40 CFR 63.1427 - Process vent requirements for processes using extended cookout as an epoxide emission reduction...

Code of Federal Regulations, 2014 CFR

2014-07-01

... = Concentration of epoxide in the reactor liquid at the beginning of the time period, weight percent. k = Reaction rate constant, 1/hr. t = Time, hours. Note: This equation assumes a first order reaction with respect... process knowledge, reaction kinetics, and engineering knowledge, in accordance with paragraph (a)(2)(i) of...

40 CFR 63.1427 - Process vent requirements for processes using extended cookout as an epoxide emission reduction...

Code of Federal Regulations, 2012 CFR

2012-07-01

... reactor liquid at the beginning of the time period, weight percent. k = Reaction rate constant, 1/hr. t = Time, hours. Note: This equation assumes a first order reaction with respect to epoxide concentration... measuring the concentration of the unreacted epoxide, or by using process knowledge, reaction kinetics, and...

40 CFR 63.1427 - Process vent requirements for processes using extended cookout as an epoxide emission reduction...

Code of Federal Regulations, 2013 CFR

2013-07-01

... = Concentration of epoxide in the reactor liquid at the beginning of the time period, weight percent. k = Reaction rate constant, 1/hr. t = Time, hours. Note: This equation assumes a first order reaction with respect... process knowledge, reaction kinetics, and engineering knowledge, in accordance with paragraph (a)(2)(i) of...

Predicting river travel time from hydraulic characteristics

USGS Publications Warehouse

Jobson, H.E.

2001-01-01

Predicting the effect of a pollutant spill on downstream water quality is primarily dependent on the water velocity, longitudinal mixing, and chemical/physical reactions. Of these, velocity is the most important and difficult to predict. This paper provides guidance on extrapolating travel-time information from one within bank discharge to another. In many cases, a time series of discharge (such as provided by a U.S. Geological Survey stream gauge) will provide an excellent basis for this extrapolation. Otherwise, the accuracy of a travel time extrapolation based on a resistance equation can be greatly improved by assuming the total flow area is composed of two parts, an active and an inactive area. For 60 reaches of 12 rivers with slopes greater than about 0.0002, travel times could be predicted to within about 10% by computing the active flow area using the Manning equation with n = 0.035 and assuming a constant inactive area for each reach. The predicted travel times were not very sensitive to the assumed values of bed slope or channel width.

Alfven waves associated with long cylindrical satellites

NASA Technical Reports Server (NTRS)

Venkataraman, N. S.; Gustafson, W. A.

1973-01-01

The Alfven wave excited by a long cylindrical satellite moving with a constant velocity at an angle relative to a uniform magnetic field has been calculated. Assuming a plasma with infinite conductivity, the linearized momentum equation and Maxwell's equations are applied to a cylindrical satellite carrying a variable current. The induced magnetic field is determined, and it is shown that the Alfven disturbance zone is of limited extent, depending on the satellite shape. The wave drag coefficient is calculated and shown to be small compared to the induction drag coefficient at all altitudes considered.

Computing aerodynamic sound using advanced statistical turbulence theories

NASA Technical Reports Server (NTRS)

Hecht, A. M.; Teske, M. E.; Bilanin, A. J.

1981-01-01

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

A reaction limited in vivo dissolution model for the study of drug absorption: Towards a new paradigm for the biopharmaceutic classification of drugs.

PubMed

Macheras, Panos; Iliadis, Athanassios; Melagraki, Georgia

2018-05-30

The aim of this work is to develop a gastrointestinal (GI) drug absorption model based on a reaction limited model of dissolution and consider its impact on the biopharmaceutic classification of drugs. Estimates for the fraction of dose absorbed as a function of dose, solubility, reaction/dissolution rate constant and the stoichiometry of drug-GI fluids reaction/dissolution were derived by numerical solution of the model equations. The undissolved drug dose and the reaction/dissolution rate constant drive the dissolution rate and determine the extent of absorption when high-constant drug permeability throughout the gastrointestinal tract is assumed. Dose is an important element of drug-GI fluids reaction/dissolution while solubility exclusively acts as an upper limit for drug concentrations in the lumen. The 3D plots of fraction of dose absorbed as a function of dose and reaction/dissolution rate constant for highly soluble and low soluble drugs for different "stoichiometries" (0.7, 1.0, 2.0) of the drug-reaction/dissolution with the GI fluids revealed that high extent of absorption was found assuming high drug- reaction/dissolution rate constant and high drug solubility. The model equations were used to simulate in vivo supersaturation and precipitation phenomena. The model developed provides the theoretical basis for the interpretation of the extent of drug's absorption on the basis of the parameters associated with the drug-GI fluids reaction/dissolution. A new paradigm emerges for the biopharmaceutic classification of drugs, namely, a model independent biopharmaceutic classification scheme of four drug categories based on either the fulfillment or not of the current dissolution criteria and the high or low % drug metabolism. Copyright © 2018. Published by Elsevier B.V.

New limits on coupled dark energy model after Planck 2015

NASA Astrophysics Data System (ADS)

Li, Hang; Yang, Weiqiang; Wu, Yabo; Jiang, Ying

2018-06-01

We used the Planck 2015 cosmic microwave background anisotropy, baryon acoustic oscillation, type-Ia supernovae, redshift-space distortions, and weak gravitational lensing to test the model parameter space of coupled dark energy. We assumed the constant and time-varying equation of state parameter for dark energy, and treated dark matter and dark energy as the fluids whose energy transfer was proportional to the combined term of the energy densities and equation of state, such as Q = 3 Hξ(1 +wx) ρx and Q = 3 Hξ [ 1 +w0 +w1(1 - a) ] ρx, the full space of equation of state could be measured when we considered the term (1 +wx) in the energy exchange. According to the joint observational constraint, the results showed that wx = - 1.006-0.027+0.047 and ξ = 0.098-0.098>+0.026 for coupled dark energy with a constant equation of state, w0 = -1.076-0.076+0.085, w1 = - 0.069-0.319+0.361, and ξ = 0.210-0.210+0.048 for a variable equation of state. We did not get any clear evidence for the coupling in the dark fluids at 1 σ region.

On geological interpretations of crystal size distributions: Constant vs. proportionate growth

USGS Publications Warehouse

Eberl, D.D.; Kile, D.E.; Drits, V.A.

2002-01-01

Geological interpretations of crystal size distributions (CSDs) depend on understanding the crystal growth laws that generated the distributions. Most descriptions of crystal growth, including a population-balance modeling equation that is widely used in petrology, assume that crystal growth rates at any particular time are identical for all crystals, and, therefore, independent of crystal size. This type of growth under constant conditions can be modeled by adding a constant length to the diameter of each crystal for each time step. This growth equation is unlikely to be correct for most mineral systems because it neither generates nor maintains the shapes of lognormal CSDs, which are among the most common types of CSDs observed in rocks. In an alternative approach, size-dependent (proportionate) growth is modeled approximately by multiplying the size of each crystal by a factor, an operation that maintains CSD shape and variance, and which is in accord with calcite growth experiments. The latter growth law can be obtained during supply controlled growth using a modified version of the Law of Proportionate Effect (LPE), an equation that simulates the reaction path followed by a CSD shape as mean size increases.

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

NASA Technical Reports Server (NTRS)

Schneider, J.; Boccio, J.

1972-01-01

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

Implications of a positive cosmological constant for general relativity.

PubMed

Ashtekar, Abhay

2017-10-01

Most of the literature on general relativity over the last century assumes that the cosmological constant [Formula: see text] is zero. However, by now independent observations have led to a consensus that the dynamics of the universe is best described by Einstein's equations with a small but positive [Formula: see text]. Interestingly, this requires a drastic revision of conceptual frameworks commonly used in general relativity, no matter how small [Formula: see text] is. We first explain why, and then summarize the current status of generalizations of these frameworks to include a positive [Formula: see text], focusing on gravitational waves.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Brane world in non-Riemannian geometry

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

Maier, R.; Falciano, F. T.

2011-03-15

We carefully investigate the modified Einstein's field equation in a 4-dimensional (3-brane) arbitrary manifold embedded in a 5-dimensional non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or anti-de Sitter, where a 5-dimensional cosmological constant emerges from the torsion.

Growth and Doping of Al(x)Ga(1-x)N Films by Electron Cyclotron Resonance Assisted Molecular Beam Epitaxy

DTIC Science & Technology

1993-05-30

shown in Figures 9a and 9b. The carrier concentration was computed from the measured values of the Hall coefficient, RH , using the equation n (5) eRH...The electron concentrations in Figure 1 were calculated from the expression 1 (1) eRjj where RH is the Hall constant. Equation (1) assumes electron...expressions: 2 2RH fcP + ,’dP• (2) RH = (ncp + nd/pd) 2 e 1 p 1 (3) ncelc + ndel.d where nc and nd are the concentrations of conducting carriers in the

An integral turbulent kinetic energy analysis of free shear flows

NASA Technical Reports Server (NTRS)

Peters, C. E.; Phares, W. J.

1973-01-01

Mixing of coaxial streams is analyzed by application of integral techniques. An integrated turbulent kinetic energy (TKE) equation is solved simultaneously with the integral equations for the mean flow. Normalized TKE profile shapes are obtained from incompressible jet and shear layer experiments and are assumed to be applicable to all free turbulent flows. The shear stress at the midpoint of the mixing zone is assumed to be directly proportional to the local TKE, and dissipation is treated with a generalization of the model developed for isotropic turbulence. Although the analysis was developed for ducted flows, constant-pressure flows were approximated with the duct much larger than the jet. The axisymmetric flows under consideration were predicted with reasonable accuracy. Fairly good results were also obtained for the fully developed two-dimensional shear layers, which were computed as thin layers at the boundary of a large circular jet.

Intertwining solutions for magnetic relativistic Hartree type equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

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

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

Reflection and Refraction of Light in Absorbing Media

NASA Astrophysics Data System (ADS)

Katsumata, Koichi; Sasaki, Shosuke

2018-05-01

The results of a rigorous calculation of optical phenomena in absorbing media based on Maxwell's equations are reported. In the case of an absorbing dielectric, we assume a complex dielectric constant. We find an expression for the angle of refraction as a function of the incident angle and the real and imaginary parts of the complex dielectric constant, all of which are real. The amplitudes of the reflected and transmitted waves are calculated on the same footing. These amplitudes are shown to be complex, from which we deduce the magnitude and phase change of the reflection and transmission coefficients. The same argument applies to an absorbing magnetic material if we replace the complex dielectric constant by a complex magnetic permeability.

An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis

NASA Technical Reports Server (NTRS)

Williams, Craig Hamilton

1995-01-01

A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

NASA Technical Reports Server (NTRS)

Eckert, E.R.G.; Livingood, John N.B.

1951-01-01

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

Mathematical modeling of PDC bit drilling process based on a single-cutter mechanics

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

Wojtanowicz, A.K.; Kuru, E.

1993-12-01

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter`s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verificationsmore » of the model. Qualitative verification shows that the model`s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model`s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.« less

Affine theory of gravitation

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2014-01-01

We propose a theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct a simple dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is a polynomial function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, . We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through . We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant if the tensor is regarded as proportional to the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with and provides a natural system of units in gravitational physics. This theory therefore provides a physical construction of the metric as a polynomial function of the connection, and explains dark energy as an intrinsic property of spacetime.

De Sitter universe described by a binary mixture with a variable cosmological constant λ

NASA Astrophysics Data System (ADS)

Biswal, S. K.

2018-04-01

We have constructed a self-consistent system of Bianchi Type VI0 cosmology, and mingling of perfect fluid and dark energy in five dimensions. The usual equation of state p = γ ρ with γ \\in [0, 1] is chosen by the perfect fluid. The dark energy assumed to be chosen is taken into consideration to be either the quintessence or Chaplygin gas. The same solutions pertaining to the corresponding the field equations of Einstein are obtained as a quadrature. State parameter's equations for dark energy ω is found to be consistent enough with the recent observations of SNe Ia data (SNe Ia data with CMBR anisotropy) and galaxy clustering statistics. Here our models predict that the rate of expansion of Universe would increase with passage of time. The cosmological constant Λ is traced as a declining function of time and it gets nearer to a small positive value later on which is supported by the results from the current supernovae Ia observations. Also a detail discussion is made on the physical and geometrical aspects of the models.

Renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, Leslie M.

1989-01-01

The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.

A modification of Einstein-Schrödinger theory that contains both general relativity and electrodynamics

NASA Astrophysics Data System (ADS)

Shifflett, J. A.

2008-08-01

We modify the Einstein-Schrödinger theory to include a cosmological constant Λ z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ b which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ z + Λ b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as | Λ z | → ∞. For | Λ z | ~ 1/(Planck length)2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10-16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~10-66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

Effect of static porosity fluctuations on reactive transport in a porous medium

NASA Astrophysics Data System (ADS)

L'Heureux, Ivan

2018-02-01

Reaction-diffusive transport phenomena in porous media are ubiquitous in engineering applications, biological and geochemical systems. The porosity field is usually random in space, but most models consider the porosity field as a well-defined deterministic function of space and time and ignore the porosity fluctuations. They use a reaction-diffusion equation written in terms of an average porosity and average concentration fields. In this contribution, we treat explicitly the effect of spatial porosity fluctuations on the dynamics of a concentration field for the case of a one-dimensional reaction-transport system with nonlinear kinetics. Three basic assumptions are considered. (i) The porosity fluctuations are assumed to have Gaussian properties and an arbitrary variance; (ii) we assume that the noise correlation length is small compared to the relevant macroscopic length scale; (iii) and we assume that the kinetics of the reactive term in the equations for the fluctuations is a self-consistently determined constant. Elimination of the fluctuating part of the concentration field from the dynamics leads to a renormalized equation involving the average concentration field. It is shown that the noise leads to a renormalized (generally smaller) diffusion coefficient and renormalized kinetics. Within the framework of the approximations used, numerical simulations are in agreement with our theory. We show that the porosity fluctuations may have a significant effect on the transport of a reactive species, even in the case of a homogeneous average porosity.

Brane-world black hole solutions via a confining potential

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

Heydari-Fard, M.; Sepangi, H. R.; Razmi, H.

2007-09-15

Using a confining potential, we consider spherically symmetric vacuum (static black hole) solutions in a brane-world scenario. Working with a constant curvature bulk, two interesting cases/solutions are studied. A Schwarzschild-de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant is obtained which confirms the idea that an extra term in the field equations on the brane can play the role of a positive cosmological constant and may be used to account for the accelerated expansion of the universe. The other solution is one in which we can have a proper potential to explainmore » the galaxy rotation curves without assuming the existence of dark matter and without working with new modified theories (modified Newtonian dynamics)« less

Squeeze-film flow between a flat impermeable bearing and an anisotropic porous bed

NASA Astrophysics Data System (ADS)

Karmakar, Timir; Raja Sekhar, G. P.

2018-04-01

We consider a theoretical model of the squeeze film in the presence of a porous bed. The gap between the porous bed and the bearing is assumed to be filled with a Newtonian fluid. We use the Navier-Stokes equation in the fluid region and the Darcy equation in the fluid filled porous region. Lubrication approximation is used to derive the corresponding evolution equation for the film thickness. We use G. S. Beavers and D. D. Joseph ["Boundary conditions at a naturally permeable wall," J. Fluid. Mech. 30, 197-207 (1967)] and M. Le Bars and M. G. Worster ["Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification," J. Fluid. Mech. 550, 149-173 (2006)] condition at the liquid porous interface and present a detailed analysis on the corresponding impact. We assume that the porous bed is anisotropic in nature with permeabilities K2 and K1 along the principal axes. Accordingly, the anisotropic angle ϕ is taken as the angle between the horizontal direction and principal axis with permeability K2. We show that the anisotropic permeability ratio and the anisotropic angle make a significant influence on the contact time, flux, velocity, etc. Contact time to meet the porous bed when a bearing approaches under a constant prescribed load is estimated. We present some important findings (relevant to the knee joint) based on the anisotropic properties of the human cartilage. For a prescribed constant load, we have estimated the time duration, during which a healthy human knee remains fluid lubricated.

Theoretical study of interactions of BSA protein in a NaCl aqueous solution

NASA Astrophysics Data System (ADS)

Pellicane, Giuseppe; Cavero, Miguel

2013-03-01

Bovine Serum Albumine (BSA) aqueous solutions in the presence of NaCl are investigated for different protein concentrations and low to intermediate ionic strengths. Protein interactions are modeled via a charge-screened colloidal model, in which the range of the potential is determined by the Debye-Hückel constant. We use Monte Carlo computer simulations to calculate the structure factor, and assume an oblate ellipsoidal form factor for BSA. The theoretical scattered intensities are found in good agreement with the experimental small angle X-ray scattering intensities available in the literature. The performance of well-known integral equation closures to the Ornstein-Zernike equation, namely the mean spherical approximation, the Percus-Yevick, and the hypernetted chain equations, is also assessed with respect to computer simulation.

Bidirectional plant canopy reflection models derived from the radiation transfer equation

NASA Technical Reports Server (NTRS)

Beeth, D. R.

1975-01-01

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

An improved exceedance theory for combined random stresses

NASA Technical Reports Server (NTRS)

Lester, H. C.

1974-01-01

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

PubMed Central

Yogurtcu, Osman N.; Johnson, Margaret E.

2015-01-01

The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems. PMID:26328828

Application of the compensated arrhenius formalism to dielectric relaxation.

PubMed

Petrowsky, Matt; Frech, Roger

2009-12-17

The temperature dependence of the dielectric rate constant, defined as the reciprocal of the dielectric relaxation time, is examined for several groups of organic solvents. Early studies of linear alcohols using a simple Arrhenius equation found that the activation energy was dependent on the chain length of the alcohol. This paper re-examines the earlier data using a compensated Arrhenius formalism that assumes the presence of a temperature-dependent static dielectric constant in the exponential prefactor. Scaling temperature-dependent rate constants to isothermal rate constants so that the dielectric constant dependence is removed results in calculated energies of activation E(a) in which there is a small increase with chain length. These energies of activation are very similar to those calculated from ionic conductivity data using compensated Arrhenius formalism. This treatment is then extended to dielectic relaxation data for n-alkyl bromides, n-nitriles, and n-acetates. The exponential prefactor is determined by dividing the temperature-dependent rate constants by the Boltzmann term exp(-E(a)/RT). Plotting the prefactors versus the static dielectric constant places the data on a single master curve for each group of solvents.

Dissolution process analysis using model-free Noyes-Whitney integral equation.

PubMed

Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto

2013-02-01

Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.

Tachyon constant-roll inflation

NASA Astrophysics Data System (ADS)

Mohammadi, A.; Saaidi, Kh.; Golanbari, T.

2018-04-01

The constant-roll inflation is studied where the inflaton is taken as a tachyon field. Based on this approach, the second slow-roll parameter is taken as a constant which leads to a differential equation for the Hubble parameter. Finding an exact solution for the Hubble parameter is difficult and leads us to a numerical solution for the Hubble parameter. On the other hand, since in this formalism the slow-roll parameter η is constant and could not be assumed to be necessarily small, the perturbation parameters should be reconsidered again which, in turn, results in new terms appearing in the amplitude of scalar perturbations and the scalar spectral index. Utilizing the numerical solution for the Hubble parameter, we estimate the perturbation parameter at the horizon exit time and compare it with observational data. The results show that, for specific values of the constant parameter η , we could have an almost scale-invariant amplitude of scalar perturbations. Finally, the attractor behavior for the solution of the model is presented, and we determine that the feature could be properly satisfied.

Radial oscillations of strange quark stars admixed with condensed dark matter

NASA Astrophysics Data System (ADS)

Panotopoulos, G.; Lopes, Ilídio

2017-10-01

We compute the 20 lowest frequency radial oscillation modes of strange stars admixed with condensed dark matter. We assume a self-interacting bosonic dark matter, and we model dark matter inside the star as a Bose-Einstein condensate. In this case the equation of state is a polytropic one with index 1 +1 /n =2 and a constant K that is computed in terms of the mass of the dark matter particle and the scattering length. Assuming a mass and a scattering length compatible with current observational bounds for self-interacting dark matter, we have integrated numerically first the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium, and then the equations for the perturbations ξ =Δ r /r and η =Δ P /P . For a compact object with certain mass and radius we have considered here three cases, namely no dark matter at all and two different dark matter scenarios. Our results show that (i) the separation between consecutive modes increases with the amount of dark matter, and (ii) the effect is more pronounced for higher order modes. These effects are relevant even for a strange star made of 5% dark matter.

An annual model of SSM/I radiobrightness for dry soil

NASA Technical Reports Server (NTRS)

Liou, Yuei-An; England, A. W.

1992-01-01

An annual model is presented of the temperature structure within a homogeneous, dry soil halfspace that is subject to both diurnal and annual insolation, radiant heating from the atmosphere, sensible heat exchange with the atmosphere, and radiant cooling. The thermal constitutive properties of the soil are assumed to be constant so that the heat flow equation can be solved analytically. For computational economy, a variable time interval Laplace transform method is developed to predict the temperature.

Comparison with Analytical Solution: Generation and Radiation of Acoustic Waves from a 2-D Shear Layer

NASA Technical Reports Server (NTRS)

Dahl, Milo D.

2000-01-01

An acoustic source inside of a 2-D jet excites an instability wave in the shear layer resulting in sound radiating away from the shear layer. Solve the linearized Euler equations to predict the sound radiation outside of the jet. The jet static pressure is assumed to be constant. The jet flow is parallel and symmetric about the x-axis. Use a symmetry boundary condition along the x-axis.

