 7-day mean low-flow statistic for a recurrence interval of 10 years, indicates a weighted drainage-area ratio method provides better estimates than regional regression equations for an ungaged site on a gaged stream in Iowa when the drainage-area ratio is between 0.5 and 1.4. These regression equations will be implemented within the U.S. Geological Survey StreamStats web-based geographic-information-system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the seven selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these seven selected statistics are provided for the streamgage.

Boiling Temperature vs. Composition. An Almost-Exact Explicit Equation for a Binary Mixture Following Raoult's Law.

ERIC Educational Resources Information Center

Cardinali, Mario Emilio; Giomini, Claudio

1989-01-01

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

A multigrid solver for the semiconductor equations

NASA Technical Reports Server (NTRS)

Bachmann, Bernhard

1993-01-01

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

Rimonabant reduces the essential value of food in the genetically obese Zucker rat: an exponential demand analysis.

PubMed

Rasmussen, Erin B; Reilly, William; Buckley, Jessica; Boomhower, Steven R

2012-02-01

Research on free-food intake suggests that cannabinoids are implicated in the regulation of feeding. Few studies, however, have characterized how environmental factors that affect food procurement interact with cannabinoid drugs that reduce food intake. Demand analysis provides a framework to understand how cannabinoid blockers, such as rimonabant, interact with effort in reducing demand for food. The present study examined the effects rimonabant had on demand for sucrose in obese Zucker rats when effort to obtain food varied and characterized the data using the exponential ("essential value") model of demand. Twenty-nine male (15 lean, 14 obese) Zucker rats lever-pressed under eight fixed ratio (FR) schedules of sucrose reinforcement, in which the number of lever-presses to gain access to a single sucrose pellet varied between 1 and 300. After behavior stabilized under each FR schedule, acute doses of rimonabant (1-10mg/kg) were administered prior to some sessions. The number of food reinforcers and responses in each condition was averaged and the exponential and linear demand equations were fit to the data. These demand equations quantify the value of a reinforcer by its sensitivity to price (FR) increases. Under vehicle conditions, obese Zucker rats consumed more sucrose pellets than leans at smaller fixed ratios; however, they were equally sensitive to price increases with both models of demand. Rimonabant dose-dependently reduced reinforcers and responses for lean and obese rats across all FR schedules. Data from the exponential analysis suggest that rimonabant dose-dependently increased elasticity, i.e., reduced the essential value of sucrose, a finding that is consistent with graphical depictions of normalized demand curves. Copyright © 2011 Elsevier Inc. All rights reserved.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

Estimating Flow-Duration and Low-Flow Frequency Statistics for Unregulated Streams in Oregon

USGS Publications Warehouse

Risley, John; Stonewall, Adam J.; Haluska, Tana

2008-01-01

Flow statistical datasets, basin-characteristic datasets, and regression equations were developed to provide decision makers with surface-water information needed for activities such as water-quality regulation, water-rights adjudication, biological habitat assessment, infrastructure design, and water-supply planning and management. The flow statistics, which included annual and monthly period of record flow durations (5th, 10th, 25th, 50th, and 95th percent exceedances) and annual and monthly 7-day, 10-year (7Q10) and 7-day, 2-year (7Q2) low flows, were computed at 466 streamflow-gaging stations at sites with unregulated flow conditions throughout Oregon and adjacent areas of neighboring States. Regression equations, created from the flow statistics and basin characteristics of the stations, can be used to estimate flow statistics at ungaged stream sites in Oregon. The study area was divided into 10 regression modeling regions based on ecological, topographic, geologic, hydrologic, and climatic criteria. In total, 910 annual and monthly regression equations were created to predict the 7 flow statistics in the 10 regions. Equations to predict the five flow-duration exceedance percentages and the two low-flow frequency statistics were created with Ordinary Least Squares and Generalized Least Squares regression, respectively. The standard errors of estimate of the equations created to predict the 5th and 95th percent exceedances had medians of 42.4 and 64.4 percent, respectively. The standard errors of prediction of the equations created to predict the 7Q2 and 7Q10 low-flow statistics had medians of 51.7 and 61.2 percent, respectively. Standard errors for regression equations for sites in western Oregon were smaller than those in eastern Oregon partly because of a greater density of available streamflow-gaging stations in western Oregon than eastern Oregon. High-flow regression equations (such as the 5th and 10th percent exceedances) also generally were more accurate than the low-flow regression equations (such as the 95th percent exceedance and 7Q10 low-flow statistic). The regression equations predict unregulated flow conditions in Oregon. Flow estimates need to be adjusted if they are used at ungaged sites that are regulated by reservoirs or affected by water-supply and agricultural withdrawals if actual flow conditions are of interest. The regression equations are installed in the USGS StreamStats Web-based tool (http://water.usgs.gov/osw/streamstats/index.html, accessed July 16, 2008). StreamStats provides users with a set of annual and monthly flow-duration and low-flow frequency estimates for ungaged sites in Oregon in addition to the basin characteristics for the sites. Prediction intervals at the 90-percent confidence level also are automatically computed.

Methods for estimating selected low-flow frequency statistics for unregulated streams in Kentucky

USGS Publications Warehouse

Martin, Gary R.; Arihood, Leslie D.

2010-01-01

This report provides estimates of, and presents methods for estimating, selected low-flow frequency statistics for unregulated streams in Kentucky including the 30-day mean low flows for recurrence intervals of 2 and 5 years (30Q2 and 30Q5) and the 7-day mean low flows for recurrence intervals of 5, 10, and 20 years (7Q2, 7Q10, and 7Q20). Estimates of these statistics are provided for 121 U.S. Geological Survey streamflow-gaging stations with data through the 2006 climate year, which is the 12-month period ending March 31 of each year. Data were screened to identify the periods of homogeneous, unregulated flows for use in the analyses. Logistic-regression equations are presented for estimating the annual probability of the selected low-flow frequency statistics being equal to zero. Weighted-least-squares regression equations were developed for estimating the magnitude of the nonzero 30Q2, 30Q5, 7Q2, 7Q10, and 7Q20 low flows. Three low-flow regions were defined for estimating the 7-day low-flow frequency statistics. The explicit explanatory variables in the regression equations include total drainage area and the mapped streamflow-variability index measured from a revised statewide coverage of this characteristic. The percentage of the station low-flow statistics correctly classified as zero or nonzero by use of the logistic-regression equations ranged from 87.5 to 93.8 percent. The average standard errors of prediction of the weighted-least-squares regression equations ranged from 108 to 226 percent. The 30Q2 regression equations have the smallest standard errors of prediction, and the 7Q20 regression equations have the largest standard errors of prediction. The regression equations are applicable only to stream sites with low flows unaffected by regulation from reservoirs and local diversions of flow and to drainage basins in specified ranges of basin characteristics. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features.

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

NASA Astrophysics Data System (ADS)

Shchigolev, V. K.; Bezbatko, D. N.

2018-04-01

The present study deals with the Friedmann-Robertson-Walker cosmological models with Yang-Mills (YM) fields in Lyra geometry. The energy-momentum tensor of the YM fields for our models is obtained with the help of an exact solution to the YM equations with minimal coupling to gravity. Two specific exact solutions of the model are obtained regarding the effective equation of state and the exponential law of expansion. The physical and geometric behavior of the model is also discussed.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

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

Exact anisotropic viscous fluid solutions of Einstein's equations

NASA Astrophysics Data System (ADS)

Goenner, H. F. M.; Kowalewski, F.

1989-05-01

A method for obtaining anisotropic, rotationless viscous fluid matter solutions of Bianchi type I and Segré type [1, 111] with the barotropic equation of state is presented. Solutions for which the anisotropy decreases exponentially or with a power law as well as solutions with average Hubble parameterH ˜t -1 are discussed. Also, a class of solutions with constant anisotropy and Bianchi type VIh is found. The dominant energy condition holds and the transport coefficients show the right sign.

The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Shan; Liu, Zaiming

2010-03-01

In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

Regression Equations for Monthly and Annual Mean and Selected Percentile Streamflows for Ungaged Rivers in Maine

USGS Publications Warehouse

Dudley, Robert W.

2015-12-03

The largest average errors of prediction are associated with regression equations for the lowest streamflows derived for months during which the lowest streamflows of the year occur (such as the 5 and 1 monthly percentiles for August and September). The regression equations have been derived on the basis of streamflow and basin characteristics data for unregulated, rural drainage basins without substantial streamflow or drainage modifications (for example, diversions and (or) regulation by dams or reservoirs, tile drainage, irrigation, channelization, and impervious paved surfaces), therefore using the equations for regulated or urbanized basins with substantial streamflow or drainage modifications will yield results of unknown error. Input basin characteristics derived using techniques or datasets other than those documented in this report or using values outside the ranges used to develop these regression equations also will yield results of unknown error.

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.

A Semi-Analytical Extraction Method for Interface and Bulk Density of States in Metal Oxide Thin-Film Transistors

PubMed Central

Chen, Weifeng; Wu, Weijing; Zhou, Lei; Xu, Miao; Wang, Lei; Peng, Junbiao

2018-01-01

A semi-analytical extraction method of interface and bulk density of states (DOS) is proposed by using the low-frequency capacitance–voltage characteristics and current–voltage characteristics of indium zinc oxide thin-film transistors (IZO TFTs). In this work, an exponential potential distribution along the depth direction of the active layer is assumed and confirmed by numerical solution of Poisson’s equation followed by device simulation. The interface DOS is obtained as a superposition of constant deep states and exponential tail states. Moreover, it is shown that the bulk DOS may be represented by the superposition of exponential deep states and exponential tail states. The extracted values of bulk DOS and interface DOS are further verified by comparing the measured transfer and output characteristics of IZO TFTs with the simulation results by a 2D device simulator ATLAS (Silvaco). As a result, the proposed extraction method may be useful for diagnosing and characterising metal oxide TFTs since it is fast to extract interface and bulk density of states (DOS) simultaneously. PMID:29534492

Comparative evaluation of urban storm water quality models

NASA Astrophysics Data System (ADS)

Vaze, J.; Chiew, Francis H. S.

2003-10-01

The estimation of urban storm water pollutant loads is required for the development of mitigation and management strategies to minimize impacts to receiving environments. Event pollutant loads are typically estimated using either regression equations or "process-based" water quality models. The relative merit of using regression models compared to process-based models is not clear. A modeling study is carried out here to evaluate the comparative ability of the regression equations and process-based water quality models to estimate event diffuse pollutant loads from impervious surfaces. The results indicate that, once calibrated, both the regression equations and the process-based model can estimate event pollutant loads satisfactorily. In fact, the loads estimated using the regression equation as a function of rainfall intensity and runoff rate are better than the loads estimated using the process-based model. Therefore, if only estimates of event loads are required, regression models should be used because they are simpler and require less data compared to process-based models.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

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

Pendulum Mass Affects the Measurement of Articular Friction Coefficient

PubMed Central

Akelman, Matthew R.; Teeple, Erin; Machan, Jason T.; Crisco, Joseph J.; Jay, Gregory D.; Fleming, Braden C.

2012-01-01

Friction measurements of articular cartilage are important to determine the relative tribologic contributions made by synovial fluid or cartilage, and to assess the efficacy of therapies for preventing the development of post-traumatic osteoarthritis. Stanton’s equation is the most frequently used formula for estimating the whole joint friction coefficient (μ) of an articular pendulum, and assumes pendulum energy loss through a mass-independent mechanism. This study examines if articular pendulum energy loss is indeed mass independent, and compares Stanton’s model to an alternative model, which incorporates viscous damping, for calculating μ. Ten loads (25-100% body weight) were applied in a random order to an articular pendulum using the knees of adult male Hartley guinea pigs (n = 4) as the fulcrum. Motion of the decaying pendulum was recorded and μ was estimated using two models: Stanton’s equation, and an exponential decay function incorporating a viscous damping coefficient. μ estimates decreased as mass increased for both models. Exponential decay model fit error values were 82% less than the Stanton model. These results indicate that μ decreases with increasing mass, and that an exponential decay model provides a better fit for articular pendulum data at all mass values. In conclusion, inter-study comparisons of articular pendulum μ values should not be made without recognizing the loads used, as μ values are mass dependent. PMID:23122223

Pendulum mass affects the measurement of articular friction coefficient.

PubMed

Akelman, Matthew R; Teeple, Erin; Machan, Jason T; Crisco, Joseph J; Jay, Gregory D; Fleming, Braden C

2013-02-01

Friction measurements of articular cartilage are important to determine the relative tribologic contributions made by synovial fluid or cartilage, and to assess the efficacy of therapies for preventing the development of post-traumatic osteoarthritis. Stanton's equation is the most frequently used formula for estimating the whole joint friction coefficient (μ) of an articular pendulum, and assumes pendulum energy loss through a mass-independent mechanism. This study examines if articular pendulum energy loss is indeed mass independent, and compares Stanton's model to an alternative model, which incorporates viscous damping, for calculating μ. Ten loads (25-100% body weight) were applied in a random order to an articular pendulum using the knees of adult male Hartley guinea pigs (n=4) as the fulcrum. Motion of the decaying pendulum was recorded and μ was estimated using two models: Stanton's equation, and an exponential decay function incorporating a viscous damping coefficient. μ estimates decreased as mass increased for both models. Exponential decay model fit error values were 82% less than the Stanton model. These results indicate that μ decreases with increasing mass, and that an exponential decay model provides a better fit for articular pendulum data at all mass values. In conclusion, inter-study comparisons of articular pendulum μ values should not be made without recognizing the loads used, as μ values are mass dependent. Copyright © 2012 Elsevier Ltd. All rights reserved.

Boundary control of anti-symmetric vibration of satellite with flexible appendages in planar motion with exponential stability

NASA Astrophysics Data System (ADS)

Rad, Hossein Kaviani; Salarieh, Hassan; Alasty, Aria; Vatankhah, Ramin

2018-06-01

In this research, we have investigated the planar maneuver of a flexible satellite with appendages anti-symmetric vibration. The hybrid governing equations are comprised of coupled partial and ordinary differential equations which are derived by employing Hamilton's principle. In this paper, control goals are the tracking desired pitch angle along with the flexible appendages vibration suppression simultaneously by using only one control torque which is applied to the central hub. The boundary control is proposed to fulfill these control aims; furthermore, this boundary control ensures that spillover instability phenomenon is eliminated, and in-domain sensors and actuators implement are excluded. Indeed, the proposed boundary control is able to stabilize an infinite number of vibration modes, which is one of the important benefits of the proposed control when it is considered that different factors including external disturbances and even the satellite maneuver can excite the various vibration modes of the flexible appendages and consequently the excitement of the high order vibration modes will be possible. Lyapunov's direct method is used to prove the exponential stability; moreover, this Proof is achieved in absence of any damping effect in modeling the vibrations of flexible appendages. In addition, the procedure for finding the boundary control coefficients which ensures the exponential stability is provided. Eventually, numerical simulations are presented to illustrate the effectiveness of the proposed boundary control.

A thermodynamic equation of jamming

NASA Astrophysics Data System (ADS)

Lu, Kevin; Pirouz Kavehpour, H.

2008-03-01

Materials ranging from sand to fire-retardant to toothpaste are considered fragile, able to exhibit both solid and fluid-like properties across the jamming transition. Guided by granular flow experiments, our equation of jammed states is path-dependent, definable at different athermal equilibrium states. The non-equilibrium thermodynamics based on a structural temperature incorporate physical ageing to address the non-exponential, non-Arrhenious relaxation of granular flows. In short, jamming is simply viewed as a thermodynamic transition that occurs to preserve a positive configurational entropy above absolute zero. Without any free parameters, the proposed equation-of-state governs the mechanism of shear-banding and the associated features of shear-softening and thickness-invariance.

Firing patterns in the adaptive exponential integrate-and-fire model.

PubMed

Naud, Richard; Marcille, Nicolas; Clopath, Claudia; Gerstner, Wulfram

2008-11-01

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.

Investigation of the double exponential in the current-voltage characteristics of silicon solar cells

NASA Technical Reports Server (NTRS)

Wolf, M.; Noel, G. T.; Stirn, R. J.

1976-01-01

A theoretical analysis is presented of certain peculiarities of the current-voltage characteristics of silicon solar cells, involving high values of the empirical constant A in the diode equation for a p-n junction. An attempt was made in a lab experiment to demonstrate that the saturation current which is associated with the exponential term qV/A2kT of the I-V characteristic, with A2 roughly equal to 2, originates in the space charge region and that it can be increased, as observed on ATS-1 cells, by the introduction of additional defects through low energy proton irradiation. It was shown that the proton irradiation introduces defects into the space charge region which give rise to a recombination current from this region, although the I-V characteristic is, in this case, dominated by an exponential term which has A = 1.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

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

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Statistical summary of selected physical, chemical, and toxicity characteristics and estimates of annual constituent loads in urban stormwater, Maricopa County, Arizona

USGS Publications Warehouse

Fossum, Kenneth D.; O'Day, Christie M.; Wilson, Barbara J.; Monical, Jim E.

2001-01-01

Stormwater and streamflow in Maricopa County were monitored to (1) describe the physical, chemical, and toxicity characteristics of stormwater from areas having different land uses, (2) describe the physical, chemical, and toxicity characteristics of streamflow from areas that receive urban stormwater, and (3) estimate constituent loads in stormwater. Urban stormwater and streamflow had similar ranges in most constituent concentrations. The mean concentration of dissolved solids in urban stormwater was lower than in streamflow from the Salt River and Indian Bend Wash. Urban stormwater, however, had a greater chemical oxygen demand and higher concentrations of most nutrients. Mean seasonal loads and mean annual loads of 11 constituents and volumes of runoff were estimated for municipalities in the metropolitan Phoenix area, Arizona, by adjusting regional regression equations of loads. This adjustment procedure uses the original regional regression equation and additional explanatory variables that were not included in the original equation. The adjusted equations had standard errors that ranged from 161 to 196 percent. The large standard errors of the prediction result from the large variability of the constituent concentration data used in the regression analysis. Adjustment procedures produced unsatisfactory results for nine of the regressions?suspended solids, dissolved solids, total phosphorus, dissolved phosphorus, total recoverable cadmium, total recoverable copper, total recoverable lead, total recoverable zinc, and storm runoff. These equations had no consistent direction of bias and no other additional explanatory variables correlated with the observed loads. A stepwise-multiple regression or a three-variable regression (total storm rainfall, drainage area, and impervious area) and local data were used to develop local regression equations for these nine constituents. These equations had standard errors from 15 to 183 percent.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

Numerical study for Darcy-Forchheimer flow of nanofluid due to an exponentially stretching curved surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Haider, Farwa; Muhammad, Taseer; Alsaedi, Ahmed

2018-03-01

Here Darcy-Forchheimer flow of viscous nanofluid with Brownian motion and thermophoresis is addressed. An incompressible viscous liquid saturates the porous space through Darcy-Forchheimer relation. Flow is generated by an exponentially stretching curved surface. System of partial differential equations is converted into ordinary differential system. Nonlinear systems are solved numerically by NDSolve technique. Graphs are plotted for the outcomes of various pertinent variables. Skin friction coefficient and local Nusselt and Sherwood numbers have been physically interpreted. Our results indicate that the local Nusselt and Sherwood numbers are reduced for larger values of local porosity parameter and Forchheimer number.

Thermophysical analysis for three-dimensional MHD stagnation-point flow of nano-material influenced by an exponential stretching surface

NASA Astrophysics Data System (ADS)

Ur Rehman, Fiaz; Nadeem, Sohail; Ur Rehman, Hafeez; Ul Haq, Rizwan

2018-03-01

In the present paper a theoretical investigation is performed to analyze heat and mass transport enhancement of water-based nanofluid for three dimensional (3D) MHD stagnation-point flow caused by an exponentially stretched surface. Water is considered as a base fluid. There are three (3) types of nanoparticles considered in this study namely, CuO (Copper oxide), Fe3O4 (Magnetite), and Al2O3 (Alumina) are considered along with water. In this problem we invoked the boundary layer phenomena and suitable similarity transformation, as a result our three dimensional non-linear equations of describing current problem are transmuted into nonlinear and non-homogeneous differential equations involving ordinary derivatives. We solved the final equations by applying homotopy analysis technique. Influential outcomes of aggressing parameters involved in this study, effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. It is worth mentioning that Skin-friction along x and y-direction is maximum for Copper oxide-water nanofluid and minimum for Alumina-water nanofluid. Result for local Nusselt number is maximum for Copper oxide-water nanofluid and is minimum for magnetite-water nanofluid.

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD).

PubMed

Luxton, Gary; Keall, Paul J; King, Christopher R

2008-01-07

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within approximately 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD(50), and conversely m and TD(50) are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential

NASA Astrophysics Data System (ADS)

Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito

2017-08-01

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Using regression equations built from summary data in the psychological assessment of the individual case: extension to multiple regression.

PubMed

Crawford, John R; Garthwaite, Paul H; Denham, Annie K; Chelune, Gordon J

2012-12-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because (a) not all psychologists are aware that regression equations can be built not only from raw data but also using only basic summary data for a sample, and (b) the computations involved are tedious and prone to error. In an attempt to overcome these barriers, Crawford and Garthwaite (2007) provided methods to build and apply simple linear regression models using summary statistics as data. In the present study, we extend this work to set out the steps required to build multiple regression models from sample summary statistics and the further steps required to compute the associated statistics for drawing inferences concerning an individual case. We also develop, describe, and make available a computer program that implements these methods. Although there are caveats associated with the use of the methods, these need to be balanced against pragmatic considerations and against the alternative of either entirely ignoring a pertinent data set or using it informally to provide a clinical "guesstimate." Upgraded versions of earlier programs for regression in the single case are also provided; these add the point and interval estimates of effect size developed in the present article.

Estimating selected low-flow frequency statistics and harmonic-mean flows for ungaged, unregulated streams in Indiana

USGS Publications Warehouse

Martin, Gary R.; Fowler, Kathleen K.; Arihood, Leslie D.

2016-09-06

Information on low-flow characteristics of streams is essential for the management of water resources. This report provides equations for estimating the 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years and the harmonic-mean flow at ungaged, unregulated stream sites in Indiana. These equations were developed using the low-flow statistics and basin characteristics for 108 continuous-record streamgages in Indiana with at least 10 years of daily mean streamflow data through the 2011 climate year (April 1 through March 31). The equations were developed in cooperation with the Indiana Department of Environmental Management.Regression techniques were used to develop the equations for estimating low-flow frequency statistics and the harmonic-mean flows on the basis of drainage-basin characteristics. A geographic information system was used to measure basin characteristics for selected streamgages. A final set of 25 basin characteristics measured at all the streamgages were evaluated to choose the best predictors of the low-flow statistics.Logistic-regression equations applicable statewide are presented for estimating the probability that selected low-flow frequency statistics equal zero. These equations use the explanatory variables total drainage area, average transmissivity of the full thickness of the unconsolidated deposits within 1,000 feet of the stream network, and latitude of the basin outlet. The percentage of the streamgage low-flow statistics correctly classified as zero or nonzero using the logistic-regression equations ranged from 86.1 to 88.9 percent.Generalized-least-squares regression equations applicable statewide for estimating nonzero low-flow frequency statistics use total drainage area, the average hydraulic conductivity of the top 70 feet of unconsolidated deposits, the slope of the basin, and the index of permeability and thickness of the Quaternary surficial sediments as explanatory variables. The average standard error of prediction of these regression equations ranges from 55.7 to 61.5 percent.Regional weighted-least-squares regression equations were developed for estimating the harmonic-mean flows by dividing the State into three low-flow regions. The Northern region uses total drainage area and the average transmissivity of the entire thickness of unconsolidated deposits as explanatory variables. The Central region uses total drainage area, the average hydraulic conductivity of the entire thickness of unconsolidated deposits, and the index of permeability and thickness of the Quaternary surficial sediments. The Southern region uses total drainage area and the percent of the basin covered by forest. The average standard error of prediction for these equations ranges from 39.3 to 66.7 percent.The regional regression equations are applicable only to stream sites with low flows unaffected by regulation and to stream sites with drainage basin characteristic values within specified limits. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features and for urbanized basins. Extrapolations near and beyond the applicable basin characteristic limits will have unknown errors that may be large. Equations are presented for use in estimating the 90-percent prediction interval of the low-flow statistics estimated by use of the regression equations at a given stream site.The regression equations are to be incorporated into the U.S. Geological Survey StreamStats Web-based application for Indiana. StreamStats allows users to select a stream site on a map and automatically measure the needed basin characteristics and compute the estimated low-flow statistics and associated prediction intervals.

Technique for estimating the 2- to 500-year flood discharges on unregulated streams in rural Missouri

USGS Publications Warehouse

Alexander, Terry W.; Wilson, Gary L.

1995-01-01

A generalized least-squares regression technique was used to relate the 2- to 500-year flood discharges from 278 selected streamflow-gaging stations to statistically significant basin characteristics. The regression relations (estimating equations) were defined for three hydrologic regions (I, II, and III) in rural Missouri. Ordinary least-squares regression analyses indicate that drainage area (Regions I, II, and III) and main-channel slope (Regions I and II) are the only basin characteristics needed for computing the 2- to 500-year design-flood discharges at gaged or ungaged stream locations. The resulting generalized least-squares regression equations provide a technique for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood discharges on unregulated streams in rural Missouri. The regression equations for Regions I and II were developed from stream-flow-gaging stations with drainage areas ranging from 0.13 to 11,500 square miles and 0.13 to 14,000 square miles, and main-channel slopes ranging from 1.35 to 150 feet per mile and 1.20 to 279 feet per mile. The regression equations for Region III were developed from streamflow-gaging stations with drainage areas ranging from 0.48 to 1,040 square miles. Standard errors of estimate for the generalized least-squares regression equations in Regions I, II, and m ranged from 30 to 49 percent.

A Pedagogical Approach to the Magnus Expansion

ERIC Educational Resources Information Center

Blanes, S.; Casas, F.; Oteo, J. A.; Ros, J.

2010-01-01

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the "Magnus expansion" (also known as "exponential perturbation theory") provides such unitary approximate solutions. The purpose is to illustrate the importance and…

Baldcypress Height-Diamter Equations and Their Prediction Confindence Intervals

Treesearch

Bernard R. Parresol

1992-01-01

Height-diameter relationships are an important component in yield estimation, stand description, and damage appraisals. A nonlinear exponential function used extensively in the northwest United States was chosen for bald cypress (Taxodium distichum (L.) Rich.). Homogeneity and normality of residuals were examined, and the function as well as the...

The Arrhenius equation revisited.

PubMed

Peleg, Micha; Normand, Mark D; Corradini, Maria G

2012-01-01

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.

Estimation of peak-discharge frequency of urban streams in Jefferson County, Kentucky

USGS Publications Warehouse

Martin, Gary R.; Ruhl, Kevin J.; Moore, Brian L.; Rose, Martin F.

1997-01-01

An investigation of flood-hydrograph characteristics for streams in urban Jefferson County, Kentucky, was made to obtain hydrologic information needed for waterresources management. Equations for estimating peak-discharge frequencies for ungaged streams in the county were developed by combining (1) long-term annual peakdischarge data and rainfall-runoff data collected from 1991 to 1995 in 13 urban basins and (2) long-term annual peak-discharge data in four rural basins located in hydrologically similar areas of neighboring counties. The basins ranged in size from 1.36 to 64.0 square miles. The U.S. Geological Survey Rainfall- Runoff Model (RRM) was calibrated for each of the urban basins. The calibrated models were used with long-term, historical rainfall and pan-evaporation data to simulate 79 years of annual peak-discharge data. Peak-discharge frequencies were estimated by fitting the logarithms of the annual peak discharges to a Pearson-Type III frequency distribution. The simulated peak-discharge frequencies were adjusted for improved reliability by application of bias-correction factors derived from peakdischarge frequencies based on local, observed annual peak discharges. The three-parameter and the preferred seven-parameter nationwide urban-peak-discharge regression equations previously developed by USGS investigators provided biased (high) estimates for the urban basins studied. Generalized-least-square regression procedures were used to relate peakdischarge frequency to selected basin characteristics. Regression equations were developed to estimate peak-discharge frequency by adjusting peak-dischargefrequency estimates made by use of the threeparameter nationwide urban regression equations. The regression equations are presented in equivalent forms as functions of contributing drainage area, main-channel slope, and basin development factor, which is an index for measuring the efficiency of the basin drainage system. Estimates of peak discharges for streams in the county can be made for the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals by use of the regression equations. The average standard errors of prediction of the regression equations ranges from ? 34 to ? 45 percent. The regression equations are applicable to ungaged streams in the county having a specific range of basin characteristics.

Model Robust Calibration: Method and Application to Electronically-Scanned Pressure Transducers

NASA Technical Reports Server (NTRS)

Walker, Eric L.; Starnes, B. Alden; Birch, Jeffery B.; Mays, James E.

2010-01-01

This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers.

Techniques for estimating flood-peak discharges of rural, unregulated streams in Ohio

USGS Publications Warehouse

Koltun, G.F.

2003-01-01

Regional equations for estimating 2-, 5-, 10-, 25-, 50-, 100-, and 500-year flood-peak discharges at ungaged sites on rural, unregulated streams in Ohio were developed by means of ordinary and generalized least-squares (GLS) regression techniques. One-variable, simple equations and three-variable, full-model equations were developed on the basis of selected basin characteristics and flood-frequency estimates determined for 305 streamflow-gaging stations in Ohio and adjacent states. The average standard errors of prediction ranged from about 39 to 49 percent for the simple equations, and from about 34 to 41 percent for the full-model equations. Flood-frequency estimates determined by means of log-Pearson Type III analyses are reported along with weighted flood-frequency estimates, computed as a function of the log-Pearson Type III estimates and the regression estimates. Values of explanatory variables used in the regression models were determined from digital spatial data sets by means of a geographic information system (GIS), with the exception of drainage area, which was determined by digitizing the area within basin boundaries manually delineated on topographic maps. Use of GIS-based explanatory variables represents a major departure in methodology from that described in previous reports on estimating flood-frequency characteristics of Ohio streams. Examples are presented illustrating application of the regression equations to ungaged sites on ungaged and gaged streams. A method is provided to adjust regression estimates for ungaged sites by use of weighted and regression estimates for a gaged site on the same stream. A region-of-influence method, which employs a computer program to estimate flood-frequency characteristics for ungaged sites based on data from gaged sites with similar characteristics, was also tested and compared to the GLS full-model equations. For all recurrence intervals, the GLS full-model equations had superior prediction accuracy relative to the simple equations and therefore are recommended for use.

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.

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

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

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

An equation of state based upon a ratio of polynomials (rational) form for the residual Helmholtz energy: application to nitrogen, argon and methane

NASA Astrophysics Data System (ADS)

Gomez-Osorio, Martin A.; Browne, Robert A.; Cristancho, Diego E.; Holste, James C.; Hall, Kenneth R.; Bell, Ian H.

2017-06-01

This work presents an equation of state that contains the residual Helmholtz free energy as a ratio of polynomials in density with temperature-dependent coefficients and demonstrates that it is a viable alternative for describing thermodynamic properties accurately. The specific form of the equation in this work has six density terms in the numerator, three density terms in the denominator, and five temperature parameters for each temperature-dependent coefficient. Nitrogen, argon, and methane serve as prototype fluids to demonstrate the capability of the form to describe p-ρ-T behaviour, vapour pressures, speeds of sound, and isochoric heat capacities up to 1000 MPa. Characteristic curves for several properties of nitrogen generated using the equation exhibit proper behaviour at high temperatures and pressures. Because the equation contains no exponential terms or non-integer exponents, the computational time associated with the new equation is more than a factor of 10 less than that required for similar equations with comparable accuracy.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Flood-Frequency Estimates for Streams on Kaua`i, O`ahu, Moloka`i, Maui, and Hawai`i, State of Hawai`i

USGS Publications Warehouse

Oki, Delwyn S.; Rosa, Sarah N.; Yeung, Chiu W.

2010-01-01

This study provides an updated analysis of the magnitude and frequency of peak stream discharges in Hawai`i. Annual peak-discharge data collected by the U.S. Geological Survey during and before water year 2008 (ending September 30, 2008) at stream-gaging stations were analyzed. The existing generalized-skew value for the State of Hawai`i was retained, although three methods were used to evaluate whether an update was needed. Regional regression equations were developed for peak discharges with 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals for unregulated streams (those for which peak discharges are not affected to a large extent by upstream reservoirs, dams, diversions, or other structures) in areas with less than 20 percent combined medium- and high-intensity development on Kaua`i, O`ahu, Moloka`i, Maui, and Hawai`i. The generalized-least-squares (GLS) regression equations relate peak stream discharge to quantified basin characteristics (for example, drainage-basin area and mean annual rainfall) that were determined using geographic information system (GIS) methods. Each of the islands of Kaua`i,O`ahu, Moloka`i, Maui, and Hawai`i was divided into two regions, generally corresponding to a wet region and a dry region. Unique peak-discharge regression equations were developed for each region. The regression equations developed for this study have standard errors of prediction ranging from 16 to 620 percent. Standard errors of prediction are greatest for regression equations developed for leeward Moloka`i and southern Hawai`i. In general, estimated 100-year peak discharges from this study are lower than those from previous studies, which may reflect the longer periods of record used in this study. Each regression equation is valid within the range of values of the explanatory variables used to develop the equation. The regression equations were developed using peak-discharge data from streams that are mainly unregulated, and they should not be used to estimate peak discharges in regulated streams. Use of a regression equation beyond its limits will produce peak-discharge estimates with unknown error and should therefore be avoided. Improved estimates of the magnitude and frequency of peak discharges in Hawai`i will require continued operation of existing stream-gaging stations and operation of additional gaging stations for areas such as Moloka`i and Hawai`i, where limited stream-gaging data are available.

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures

NASA Astrophysics Data System (ADS)

Belonoshko, A. B.; Saxena, S. K.

1992-10-01

A unified equation of state (EOS) is derived for 13 gases (including H2O, CO2, CH4, CO, O2, H2, Ar, N2, NH3, H2S, SO2, COS, and S2) in C-H-O-N-S-Ar system, on the basis of molecular dynamical simulated PVT data, assuming these species to be alpha-exponential-6 fluids at high temperature and pressure. The EOS equation is parameterized for these gases in the ranges of temperature and pressure 400-4000 K and 5-1000 kbar, respectively. It is shown that the equation reproduces most of the available experimental data in the limits of experimental accuracy of volume measurements.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

PubMed

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression

PubMed Central

Ding, A. Adam; Wu, Hulin

2015-01-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

1976-01-01

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Generalized master equation via aging continuous-time random walks.

PubMed

Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo

2003-11-01

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case where psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is nonstationary, thereby implying aging, while the Onsager principle is valid only in the case of fully aged systems. The case of a Poisson distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless of the nature of the waiting-time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markov. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light on the problem of how to unravel non-Markov quantum master equations.

Methods for estimating selected low-flow frequency statistics and mean annual flow for ungaged locations on streams in North Georgia

USGS Publications Warehouse

Gotvald, Anthony J.

2017-01-13

The U.S. Geological Survey, in cooperation with the Georgia Department of Natural Resources, Environmental Protection Division, developed regional regression equations for estimating selected low-flow frequency and mean annual flow statistics for ungaged streams in north Georgia that are not substantially affected by regulation, diversions, or urbanization. Selected low-flow frequency statistics and basin characteristics for 56 streamgage locations within north Georgia and 75 miles beyond the State’s borders in Alabama, Tennessee, North Carolina, and South Carolina were combined to form the final dataset used in the regional regression analysis. Because some of the streamgages in the study recorded zero flow, the final regression equations were developed using weighted left-censored regression analysis to analyze the flow data in an unbiased manner, with weights based on the number of years of record. The set of equations includes the annual minimum 1- and 7-day average streamflow with the 10-year recurrence interval (referred to as 1Q10 and 7Q10), monthly 7Q10, and mean annual flow. The final regional regression equations are functions of drainage area, mean annual precipitation, and relief ratio for the selected low-flow frequency statistics and drainage area and mean annual precipitation for mean annual flow. The average standard error of estimate was 13.7 percent for the mean annual flow regression equation and ranged from 26.1 to 91.6 percent for the selected low-flow frequency equations.The equations, which are based on data from streams with little to no flow alterations, can be used to provide estimates of the natural flows for selected ungaged stream locations in the area of Georgia north of the Fall Line. The regression equations are not to be used to estimate flows for streams that have been altered by the effects of major dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, or wastewater discharges. The regression equations should be used only for ungaged sites with drainage areas between 1.67 and 576 square miles, mean annual precipitation between 47.6 and 81.6 inches, and relief ratios between 0.146 and 0.607; these are the ranges of the explanatory variables used to develop the equations. An attempt was made to develop regional regression equations for the area of Georgia south of the Fall Line by using the same approach used during this study for north Georgia; however, the equations resulted with high average standard errors of estimates and poorly predicted flows below 0.5 cubic foot per second, which may be attributed to the karst topography common in that area.The final regression equations developed from this study are planned to be incorporated into the U.S. Geological Survey StreamStats program. StreamStats is a Web-based geographic information system that provides users with access to an assortment of analytical tools useful for water-resources planning and management, and for engineering design applications, such as the design of bridges. The StreamStats program provides streamflow statistics and basin characteristics for U.S. Geological Survey streamgage locations and ungaged sites of interest. StreamStats also can compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in Georgia.

Existence, uniqueness, and stability of stochastic neutral functional differential equations of Sobolev-type

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

Yang, Xuetao; Zhu, Quanxin, E-mail: zqx22@126.com

2015-12-15

In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii’s fixed point theorem, respectively. Furthermore, we use the Bihari’s inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

The Oscillating Circular Airfoil on the Basis of Potential Theory

NASA Technical Reports Server (NTRS)

Schade, T.; Krienes, K.

1947-01-01

Proceeding from the thesis by W. Kinner the present report treats the problem of the circular airfoil in uniform airflow executing small oscillations, the amplitudes of which correspond to whole functions of the second degree in x and y. The pressure distribution is secured by means of Prandtl's acceleration potential. It results in a system of linear equations the coefficients of which can be calculated exactly with the aid of exponential functions and Hankel's functions. The equations necessary are derived in part I; the numerical calculation follows in part II.

The perturbed Sparre Andersen model with a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Heli; Yin, Chuancun

2008-10-01

In this paper, we consider a Sparre Andersen model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the mth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case where the inter-claim times are Erlang(2) distributed and the claim size distribution is exponential is considered in some details.

Marketing percolation

NASA Astrophysics Data System (ADS)

Goldenberg, J.; Libai, B.; Solomon, S.; Jan, N.; Stauffer, D.

2000-09-01

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass, Manage. Sci. 15 (1969) 215). This mean-field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al., Physica A 277 (2000) 239) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.

Exact analytical solution of irreversible binary dynamics on networks.

PubMed

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Exact analytical solution of irreversible binary dynamics on networks

NASA Astrophysics Data System (ADS)

Laurence, Edward; Young, Jean-Gabriel; Melnik, Sergey; Dubé, Louis J.

2018-03-01

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves the equations as efficiently as possible in exponential time.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

NASA Astrophysics Data System (ADS)

Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

2018-04-01

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.

Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation

NASA Astrophysics Data System (ADS)

Zou, Li; Yu, Zong-Bing; Tian, Shou-Fu; Feng, Lian-Li; Li, Jin

2018-03-01

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.

Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

NASA Technical Reports Server (NTRS)

Klein, Vladislav; Noderer, Keith D.

1994-01-01

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

Relationship between the Decomposition Process of Coarse Woody Debris and Fungal Community Structure as Detected by High-Throughput Sequencing in a Deciduous Broad-Leaved Forest in Japan

PubMed Central

Yamashita, Satoshi; Masuya, Hayato; Abe, Shin; Masaki, Takashi; Okabe, Kimiko

2015-01-01

We examined the relationship between the community structure of wood-decaying fungi, detected by high-throughput sequencing, and the decomposition rate using 13 years of data from a forest dynamics plot. For molecular analysis and wood density measurements, drill dust samples were collected from logs and stumps of Fagus and Quercus in the plot. Regression using a negative exponential model between wood density and time since death revealed that the decomposition rate of Fagus was greater than that of Quercus. The residual between the expected value obtained from the regression curve and the observed wood density was used as a decomposition rate index. Principal component analysis showed that the fungal community compositions of both Fagus and Quercus changed with time since death. Principal component analysis axis scores were used as an index of fungal community composition. A structural equation model for each wood genus was used to assess the effect of fungal community structure traits on the decomposition rate and how the fungal community structure was determined by the traits of coarse woody debris. Results of the structural equation model suggested that the decomposition rate of Fagus was affected by two fungal community composition components: one that was affected by time since death and another that was not affected by the traits of coarse woody debris. In contrast, the decomposition rate of Quercus was not affected by coarse woody debris traits or fungal community structure. These findings suggest that, in the case of Fagus coarse woody debris, the fungal community structure is related to the decomposition process of its host substrate. Because fungal community structure is affected partly by the decay stage and wood density of its substrate, these factors influence each other. Further research on interactive effects is needed to improve our understanding of the relationship between fungal community structure and the woody debris decomposition process. PMID:26110605

Minute ventilation of cyclists, car and bus passengers: an experimental study.

PubMed

Zuurbier, Moniek; Hoek, Gerard; van den Hazel, Peter; Brunekreef, Bert

2009-10-27

Differences in minute ventilation between cyclists, pedestrians and other commuters influence inhaled doses of air pollution. This study estimates minute ventilation of cyclists, car and bus passengers, as part of a study on health effects of commuters' exposure to air pollutants. Thirty-four participants performed a submaximal test on a bicycle ergometer, during which heart rate and minute ventilation were measured simultaneously at increasing cycling intensity. Individual regression equations were calculated between heart rate and the natural log of minute ventilation. Heart rates were recorded during 280 two hour trips by bicycle, bus and car and were calculated into minute ventilation levels using the individual regression coefficients. Minute ventilation during bicycle rides were on average 2.1 times higher than in the car (individual range from 1.3 to 5.3) and 2.0 times higher than in the bus (individual range from 1.3 to 5.1). The ratio of minute ventilation of cycling compared to travelling by bus or car was higher in women than in men. Substantial differences in regression equations were found between individuals. The use of individual regression equations instead of average regression equations resulted in substantially better predictions of individual minute ventilations. The comparability of the gender-specific overall regression equations linking heart rate and minute ventilation with one previous American study, supports that for studies on the group level overall equations can be used. For estimating individual doses, the use of individual regression coefficients provides more precise data. Minute ventilation levels of cyclists are on average two times higher than of bus and car passengers, consistent with the ratio found in one small previous study of young adults. The study illustrates the importance of inclusion of minute ventilation data in comparing air pollution doses between different modes of transport.

Estimation of Magnitude and Frequency of Floods for Streams on the Island of Oahu, Hawaii

USGS Publications Warehouse

Wong, Michael F.

1994-01-01

This report describes techniques for estimating the magnitude and frequency of floods for the island of Oahu. The log-Pearson Type III distribution and methodology recommended by the Interagency Committee on Water Data was used to determine the magnitude and frequency of floods at 79 gaging stations that had 11 to 72 years of record. Multiple regression analysis was used to construct regression equations to transfer the magnitude and frequency information from gaged sites to ungaged sites. Oahu was divided into three hydrologic regions to define relations between peak discharge and drainage-basin and climatic characteristics. Regression equations are provided to estimate the 2-, 5-, 10-, 25-, 50-, and 100-year peak discharges at ungaged sites. Significant basin and climatic characteristics included in the regression equations are drainage area, median annual rainfall, and the 2-year, 24-hour rainfall intensity. Drainage areas for sites used in this study ranged from 0.03 to 45.7 square miles. Standard error of prediction for the regression equations ranged from 34 to 62 percent. Peak-discharge data collected through water year 1988, geographic information system (GIS) technology, and generalized least-squares regression were used in the analyses. The use of GIS seems to be a more flexible and consistent means of defining and calculating basin and climatic characteristics than using manual methods. Standard errors of estimate for the regression equations in this report are an average of 8 percent less than those published in previous studies.

Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised

NASA Technical Reports Server (NTRS)

Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.

1995-01-01

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.

Calculating Formulae of Proportion Factor and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Feng-Hua, Zhang; Gui-De, Zhou; Kun, Ma; Wen-Juan, Ma; Wen-Yuan, Cui; Bo, Zhang

2016-07-01

Previous studies have shown that, for the three main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the neutron exposure distribution (DNE) in the nucleosynthesis region can always be considered as an exponential function, i.e., ρAGB(τ) = C/τ0 exp(-τ/τ0) in an effective range of the neutron exposure values. However, the specific expressions of the proportion factor C and the mean neutron exposure τ0 in the exponential distribution function for different models are not completely determined in the related literature. Through dissecting the basic method to obtain the exponential DNE, and systematically analyzing the solution procedures of neutron exposure distribution functions in different stellar models, the general formulae, as well as their auxiliary equations, for calculating C and τ0 are derived. Given the discrete neutron exposure distribution Pk, the relationships of C and τ0 with the model parameters can be determined. The result of this study has effectively solved the problem to analytically calculate the DNE in the current low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.

Approximation of the exponential integral (well function) using sampling methods

NASA Astrophysics Data System (ADS)

Baalousha, Husam Musa

2015-04-01

Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.

The respiratory pressure-abdominal volume curve in a porcine model.

PubMed

Regli, Adrian; De Keulenaer, Bart Leon; Singh, Bhajan; Hockings, Lisen Emma; Noffsinger, Bill; van Heerden, Peter Vernon

2017-12-01

Increasing intra-abdominal volume (IAV) can lead to intra-abdominal hypertension (IAH) or abdominal compartment syndrome. Both are associated with raised morbidity and mortality. IAH can increase airway pressures and impair ventilation. The relationship between increasing IAV and airway pressures is not known. We therefore assessed the effect of increasing IAV on airway and intra-abdominal pressures (IAP). Seven pigs (41.4 +/-8.5 kg) received standardized anesthesia and mechanical ventilation. A latex balloon inserted in the peritoneal cavity was inflated in 1-L increments until IAP exceeded 40 cmH 2 O. Peak airway pressure (pP AW ), respiratory compliance, and IAP (bladder pressure) were measured. Abdominal compliance was calculated. Different equations were tested that best described the measured pressure-volume curves. An exponential equation best described the measured pressure-volume curves. Raising IAV increased pP AW and IAP in an exponential manner. Increases in IAP were associated with parallel increases in pP AW with an approximate 40% transmission of IAP to pP AW . The higher the IAP, the greater IAV effected pP AW and IAP. The exponential nature of the effect of IAV on pP AW and IAP implies that, in the presence of high grades of IAH, small reductions in IAV can lead to significant reductions in airway and abdominal pressures. Conversely, in the presence of normal IAP levels, large increases in IAV may not affect airway and abdominal pressures.

Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation: A Comparative Study

NASA Astrophysics Data System (ADS)

Sagheer, M.; Bilal, M.; Hussain, S.; Ahmed, R. N.

2018-03-01

This article examines a mathematical model to analyze the rotating flow of three-dimensional water based nanofluid over a convectively heated exponentially stretching sheet in the presence of transverse magnetic field with additional effects of thermal radiation, Joule heating and viscous dissipation. Silver (Ag), copper (Cu), copper oxide (CuO), aluminum oxide (Al 2 O 3 ) and titanium dioxide (TiO 2 ) have been taken under consideration as the nanoparticles and water (H 2 O) as the base fluid. Using suitable similarity transformations, the governing partial differential equations (PDEs) of the modeled problem are transformed to the ordinary differential equations (ODEs). These ODEs are then solved numerically by applying the shooting method. For the particular situation, the results are compared with the available literature. The effects of different nanoparticles on the temperature distribution are also discussed graphically and numerically. It is witnessed that the skin friction coefficient is maximum for silver based nanofluid. Also, the velocity profile is found to diminish for the increasing values of the magnetic parameter.