Gravity Scaling of a Power Reactor Water Shield

NASA Technical Reports Server (NTRS)

Reid, Robert S.; Pearson, J. Boise

2007-01-01

A similarity analysis on a water-based reactor shield examined the effect of gravity on free convection between a reactor shield inner and outer vessel boundaries. Two approaches established similarity between operation on the Earth and the Moon: 1) direct scaling of Rayleigh number equating gravity-surface heat flux products, 2) temperature difference between the wall and thermal boundary layer held constant. Nusselt number for natural convection (laminar and turbulent) is assumed of form Nu = CRa(sup n).

Application of the two-film model to the volatilization of acetone and t-butyl alcohol from water as a function of temperature

USGS Publications Warehouse

Rathbun, R.E.; Tai, D.Y.

1988-01-01

The two-film model is often used to describe the volatilization of organic substances from water. This model assumes uniformly mixed water and air phases separated by thin films of water and air in which mass transfer is by molecular diffusion. Mass-transfer coefficients for the films, commonly called film coefficients, are related through the Henry's law constant and the model equation to the overall mass-transfer coefficient for volatilization. The films are modeled as two resistances in series, resulting in additive resistances. The two-film model and the concept of additivity of resistances were applied to experimental data for acetone and t-butyl alcohol. Overall mass-transfer coefficients for the volatilization of acetone and t-butyl alcohol from water were measured in the laboratory in a stirred constant-temperature bath. Measurements were completed for six water temperatures, each at three water mixing conditions. Wind-speed was constant at about 0.1 meter per second for all experiments. Oxygen absorption coefficients were measured simultaneously with the measurement of the acetone and t-butyl alcohol mass-transfer coefficients. Gas-film coefficients for acetone, t-butyl alcohol, and water were determined by measuring the volatilization fluxes of the pure substances over a range of temperatures. Henry's law constants were estimated from data from the literature. The combination of high resistance in the gas film for solutes with low values of the Henry's law constants has not been studied previously. Calculation of the liquid-film coefficients for acetone and t-butyl alcohol from measured overall mass-transfer and gas-film coefficients, estimated Henry's law constants, and the two-film model equation resulted in physically unrealistic, negative liquid-film coefficients for most of the experiments at the medium and high water mixing conditions. An analysis of the two-film model equation showed that when the percentage resistance in the gas film is large and the gas-film resistance approaches the overall resistance in value, the calculated liquid-film coefficient becomes extremely sensitive to errors in the Henry's law constant. The negative coefficients were attributed to this sensitivity and to errors in the estimated Henry's law constants. Liquid-film coefficients for the absorption of oxygen were correlated with the stirrer Reynolds number and the Schmidt number. Application of this correlation with the experimental conditions and a molecular-diffusion coefficient adjustment resulted in values of the liquid-film coefficients for both acetone and t-butyl alcohol within the range expected for all three mixing conditions. Comparison of Henry's law constants calculated from these film coefficients and the experimental data with the constants calculated from literature data showed that the differences were small relative to the errors reported in the literature as typical for the measurement or estimation of Henry's law constants for hydrophilic compounds such as ketones and alcohols. Temperature dependence of the mass-transfer coefficients was expressed in two forms. The first, based on thermodynamics, assumed the coefficients varied as the exponential of the reciprocal absolute temperature. The second empirical approach assumed the coefficients varied as the exponential of the absolute temperature. Both of these forms predicted the temperature dependence of the experimental mass-transfer coefficients with little error for most of the water temperature range likely to be found in streams and rivers. Liquid-film and gas-film coefficients for acetone and t-butyl alcohol were similar in value. However, depending on water mixing conditions, overall mass-transfer coefficients for acetone were from two to four times larger than the coefficients for t-butyl alcohol. This difference in behavior of the coefficients resulted because the Henry's law constant for acetone was about three times larger than that of

Energy absorption by a magnetic nanoparticle suspension in a rotating field

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

Raikher, Yu. L.; Stepanov, V. I., E-mail: stepanov@icmm.ru

Heat generation by viscous dissipation in a dilute suspension of single-domain ferromagnetic particles in a rotating magnetic field is analyzed by assuming that the suspended particles have a high magnetic rigidity. The problem is solved by using a kinetic approach based on a rotational diffusion equation. Behavior of specific loss power (SLP) as a function of field strength H and frequency {omega} is examined at constant temperature. SLP increases as either of these parameters squared when the other is constant, eventually approaching a saturation value. The function SLP(H, {omega}) can be used to determine optimal and admissible ranges of magneticallymore » induced heating.« less

Exact solutions of kinetic equations in an autocatalytic growth model.

PubMed

Jędrak, Jakub

2013-02-01

Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke [J. Am. Chem. Soc. 119, 10382 (1997)]. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ(k)=s(k)(ξ(1))[proportionality]ξ(1)(k)/k was obtained, while in the latter, the functional form of s(k)(ξ(1)) is more complicated. In both cases, ξ(1)(t)=h(μ)(M(μ)(t)) is a function of the moments of the mass distribution. Both functions, s(k)(ξ(1)) and h(μ)(M(μ)), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system.

On Faraday Instability in Magnetic Liquids: Ince-Erdelyi Approach Applied to the Hill Equation Describing Oscillations of a Ferrofluid Free Surface

NASA Astrophysics Data System (ADS)

Hennenberg, M.; Slavtchev, S.; Valchev, G.

2013-12-01

When an isothermal ferrofluid is submitted to an oscillating magnetic field, the initially motionless liquid free surface can start to oscillate. This physical phenomenon is similar to the Faraday instability for usual Newtonian liquids subjected to a mechanical oscillation. In the present paper, we consider the magnetic field as a sum of a constant part and a time periodic part. Two different cases for the constant part of the field, being vertical in the first one or horizontal in the second one are studied. Assuming both ferrofluid magnetization and magnetic field to be collinear, we develop the linear stability analysis of the motionless reference state taking into account the Kelvin magnetic forces. The Laplace law describing the free surface deformation reduces to Hill's equation, which is studied using the classical method of Ince and Erdelyi. Inside this framework, we obtain the transition conditions leading to the free surface oscillations.

The change law of the universe

NASA Astrophysics Data System (ADS)

Yongquan, Han

The ideal gas state equation is not applicable to ordinary gas, it should be applied to the Electromagnetic ''gas'' that is applied to the radiation, the radiation should be the ultimate state of matter changes or initial state, the universe is filled with radiation. That is, the ideal gas equation of state is suitable for the Singular point and the universe. Maybe someone consider that, there is no vessel can accommodate radiation, it is because the Ordinary container is too small to accommodate, if the radius of your container is the distance that Light through an hour, would you still think it can't accommodates radiation? Modern scientific determinate that the radius of the universe now is about 1027 m, assuming that the universe is a sphere whose volume is approximately: V = 4.19 × 1081 cubic meters, the temperature radiation of the universe (cosmic microwave background radiation temperature of the universe, should be the closest the average temperature of the universe) T = 3.15k, radiation pressure P = 5 Ã 10-6 N / m 2, according to the law of ideal gas state equation, PV / T = 6 à 1075, the value of this constant is the universe, The singular point should also equal to the constant

Water Pulsejet Research

DTIC Science & Technology

1977-08-01

pulsejet. C W W/pW2 X3A, a work coefficient D Pipe diameter = 2R E Young’s modulus, or kinetic energy f D’Arcy friction factor , or stress g Acceleration due...to con- tact the hot region to provide a supply of steam for later condensation. This factor may account for the somewhat more stable operation of a...momentum in the wake. (c) Equation (1) assumes that the [)’Arcy friction factor f is constant, so that skin friction terms cancel out. The magnitu|de of

Using Enthalpy as a Prognostic Variable in Atmospheric Modelling with Variable Composition

DTIC Science & Technology

2016-04-14

the first place. It then becomes clear that specific enthalpy provides a viable alternative to account for the effects of composi- tional changes on...forces. It is also assumed that external forces acting on a molecule are proportional to its mass, mi , as is the case with the gravity or Coriolis ...relative humidity and is introduced into Equation (11) to account for the effects of water vapour on the gas constant R and, consequently, on the

Optimal Damping of Perturbations of Moving Thermoelastic Panel

NASA Astrophysics Data System (ADS)

Banichuk, N. V.; Ivanova, S. Yu.

2018-01-01

The translational motion of a thermoelastic web subject to transverse vibrations caused by initial perturbations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic panel simply supported at its ends. The problem of optimal damping of vibrations when applying active transverse actions is formulated. For solving the optimization problem, modern methods developed in control theory for systems with distributed parameters described by partial differential equations are used.

Implications of the Equation of Transfer within the Visible and Infrared Spectrum

DTIC Science & Technology

1982-08-01

spectrum at twilight leigh or molecular scattering Rs Is highly wavelength and night but will not be dealt with herein. dependent being proportional to the...with wavelength, by atomic or molecular collision. The atmosphere is The path function due to scattering is the integral of assumed to be in local...speed of light, h is the Planck constant and band spectra are molecular and tend to be at the longer wavelengths. The continua are essentially part of

Exposure of a Food Crop to Trichloroethylene from a Contaminated Aquifer

DTIC Science & Technology

1994-09-01

Chemicals From Soils," Chemosphere, 17(122): 2299-2323. 1988 Serway , Raymond A . Physics for Scientists and Engineers, (Second Edition). Philadelphia...trajectory equation ( Serway , 1986:61): Vd sin ( a ) td = g a = initial angle of trajectory (assume 300) g = acceleration due to gravity (980 cm / s2) This is...1 N/m2 ( Serway , 1986:317) For this Henrys constant and unstirred water, Chiou indicates an a of .9 (Chiou, 1979:235). The a for unstirred water is

Control of vibrations of a moving beam

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Relativistic polytropic spheres with electric charge: Compact stars, compactness and mass bounds, and quasiblack hole configurations

NASA Astrophysics Data System (ADS)

Arbañil, José D. V.; Zanchin, Vilson T.

2018-05-01

We study the static equilibrium configurations of uncharged and charged spheres composed by a relativistic polytropic fluid, and we compare with those of spheres composed by a nonrelativistic polytropic fluid, the later case being already studied in a previous work [J. D. Arbañil, P. S. Lemos, and V. T. Zanchin, Phys. Rev. D 88, 084023 (2013), 10.1103/PhysRevD.88.084023]. An equation of state connecting the pressure p and the energy density ρ is assumed. In the nonrelativistic fluid case, the connection is through a nonrelativistic polytropic equation of state, p =ω ργ , with ω and γ being respectively the polytropic constant and the polytropic exponent. In the relativistic fluid case, the connection is through a relativistic polytropic equation of state, p =ω δγ, with δ =ρ -p /(γ -1 ), and δ being the rest-mass density of the fluid. For the electric charge distribution, we assume that the charge density ρe is proportional to the energy density ρ , ρe=α ρ , with α being a constant such that 0 ≤|α |≤1 . The study is developed by integrating numerically the hydrostatic equilibrium equation. Some properties of the charged spheres such as the gravitational mass, the total electric charge, the radius, the surface redshift, and the speed of sound are analyzed by varying the central rest-mass density, the charge fraction, and the polytropic exponent. In addition, some limits that arise in general relativity, such as the Chandrasekhar limit, the Oppenheimer-Volkoff limit, the Buchdahl bound, and the Buchdahl-Andréasson bound are studied. It is confirmed that charged relativistic polytropic spheres with γ →∞ and α →1 saturate the Buchdahl-Andréasson bound, thus indicating that it reaches the quasiblack hole configuration. We show by means of numerical analysis that, as expected, the major differences between the two cases appear in the high energy density region.

Does phenomenological kinetics provide an adequate description of heterogeneous catalytic reactions?

PubMed

Temel, Burcin; Meskine, Hakim; Reuter, Karsten; Scheffler, Matthias; Metiu, Horia

2007-05-28

Phenomenological kinetics (PK) is widely used in the study of the reaction rates in heterogeneous catalysis, and it is an important aid in reactor design. PK makes simplifying assumptions: It neglects the role of fluctuations, assumes that there is no correlation between the locations of the reactants on the surface, and considers the reacting mixture to be an ideal solution. In this article we test to what extent these assumptions damage the theory. In practice the PK rate equations are used by adjusting the rate constants to fit the results of the experiments. However, there are numerous examples where a mechanism fitted the data and was shown later to be erroneous or where two mutually exclusive mechanisms fitted well the same set of data. Because of this, we compare the PK equations to "computer experiments" that use kinetic Monte Carlo (kMC) simulations. Unlike in real experiments, in kMC the structure of the surface, the reaction mechanism, and the rate constants are known. Therefore, any discrepancy between PK and kMC must be attributed to an intrinsic failure of PK. We find that the results obtained by solving the PK equations and those obtained from kMC, while using the same rate constants and the same reactions, do not agree. Moreover, when we vary the rate constants in the PK model to fit the turnover frequencies produced by kMC, we find that the fit is not adequate and that the rate constants that give the best fit are very different from the rate constants used in kMC. The discrepancy between PK and kMC for the model of CO oxidation used here is surprising since the kMC model contains no lateral interactions that would make the coverage of the reactants spatially inhomogeneous. Nevertheless, such inhomogeneities are created by the interplay between the rate of adsorption, of desorption, and of vacancy creation by the chemical reactions.

On the nature of liquid junction and membrane potentials.

PubMed

Perram, John W; Stiles, Peter J

2006-09-28

Whenever a spatially inhomogeneous electrolyte, composed of ions with different mobilities, is allowed to diffuse, charge separation and an electric potential difference is created. Such potential differences across very thin membranes (e.g. biomembranes) are often interpreted using the steady state Goldman equation, which is usually derived by assuming a spatially constant electric field. Through the fundamental Poisson equation of electrostatics, this implies the absence of free charge density that must provide the source of any such field. A similarly paradoxical situation is encountered for thick membranes (e.g. in ion-selective electrodes) for which the diffusion potential is normally interpreted using the Henderson equation. Standard derivations of the Henderson equation appeal to local electroneutrality, which is also incompatible with sources of electric fields, as these require separated charges. We analyse self-consistent solutions of the Nernst-Planck-Poisson equations for a 1 : 1-univalent electrolyte to show that the Goldman and Henderson steady-state membrane potentials are artefacts of extraneous charges created in the reservoirs of electrolyte solution on either side of the membrane, due to the unphysical nature of the usual (Dirichlet) boundary conditions assumed to apply at the membrane-electrolyte interfaces. We also show, with the aid of numerical simulations, that a transient electric potential difference develops in any confined, but initially non-uniform, electrolyte solution. This potential difference ultimately decays to zero in the real steady state of the electrolyte, which corresponds to thermodynamic equilibrium. We explain the surprising fact that such transient potential differences are well described by the Henderson equation by using a computer algebra system to extend previous steady-state singular perturbation theories to the time-dependent case. Our work therefore accounts for the success of the Henderson equation in analysing experimental liquid-junction potentials.

Stable plume rise in a shear layer.

PubMed

Overcamp, Thomas J

2007-03-01

Solutions are given for plume rise assuming a power-law wind speed profile in a stably stratified layer for point and finite sources with initial vertical momentum and buoyancy. For a constant wind speed, these solutions simplify to the conventional plume rise equations in a stable atmosphere. In a shear layer, the point of maximum rise occurs further downwind and is slightly lower compared with the plume rise with a constant wind speed equal to the wind speed at the top of the stack. If the predictions with shear are compared with predictions for an equivalent average wind speed over the depth of the plume, the plume rise with shear is higher than plume rise with an equivalent average wind speed.

Proton and metal ion binding to natural organic polyelectrolytes-II. Preliminary investigation with a peat and a humic acid

USGS Publications Warehouse

Marinsky, J.A.; Reddy, M.M.

1984-01-01

We summarize here experimental studies of proton and metal ion binding to a peat and a humic acid. Data analysis is based on a unified physico-chemical model for reaction of simple ions with polyelectrolytes employing a modified Henderson-Hasselbalch equation. Peat exhibited an apparent intrinsic acid dissociation constant of 10-4.05, and an apparent intrinsic metal ion binding constant of: 400 for cadmium ion; 600 for zinc ion; 4000 for copper ion; 20000 for lead ion. A humic acid was found to have an apparent intrinsic proton binding constant of 10-2.6. Copper ion binding to this humic acid sample occurred at two types of sites. The first site exhibited reaction characteristics which were independent of solution pH and required the interaction of two ligands on the humic acid matrix to simultaneously complex with each copper ion. The second complex species is assumed to be a simple monodentate copper ion-carboxylate species with a stability constant of 18. ?? 1984.

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy.

PubMed

Shizgal, Bernie D

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988)JSTPBS0022-471510.1007/BF01016429].

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy

NASA Astrophysics Data System (ADS)

Shizgal, Bernie D.

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988), 10.1007/BF01016429].

Optimal Electrodynamic Tether Phasing Maneuvers

NASA Technical Reports Server (NTRS)

Bitzer, Matthew S.; Hall, Christopher D.

2007-01-01

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

The dynamics and optimal control of spinning spacecraft with movable telescoping appendages. Part C: Effect of flexibility during boom deployment

NASA Technical Reports Server (NTRS)

Bainum, P. M.; James, P. K.

1977-01-01

The dynamics of a spinning symmetrical spacecraft system during the deployment (or retraction) of flexible boom-type appendages were investigated. The effect of flexibility during boom deployment is treated by modelling the deployable members as compound spherical pendula of varying length (according to a control law). The orientation of the flexible booms with respect to the hub, is described by a sequence of two Euler angles. The boom members contain a flexural stiffness which can be related to an assumed effective restoring linear spring constant, and structural damping which effects the entire system. Linearized equations of motion for this system, when the boom length is constant, involve periodic coefficients with the frequency of the hub spin. A bounded transformation is found which converts this system into a kinematically equivalent one involving only constant coefficients.

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

PubMed

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

2016-03-01

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

Dynamic wormhole solutions in Einstein-Cartan gravity

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi

2017-12-01

In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

Transient temperature distributions in simple conducting bodies steadily heated through a laminar boundary layer

NASA Technical Reports Server (NTRS)

Parker, Hermon M

1953-01-01

An analysis is made of the transient heat-conduction effects in three simple semi-infinite bodies: the flat insulated plate, the conical shell, and the slender solid cone. The bodies are assumed to have constant initial temperatures and, at zero time, to begin to move at a constant speed and zero angle of attack through a homogeneous atmosphere. The heat input is taken as that through a laminar boundary layer. Radiation heat transfer and transverse temperature gradients are assumed to be zero. The appropriate heat-conduction equations are solved by an iteration method, the zeroeth-order terms describing the situation in the limit of small time. The method is presented and the solutions are calculated to three orders which are sufficient to give reasonably accurate results when the forward edge has attained one-half the total temperature rise (nose half-rise time). Flight Mach number and air properties occur as parameters in the result. Approximate expressions for the extent of the conduction region and nose half-rise times as functions of the parameters of the problem are presented. (author)

Cosmology with galaxy cluster phase spaces

NASA Astrophysics Data System (ADS)

Stark, Alejo; Miller, Christopher J.; Huterer, Dragan

2017-07-01

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range 0 ≤z ≤0.8 , after applying a conservative 80% mass scatter prior on each cluster and marginalizing over all other parameters, we forecast 1 σ constraints on the dark energy equation of state w and matter density parameter ΩM of σw=0.138 (0.431 ) and σΩM=0.007(0.025 ) in a flat universe. Assuming 40% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the Chevallier-Polarski-Linder parametrization of the dark energy equation of state parameters w0 and wa with 100 clusters in the same redshift range: σw 0=0.191 and σwa=2.712. Dropping the assumption of flatness and assuming w =-1 we also attain competitive constraints on the matter and dark energy density parameters: σΩ M=0.101 and σΩ Λ=0.197 for 100 clusters uniformly distributed in the range 0 ≤z ≤0.8 after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future.

Macroscopic neural mass model constructed from a current-based network model of spiking neurons.

PubMed

Umehara, Hiroaki; Okada, Masato; Teramae, Jun-Nosuke; Naruse, Yasushi

2017-02-01

Neural mass models (NMMs) are efficient frameworks for describing macroscopic cortical dynamics including electroencephalogram and magnetoencephalogram signals. Originally, these models were formulated on an empirical basis of synaptic dynamics with relatively long time constants. By clarifying the relations between NMMs and the dynamics of microscopic structures such as neurons and synapses, we can better understand cortical and neural mechanisms from a multi-scale perspective. In a previous study, the NMMs were analytically derived by averaging the equations of synaptic dynamics over the neurons in the population and further averaging the equations of the membrane-potential dynamics. However, the averaging of synaptic current assumes that the neuron membrane potentials are nearly time invariant and that they remain at sub-threshold levels to retain the conductance-based model. This approximation limits the NMM to the non-firing state. In the present study, we newly propose a derivation of a NMM by alternatively approximating the synaptic current which is assumed to be independent of the membrane potential, thus adopting a current-based model. Our proposed model releases the constraint of the nearly constant membrane potential. We confirm that the obtained model is reducible to the previous model in the non-firing situation and that it reproduces the temporal mean values and relative power spectrum densities of the average membrane potentials for the spiking neurons. It is further ensured that the existing NMM properly models the averaged dynamics over individual neurons even if they are spiking in the populations.

Reconstructions of the dark-energy equation of state and the inflationary potential

NASA Astrophysics Data System (ADS)

Barrow, John D.; Paliathanasis, Andronikos

2018-07-01

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations ns and the tensor to scalar ratio r. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that ns-1=h( r) . For the function h( r) , we consider three cases, where h( r) is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

Comparison of constitutive flow resistance equations based on the Manning and Chezy equations applied to natural rivers

USGS Publications Warehouse

Bjerklie, David M.; Dingman, S. Lawrence; Bolster, Carl H.