Constitutive behavior and processing maps of low-expansion GH909 superalloy

NASA Astrophysics Data System (ADS)

Yao, Zhi-hao; Wu, Shao-cong; Dong, Jian-xin; Yu, Qiu-ying; Zhang, Mai-cang; Han, Guang-wei

2017-04-01

The hot deformation behavior of GH909 superalloy was studied systematically using isothermal hot compression tests in a temperature range of 960 to 1040°C and at strain rates from 0.02 to 10 s-1 with a height reduction as large as 70%. The relations considering flow stress, temperature, and strain rate were evaluated via power-law, hyperbolic sine, and exponential constitutive equations under different strain conditions. An exponential equation was found to be the most appropriate for process modeling. The processing maps for the superalloy were constructed for strains of 0.2, 0.4, 0.6, and 0.8 on the basis of the dynamic material model, and a total processing map that includes all the investigated strains was proposed. Metallurgical instabilities in the instability domain mainly located at higher strain rates manifested as adiabatic shear bands and cracking. The stability domain occurred at 960-1040°C and at strain rates less than 0.2 s-1; these conditions are recommended for optimum hot working of GH909 superalloy.

Evaluation of the recrystallization kinetics of hot-melt extruded polymeric solid dispersions using an improved Avrami equation

PubMed Central

Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A.

2017-01-01

The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied. PMID:25224341

Evaluation of the recrystallization kinetics of hot-melt extruded polymeric solid dispersions using an improved Avrami equation.

PubMed

Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A

2015-01-01

The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied.

Validation of Core Temperature Estimation Algorithm

DTIC Science & Technology

2016-01-29

plot of observed versus estimated core temperature with the line of identity (dashed) and the least squares regression line (solid) and line equation...estimated PSI with the line of identity (dashed) and the least squares regression line (solid) and line equation in the top left corner. (b) Bland...for comparison. The root mean squared error (RMSE) was also computed, as given by Equation 2.

A local equation for differential diagnosis of β-thalassemia trait and iron deficiency anemia by logistic regression analysis in Southeast Iran.

PubMed

Sargolzaie, Narjes; Miri-Moghaddam, Ebrahim

2014-01-01

The most common differential diagnosis of β-thalassemia (β-thal) trait is iron deficiency anemia. Several red blood cell equations were introduced during different studies for differential diagnosis between β-thal trait and iron deficiency anemia. Due to genetic variations in different regions, these equations cannot be useful in all population. The aim of this study was to determine a native equation with high accuracy for differential diagnosis of β-thal trait and iron deficiency anemia for the Sistan and Baluchestan population by logistic regression analysis. We selected 77 iron deficiency anemia and 100 β-thal trait cases. We used binary logistic regression analysis and determined best equations for probability prediction of β-thal trait against iron deficiency anemia in our population. We compared diagnostic values and receiver operative characteristic (ROC) curve related to this equation and another 10 published equations in discriminating β-thal trait and iron deficiency anemia. The binary logistic regression analysis determined the best equation for best probability prediction of β-thal trait against iron deficiency anemia with area under curve (AUC) 0.998. Based on ROC curves and AUC, Green & King, England & Frazer, and then Sirdah indices, respectively, had the most accuracy after our equation. We suggest that to get the best equation and cut-off in each region, one needs to evaluate specific information of each region, specifically in areas where populations are homogeneous, to provide a specific formula for differentiating between β-thal trait and iron deficiency anemia.

Methods for estimating flood frequency in Montana based on data through water year 1998

USGS Publications Warehouse

Parrett, Charles; Johnson, Dave R.

2004-01-01

Annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (T-year floods) were determined for 660 gaged sites in Montana and in adjacent areas of Idaho, Wyoming, and Canada, based on data through water year 1998. The updated flood-frequency information was subsequently used in regression analyses, either ordinary or generalized least squares, to develop equations relating T-year floods to various basin and climatic characteristics, equations relating T-year floods to active-channel width, and equations relating T-year floods to bankfull width. The equations can be used to estimate flood frequency at ungaged sites. Montana was divided into eight regions, within which flood characteristics were considered to be reasonably homogeneous, and the three sets of regression equations were developed for each region. A measure of the overall reliability of the regression equations is the average standard error of prediction. The average standard errors of prediction for the equations based on basin and climatic characteristics ranged from 37.4 percent to 134.1 percent. Average standard errors of prediction for the equations based on active-channel width ranged from 57.2 percent to 141.3 percent. Average standard errors of prediction for the equations based on bankfull width ranged from 63.1 percent to 155.5 percent. In most regions, the equations based on basin and climatic characteristics generally had smaller average standard errors of prediction than equations based on active-channel or bankfull width. An exception was the Southeast Plains Region, where all equations based on active-channel width had smaller average standard errors of prediction than equations based on basin and climatic characteristics or bankfull width. Methods for weighting estimates derived from the basin- and climatic-characteristic equations and the channel-width equations also were developed. The weights were based on the cross correlation of residuals from the different methods and the average standard errors of prediction. When all three methods were combined, the average standard errors of prediction ranged from 37.4 percent to 120.2 percent. Weighting of estimates reduced the standard errors of prediction for all T-year flood estimates in four regions, reduced the standard errors of prediction for some T-year flood estimates in two regions, and provided no reduction in average standard error of prediction in two regions. A computer program for solving the regression equations, weighting estimates, and determining reliability of individual estimates was developed and placed on the USGS Montana District World Wide Web page. A new regression method, termed Region of Influence regression, also was tested. Test results indicated that the Region of Influence method was not as reliable as the regional equations based on generalized least squares regression. Two additional methods for estimating flood frequency at ungaged sites located on the same streams as gaged sites also are described. The first method, based on a drainage-area-ratio adjustment, is intended for use on streams where the ungaged site of interest is located near a gaged site. The second method, based on interpolation between gaged sites, is intended for use on streams that have two or more streamflow-gaging stations.

Flood-frequency prediction methods for unregulated streams of Tennessee, 2000

USGS Publications Warehouse

Law, George S.; Tasker, Gary D.

2003-01-01

Up-to-date flood-frequency prediction methods for unregulated, ungaged rivers and streams of Tennessee have been developed. Prediction methods include the regional-regression method and the newer region-of-influence method. The prediction methods were developed using stream-gage records from unregulated streams draining basins having from 1 percent to about 30 percent total impervious area. These methods, however, should not be used in heavily developed or storm-sewered basins with impervious areas greater than 10 percent. The methods can be used to estimate 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence-interval floods of most unregulated rural streams in Tennessee. A computer application was developed that automates the calculation of flood frequency for unregulated, ungaged rivers and streams of Tennessee. Regional-regression equations were derived by using both single-variable and multivariable regional-regression analysis. Contributing drainage area is the explanatory variable used in the single-variable equations. Contributing drainage area, main-channel slope, and a climate factor are the explanatory variables used in the multivariable equations. Deleted-residual standard error for the single-variable equations ranged from 32 to 65 percent. Deleted-residual standard error for the multivariable equations ranged from 31 to 63 percent. These equations are included in the computer application to allow easy comparison of results produced by the different methods. The region-of-influence method calculates multivariable regression equations for each ungaged site and recurrence interval using basin characteristics from 60 similar sites selected from the study area. Explanatory variables that may be used in regression equations computed by the region-of-influence method include contributing drainage area, main-channel slope, a climate factor, and a physiographic-region factor. Deleted-residual standard error for the region-of-influence method tended to be only slightly smaller than those for the regional-regression method and ranged from 27 to 62 percent.

Techniques for estimating magnitude and frequency of peak flows for Pennsylvania streams

USGS Publications Warehouse

Stuckey, Marla H.; Reed, Lloyd A.

2000-01-01

Regression equations for estimating the magnitude and frequency of floods on ungaged streams in Pennsylvania with drainage areas less that 2,000 square miles were developed on the basis of peak-flow data collected at 313 streamflow-gaging stations. All streamflow-gaging stations used in the development of the equations had 10 or more years of record and include active and discontinued continuous-record and crest-stage partial-record streamflow-gaging stations. Regional regression equations were developed for flood flows expected every 10, 25, 50, 100, and 500 years by the use of a weighted multiple linear regression model.The State was divided into two regions. The largest region, Region A, encompasses about 78 percent of Pennsylvania. The smaller region, Region B, includes only the northwestern part of the State. Basin characteristics used in the regression equations for Region A are drainage area, percentage of forest cover, percentage of urban development, percentage of basin underlain by carbonate bedrock, and percentage of basin controlled by lakes, swamps, and reservoirs. Basin characteristics used in the regression equations for Region B are drainage area and percentage of basin controlled by lakes, swamps, and reservoirs. The coefficient of determination (R2) values for the five flood-frequency equations for Region A range from 0.93 to 0.82, and for Region B, the range is from 0.96 to 0.89.While the regression equations can be used to predict the magnitude and frequency of peak flows for most streams in the State, they should not be used for streams with drainage areas greater than 2,000 square miles or less than 1.5 square miles, for streams that drain extensively mined areas, or for stream reaches immediately below flood-control reservoirs. In addition, the equations presented for Region B should not be used if the stream drains a basin with more than 5 percent urban development.

Estimation of flood discharges at selected annual exceedance probabilities for unregulated, rural streams in Vermont, with a section on Vermont regional skew regression

USGS Publications Warehouse

Olson, Scott A.; with a section by Veilleux, Andrea G.

2014-01-01

This report provides estimates of flood discharges at selected annual exceedance probabilities (AEPs) for streamgages in and adjacent to Vermont and equations for estimating flood discharges at AEPs of 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent (recurrence intervals of 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-years, respectively) for ungaged, unregulated, rural streams in Vermont. The equations were developed using generalized least-squares regression. Flood-frequency and drainage-basin characteristics from 145 streamgages were used in developing the equations. The drainage-basin characteristics used as explanatory variables in the regression equations include drainage area, percentage of wetland area, and the basin-wide mean of the average annual precipitation. The average standard errors of prediction for estimating the flood discharges at the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP with these equations are 34.9, 36.0, 38.7, 42.4, 44.9, 47.3, 50.7, and 55.1 percent, respectively. Flood discharges at selected AEPs for streamgages were computed by using the Expected Moments Algorithm. To improve estimates of the flood discharges for given exceedance probabilities at streamgages in Vermont, a new generalized skew coefficient was developed. The new generalized skew for the region is a constant, 0.44. The mean square error of the generalized skew coefficient is 0.078. This report describes a technique for using results from the regression equations to adjust an AEP discharge computed from a streamgage record. This report also describes a technique for using a drainage-area adjustment to estimate flood discharge at a selected AEP for an ungaged site upstream or downstream from a streamgage. The final regression equations and the flood-discharge frequency data used in this study will be available in StreamStats. StreamStats is a World Wide Web application providing automated regression-equation solutions for user-selected sites on streams.

GLASS VISCOSITY AS A FUNCTION OF TEMPERATURE AND COMPOSITION: A MODEL BASED ON ADAM-GIBBS EQUATION

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

Hrma, Pavel R.

2008-07-01

Within the temperature range and composition region of processing and product forming, the viscosity of commercial and waste glasses spans over 12 orders of magnitude. This paper shows that a generalized Adam-Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity-temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients weremore » obtained by fitting the generalized Adam-Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel-Fulcher-Tammann equation, original and modified, the Avramov equation, and the Douglass-Doremus equation) were fitted to float glass data series and compared with the Adam-Gibbs equation, showing that Adam-Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.« less

Predictive equations for the estimation of body size in seals and sea lions (Carnivora: Pinnipedia)

PubMed Central

Churchill, Morgan; Clementz, Mark T; Kohno, Naoki

2014-01-01

Body size plays an important role in pinniped ecology and life history. However, body size data is often absent for historical, archaeological, and fossil specimens. To estimate the body size of pinnipeds (seals, sea lions, and walruses) for today and the past, we used 14 commonly preserved cranial measurements to develop sets of single variable and multivariate predictive equations for pinniped body mass and total length. Principal components analysis (PCA) was used to test whether separate family specific regressions were more appropriate than single predictive equations for Pinnipedia. The influence of phylogeny was tested with phylogenetic independent contrasts (PIC). The accuracy of these regressions was then assessed using a combination of coefficient of determination, percent prediction error, and standard error of estimation. Three different methods of multivariate analysis were examined: bidirectional stepwise model selection using Akaike information criteria; all-subsets model selection using Bayesian information criteria (BIC); and partial least squares regression. The PCA showed clear discrimination between Otariidae (fur seals and sea lions) and Phocidae (earless seals) for the 14 measurements, indicating the need for family-specific regression equations. The PIC analysis found that phylogeny had a minor influence on relationship between morphological variables and body size. The regressions for total length were more accurate than those for body mass, and equations specific to Otariidae were more accurate than those for Phocidae. Of the three multivariate methods, the all-subsets approach required the fewest number of variables to estimate body size accurately. We then used the single variable predictive equations and the all-subsets approach to estimate the body size of two recently extinct pinniped taxa, the Caribbean monk seal (Monachus tropicalis) and the Japanese sea lion (Zalophus japonicus). Body size estimates using single variable regressions generally under or over-estimated body size; however, the all-subset regression produced body size estimates that were close to historically recorded body length for these two species. This indicates that the all-subset regression equations developed in this study can estimate body size accurately. PMID:24916814

Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability

PubMed Central

Ihlen, Espen A. F.; van Schooten, Kimberley S.; Bruijn, Sjoerd M.; Pijnappels, Mirjam; van Dieën, Jaap H.

2017-01-01

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability. PMID:28900400

The National Flood Frequency Program, version 3 : a computer program for estimating magnitude and frequency of floods for ungaged sites

USGS Publications Warehouse

Ries, Kernell G.; Crouse, Michele Y.

2002-01-01

For many years, the U.S. Geological Survey (USGS) has been developing regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally, these equations have been developed on a Statewide or metropolitan-area basis as part of cooperative study programs with specific State Departments of Transportation. In 1994, the USGS released a computer program titled the National Flood Frequency Program (NFF), which compiled all the USGS available regression equations for estimating the magnitude and frequency of floods in the United States and Puerto Rico. NFF was developed in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency. Since the initial release of NFF, the USGS has produced new equations for many areas of the Nation. A new version of NFF has been developed that incorporates these new equations and provides additional functionality and ease of use. NFF version 3 provides regression-equation estimates of flood-peak discharges for unregulated rural and urban watersheds, flood-frequency plots, and plots of typical flood hydrographs for selected recurrence intervals. The Program also provides weighting techniques to improve estimates of flood-peak discharges for gaging stations and ungaged sites. The information provided by NFF should be useful to engineers and hydrologists for planning and design applications. This report describes the flood-regionalization techniques used in NFF and provides guidance on the applicability and limitations of the techniques. The NFF software and the documentation for the regression equations included in NFF are available at http://water.usgs.gov/software/nff.html.

The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

NASA Astrophysics Data System (ADS)

Olano, C. A.

2009-11-01

Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced exact solutions for the four media in terms of elemental functions. The exact solution for shock wave propagation in a medium of quadratic hyperbolic-secant density distribution is very appropriate to describe the growth of superbubbles in the Galactic disk. Member of the Carrera del Investigador Científico del CONICET, Argentina.

Simplified Two-Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydorgen/Oxygen

NASA Technical Reports Server (NTRS)

Molnar, Melissa; Marek, C. John

2005-01-01

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two-time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (> 1 x 10(exp -20) moles/cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T4). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/air fuel and for the H2/O2. A similar correlation is also developed using data from NASA s Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T4) as a function of overall fuel/air ratio, pressure and initial temperature (T3). High values of the regression coefficient R2 are obtained.

Summary of Simplified Two Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydrogen/Oxygen

NASA Technical Reports Server (NTRS)

Marek, C. John; Molnar, Melissa

2005-01-01

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (greater than l x 10(exp -20)) moles per cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T(sub 4)). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/Air fuel and for H2/O2. A similar correlation is also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T(sub 4)) as a function of overall fuel/air ratio, pressure and initial temperature (T(sub 3)). High values of the regression coefficient R squared are obtained.

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St. Clair River system (Michigan, USA)

USGS Publications Warehouse

Craig, Jaquelyn M.; Thomas, Michael V.; Nichols, Susan Jerrine

2005-01-01

Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length–weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May–September, 1997–2002. Analysis of covariance found no difference in the length–weight relationship between sampling gear or sex. Least-squares regression of log10W × log10TL produced the overall equation logW = 3.365logTL − 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn = W/[(4.786 × 10−10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes.

Kinetic Equation for an Unstable Plasma

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

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Stability of flat spacetime in quantum gravity

NASA Astrophysics Data System (ADS)

Jordan, R. D.

1987-12-01

In a previous paper, a modified effective-action formalism was developed which produces equations satisfied by the expectation value of the field, rather than the usual in-out average. Here this formalism is applied to a quantized scalar field in a background which is a small perturbation from Minkowski spacetime. The one-loop effective field equation describes the back reaction of created particles on the gravitational field, and is calculated in this paper to linear order in the perturbation. In this way we rederive an equation first found by Horowitz using completely different methods. This equation possesses exponentially growing solutions, so we confirm Horowitz's conclusion that flat spacetime is unstable in this approximation to the theory. The new derivation shows that the field equation is just as useful as the one-loop approximation to the in-out equation, contrary to earlier arguments. However, the instability suggests that the one-loop approximation cannot be trusted for gravity. These results are compared with the corresponding situation in QED and QCD.

Solvent dynamics and electron transfer reactions

NASA Astrophysics Data System (ADS)

Rasaiah, Jayendran C.; Zhu, Jianjun

1994-02-01

Recent experimental and theoretical studies of the influence of solvent dynamics on electron transfer (ET) reactions are discussed. It is seen that the survival probabilities of the reactants and products can be obtained as the solution to an integral equation using experimental or simulation data on the solvation dynamics. The theory developed for ET between thermally equilibrated reactants in solution, in which the ligand vibrations were treated classically, is extended to include quantum effects on the inner-shell ligand vibration and electron transfer from a nonequilibrium initial state prepared, for example, by laser excitation. This leads to a slight modification of the integral equation which is easily solved on a personal computer to provide results that can be directly compared with experiment. Analytic approximations to the solutions of the integral equation, ranging from a single exponential to multiexponential time dependence of the survival probabilities are discussed. The rate constant for the single exponential decay of the reactants interpolates between the thermal equilibrium rate constant kie (that is independent of solvent dynamics) and a diffusion controlled rate constant kid (determined by solvent dynamics) and also between the wide (A=0) and narrow (A=1) window limits dominated by inner-sphere ligand vibration and outer-sphere solvent reorganization respectively. The explicit dependence of the integral equation solutions on solvation dynamics S(t), the free energy of reaction ΔG0, the total reorganization energy λ and its partitioning between ligand vibration λq and solvent polarization fluctuations λ0, and the nature of the initial state should be useful in the analysis and design of ET experiments in different solvents.

An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.

Exponential evolution: implications for intelligent extraterrestrial life.

PubMed

Russell, D A

1983-01-01

Some measures of biologic complexity, including maximal levels of brain development, are exponential functions of time through intervals of 10(6) to 10(9) yrs. Biological interactions apparently stimulate evolution but physical conditions determine the time required to achieve a given level of complexity. Trends in brain evolution suggest that other organisms could attain human levels within approximately 10(7) yrs. The number (N) and longevity (L) terms in appropriate modifications of the Drake Equation, together with trends in the evolution of biological complexity on Earth, could provide rough estimates of the prevalence of life forms at specified levels of complexity within the Galaxy. If life occurs throughout the cosmos, exponential evolutionary processes imply that higher intelligence will soon (10(9) yrs) become more prevalent than it now is. Changes in the physical universe become less rapid as time increases from the Big Bang. Changes in biological complexity may be most rapid at such later times. This lends a unique and symmetrical importance to early and late universal times.

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

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Regression equations for estimating flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-Year recurrence intervals in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2004-01-01

Multiple linear-regression equations were developed to estimate the magnitudes of floods in Connecticut for recurrence intervals ranging from 2 to 500 years. The equations can be used for nonurban, unregulated stream sites in Connecticut with drainage areas ranging from about 2 to 715 square miles. Flood-frequency data and hydrologic characteristics from 70 streamflow-gaging stations and the upstream drainage basins were used to develop the equations. The hydrologic characteristics?drainage area, mean basin elevation, and 24-hour rainfall?are used in the equations to estimate the magnitude of floods. Average standard errors of prediction for the equations are 31.8, 32.7, 34.4, 35.9, 37.6 and 45.0 percent for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals, respectively. Simplified equations using only one hydrologic characteristic?drainage area?also were developed. The regression analysis is based on generalized least-squares regression techniques. Observed flows (log-Pearson Type III analysis of the annual maximum flows) from five streamflow-gaging stations in urban basins in Connecticut were compared to flows estimated from national three-parameter and seven-parameter urban regression equations. The comparison shows that the three- and seven- parameter equations used in conjunction with the new statewide equations generally provide reasonable estimates of flood flows for urban sites in Connecticut, although a national urban flood-frequency study indicated that the three-parameter equations significantly underestimated flood flows in many regions of the country. Verification of the accuracy of the three-parameter or seven-parameter national regression equations using new data from Connecticut stations was beyond the scope of this study. A technique for calculating flood flows at streamflow-gaging stations using a weighted average also is described. Two estimates of flood flows?one estimate based on the log-Pearson Type III analyses of the annual maximum flows at the gaging station, and the other estimate from the regression equation?are weighted together based on the years of record at the gaging station and the equivalent years of record value determined from the regression. Weighted averages of flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are tabulated for the 70 streamflow-gaging stations used in the regression analysis. Generally, weighted averages give the most accurate estimate of flood flows at gaging stations. An evaluation of the Connecticut's streamflow-gaging network was performed to determine whether the spatial coverage and range of geographic and hydrologic conditions are adequately represented for transferring flood characteristics from gaged to ungaged sites. Fifty-one of 54 stations in the current (2004) network support one or more flood needs of federal, state, and local agencies. Twenty-five of 54 stations in the current network are considered high-priority stations by the U.S. Geological Survey because of their contribution to the longterm understanding of floods, and their application for regionalflood analysis. Enhancements to the network to improve overall effectiveness for regionalization can be made by increasing the spatial coverage of gaging stations, establishing stations in regions of the state that are not well-represented, and adding stations in basins with drainage area sizes not represented. Additionally, the usefulness of the network for characterizing floods can be maintained and improved by continuing operation at the current stations because flood flows can be more accurately estimated at stations with continuous, long-term record.

Stabilisation of time-varying linear systems via Lyapunov differential equations

NASA Astrophysics Data System (ADS)

Zhou, Bin; Cai, Guang-Bin; Duan, Guang-Ren

2013-02-01

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches.

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.

Curl forces and the nonlinear Fokker-Planck equation.

PubMed

Wedemann, R S; Plastino, A R; Tsallis, C

2016-12-01

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

A study on industrial accident rate forecasting and program development of estimated zero accident time in Korea.

PubMed

Kim, Tae-gu; Kang, Young-sig; Lee, Hyung-won

2011-01-01

To begin a zero accident campaign for industry, the first thing is to estimate the industrial accident rate and the zero accident time systematically. This paper considers the social and technical change of the business environment after beginning the zero accident campaign through quantitative time series analysis methods. These methods include sum of squared errors (SSE), regression analysis method (RAM), exponential smoothing method (ESM), double exponential smoothing method (DESM), auto-regressive integrated moving average (ARIMA) model, and the proposed analytic function method (AFM). The program is developed to estimate the accident rate, zero accident time and achievement probability of an efficient industrial environment. In this paper, MFC (Microsoft Foundation Class) software of Visual Studio 2008 was used to develop a zero accident program. The results of this paper will provide major information for industrial accident prevention and be an important part of stimulating the zero accident campaign within all industrial environments.

Age Estimation of Infants Through Metric Analysis of Developing Anterior Deciduous Teeth.

PubMed

Viciano, Joan; De Luca, Stefano; Irurita, Javier; Alemán, Inmaculada

2018-01-01

This study provides regression equations for estimation of age of infants from the dimensions of their developing deciduous teeth. The sample comprises 97 individuals of known sex and age (62 boys, 35 girls), aged between 2 days and 1,081 days. The age-estimation equations were obtained for the sexes combined, as well as for each sex separately, thus including "sex" as an independent variable. The values of the correlations and determination coefficients obtained for each regression equation indicate good fits for most of the equations obtained. The "sex" factor was statistically significant when included as an independent variable in seven of the regression equations. However, the "sex" factor provided an advantage for age estimation in only three of the equations, compared to those that did not include "sex" as a factor. These data suggest that the ages of infants can be accurately estimated from measurements of their developing deciduous teeth. © 2017 American Academy of Forensic Sciences.