2005-01-01

A set of conceptually derived in‐bank river discharge–estimating equations (models), based on the Manning and Chezy equations, are calibrated and validated using a database of 1037 discharge measurements in 103 rivers in the United States and New Zealand. The models are compared to a multiple regression model derived from the same data. The comparison demonstrates that in natural rivers, using an exponent on the slope variable of 0.33 rather than the traditional value of 0.5 reduces the variance associated with estimating flow resistance. Mean model uncertainty, assuming a constant value for the conductance coefficient, is less than 5% for a large number of estimates, and 67% of the estimates would be accurate within 50%. The models have potential application where site‐specific flow resistance information is not available and can be the basis for (1) a general approach to estimating discharge from remotely sensed hydraulic data, (2) comparison to slope‐area discharge estimates, and (3) large‐scale river modeling.

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.

1976-01-01

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

NASA Astrophysics Data System (ADS)

Partov, Doncho; Kantchev, Vesselin

2011-09-01

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete E c (t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

Coagulation algorithms with size binning

NASA Technical Reports Server (NTRS)

Statton, David M.; Gans, Jason; Williams, Eric

1994-01-01

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Reversible exciplex formation followed charge separation.

PubMed

Petrova, M V; Burshtein, A I

2008-12-25

The reversible exciplex formation followed by its decomposition into an ion pair is considered, taking into account the subsequent geminate and bulk ion recombination to the triplet and singlet products (in excited and ground states). The integral kinetic equations are derived for all state populations, assuming that the spin conversion is performed by the simplest incoherent (rate) mechanism. When the forward and backward electron transfer is in contact as well as all dissociation/association reactions of heavy particles, the kernels of integral equations are specified and expressed through numerous reaction constants and characteristics of encounter diffusion. The solutions of these equations are used to specify the quantum yields of the excited state and exciplex fluorescence induced by pulse or stationary pumping. In the former case, the yields of the free ions and triplet products are also found, while in the latter case their stationary concentrations are obtained.

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.; Chen, L. T.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

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

Pereira, S.H.; Pinho, A.S.S.; Silva, J.M. Hoff da

In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model Λ( t )=Λ{sub *}+3β H {sup 2}, where Λ{sub *} and β are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parametersmore » Ω {sub m} and β, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.« less

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Gaffney, R. L., Jr.

2007-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter. M.S. Thesis

NASA Technical Reports Server (NTRS)

Chen, L. T.

1975-01-01

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

On the expected discounted penalty functions for two classes of risk processes under a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Lu, Zhaoyang; Xu, Wei; Sun, Decai; Han, Weiguo

2009-10-01

In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, respectively. When the surplus is above this threshold level, dividends are paid at a constant rate that does not exceed the premium rate. Two systems of integro-differential equations for discounted penalty functions are derived, based on whether the surplus is above this threshold level. Laplace transformations of the discounted penalty functions when the surplus is below the threshold level are obtained. And we also derive a system of renewal equations satisfied by the discounted penalty function with initial surplus above the threshold strategy via the Dickson-Hipp operator. Finally, analytical solutions of the two systems of integro-differential equations are presented.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Gaffney, R. L., Jr.; Xiao, X.; Edwards, J. R.; Hassan, H. A.

2005-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Earth Reflected Solar Radiation Incident upon an Arbitrarily Oriented Spinning Flat Plate

NASA Technical Reports Server (NTRS)

Cunningham, Fred G.

1963-01-01

A general derivation is given for the earth reflected solar radiation input to a flat plate--a solar cell paddle, for example--which is spinning about an axis coincident with the axis of symmetry of the satellite to which it is affixed. The resulting equations are written for the general case so that arbitrary orientations of the spin axis with respect to the earth-satellite line and arbitrary orientations of the normal to the plate with respect to the spin axis can be treated. No attempt is made to perform the resulting integrations because of the complexity of the equations; nor is there any attempt to delineate the integration limits for the general case. However, the equations governing these limits are given. The appendixes contain: the results, in graphical form, of two representative examples; the general computer program for the calculation is given in Fortran notation; and the results of a calculation of the distribution of albedo energy on the proposed Echo II satellite. The value of the mean solar constant used is 1.395 times 10 (sup 4) ergs per centimeters-squared per second; the mean albedo of the earth is assumed to be 0.34; and the earth is assumed to be a diffuse reflector.

A dynamic response model for pressure sensors in continuum and high Knudsen number flows with large temperature gradients

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Petersen, Brian J.; Scott, David D.

1996-01-01

This paper develops a dynamic model for pressure sensors in continuum and rarefied flows with longitudinal temperature gradients. The model was developed from the unsteady Navier-Stokes momentum, energy, and continuity equations and was linearized using small perturbations. The energy equation was decoupled from momentum and continuity assuming a polytropic flow process. Rarefied flow conditions were accounted for using a slip flow boundary condition at the tubing wall. The equations were radially averaged and solved assuming gas properties remain constant along a small tubing element. This fundamental solution was used as a building block for arbitrary geometries where fluid properties may also vary longitudinally in the tube. The problem was solved recursively starting at the transducer and working upstream in the tube. Dynamic frequency response tests were performed for continuum flow conditions in the presence of temperature gradients. These tests validated the recursive formulation of the model. Model steady-state behavior was analyzed using the final value theorem. Tests were performed for rarefied flow conditions and compared to the model steady-state response to evaluate the regime of applicability. Model comparisons were excellent for Knudsen numbers up to 0.6. Beyond this point, molecular affects caused model analyses to become inaccurate.

On the Henry constant and isosteric heat at zero loading in gas phase adsorption.

PubMed

Do, D D; Nicholson, D; Do, H D

2008-08-01

The Henry constant and the isosteric heat of adsorption at zero loading are commonly used as indicators of the strength of the affinity of an adsorbate for a solid adsorbent. It is assumed that (i) they are observable in practice, (ii) the Van Hoff's plot of the logarithm of the Henry constant versus the inverse of temperature is always linear and the slope is equal to the heat of adsorption, and (iii) the isosteric heat of adsorption at zero loading is either constant or weakly dependent on temperature. We show in this paper that none of these three points is necessarily correct, first because these variables might not be observable since they are outside the range of measurability; second that the linearity of the Van Hoff plot breaks down at very high temperature, and third that the isosteric heat versus loading is a strong function of temperature. We demonstrate these points using Monte Carlo integration and Monte Carlo simulation of adsorption of various gases on a graphite surface. Another issue concerning the Henry constant is related to the way the adsorption excess is defined. The most commonly used equation is the one that assumes that the void volume is the volume extended all the way to a boundary passing through the centres of the outermost solid atoms. With this definition the Henry constant can become negative at high temperatures. Although adsorption at these temperatures may not be practical because of the very low value of the Henry constant, it is more useful to define the Henry constant in such a way that it is always positive at all temperatures. Here we propose the use of the accessible volume; the volume probed by the adsorbate when it is in nonpositive regions of the potential, to calculate the Henry constant.

Aeromechanical stability of helicopters with a bearingless main rotor. Part 1: Equations of motion

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1978-01-01

Equations of motion for a coupled rotor-body system were derived for the purpose of studying air and ground resonance characteristics of helicopters that have bearingless main rotors. For the fuselage, only four rigid body degrees of freedom are considered; longitudinal and lateral translations, pitch, and roll. The rotor is assumed to consist of three or more rigid blades. Each blade is joined to the hub by means of a flexible beam segment (flexbeam or strap). Pitch change is accomplished by twisting the flexbeam with the pitch-control system, the characteristics of which are variable. Thus, the analysis is capable of implicitly treating aeroelastic couplings generated by the flexbeam elastic deflections, the pitch-control system, and the angular offsets of the blade and flexbeam. The linearized equations are written in the nonrotating system retaining only the cyclic rotor modes; thus, they comprise a system of homogeneous ordinary differential equations with constant coefficients. All contributions to the linearized perturbation equations from inertia, gravity, quasi-steady aerodynamics, and the flexbeam equilibrium deflections are retained exactly.

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

NASA Technical Reports Server (NTRS)

Carleton, O.

1972-01-01

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

Exact solutions to quadratic gravity

NASA Astrophysics Data System (ADS)

Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

2017-04-01

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

Optimal trajectories for the Aeroassisted Flight Experiment. Part 2: Equations of motion in an inertial system

NASA Technical Reports Server (NTRS)

Miele, A.; Zhao, Z. G.; Lee, W. Y.

1989-01-01

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The AFE refers to the study of the free flight of an autonomous spacecraft, shuttle-launched and shuttle-recovered. Its purpose is to gather atmospheric entry environmental data for use in designing aeroassisted orbital transfer vehicles (AOTV). It is assumed that: (1) the spacecraft is a particle of constant mass; (2) the Earth is rotating with constant angular velocity; (3) the Earth is an oblate planet, and the gravitational potential depends on both the radial distance and the latitude (harmonics of order higher than four are ignored); and (4) the atmosphere is at rest with respect to the Earth. Under these assumptions, the equations of motion for hypervelocity atmospheric flight (which can be used not only for AFE problems, but also for AOT problems and space shuttle problems) are derived in an inertial system. Transformation relations are supplied which allow one to pass from quantities computed in an inertial system to quantities computed in an Earth-fixed system and vice versa.

Optimal trajectories for the Aeroassisted Flight Experiment. Part 1: Equations of motion in an Earth-fixed system

NASA Technical Reports Server (NTRS)

Miele, A.; Zhao, Z. G.; Lee, W. Y.

1989-01-01

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The AFE refers to the study of the free flight of an autonomous spacecraft, shuttle-launched and shuttle-recovered. Its purpose is to gather atmospheric entry environmental data for use in designing aeroassisted orbital transfer vehicles (AOTV). It is assumed that: (1) the spacecraft is a particle of constant mass; (2) the Earth is rotating with constant angular velocity; (3) the Earth is an oblate planet, and the gravitational potential depends on both the radial distance and the latitude (harmonics of order higher than four are ignored); and (4) the atmosphere is at rest with respect to the Earth. Under these assumptions, the equations of motion for hypervelocity atmospheric flight (which can be used not only for AFE problems, but also for AOT problems and space shuttle problems) are derived in an Earth-fixed system. Transformation relations are supplied which allow one to pass from quantities computed in an Earth-fixed system to quantities computed in an inertial system, and vice versa.

Expanding Taylor bubble under constant heat flux

NASA Astrophysics Data System (ADS)

Voirand, Antoine; Benselama, Adel M.; Ayel, Vincent; Bertin, Yves

2016-09-01

Modelization of non-isothermal bubbles expanding in a capillary, as a contribution to the understanding of the physical phenomena taking place in Pulsating Heat Pipes (PHPs), is the scope of this paper. The liquid film problem is simplified and solved, while the thermal problem takes into account a constant heat flux density applied at the capillary tube wall, exchanging with the liquid film surrounding the bubble and also with the capillary tube outside medium. The liquid slug dynamics is solved using the Lucas-Washburn equation. Mass and energy balance on the vapor phase allow governing equations of bubble expansion to be written. The liquid and vapor phases are coupled only through the saturation temperature associated with the vapor pressure, assumed to be uniform throughout the bubble. Results show an over-heating of the vapor phase, although the particular thermal boundary condition used here always ensures an evaporative mass flux at the liquid-vapor interface. Global heat exchange is also investigated, showing a strong decreasing of the PHP performance to convey heat by phase change means for large meniscus velocities.

Viscous, radiating hypersonic flow about a blunt body

NASA Technical Reports Server (NTRS)

Passamaneck, R. S.

1974-01-01

The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.

Eddy diffusivity of quasi-neutrally-buoyant inertial particles

NASA Astrophysics Data System (ADS)

Martins Afonso, Marco; Muratore-Ginanneschi, Paolo; Gama, Sílvio M. A.; Mazzino, Andrea

2018-04-01

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

Tunneling-assisted transport of carriers through heterojunctions.

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

Wampler, William R.; Myers, Samuel M.; Modine, Normand A.

The formulation of carrier transport through heterojunctions by tunneling and thermionic emission is derived from first principles. The treatment of tunneling is discussed at three levels of approximation: numerical solution of the one-band envelope equation for an arbitrarily specified potential profile; the WKB approximation for an arbitrary potential; and, an analytic formulation assuming constant internal field. The effects of spatially varying carrier chemical potentials over tunneling distances are included. Illustrative computational results are presented. The described approach is used in exploratory physics models of irradiated heterojunction bipolar transistors within Sandia's QASPR program.

Scale Dependence of Dark Energy Antigravity

NASA Astrophysics Data System (ADS)

Perivolaropoulos, L.

2002-09-01

We investigate the effects of negative pressure induced by dark energy (cosmological constant or quintessence) on the dynamics at various astrophysical scales. Negative pressure induces a repulsive term (antigravity) in Newton's law which dominates on large scales. Assuming a value of the cosmological constant consistent with the recent SnIa data we determine the critical scale $r_c$ beyond which antigravity dominates the dynamics ($r_c \\sim 1Mpc $) and discuss some of the dynamical effects implied. We show that dynamically induced mass estimates on the scale of the Local Group and beyond are significantly modified due to negative pressure. We also briefly discuss possible dynamical tests (eg effects on local Hubble flow) that can be applied on relatively small scales (a few $Mpc$) to determine the density and equation of state of dark energy.

A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 1; Model Development and Parametric Response

NASA Technical Reports Server (NTRS)

Smialek, James L.

2002-01-01

An equation has been developed to model the iterative scale growth and spalling process that occurs during cyclic oxidation of high temperature materials. Parabolic scale growth and spalling of a constant surface area fraction have been assumed. Interfacial spallation of the only the thickest segments was also postulated. This simplicity allowed for representation by a simple deterministic summation series. Inputs are the parabolic growth rate constant, the spall area fraction, oxide stoichiometry, and cycle duration. Outputs include the net weight change behavior, as well as the total amount of oxygen and metal consumed, the total amount of oxide spalled, and the mass fraction of oxide spalled. The outputs all follow typical well-behaved trends with the inputs and are in good agreement with previous interfacial models.

Extensions of the Einstein-Schrodinger non-symmetric theory of gravity

NASA Astrophysics Data System (ADS)

Shifflett, James A.

We modify the Einstein-Schrödinger theory to include a cosmological constant L z which multiplies the symmetric metric. The cosmological constant L z is assumed to be nearly cancelled by Schrödinger's cosmological constant L b which multiplies the nonsymmetric fundamental tensor, such that the total L = L z + L b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |L z | [arrow right] oo. For |L z | ~ 1/(Planck length) 2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10 -16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein- Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~ 10 -66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory. Peri-center advance, deflection of light and time delay of light have a fractional difference of < 10 -56 compared to Einstein-Maxwell theory for worst-case parameters. When a spin-1/2 field is included in the Lagrangian, the theory gives the ordinary Dirac equation, and the charged solution results in fractional shifts of < 10 -50 in Hydrogen atom energy levels. Newman-Penrose methods are used to derive an exact solution of the connection equations, and to show that the charged solution is Petrov type- D like the Reissner-Nordström solution. The Newman-Penrose asymptotically flat [Special characters omitted.] (1/ r 2 ) expansion of the field equations is shown to match Einstein-Maxwell theory. Finally we generalize the theory to non-Abelian fields, and show that a special case of the resulting theory closely approximates Einstein-Weinberg-Salam theory.

Early-time solution of the horizontal unconfined aquifer in the build-up phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-04-01

The Boussinesq equation is a dynamical equation for the free surface of saturated subsurface flows over an impervious bed. Boussinesq equation is non-linear. The non-linearity comes from the reduction of the dimensionality of the problem: The flow is assumed to be vertically homogeneous, therefore the flow rate through a cross section of the flow is proportional to the free surface height times the hydraulic gradient, which is assumed to be equal to the slope of the free surface (Dupuit approximation). In general, 'vertically' means normally on the bed; combining the Dupuit approximation with the continuity equation leads to the Boussinesq equation. There are very few transient exact solutions. Self- similar solutions have been constructed in the past by various authors. A power series type of solution was derived for a self-similar Boussinesq equation by Barenblatt in 1990. That type of solution has generated a certain amount of literature. For the unconfined flow case for zero recharge rate Boussinesq derived for the horizontal aquifer an exact solution assuming separation of variables. This is actually an exact asymptotic solution of the horizontal aquifer recession phase for late times. The kinematic wave is an interesting solution obtained by dropping the non-linear term in the Boussinesq equation. Although it is an approximate solution, and holds well only for small values of the Henderson and Wooding λ parameter (that is, for steep slopes, high conductivity or small recharge rate), it becomes less and less approximate for smaller values of the parameter, that is, it is asymptotically exact with respect to that parameter. In the present work we consider the case of the unconfined subsurface flow over horizontal bed in the build-up phase under constant recharge rate. This is a case with an infinite Henderson and Wooding parameter, that is, it is the limiting case where the non-linear term is present in the Boussinesq while the linear spatial derivative term goes away. Nonetheless, no analogue of the kinematic wave or the Boussinesq separable solution exists in this case. The late time state of the build-up phase under constant recharge rate is very simply the steady state solution. Our aim is to construct the early time asymptotic solution of this problem. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turn out to be asymptotic and it is regularized by re-summation techniques which are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

Recommendations for terminology and databases for biochemical thermodynamics.

PubMed

Alberty, Robert A; Cornish-Bowden, Athel; Goldberg, Robert N; Hammes, Gordon G; Tipton, Keith; Westerhoff, Hans V

2011-05-01

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature. Copyright © 2011 Elsevier B.V. All rights reserved.

Modeling multidomain hydraulic properties of shrink-swell soils

NASA Astrophysics Data System (ADS)

Stewart, Ryan D.; Abou Najm, Majdi R.; Rupp, David E.; Selker, John S.

2016-10-01

Shrink-swell soils crack and become compacted as they dry, changing properties such as bulk density and hydraulic conductivity. Multidomain models divide soil into independent realms that allow soil cracks to be incorporated into classical flow and transport models. Incongruously, most applications of multidomain models assume that the porosity distributions, bulk density, and effective saturated hydraulic conductivity of the soil are constant. This study builds on a recently derived soil shrinkage model to develop a new multidomain, dual-permeability model that can accurately predict variations in soil hydraulic properties due to dynamic changes in crack size and connectivity. The model only requires estimates of soil gravimetric water content and a minimal set of parameters, all of which can be determined using laboratory and/or field measurements. We apply the model to eight clayey soils, and demonstrate its ability to quantify variations in volumetric water content (as can be determined during measurement of a soil water characteristic curve) and transient saturated hydraulic conductivity, Ks (as can be measured using infiltration tests). The proposed model is able to capture observed variations in Ks of one to more than two orders of magnitude. In contrast, other dual-permeability models assume that Ks is constant, resulting in the potential for large error when predicting water movement through shrink-swell soils. Overall, the multidomain model presented here successfully quantifies fluctuations in the hydraulic properties of shrink-swell soil matrices, and are suitable for use in physical flow and transport models based on Darcy's Law, the Richards Equation, and the advection-dispersion equation.

Competition kinetics using the UV/H2O2 process: a structure reactivity correlation for the rate constants of hydroxyl radicals toward nitroaromatic compounds.

PubMed

García Einschlag, Fernando S; Carlos, Luciano; Capparelli, Alberto L

2003-10-01

The rate constants for hydroxyl radical reaction toward a set of nitroaromatic substrates kS, have been measured at 25 degrees C using competition experiments in the UV/H2O2 process. For a given pair of substrates S1 and S2, the relative reactivity beta (defined as kS1/kS2) was calculated from the slope of the corresponding double logarithmic plot, i.e., of ln[S1] vs. ln[S2]. This method is more accurate and remained linear for larger conversions in comparison with the plots of ln[S1] and ln[S2] against time. The rate constants measured ranged from 0.33 to 8.6 x 10(9) M(-1)s(-1). A quantitative structure-reactivity relationship was found using the Hammett equation. Assuming sigma values to be additive, a value of -0.60 was obtained for the reaction constant rho. This value agrees with the high reactivity and the electrophilic nature of HO* radical.

Application of the Modified Compaction Material Model to the Analysis of Landmine Detonation in Soil with Various Degrees of Water Saturation

DTIC Science & Technology

2007-01-01

Equation of State R2 – Constant in JWL Equation of State σ – Yield Stress T – Temperature...v – Specific volume w – Constant in JWL Equation of State x – Spatial coordinate y – Spatial coordinate Y – Yield stress Subscripts Comp – Value at...Constant in JWL Equation of State α – Porosity B – Compaction Modulus B1 – Strain Hardening Constant B2 – Constant in JWL Equation of State

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

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

Klain, Kimberly L.

The behavior of symmetrical coupled-core systems has been extensively studied, yet there is a dearth of research on asymmetrical systems due to the increased complexity of the analysis of such systems. In this research, the multipoint kinetics method is applied to asymmetrical zeropower, subcritical, bare metal reactor systems. Existing research on asymmetrical reactor systems assumes symmetry in the neutronic coupling; however, it will be shown that this cannot always be assumed. Deep subcriticality adds another layer of complexity and requires modification of the multipoint kinetics equations to account for the effect of the external neutron source. A modified set ofmore » multipoint kinetics equations is derived with this in mind. Subsequently, the Rossi-alpha equations are derived for a two-region asymmetrical reactor system. The predictive capabilities of the radiation transport code MCNP6 for neutron noise experiments are shown in a comparison to the results of a series of Rossi-alpha measurements performed by J. Mihalczo utilizing a coupled set of symmetrical bare highly-enriched uranium (HEU) cylinders. The ptrac option within MCNP6 can generate time-tagged counts in a cell (list-mode data). The list-mode data can then be processed similarly to measured data to obtain values for system parameters such as the dual prompt neutron decay constants observable in a coupled system. The results from the ptrac simulations agree well with the historical measured values. A series of case studies are conducted to study the effects of geometrical asymmetry in the coupling between two bare metal HEU cylinders. While the coupling behavior of symmetrical systems has been reported on extensively, that of asymmetrical systems remains sparse. In particular, it appears that there has been no previous research in obtaining the coupling time constants for asymmetrically-coupled systems. The difficulty in observing such systems is due in part to the inability to determine the individual coupling coefficients from measurement: unlike the symmetrical cases, only the product of the values can be obtained. A method is proposed utilizing MCNP6 tally ratios to separate the coupling coefficients for such systems. This work provides insight into the behavior of asymmetrically-coupled systems as the separation distance between the two cores is changed and also as the asymmetry is increased. As the asymmetry increases, both the slower and the faster observable prompt neutron decay constants increase in magnitude. The coupling time constants are determined from the measured decay constants. As the separation distance increases, both coupling coefficients decrease as expected. Based on these findings, an effective computational method utilizing MCNP6 and the Rossialpha technique can be applied to the prediction of asymmetrical coupled system measurements.« less

Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: exact solution of the Navier-Stokes equation.