Peak-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Peak-flow annual exceedance probabilities, also called probability-percent chance flow estimates, and regional regression equations are provided describing the peak-flow characteristics of Virginia streams. Statistical methods are used to evaluate peak-flow data. Analysis of Virginia peak-flow data collected from 1895 through 2007 is summarized. Methods are provided for estimating unregulated peak flow of gaged and ungaged streams. Station peak-flow characteristics identified by fitting the logarithms of annual peak flows to a Log Pearson Type III frequency distribution yield annual exceedance probabilities of 0.5, 0.4292, 0.2, 0.1, 0.04, 0.02, 0.01, 0.005, and 0.002 for 476 streamgaging stations. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression model equations for six physiographic regions to estimate regional annual exceedance probabilities at gaged and ungaged sites. Weighted peak-flow values that combine annual exceedance probabilities computed from gaging station data and from regional regression equations provide improved peak-flow estimates. Text, figures, and lists are provided summarizing selected peak-flow sites, delineated physiographic regions, peak-flow estimates, basin characteristics, regional regression model equations, error estimates, definitions, data sources, and candidate regression model equations. This study supersedes previous studies of peak flows in Virginia.

Techniques for estimating peak-streamflow frequency for unregulated streams and streams regulated by small floodwater retarding structures in Oklahoma

USGS Publications Warehouse

Tortorelli, Robert L.

1997-01-01

Statewide regression equations for Oklahoma were determined for estimating peak discharge and flood frequency for selected recurrence intervals from 2 to 500 years for ungaged sites on natural unregulated streams. The most significant independent variables required to estimate peak-streamflow frequency for natural unregulated streams in Oklahoma are contributing drainage area, main-channel slope, and mean-annual precipitation. The regression equations are applicable for watersheds with drainage areas less than 2,510 square miles that are not affected by regulation from manmade works. Limitations on the use of the regression relations and the reliability of regression estimates for natural unregulated streams are discussed. Log-Pearson Type III analysis information, basin and climatic characteristics, and the peak-stream-flow frequency estimates for 251 gaging stations in Oklahoma and adjacent states are listed. Techniques are presented to make a peak-streamflow frequency estimate for gaged sites on natural unregulated streams and to use this result to estimate a nearby ungaged site on the same stream. For ungaged sites on urban streams, an adjustment of the statewide regression equations for natural unregulated streams can be used to estimate peak-streamflow frequency. For ungaged sites on streams regulated by small floodwater retarding structures, an adjustment of the statewide regression equations for natural unregulated streams can be used to estimate peak-streamflow frequency. The statewide regression equations are adjusted by substituting the drainage area below the floodwater retarding structures, or drainage area that represents the percentage of the unregulated basin, in the contributing drainage area parameter to obtain peak-streamflow frequency estimates.

Robust Variable Selection with Exponential Squared Loss.

PubMed

Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping

2013-04-01

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are [Formula: see text] and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.

Robust Variable Selection with Exponential Squared Loss

PubMed Central

Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping

2013-01-01

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are n-consistent and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods. PMID:23913996

A secure distributed logistic regression protocol for the detection of rare adverse drug events

PubMed Central

El Emam, Khaled; Samet, Saeed; Arbuckle, Luk; Tamblyn, Robyn; Earle, Craig; Kantarcioglu, Murat

2013-01-01

Background There is limited capacity to assess the comparative risks of medications after they enter the market. For rare adverse events, the pooling of data from multiple sources is necessary to have the power and sufficient population heterogeneity to detect differences in safety and effectiveness in genetic, ethnic and clinically defined subpopulations. However, combining datasets from different data custodians or jurisdictions to perform an analysis on the pooled data creates significant privacy concerns that would need to be addressed. Existing protocols for addressing these concerns can result in reduced analysis accuracy and can allow sensitive information to leak. Objective To develop a secure distributed multi-party computation protocol for logistic regression that provides strong privacy guarantees. Methods We developed a secure distributed logistic regression protocol using a single analysis center with multiple sites providing data. A theoretical security analysis demonstrates that the protocol is robust to plausible collusion attacks and does not allow the parties to gain new information from the data that are exchanged among them. The computational performance and accuracy of the protocol were evaluated on simulated datasets. Results The computational performance scales linearly as the dataset sizes increase. The addition of sites results in an exponential growth in computation time. However, for up to five sites, the time is still short and would not affect practical applications. The model parameters are the same as the results on pooled raw data analyzed in SAS, demonstrating high model accuracy. Conclusion The proposed protocol and prototype system would allow the development of logistic regression models in a secure manner without requiring the sharing of personal health information. This can alleviate one of the key barriers to the establishment of large-scale post-marketing surveillance programs. We extended the secure protocol to account for correlations among patients within sites through generalized estimating equations, and to accommodate other link functions by extending it to generalized linear models. PMID:22871397

A secure distributed logistic regression protocol for the detection of rare adverse drug events.

PubMed

El Emam, Khaled; Samet, Saeed; Arbuckle, Luk; Tamblyn, Robyn; Earle, Craig; Kantarcioglu, Murat

2013-05-01

There is limited capacity to assess the comparative risks of medications after they enter the market. For rare adverse events, the pooling of data from multiple sources is necessary to have the power and sufficient population heterogeneity to detect differences in safety and effectiveness in genetic, ethnic and clinically defined subpopulations. However, combining datasets from different data custodians or jurisdictions to perform an analysis on the pooled data creates significant privacy concerns that would need to be addressed. Existing protocols for addressing these concerns can result in reduced analysis accuracy and can allow sensitive information to leak. To develop a secure distributed multi-party computation protocol for logistic regression that provides strong privacy guarantees. We developed a secure distributed logistic regression protocol using a single analysis center with multiple sites providing data. A theoretical security analysis demonstrates that the protocol is robust to plausible collusion attacks and does not allow the parties to gain new information from the data that are exchanged among them. The computational performance and accuracy of the protocol were evaluated on simulated datasets. The computational performance scales linearly as the dataset sizes increase. The addition of sites results in an exponential growth in computation time. However, for up to five sites, the time is still short and would not affect practical applications. The model parameters are the same as the results on pooled raw data analyzed in SAS, demonstrating high model accuracy. The proposed protocol and prototype system would allow the development of logistic regression models in a secure manner without requiring the sharing of personal health information. This can alleviate one of the key barriers to the establishment of large-scale post-marketing surveillance programs. We extended the secure protocol to account for correlations among patients within sites through generalized estimating equations, and to accommodate other link functions by extending it to generalized linear models.

The Bland-Altman Method Should Not Be Used in Regression Cross-Validation Studies

ERIC Educational Resources Information Center

O'Connor, Daniel P.; Mahar, Matthew T.; Laughlin, Mitzi S.; Jackson, Andrew S.

2011-01-01

The purpose of this study was to demonstrate the bias in the Bland-Altman (BA) limits of agreement method when it is used to validate regression models. Data from 1,158 men were used to develop three regression equations to estimate maximum oxygen uptake (R[superscript 2] = 0.40, 0.61, and 0.82, respectively). The equations were evaluated in a…

Penalized nonparametric scalar-on-function regression via principal coordinates

PubMed Central

Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu

2016-01-01

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. PMID:29217963

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.

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

NASA Astrophysics Data System (ADS)

Shaikh, A. Y.

2016-07-01

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

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

Dorofeenko, V. G.; Krasovitskiy, V. B.; Turikov, V. A.

2012-06-15

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period,more » is used to describe steady-state nonlinear oscillations in plasma.« less

Decay of homogeneous turbulence from a specified state

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1972-01-01

The homogeneous turbulence problem is formulated by first specifying the multipoint velocity correlations or their spectral equivalents at an initial time. Those quantities, together with the correlation or spectral equations, are then used to calculate initial time derivatives of correlations or spectra. The derivatives in turn are used in time series to calculate the evolution of turbulence quantities with time. When the problem is treated in this way, the correlation equations are closed by the initial specification of the turbulence and no closure assumption is necessary. An exponential series which is an iterative solution of the Navier stokes equations gave much better results than a Taylor power series when used with the limited available initial data. In general, the agreement between theory and experiment was good.

Time-marching transonic flutter solutions including angle-of-attack effects

NASA Technical Reports Server (NTRS)

Edwards, J. W.; Bennett, R. M.; Whitlow, W., Jr.; Seidel, D. A.

1982-01-01

Transonic aeroelastic solutions based upon the transonic small perturbation potential equation were studied. Time-marching transient solutions of plunging and pitching airfoils were analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations were evaluated. The HYTRAN2 code was used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In the code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

Shuttle program: Computing atmospheric scale height for refraction corrections

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Methods for computing the atmospheric scale height to determine radio wave refraction were investigated for different atmospheres, and different angles of elevation. Tables of refractivity versus altitude are included. The equations used to compute the refraction corrections are given. It is concluded that very accurate corrections are determined with the assumption of an exponential atmosphere.

Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2012-01-01

Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…

On the Interface of Probabilistic and PDE Methods in a Multifactor Term Structure Theory

ERIC Educational Resources Information Center

Mamon, Rogemar S.

2004-01-01

Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of…

Methods for estimating magnitude and frequency of 1-, 3-, 7-, 15-, and 30-day flood-duration flows in Arizona

USGS Publications Warehouse

Kennedy, Jeffrey R.; Paretti, Nicholas V.; Veilleux, Andrea G.

2014-01-01

Regression equations, which allow predictions of n-day flood-duration flows for selected annual exceedance probabilities at ungaged sites, were developed using generalized least-squares regression and flood-duration flow frequency estimates at 56 streamgaging stations within a single, relatively uniform physiographic region in the central part of Arizona, between the Colorado Plateau and Basin and Range Province, called the Transition Zone. Drainage area explained most of the variation in the n-day flood-duration annual exceedance probabilities, but mean annual precipitation and mean elevation were also significant variables in the regression models. Standard error of prediction for the regression equations varies from 28 to 53 percent and generally decreases with increasing n-day duration. Outside the Transition Zone there are insufficient streamgaging stations to develop regression equations, but flood-duration flow frequency estimates are presented at select streamgaging stations.

Systolic time interval v heart rate regression equations using atropine: reproducibility studies.

PubMed Central

Kelman, A W; Sumner, D J; Whiting, B

1981-01-01

1. Systolic time intervals (STI) were recorded in six normal male subjects over a period of 3 weeks. On one day per week, each subject received incremental doses of atropine intravenously to increase heart rate, allowing the determination of individual STI v HR regression equations. On the other days STI were recorded with the subjects resting, in the supine position. 2. There were highly significant regression relationships between heart rate and both LVET and QS2, but not between heart rate and PEP. 3. The regression relationships showed little intra-subject variability, but a large degree of inter-subject variability: they proved adequate to correct the STI for the daily fluctuations in heart rate. 4. Administration of small doses of atropine intravenously provides a satisfactory and convenient method of deriving individual STI v HR regression equations which can be applied over a period of weeks. PMID:7248136

Systolic time interval v heart rate regression equations using atropine: reproducibility studies.

PubMed

Kelman, A W; Sumner, D J; Whiting, B

1981-07-01

1. Systolic time intervals (STI) were recorded in six normal male subjects over a period of 3 weeks. On one day per week, each subject received incremental doses of atropine intravenously to increase heart rate, allowing the determination of individual STI v HR regression equations. On the other days STI were recorded with the subjects resting, in the supine position. 2. There were highly significant regression relationships between heart rate and both LVET and QS2, but not between heart rate and PEP. 3. The regression relationships showed little intra-subject variability, but a large degree of inter-subject variability: they proved adequate to correct the STI for the daily fluctuations in heart rate. 4. Administration of small doses of atropine intravenously provides a satisfactory and convenient method of deriving individual STI v HR regression equations which can be applied over a period of weeks.

First off-time treatment prostate-specific antigen kinetics predicts survival in intermittent androgen deprivation for prostate cancer.

PubMed

Sanchez-Salas, Rafael; Olivier, Fabien; Prapotnich, Dominique; Dancausa, José; Fhima, Mehdi; David, Stéphane; Secin, Fernando P; Ingels, Alexandre; Barret, Eric; Galiano, Marc; Rozet, François; Cathelineau, Xavier

2016-01-01

Prostate-specific antigen (PSA) doubling time is relying on an exponential kinetic pattern. This pattern has never been validated in the setting of intermittent androgen deprivation (IAD). Objective is to analyze the prognostic significance for PCa of recurrent patterns in PSA kinetics in patients undergoing IAD. A retrospective study was conducted on 377 patients treated with IAD. On-treatment period (ONTP) consisted of gonadotropin-releasing hormone agonist injections combined with oral androgen receptor antagonist. Off-treatment period (OFTP) began when PSA was lower than 4 ng/ml. ONTP resumed when PSA was higher than 20 ng/ml. PSA values of each OFTP were fitted with three basic patterns: exponential (PSA(t) = λ.e(αt)), linear (PSA(t) = a.t), and power law (PSA(t) = a.t(c)). Univariate and multivariate Cox regression model analyzed predictive factors for oncologic outcomes. Only 45% of the analyzed OFTPs were exponential. Linear and power law PSA kinetics represented 7.5% and 7.7%, respectively. Remaining fraction of analyzed OFTPs (40%) exhibited complex kinetics. Exponential PSA kinetics during the first OFTP was significantly associated with worse oncologic outcome. The estimated 10-year cancer-specific survival (CSS) was 46% for exponential versus 80% for nonexponential PSA kinetics patterns. The corresponding 10-year probability of castration-resistant prostate cancer (CRPC) was 69% and 31% for the two patterns, respectively. Limitations include retrospective design and mixed indications for IAD. PSA kinetic fitted with exponential pattern in approximately half of the OFTPs. First OFTP exponential PSA kinetic was associated with a shorter time to CRPC and worse CSS. © 2015 Wiley Periodicals, Inc.

The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

NASA Technical Reports Server (NTRS)

Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

1976-01-01

The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

Laplace-transform-based method to calculate back-reflected radiance from an isotropically scattering half-space

NASA Astrophysics Data System (ADS)

Rinzema, K.; Hoenders, B. J.; Ferwerda, H. A.

1997-07-01

We present a method to determine the back-reflected radiance from an isotropically scattering half-space with matched boundary. This method has the advantage that it leads very quickly to the relevant equations, the numerical solution of which is also quite easy. Essentially, the method is derived from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grow exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree very well with what is found in the literature.

Weather adjustment using seemingly unrelated regression

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

Noll, T.A.

1995-05-01

Seemingly unrelated regression (SUR) is a system estimation technique that accounts for time-contemporaneous correlation between individual equations within a system of equations. SUR is suited to weather adjustment estimations when the estimation is: (1) composed of a system of equations and (2) the system of equations represents either different weather stations, different sales sectors or a combination of different weather stations and different sales sectors. SUR utilizes the cross-equation error values to develop more accurate estimates of the system coefficients than are obtained using ordinary least-squares (OLS) estimation. SUR estimates can be generated using a variety of statistical software packagesmore » including MicroTSP and SAS.« less

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section

PubMed Central

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-01-01

Abstract Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients. In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation. In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 − 0.022X2 − 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants. This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section. PMID:28834913

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section.

PubMed

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-08-01

Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients.In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation.In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 - 0.022X2 - 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants.This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section.

Compensated Arrhenius formalism applied to a conductivity study in poly(propylene glycol) diacrylate monomers.

PubMed

Dubois, F; Derouiche, Y; Leblond, J M; Maschke, U; Douali, R

2015-09-01

The temperature dependence of the ionic conductivity is studied in a series of poly(propylene glycol) diacrylate monomers. The experimental data are analyzed by means of the approach recently proposed by Petrowsky et al. [J. Phys. Chem. B. 113, 5996 (2009)10.1021/jp810095g]. This so-called compensated Arrhenius formalism (CAF) approach takes into account the influence of the dielectric permittivity on the exponential prefactor in the classical Arrhenius equation. The experimental data presented in this paper show a good agreement with the CAF; this means that the exponential prefactor is principally dielectric permittivity dependent. The compensated data revealed two conduction processes with different activation energies; they correspond to low and high temperature ranges, respectively.

Compensated Arrhenius formalism applied to a conductivity study in poly(propylene glycol) diacrylate monomers

NASA Astrophysics Data System (ADS)

Dubois, F.; Derouiche, Y.; Leblond, J. M.; Maschke, U.; Douali, R.

2015-09-01

The temperature dependence of the ionic conductivity is studied in a series of poly(propylene glycol) diacrylate monomers. The experimental data are analyzed by means of the approach recently proposed by Petrowsky et al. [J. Phys. Chem. B. 113, 5996 (2009), 10.1021/jp810095g]. This so-called compensated Arrhenius formalism (CAF) approach takes into account the influence of the dielectric permittivity on the exponential prefactor in the classical Arrhenius equation. The experimental data presented in this paper show a good agreement with the CAF; this means that the exponential prefactor is principally dielectric permittivity dependent. The compensated data revealed two conduction processes with different activation energies; they correspond to low and high temperature ranges, respectively.

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry.

PubMed

Ouyang, Wenjun; Subotnik, Joseph E

2017-05-07

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

An allometric scaling relation based on logistic growth of cities

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2014-08-01

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential allometry", which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the abovementioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed "logistic allometry". The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.

Mathematical Modeling of Extinction of Inhomogeneous Populations

PubMed Central

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

Wind tunnel test of Teledyne Geotech model 1564B cup anemometer

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

Parker, M.J.; Addis, R.P.

1991-04-04

The Department of Energy (DOE) Environment, Safety and Health Compliance Assessment (Tiger Team) of the Savannah River Site (SRS) questioned the method by which wind speed sensors (cup anemometers) are calibrated by the Environmental Technology Section (ETS). The Tiger Team member was concerned that calibration data was generated by running the wind tunnel to only 26 miles per hour (mph) when speeds exceeding 50 mph are readily obtainable. A wind tunnel experiment was conducted and confirmed the validity of the practice. Wind speeds common to SRS (6 mph) were predicted more accurately by 0--25 mph regression equations than 0--50 mphmore » regression equations. Higher wind speeds were slightly overpredicted by the 0--25 mph regression equations when compared to 0--50 mph regression equations. However, the greater benefit of more accurate lower wind speed predictions accuracy outweight the benefit of slightly better high (extreme) wind speed predictions. Therefore, it is concluded that 0--25 mph regression equations should continue to be utilized by ETS at SRS. During the Department of Energy Tiger Team audit, concerns were raised about the calibration of SRS cup anemometers. Wind speed is measured by ETS with Teledyne Geotech model 1564B cup anemometers, which are calibrated in the ETS wind tunnel. Linear regression lines are fitted to data points of tunnel speed versus anemometer output voltages up to 25 mph. The regression coefficients are then implemented into the data acquisition computer software when an instrument is installed in the field. The concern raised was that since the wind tunnel at SRS is able to generate a maximum wind speed higher than 25 mph, errors may be introduced in not using the full range of the wind tunnel.« less

Wind tunnel test of Teledyne Geotech model 1564B cup anemometer

NASA Astrophysics Data System (ADS)

Parker, M. J.; Addis, R. P.

1991-04-01

The Department of Energy (DOE) Environment, Safety, and Health Compliance Assessment (Tiger Team) of the Savannah River Site (SRS) questioned the method by which wind speed sensors (cup anemometers) are calibrated by the Environmental Technology Section (ETS). The Tiger Team member was concerned that calibration data was generated by running the wind tunnel to only 26 miles per hour (mph) when speeds exceeding 50 mph are readily obtainable. A wind tunnel experiment was conducted and confirmed the validity of the practice. Wind speeds common to SRS (6 mph) were predicted more accurately by 0-25 mph regression equations than 0-50 mph regression equations. Higher wind speeds were slightly overpredicted by the 0-25 mph regression equations when compared to 0-50 mph regression equations. However, the greater benefit of more accurate lower wind speed predictions accuracy outweigh the benefit of slightly better high (extreme) wind speed predictions. Therefore, it is concluded that 0-25 mph regression equations should continue to be utilized by ETS at SRS. During the Department of Energy Tiger Team audit, concerns were raised about the calibration of SRS cup anemometers. Wind speed is measured by ETS with Teledyne Geotech model 1564B cup anemometers, which are calibrated in the ETS wind tunnel. Linear regression lines are fitted to data points of tunnel speed versus anemometer output voltages up to 25 mph. The regression coefficients are then implemented into the data acquisition computer software when an instrument is installed in the field. The concern raised was that since the wind tunnel at SRS is able to generate a maximum wind speed higher than 25 mph, errors may be introduced in not using the full range of the wind tunnel.

Evaluation of the magnitude and frequency of floods in urban watersheds in Phoenix and Tucson, Arizona

USGS Publications Warehouse

Kennedy, Jeffrey R.; Paretti, Nicholas V.

2014-01-01

Flooding in urban areas routinely causes severe damage to property and often results in loss of life. To investigate the effect of urbanization on the magnitude and frequency of flood peaks, a flood frequency analysis was carried out using data from urbanized streamgaging stations in Phoenix and Tucson, Arizona. Flood peaks at each station were predicted using the log-Pearson Type III distribution, fitted using the expected moments algorithm and the multiple Grubbs-Beck low outlier test. The station estimates were then compared to flood peaks estimated by rural-regression equations for Arizona, and to flood peaks adjusted for urbanization using a previously developed procedure for adjusting U.S. Geological Survey rural regression peak discharges in an urban setting. Only smaller, more common flood peaks at the 50-, 20-, 10-, and 4-percent annual exceedance probabilities (AEPs) demonstrate any increase in magnitude as a result of urbanization; the 1-, 0.5-, and 0.2-percent AEP flood estimates are predicted without bias by the rural-regression equations. Percent imperviousness was determined not to account for the difference in estimated flood peaks between stations, either when adjusting the rural-regression equations or when deriving urban-regression equations to predict flood peaks directly from basin characteristics. Comparison with urban adjustment equations indicates that flood peaks are systematically overestimated if the rural-regression-estimated flood peaks are adjusted upward to account for urbanization. At nearly every streamgaging station in the analysis, adjusted rural-regression estimates were greater than the estimates derived using station data. One likely reason for the lack of increase in flood peaks with urbanization is the presence of significant stormwater retention and detention structures within the watershed used in the study.

The existence of almost periodic solutions of certain perturbation systems

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Lin, Muren; Cao, Jinde

2005-10-01

Certain almost periodic perturbation systems are considered in this paper. By using the roughness theory of exponential dichotomies and the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of the above systems. Our results generalize those in [J.K. Hale, Ordinary Differential Equations, Krieger, Huntington, 1980; C. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (1992) 173-181; M. Lin, The existence of almost periodic solution and bounded solution of perturbation systems, Acta Math. Sinica 22A (2002) 61-70 (in Chinese); W.A. Coppel, Almost periodic properties of ordinary differential equations, Ann. Math. Pura Appl. 76 (1967) 27-50; A.M. Fink, Almost Periodic Differential Equations, Lecture Notes in Math., vol. 377, Springer-Verlag, New York, 1974; Y. Xia, F. Chen, A. Chen, J. Cao, Existence and global attractivity of an almost periodic ecological model, Appl. Math. Comput. 157 (2004) 449-475].

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

Monitoring heavy metal Cr in soil based on hyperspectral data using regression analysis

NASA Astrophysics Data System (ADS)

Zhang, Ningyu; Xu, Fuyun; Zhuang, Shidong; He, Changwei

2016-10-01

Heavy metal pollution in soils is one of the most critical problems in the global ecology and environment safety nowadays. Hyperspectral remote sensing and its application is capable of high speed, low cost, less risk and less damage, and provides a good method for detecting heavy metals in soil. This paper proposed a new idea of applying regression analysis of stepwise multiple regression between the spectral data and monitoring the amount of heavy metal Cr by sample points in soil for environmental protection. In the measurement, a FieldSpec HandHeld spectroradiometer is used to collect reflectance spectra of sample points over the wavelength range of 325-1075 nm. Then the spectral data measured by the spectroradiometer is preprocessed to reduced the influence of the external factors, and the preprocessed methods include first-order differential equation, second-order differential equation and continuum removal method. The algorithms of stepwise multiple regression are established accordingly, and the accuracy of each equation is tested. The results showed that the accuracy of first-order differential equation works best, which makes it feasible to predict the content of heavy metal Cr by using stepwise multiple regression.

Tsallis’ quantum q-fields

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-05-01

We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Mean annual runoff and peak flow estimates based on channel geometry of streams in northeastern and western Montana

USGS Publications Warehouse

Parrett, Charles; Omang, R.J.; Hull, J.A.

1983-01-01

Equations for estimating mean annual runoff and peak discharge from measurements of channel geometry were developed for western and northeastern Montana. The study area was divided into two regions for the mean annual runoff analysis, and separate multiple-regression equations were developed for each region. The active-channel width was determined to be the most important independent variable in each region. The standard error of estimate for the estimating equation using active-channel width was 61 percent in the Northeast Region and 38 percent in the West region. The study area was divided into six regions for the peak discharge analysis, and multiple regression equations relating channel geometry and basin characteristics to peak discharges having recurrence intervals of 2, 5, 10, 25, 50 and 100 years were developed for each region. The standard errors of estimate for the regression equations using only channel width as an independent variable ranged from 35 to 105 percent. The standard errors improved in four regions as basin characteristics were added to the estimating equations. (USGS)

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Estimation of premorbid general fluid intelligence using traditional Chinese reading performance in Taiwanese samples.

PubMed

Chen, Ying-Jen; Ho, Meng-Yang; Chen, Kwan-Ju; Hsu, Chia-Fen; Ryu, Shan-Jin

2009-08-01

The aims of the present study were to (i) investigate if traditional Chinese word reading ability can be used for estimating premorbid general intelligence; and (ii) to provide multiple regression equations for estimating premorbid performance on Raven's Standard Progressive Matrices (RSPM), using age, years of education and Chinese Graded Word Reading Test (CGWRT) scores as predictor variables. Four hundred and twenty-six healthy volunteers (201 male, 225 female), aged 16-93 years (mean +/- SD, 41.92 +/- 18.19 years) undertook the tests individually under supervised conditions. Seventy percent of subjects were randomly allocated to the derivation group (n = 296), and the rest to the validation group (n = 130). RSPM score was positively correlated with CGWRT score and years of education. RSPM and CGWRT scores and years of education were also inversely correlated with age, but the declining trend for RSPM performance against age was steeper than that for CGWRT performance. Separate multiple regression equations were derived for estimating RSPM scores using different combinations of age, years of education, and CGWRT score for both groups. The multiple regression coefficient of each equation ranged from 0.71 to 0.80 with the standard error of estimate between 7 and 8 RSPM points. When fitting the data of one group to the equations derived from its counterpart group, the cross-validation multiple regression coefficients ranged from 0.71 to 0.79. There were no significant differences in the 'predicted-obtained' RSPM discrepancies between any equations. The regression equations derived in the present study may provide a basis for estimating premorbid RSPM performance.

Viability estimation of pepper seeds using time-resolved photothermal signal characterization

NASA Astrophysics Data System (ADS)

Kim, Ghiseok; Kim, Geon-Hee; Lohumi, Santosh; Kang, Jum-Soon; Cho, Byoung-Kwan

2014-11-01

We used infrared thermal signal measurement system and photothermal signal and image reconstruction techniques for viability estimation of pepper seeds. Photothermal signals from healthy and aged seeds were measured for seven periods (24, 48, 72, 96, 120, 144, and 168 h) using an infrared camera and analyzed by a regression method. The photothermal signals were regressed using a two-term exponential decay curve with two amplitudes and two time variables (lifetime) as regression coefficients. The regression coefficients of the fitted curve showed significant differences for each seed groups, depending on the aging times. In addition, the viability of a single seed was estimated by imaging of its regression coefficient, which was reconstructed from the measured photothermal signals. The time-resolved photothermal characteristics, along with the regression coefficient images, can be used to discriminate the aged or dead pepper seeds from the healthy seeds.

Estimating air drying times of lumber with multiple regression

Treesearch

William T. Simpson

2004-01-01

In this study, the applicability of a multiple regression equation for estimating air drying times of red oak, sugar maple, and ponderosa pine lumber was evaluated. The equation allows prediction of estimated air drying times from historic weather records of temperature and relative humidity at any desired location.

National scale biomass estimators for United States tree species

Treesearch

Jennifer C. Jenkins; David C. Chojnacky; Linda S. Heath; Richard A. Birdsey

2003-01-01

Estimates of national-scale forest carbon (C) stocks and fluxes are typically based on allometric regression equations developed using dimensional analysis techniques. However, the literature is inconsistent and incomplete with respect to large-scale forest C estimation. We compiled all available diameter-based allometric regression equations for estimating total...

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

Comparison of methods for the prediction of human clearance from hepatocyte intrinsic clearance for a set of reference compounds and an external evaluation set.

PubMed

Yamagata, Tetsuo; Zanelli, Ugo; Gallemann, Dieter; Perrin, Dominique; Dolgos, Hugues; Petersson, Carl

2017-09-01

1. We compared direct scaling, regression model equation and the so-called "Poulin et al." methods to scale clearance (CL) from in vitro intrinsic clearance (CL int ) measured in human hepatocytes using two sets of compounds. One reference set comprised of 20 compounds with known elimination pathways and one external evaluation set based on 17 compounds development in Merck (MS). 2. A 90% prospective confidence interval was calculated using the reference set. This interval was found relevant for the regression equation method. The three outliers identified were justified on the basis of their elimination mechanism. 3. The direct scaling method showed a systematic underestimation of clearance in both the reference and evaluation sets. The "Poulin et al." and the regression equation methods showed no obvious bias in either the reference or evaluation sets. 4. The regression model equation was slightly superior to the "Poulin et al." method in the reference set and showed a better absolute average fold error (AAFE) of value 1.3 compared to 1.6. A larger difference was observed in the evaluation set were the regression method and "Poulin et al." resulted in an AAFE of 1.7 and 2.6, respectively (removing the three compounds with known issues mentioned above). A similar pattern was observed for the correlation coefficient. Based on these data we suggest the regression equation method combined with a prospective confidence interval as the first choice for the extrapolation of human in vivo hepatic metabolic clearance from in vitro systems.

Paleoflood investigations to improve peak-streamflow regional-regression equations for natural streamflow in eastern Colorado, 2015

USGS Publications Warehouse

Kohn, Michael S.; Stevens, Michael R.; Harden, Tessa M.; Godaire, Jeanne E.; Klinger, Ralph E.; Mommandi, Amanullah

2016-09-09

The U.S. Geological Survey (USGS), in cooperation with the Colorado Department of Transportation, developed regional-regression equations for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, 0.2-percent annual exceedance-probability discharge (AEPD) for natural streamflow in eastern Colorado. A total of 188 streamgages, consisting of 6,536 years of record and a mean of approximately 35 years of record per streamgage, were used to develop the peak-streamflow regional-regression equations. The estimated AEPDs for each streamgage were computed using the USGS software program PeakFQ. The AEPDs were determined using systematic data through water year 2013. Based on previous studies conducted in Colorado and neighboring States and on the availability of data, 72 characteristics (57 basin and 15 climatic characteristics) were evaluated as candidate explanatory variables in the regression analysis. Paleoflood and non-exceedance bound ages were established based on reconnaissance-level methods. Multiple lines of evidence were used at each streamgage to arrive at a conclusion (age estimate) to add a higher degree of certainty to reconnaissance-level estimates. Paleoflood or nonexceedance bound evidence was documented at 41 streamgages, and 3 streamgages had previously collected paleoflood data.To determine the peak discharge of a paleoflood or non-exceedanc bound, two different hydraulic models were used.The mean standard error of prediction (SEP) for all 8 AEPDs was reduced approximately 25 percent compared to the previous flood-frequency study. For paleoflood data to be effective in reducing the SEP in eastern Colorado, a larger ratio than 44 of 188 (23 percent) streamgages would need paleoflood data and that paleoflood data would need to increase the record length by more than 25 years for the 1-percent AEPD. The greatest reduction in SEP for the peak-streamflow regional-regression equations was observed when additional new basin characteristics were included in the peak-streamflow regional-regression equations and when eastern Colorado was divided into two separate hydrologic regions. To make further reductions in the uncertainties of the peak-streamflow regional-regression equations in the Foothills and Plains hydrologic regions, additional streamgages or crest-stage gages are needed to collect peak-streamflow data on natural streams in eastern Colorado.Generalized-Least Squares regression was used to compute the final peak-streamflow regional-regression equations for peak-streamflow. Dividing eastern Colorado into two new individual regions at –104° longitude resulted in peak-streamflow regional-regression equations with the smallest SEP. The new hydrologic region located between –104° longitude and the Kansas-Nebraska State line will be designated the Plains hydrologic region and the hydrologic region comprising the rest of eastern Colorado located west of the –104° longitude and east of the Rocky Mountains and below 7,500 feet in the South Platte River Basin and below 9,000 feet in the Arkansas River Basin will be designated the Foothills hydrologic region.

Effects of Economy Type and Nicotine on the Essential Value of Food in Rats

ERIC Educational Resources Information Center

Cassidy, Rachel N.; Dallery, Jesse

2012-01-01

The exponential demand equation proposed by Hursh and Silberberg (2008) provides an estimate of the essential value of a good as a function of price. The model predicts that essential value should remain constant across changes in the magnitude of a reinforcer, but may change as a function of motivational operations. In Experiment 1, rats' demand…

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

The rational parameterization theorem for multisite post-translational modification systems.

PubMed

Thomson, Matthew; Gunawardena, Jeremy

2009-12-21

Post-translational modification of proteins plays a central role in cellular regulation but its study has been hampered by the exponential increase in substrate modification forms ("modforms") with increasing numbers of sites. We consider here biochemical networks arising from post-translational modification under mass-action kinetics, allowing for multiple substrates, having different types of modification (phosphorylation, methylation, acetylation, etc.) on multiple sites, acted upon by multiple forward and reverse enzymes (in total number L), using general enzymatic mechanisms. These assumptions are substantially more general than in previous studies. We show that the steady-state modform concentrations constitute an algebraic variety that can be parameterized by rational functions of the L free enzyme concentrations, with coefficients which are rational functions of the rate constants. The parameterization allows steady states to be calculated by solving L algebraic equations, a dramatic reduction compared to simulating an exponentially large number of differential equations. This complexity collapse enables analysis in contexts that were previously intractable and leads to biological predictions that we review. Our results lay a foundation for the systems biology of post-translational modification and suggest deeper connections between biochemical networks and algebraic geometry.

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein-Gauss-Bonnet model with a Λ -term

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Kobtsev, A. A.

2018-02-01

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned Λ = Λ (x, l, α ) depends upon the ratio h/H = x, l and the ratio α = α _2/α _1 of two constants (α _2 and α _1) of the model. For fixed Λ , α and l > 2 the equation Λ (x,l,α ) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l =3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

DNA electrophoresis in agarose gels: effects of field and gel concentration on the exponential dependence of reciprocal mobility on DNA length.

PubMed

Rill, Randolph L; Beheshti, Afshin; Van Winkle, David H

2002-08-01

Electrophoretic mobilities of DNA molecules ranging in length from 200 to 48 502 base pairs (bp) were measured in agarose gels with concentrations T = 0.5% to 1.3% at electric fields from E = 0.71 to 5.0 V/cm. This broad data set determines a range of conditions over which the new interpolation equation nu(L) = (beta+alpha(1+exp(-L/gamma))(-1) can be used to relate mobility to length with high accuracy. Mobility data were fit with chi(2) > 0.999 for all gel concentrations and fields ranging from 2.5 to 5 V/cm, and for lower fields at low gel concentrations. Analyses using so-called reptation plots (Rousseau, J., Drouin, G., Slater, G. W., Phys. Rev. Lett. 1997, 79, 1945-1948) indicate that this simple exponential relation is obeyed well when there is a smooth transition from the Ogston sieving regime to the reptation regime with increasing DNA length. Deviations from this equation occur when DNA migration is hindered, apparently by entropic-trapping, which is favored at low fields and high gel concentrations in the ranges examined.

Control of Growth Rate by Initial Substrate Concentration at Values Below Maximum Rate

PubMed Central

Gaudy, Anthony F.; Obayashi, Alan; Gaudy, Elizabeth T.

1971-01-01

The hyperbolic relationship between specific growth rate, μ, and substrate concentration, proposed by Monod and used since as the basis for the theory of steady-state growth in continuous-flow systems, was tested experimentally in batch cultures. Use of a Flavobacterium sp. exhibiting a high saturation constant for growth in glucose minimal medium allowed direct measurement of growth rate and substrate concentration throughout the growth cycle in medium containing a rate-limiting initial concentration of glucose. Specific growth rates were also measured for a wide range of initial glucose concentrations. A plot of specific growth rate versus initial substrate concentration was found to fit the hyperbolic equation. However, the instantaneous relationship between specific growth rate and substrate concentration during growth, which is stated by the equation, was not observed. Well defined exponential growth phases were developed at initial substrate concentrations below that required for support of the maximum exponential growth rate and a constant doubling time was maintained until 50% of the substrate had been used. It is suggested that the external substrate concentration initially present “sets” the specific growth rate by establishing a steady-state internal concentration of substrate, possibly through control of the number of permeation sites. PMID:5137579

Control of three-dimensional waves on thin liquid films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Gomes, Susana; Pavliotis, Greg; Papageorgiou, Demetrios

2017-11-01

We consider a weakly nonlinear model for interfacial waves on three-dimensional thin films on inclined flat planes - the Kuramoto-Sivashinsky equation. The flow is driven by gravity, and is allowed to be overlying or hanging on the flat substrate. Blowing and suction controls are applied at the substrate surface. We explore the instability of the transverse modes for hanging arrangements, which are unbounded and grow exponentially. The structure of the equations allows us to construct optimal transverse controls analytically to prevent this transverse growth. We also may consider the influence of transverse modes on overlying film flows, these modes are damped out if uncontrolled. We also consider the more physical concept of point actuated controls which are modelled using Dirac delta functions. We first study the case of proportional control, where the actuation at a point depends on the local interface height alone. Here, we study the influence of control strength and number/location of actuators on the possible stabilization of the zero solution. We also consider the full feedback problem, which assumes that we can observe the full interface and allow communication between actuators. Using these controls we can obtain exponential stability where proportional controls fail, and stabilize non-trivial solutions.

Properties of one-dimensional anharmonic lattice solitons

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

2000-12-01

The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

Stress relaxation study of fillers for directly compressed tablets

PubMed Central

Rehula, M.; Adamek, R.; Spacek, V.

2012-01-01

It is possible to assess viscoelastic properties of materials by means of the stress relaxation test. This method records the decrease in pressing power in a tablet at its constant height. The cited method was used to evaluate the time-dependent deformation for six various materials: microcrystalline cellulose, cellulose powder, hydroxypropyl methylcellulose, mannitol, lactose monohydrate, and hydrogen phosphate monohydrate. The decrease in pressing powering of a tablet during a 180 s period was described mathematically by the parameters of three exponential equations, where the whole course of the stress relaxation is divided into three individual processes (instant elastic deformation, retarded elastic deformation and permanent plastic deformation). Three values of the moduli of plasticity and elasticity were calculated for each compound. The values of elastic parameters ATi have a strong relationship with bulk density. The plastic parameters PTi represent particle tendency to form bonds. The values of plasticity in the third process PT3 ranged from 400 to 600 MPas. Mannitol had higher plasticity and lactose monohydrate on the contrary reduced plasticity. A linear relation exists between AT3 and PT3 for the third process. No similar interpretation of moduli calculated on the basis of three exponential equations has been realized yet. PMID:24850972

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

Methods for estimating peak-flow frequencies at ungaged sites in Montana based on data through water year 2011: Chapter F in Montana StreamStats

USGS Publications Warehouse

Sando, Roy; Sando, Steven K.; McCarthy, Peter M.; Dutton, DeAnn M.

2016-04-05

The U.S. Geological Survey (USGS), in cooperation with the Montana Department of Natural Resources and Conservation, completed a study to update methods for estimating peak-flow frequencies at ungaged sites in Montana based on peak-flow data at streamflow-gaging stations through water year 2011. The methods allow estimation of peak-flow frequencies (that is, peak-flow magnitudes, in cubic feet per second, associated with annual exceedance probabilities of 66.7, 50, 42.9, 20, 10, 4, 2, 1, 0.5, and 0.2 percent) at ungaged sites. The annual exceedance probabilities correspond to 1.5-, 2-, 2.33-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively.Regional regression analysis is a primary focus of Chapter F of this Scientific Investigations Report, and regression equations for estimating peak-flow frequencies at ungaged sites in eight hydrologic regions in Montana are presented. The regression equations are based on analysis of peak-flow frequencies and basin characteristics at 537 streamflow-gaging stations in or near Montana and were developed using generalized least squares regression or weighted least squares regression.All of the data used in calculating basin characteristics that were included as explanatory variables in the regression equations were developed for and are available through the USGS StreamStats application (http://water.usgs.gov/osw/streamstats/) for Montana. StreamStats is a Web-based geographic information system application that was created by the USGS to provide users with access to an assortment of analytical tools that are useful for water-resource planning and management. The primary purpose of the Montana StreamStats application is to provide estimates of basin characteristics and streamflow characteristics for user-selected ungaged sites on Montana streams. The regional regression equations presented in this report chapter can be conveniently solved using the Montana StreamStats application.Selected results from this study were compared with results of previous studies. For most hydrologic regions, the regression equations reported for this study had lower mean standard errors of prediction (in percent) than the previously reported regression equations for Montana. The equations presented for this study are considered to be an improvement on the previously reported equations primarily because this study (1) included 13 more years of peak-flow data; (2) included 35 more streamflow-gaging stations than previous studies; (3) used a detailed geographic information system (GIS)-based definition of the regulation status of streamflow-gaging stations, which allowed better determination of the unregulated peak-flow records that are appropriate for use in the regional regression analysis; (4) included advancements in GIS and remote-sensing technologies, which allowed more convenient calculation of basin characteristics and investigation of many more candidate basin characteristics; and (5) included advancements in computational and analytical methods, which allowed more thorough and consistent data analysis.This report chapter also presents other methods for estimating peak-flow frequencies at ungaged sites. Two methods for estimating peak-flow frequencies at ungaged sites located on the same streams as streamflow-gaging stations are described. Additionally, envelope curves relating maximum recorded annual peak flows to contributing drainage area for each of the eight hydrologic regions in Montana are presented and compared to a national envelope curve. In addition to providing general information on characteristics of large peak flows, the regional envelope curves can be used to assess the reasonableness of peak-flow frequency estimates determined using the regression equations.

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma

USGS Publications Warehouse

Esralew, Rachel A.; Smith, S. Jerrod

2010-01-01

Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma. Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states. A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5. Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations. Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma). A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation. The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected. The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region. Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent vari

Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems

NASA Astrophysics Data System (ADS)

Mei, Lijie; Wu, Xinyuan

2017-06-01

Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

Growth and mortality of larval Myctophum affine (Myctophidae, Teleostei).

PubMed

Namiki, C; Katsuragawa, M; Zani-Teixeira, M L

2015-04-01

The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south-eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L(S)). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird-Gompertz model. The exponential model best fitted the data, and L(0) values from exponential and Laird-Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L(S)). The average growth rate (0·33 mm day(-1)) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area. © 2015 The Fisheries Society of the British Isles.

[Effects of soil properties on the stabilization process of cadmium in Cd alone and Cd-Pb contaminated soils].

PubMed

Wu, Man; Xu, Ming-Gang; Zhang, Wen-Ju; Wu, Hai-Wen

2012-07-01

In order to clarify the effects of soil properties on the stabilization process of the cadmium (Cd) added, 11 different soils were collected and incubated under a moisture content of 65%-70% at 25 degrees C. The changes of available Cd contents with incubation time (in 360 days) in Cd and Cd-Pb contaminated treatments were determined. The stabilization process was simulated using dynamic equations. The results showed that after 1.0 mg x kg(-1) Cd or 500 mg x kg(-1) Pb + 1.0 mg x kg(-1) Cd were added into the soil, the available Cd content decreased rapidly during the first 15 days, and then the decreasing rate slowed down, with an equilibrium content reached after 60 days' incubation. In Cd-Pb contaminated soils, the presence of Pb increased the content of available Cd. The stabilization process of Cd could be well described by the second-order equation and the first order exponential decay; meanwhile, dynamic parameters including equilibrium content and stabilization velocity were used to characterize the stabilization process of Cd. These two key dynamic parameters were significantly affected by soil properties. Correlation analysis and stepwise regression suggested that high pH and high cation exchange capacity (CEC) significantly retarded the availability of Cd. High pH had the paramount effect on the equilibrium content. The stabilization velocity of Cd was influenced by the soil texture. It took shorter time for Cd to get stabilized in sandy soil than in the clay.

Development, triploblastism, physics of wetting and the Cambrian explosion.

PubMed

Fleury, Vincent

2013-09-01

The Cambrian explosion is characterized by the sudden outburst of organized animal plans, which occurred circa 530 M years ago. Around that time, many forms of animal life appeared, including several which have since disappeared. There is no general consensus about "why" this happened, and why it had any form of suddenness. However, all organized animal plans share a common feature: they are triploblastic, i.e., composed of 3 layers of tissue, endoderm, ectoderm and mesoderm. I show here that, within simple hypotheses, the formation of the mesoderm has intrinsically a physical exponential dynamics, leading rapidly to triploblastism, and eventually, to animal formation. A novel physico-mathematical framework including epithelium-mesenchyme transition, visco-elastic constitutive equations, and conservation laws, is presented which allows one to describe gastrulation as a self-wetting phenomenon of a soft solid onto itself. This phenomenon couples differentiation and migration during gastrulation, and leads in a closed form to an exponential scaling law for the formation of the mesoderm. Therefore, the Cambrian explosion might have started, actually, by a true viscoelastic "explosion": the exponential run-away of mesenchymal cells.

A Comparison of Regional and SiteSpecific Volume Estimation Equations

Treesearch

Joe P. McClure; Jana Anderson; Hans T. Schreuder

1987-01-01

Regression equations for volume by region and site class were examined for lobiolly pine. The regressions for the Coastal Plain and Piedmont regions had significantly different slopes. The results shared important practical differences in percentage of confidence intervals containing the true total volume and in percentage of estimates within a specific proportion of...

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

ERIC Educational Resources Information Center

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

Film Boiling Heat Transfer Properties of Liquid Hydrogen in Natural Convection

NASA Astrophysics Data System (ADS)

Horie, Y.; Shirai, Y.; Shiotsu, M.; Matsuzawa, T.; Yoneda, K.; Shigeta, H.; Tatsumoto, H.; Hata, K.; Naruo, Y.; Kobayashi, H.; Inatani, Y.

Film boiling heat transfer properties of LH2 for various pressures and subcooling conditions were measured by applying electric current to give an exponential heat input to a PtCo wire with a diameter of 1.2 mm submerged in LH2. The heated wire was set to be horizontal to the ground. The heat transfer coefficient in the film boiling region was higher for higher pressure and higher subcooling. The experimental results are compared with the equation of pool film boiling heat transfer. It is confirmed that the pool film boiling heat transfer coefficients in LH2 can be expressed by this equation.

The equation of state of predominant detonation products

NASA Astrophysics Data System (ADS)

Zaug, Joseph; Crowhurst, Jonathan; Bastea, Sorin; Fried, Laurence

2009-06-01

The equation of state of detonation products, when incorporated into an experimentally grounded thermochemical reaction algorithm can be used to predict the performance of explosives. Here we report laser based Impulsive Stimulated Light Scattering measurements of the speed of sound from a variety of polar and nonpolar detonation product supercritical fluids and mixtures. The speed of sound data are used to improve the exponential-six potentials employed within the Cheetah thermochemical code. We will discuss the improvements made to Cheetah in terms of predictions vs. measured performance data for common polymer blended explosives. Accurately computing the chemistry that occurs from reacted binder materials is one important step forward in our efforts.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Similarity Solutions on Mixed Convection Heat Transfer from a Horizontal Surface Saturated in a Porous Medium with Internal Heat Generation

NASA Astrophysics Data System (ADS)

Ferdows, M.; Liu, D.