PubMed

Otevrel, Marek; Klepárník, Karel

2002-10-01

The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

DOE PAGES

Lu, Zhiming

2018-01-30

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

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

Lu, Zhiming

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

A parametric analysis of waves propagating in a porous solid saturated by a three-phase fluid.

PubMed

Santos, Juan E; Savioli, Gabriela B

2015-11-01

This paper presents an analysis of a model for the propagation of waves in a poroelastic solid saturated by a three-phase viscous, compressible fluid. The constitutive relations and the equations of motion are stated first. Then a plane wave analysis determines the phase velocities and attenuation coefficients of the four compressional waves and one shear wave that propagate in this type of medium. A procedure to compute the elastic constants in the constitutive relations is defined next. Assuming the knowledge of the shear modulus of the dry matrix, the other elastic constants in the stress-strain relations are determined by employing ideal gedanken experiments generalizing those of Biot's theory for single-phase fluids. These experiments yield expressions for the elastic constants in terms of the properties of the individual solid and fluids phases. Finally the phase velocities and attenuation coefficients of all waves are computed for a sample of Berea sandstone saturated by oil, gas, and water.

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

NASA Astrophysics Data System (ADS)

Nazari, Saman; Toghraie, Davood

2017-03-01

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

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

Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thicknessmore » direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.« less

Modeling Neutral Densities Downstream of a Gridded Ion Thruster

NASA Technical Reports Server (NTRS)

Soulas, George C.

2010-01-01

The details of a model for determining the neutral density downstream of a gridded ion thruster are presented. An investigation of the possible sources of neutrals emanating from and surrounding a NEXT ion thruster determined that the most significant contributors to the downstream neutral density include discharge chamber neutrals escaping through the perforated grids, neutrals escaping from the neutralizer, and vacuum facility background neutrals. For the neutral flux through the grids, near- and far-field equations are presented for rigorously determining the neutral density downstream of a cylindrical aperture. These equations are integrated into a spherically-domed convex grid geometry with a hexagonal array of apertures for determining neutral densities downstream of the ion thruster grids. The neutrals escaping from an off-center neutralizer are also modeled assuming diffuse neutral emission from the neutralizer keeper orifice. Finally, the effect of the surrounding vacuum facility neutrals is included and assumed to be constant. The model is used to predict the neutral density downstream of a NEXT ion thruster with and without neutralizer flow and a vacuum facility background pressure. The impacts of past simplifying assumptions for predicting downstream neutral densities are also examined for a NEXT ion thruster.

Distance measurements from supernovae and dark energy constraints

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

Wang Yun

2009-12-15

Constraints on dark energy from current observational data are sensitive to how distances are measured from Type Ia supernova (SN Ia) data. We find that flux averaging of SNe Ia can be used to test the presence of unknown systematic uncertainties, and yield more robust distance measurements from SNe Ia. We have applied this approach to the nearby+SDSS+ESSENCE+SNLS+HST set of 288 SNe Ia, and the 'Constitution' set of 397 SNe Ia. Combining the SN Ia data with cosmic microwave background anisotropy data from Wilkinson Microwave Anisotropy Probe 5 yr observations, the Sloan Digital Sky Survey baryon acoustic oscillation measurements, themore » data of 69 gamma-ray bursts (GRBs) , and the Hubble constant measurement from the Hubble Space Telescope project SHOES, we measure the dark energy density function X(z){identical_to}{rho}{sub X}(z)/{rho}{sub X}(0) as a free function of redshift (assumed to be a constant at z>1 or z>1.5). Without the flux averaging of SNe Ia, the combined data using the Constitution set of SNe Ia seem to indicate a deviation from a cosmological constant at {approx}95% confidence level at 0 < or apporx. z < or approx. 0.8; they are consistent with a cosmological constant at {approx}68% confidence level when SNe Ia are flux averaged. The combined data using the nearby+SDSS+ESSENCE+SNLS+HST data set of SNe Ia are consistent with a cosmological constant at 68% confidence level with or without flux averaging of SNe Ia, and give dark energy constraints that are significantly more stringent than that using the Constitution set of SNe Ia. Assuming a flat Universe, dark energy is detected at >98% confidence level for z{<=}0.75 using the combined data with 288 SNe Ia from nearby+SDSS+ESSENCE+SNLS+HST, independent of the assumptions about X(z{>=}1). We quantify dark energy constraints without assuming a flat Universe using the dark energy figure of merit for both X(z) and a dark energy equation-of-state linear in the cosmic scale factor.« less

Finite magnetic relaxation in x-space magnetic particle imaging: Comparison of measurements and ferrohydrodynamic models.

PubMed

Dhavalikar, R; Hensley, D; Maldonado-Camargo, L; Croft, L R; Ceron, S; Goodwill, P W; Conolly, S M; Rinaldi, C

2016-08-03

Magnetic Particle Imaging (MPI) is an emerging tomographic imaging technology that detects magnetic nanoparticle tracers by exploiting their non-linear magnetization properties. In order to predict the behavior of nanoparticles in an imager, it is possible to use a non-imaging MPI relaxometer or spectrometer to characterize the behavior of nanoparticles in a controlled setting. In this paper we explore the use of ferrohydrodynamic magnetization equations for predicting the response of particles in an MPI relaxometer. These include a magnetization equation developed by Shliomis (Sh) which has a constant relaxation time and a magnetization equation which uses a field-dependent relaxation time developed by Martsenyuk, Raikher and Shliomis (MRSh). We compare the predictions from these models with measurements and with the predictions based on the Langevin function that assumes instantaneous magnetization response of the nanoparticles. The results show good qualitative and quantitative agreement between the ferrohydrodynamic models and the measurements without the use of fitting parameters and provide further evidence of the potential of ferrohydrodynamic modeling in MPI.

Two-dimensional numerical simulation of a Stirling engine heat exchanger

NASA Technical Reports Server (NTRS)

Ibrahim, Mounir; Tew, Roy C.; Dudenhoefer, James E.

1989-01-01

The first phase of an effort to develop multidimensional models of Stirling engine components is described. The ultimate goal is to model an entire engine working space. Parallel plate and tubular heat exchanger models are described, with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects). The model assumes laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations describing the model have been solved using the Crack-Nicloson finite-difference scheme. Model predictions are compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement is obtained for flow both in circular tubes and between parallel plates. The computational heat transfer results are in good agreement with the analytical heat transfer results for parallel plates.

The importance of excluded solvent volume effects in computing hydration free energies.

PubMed

Yang, Pei-Kun; Lim, Carmay

2008-11-27

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Stability analysis of nanoscale surface patterns in stressed solids

NASA Astrophysics Data System (ADS)

Kostyrko, Sergey A.; Shuvalov, Gleb M.

2018-05-01

Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

Attitude dynamics simulation subroutines for systems of hinge-connected rigid bodies with nonrigid appendages

NASA Technical Reports Server (NTRS)

Fleischer, G. E.; Likins, P. W.

1975-01-01

Three computer subroutines designed to solve the vector-dyadic differential equations of rotational motion for systems that may be idealized as a collection of hinge-connected rigid bodies assembled in a tree topology, with an optional flexible appendage attached to each body are reported. Deformations of the appendages are mathematically represented by modal coordinates and are assumed small. Within these constraints, the subroutines provide equation solutions for (1) the most general case of unrestricted hinge rotations, with appendage base bodies nominally rotating at a constant speed, (2) the case of unrestricted hinge rotations between rigid bodies, with the restriction that those rigid bodies carrying appendages are nominally nonspinning, and (3) the case of small hinge rotations and nominally nonrotating appendages. Sample problems and their solutions are presented to illustrate the utility of the computer programs.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

A finite element formulation for supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Development of a new model for batch sedimentation and application to secondary settling tanks design.

PubMed

Karamisheva, Ralica D; Islam, M A

2005-01-01

Assuming that settling takes place in two zones (a constant rate zone and a variable rate zone), a model using four parameters accounting for the nature of the water-suspension system has been proposed for describing batch sedimentation processes. The sludge volume index (SVI) has been expressed in terms of these parameters. Some disadvantages of the SVI application as a design parameter have been pointed out, and it has been shown that a relationship between zone settling velocity and sludge concentration is more consistent for describing the settling behavior and for design of settling tanks. The permissible overflow rate has been related to the technological parameters of secondary settling tank by simple working equations. The graphical representations of these equations could be used to optimize the design and operation of secondary settling tanks.

Adaptive Techniques to Correct for Effects of Ionospheric Refraction in Navigation, Surveillance and Communications Systems.

DTIC Science & Technology

1983-02-03

solair cycle, 3. Gma5. Me., $4, 5792, 1979. rejer, B.G., F .C. mallay, rawsheric irreruaritiel, ms. amp" spew Phys., 18, 401. 1960. Iealis,R.R, P.C...simplification of equation (26) can be achieved if we assume that the energy density W(k1) of Langmuir waves is constant inside a cylinder of radius kr and height...heating term arising from electron energy dissipation in the high-frequency wave fields. ., C C*°" i. -7 ’ / d (11) y.n, * inok . 6V, 0 t) (M) 37 -o

The effects of magnetohydrodynamic and radiation on flow of second grade fluid past an infinite inclined plate in porous medium

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

Ismail, Zulkhibri; Khan, Ilyas; Nasir, Nadirah Mohd

2015-02-03

An analysis of the exact solutions of second grade fluid problem for unsteady magnetohydrodynamic (MHD) flows past an infinite inclined plate in a porous medium is presented. It is assumed that the bounding infinite inclined plate has a constant temperature with radiation effects. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations, and all the boundary and initial conditions. The influence of various parameters on the velocity has been illustrated graphically and analyzed.

Vacuum fluctuations of the supersymmetric field in curved background

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Guberina, Branko

2012-01-01

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.

Filling of a Poisson trap by a population of random intermittent searchers.

PubMed

Bressloff, Paul C; Newby, Jay M

2012-03-01

We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→∞, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f(n)(t). The latter is determined by the integrated Poisson rate μ(t)=∫(0)(t)λ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n.

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.

Vapor condensation on liquid surface due to laminar jet-induced mixing: The effects of system parameters

NASA Technical Reports Server (NTRS)

Lin, Chin-Shun; Hasan, Mohammad M.

1989-01-01

The effects of system parameters on the interface condensation rate in a laminar jet induced mixing tank are numerically studied. The physical system consists of a partially filled cylindrical tank with a slightly subcooled jet discharged from the center of the tank bottom toward the liquid-vapor interface which is at a saturation temperature corresponding to the constant tank pressure. Liquid is also withdrawn from the outer part of the tank bottom to maintain the constant liquid level. The jet velocity is selected to be low enough such that the free surface is approximately flat. The effect of vapor superheat is assumed to be negligible. Therefore, the interface condensation rate can be determined from the resulting temperature field in the liquid region alone. The nondimensional form of the steady state conservation equations are solved by a finite difference method for various system parameters including liquid height to tank diameter ratio, tank to jet diameter ratio, liquid inflow to outflow area ratio, and a heat leak parameter which characterizes the uniform wall heat flux. Detailed analyses based on the numerical solutions are performed and simplified equations are suggested for the prediction of condensation rate.

Schottky diode model for non-parabolic dispersion in narrow-gap semiconductor and few-layer graphene

NASA Astrophysics Data System (ADS)

Ang, Yee Sin; Ang, L. K.; Zubair, M.

Despite the fact that the energy dispersions are highly non-parabolic in many Schottky interfaces made up of 2D material, experimental results are often interpreted using the conventional Schottky diode equation which, contradictorily, assumes a parabolic energy dispersion. In this work, the Schottky diode equation is derived for narrow-gap semiconductor and few-layer graphene where the energy dispersions are highly non-parabolic. Based on Kane's non-parabolic band model, we obtained a more general Kane-Schottky scaling relation of J (T2 + γkBT3) which connects the contrasting J T2 in the conventional Schottky interface and the J T3 scaling in graphene-based Schottky interface via a non-parabolicity parameter, γ. For N-layer graphene of ABC -stacking and of ABA -stacking, the scaling relation follows J T 2 / N + 1 and J T3 respectively. Intriguingly, the Richardson constant extracted from the experimental data using an incorrect scaling can differ with the actual value by more than two orders of magnitude. Our results highlights the importance of using the correct scaling relation in order to accurately extract important physical properties, such as the Richardson constant and the Schottky barrier's height.

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

NASA Astrophysics Data System (ADS)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

A Critical Protection Level Derived from Dengue Infection Mathematical Model Considering Asymptomatic and Symptomatic Classes

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2013-04-01

In this paper we formulate a model of dengue fever transmission by considering the presence of asymptomatic and symptomatic compartments. The model takes the form as a system of differential equations representing a host-vector SIR (Susceptible - Infective -Recovered) disease transmission. It is assumed that both host and vector populations are constant. It is also assumed that reinfection of recovered hosts by the disease is possible due to a wanning immunity in human body. We analyze the model to determine the qualitative behavior of the model solution and use the concept of effective basic reproduction number (fraktur Rp) as a control criteria of the disease transmission. The effect of mosquito biting protection (e.g. by using insect repellent) is also considered. We compute the long-term ratio of the asymptomatic and symptomatic classes and show a condition for which the iceberg phenomenon could appear.

On multisoliton solutions of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam

2015-09-01

We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation {z}{yy}+{(1/z)}{xx}+2=0 from a given seed. A construction of corresponding surfaces of constant astigmatism is then a matter of routine. As a special case, we consider multisoliton solutions of the constant astigmatism equation defined as counterparts of famous multisoliton solutions of the sine-Gordon equation. A few particular examples are surveyed as well.

Cyclic phase change in a cylindrical thermal energy storage capsule

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

Hasan, M.; Mujumdar, A.S.; Weber, M.E.

1983-12-01

This paper is concerned with a practical melting/freezing problem in conjunction with the more realistic case of a cyclic phase change thermal energy storage device. In this model the phase change medium is encapsulated in long cylindrical tubes, the surface temperature of which is allowed to vary sinusoidally with time about the discrete freezing temperature. Initial temperature of the medium is assumed to be constant at a temperature above or below the freezing/melting temperature. Natural convection in the melt is assumed to be negligible and the variations in the depth of freezing and/or melting in each half cycle is ignored.more » Depending on the half-cycle parameters the problem is simplified to either freezing or melting. The governing one-dimensional heat diffusion equations for both phases are solved by the Finite Integral Transform techniques. The kernels for the transformation are the time-dependent eigen functions separately defined for each phases. This extended transform method can accomodate any time-dependent surface temperature variation. The application of the transform generated a series of coupled, nonlinear first order differential equations, which are solved by Runge Kutta-Verner fifth and sixth order method. Dimensionless solutions of temperature variations in both phases, fusion front position and the fraction solidified (or melted) are displayed graphically to aid in practical calculations. For the special case of a constant surface temperature, comparisons are made between the present results and the existing integral and purely numerical results. The results are found to compare favourably. Results for fractional solidification (or melting and interface position are also compared with the simple Conduction Shape Factor method, after allowing for the time-dependent boundary conditions. Once again the results agree reasonably well.« less

More exact solutions of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam

2018-01-01

By using Bäcklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation zyy +(1 / z) xx + 2 = 0 are generated from a seed which corresponds to Lipschitz surfaces of constant astigmatism.

Interaction of anisotropic dark energy fluid with perfect fluid in the presence of cosmological term Λ

NASA Astrophysics Data System (ADS)

Singh, S. Surendra

2018-05-01

Considering the locally rotationally symmetric (LRS) Bianchi type-I metric with cosmological constant Λ, Einstein’s field equations are discussed based on the background of anisotropic fluid. We assumed the condition A = B 1 m for the metric potentials A and B, where m is a positive constant to obtain the viable model of the Universe. It is found that Λ(t) is positive and inversely proportional to time. The values of matter-energy density Ωm, dark energy density ΩΛ and deceleration parameter q are found to be consistent with the values of WMAP observations. State finder parameters and anisotropic deviation parameter are also investigated. It is also observed that the derived model is an accelerating, shearing and non-rotating Universe. Some of the asymptotic and geometrical behaviors of the derived models are investigated with the age of the Universe.

Fracture study of windshield glass panes

NASA Technical Reports Server (NTRS)

Yeh, H. Y.

1987-01-01

The major stresses which cause crack propagation in windshield glass panes are induced by bending moments which result from the pressure differentials across the panes. Hence the stress intensity factors for the finite plate with the semi-elliptical surface flaw and edge crack under the bending moments are examined. The results show that the crack growth will be upperbound if it is computed by using the stress intensity factor for the finite plate with the edge crack subjected to pure bending moments. Furthermore, if the ratio of crack depth to plate thickness, a/t, is within 0.3, the stress intensity factor can be conservatively assumed to be constant at the value of a/t equal to zero. A simplified equation to predict the structural life of glass panes is derived based on constant stress intensity factor. The accuracy of structural life is mainly dependent on how close the empirical parameter, m, can be estimated.

Rough-to-smooth transition of an equilibrium neutral constant stress layer

NASA Technical Reports Server (NTRS)

Logan, E., Jr.; Fichtl, G. H.

1975-01-01

Purpose of research on rough-to-smooth transition of an equilibrium neutral constant stress layer is to develop a model for low-level atmospheric flow over terrains of abruptly changing roughness, such as those occurring near the windward end of a landing strip, and to use the model to derive functions which define the extent of the region affected by the roughness change and allow adequate prediction of wind and shear stress profiles at all points within the region. A model consisting of two bounding logarithmic layers and an intermediate velocity defect layer is assumed, and dimensionless velocity and stress distribution functions which meet all boundary and matching conditions are hypothesized. The functions are used in an asymptotic form of the equation of motion to derive a relation which governs the growth of the internal boundary layer. The growth relation is used to predict variation of surface shear stress.

Two-dimensional numerical simulation of a Stirling engine heat exchanger

NASA Technical Reports Server (NTRS)

Ibrahim, Mounir B.; Tew, Roy C.; Dudenhoefer, James E.

1989-01-01

The first phase of an effort to develop multidimensional models of Stirling engine components is described; the ultimate goal is to model an entire engine working space. More specifically, parallel plate and tubular heat exchanger models with emphasis on the central part of the channel (i.e., ignoring hydrodynamic and thermal end effects) are described. The model assumes: laminar, incompressible flow with constant thermophysical properties. In addition, a constant axial temperature gradient is imposed. The governing equations, describing the model, were solved using Crank-Nicloson finite-difference scheme. Model predictions were compared with analytical solutions for oscillating/reversing flow and heat transfer in order to check numerical accuracy. Excellent agreement was obtained for the model predictions with analytical solutions available for both flow in circular tubes and between parallel plates. Also the heat transfer computational results are in good agreement with the heat transfer analytical results for parallel plates.

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy. III - Weakly nonlinear theory

NASA Technical Reports Server (NTRS)

Wheeler, A. A.; Mcfadden, G. B.; Coriell, S. R.; Hurle, D. T. J.

1990-01-01

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.

The three-dimensional steady radial expansion of a viscous gas from a sonic source into a vacuum.

NASA Technical Reports Server (NTRS)

Bush, W. B.; Rosen, R.

1971-01-01

The three-dimensional steady radial expansion of a viscous, heat-conducting, compressible fluid from a spherical sonic source into a vacuum is analyzed using the Navier-Stokes equations as a basis. It is assumed that the model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Limiting forms for the flow variable solutions are studied for the Reynolds number based on the sonic source conditions, going to infinity and the Newtonian parameter both fixed and going to zero. For the case of the viscosity-temperature exponent between .5 and 1, it is shown that the velocity as well as the pressure approach zero as the radial distance goes to infinity. The formulations of the distinct regions that span the domain extending from the sonic source to the vacuum are presented.

Modeling Attitude Dynamics in Simulink: A Study of the Rotational and Translational Motion of a Spacecraft Given Torques and Impulses Generated by RMS Hand Controllers

NASA Technical Reports Server (NTRS)

Mauldin, Rebecca H.

2010-01-01

In order to study and control the attitude of a spacecraft, it is necessary to understand the natural motion of a body in orbit. Assuming a spacecraft to be a rigid body, dynamics describes the complete motion of the vehicle by the translational and rotational motion of the body. The Simulink Attitude Analysis Model applies the equations of rigid body motion to the study of a spacecraft?s attitude in orbit. Using a TCP/IP connection, Matlab reads the values of the Remote Manipulator System (RMS) hand controllers and passes them to Simulink as specified torque and impulse profiles. Simulink then uses the governing kinematic and dynamic equations of a rigid body in low earth orbit (LE0) to plot the attitude response of a spacecraft for five seconds given known applied torques and impulses, and constant principal moments of inertia.

Dynamic stability of spinning pretwisted beams subjected to axial random forces

NASA Astrophysics Data System (ADS)

Young, T. H.; Gau, C. Y.

2003-11-01

This paper studies the dynamic stability of a pretwisted cantilever beam spinning along its longitudinal axis and subjected to an axial random force at the free end. The axial force is assumed as the sum of a constant force and a random process with a zero mean. Due to this axial force, the beam may experience parametric random instability. In this work, the finite element method is first applied to yield discretized system equations. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the mean-square stability criterion is utilized to determine the stability condition of the system. Numerical results show that the stability boundary of the system converges as the first three modes are taken into calculation. Before the convergence is reached, the stability condition predicted is not conservative enough.

A note on the velocity derivative flatness factor in decaying HIT

NASA Astrophysics Data System (ADS)

Djenidi, L.; Danaila, L.; Antonia, R. A.; Tang, S.

2017-05-01

We develop an analytical expression for the velocity derivative flatness factor, F, in decaying homogenous and isotropic turbulence (HIT) starting with the transport equation of the third-order moment of the velocity increment and assuming self-preservation. This expression, fully consistent with the Navier-Stokes equations, relates F to the product between the second-order pressure derivative (∂2p /∂x2) and second-order moment of the longitudinal velocity derivative ((∂u/∂x ) 2), highlighting the role the pressure plays in the scaling of the fourth-order moment of the longitudinal velocity derivative. It is also shown that F has an upper bound which follows the integral of k*4Ep*(k* ) where Ep and k are the pressure spectrum and the wavenumber, respectively (the symbol * represents the Kolmogorov normalization). Direct numerical simulations of forced HIT suggest that this integral converges toward a constant as the Reynolds number increases.

Low-momentum ghost dressing function and the gluon mass

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

Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.

2010-09-01

We study the low-momentum ghost propagator Dyson-Schwinger equation in the Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular Dyson-Schwinger equation solutions (the zero-momentum ghost dressing function not diverging) appear to emerge, and we show the ghost propagator to be described by an asymptotic expression reliable up to the order O(q{sup 2}). That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well some low-momentum ghost propagator data [I. L. Bogolubsky, E. M. Ilgenfritz, M.more » Muller-Preussker, and A. Sternbeck, Phys. Lett. B 676, 69 (2009); Proc. Sci., LAT2007 (2007) 290] from big-volume lattice simulations where the so-called ''simulated annealing algorithm'' is applied to fix the Landau gauge.« less

Toroidal Ampere-Faraday Equations Solved Consistently with the CQL3D Fokker-Planck Time-Evolution

NASA Astrophysics Data System (ADS)

Harvey, R. W.; Petrov, Yu. V.

2013-10-01

A self-consistent, time-dependent toroidal electric field calculation is a key feature of a complete 3D Fokker-Planck kinetic distribution radial transport code for f(v,theta,rho,t). In the present CQL3D finite-difference model, the electric field E(rho,t) is either prescribed, or iteratively adjusted to obtain prescribed toroidal or parallel currents. We discuss first results of an implementation of the Ampere-Faraday equation for the self-consistent toroidal electric field, as applied to the runaway electron production in tokamaks due to rapid reduction of the plasma temperature as occurs in a plasma disruption. Our previous results assuming a constant current density (Lenz' Law) model showed that prompt ``hot-tail runaways'' dominated ``knock-on'' and Dreicer ``drizzle'' runaways; we will examine modifications due to the more complete Ampere-Faraday solution. Work supported by US DOE under DE-FG02-ER54744.

A finite-element analysis for steady and oscillatory subsonic flow around complex configurations

NASA Technical Reports Server (NTRS)

Chen, L. T.; Suciu, E. O.; Morino, L.

1974-01-01

The problem of potential subsonic flow around complex configurations is considered. The solution is given of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented. The results obtained with the above formulation are compared with existing analytical and experimental results.

Integrodifference equations in patchy landscapes : II: population level consequences.

PubMed

Musgrave, Jeffrey; Lutscher, Frithjof

2014-09-01

We analyze integrodifference equations (IDEs) in patchy landscapes. Movement is described by a dispersal kernel that arises from a random walk model with patch dependent diffusion, settling, and mortality rates, and it incorporates individual behavior at an interface between two patch types. Growth follows a simple Beverton-Holt growth or linear decay. We obtain explicit formulae for the critical domain-size problem, and we illustrate how different individual behavior at the boundary between two patch types affects this quantity. We also study persistence conditions on an infinite, periodic, patchy landscape. We observe that if the population can persist on the landscape, the spatial profile of the invasion evolves into a discontinuous traveling periodic wave that moves with constant speed. Assuming linear determinacy, we calculate the dispersion relation and illustrate how movement behavior affects invasion speed. Numerical simulations justify our approach by showing a close correspondence between the spread rate obtained from the dispersion relation and from numerical simulations.

SCBUCKLE user's manual: Buckling analysis program for simple supported and clamped panels

NASA Technical Reports Server (NTRS)

Cruz, Juan R.

1993-01-01

The program SCBUCKLE calculates the buckling loads and mode shapes of cylindrically curved, rectangular panels. The panel is assumed to have no imperfections. SCBUCKLE is capable of analyzing specially orthotropic symmetric panels (i.e., A(sub 16) = A(sub 26) = 0.0, D(sub 16) = D(sub 26) = 0.0, B(sub ij) = 0.0). The analysis includes first-order transverse shear theory and is capable of modeling sandwich panels. The analysis supports two types of boundary conditions: either simply supported or clamped on all four edges. The panel can be subjected to linearly varying normal loads N(sub x) and N(sub y) in addition to a constant shear load N(sub xy). The applied loads can be divided into two parts: a preload component; and a variable (eigenvalue-dependent) component. The analysis is based on the modified Donnell's equations for shallow shells. The governing equations are solved by Galerkin's method.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub 0)/I) and pressure ratio (P/P(sub 0)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and c quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an in- situ intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP)) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub o)/I) and pressure ratio (P/P(sub o)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an insitu intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

Measurement error, time lag, unmeasured confounding: Considerations for longitudinal estimation of the effect of a mediator in randomised clinical trials.

PubMed

Goldsmith, K A; Chalder, T; White, P D; Sharpe, M; Pickles, A

2018-06-01

Clinical trials are expensive and time-consuming and so should also be used to study how treatments work, allowing for the evaluation of theoretical treatment models and refinement and improvement of treatments. These treatment processes can be studied using mediation analysis. Randomised treatment makes some of the assumptions of mediation models plausible, but the mediator-outcome relationship could remain subject to bias. In addition, mediation is assumed to be a temporally ordered longitudinal process, but estimation in most mediation studies to date has been cross-sectional and unable to explore this assumption. This study used longitudinal structural equation modelling of mediator and outcome measurements from the PACE trial of rehabilitative treatments for chronic fatigue syndrome (ISRCTN 54285094) to address these issues. In particular, autoregressive and simplex models were used to study measurement error in the mediator, different time lags in the mediator-outcome relationship, unmeasured confounding of the mediator and outcome, and the assumption of a constant mediator-outcome relationship over time. Results showed that allowing for measurement error and unmeasured confounding were important. Contemporaneous rather than lagged mediator-outcome effects were more consistent with the data, possibly due to the wide spacing of measurements. Assuming a constant mediator-outcome relationship over time increased precision.

Measurement error, time lag, unmeasured confounding: Considerations for longitudinal estimation of the effect of a mediator in randomised clinical trials

PubMed Central

Goldsmith, KA; Chalder, T; White, PD; Sharpe, M; Pickles, A

2016-01-01

Clinical trials are expensive and time-consuming and so should also be used to study how treatments work, allowing for the evaluation of theoretical treatment models and refinement and improvement of treatments. These treatment processes can be studied using mediation analysis. Randomised treatment makes some of the assumptions of mediation models plausible, but the mediator–outcome relationship could remain subject to bias. In addition, mediation is assumed to be a temporally ordered longitudinal process, but estimation in most mediation studies to date has been cross-sectional and unable to explore this assumption. This study used longitudinal structural equation modelling of mediator and outcome measurements from the PACE trial of rehabilitative treatments for chronic fatigue syndrome (ISRCTN 54285094) to address these issues. In particular, autoregressive and simplex models were used to study measurement error in the mediator, different time lags in the mediator–outcome relationship, unmeasured confounding of the mediator and outcome, and the assumption of a constant mediator–outcome relationship over time. Results showed that allowing for measurement error and unmeasured confounding were important. Contemporaneous rather than lagged mediator–outcome effects were more consistent with the data, possibly due to the wide spacing of measurements. Assuming a constant mediator–outcome relationship over time increased precision. PMID:27647810

Documentation of a computer program to simulate aquifer-system compaction using the modular finite-difference ground-water flow model

USGS Publications Warehouse

Leake, S.A.; Prudic, David E.

1988-01-01

The process of permanent compaction is not routinely included in simulations of groundwater flow. To simulate storage changes from both elastic and inelastic compaction, a computer program was written for use with the U. S. Geological Survey modular finite-difference groundwater flow model. The new program is called the Interbed-Storage Package. In the Interbed-Storage Package, elastic compaction or expansion is assumed to be proportional to change in head. The constant of proportionality is the product of skeletal component of elastic specific storage and thickness of the sediments. Similarly, inelastic compaction is assumed to be proportional to decline in head. The constant of proportionality is the product of the skeletal component of inelastic specific storage and the thickness of the sediments. Storage changes are incorporated into the groundwater flow model by adding an additional term to the flow equation. Within a model time step, the package appropriately apportions storage changes between elastic and inelastic components on the basis of the relation of simulated head to the previous minimum head. Another package that allows for a time-varying specified-head boundary is also documented. This package was written to reduce the data requirements for test simulations of the Interbed-Storage Package. (USGS)

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

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

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

An analytical approach for the calculation of stress-intensity factors in transformation-toughened ceramics

NASA Astrophysics Data System (ADS)

Müller, W. H.

1990-12-01

Stress-induced transformation toughening in Zirconia-containing ceramics is described analytically by means of a quantitative model: A Griffith crack which interacts with a transformed, circular Zirconia inclusion. Due to its volume expansion, a ZrO2-particle compresses its flanks, whereas a particle in front of the crack opens the flanks such that the crack will be attracted and finally absorbed. Erdogan's integral equation technique is applied to calculate the dislocation functions and the stress-intensity-factors which correspond to these situations. In order to derive analytical expressions, the elastic constants of the inclusion and the matrix are assumed to be equal.

Anisotropic Bianchi Type-I and Type-II Bulk Viscous String Cosmological Models Coupled with Zero Mass Scalar Field

NASA Astrophysics Data System (ADS)

Venkateswarlu, R.; Sreenivas, K.

2014-06-01

The LRS Bianchi type-I and type-II string cosmological models are studied when the source for the energy momentum tensor is a bulk viscous stiff fluid containing one dimensional strings together with zero-mass scalar field. We have obtained the solutions of the field equations assuming a functional relationship between metric coefficients when the metric is Bianchi type-I and constant deceleration parameter in case of Bianchi type-II metric. The physical and kinematical properties of the models are discussed in each case. The effects of Viscosity on the physical and kinematical properties are also studied.

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications

NASA Technical Reports Server (NTRS)

Tseng, K.; Morino, L.

1975-01-01

A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.

The phonon-polariton spectrum of one-dimensional Rudin-Shapiro photonic superlattices with uniaxial polar materials

NASA Astrophysics Data System (ADS)

Gómez-Urrea, H. A.; Duque, C. A.; Mora-Ramos, M. E.

2015-11-01

The properties of the optical-phonon-associated polaritonic modes that appear under oblique light incidence in 1D superlattices made of photonic materials are studied. The investigated systems result from the periodic repetition of quasiregular Rudin-Shapiro (RS) multilayer units. It is assume that the structure consists of both passive non-dispersive layers of constant refraction index and active layers of uniaxial polar materials. In particular, we consider III-V wurtzite nitrides. The optical axis of these polaritonic materials is taken along the growth direction. Maxwell equations are solved using the transfer matrix technique for all admissible values of the incidence angle.

On a model of the processes of maintaining a technological area by a manipulator

NASA Astrophysics Data System (ADS)

Ghukasyan, A. A.; Ordyan, A. Ya

2018-04-01

The research refers to the results of mathematical modeling of the process of maintaining a technological area which consists of unstable or fixed objects (targets) and a controlled multi-link manipulator [1–9]. It is assumed that, in the maintenance process, the dynamic characteristics and the phase vector of the manipulator state can change at certain finite times depending on the mass of the cargo or instrument [10, 11]. Some controllability problems are investigated in the case where the manipulator motion on each maintenance interval is described by linear differential equations with constant coefficients and the motions of the objects are given.

Off-Axis Driven Current Effects on ETB and ITB Formations based on Bifurcation Concept

NASA Astrophysics Data System (ADS)

Pakdeewanich, J.; Onjun, T.; Chatthong, B.

2017-09-01

This research studies plasma performance in fusion Tokamak system by investigating parameters such as plasma pressure in the presence of an edge transport barrier (ETB) and an internal transport barrier (ITB) as the off-axis driven current position is varied. The plasma is modeled based on the bifurcation concept using a suppression function that can result in formation of transport barriers. In this model, thermal and particle transport equations, including both neoclassical and anomalous effects, are solved simultaneously in slab geometry. The neoclassical coefficients are assumed to be constant while the anomalous coefficients depend on gradients of local pressure and density. The suppression function, depending on flow shear and magnetic shear, is assumed to affect only on the anomalous channel. The flow shear can be calculated from the force balance equation, while the magnetic shear is calculated from the given plasma current. It is found that as the position of driven current peak is moved outwards from the plasma center, the central pressure is increased. But at some point it stars to decline, mostly when the driven current peak has reached the outer half of the plasma. The higher pressure value results from the combination of ETB and ITB formations. The drop in central pressure occurs because ITB stats to disappear.

Towards the quantization of Eddington-inspired-Born-Infeld theory

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

Bouhmadi-López, Mariam; Chen, Che-Yu, E-mail: mbl@ubi.pt, E-mail: b97202056@gmail.com

2016-11-01

The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantommore » perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.« less

Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles

PubMed Central

Matsumoto, Yorimi

1967-01-01

Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dls, from the relation, See PDF for Equation From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (P 0 - P)/T for dP/dt and (P 0 - P)/(P + a) times b for v, dP/dls = (P + a) /bT, where P < P 0, and a, b are constants for any lengths l ≤ l 0 (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, l 0, although the series elastic, ls, and the contractile component, lc, are changing, the total muscle length, l 0 remains fixed and therefore the time constant, T. Integrating, See PDF for Equation the stress-strain relation for the series elastic element, See PDF for Equation is obtained; l sc0 - ls + l c0where l co equals the contractile component length for a muscle exerting a tension of P 0. For a given P/P 0, ls is uniquely determined and must be the same whether on the isotonic or isometric length-tension-time curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other. PMID:6033578

Theory and application of an approximate model of saltwater upconing in aquifers

USGS Publications Warehouse

McElwee, C.; Kemblowski, M.

1990-01-01

Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where hydrodynamic dispersion into a transition zone is the primary mechanism for moving salt water to the river. The current model could be useful in situations involving dense saltwater layers. ?? 1990.

On the estimation of the reproduction number based on misreported epidemic data.

PubMed

Azmon, Amin; Faes, Christel; Hens, Niel

2014-03-30

Epidemic data often suffer from underreporting and delay in reporting. In this paper, we investigated the impact of delays and underreporting on estimates of reproduction number. We used a thinned version of the epidemic renewal equation to describe the epidemic process while accounting for the underlying reporting system. Assuming a constant reporting parameter, we used different delay patterns to represent the delay structure in our model. Instead of assuming a fixed delay distribution, we estimated the delay parameters while assuming a smooth function for the reproduction number over time. In order to estimate the parameters, we used a Bayesian semiparametric approach with penalized splines, allowing both flexibility and exact inference provided by MCMC. To show the performance of our method, we performed different simulation studies. We conducted sensitivity analyses to investigate the impact of misspecification of the delay pattern and the impact of assuming nonconstant reporting parameters on the estimates of the reproduction numbers. We showed that, whenever available, additional information about time-dependent underreporting can be taken into account. As an application of our method, we analyzed confirmed daily A(H1N1) v2009 cases made publicly available by the World Health Organization for Mexico and the USA. Copyright © 2013 John Wiley & Sons, Ltd.

Effects of radial distribution of entropy diffusivity on critical modes of anelastic thermal convection in rotating spherical shells

NASA Astrophysics Data System (ADS)

Sasaki, Youhei; Takehiro, Shin-ichi; Ishiwatari, Masaki; Yamada, Michio

2018-03-01

Linear stability analysis of anelastic thermal convection in a rotating spherical shell with entropy diffusivities varying in the radial direction is performed. The structures of critical convection are obtained in the cases of four different radial distributions of entropy diffusivity; (1) κ is constant, (2) κT0 is constant, (3) κρ0 is constant, and (4) κρ0T0 is constant, where κ is the entropy diffusivity, T0 is the temperature of basic state, and ρ0 is the density of basic state, respectively. The ratio of inner and outer radii, the Prandtl number, the polytropic index, and the density ratio are 0.35, 1, 2, and 5, respectively. The value of the Ekman number is 10-3 or 10-5 . In the case of (1), where the setup is same as that of the anelastic dynamo benchmark (Jones et al., 2011), the structure of critical convection is concentrated near the outer boundary of the spherical shell around the equator. However, in the cases of (2), (3) and (4), the convection columns attach the inner boundary of the spherical shell. A rapidly rotating annulus model for anelastic systems is developed by assuming that convection structure is uniform in the axial direction taking into account the strong effect of Coriolis force. The annulus model well explains the characteristics of critical convection obtained numerically, such as critical azimuthal wavenumber, frequency, Rayleigh number, and the cylindrically radial location of convection columns. The radial distribution of entropy diffusivity, or more generally, diffusion properties in the entropy equation, is important for convection structure, because it determines the distribution of radial basic entropy gradient which is crucial for location of convection columns.

Combined electroosmotically and pressure driven flow in soft nanofluidics.

PubMed

Matin, Meisam Habibi; Ohshima, Hiroyuki

2015-12-15

The present study is devoted to the analysis of mixed electroosmotic and pressure driven flows through a soft charged nanochannel considering boundary slip and constant charge density on the walls of the slit channel. The sources of the fluid flow are the pressure gradient along the channel axis and the electrokinetic effects that trigger an electroosmotic flow under the influence of a uniformly applied electric field. The polyelectrolyte layer (PEL) is denoted as a fixed charge layer (FCL) and the electrolyte ions can be present both inside and outside the PEL i.e., the PEL-electrolyte interface acts as a semi-penetrable membrane. The Poisson-Boltzmann equation is solved assuming the Debye-Hückel linearization for the low electric potential to provide us with analytical closed form solutions for the conservation equations. The conservation equations are solved to obtain the electric potential and velocity distributions in terms of governing dimensionless parameters. The results for the dimensionless electric potential, the dimensionless velocity and Poiseuille number are presented graphically and discussed in detail. Copyright © 2015 Elsevier Inc. All rights reserved.

Finite magnetic relaxation in x-space magnetic particle imaging: Comparison of measurements and ferrohydrodynamic models

PubMed Central

Dhavalikar, R; Hensley, D; Maldonado-Camargo, L; Croft, L R; Ceron, S; Goodwill, P W; Conolly, S M

2016-01-01

Magnetic Particle Imaging (MPI) is an emerging tomographic imaging technology that detects magnetic nanoparticle tracers by exploiting their non-linear magnetization properties. In order to predict the behavior of nanoparticles in an imager, it is possible to use a non-imaging MPI relaxometer or spectrometer to characterize the behavior of nanoparticles in a controlled setting. In this paper we explore the use of ferrohydrodynamic magnetization equations for predicting the response of particles in an MPI relaxometer. These include a magnetization equation developed by Shliomis (Sh) which has a constant relaxation time and a magnetization equation which uses a field-dependent relaxation time developed by Martsenyuk, Raikher and Shliomis (MRSh). We compare the predictions from these models with measurements and with the predictions based on the Langevin function that assumes instantaneous magnetization response of the nanoparticles. The results show good qualitative and quantitative agreement between the ferrohydrodynamic models and the measurements without the use of fitting parameters and provide further evidence of the potential of ferrohydrodynamic modeling in MPI. PMID:27867219

Fields and Plasma Structures Around ``Shining'' Black Holes: Solitary Rings and Tri-dimensional Topologies

NASA Astrophysics Data System (ADS)

Coppi, B.

2012-03-01

Field and plasma configurations that can be the distinguishing feature of and surround ``shining'' black holes have been identified. Considering the observation of the Quasi Periodic Oscillations that can be associated with inhomogeneous rotating plasmas, tri-dimensional rotating configurations have been looked for and found under special conditions. One is that these configurations are radially localized, such as narrow plasma ring pairs. Another is that the rotation frequency is nearly constant over the rings. Only axisymmetric local configurations consisting of solitary plasma rings or periodic sequences of rings are found when the gradient of the rotation frequency is (locally) significant. Assuming that the plasma pressure is scalar the problem is reduced to the solution of two coupled non-linear differential equations. One, the ``Master Equation'' [1], relates the magnetic surface function to the plasma rotation frequency that is connected to the gravity field. The other, the Vertical Equilibrium Equation, relates the plasma pressure gradient to both the Lorentz force and to the plasma density profile through the gravitational force.[4pt] [1] B. Coppi, Phys. Plasmas 18, 032901 (2011).

On the modelling of non-reactive and reactive turbulent combustor flows

NASA Technical Reports Server (NTRS)

Nikjooy, Mohammad; So, Ronald M. C.

1987-01-01

A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity

NASA Astrophysics Data System (ADS)

Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J.

2017-11-01

Though not a part of mainstream physics, Salam's theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving SU(3) color charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require color interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order 1 {GeV}^{-1}. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective strong cosmological constant, Λ f. This introduces a strong de Sitter radius for strongly interacting fermions, producing a confining bubble, which allows us to identify Λ f with the `bag constant' of the MIT bag model, B ˜eq 2 × 10^{14} {g} {cm}^{-3}. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalized Buchdahl inequalities for a strong gravity `particle', giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of Λ _f, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed.