2017-02-01

The aim of this work is to study the mixed convection boundary layer flow from a horizontal surface embedded in a porous medium with exponential decaying internal heat generation (IHG). Boundary layer equations are reduced to two ordinary differential equations for the dimensionless stream function and temperature with two parameters: ɛ, the mixed convection parameter, and λ, the exponent of x. This problem is numerically solved with a system of parameters using built-in codes in Maple. The influences of these parameters on velocity and temperature profiles, and the Nusselt number, are thoroughly compared and discussed.

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

Rasmussen, Martin; Hastings, Alan; Smith, Matthew J.

We develop a theory for residence times and mean ages for nonautonomous compartmental systems. Using the McKendrick–von Forster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of residence time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory is consistent with the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the carbon cycle, which is a simplified version of the Carnegie–Ames–Stanfordmore » approach (CASA) model.« less

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

NASA Technical Reports Server (NTRS)

Desmarais, R. N.; Rowe, W. S.

1984-01-01

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

Squared exponential covariance function for prediction of hydrocarbon in seabed logging application

NASA Astrophysics Data System (ADS)

Mukhtar, Siti Mariam; Daud, Hanita; Dass, Sarat Chandra

2016-11-01

Seabed Logging technology (SBL) has progressively emerged as one of the demanding technologies in Exploration and Production (E&P) industry. Hydrocarbon prediction in deep water areas is crucial task for a driller in any oil and gas company as drilling cost is very expensive. Simulation data generated by Computer Software Technology (CST) is used to predict the presence of hydrocarbon where the models replicate real SBL environment. These models indicate that the hydrocarbon filled reservoirs are more resistive than surrounding water filled sediments. Then, as hydrocarbon depth is increased, it is more challenging to differentiate data with and without hydrocarbon. MATLAB is used for data extractions for curve fitting process using Gaussian process (GP). GP can be classified into regression and classification problems, where this work only focuses on Gaussian process regression (GPR) problem. Most popular choice to supervise GPR is squared exponential (SE), as it provides stability and probabilistic prediction in huge amounts of data. Hence, SE is used to predict the presence or absence of hydrocarbon in the reservoir from the data generated.

Multivariate Time Series Forecasting of Crude Palm Oil Price Using Machine Learning Techniques

NASA Astrophysics Data System (ADS)

Kanchymalay, Kasturi; Salim, N.; Sukprasert, Anupong; Krishnan, Ramesh; Raba'ah Hashim, Ummi

2017-08-01

The aim of this paper was to study the correlation between crude palm oil (CPO) price, selected vegetable oil prices (such as soybean oil, coconut oil, and olive oil, rapeseed oil and sunflower oil), crude oil and the monthly exchange rate. Comparative analysis was then performed on CPO price forecasting results using the machine learning techniques. Monthly CPO prices, selected vegetable oil prices, crude oil prices and monthly exchange rate data from January 1987 to February 2017 were utilized. Preliminary analysis showed a positive and high correlation between the CPO price and soy bean oil price and also between CPO price and crude oil price. Experiments were conducted using multi-layer perception, support vector regression and Holt Winter exponential smoothing techniques. The results were assessed by using criteria of root mean square error (RMSE), means absolute error (MAE), means absolute percentage error (MAPE) and Direction of accuracy (DA). Among these three techniques, support vector regression(SVR) with Sequential minimal optimization (SMO) algorithm showed relatively better results compared to multi-layer perceptron and Holt Winters exponential smoothing method.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

Thermal requirements of Dermanyssus gallinae (De Geer, 1778) (Acari: Dermanyssidae).

PubMed

Tucci, Edna Clara; do Prado, Angelo P; de Araújo, Raquel Pires

2008-01-01

The thermal requirements for development of Dermanyssus gallinae were studied under laboratory conditions at 15, 20, 25, 30 and 35 degrees C, a 12h photoperiod and 60-85% RH. The thermal requirements for D. gallinae were as follows. Preoviposition: base temperature 3.4 degrees C, thermal constant (k) 562.85 degree-hours, determination coefficient (R(2)) 0.59, regression equation: Y= -0.006035 + 0.001777x. Egg: base temperature 10.60 degrees C, thermal constant (k) 689.65 degree-hours, determination coefficient (R(2)) 0.94, regression equation: Y= -0.015367 + 0.001450x. Larva: base temperature 9.82 degrees C, thermal constant (k) 464.91 degree-hours, determination coefficient (R(2)) 0.87, regression equation: Y= -0.021123 + 0.002151x. Protonymph: base temperature 10.17 degrees C, thermal constant (k) 504.49 degree-hours, determination coefficient (R(2)) 0.90, regression equation: Y= -0.020152 + 0.001982x. Deutonymph: base temperature 11.80 degrees C, thermal constant (k) 501.11 degree-hours, determination coefficient (R(2)) 0.99, regression equation: Y= -0.023555 + 0.001996x. The results obtained showed that 15 to 42 generations of Dermanyssus gallinae may occur during the year in the State of São Paulo, as estimated based on isotherm charts. Dermanyssus gallinae may develop continually in the State of São Paulo, with a population decrease in the winter. There were differences between the developmental stages of D. gallinae in relation to thermal requirements.

Turbulence in a gaseous hydrogen-liquid oxygen rocket combustion chamber

NASA Technical Reports Server (NTRS)

Lebas, J.; Tou, P.; Ohara, J.

1975-01-01

The intensity of turbulence and the Lagrangian correlation coefficient for a LOX-GH2 rocket combustion chamber was determined from experimental measurements of tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and a numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber, and an exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the value of the intensity of turbulence reaches a maximum of 14% at a location about 7" downstream from the injector. The Lagrangian correlation coefficient associated with this value is given by the above exponential expression where alpha = 10,000/sec.

Transfer potentials shape and equilibrate monetary systems

NASA Astrophysics Data System (ADS)

Fischer, Robert; Braun, Dieter

2003-04-01

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economist's quantity theory ( MV= PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape Gaussian, tent-shape exponential, Boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time-dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.

Stature estimation equations for South Asian skeletons based on DXA scans of contemporary adults.

PubMed

Pomeroy, Emma; Mushrif-Tripathy, Veena; Wells, Jonathan C K; Kulkarni, Bharati; Kinra, Sanjay; Stock, Jay T

2018-05-03

Stature estimation from the skeleton is a classic anthropological problem, and recent years have seen the proliferation of population-specific regression equations. Many rely on the anatomical reconstruction of stature from archaeological skeletons to derive regression equations based on long bone lengths, but this requires a collection with very good preservation. In some regions, for example, South Asia, typical environmental conditions preclude the sufficient preservation of skeletal remains. Large-scale epidemiological studies that include medical imaging of the skeleton by techniques such as dual-energy X-ray absorptiometry (DXA) offer new potential datasets for developing such equations. We derived estimation equations based on known height and bone lengths measured from DXA scans from the Andhra Pradesh Children and Parents Study (Hyderabad, India). Given debates on the most appropriate regression model to use, multiple methods were compared, and the performance of the equations was tested on a published skeletal dataset of individuals with known stature. The equations have standard errors of estimates and prediction errors similar to those derived using anatomical reconstruction or from cadaveric datasets. As measured by the number of significant differences between true and estimated stature, and the prediction errors, the new equations perform as well as, and generally better than, published equations commonly used on South Asian skeletons or based on Indian cadaveric datasets. This study demonstrates the utility of DXA scans as a data source for developing stature estimation equations and offer a new set of equations for use with South Asian datasets. © 2018 Wiley Periodicals, Inc.

Application of stepwise multiple regression techniques to inversion of Nimbus 'IRIS' observations.

NASA Technical Reports Server (NTRS)

Ohring, G.

1972-01-01

Exploratory studies with Nimbus-3 infrared interferometer-spectrometer (IRIS) data indicate that, in addition to temperature, such meteorological parameters as geopotential heights of pressure surfaces, tropopause pressure, and tropopause temperature can be inferred from the observed spectra with the use of simple regression equations. The technique of screening the IRIS spectral data by means of stepwise regression to obtain the best radiation predictors of meteorological parameters is validated. The simplicity of application of the technique and the simplicity of the derived linear regression equations - which contain only a few terms - suggest usefulness for this approach. Based upon the results obtained, suggestions are made for further development and exploitation of the stepwise regression analysis technique.

Selected Streamflow Statistics and Regression Equations for Predicting Statistics at Stream Locations in Monroe County, Pennsylvania

USGS Publications Warehouse

Thompson, Ronald E.; Hoffman, Scott A.

2006-01-01

A suite of 28 streamflow statistics, ranging from extreme low to high flows, was computed for 17 continuous-record streamflow-gaging stations and predicted for 20 partial-record stations in Monroe County and contiguous counties in north-eastern Pennsylvania. The predicted statistics for the partial-record stations were based on regression analyses relating inter-mittent flow measurements made at the partial-record stations indexed to concurrent daily mean flows at continuous-record stations during base-flow conditions. The same statistics also were predicted for 134 ungaged stream locations in Monroe County on the basis of regression analyses relating the statistics to GIS-determined basin characteristics for the continuous-record station drainage areas. The prediction methodology for developing the regression equations used to estimate statistics was developed for estimating low-flow frequencies. This study and a companion study found that the methodology also has application potential for predicting intermediate- and high-flow statistics. The statistics included mean monthly flows, mean annual flow, 7-day low flows for three recurrence intervals, nine flow durations, mean annual base flow, and annual mean base flows for two recurrence intervals. Low standard errors of prediction and high coefficients of determination (R2) indicated good results in using the regression equations to predict the statistics. Regression equations for the larger flow statistics tended to have lower standard errors of prediction and higher coefficients of determination (R2) than equations for the smaller flow statistics. The report discusses the methodologies used in determining the statistics and the limitations of the statistics and the equations used to predict the statistics. Caution is indicated in using the predicted statistics for small drainage area situations. Study results constitute input needed by water-resource managers in Monroe County for planning purposes and evaluation of water-resources availability.

Estimating peak discharges, flood volumes, and hydrograph shapes of small ungaged urban streams in Ohio

USGS Publications Warehouse

Sherwood, J.M.

1986-01-01

Methods are presented for estimating peak discharges, flood volumes and hydrograph shapes of small (less than 5 sq mi) urban streams in Ohio. Examples of how to use the various regression equations and estimating techniques also are presented. Multiple-regression equations were developed for estimating peak discharges having recurrence intervals of 2, 5, 10, 25, 50, and 100 years. The significant independent variables affecting peak discharge are drainage area, main-channel slope, average basin-elevation index, and basin-development factor. Standard errors of regression and prediction for the peak discharge equations range from +/-37% to +/-41%. An equation also was developed to estimate the flood volume of a given peak discharge. Peak discharge, drainage area, main-channel slope, and basin-development factor were found to be the significant independent variables affecting flood volumes for given peak discharges. The standard error of regression for the volume equation is +/-52%. A technique is described for estimating the shape of a runoff hydrograph by applying a specific peak discharge and the estimated lagtime to a dimensionless hydrograph. An equation for estimating the lagtime of a basin was developed. Two variables--main-channel length divided by the square root of the main-channel slope and basin-development factor--have a significant effect on basin lagtime. The standard error of regression for the lagtime equation is +/-48%. The data base for the study was established by collecting rainfall-runoff data at 30 basins distributed throughout several metropolitan areas of Ohio. Five to eight years of data were collected at a 5-min record interval. The USGS rainfall-runoff model A634 was calibrated for each site. The calibrated models were used in conjunction with long-term rainfall records to generate a long-term streamflow record for each site. Each annual peak-discharge record was fitted to a Log-Pearson Type III frequency curve. Multiple-regression techniques were then used to analyze the peak discharge data as a function of the basin characteristics of the 30 sites. (Author 's abstract)

An evaluation of regression methods to estimate nutritional condition of canvasbacks and other water birds

USGS Publications Warehouse

Sparling, D.W.; Barzen, J.A.; Lovvorn, J.R.; Serie, J.R.

1992-01-01

Regression equations that use mensural data to estimate body condition have been developed for several water birds. These equations often have been based on data that represent different sexes, age classes, or seasons, without being adequately tested for intergroup differences. We used proximate carcass analysis of 538 adult and juvenile canvasbacks (Aythya valisineria ) collected during fall migration, winter, and spring migrations in 1975-76 and 1982-85 to test regression methods for estimating body condition.

Continuous water-quality monitoring and regression analysis to estimate constituent concentrations and loads in the Red River of the North at Fargo and Grand Forks, North Dakota, 2003-12

USGS Publications Warehouse

Galloway, Joel M.

2014-01-01

The Red River of the North (hereafter referred to as “Red River”) Basin is an important hydrologic region where water is a valuable resource for the region’s economy. Continuous water-quality monitors have been operated by the U.S. Geological Survey, in cooperation with the North Dakota Department of Health, Minnesota Pollution Control Agency, City of Fargo, City of Moorhead, City of Grand Forks, and City of East Grand Forks at the Red River at Fargo, North Dakota, from 2003 through 2012 and at Grand Forks, N.Dak., from 2007 through 2012. The purpose of the monitoring was to provide a better understanding of the water-quality dynamics of the Red River and provide a way to track changes in water quality. Regression equations were developed that can be used to estimate concentrations and loads for dissolved solids, sulfate, chloride, nitrate plus nitrite, total phosphorus, and suspended sediment using explanatory variables such as streamflow, specific conductance, and turbidity. Specific conductance was determined to be a significant explanatory variable for estimating dissolved solids concentrations at the Red River at Fargo and Grand Forks. The regression equations provided good relations between dissolved solid concentrations and specific conductance for the Red River at Fargo and at Grand Forks, with adjusted coefficients of determination of 0.99 and 0.98, respectively. Specific conductance, log-transformed streamflow, and a seasonal component were statistically significant explanatory variables for estimating sulfate in the Red River at Fargo and Grand Forks. Regression equations provided good relations between sulfate concentrations and the explanatory variables, with adjusted coefficients of determination of 0.94 and 0.89, respectively. For the Red River at Fargo and Grand Forks, specific conductance, streamflow, and a seasonal component were statistically significant explanatory variables for estimating chloride. For the Red River at Grand Forks, a time component also was a statistically significant explanatory variable for estimating chloride. The regression equations for chloride at the Red River at Fargo provided a fair relation between chloride concentrations and the explanatory variables, with an adjusted coefficient of determination of 0.66 and the equation for the Red River at Grand Forks provided a relatively good relation between chloride concentrations and the explanatory variables, with an adjusted coefficient of determination of 0.77. Turbidity and streamflow were statistically significant explanatory variables for estimating nitrate plus nitrite concentrations at the Red River at Fargo and turbidity was the only statistically significant explanatory variable for estimating nitrate plus nitrite concentrations at Grand Forks. The regression equation for the Red River at Fargo provided a relatively poor relation between nitrate plus nitrite concentrations, turbidity, and streamflow, with an adjusted coefficient of determination of 0.46. The regression equation for the Red River at Grand Forks provided a fair relation between nitrate plus nitrite concentrations and turbidity, with an adjusted coefficient of determination of 0.73. Some of the variability that was not explained by the equations might be attributed to different sources contributing nitrates to the stream at different times. Turbidity, streamflow, and a seasonal component were statistically significant explanatory variables for estimating total phosphorus at the Red River at Fargo and Grand Forks. The regression equation for the Red River at Fargo provided a relatively fair relation between total phosphorus concentrations, turbidity, streamflow, and season, with an adjusted coefficient of determination of 0.74. The regression equation for the Red River at Grand Forks provided a good relation between total phosphorus concentrations, turbidity, streamflow, and season, with an adjusted coefficient of determination of 0.87. For the Red River at Fargo, turbidity and streamflow were statistically significant explanatory variables for estimating suspended-sediment concentrations. For the Red River at Grand Forks, turbidity was the only statistically significant explanatory variable for estimating suspended-sediment concentration. The regression equation at the Red River at Fargo provided a good relation between suspended-sediment concentration, turbidity, and streamflow, with an adjusted coefficient of determination of 0.95. The regression equation for the Red River at Grand Forks provided a good relation between suspended-sediment concentration and turbidity, with an adjusted coefficient of determination of 0.96.

A stream-gaging network analysis for the 7-day, 10-year annual low flow in New Hampshire streams

USGS Publications Warehouse

Flynn, Robert H.

2003-01-01

The 7-day, 10-year (7Q10) low-flow-frequency statistic is a widely used measure of surface-water availability in New Hampshire. Regression equations and basin-characteristic digital data sets were developed to help water-resource managers determine surface-water resources during periods of low flow in New Hampshire streams. These regression equations and data sets were developed to estimate streamflow statistics for the annual and seasonal low-flow-frequency, and period-of-record and seasonal period-of-record flow durations. generalized-least-squares (GLS) regression methods were used to develop the annual 7Q10 low-flow-frequency regression equation from 60 continuous-record stream-gaging stations in New Hampshire and in neighboring States. In the regression equation, the dependent variables were the annual 7Q10 flows at the 60 stream-gaging stations. The independent (or predictor) variables were objectively selected characteristics of the drainage basins that contribute flow to those stations. In contrast to ordinary-least-squares (OLS) regression analysis, GLS-developed estimating equations account for differences in length of record and spatial correlations among the flow-frequency statistics at the various stations.A total of 93 measurable drainage-basin characteristics were candidate independent variables. On the basis of several statistical parameters that were used to evaluate which combination of basin characteristics contribute the most to the predictive power of the equations, three drainage-basin characteristics were determined to be statistically significant predictors of the annual 7Q10: (1) total drainage area, (2) mean summer stream-gaging station precipitation from 1961 to 90, and (3) average mean annual basinwide temperature from 1961 to 1990.To evaluate the effectiveness of the stream-gaging network in providing regional streamflow data for the annual 7Q10, the computer program GLSNET (generalized-least-squares NETwork) was used to analyze the network by application of GLS regression between streamflow and the climatic and basin characteristics of the drainage basin upstream from each stream-gaging station. Improvement to the predictive ability of the regression equations developed for the network analyses is measured by the reduction in the average sampling-error variance, and can be achieved by collecting additional streamflow data at existing stations. The predictive ability of the regression equations is enhanced even further with the addition of new stations to the network. Continued data collection at unregulated stream-gaging stations with less than 14 years of record resulted in the greatest cost-weighted reduction to the average sampling-error variance of the annual 7Q10 regional regression equation. The addition of new stations in basins with underrepresented values for the independent variables of the total drainage area, average mean annual basinwide temperature, or mean summer stream-gaging station precipitation in the annual 7Q10 regression equation yielded a much greater cost-weighted reduction to the average sampling-error variance than when more data were collected at existing unregulated stations. To maximize the regional information obtained from the stream-gaging network for the annual 7Q10, ranking of the streamflow data can be used to determine whether an active station should be continued or if a new or discontinued station should be activated for streamflow data collection. Thus, this network analysis can help determine the costs and benefits of continuing the operation of a particular station or activating a new station at another location to predict the 7Q10 at ungaged stream reaches. The decision to discontinue an existing station or activate a new station, however, must also consider its contribution to other water-resource analyses such as flood management, water quality, or trends in land use or climatic change.

Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules

NASA Astrophysics Data System (ADS)

Celik, E.; Bulut, H.; Baskonus, H. M.

2018-05-01

In this manuscript, the modified exp (- Ω (ξ )) -expansion function method is implemented to find the new solutions to the nonlinear differential equation being the transmission line model. We obtain some new solutions to this model such as complex, exponential, trigonometric and hyperbolic functions. We plot the two- and three-dimensional surfaces of each solutions obtained in this manuscript.

Patterns of Reinforcement and the Essential Values of Brands: I. Incorporation of Utilitarian and Informational Reinforcement into the Estimation of Demand

ERIC Educational Resources Information Center

Yan, Ji; Foxall, Gordon R.; Doyle, John R.

2012-01-01

Essential value is defined by Hursh and Silberberg (2008) as the value of reinforcers, presented in an exponential model (Equation 1). This study extends previous research concerned with animal behavior or human responding in therapeutic situations. We applied 9 available demand curves to consumer data that included 10,000+ data points collected…

Techniques for the determination of mass properties of earth-to-orbit transportation systems

NASA Technical Reports Server (NTRS)

Macconochie, I. O.; Klich, P. J.

1978-01-01

One estimating technique involves trending whereby projections of overall mass properties of vehicles are determined with few inputs. The second technique involves trending of individual subsystems using equations of the form KXN to the nth power or KX. Some constants and exponentials are provided for sample subsystems. Mass properties are reported in a format recommended by mil spec - 38310.

Stability of the thermodynamic equilibrium - A test of the validity of dynamic models as applied to gyroviscous perpendicular magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Faghihi, Mustafa; Scheffel, Jan; Spies, Guenther O.

1988-05-01

Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfven waves in a spatially homogeneous static equilibrium with scalar pressure.

Recent advances in spin-free state-specific and state-universal multi-reference coupled cluster formalisms: A unitary group adapted approach

NASA Astrophysics Data System (ADS)

Maitra, Rahul; Sinha, Debalina; Sen, Sangita; Shee, Avijit; Mukherjee, Debashis

2012-06-01

We present here the formulations and implementations of Mukherjee's State-Specific and State-Universal Multi-reference Coupled Cluster theories, which are explicitly spin free being obtained via the Unitary Group Adapted (UGA) approach, and thus, do not suffer from spin-contamination. We refer to them as UGA-SSMRCC and UGASUMRCC respectively. We propose a new multi-exponential cluster Ansatz analogous to but different from the one suggested by Jeziorski and Monkhorst (JM). Unlike the JM Ansatz, our choice involves spin-free unitary generators for the cluster operators and we replace the traditional exponential structure for the wave-operator by a suitable normal ordered exponential. We sketch the consequences of choosing our Ansatz, which leads to fully spin-free finite power series structure of the direct term of the MRCC equations. The UGA-SUMRCC follows from a suitable hierarchical generation of the cluster amplitudes of increasing rank, while the UGA-SSMRCC requires suitable sufficiency conditions to arrive at a well-defined set of equations for the cluster amplitudes. We discuss two distinct and inequivalent sufficiency conditions and their pros and cons. We also discuss a variant of the UGA-SSMRCC, where the number of cluster amplitudes can be drastically reduced by internal contraction of the two-body inactive cluster amplitudes. These are the most numerous, and thus a spin-free internally contracted description will lead to a high speed-up factor. We refer to this as ICID-UGA-SSMRCC. Essentially the same mathematical manipulations provide us with the UGA-SUMRCC theory as well. Pilot numerical results are presented to indicate the promise and the efficacy of all the three methods.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

NASA Astrophysics Data System (ADS)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

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

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; ...

2017-10-24

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Pattern analysis of total item score and item response of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative sample of US adults

PubMed Central

Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Yutaka, Ono; Furukawa, Toshiaki A.

2017-01-01

Background Several recent studies have shown that total scores on depressive symptom measures in a general population approximate an exponential pattern except for the lower end of the distribution. Furthermore, we confirmed that the exponential pattern is present for the individual item responses on the Center for Epidemiologic Studies Depression Scale (CES-D). To confirm the reproducibility of such findings, we investigated the total score distribution and item responses of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative study. Methods Data were drawn from the National Survey of Midlife Development in the United States (MIDUS), which comprises four subsamples: (1) a national random digit dialing (RDD) sample, (2) oversamples from five metropolitan areas, (3) siblings of individuals from the RDD sample, and (4) a national RDD sample of twin pairs. K6 items are scored using a 5-point scale: “none of the time,” “a little of the time,” “some of the time,” “most of the time,” and “all of the time.” The pattern of total score distribution and item responses were analyzed using graphical analysis and exponential regression model. Results The total score distributions of the four subsamples exhibited an exponential pattern with similar rate parameters. The item responses of the K6 approximated a linear pattern from “a little of the time” to “all of the time” on log-normal scales, while “none of the time” response was not related to this exponential pattern. Discussion The total score distribution and item responses of the K6 showed exponential patterns, consistent with other depressive symptom scales. PMID:28289560

Use of Thematic Mapper for water quality assessment

NASA Technical Reports Server (NTRS)

Horn, E. M.; Morrissey, L. A.