Evaluation of Improvements to Brayton Cycle Performance.

DTIC Science & Technology

1986-05-29

cogeneration systems. They are International Power Technology (IPT), Palo Alto, California and Mechanical Technology, Inc. (MTI), Latham, New York [13]. IPT...constant (10) For a constant Reynold’s number and dimensions, the friction factor will be constant. The relationship for friction of internal ...equation for the friction factor of internal turbulent flow is expressed as Ap -friction =f(Re) - constant. (12) pV 2 Applying Equation (11), Equation (12

A rigorous multiple independent binding site model for determining cell-based equilibrium dissociation constants.

PubMed

Drake, Andrew W; Klakamp, Scott L

2007-01-10

A new 4-parameter nonlinear equation based on the standard multiple independent binding site model (MIBS) is presented for fitting cell-based ligand titration data in order to calculate the ligand/cell receptor equilibrium dissociation constant and the number of receptors/cell. The most commonly used linear (Scatchard Plot) or nonlinear 2-parameter model (a single binding site model found in commercial programs like Prism(R)) used for analysis of ligand/receptor binding data assumes only the K(D) influences the shape of the titration curve. We demonstrate using simulated data sets that, depending upon the cell surface receptor expression level, the number of cells titrated, and the magnitude of the K(D) being measured, this assumption of always being under K(D)-controlled conditions can be erroneous and can lead to unreliable estimates for the binding parameters. We also compare and contrast the fitting of simulated data sets to the commonly used cell-based binding equation versus our more rigorous 4-parameter nonlinear MIBS model. It is shown through these simulations that the new 4-parameter MIBS model, when used for cell-based titrations under optimal conditions, yields highly accurate estimates of all binding parameters and hence should be the preferred model to fit cell-based experimental nonlinear titration data.

Macroscopic Quantum Phase-Locking Model for the Quantum Hall = Effect

NASA Astrophysics Data System (ADS)

Wang, Te-Chun; Gou, Yih-Shun

1997-08-01

A macroscopic model of nonlinear dissipative phase-locking between a Josephson-like frequency and a macroscopic electron wave frequency is proposed to explain the Quantum Hall Effect. It is well known that a r.f-biased Josephson junction displays a collective phase-locking behavior which can be described by a non-autonomous second order equation or an equivalent 2+1-dimensional dynamical system. Making a direct analogy between the QHE and the Josephson system, this report proposes a computer-solving nonlinear dynamical model for the quantization of the Hall resistance. In this model, the Hall voltage is assumed to be proportional to a Josephson-like frequency and the Hall current is assumed related to a coherent electron wave frequency. The Hall resistance is shown to be quantized in units of the fine structure constant as the ratio of these two frequencies are locked into a rational winding number. To explain the sample-width dependence of the critical current, the 2DEG under large applied current is further assumed to develop a Josephson-like junction array in which all Josephson-like frequencies are synchronized. Other remarkable features of the QHE such as the resistance fluctuation and the even-denominator states are also discussed within this picture.

Stability of Electrons in the Virtual Cathode Region of an IEC

NASA Astrophysics Data System (ADS)

Kim, Hyng-Jin; Miley, George; Momota, Hiromu

2003-04-01

In the Inertial Electrostatic Confinement (IEC) device, electrons are confined inside a virtual anode that in turn confines ions. Prior stability studies [1, 2] have considered systems in which one species is electrostatically confined by the other, and either or both species are out of local thermal equilibrium. In the present research, electron stability in the virtual cathode region of an ion injected IEC is being studied. The ion density in an IEC is non-uniform due to the radial electrostatic potential, and increases toward the center region. The potential near the virtual cathode is assumed to have a parabolic shape and is determined assuming that the net space charge density is constant in that region. The corresponding ion distribution function is assumed to have the form f = C [sigma] (H W) /L^0.5 and the electron response is taken to be diabatic. Then using a variational principle after linearizing the hydrodynamic equations, stability properties of the electron layer are determined. Results will be presented as a function of injected ion/electron current ratios. 1. L. Chacon and D. C. Barnes, Phys. Plasma 7, 4774 (2000). 2. D. C. Barnes, L. Chacon, and J. M. Finn, Phys. Plasmas 9, 4448 (2002).

Anisotropic string cosmological model in Brans–Dicke theory of gravitation with time-dependent deceleration parameter

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

Maurya, D. Ch., E-mail: dcmaurya563@gmail.com; Zia, R., E-mail: rashidzya@gmail.com; Pradhan, A., E-mail: pradhan.anirudh@gmail.com

We discuss a spatially homogeneous and anisotropic string cosmological models in the Brans–Dicke theory of gravitation. For a spatially homogeneous metric, it is assumed that the expansion scalar θ is proportional to the shear scalar σ. This condition leads to A = kB{sup m}, where k and m are constants. With these assumptions and also assuming a variable scale factor a = a(t), we find solutions of the Brans–Dicke field equations. Various phenomena like the Big Bang, expanding universe, and shift from anisotropy to isotropy are observed in the model. It can also be seen that in early stage ofmore » the evolution of the universe, strings dominate over particles, whereas the universe is dominated by massive strings at the late time. Some physical and geometrical behaviors of the models are also discussed and observed to be in good agreement with the recent observations of SNe la supernovae.« less

Isothermal absorption of soluble gases by atmospheric nanoaerosols

NASA Astrophysics Data System (ADS)

Elperin, T.; Fominykh, A.; Krasovitov, B.; Lushnikov, A.

2013-01-01

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO2), dinitrogen trioxide (N2O3), and chlorine (Cl2) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.

Isothermal absorption of soluble gases by atmospheric nanoaerosols.

PubMed

Elperin, T; Fominykh, A; Krasovitov, B; Lushnikov, A

2013-01-01

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO(2)), dinitrogen trioxide (N(2)O(3)), and chlorine (Cl(2)) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.

PubMed

Bressloff, Paul C

2015-01-01

We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous to the modified activity-based equations generated from a neural master equation.

Covariant Uniform Acceleration

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Scarr, Tzvi

2013-04-01

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation , where F is the 3D force and p = m0γv is the 3D relativistic momentum. The standard 4D equation is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We introduce the 4D velocity, an adaptation of Horwitz and Piron s notion of "off-shell." We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.

Relaxation Dynamics of a Granular Pile on a Vertically Vibrating Plate

NASA Astrophysics Data System (ADS)

Tsuji, Daisuke; Otsuki, Michio; Katsuragi, Hiroaki

2018-03-01

Nonlinear relaxation dynamics of a vertically vibrated granular pile is experimentally studied. In the experiment, the flux and slope on the relaxing pile are measured by using a high-speed laser profiler. The relation of these quantities can be modeled by the nonlinear transport law assuming the uniform vibrofluidization of an entire pile. The fitting parameter in this model is only the relaxation efficiency, which characterizes the energy conversion rate from vertical vibration into horizontal transport. We demonstrate that this value is a constant independent of experimental conditions. The actual relaxation is successfully reproduced by the continuity equation with the proposed model. Finally, its specific applicability toward an astrophysical phenomenon is shown.

An internal crack parallel to the boundary of a nonhomogeneous half plane under thermal loading

NASA Astrophysics Data System (ADS)

Jin, Zhi-He; Noda, Naotake

1993-05-01

This paper considers the crack problem for a semi-infinite nonhomogeneous thermoelastic solid subjected to steady heat flux over the boundary. The crack faces are assumed to be insulated. The research is aimed at understanding the effect of nonhomogeneities of materials on stress intensity factors. By using the Fourier transform, the problem is reduced to a system of singular integral equations which are solved numerically. Results are presented illustrating the influence of the nonhomogeneity of the material on the stress intensity factors. Zero Mode I stress intensity factors are found for some groups of the material constants, which may be interesting for the understanding of compositions of advanced Functionally Gradient Materials.

A viscous-inviscid interactive compressor calculations

NASA Technical Reports Server (NTRS)

Johnston, W.; Sockol, P. M.

1978-01-01

A viscous-inviscid interactive procedure for subsonic flow is developed and applied to an axial compressor stage. Calculations are carried out on a two-dimensional blade-to-blade region of constant radius assumed to occupy a mid-span location. Hub and tip effects are neglected. The Euler equations are solved by MacCormack's method, a viscous marching procedure is used in the boundary layers and wake, and an iterative interaction scheme is constructed that matches them in a way that incorporates information related to momentum and enthalpy thicknesses as well as the displacement thickness. The calculations are quasi-three-dimensional in the sense that the boundary layer and wake solutions allow for the presence of spanwise (radial) velocities.

Finite element modeling of frictionally restrained composite interfaces

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Creep rupture of polymer-matrix composites

NASA Technical Reports Server (NTRS)

Brinson, H. F.; Morris, D. H.; Griffith, W. I.

1981-01-01

The time-dependent creep-rupture process in graphite-epoxy laminates is examined as a function of temperature and stress level. Moisture effects are not considered. An accelerated characterization method of composite-laminate viscoelastic modulus and strength properties is reviewed. It is shown that lamina-modulus master curves can be obtained using a minimum of normally performed quality-control-type testing. Lamina-strength master curves, obtained by assuming a constant-strain-failure criterion, are presented along with experimental data, and reasonably good agreement is shown to exist between the two. Various phenomenological delayed failure models are reviewed and two (the modified rate equation and the Larson-Miller parameter method) are compared to creep-rupture data with poor results.

Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

NASA Technical Reports Server (NTRS)

Cole, G. L.; Willoh, R. G.

1975-01-01

A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation

PubMed Central

Case, K. M.

1985-01-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n ≥ 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional Jn(n+2) = -1/18 [unk] yn+2q by taking repeated Poisson brackets with the Hamiltonian. PMID:16593588

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation.

PubMed

Case, K M

1985-08-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n >/= 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J(n) ((n+2)) = -1/18 [unk] y(n+2)q by taking repeated Poisson brackets with the Hamiltonian.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Magnetic minerals' classification for sources of magnetic anomalies

NASA Astrophysics Data System (ADS)

Kletetschka, G.; Wieczorek, M. A.

2016-12-01

Our analysis allows interpretation of magnetic anomalies detected in meteorites, on Mars and Moon, and other bodies where the sources of magnetic field can be assumed to be thermoremanent magnetization (Mtr). We show how the specific approach allows reconsideration of the major magnetic carriers on Moon and Mars. Furthermore we are deriving a generalized equation for iron concentration estimate from magnetizations derived from crustal magnetic anomalies on the Moon. There is fundamental linear relation between the magnetic efficiency of thermoremanent magnetization Mtr measured at room temperature and level of the ambient field present at the time of acquisition. We used experimental data for derivation of the empirical constants for paleofield estimate equations. Specific magnetic mineral carriers from single domain (SD) through pseudosingle domain (PSD) to multidomain (MD) states include iron, meteoritic iron, magnetite, maghemite, pyrrhotite, and hematite. The Mtr/Msr is linearly proportional to the product of the magnetizing field and saturation remanence, while the proportionality constant is independent of magnetic mineralogy, domain state, or composition. We show that the level of magnetic paleofield record relates to two types of demagnetizing field that act as a barrier against the domain wall pinning during the magnetic acquisition. The first type of demagnetizing field relates to saturation magnetization constant derived from the distribution of Bohr's magnetons within the crystal lattice. The second type of demagnetizing field originates from the effect of shape of the magnetic minerals. Knowledge of the character of these demagnetizing fields is a prerequisite for paleofield estimates from rocks containing known magnetic mineralogy and magnetic shape anisotropy.

Effect of solute immobilization on the stability problem within the fractional model in the solute analog of the Horton-Rogers-Lapwood problem.

PubMed

Klimenko, Lyudmila S; Maryshev, Boris S

2017-11-24

The paper is devoted to the linear stability analysis within the solute analogue of the Horton-Rogers-Lapwood (HRL) problem. The solid nanoparticles are treated as solute within the continuous approach. Therefore, we consider the infinite horizontal porous layer saturated with a mixture (carrier fluid and solute). Solute transport in porous media is very often complicated by solute immobilization on a solid matrix of porous media. Solute immobilization (solute sorption) is taken into account within the fractal model of the MIM approach. According to this model a solute in porous media immobilizes within random time intervals and the distribution of such random variable does not have a finite mean value, which has a good agreement with some experiments. The solute concentration difference between the layer boundaries is assumed as constant. We consider two cases of horizontal external filtration flux: constant and time-modulated. For the constant flux the system of equations that determines the frequency of neutral oscillations and the critical value of the Rayleigh-Darcy number is derived. Neutral curves of the critical parameters on the governing parameters are plotted. Stability maps are obtained numerically in a wide range of parameters of the system. We have found that taking immobilization into account leads to an increase in the critical value of the Rayleigh-Darcy number with an increase in the intensity of the external filtration flux. The case of weak time-dependent external flux is investigated analytically. We have shown that the modulated external flux leads to an increase in the critical value of the Rayleigh-Darcy number and a decrease in the critical wave number. For moderate time-dependent filtration flux the differential equation with Caputo fractional derivatives has been obtained for the description of the behavior near the convection instability threshold. This equation is analyzed numerically by the Floquet method; the parametric excitation of convection is observed.

An effective description of dark matter and dark energy in the mildly non-linear regime

DOE PAGES

Lewandowski, Matthew; Maleknejad, Azadeh; Senatore, Leonardo

2017-05-18

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. Furthermore, the Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

Solar Power Satellite system in formation on a common geostationary orbit

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Winter, O. C.

2017-10-01

The diurnal day-night cycle severely limits the Terrestrial solar power. To overcome this limitation, a Solar Power Satellite (SPS) system, consisting of a sunlight reflector and a microwave energy generator-transmitter in formation, is presented in this work. The microwave transmitting satellite (MTS) is placed on a common geostationary orbit (GEO) in the Earth’s equatorial plane, and the sunlight reflector uses the solar radiation pressure to achieve quasi-periodic orbits about the MTS, so that the sunlight is always redirected to the MTS, which converts the solar energy in electromagnetic power and transmits it by microwaves to an Earth-receiving antenna. Assuming the sun line direction constant at dierent seasons (i.e. autumn/spring equinoxes and winter and summer solstices), previous studies have shown the existence of a family of displaced ecliptic orbits above or below the equatorial plane of the Earth around a GEO. In this study, the position of the Sun is assumed on the ecliptic plane with a mean obliquity (inclination of Earth’s equator with respect to the ecliptic) of 23.5◦. A linear solution as an initial condition for the full equations of motions about a GEO, which yields bounded orbit for the sunlight reflector about the MTS in the Earth-satellite two-body problem with solar radiation pressure. To redirect the sunlight to the MTS, the law of reflection is satisfied by the space mirror attitude.

An effective description of dark matter and dark energy in the mildly non-linear regime

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

Lewandowski, Matthew; Maleknejad, Azadeh; Senatore, Leonardo

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. Furthermore, the Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

An effective description of dark matter and dark energy in the mildly non-linear regime

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

Lewandowski, Matthew; Senatore, Leonardo; Maleknejad, Azadeh, E-mail: matthew.lewandowski@cea.fr, E-mail: azade@ipm.ir, E-mail: senatore@stanford.edu

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

Cosmic equilibration: A holographic no-hair theorem from the generalized second law

NASA Astrophysics Data System (ADS)

Carroll, Sean M.; Chatwin-Davies, Aidan

2018-02-01

In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

On the interaction between the external magnetic field and nanofluid inside a vertical square duct

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

Ali, Kashif; Ahmad, Shabbir; Ahmad, Shahzad, E-mail: shahzadahmadbzu@gmail.com

In this paper, we numerically study how the external magnetic field influences the flow and thermal characteristics of nanofluid inside a vertical square duct. The flow is considered to be laminar and hydrodynamically as well as thermally developed, whereas the thermal boundary condition of constant heat flux per unit axial length with constant peripheral temperature at any cross section, is assumed. The governing equations are solved using the spectral method and the finite difference method. Excellent comparison is noted in the numerical results given by the two methods but the spectral method is found to be superior in terms ofmore » both efficiency and accuracy. We have noted that the flow reversal due to high Raleigh number may be controlled by applying an external magnetic field of suitable strength. Moreover, the Nusselt number is found to be almost a linear function of the nanoparticle volume fraction parameter, for different values of the Raleigh number and the magnetic parameter.« less

Neutron stars in the braneworld within the Eddington-inspired Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Prasetyo, I.; Husin, I.; Qauli, A. I.; Ramadhan, H. S.; Sulaksono, A.

2018-01-01

We propose the disappearance of "the hyperon puzzle" in neutron star (NS) by invoking two new-physics prescriptions: modified gravity theory and braneworld scenario. By assuming that NS lives on a 3-brane within a 5d empty AdS bulk, gravitationally governed by Eddington-inspired Born-Infeld (EiBI) theory, the field equations can be effectively cast into the usual Einstein's with "apparent" anisotropic energy-momentum tensor. Solving the corresponding brane-TOV equations numerically, we study its mass-radius relation. It is known that the appearance of finite brane tension λ reduces the compactness of the star. The compatibility of the braneworld results with observational constraints of NS mass and radius can be restored in our model by varying the EiBI's coupling constant, κ. We found that within the astrophysically-accepted range of parameters (0<κ<6×106m2 and λgg1 MeV4) the NS can have mass ~2.1 Msolar and radius ~10 km.

Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2003-01-01

The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

Fisher-Wright model with deterministic seed bank and selection.

PubMed

Koopmann, Bendix; Müller, Johannes; Tellier, Aurélien; Živković, Daniel

2017-04-01

Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached. Copyright © 2016 Elsevier Inc. All rights reserved.

Dynamic modeling of reversible methanolysis of Jatropha curcas oil to biodiesel.

PubMed

Syam, Azhari M; Hamid, Hamidah A; Yunus, Robiah; Rashid, Umer

2013-01-01

Many kinetics studies on methanolysis assumed the reactions to be irreversible. The aim of the present work was to study the dynamic modeling of reversible methanolysis of Jatropha curcas oil (JCO) to biodiesel. The experimental data were collected under the optimal reaction conditions: molar ratio of methanol to JCO at 6 : 1, reaction temperature of 60°C, 60 min of reaction time, and 1% w/w of catalyst concentration. The dynamic modeling involved the derivation of differential equations for rates of three stepwise reactions. The simulation study was then performed on the resulting equations using MATLAB. The newly developed reversible models were fitted with various rate constants and compared with the experimental data for fitting purposes. In addition, analysis of variance was done statistically to evaluate the adequacy and quality of model parameters. The kinetics study revealed that the reverse reactions were significantly slower than forward reactions. The activation energies ranged from 6.5 to 44.4 KJ mol⁻¹.

Dynamic Modeling of Reversible Methanolysis of Jatropha curcas Oil to Biodiesel

PubMed Central

Syam, Azhari M.; Hamid, Hamidah A.; Yunus, Robiah; Rashid, Umer

2013-01-01

Many kinetics studies on methanolysis assumed the reactions to be irreversible. The aim of the present work was to study the dynamic modeling of reversible methanolysis of Jatropha curcas oil (JCO) to biodiesel. The experimental data were collected under the optimal reaction conditions: molar ratio of methanol to JCO at 6 : 1, reaction temperature of 60°C, 60 min of reaction time, and 1% w/w of catalyst concentration. The dynamic modeling involved the derivation of differential equations for rates of three stepwise reactions. The simulation study was then performed on the resulting equations using MATLAB. The newly developed reversible models were fitted with various rate constants and compared with the experimental data for fitting purposes. In addition, analysis of variance was done statistically to evaluate the adequacy and quality of model parameters. The kinetics study revealed that the reverse reactions were significantly slower than forward reactions. The activation energies ranged from 6.5 to 44.4 KJ mol−1. PMID:24363616

An evaluation of the wind chill factor: its development and applicability.

PubMed

Bluestein, M

1998-04-01

The wind chill factor has become a standard meteorologic term in cold climates. Meteorologic charts provide wind chill temperatures meant to represent the hypothetical air temperature that would, under conditions of no wind, effect the same heat loss from unclothed human skin as does the actual combination of air temperature and wind velocity. As this wind chill factor has social and economic significance, an investigation was conducted on the development of this factor and its applicability based on modern heat transfer principles. The currently used wind chill factor was found to be based on a primitive study conducted by the U.S. Antarctic Service over 50 years ago. The resultant equation for the wind chill temperature assumes an unrealistic constant skin temperature and utilizes heat transfer coefficients that differ markedly from those obtained from equations of modern convective heat transfer methods. The combined effect of these two factors is to overestimate the effect of a given wind velocity and to predict a wind chill temperature that is too low.

Application of differential game theory to role-determination in aerial combat

NASA Technical Reports Server (NTRS)

Merz, A. W.

1975-01-01

The development of criteria which specify the roles of pursuer and evader as functions of the relative geometry and of the important parameters of the problem are discussed. A reduced-order model of the relative motion is derived and discussed. In this model, the two aircraft move in the same plane at unequal but constant speeds, and with different maximum turn rates. The equations of relative motion are of third order, the dependent variables being the relative range, bearing, and heading of the two aircraft. Termination of the pursuit-evasion game is defined by either the heading-limited or the range-limited end condition. These are geometric conditions for which the evading aircraft is in front of the other, with the relative heading and relative range satisfying certain inequalities. Retrograde solutions to the equations of relative motion were used with the derived optimal terminal maneuvers to find where an assumed set of end conditions could have begun.

A generalised age- and phase-structured model of human tumour cell populations both unperturbed and exposed to a range of cancer therapies.