1984-01-01

The evaluation of simulated TM data obtained on an ER-2 aircraft at twenty-five predesignated sample sites for mapping water quality factors such as conductivity, pH, suspended solids, turbidity, temperature, and depth, is discussed. Using a multiple regression for the seven TM bands, an equation is developed for the suspended solids. TM bands 1, 2, 3, 4, and 6 are used with logarithm conductivity in a multiple regression. The assessment of regression equations for a high coefficient of determination (R-squared) and statistical significance is considered. Confidence intervals about the mean regression point are calculated in order to assess the robustness of the regressions used for mapping conductivity, turbidity, and suspended solids, and by regressing random subsamples of sites and comparing the resultant range of R-squared, cross validation is conducted.

Development of Multiple Regression Equations To Predict Fourth Graders' Achievement in Reading and Selected Content Areas.

ERIC Educational Resources Information Center

Hafner, Lawrence E.

A study developed a multiple regression prediction equation for each of six selected achievement variables in a popular standardized test of achievement. Subjects, 42 fourth-grade pupils randomly selected across several classes in a large elementary school in a north Florida city, were administered several standardized tests to determine predictor…

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

Flood characteristics of urban watersheds in the United States

USGS Publications Warehouse

Sauer, Vernon B.; Thomas, W.O.; Stricker, V.A.; Wilson, K.V.

1983-01-01

A nationwide study of flood magnitude and frequency in urban areas was made for the purpose of reviewing available literature, compiling an urban flood data base, and developing methods of estimating urban floodflow characteristics in ungaged areas. The literature review contains synopses of 128 recent publications related to urban floodflow. A data base of 269 gaged basins in 56 cities and 31 States, including Hawaii, contains a wide variety of topographic and climatic characteristics, land-use variables, indices of urbanization, and flood-frequency estimates. Three sets of regression equations were developed to estimate flood discharges for ungaged sites for recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years. Two sets of regression equations are based on seven independent parameters and the third is based on three independent parameters. The only difference in the two sets of seven-parameter equations is the use of basin lag time in one and lake and reservoir storage in the other. Of primary importance in these equations is an independent estimate of the equivalent rural discharge for the ungaged basin. The equations adjust the equivalent rural discharge to an urban condition. The primary adjustment factor, or index of urbanization, is the basin development factor, a measure of the extent of development of the drainage system in the basin. This measure includes evaluations of storm drains (sewers), channel improvements, and curb-and-gutter streets. The basin development factor is statistically very significant and offers a simple and effective way of accounting for drainage development and runoff response in urban areas. Percentage of impervious area is also included in the seven-parameter equations as an additional measure of urbanization and apparently accounts for increased runoff volumes. This factor is not highly significant for large floods, which supports the generally held concept that imperviousness is not a dominant factor when soils become more saturated during large storms. Other parameters in the seven-parameter equations include drainage area size, channel slope, rainfall intensity, lake and reservoir storage, and basin lag time. These factors are all statistically significant and provide logical indices of basin conditions. The three-parameter equations include only the three most significant parameters: rural discharge, basin-development factor, and drainage area size. All three sets of regression equations provide unbiased estimates of urban flood frequency. The seven-parameter regression equations without basin lag time have average standard errors of regression varying from ? 37 percent for the 5-year flood to ? 44 percent for the 100-year flood and ? 49 percent for the 500-year flood. The other two sets of regression equations have similar accuracy. Several tests for bias, sensitivity, and hydrologic consistency are included which support the conclusion that the equations are useful throughout the United States. All estimating equations were developed from data collected on drainage basins where temporary in-channel storage, due to highway embankments, was not significant. Consequently, estimates made with these equations do not account for the reducing effect of this temporary detention storage.

Regression equations for estimation of annual peak-streamflow frequency for undeveloped watersheds in Texas using an L-moment-based, PRESS-minimized, residual-adjusted approach

USGS Publications Warehouse

Asquith, William H.; Roussel, Meghan C.

2009-01-01

Annual peak-streamflow frequency estimates are needed for flood-plain management; for objective assessment of flood risk; for cost-effective design of dams, levees, and other flood-control structures; and for design of roads, bridges, and culverts. Annual peak-streamflow frequency represents the peak streamflow for nine recurrence intervals of 2, 5, 10, 25, 50, 100, 200, 250, and 500 years. Common methods for estimation of peak-streamflow frequency for ungaged or unmonitored watersheds are regression equations for each recurrence interval developed for one or more regions; such regional equations are the subject of this report. The method is based on analysis of annual peak-streamflow data from U.S. Geological Survey streamflow-gaging stations (stations). Beginning in 2007, the U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, began a 3-year investigation concerning the development of regional equations to estimate annual peak-streamflow frequency for undeveloped watersheds in Texas. The investigation focuses primarily on 638 stations with 8 or more years of data from undeveloped watersheds and other criteria. The general approach is explicitly limited to the use of L-moment statistics, which are used in conjunction with a technique of multi-linear regression referred to as PRESS minimization. The approach used to develop the regional equations, which was refined during the investigation, is referred to as the 'L-moment-based, PRESS-minimized, residual-adjusted approach'. For the approach, seven unique distributions are fit to the sample L-moments of the data for each of 638 stations and trimmed means of the seven results of the distributions for each recurrence interval are used to define the station specific, peak-streamflow frequency. As a first iteration of regression, nine weighted-least-squares, PRESS-minimized, multi-linear regression equations are computed using the watershed characteristics of drainage area, dimensionless main-channel slope, and mean annual precipitation. The residuals of the nine equations are spatially mapped, and residuals for the 10-year recurrence interval are selected for generalization to 1-degree latitude and longitude quadrangles. The generalized residual is referred to as the OmegaEM parameter and represents a generalized terrain and climate index that expresses peak-streamflow potential not otherwise represented in the three watershed characteristics. The OmegaEM parameter was assigned to each station, and using OmegaEM, nine additional regression equations are computed. Because of favorable diagnostics, the OmegaEM equations are expected to be generally reliable estimators of peak-streamflow frequency for undeveloped and ungaged stream locations in Texas. The mean residual standard error, adjusted R-squared, and percentage reduction of PRESS by use of OmegaEM are 0.30log10, 0.86, and -21 percent, respectively. Inclusion of the OmegaEM parameter provides a substantial reduction in the PRESS statistic of the regression equations and removes considerable spatial dependency in regression residuals. Although the OmegaEM parameter requires interpretation on the part of analysts and the potential exists that different analysts could estimate different values for a given watershed, the authors suggest that typical uncertainty in the OmegaEM estimate might be about +or-0.1010. Finally, given the two ensembles of equations reported herein and those in previous reports, hydrologic design engineers and other analysts have several different methods, which represent different analytical tracks, to make comparisons of peak-streamflow frequency estimates for ungaged watersheds in the study area.

Phase mixing of Alfvén waves in axisymmetric non-reflective magnetic plasma configurations

NASA Astrophysics Data System (ADS)

Petrukhin, N. S.; Ruderman, M. S.; Shurgalina, E. G.

2018-02-01

We study damping of phase-mixed Alfvén waves propagating in non-reflective axisymmetric magnetic plasma configurations. We derive the general equation describing the attenuation of the Alfvén wave amplitude. Then we applied the general theory to a particular case with the exponentially divergent magnetic field lines. The condition that the configuration is non-reflective determines the variation of the plasma density along the magnetic field lines. The density profiles exponentially decreasing with the height are not among non-reflective density profiles. However, we managed to find non-reflective profiles that fairly well approximate exponentially decreasing density. We calculate the variation of the total wave energy flux with the height for various values of shear viscosity. We found that to have a substantial amount of wave energy dissipated at the lower corona, one needs to increase shear viscosity by seven orders of magnitude in comparison with the value given by the classical plasma theory. An important result that we obtained is that the efficiency of the wave damping strongly depends on the density variation with the height. The stronger the density decrease, the weaker the wave damping is. On the basis of this result, we suggested a physical explanation of the phenomenon of the enhanced wave damping in equilibrium configurations with exponentially diverging magnetic field lines.

Evo-SETI: A Mathematical Tool for Cladistics, Evolution, and SETI.

PubMed

Maccone, Claudio

2017-04-06

The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time . We call b -lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b -lognormal in the time . Next, our "Peak-Locus Theorem" translates cladistics : each species created by evolution is a b -lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called "Geometric Brownian Motion" (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b -lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The "molecular clock" is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) "cubic" evolution: a curve of logarithmic increase.

Techniques for Estimating the Magnitude and Frequency of Peak Flows on Small Streams in Minnesota Based on Data through Water Year 2005

USGS Publications Warehouse

Lorenz, David L.; Sanocki, Chris A.; Kocian, Matthew J.

2010-01-01

Knowledge of the peak flow of floods of a given recurrence interval is essential for regulation and planning of water resources and for design of bridges, culverts, and dams along Minnesota's rivers and streams. Statistical techniques are needed to estimate peak flow at ungaged sites because long-term streamflow records are available at relatively few places. Because of the need to have up-to-date peak-flow frequency information in order to estimate peak flows at ungaged sites, the U.S. Geological Survey (USGS) conducted a peak-flow frequency study in cooperation with the Minnesota Department of Transportation and the Minnesota Pollution Control Agency. Estimates of peak-flow magnitudes for 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are presented for 330 streamflow-gaging stations in Minnesota and adjacent areas in Iowa and South Dakota based on data through water year 2005. The peak-flow frequency information was subsequently used in regression analyses to develop equations relating peak flows for selected recurrence intervals to various basin and climatic characteristics. Two statistically derived techniques-regional regression equation and region of influence regression-can be used to estimate peak flow on ungaged streams smaller than 3,000 square miles in Minnesota. Regional regression equations were developed for selected recurrence intervals in each of six regions in Minnesota: A (northwestern), B (north central and east central), C (northeastern), D (west central and south central), E (southwestern), and F (southeastern). The regression equations can be used to estimate peak flows at ungaged sites. The region of influence regression technique dynamically selects streamflow-gaging stations with characteristics similar to a site of interest. Thus, the region of influence regression technique allows use of a potentially unique set of gaging stations for estimating peak flow at each site of interest. Two methods of selecting streamflow-gaging stations, similarity and proximity, can be used for the region of influence regression technique. The regional regression equation technique is the preferred technique as an estimate of peak flow in all six regions for ungaged sites. The region of influence regression technique is not appropriate for regions C, E, and F because the interrelations of some characteristics of those regions do not agree with the interrelations throughout the rest of the State. Both the similarity and proximity methods for the region of influence technique can be used in the other regions (A, B, and D) to provide additional estimates of peak flow. The peak-flow-frequency estimates and basin characteristics for selected streamflow-gaging stations and regional peak-flow regression equations are included in this report.

Using phenomenological models for forecasting the 2015 Ebola challenge.

PubMed

Pell, Bruce; Kuang, Yang; Viboud, Cecile; Chowell, Gerardo

2018-03-01

The rising number of novel pathogens threatening the human population has motivated the application of mathematical modeling for forecasting the trajectory and size of epidemics. We summarize the real-time forecasting results of the logistic equation during the 2015 Ebola challenge focused on predicting synthetic data derived from a detailed individual-based model of Ebola transmission dynamics and control. We also carry out a post-challenge comparison of two simple phenomenological models. In particular, we systematically compare the logistic growth model and a recently introduced generalized Richards model (GRM) that captures a range of early epidemic growth profiles ranging from sub-exponential to exponential growth. Specifically, we assess the performance of each model for estimating the reproduction number, generate short-term forecasts of the epidemic trajectory, and predict the final epidemic size. During the challenge the logistic equation consistently underestimated the final epidemic size, peak timing and the number of cases at peak timing with an average mean absolute percentage error (MAPE) of 0.49, 0.36 and 0.40, respectively. Post-challenge, the GRM which has the flexibility to reproduce a range of epidemic growth profiles ranging from early sub-exponential to exponential growth dynamics outperformed the logistic growth model in ascertaining the final epidemic size as more incidence data was made available, while the logistic model underestimated the final epidemic even with an increasing amount of data of the evolving epidemic. Incidence forecasts provided by the generalized Richards model performed better across all scenarios and time points than the logistic growth model with mean RMS decreasing from 78.00 (logistic) to 60.80 (GRM). Both models provided reasonable predictions of the effective reproduction number, but the GRM slightly outperformed the logistic growth model with a MAPE of 0.08 compared to 0.10, averaged across all scenarios and time points. Our findings further support the consideration of transmission models that incorporate flexible early epidemic growth profiles in the forecasting toolkit. Such models are particularly useful for quickly evaluating a developing infectious disease outbreak using only case incidence time series of the early phase of an infectious disease outbreak. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2006-01-01

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Application of the sine-Poisson equation in solar magnetostatics

NASA Technical Reports Server (NTRS)

Webb, G. M.; Zank, G. P.

1990-01-01

Solutions of the sine-Poisson equations are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model (j) is directed along the x-axis, where x is the horizontal ignorable coordinate; (j) varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. Solutions for the magnetostatic potential A corresponding to the one-soliton, two-soliton, and breather solutions of the sine-Gordon equation are studied. Depending on the values of the free parameters in the soliton solutions, horizontally periodic magnetostatic structures are obtained possessing either a single X-type neutral point, multiple neural X-points, or solutions without X-points.

Relationships between Heavy Metal Concentrations in Roadside Topsoil and Distance to Road Edge Based on Field Observations in the Qinghai-Tibet Plateau, China

PubMed Central

Yan, Xuedong; Gao, Dan; Zhang, Fan; Zeng, Chen; Xiang, Wang; Zhang, Man

2013-01-01

This study investigated the spatial distribution of copper (Cu), zinc (Zn), cadmium (Cd), lead (Pb), chromium (Cr), cobalt (Co), nickel (Ni) and arsenic (As) in roadside topsoil in the Qinghai-Tibet Plateau and evaluated the potential environmental risks of these roadside heavy metals due to traffic emissions. A total of 120 topsoil samples were collected along five road segments in the Qinghai-Tibet Plateau. The nonlinear regression method was used to formulize the relationship between the metal concentrations in roadside soils and roadside distance. The Hakanson potential ecological risk index method was applied to assess the degrees of heavy metal contaminations. The regression results showed that both of the heavy metals’ concentrations and their ecological risk indices decreased exponentially with the increase of roadside distance. The large R square values of the regression models indicate that the exponential regression method can suitably describe the relationship between heavy metal accumulation and roadside distance. For the entire study region, there was a moderate level of potential ecological risk within a 10 m roadside distance. However, Cd was the only prominent heavy metal which posed potential hazard to the local soil ecosystem. Overall, the rank of risk contribution to the local environments among the eight heavy metals was Cd > As > Ni > Pb > Cu > Co > Zn > Cr. Considering that Cd is a more hazardous heavy metal than other elements for public health, the local government should pay special attention to this traffic-related environmental issue. PMID:23439515

Estimation of Flood Discharges at Selected Recurrence Intervals for Streams in New Hampshire

USGS Publications Warehouse

Olson, Scott A.

2009-01-01

This report provides estimates of flood discharges at selected recurrence intervals for streamgages in and adjacent to New Hampshire and equations for estimating flood discharges at recurrence intervals of 2-, 5-, 10-, 25-, 50-, 100-, and 500-years for ungaged, unregulated, rural streams in New Hampshire. The equations were developed using generalized least-squares regression. Flood-frequency and drainage-basin characteristics from 117 streamgages were used in developing the equations. The drainage-basin characteristics used as explanatory variables in the regression equations include drainage area, mean April precipitation, percentage of wetland area, and main channel slope. The average standard error of prediction for estimating the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence interval flood discharges with these equations are 30.0, 30.8, 32.0, 34.2, 36.0, 38.1, and 43.4 percent, respectively. Flood discharges at selected recurrence intervals for selected streamgages were computed following the guidelines in Bulletin 17B of the U.S. Interagency Advisory Committee on Water Data. To determine the flood-discharge exceedence probabilities at streamgages in New Hampshire, a new generalized skew coefficient map covering the State was developed. The standard error of the data on new map is 0.298. To improve estimates of flood discharges at selected recurrence intervals for 20 streamgages with short-term records (10 to 15 years), record extension using the two-station comparison technique was applied. The two-station comparison method uses data from a streamgage with long-term record to adjust the frequency characteristics at a streamgage with a short-term record. A technique for adjusting a flood-discharge frequency curve computed from a streamgage record with results from the regression equations is described in this report. Also, a technique is described for estimating flood discharge at a selected recurrence interval for an ungaged site upstream or downstream from a streamgage using a drainage-area adjustment. The final regression equations and the flood-discharge frequency data used in this study will be available in StreamStats. StreamStats is a World Wide Web application providing automated regression-equation solutions for user-selected sites on streams.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation

NASA Astrophysics Data System (ADS)

Amadori, Debora; Ha, Seung-Yeal; Park, Jinyeong

2017-01-01

The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.

Escherichia coli bacteria density in relation to turbidity, streamflow characteristics, and season in the Chattahoochee River near Atlanta, Georgia, October 2000 through September 2008—Description, statistical analysis, and predictive modeling

USGS Publications Warehouse

Lawrence, Stephen J.

2012-01-01

Regression analyses show that E. coli density in samples was strongly related to turbidity, streamflow characteristics, and season at both sites. The regression equation chosen for the Norcross data showed that 78 percent of the variability in E. coli density (in log base 10 units) was explained by the variability in turbidity values (in log base 10 units), streamflow event (dry-weather flow or stormflow), season (cool or warm), and an interaction term that is the cross product of streamflow event and turbidity. The regression equation chosen for the Atlanta data showed that 76 percent of the variability in E. coli density (in log base 10 units) was explained by the variability in turbidity values (in log base 10 units), water temperature, streamflow event, and an interaction term that is the cross product of streamflow event and turbidity. Residual analysis and model confirmation using new data indicated the regression equations selected at both sites predicted E. coli density within the 90 percent prediction intervals of the equations and could be used to predict E. coli density in real time at both sites.

Long time, large scale properties of the noisy driven-diffusion equation

NASA Astrophysics Data System (ADS)

Prakash, J. Ravi; Bouchaud, J. P.; Edwards, S. F.

1994-07-01

We study the driven-diffusion equation, describing the dynamics of density fluctuations delta-rho(x-vector, t) in powders or traffic flows. We have performed quite detailed numerical simulations of this equation in one dimension, focusing in particular on the scaling behavior of the correlation function (delta-rho(x-vector, t)delta-rho(0, 0)). One of our motivations was to assess the validity of various theoretical approaches, such as Renormalization Group and different self consistent truncation schemes, to these nonlinear dynamical equations. Although all of them are seen to predict correctly the scaling exponents, only one of them (where the non-exponential nature of the relaxation is taken into account) is able to reproduce satisfactorily the value of the numerical prefactors. Several other interesting issues, such as the noise spectrum of the output current, or the statistics of distance between jams (showing a transition between a `laminar' regime for small noise to a `jammed' regime for higher noise) are also investigated.

Predicting Diameter at Breast Height from Stump Diameters for Northeastern Tree Species

Treesearch

Eric H. Wharton; Eric H. Wharton

1984-01-01

Presents equations to predict diameter at breast height from stump diameter measurements for 17 northeastern tree species. Simple linear regression was used to develop the equations. Application of the equations is discussed.

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

Chęcińska, Agata; Heaney, Libby; Pollock, Felix A.

Motivated by a proposed olfactory mechanism based on a vibrationally activated molecular switch, we study electron transport within a donor-acceptor pair that is coupled to a vibrational mode and embedded in a surrounding environment. We derive a polaron master equation with which we study the dynamics of both the electronic and vibrational degrees of freedom beyond previously employed semiclassical (Marcus-Jortner) rate analyses. We show (i) that in the absence of explicit dissipation of the vibrational mode, the semiclassical approach is generally unable to capture the dynamics predicted by our master equation due to both its assumption of one-way (exponential) electronmore » transfer from donor to acceptor and its neglect of the spectral details of the environment; (ii) that by additionally allowing strong dissipation to act on the odorant vibrational mode, we can recover exponential electron transfer, though typically at a rate that differs from that given by the Marcus-Jortner expression; (iii) that the ability of the molecular switch to discriminate between the presence and absence of the odorant, and its sensitivity to the odorant vibrational frequency, is enhanced significantly in this strong dissipation regime, when compared to the case without mode dissipation; and (iv) that details of the environment absent from previous Marcus-Jortner analyses can also dramatically alter the sensitivity of the molecular switch, in particular, allowing its frequency resolution to be improved. Our results thus demonstrate the constructive role dissipation can play in facilitating sensitive and selective operation in molecular switch devices, as well as the inadequacy of semiclassical rate equations in analysing such behaviour over a wide range of parameters.« less

Methods for estimating annual exceedance probability discharges for streams in Arkansas, based on data through water year 2013

USGS Publications Warehouse

Wagner, Daniel M.; Krieger, Joshua D.; Veilleux, Andrea G.

2016-08-04

In 2013, the U.S. Geological Survey initiated a study to update regional skew, annual exceedance probability discharges, and regional regression equations used to estimate annual exceedance probability discharges for ungaged locations on streams in the study area with the use of recent geospatial data, new analytical methods, and available annual peak-discharge data through the 2013 water year. An analysis of regional skew using Bayesian weighted least-squares/Bayesian generalized-least squares regression was performed for Arkansas, Louisiana, and parts of Missouri and Oklahoma. The newly developed constant regional skew of -0.17 was used in the computation of annual exceedance probability discharges for 281 streamgages used in the regional regression analysis. Based on analysis of covariance, four flood regions were identified for use in the generation of regional regression models. Thirty-nine basin characteristics were considered as potential explanatory variables, and ordinary least-squares regression techniques were used to determine the optimum combinations of basin characteristics for each of the four regions. Basin characteristics in candidate models were evaluated based on multicollinearity with other basin characteristics (variance inflation factor < 2.5) and statistical significance at the 95-percent confidence level (p ≤ 0.05). Generalized least-squares regression was used to develop the final regression models for each flood region. Average standard errors of prediction of the generalized least-squares models ranged from 32.76 to 59.53 percent, with the largest range in flood region D. Pseudo coefficients of determination of the generalized least-squares models ranged from 90.29 to 97.28 percent, with the largest range also in flood region D. The regional regression equations apply only to locations on streams in Arkansas where annual peak discharges are not substantially affected by regulation, diversion, channelization, backwater, or urbanization. The applicability and accuracy of the regional regression equations depend on the basin characteristics measured for an ungaged location on a stream being within range of those used to develop the equations.

Compensation effect during the pyrolysis of tyres and bamboo.

PubMed

Mui, Edward L K; Cheung, W H; Lee, Vinci K C; McKay, Gordon

2010-05-01

Pyrolysis parameters (e.g. pre-exponential factor A, and activation energy E) of two waste materials, namely, tyre rubber and bamboo scaffolding, based on the Arrhenius equation were obtained from weight loss data via thermogravimetry at different heating rates. The compensation effect, which suggests that the linear variation in the pre-exponential factor and the activation energy, was observed for these materials. This can be attributed to the variety of active sites over the reactant surface in the course of decomposition. The calculated data from several revised, first-order models were compared with similar models in the literature. It has been shown that both literature and our calculated data exhibit high linearity in terms of lnA and E, revealing that the latter agree well with other researchers' work. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Adaptive exponential integrate-and-fire model as an effective description of neuronal activity.

PubMed

Brette, Romain; Gerstner, Wulfram

2005-11-01

We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (+/-2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.

Methods for estimating low-flow statistics for Massachusetts streams

USGS Publications Warehouse

Ries, Kernell G.; Friesz, Paul J.