PubMed

Basse, Britta; Ubezio, Paolo

2007-07-01

We develop a general mathematical model for a population of cells differentiated by their position within the cell division cycle. A system of partial differential equations governs the kinetics of cell densities in certain phases of the cell division cycle dependent on time t (hours) and an age-like variable tau (hours) describing the time since arrival in a particular phase of the cell division cycle. Transition rate functions control the transfer of cells between phases. We first obtain a theoretical solution on the infinite domain -infinity < t < infinity. We then assume that age distributions at time t=0 are known and write our solution in terms of these age distributions on t=0. In practice, of course, these age distributions are unknown. All is not lost, however, because a cell line before treatment usually lies in a state of asynchronous balanced growth where the proportion of cells in each phase of the cell cycle remain constant. We assume that an unperturbed cell line has four distinct phases and that the rate of transition between phases is constant within a short period of observation ('short' relative to the whole history of the tumour growth) and we show that under certain conditions, this is equivalent to exponential growth or decline. We can then gain expressions for the age distributions. So, in short, our approach is to assume that we have an unperturbed cell line on t

Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Wen, Zhang

2015-05-01

This article presents a numerical study to investigate the combined role of partial well penetration (PWP) and non-Darcy effects concerning the performance of groundwater production wells. A finite difference model is developed in MATLAB to solve the two-dimensional mixed-type boundary value problem associated with flow to a partially penetrating well within a cylindrical confined aquifer. Non-Darcy effects are incorporated using the Forchheimer equation. The model is verified by comparison to results from existing semi-analytical solutions concerning the same problem but assuming Darcy's law. A sensitivity analysis is presented to explore the problem of concern. For constant pressure production, Non-Darcy effects lead to a reduction in production rate, as compared to an equivalent problem solved using Darcy's law. For fully penetrating wells, this reduction in production rate becomes less significant with time. However, for partially penetrating wells, the reduction in production rate persists for much larger times. For constant production rate scenarios, the combined effect of PWP and non-Darcy flow takes the form of a constant additional drawdown term. An approximate solution for this loss term is obtained by performing linear regression on the modeling results.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

Analytical Equations for Orbital Transfer Maneuvers of a Vehicle Using Constant Low Thrust

DTIC Science & Technology

1981-12-01

136auks" ,b , .. .. a. AFIT/GA/AA/81D -3 ANALITICAL EQUATIOIS FOR OR.BITAL TRASFER MANIUVRS OF A V 1CI, USING CONSTANT LOW THRUST THESIS AFIT/GA/AA...nondimensional radius ( )m - specified values vii. AFIT/GA/AA/81D -3 Abstract The object of this study is to derive a set of equations which predict the...study is to derive a set of equations which predict the results of orbital maneuvers of vehicles using constant low thrust. These equations are

Impact of Future Climate on Radial Growth of Four Major Boreal Tree Species in the Eastern Canadian Boreal Forest

PubMed Central

Huang, Jian-Guo; Bergeron, Yves; Berninger, Frank; Zhai, Lihong; Tardif, Jacques C.; Denneler, Bernhard

2013-01-01

Immediate phenotypic variation and the lagged effect of evolutionary adaptation to climate change appear to be two key processes in tree responses to climate warming. This study examines these components in two types of growth models for predicting the 2010–2099 diameter growth change of four major boreal species Betula papyrifera, Pinus banksiana, Picea mariana, and Populus tremuloides along a broad latitudinal gradient in eastern Canada under future climate projections. Climate-growth response models for 34 stands over nine latitudes were calibrated and cross-validated. An adaptive response model (A-model), in which the climate-growth relationship varies over time, and a fixed response model (F-model), in which the relationship is constant over time, were constructed to predict future growth. For the former, we examined how future growth of stands in northern latitudes could be forecasted using growth-climate equations derived from stands currently growing in southern latitudes assuming that current climate in southern locations provide an analogue for future conditions in the north. For the latter, we tested if future growth of stands would be maximally predicted using the growth-climate equation obtained from the given local stand assuming a lagged response to climate due to genetic constraints. Both models predicted a large growth increase in northern stands due to more benign temperatures, whereas there was a minimal growth change in southern stands due to potentially warm-temperature induced drought-stress. The A-model demonstrates a changing environment whereas the F-model highlights a constant growth response to future warming. As time elapses we can predict a gradual transition between a response to climate associated with the current conditions (F-model) to a more adapted response to future climate (A-model). Our modeling approach provides a template to predict tree growth response to climate warming at mid-high latitudes of the Northern Hemisphere. PMID:23468879

Impact of future climate on radial growth of four major boreal tree species in the Eastern Canadian boreal forest.

PubMed

Huang, Jian-Guo; Bergeron, Yves; Berninger, Frank; Zhai, Lihong; Tardif, Jacques C; Denneler, Bernhard

2013-01-01

Immediate phenotypic variation and the lagged effect of evolutionary adaptation to climate change appear to be two key processes in tree responses to climate warming. This study examines these components in two types of growth models for predicting the 2010-2099 diameter growth change of four major boreal species Betula papyrifera, Pinus banksiana, Picea mariana, and Populus tremuloides along a broad latitudinal gradient in eastern Canada under future climate projections. Climate-growth response models for 34 stands over nine latitudes were calibrated and cross-validated. An adaptive response model (A-model), in which the climate-growth relationship varies over time, and a fixed response model (F-model), in which the relationship is constant over time, were constructed to predict future growth. For the former, we examined how future growth of stands in northern latitudes could be forecasted using growth-climate equations derived from stands currently growing in southern latitudes assuming that current climate in southern locations provide an analogue for future conditions in the north. For the latter, we tested if future growth of stands would be maximally predicted using the growth-climate equation obtained from the given local stand assuming a lagged response to climate due to genetic constraints. Both models predicted a large growth increase in northern stands due to more benign temperatures, whereas there was a minimal growth change in southern stands due to potentially warm-temperature induced drought-stress. The A-model demonstrates a changing environment whereas the F-model highlights a constant growth response to future warming. As time elapses we can predict a gradual transition between a response to climate associated with the current conditions (F-model) to a more adapted response to future climate (A-model). Our modeling approach provides a template to predict tree growth response to climate warming at mid-high latitudes of the Northern Hemisphere.

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation

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

Case, K.M.

1985-08-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n greater than or equal to 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J/sub n/sup (n+2)/ = -1/18 integral y/sup n+2/ q by taking repeated Poisson brackets with the Hamiltonian.

A Variable Turbulent Schmidt Number Formulation for Scramjet Application

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Cutler, A. D.

2004-01-01

In high speed engines, thorough turbulent mixing of fuel and air is required to obtain high performance and high efficiency. Thus, the ability to predict turbulent mixing is crucial in obtaining accurate numerical simulation of an engine and its performance. Current state of the art in CFD simulation is to assume both turbulent Prandtl number and Schmidt numbers to be constants. However, since the mixing of fuel and air is inversely proportional to the Schmidt number, a value of 0.45 for the Schmidt number will produce twice as much diffusion as that with a value of 0.9. Because of this, current CFD tools and models have not been able to provide the needed guidance required for the efficient design of a scramjet engine. The goal of this investigation is to develop the framework needed to calculate turbulent Prandtl and Schmidt numbers as part of the solution. This requires four additional equations: two for the temperature variance and its dissipation rate and two for the concentration variance and its dissipation rate. In the current investigation emphasis will be placed on studying mixing without reactions. For such flows, variable Prandtl number does not play a major role in determining the flow. This, however, will have to be addressed when combustion is present. The approach to be used is similar to that used to develop the k-zeta model. In this approach, relevant equations are derived from the exact Navier-Stokes equations and each individual correlation is modeled. This ensures that relevant physics is incorporated into the model equations. This task has been accomplished. The final set of equations have no wall or damping functions. Moreover, they are tensorially consistent and Galilean invariant. The derivation of the model equations is rather lengthy and thus will not be incorporated into this abstract, but will be included in the final paper. As a preliminary to formulating the proposed model, the original k-zeta model with constant turbulent Prandtl and Schmidt numbers is used to model the supersonic coaxial jet mixing experiments involving He, O2 and air.

Numerical Recovering of a Speed of Sound by the BC-Method in 3D

NASA Astrophysics Data System (ADS)

Pestov, Leonid; Bolgova, Victoria; Danilin, Alexandr

We develop the numerical algorithm for solving the inverse problem for the wave equation by the Boundary Control method. The problem, which we refer to as a forward one, is an initial boundary value problem for the wave equation with zero initial data in the bounded domain. The inverse problem is to find the speed of sound c(x) by the measurements of waves induced by a set of boundary sources. The time of observation is assumed to be greater then two acoustical radius of the domain. The numerical algorithm for sound reconstruction is based on two steps. The first one is to find a (sufficiently large) number of controls {f_j} (the basic control is defined by the position of the source and some time delay), which generates the same number of known harmonic functions, i.e. Δ {u_j}(.,T) = 0 , where {u_j} is the wave generated by the control {f_j} . After that the linear integral equation w.r.t. the speed of sound is obtained. The piecewise constant model of the speed is used. The result of numerical testing of 3-dimensional model is presented.

Body fat from body density: Underwater weighing vs. dual-photon absorptiometry

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

Wang, J.; Heymsfield, S.B.; Aulet, M.

1989-06-01

We measured fat in 286 healthy volunteers by underwater weighing (FUWW) and dual-photon absorptiometry (FDPA) to develop a translation table for the differing results from these entirely different techniques and to study the sources of these differences. In 99 males and 187 females aged 19-94 yr, fatness was 7-47%. Prediction equations are presented for FUWW-FDPA (delta F), density of lean body mass (DLBM), and FDPA. FUWW and FDPA were significantly different from each other (P less than 0.01). Calculated DLBM is less than the assumed constant of 1.10 (P less than 0.01), ranging widely from 1.05 to 1.13 and beingmore » highly correlated with the ratio of total body bone mineral to lean body mass (TBBM/LBM). delta F, the differences between FUWW and FDPA measurements in individual subjects, varied widely (-7 to +11% in males and -18 to +13% in females). The difference was positively correlated with the DLBM. FUWW was no better than anthropometrics in equations for predicting FDPA. The FDPA predicted from anthropometrics showed smaller standard errors than when FUWW was used. Neither anthropometrics nor FUWW equations are clearly superior to those previously available.« less

The Covariant Formulation of Maxwell's Equations Expressed in a Form Independent of Specific Units

ERIC Educational Resources Information Center

Heras, Jose A.; Baez, G.

2009-01-01

The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are then specialized to the most commonly used systems of units: Gaussian, SI and Heaviside-Lorentz by giving…

Analytical Solution for Time-drawdown Response to Constant Pumping from a Homogeneous, Confined Horizontal Aquifer with Unidirectional Flow

NASA Astrophysics Data System (ADS)

Parrish, K. E.; Zhang, J.; Teasdale, E.

2007-12-01

An exact analytical solution to the ordinary one-dimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and one-dimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two- dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, high-permeability trench inside a low-permeability porous media. In addition, it can be used to analyze time-drawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time- constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and discussed for confined and unconfined conditions.

An accurate estimation method of kinematic viscosity for standard viscosity liquids

NASA Astrophysics Data System (ADS)

Kurano, Y.; Kobayashi, H.; Yoshida, K.; Imai, H.

1992-07-01

Deming's method of least squares is introduced to make an accurate kinematic viscosity estimation for a series of 13 standard-viscosity liquids at any desired temperature. The empirical ASTM kinematic viscosity-temperature equation is represented in the form loglog( v+c)=a-b log T, where v (in mm2. s-1) is the kinematic viscosity at temperature T (in K), a and b are the constants for a given liquid, and c has a variable value. In the present application, however, c is assumed to have a constant value for each standard-viscosity liquid, as do a and b in the ASTM equation. This assumption has since been verified experimentally for all standard-viscosity liquids. The kinematic viscosities for the 13 standard-viscosity liquids have been measured with a high accuracy in the temperature range of 20 40°C using a series of the NRLM capillary master viscometers with an automatic flow time detection system. The deviations between measured and estimated kinematic viscosities were less than ±0.04% for the 10 standard-viscosity liquids JS2.5 to JS2000 and ±0.11% for the 3 standard-viscosity liquids JS15H to JS200H, respectively. From the above investigation, it was revealed that the uncertainty in the present estimation method is less than one-third that in the usual ASTM method.

Stability of libration points in the restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Aggarwal, Rajiv; Suraj, Md. Sanam; Bisht, Virender Singh

2016-10-01

We have investigated the stability of the Lagrangian solutions for the restricted four-body problem with variable mass. It has been assumed that the three primaries with masses m1, m2 and m3 form an equilateral triangle, wherein m2=m3. According to Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), the infinitesimal body varies its mass m with time. The space-time transformations of Meshcherskii (Studies on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1949) are used by taking the values of the parameters q=1/2, k=0, n=1. The equations of motion of the infinitesimal body with variable mass have been determined. The equations of motion of the current problem differ from the ones of the restricted four-body problem with constant mass. There exist eight libration points, out of which two are collinear with the primary m1 and the rest are non-collinear for a fixed value of parameters γ (m {at time} t/m {at initial time}, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2) and μ=0.019 (the mass parameter). All the libration points are found to be unstable. The zero velocity surfaces (ZVS) are also drawn and regions of motion are discussed.

Inflation in a closed universe

NASA Astrophysics Data System (ADS)

Ratra, Bharat

2017-11-01

To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and nonrelativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking's prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wave number in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

Constitutive Modelling of Resins in the Stiffness Domain

NASA Astrophysics Data System (ADS)

Klasztorny, M.

2004-09-01

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.

Crystalline heterogeneities and instabilities in thermally convecting magma chamber

NASA Astrophysics Data System (ADS)

Culha, C.; Suckale, J.; Qin, Z.

2016-12-01

A volcanic vent can supply different densities of crystals over an eruption time period. This has been seen in Hawai'i's Kilauea Iki 1959 eruption; however it is not common for all Kilauea or basaltic eruptions. We ask the question: Under what conditions can homogenous magma chamber cultivate crystalline heterogeneities? In some laboratory experiments and numerical simulations, a horizontal variation is observed. The region where crystals reside is identified as a retention zone: convection velocity balances settling velocity. Simulations and experiments that observe retention zones assume crystals do not alter the convection in the fluid. However, a comparison of experiments and simulations of convecting magma with crystals suggest that large crystal volume densities and crystal sizes alter fluid flow considerably. We introduce a computational method that fully resolves the crystalline phase. To simulate basaltic magma chambers in thermal convection, we built a numerical solver of the Navier-Stoke's equation, continuity equation, and energy equation. The modeled magma is assumed to be a viscous, incompressible fluid with a liquid and solid phase. Crystals are spherical, rigid bodies. We create Rayleigh-Taylor instability through a cool top layer and hot bottom layer and update magma density while keeping crystal temperature and size constant. Our method provides a detailed picture of magma chambers, which we compare to other models and experiments to identify when and how crystals alter magma chamber convection. Alterations include stratification, differential settling and instabilities. These characteristics are dependent on viscosity, convection vigor, crystal volume density and crystal characteristics. We reveal that a volumetric crystal density variation may occur over an eruption time period, if right conditions are met to form stratifications and instabilities in magma chambers. These conditions are realistic for Kilauea Iki's 1959 eruption.

Equations for description of nonlinear standing waves in constant-cross-sectioned resonators.

PubMed

Bednarik, Michal; Cervenka, Milan

2014-03-01

This work is focused on investigation of applicability of two widely used model equations for description of nonlinear standing waves in constant-cross-sectioned resonators. The investigation is based on the comparison of numerical solutions of these model equations with solutions of more accurate model equations whose validity has been verified experimentally in a number of published papers.

Large numbers hypothesis. IV - The cosmological constant and quantum physics

NASA Technical Reports Server (NTRS)

Adams, P. J.

1983-01-01

In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.

Rapid-Equilibrium Enzyme Kinetics

ERIC Educational Resources Information Center

Alberty, Robert A.

2008-01-01

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful because if experimental data can be fit by these simpler rate equations, the Michaelis constants can be interpreted as equilibrium constants. However, for some reactions it is necessary to use the more complicated steady-state rate equations. Thermodynamics is…

Stresses in adhesively bonded joints - A closed-form solution

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1981-01-01

The general plane strain problem of adhesively bonded structures consisting of two different, orthotropic adherends is considered, under the assumption that adherend thicknesses are constant and small in relation to the lateral dimensions of the bonded region, so that they may be treated as plates. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form, with a single lap joint and a stiffened plate under various loading conditions being considered as examples. It is found that the plate theory used in the analysis not only predicts the correct trend for adhesive stresses but gives surprisingly accurate results, the solution being obtained by assuming linear stress-strain relations for the adhesive.

Optimal low thrust geocentric transfer. [mission analysis computer program

NASA Technical Reports Server (NTRS)

Edelbaum, T. N.; Sackett, L. L.; Malchow, H. L.

1973-01-01

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

Transient radiation in an anisotropic magnetodielectric plate in a waveguide

NASA Astrophysics Data System (ADS)

Gevorkyan, E. A.

2017-02-01

We have considered transient radiation of a charged particle in an anisotropic magnetodielectric plate placed into a regular waveguide. It is assumed that the charged particle passes through the plate moving at a constant velocity perpendicularly to the waveguide axis. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in different regions of the waveguide have been obtained. Energies of transient radiation of the moving particle have been calculated. The properties of transient radiation and Vavilov-Cherenkov radiation have been analyzed for the case of a rectangular waveguide. Energies of transient radiation have been calculated for the case of a "thin" plate in the waveguide, when the wavelength in the plate is much greater than the length of the plate.

Rough-to-smooth transition of an equilibrium neutral constant stress layer. [atmospheric flow over rough terrain

NASA Technical Reports Server (NTRS)

Logan, E., Jr.; Fichtl, G. H.

1975-01-01

A model is proposed for low-level atmospheric flows over terrains of changing roughness length, such as those found at the windward end of landing strips adjoining rough terrain. The proposed model is used to develop a prediction technique for calculating transition wind and shear-stress profiles in the region following surface roughness discontinuity. The model for the transition region comprises two layers: a logarithmic layer and a buffer layer. The flow is assumed to be steady, two-dimensional, and incompressible, with neutral hydrostatic stability. A diagram is presented for a typical wind profile in the transition region, obtained from the logarithmic and velocity defect profiles using shear stress calculated by relevant equations.

Why is it so difficult to determine the yield of indoor cannabis plantations? A case study from the Netherlands.

PubMed

Vanhove, Wouter; Maalsté, Nicole; Van Damme, Patrick

2017-07-01

Together, the Netherlands and Belgium are the largest indoor cannabis producing countries in Europe. In both countries, legal prosecution procedure of convicted illicit cannabis growers usually includes recovery of the profits gained. However, it is not easy to make a reliable estimation of the latter profits, due to the wide range of factors that determine indoor cannabis yields and eventual selling prices. In the Netherlands, since 2005, a reference model is used that assumes a constant yield (g) per plant for a given indoor cannabis plant density. Later, in 2011, a new model was developed in Belgium for yield estimation of Belgian indoor cannabis plantations that assumes a constant yield per m 2 of growth surface, provided that a number of growth conditions are met. Indoor cannabis plantations in the Netherlands and Belgium share similar technical characteristics. As a result, for indoor cannabis plantations in both countries, both aforementioned yield estimation models should yield similar yield estimations. By means of a real-case study from the Netherlands, we show that the reliability of both models is hampered by a number of flaws and unmet preconditions. The Dutch model is based on a regression equation that makes use of ill-defined plant development stages, assumes a linear plant growth, does not discriminate between different plantation size categories and does not include other important yield determining factors (such as fertilization). The Belgian model addresses some of the latter shortcomings, but its applicability is constrained by a number of pre-conditions including plantation size between 50 and 1000 plants; cultivation in individual pots with peat soil; 600W (electrical power) assimilation lamps; constant temperature between 20°C and 30°C; adequate fertilizer application and plants unaffected by pests and diseases. Judiciary in both the Netherlands and Belgium require robust indoor cannabis yield models for adequate legal prosecution of illicit indoor cannabis growth operations. To that aim, the current models should be optimized whereas the validity of their application should be examined case by case. Copyright © 2017 Elsevier B.V. All rights reserved.

New perspectives on constant-roll inflation

NASA Astrophysics Data System (ADS)

Cicciarella, Francesco; Mabillard, Joel; Pieroni, Mauro

2018-01-01

We study constant-roll inflation using the β-function formalism. We show that the constant rate of the inflaton roll is translated into a first order differential equation for the β-function which can be solved easily. The solutions to this equation correspond to the usual constant-roll models. We then construct, by perturbing these exact solutions, more general classes of models that satisfy the constant-roll equation asymptotically. In the case of an asymptotic power law solution, these corrections naturally provide an end to the inflationary phase. Interestingly, while from a theoretical point of view (in particular in terms of the holographic interpretation) these models are intrinsically different from standard slow-roll inflation, they may have phenomenological predictions in good agreement with present cosmological data.

Expanding space-time and variable vacuum energy

NASA Astrophysics Data System (ADS)

Parmeggiani, Claudio

2017-08-01

The paper describes a cosmological model which contemplates the presence of a vacuum energy varying, very slightly (now), with time. The constant part of the vacuum energy generated, some 6 Gyr ago, a deceleration/acceleration transition of the metric expansion; so now, in an aged Universe, the expansion is inexorably accelerating. The vacuum energy varying part is instead assumed to be eventually responsible of an acceleration/deceleration transition, which occurred about 14 Gyr ago; this transition has a dynamic origin: it is a consequence of the general relativistic Einstein-Friedmann equations. Moreover, the vacuum energy (constant and variable) is here related to the zero-point energy of some quantum fields (scalar, vector, or spinor); these fields are necessarily described in a general relativistic way: their structure depends on the space-time metric, typically non-flat. More precisely, the commutators of the (quantum field) creation/annihilation operators are here assumed to depend on the local value of the space-time metric tensor (and eventually of its curvature); furthermore, these commutators rapidly decrease for high momentum values and they reduce to the standard ones for a flat metric. In this way, the theory is ”gravitationally” regularized; in particular, the zero-point (vacuum) energy density has a well defined value and, for a non static metric, depends on the (cosmic) time. Note that this varying vacuum energy can be negative (Fermi fields) and that a change of its sign typically leads to a minimum for the metric expansion factor (a ”bounce”).