2000-01-01

Methods and computer software are described in this report for determining flow duration, low-flow frequency statistics, and August median flows. These low-flow statistics can be estimated for unregulated streams in Massachusetts using different methods depending on whether the location of interest is at a streamgaging station, a low-flow partial-record station, or an ungaged site where no data are available. Low-flow statistics for streamgaging stations can be estimated using standard U.S. Geological Survey methods described in the report. The MOVE.1 mathematical method and a graphical correlation method can be used to estimate low-flow statistics for low-flow partial-record stations. The MOVE.1 method is recommended when the relation between measured flows at a partial-record station and daily mean flows at a nearby, hydrologically similar streamgaging station is linear, and the graphical method is recommended when the relation is curved. Equations are presented for computing the variance and equivalent years of record for estimates of low-flow statistics for low-flow partial-record stations when either a single or multiple index stations are used to determine the estimates. The drainage-area ratio method or regression equations can be used to estimate low-flow statistics for ungaged sites where no data are available. The drainage-area ratio method is generally as accurate as or more accurate than regression estimates when the drainage-area ratio for an ungaged site is between 0.3 and 1.5 times the drainage area of the index data-collection site. Regression equations were developed to estimate the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow for ungaged sites in Massachusetts. Streamflow statistics and basin characteristics for 87 to 133 streamgaging stations and low-flow partial-record stations were used to develop the equations. The streamgaging stations had from 2 to 81 years of record, with a mean record length of 37 years. The low-flow partial-record stations had from 8 to 36 streamflow measurements, with a median of 14 measurements. All basin characteristics were determined from digital map data. The basin characteristics that were statistically significant in most of the final regression equations were drainage area, the area of stratified-drift deposits per unit of stream length plus 0.1, mean basin slope, and an indicator variable that was 0 in the eastern region and 1 in the western region of Massachusetts. The equations were developed by use of weighted-least-squares regression analyses, with weights assigned proportional to the years of record and inversely proportional to the variances of the streamflow statistics for the stations. Standard errors of prediction ranged from 70.7 to 17.5 percent for the equations to predict the 7-day, 10-year low flow and 50-percent duration flow, respectively. The equations are not applicable for use in the Southeast Coastal region of the State, or where basin characteristics for the selected ungaged site are outside the ranges of those for the stations used in the regression analyses. A World Wide Web application was developed that provides streamflow statistics for data collection stations from a data base and for ungaged sites by measuring the necessary basin characteristics for the site and solving the regression equations. Output provided by the Web application for ungaged sites includes a map of the drainage-basin boundary determined for the site, the measured basin characteristics, the estimated streamflow statistics, and 90-percent prediction intervals for the estimates. An equation is provided for combining regression and correlation estimates to obtain improved estimates of the streamflow statistics for low-flow partial-record stations. An equation is also provided for combining regression and drainage-area ratio estimates to obtain improved e

Methods for determining magnitude and frequency of floods in California, based on data through water year 2006

USGS Publications Warehouse

Gotvald, Anthony J.; Barth, Nancy A.; Veilleux, Andrea G.; Parrett, Charles

2012-01-01

Methods for estimating the magnitude and frequency of floods in California that are not substantially affected by regulation or diversions have been updated. Annual peak-flow data through water year 2006 were analyzed for 771 streamflow-gaging stations (streamgages) in California having 10 or more years of data. Flood-frequency estimates were computed for the streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to logarithms of annual peak flows for each streamgage. Low-outlier and historic information were incorporated into the flood-frequency analysis, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low outliers. Special methods for fitting the distribution were developed for streamgages in the desert region in southeastern California. Additionally, basin characteristics for the streamgages were computed by using a geographical information system. Regional regression analysis, using generalized least squares regression, was used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins in California that are outside of the southeastern desert region. Flood-frequency estimates and basin characteristics for 630 streamgages were combined to form the final database used in the regional regression analysis. Five hydrologic regions were developed for the area of California outside of the desert region. The final regional regression equations are functions of drainage area and mean annual precipitation for four of the five regions. In one region, the Sierra Nevada region, the final equations are functions of drainage area, mean basin elevation, and mean annual precipitation. Average standard errors of prediction for the regression equations in all five regions range from 42.7 to 161.9 percent. For the desert region of California, an analysis of 33 streamgages was used to develop regional estimates of all three parameters (mean, standard deviation, and skew) of the log-Pearson Type III distribution. The regional estimates were then used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins. The final regional regression equations are functions of drainage area. Average standard errors of prediction for these regression equations range from 214.2 to 856.2 percent. Annual peak-flow data through water year 2006 were analyzed for eight streamgages in California having 10 or more years of data considered to be affected by urbanization. Flood-frequency estimates were computed for the urban streamgages by fitting a Pearson Type III distribution to logarithms of annual peak flows for each streamgage. Regression analysis could not be used to develop flood-frequency estimation equations for urban streams because of the limited number of sites. Flood-frequency estimates for the eight urban sites were graphically compared to flood-frequency estimates for 630 non-urban sites. The regression equations developed from this study will be incorporated into the U.S. Geological Survey (USGS) StreamStats program. The StreamStats program is a Web-based application that provides streamflow statistics and basin characteristics for USGS streamgages and ungaged sites of interest. StreamStats can also compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in California.

Estimates of streamflow characteristics for selected small streams, Baker River basin, Washington

USGS Publications Warehouse

Williams, John R.

1987-01-01

Regression equations were used to estimate streamflow characteristics at eight ungaged sites on small streams in the Baker River basin in the North Cascade Mountains, Washington, that could be suitable for run-of-the-river hydropower development. The regression equations were obtained by relating known streamflow characteristics at 25 gaging stations in nearby basins to several physical and climatic variables that could be easily measured in gaged or ungaged basins. The known streamflow characteristics were mean annual flows, 1-, 3-, and 7-day low flows and high flows, mean monthly flows, and flow duration. Drainage area and mean annual precipitation were not the most significant variables in all the regression equations. Variance in the low flows and the summer mean monthly flows was reduced by including an index of glacierized area within the basin as a third variable. Standard errors of estimate of the regression equations ranged from 25 to 88%, and the largest errors were associated with the low flow characteristics. Discharge measurements made at the eight sites near midmonth each month during 1981 were used to estimate monthly mean flows at the sites for that period. These measurements also were correlated with concurrent daily mean flows from eight operating gaging stations. The correlations provided estimates of mean monthly flows that compared reasonably well with those estimated by the regression analyses. (Author 's abstract)

Siphons, Water Clocks, Cooling Coffee, and Leaking Capacitors: Classroom Activities and a Few Equations to Help Students Understand Radioactive Decay and Other Exponential Processes

ERIC Educational Resources Information Center

Brady, John B.

2009-01-01

Although an understanding of radiometric dating is central to the preparation of every geologist, many students struggle with the concepts and mathematics of radioactive decay. Physical demonstrations and hands-on experiments can be used to good effect in addressing this teaching conundrum. Water, heat, and electrons all move or flow in response…

Configurational coupled cluster approach with applications to magnetic model systems

NASA Astrophysics Data System (ADS)

Wu, Siyuan; Nooijen, Marcel

2018-05-01

A general exponential, coupled cluster like, approach is discussed to extract an effective Hamiltonian in configurational space, as a sum of 1-body, 2-body up to n-body operators. The simplest two-body approach is illustrated by calculations on simple magnetic model systems. A key feature of the approach is that equations up to a certain rank do not depend on higher body cluster operators.

An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

NASA Astrophysics Data System (ADS)

Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

2017-11-01

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times.

PubMed

Cator, E; van de Bovenkamp, R; Van Mieghem, P

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

Econometrics of exhaustible resource supply: a theory and an application. Final report

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

Epple, D.; Hansen, L.P.

1981-12-01

An econometric model of US oil and natural gas discoveries is developed in this study. The econometric model is explicitly derived as the solution to the problem of maximizing the expected discounted after tax present value of revenues net of exploration, development, and production costs. The model contains equations representing producers' formation of price expectations and separate equations giving producers' optimal exploration decisions contingent on expected prices. A procedure is developed for imposing resource base constraints (e.g., ultimate recovery estimates based on geological analysis) when estimating the econometric model. The model is estimated using aggregate post-war data for the Unitedmore » States. Production from a given addition to proved reserves is assumed to follow a negative exponential path, and additions of proved reserves from a given discovery are assumed to follow a negative exponential path. Annual discoveries of oil and natural gas are estimated as latent variables. These latent variables are the endogenous variables in the econometric model of oil and natural gas discoveries. The model is estimated without resource base constraints. The model is also estimated imposing the mean oil and natural gas ultimate recovery estimates of the US Geological Survey. Simulations through the year 2020 are reported for various future price regimes.« less

Susceptible-infected-susceptible epidemics on networks with general infection and cure times

NASA Astrophysics Data System (ADS)

Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Understanding road surface pollutant wash-off and underlying physical processes using simulated rainfall.

PubMed

Egodawatta, Prasanna; Goonetilleke, Ashantha

2008-01-01

Pollutant wash-off is one of the key pollutant processes that detailed knowledge is required in order to develop successful treatment design strategies for urban stormwater. Unfortunately, current knowledge relating to pollutant wash-off is limited. This paper presents the outcomes of a detailed investigation into pollutant wash-off on residential road surfaces. The investigations consisted of research methodologies formulated to overcome the physical constraints due to the heterogeneity of urban paved surfaces and the dependency on naturally occurring rainfall. This entailed the use of small road surface plots and artificially simulated rainfall. Road surfaces were selected due to its critical importance as an urban stormwater pollutant source. The study results showed that the influence of initially available pollutants on the wash-off process was limited. Furthermore, pollutant wash-off from road surfaces can be replicated using an exponential equation. However, the typical version of the exponential wash-off equation needs to be modified by introducing a non dimensional factor referred to as 'capacity factor' CF. Three rainfall intensity ranges were identified where the variation of CF can be defined. Furthermore, it was found that particulate density rather than size is the critical parameter that influences the process of pollutant wash-off. (c) IWA Publishing 2008.

Power law expansion of the early universe for a V (a) = kan potential

NASA Astrophysics Data System (ADS)

Freitas, Augusto S.

2018-01-01

In a recent paper, He, Gao and Cai [Phys. Rev. D 89, 083510 (2014)], found a rigorous proof, based on analytical solutions of the Wheeler-DeWitt (WDWE) equation, of the spontaneous creation of the universe from nothing. The solutions were obtained from a classical potential V = ka2, where a is the scale factor. In this paper, we present a complementary (to that of He, Gao and Cai) solution to the WDWE equation with V = kan. I have found an exponential expansion of the true vacuum bubble for all scenarios. In all scenarios, we found a power law behavior of the scale factor result which is in agreement with another studies.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.

PubMed

Fürst, Martin L R; Mendl, Christian B; Spohn, Herbert

2013-07-01

The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Gravity discharge vessel revisited: An explicit Lambert W function solution

NASA Astrophysics Data System (ADS)

Digilov, Rafael M.

2017-07-01

Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.

A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme

NASA Astrophysics Data System (ADS)

Ochsenfeld, Christian; Head-Gordon, Martin

1997-05-01

To exploit the exponential decay found in numerical studies for the density matrix and its derivative with respect to nuclear displacements, we reformulate the coupled perturbed self-consistent field (CPSCF) equations and a quadratically convergent SCF (QCSCF) method for Hartree-Fock and density functional theory within a local density matrix-based scheme. Our D-CPSCF (density matrix-based CPSCF) and D-QCSCF schemes open the way for exploiting sparsity and to achieve asymptotically linear scaling of computational complexity with molecular size ( M), in case of D-CPSCF for all O( M) derivative densities. Furthermore, these methods are even for small molecules strongly competitive to conventional algorithms.

The damped wave equation with unbounded damping

NASA Astrophysics Data System (ADS)

Freitas, Pedro; Siegl, Petr; Tretter, Christiane

2018-06-01

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.

Instability of the cored barotropic disc: the linear eigenvalue formulation

NASA Astrophysics Data System (ADS)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E.; Bhrawy, A.

2006-06-01

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of ( is the number of retained modes of polynomial approximations). This paper presents some efficient spectral algorithms, which have a condition number of , based on the Jacobi?Galerkin methods of second-order elliptic equations in one and two space variables. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. The complexities of the algorithms are a small multiple of operations for a -dimensional domain with unknowns, while the convergence rates of the algorithms are exponentials with smooth solutions.

Coagulation-Fragmentation Model for Animal Group-Size Statistics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.

2017-04-01

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent -2/3 for small size to -3/2 for large size, with an exponential cutoff.

Bankfull characteristics of Ohio streams and their relation to peak streamflows

USGS Publications Warehouse

Sherwood, James M.; Huitger, Carrie A.

2005-01-01

Regional curves, simple-regression equations, and multiple-regression equations were developed to estimate bankfull width, bankfull mean depth, bankfull cross-sectional area, and bankfull discharge of rural, unregulated streams in Ohio. The methods are based on geomorphic, basin, and flood-frequency data collected at 50 study sites on unregulated natural alluvial streams in Ohio, of which 40 sites are near streamflow-gaging stations. The regional curves and simple-regression equations relate the bankfull characteristics to drainage area. The multiple-regression equations relate the bankfull characteristics to drainage area, main-channel slope, main-channel elevation index, median bed-material particle size, bankfull cross-sectional area, and local-channel slope. Average standard errors of prediction for bankfull width equations range from 20.6 to 24.8 percent; for bankfull mean depth, 18.8 to 20.6 percent; for bankfull cross-sectional area, 25.4 to 30.6 percent; and for bankfull discharge, 27.0 to 78.7 percent. The simple-regression (drainage-area only) equations have the highest average standard errors of prediction. The multiple-regression equations in which the explanatory variables included drainage area, main-channel slope, main-channel elevation index, median bed-material particle size, bankfull cross-sectional area, and local-channel slope have the lowest average standard errors of prediction. Field surveys were done at each of the 50 study sites to collect the geomorphic data. Bankfull indicators were identified and evaluated, cross-section and longitudinal profiles were surveyed, and bed- and bank-material were sampled. Field data were analyzed to determine various geomorphic characteristics such as bankfull width, bankfull mean depth, bankfull cross-sectional area, bankfull discharge, streambed slope, and bed- and bank-material particle-size distribution. The various geomorphic characteristics were analyzed by means of a combination of graphical and statistical techniques. The logarithms of the annual peak discharges for the 40 gaged study sites were fit by a Pearson Type III frequency distribution to develop flood-peak discharges associated with recurrence intervals of 2, 5, 10, 25, 50, and 100 years. The peak-frequency data were related to geomorphic, basin, and climatic variables by multiple-regression analysis. Simple-regression equations were developed to estimate 2-, 5-, 10-, 25-, 50-, and 100-year flood-peak discharges of rural, unregulated streams in Ohio from bankfull channel cross-sectional area. The average standard errors of prediction are 31.6, 32.6, 35.9, 41.5, 46.2, and 51.2 percent, respectively. The study and methods developed are intended to improve understanding of the relations between geomorphic, basin, and flood characteristics of streams in Ohio and to aid in the design of hydraulic structures, such as culverts and bridges, where stability of the stream and structure is an important element of the design criteria. The study was done in cooperation with the Ohio Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration.

A family of nonlinear Schrödinger equations admitting q-plane wave solutions

NASA Astrophysics Data System (ADS)

Nobre, F. D.; Plastino, A. R.

2017-08-01

Nonlinear Schrödinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrödinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q → 1. A classical field theory shows that, due to these nonlinearities, an extra field Φ (x → , t) (besides the usual one Ψ (x → , t)) must be introduced for consistency. The new field can be identified with Ψ* (x → , t) only when q → 1. For q ≠ 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Ψ (x → , t) and Φ (x → , t). These equations reduce to the usual pair of complex-conjugate ones only in the q → 1 limit. Interestingly, the nonlinear equations obeyed by Ψ (x → , t) and Φ (x → , t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.

Comparison of anatomical, functional and regression methods for estimating the rotation axes of the forearm.

PubMed

Fraysse, François; Thewlis, Dominic

2014-11-07

Numerous methods exist to estimate the pose of the axes of rotation of the forearm. These include anatomical definitions, such as the conventions proposed by the ISB, and functional methods based on instantaneous helical axes, which are commonly accepted as the modelling gold standard for non-invasive, in-vivo studies. We investigated the validity of a third method, based on regression equations, to estimate the rotation axes of the forearm. We also assessed the accuracy of both ISB methods. Axes obtained from a functional method were considered as the reference. Results indicate a large inter-subject variability in the axes positions, in accordance with previous studies. Both ISB methods gave the same level of accuracy in axes position estimations. Regression equations seem to improve estimation of the flexion-extension axis but not the pronation-supination axis. Overall, given the large inter-subject variability, the use of regression equations cannot be recommended. Copyright © 2014 Elsevier Ltd. All rights reserved.

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

USGS Publications Warehouse

Wood, Molly S.; Fosness, Ryan L.; Skinner, Kenneth D.; Veilleux, Andrea G.

2016-06-27

The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations.Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R2>92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R2>95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R2<78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows.A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5.The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions.The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Equations for predicting biomass in 2- to 6-year-old Eucalyptus saligna in Hawaii

Treesearch

Craig D. Whitesell; Susan C. Miyasaka; Robert F. Strand; Thomas H. Schubert; Katharine E. McDuffie

1988-01-01

Eucalyptus saligna trees grown in short-rotation plantations on the island of Hawaii were measured, harvested, and weighed to provide data for developing regression equations using non-destructive stand measurements. Regression analysis of the data from 190 trees in the 2.0- to 3.5-year range and 96 trees in the 4- to 6-year range related stem-only...

Estimating parameters for tree basal area growth with a system of equations and seemingly unrelated regressions

Treesearch

Charles E. Rose; Thomas B. Lynch

2001-01-01

A method was developed for estimating parameters in an individual tree basal area growth model using a system of equations based on dbh rank classes. The estimation method developed is a compromise between an individual tree and a stand level basal area growth model that accounts for the correlation between trees within a plot by using seemingly unrelated regression (...

Regression Levels of Selected Affective Factors on Science Achievement: A Structural Equation Model with TIMSS 2011 Data

ERIC Educational Resources Information Center

Akilli, Mustafa

2015-01-01

The aim of this study is to demonstrate the science success regression levels of chosen emotional features of 8th grade students using Structural Equation Model. The study was conducted by the analysis of students' questionnaires and science success in TIMSS 2011 data using SEM. Initially, the factors that are thought to have an effect on science…

Low-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Low-flow annual non-exceedance probabilities (ANEP), called probability-percent chance (P-percent chance) flow estimates, regional regression equations, and transfer methods are provided describing the low-flow characteristics of Virginia streams. Statistical methods are used to evaluate streamflow data. Analysis of Virginia streamflow data collected from 1895 through 2007 is summarized. Methods are provided for estimating low-flow characteristics of gaged and ungaged streams. The 1-, 4-, 7-, and 30-day average streamgaging station low-flow characteristics for 290 long-term, continuous-record, streamgaging stations are determined, adjusted for instances of zero flow using a conditional probability adjustment method, and presented for non-exceedance probabilities of 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, 0.02, 0.01, and 0.005. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression equations to estimate annual non-exceedance probabilities at gaged and ungaged sites and are summarized for 290 long-term, continuous-record streamgaging stations, 136 short-term, continuous-record streamgaging stations, and 613 partial-record streamgaging stations. Regional regression equations for six physiographic regions use basin characteristics to estimate 1-, 4-, 7-, and 30-day average low-flow annual non-exceedance probabilities at gaged and ungaged sites. Weighted low-flow values that combine computed streamgaging station low-flow characteristics and annual non-exceedance probabilities from regional regression equations provide improved low-flow estimates. Regression equations developed using the Maintenance of Variance with Extension (MOVE.1) method describe the line of organic correlation (LOC) with an appropriate index site for low-flow characteristics at 136 short-term, continuous-record streamgaging stations and 613 partial-record streamgaging stations. Monthly streamflow statistics computed on the individual daily mean streamflows of selected continuous-record streamgaging stations and curves describing flow-duration are presented. Text, figures, and lists are provided summarizing low-flow estimates, selected low-flow sites, delineated physiographic regions, basin characteristics, regression equations, error estimates, definitions, and data sources. This study supersedes previous studies of low flows in Virginia.

Regression equations for estimating concentrations of selected water-quality constituents for selected gaging stations in the Red River of the North Basin, North Dakota, Minnesota, and South Dakota

USGS Publications Warehouse

Williams-Sether, Tara

2004-01-01

The Dakota Water Resources Act, passed by the U.S. Congress on December 15, 2000, authorized the Secretary of the Interior to conduct a comprehensive study of future water-quantity and quality needs of the Red River of the North Basin in North Dakota and possible options to meet those water needs. Previous Red River of the North Basin studies conducted by the Bureau of Reclamation used streamflow and water-quality data bases developed by the U.S. Geological Survey that included data for 1931-84. As a result of the recent congressional authorization and results of previous studies by the Bureau of Reclamation, redevelopment of the streamflow and water-quality data bases with current data through 1999 are needed in order to evaluate and predict the water-quantity and quality effects within the Red River of the North Basin. This report provides updated statistical summaries of selected water-quality constituents and streamflow and the regression relations between them.  Available data for 1931-99 were used to develop regression equations between 5 selected water-quality constituents and streamflow for 38 gaging stations in the Red River of the North Basin. The water-quality constituents that were regressed against streamflow were hardness (as CaCO3), sodium, chloride, sulfate, and dissolved solids. Statistical summaries of the selected water-quality constituents and streamflow for the gaging stations used in the regression equations development and the applications and limitations of the regression equations are presented in this report.

Mean Excess Function as a method of identifying sub-exponential tails: Application to extreme daily rainfall

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

Identifying precisely the distribution tail of a geophysical variable is tough, or, even impossible. First, the tail is the part of the distribution for which we have the less empirical information available; second, a universally accepted definition of tail does not and cannot exist; and third, a tail may change over time due to long-term changes. Unfortunately, the tail is the most important part of the distribution as it dictates the estimates of exceedance probabilities or return periods. Fortunately, based on their tail behavior, probability distributions can be generally categorized into two major families, i.e., sub-exponentials (heavy-tailed) and hyper-exponentials (light-tailed). This study aims to update the Mean Excess Function (MEF), providing a useful tool in order to asses which type of tail better describes empirical data. The MEF is based on the mean value of a variable over a threshold and results in a zero slope regression line when applied for the Exponential distribution. Here, we construct slope confidence intervals for the Exponential distribution as functions of sample size. The validation of the method using Monte Carlo techniques on four theoretical distributions covering major tail cases (Pareto type II, Log-normal, Weibull and Gamma) revealed that it performs well especially for large samples. Finally, the method is used to investigate the behavior of daily rainfall extremes; thousands of rainfall records were examined, from all over the world and with sample size over 100 years, revealing that heavy-tailed distributions can describe more accurately rainfall extremes.

Proportional Feedback Control of Energy Intake During Obesity Pharmacotherapy.

PubMed

Hall, Kevin D; Sanghvi, Arjun; Göbel, Britta

2017-12-01

Obesity pharmacotherapies result in an exponential time course for energy intake whereby large early decreases dissipate over time. This pattern of declining drug efficacy to decrease energy intake results in a weight loss plateau within approximately 1 year. This study aimed to elucidate the physiology underlying the exponential decay of drug effects on energy intake. Placebo-subtracted energy intake time courses were examined during long-term obesity pharmacotherapy trials for 14 different drugs or drug combinations within the theoretical framework of a proportional feedback control system regulating human body weight. Assuming each obesity drug had a relatively constant effect on average energy intake and did not affect other model parameters, our model correctly predicted that long-term placebo-subtracted energy intake was linearly related to early reductions in energy intake according to a prespecified equation with no free parameters. The simple model explained about 70% of the variance between drug studies with respect to the long-term effects on energy intake, although a significant proportional bias was evident. The exponential decay over time of obesity pharmacotherapies to suppress energy intake can be interpreted as a relatively constant effect of each drug superimposed on a physiological feedback control system regulating body weight. © 2017 The Obesity Society.

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

Wen, J. T.; Bayard, D. S.

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Molecular sensing using monolayer floating gate, fully depleted SOI MOSFET acting as an exponential transducer.

PubMed

Takulapalli, Bharath R

2010-02-23

Field-effect transistor-based chemical sensors fall into two broad categories based on the principle of signal transduction-chemiresistor or Schottky-type devices and MOSFET or inversion-type devices. In this paper, we report a new inversion-type device concept-fully depleted exponentially coupled (FDEC) sensor, using molecular monolayer floating gate fully depleted silicon on insulator (SOI) MOSFET. Molecular binding at the chemical-sensitive surface lowers the threshold voltage of the device inversion channel due to a unique capacitive charge-coupling mechanism involving interface defect states, causing an exponential increase in the inversion channel current. This response of the device is in opposite direction when compared to typical MOSFET-type sensors, wherein inversion current decreases in a conventional n-channel sensor device upon addition of negative charge to the chemical-sensitive device surface. The new sensor architecture enables ultrahigh sensitivity along with extraordinary selectivity. We propose the new sensor concept with the aid of analytical equations and present results from our experiments in liquid phase and gas phase to demonstrate the new principle of signal transduction. We present data from numerical simulations to further support our theory.