SPH modelling of energy partitioning during impacts on Venus

NASA Technical Reports Server (NTRS)

Takata, T.; Ahrens, T. J.

1993-01-01

Impact cratering of the Venusian planetary surface by meteorites was investigated numerically using the Smoothed Particle Hydrodynamics (SPH) method. Venus presently has a dense atmosphere. Vigorous transfer of energy between impacting meteorites, the planetary surface, and the atmosphere is expected during impact events. The investigation concentrated on the effects of the atmosphere on energy partitioning and the flow of ejecta and gas. The SPH method is particularly suitable for studying complex motion, especially because of its ability to be extended to three dimensions. In our simulations, particles representing impactors and targets are initially set to a uniform density, and those of atmosphere are set to be in hydrostatic equilibrium. Target, impactor, and atmosphere are represented by 9800, 80, and 4200 particles, respectively. A Tillotson equation of state for granite is assumed for the target and impactor, and an ideal gas with constant specific heat ratio is used for the atmosphere. Two dimensional axisymmetric geometry was assumed and normal impacts of 10km diameter projectiles with velocities of 5, 10, 20, and 40 km/s, both with and without an atmosphere present were modeled.

Models for mirror symmetry breaking via β-sheet-controlled copolymerization: (i) mass balance and (ii) probabilistic treatment.

PubMed

Blanco, Celia; Hochberg, David

2012-12-06

Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic β-sheet-controlled polymerization operative in both surface crystallites as well as in solution. We develop two complementary theoretical models for these template-induced desymmetrization processes leading to multicomponent homochiral copolymers. First, assuming reversible β-sheet formation, the equilibrium between the free monomer pool and the polymer strand within the template is assumed. This yields coupled nonlinear mass balance equations whose solutions are used to calculate enantiomeric excesses and average lengths of the homochiral chains formed. The second approach is a probabilistic treatment based on random polymerization. The occlusion probabilities depend on the polymerization activation energies for each monomer species and are proportional to the concentrations of the monomers in solution in the constant pool approximation. The monomer occlusion probabilities are represented geometrically in terms of unit simplexes from which conditions for maximizing or minimizing the likelihood for mirror symmetry breaking can be determined.

Evaluation and Improvement of Liquid Propellant Rocket Chugging Analysis Techniques. Part 2: a Study of Low Frequency Combustion Instability in Rocket Engine Preburners Using a Heterogeneous Stirred Tank Reactor Model. Final Report M.S. Thesis - Aug. 1987

NASA Technical Reports Server (NTRS)

Bartrand, Timothy A.

1988-01-01

During the shutdown of the space shuttle main engine, oxygen flow is shut off from the fuel preburner and helium is used to push the residual oxygen into the combustion chamber. During this process a low frequency combustion instability, or chug, occurs. This chug has resulted in damage to the engine's augmented spark igniter due to backflow of the contents of the preburner combustion chamber into the oxidizer feed system. To determine possible causes and fixes for the chug, the fuel preburner was modeled as a heterogeneous stirred tank combustion chamber, a variable mass flow rate oxidizer feed system, a constant mass flow rate fuel feed system and an exit turbine. Within the combustion chamber gases were assumed perfectly mixed. To account for liquid in the combustion chamber, a uniform droplet distribution was assumed to exist in the chamber, with mean droplet diameter determined from an empirical relation. A computer program was written to integrate the resulting differential equations. Because chamber contents were assumed perfectly mixed, the fuel preburner model erroneously predicted that combustion would not take place during shutdown. The combustion rate model was modified to assume that all liquid oxygen that vaporized instantaneously combusted with fuel. Using this combustion model, the effect of engine parameters on chamber pressure oscillations during the SSME shutdown was calculated.

Nonlocal conservation laws of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam; Marvan, Michal

2017-03-01

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.

High-frequency homogenization for travelling waves in periodic media.

PubMed

Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

2016-07-01

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

Constant fields and constant gradients in open ionic channels.

PubMed Central

Chen, D P; Barcilon, V; Eisenberg, R S

1992-01-01

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant. Images FIGURE 1 PMID:1376159

An Analytic Form for the Interresponse Time Analysis of Shull, Gaynor, and Grimes with Applications and Extensions

ERIC Educational Resources Information Center

Kessel, Robert; Lucke, Robert L.

2008-01-01

Shull, Gaynor and Grimes advanced a model for interresponse time distribution using probabilistic cycling between a higher-rate and a lower-rate response process. Both response processes are assumed to be random in time with a constant rate. The cycling between the two processes is assumed to have a constant transition probability that is…

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

A root-mean-square pressure fluctuations model for internal flow applications

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1985-01-01

A transport equation for the root-mean-square pressure fluctuations of turbulent flow is derived from the time-dependent momentum equation for incompressible flow. Approximate modeling of this transport equation is included to relate terms with higher order correlations to the mean quantities of turbulent flow. Three empirical constants are introduced in the model. Two of the empirical constants are estimated from homogeneous turbulence data and wall pressure fluctuations measurements. The third constant is determined by comparing the results of large eddy simulations for a plane channel flow and an annulus flow.

Energy scale of Lorentz violation in Rainbow Gravity

NASA Astrophysics Data System (ADS)

Nilsson, Nils A.; Dąbrowski, Mariusz P.

2017-12-01

We modify the standard relativistic dispersion relation in a way which breaks Lorentz symmetry-the effect is predicted in a high-energy regime of some modern theories of quantum gravity. We show that it is possible to realise this scenario within the framework of Rainbow Gravity which introduces two new energy-dependent functions f1(E) and f2(E) into the dispersion relation. Additionally, we assume that the gravitational constant G and the cosmological constant Λ also depend on energy E and introduce the scaling function h(E) in order to express this dependence. For cosmological applications we specify the functions f1 and f2 in order to fit massless particles which allows us to derive modified cosmological equations. Finally, by using Hubble+SNIa+BAO(BOSS+Lyman α)+CMB data, we constrain the energy scale ELV to be at least of the order of 1016 GeV at 1 σ which is the GUT scale or even higher 1017 GeV at 3 σ. Our claim is that this energy can be interpreted as the decoupling scale of massless particles from spacetime Lorentz violating effects.

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

NASA Astrophysics Data System (ADS)

Astashenok, Artyom V.; Elizalde, Emilio; Yurov, Artyom V.

2014-01-01

It is observed that one of Einstein-Friedmann's equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, Λ, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for Λ, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to L 2 space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for Λ>0 and a continuous one for Λ<0. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.

Dark energy and equivalence principle constraints from astrophysical tests of the stability of the fine-structure constant

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

Martins, C.J.A.P.; Pinho, A.M.M.; Alves, R.F.C.

2015-08-01

Astrophysical tests of the stability of fundamental couplings, such as the fine-structure constant α, are becoming an increasingly powerful probe of new physics. Here we discuss how these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, ζ, to the electromagnetic sector) the α variation. Specifically, current data tightly constrains a combination of ζ and the present dark energy equation of state w{sub 0}. Moreover, inmore » these models the new degree of freedom inevitably couples to nucleons (through the α dependence of their masses) and leads to violations of the Weak Equivalence Principle. We obtain indirect bounds on the Eötvös parameter η that are typically stronger than the current direct ones. We discuss the model-dependence of our results and briefly comment on how the forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.« less

Holographic Dark Energy in Brans-Dicke Theory with Logarithmic Form of Scalar Field

NASA Astrophysics Data System (ADS)

Singh, C. P.; Kumar, Pankaj

2017-10-01

In this paper, an interacting holographic dark energy model with Hubble horizon as an infra-red cut-off is considered in the framework of Brans-Dicke theory. We assume the Brans-Dicke scalar field as a logarithmic form ϕ = ϕ 0 l n( α + β a), where a is the scale factor, α and β are arbitrary constants, to interpret the physical phenomena of the Universe. The equation of state parameter w h and deceleration parameter q are obtained to discuss the dynamics of the evolution of the Universe. We present a unified model of holographic dark energy which explains the early time acceleration (inflation), medieval time deceleration and late time acceleration. It is also observed that w h may cross the phantom divide line in the late time evolution. We also discuss the cosmic coincidence problem. We obtain a time-varying density ratio of holographic dark energy to dark matter which is a constant of order one (r˜ O(1)) during early and late time evolution, and may evolve sufficiently slow at present time. Thus, the model successfully resolves the cosmic coincidence problem.

Mixed convection of magnetohydrodynamic nanofluids inside microtubes at constant wall temperature

NASA Astrophysics Data System (ADS)

Moshizi, S. A.; Zamani, M.; Hosseini, S. J.; Malvandi, A.

2017-05-01

Laminar fully developed mixed convection of magnetohydrodynamic nanofluids inside microtubes at a constant wall temperature (CWT) under the effects of a variable directional magnetic field is investigated numerically. Nanoparticles are assumed to have slip velocities relative to the base fluid owing to thermophoretic diffusion (temperature gradient driven force) and Brownian diffusion (concentration gradient driven force). The no-slip boundary condition is avoided at the fluid-solid mixture to assess the non-equilibrium region at the fluid-solid interface. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. After the effects of pertinent parameters on the pressure loss and heat transfer enhancement were considered, the figure of merit (FoM) is employed to evaluate and optimize the thermal performance of heat exchange equipment. The results indicate the optimum thermal performance is obtained when the thermophoresis overwhelms the Brownian diffusion, which is for larger nanoparticles. This enhancement boosts when the buoyancy force increases. In addition, increasing the magnetic field strength and slippage at the fluid-solid interface enhances the thermal performance.

Thermal conductivity and phonon transport properties of silicon using perturbation theory and the environment-dependent interatomic potential

NASA Astrophysics Data System (ADS)

Pascual-Gutiérrez, José A.; Murthy, Jayathi Y.; Viskanta, Raymond

2009-09-01

Silicon thermal conductivities are obtained from the solution of the linearized phonon Boltzmann transport equation without the use of any parameter-fitting. Perturbation theory is used to compute the strength of three-phonon and isotope scattering mechanisms. Matrix elements based on Fermi's golden rule are computed exactly without assuming either average or mode-dependent Grüeisen parameters, and with no underlying assumptions of crystal isotropy. The environment-dependent interatomic potential is employed to describe the interatomic force constants and the perturbing Hamiltonians. A detailed methodology to accurately find three-phonon processes satisfying energy- and momentum-conservation rules is also described. Bulk silicon thermal conductivity values are computed across a range of temperatures and shown to match experimental data very well. It is found that about two-thirds of the heat transport in bulk silicon may be attributed to transverse acoustic modes. Effective relaxation times and mean free paths are computed in order to provide a more complete picture of the detailed transport mechanisms and for use with carrier transport models based on the Boltzmann transport equation.

End-Member Formulation of Solid Solutions and Reactive Transport

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

Lichtner, Peter C.

2015-09-01

A model for incorporating solid solutions into reactive transport equations is presented based on an end-member representation. Reactive transport equations are solved directly for the composition and bulk concentration of the solid solution. Reactions of a solid solution with an aqueous solution are formulated in terms of an overall stoichiometric reaction corresponding to a time-varying composition and exchange reactions, equivalent to reaction end-members. Reaction rates are treated kinetically using a transition state rate law for the overall reaction and a pseudo-kinetic rate law for exchange reactions. The composition of the solid solution at the onset of precipitation is assumed tomore » correspond to the least soluble composition, equivalent to the composition at equilibrium. The stoichiometric saturation determines if the solid solution is super-saturated with respect to the aqueous solution. The method is implemented for a simple prototype batch reactor using Mathematica for a binary solid solution. Finally, the sensitivity of the results on the kinetic rate constant for a binary solid solution is investigated for reaction of an initially stoichiometric solid phase with an undersaturated aqueous solution.« less

THE AXISYMMETRIC FREE-CONVECTION HEAT TRANSFER ALONG A VERTICAL THIN CYLINDER WITH CONSTANT SURFACE TEMPERATURE

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

Viskanta, R.

1963-01-01

Laminar free-convection flow produced by a heated, vertical, circular cylinder for which the temperature at the outer surface of the cylinder is assumed to be uniform is analyzed. The solution of the boundary-layer equations was obtained by the perturbation method of Sparrow and Gregg, which is valid only for small values of the axial distance parameter xi ; and the integral method of Hama et al., for large values of the parameter xi . Heat-transfer results were calculated for Prandtl numbers (Pr) of 100, the Nusselt numbers (Nu) for the cylinder were higher than those for the flat plate, andmore » this difference increased as Pr decreased. It was also found that the perturbation method of solution of the free-convection boundary-layer equations becomes useless for small values of Pr because of the slow convergence of the series. The results obtained by the integral method were in good agreement with those calculated by the perturbation method for Pr approximately 1 and 0.1 < xi < 1 only; they deviated considerably for smaller values of xi . (auth)« less

Optimum flight paths of turbojet aircraft

NASA Technical Reports Server (NTRS)

Miele, Angelo

1955-01-01

The climb of turbojet aircraft is analyzed and discussed including the accelerations. Three particular flight performances are examined: minimum time of climb, climb with minimum fuel consumption, and steepest climb. The theoretical results obtained from a previous study are put in a form that is suitable for application on the following simplifying assumptions: the Mach number is considered an independent variable instead of the velocity; the variations of the airplane mass due to fuel consumption are disregarded; the airplane polar is assumed to be parabolic; the path curvatures and the squares of the path angles are disregarded in the projection of the equation of motion on the normal to the path; lastly, an ideal turbojet with performance independent of the velocity is involved. The optimum Mach number for each flight condition is obtained from the solution of a sixth order equation in which the coefficients are functions of two fundamental parameters: the ratio of minimum drag in level flight to the thrust and the Mach number which represents the flight at constant altitude and maximum lift-drag ratio.

`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.

Precipitation regions on the Earth of high energy electrons, injected by a point source moving along a circular Earth orbit

NASA Astrophysics Data System (ADS)

Kolesnikov, E. K.; Klyushnikov, G. N.

2018-05-01

In the paper we continue the study of precipitation regions of high-energy charged particles, carried out by the authors since 2002. In contrast to previous papers, where a stationary source of electrons was considered, it is assumed that the source moves along a low circular near-earth orbit with a constant velocity. The orbit position is set by the inclination angle of the orbital plane to the equatorial plane and the longitude of the ascending node. The total number of injected electrons is determined by the source strength and the number of complete revolutions that the source makes along the circumference. Construction of precipitation regions is produced using the computational algorithm based on solving of the system of ordinary differential equations. The features of the precipitation regions structure for the dipole approximation of the geomagnetic field and the symmetrical arrangement of the orbit relative to the equator are noted. The dependencies of the precipitation regions on different orbital parametres such as the incline angle, the ascending node position and kinetic energy of injected particles have been considered.

Computation of solar perturbations with Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Toroidal Ampere-Faraday Equations Solved Simultaneously with CQL3D Fokker-Planck Time-Evolution

NASA Astrophysics Data System (ADS)

Harvey, R. W. (Bob); Petrov, Yu. V. (Yuri); Forest, C. B.; La Haye, R. J.

2017-10-01

A self-consistent, time-dependent toroidal electric field calculation is a key feature of a complete 3D Fokker-Planck kinetic distribution radial transport code for f(v,theta,rho,t). We discuss benchmarking and first applications of an implementation of the Ampere-Faraday equation for the self-consistent toroidal electric field, as applied to (1) resistive turn on of applied electron cyclotron current in the DIII-D tokamak giving initial back current adjacent to the direct CD region and having possible NTM stabilization implications, and (2) runaway electron production in tokamaks due to rapid reduction of the plasma temperature as occurs in pellet injection, massive gas injection, or a plasma disruption. Our previous results assuming a constant current density (Lenz' Law) model showed that prompt ``hot-tail runaways'' dominated ``knock-on'' and Dreicer ``drizzle'' runaways; we perform full-radius modeling and examine modifications due to the more complete Ampere-Faraday solution. Presently, the implementation relies on a fixed shape eqdsk, and this limitation will be addressed in future work. Research supported by USDOE FES award ER54744.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations.

PubMed

Madanu, Sushma B; Barbel, Stanley I; Ward, Thomas

2016-06-01

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude of vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.

Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenon

NASA Astrophysics Data System (ADS)

Rodionov, Alexander V.

2017-09-01

This work presents a new approach for curing the carbuncle instability. The idea underlying the approach is to introduce some dissipation in the form of right-hand sides of the Navier-Stokes equations into the basic method of solving Euler equations; in so doing, we replace the molecular viscosity coefficient by the artificial viscosity coefficient and calculate heat conductivity assuming that the Prandtl number is constant. For the artificial viscosity coefficient we have chosen a formula that is consistent with the von Neumann and Richtmyer artificial viscosity, but has its specific features (extension to multidimensional simulations, introduction of a threshold compression intensity that restricts additional dissipation to the shock layer only). The coefficients and the expression for the characteristic mesh size in this formula are chosen from a large number of Quirk-type problem computations. The new cure for the carbuncle flaw has been tested on first-order schemes (Godunov, Roe, HLLC and AUSM+ schemes) as applied to one- and two-dimensional simulations on smooth structured grids. Its efficiency has been demonstrated on several well-known test problems.

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

NASA Astrophysics Data System (ADS)

Stolk, Christiaan C.

2016-06-01

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

Three-dimensional simulations of thin ferro-fluid films and drops in magnetic fields

NASA Astrophysics Data System (ADS)

Conroy, Devin; Wray, Alex; Matar, Omar

2016-11-01

We consider the interfacial dynamics of a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly-conducting. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and continuity equations. The magnetisation of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved with the use of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We consider the three-dimensional evolution of the film to spawise perturbations by solving the non-linear equations numerically. The constant flux configuration is considered, which corresponds to a thin film and drop flowing down an incline, and a parametric study is performed to understand the effect of a magnetic field on the stability and structure of the formed drops. EPSRC UK platform Grant MACIPh (EP/L020564/1) and programme Grant MEMPHIS (EP/K003976/1).

Kinetics of transmembrane transport of small molecules into electropermeabilized cells.

PubMed

Pucihar, Gorazd; Kotnik, Tadej; Miklavcic, Damijan; Teissié, Justin

2008-09-15

The transport of propidium iodide into electropermeabilized Chinese hamster ovary cells was monitored with a photomultiplier tube during and after the electric pulse. The influence of pulse amplitude and duration on the transport kinetics was investigated with time resolutions from 200 ns to 4 ms in intervals from 400 micros to 8 s. The transport became detectable as early as 60 micros after the start of the pulse, continued for tens of seconds after the pulse, and was faster and larger for higher pulse amplitudes and/or longer pulse durations. With fixed pulse parameters, transport into confluent monolayers of cells was slower than transport into suspended cells. Different time courses of fluorescence increase were observed during and at various times after the pulse, reflecting different transport mechanisms and ongoing membrane resealing. The data were compared to theoretical predictions of the Nernst-Planck equation. After a delay of 60 micros, the time course of fluorescence during the pulse was approximately linear, supporting a mainly electrophoretic solution of the Nernst-Planck equation. The time course after the pulse agreed with diffusional solution of the Nernst-Planck equation if the membrane resealing was assumed to consist of three distinct components, with time constants in the range of tens of microseconds, hundreds of microseconds, and tens of seconds, respectively.

Enzyme inhibition studies by integrated Michaelis-Menten equation considering simultaneous presence of two inhibitors when one of them is a reaction product.

PubMed

Bezerra, Rui M F; Pinto, Paula A; Fraga, Irene; Dias, Albino A

2016-03-01

To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers.

PubMed

Chen, Kaisheng; Hou, Jie; Huang, Zhuyang; Cao, Tong; Zhang, Jihua; Yu, Yuan; Zhang, Xinliang

2015-02-09

We experimentally demonstrate an all-optical temporal computation scheme for solving 1st- and 2nd-order linear ordinary differential equations (ODEs) with tunable constant coefficients by using Fabry-Pérot semiconductor optical amplifiers (FP-SOAs). By changing the injection currents of FP-SOAs, the constant coefficients of the differential equations are practically tuned. A quite large constant coefficient tunable range from 0.0026/ps to 0.085/ps is achieved for the 1st-order differential equation. Moreover, the constant coefficient p of the 2nd-order ODE solver can be continuously tuned from 0.0216/ps to 0.158/ps, correspondingly with the constant coefficient q varying from 0.0000494/ps(2) to 0.006205/ps(2). Additionally, a theoretical model that combining the carrier density rate equation of the semiconductor optical amplifier (SOA) with the transfer function of the Fabry-Pérot (FP) cavity is exploited to analyze the solving processes. For both 1st- and 2nd-order solvers, excellent agreements between the numerical simulations and the experimental results are obtained. The FP-SOAs based all-optical differential-equation solvers can be easily integrated with other optical components based on InP/InGaAsP materials, such as laser, modulator, photodetector and waveguide, which can motivate the realization of the complicated optical computing on a single integrated chip.

Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

NASA Technical Reports Server (NTRS)

Erdogan, F.; Civelek, M. B.

1978-01-01

A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.

Fluorescence lifetime measurements in heterogeneous scattering medium

NASA Astrophysics Data System (ADS)

Nishimura, Goro; Awasthi, Kamlesh; Furukawa, Daisuke

2016-07-01

Fluorescence lifetime in heterogeneous multiple light scattering systems is analyzed by an algorithm without solving the diffusion or radiative transfer equations. The algorithm assumes that the optical properties of medium are constant in the excitation and emission wavelength regions. If the assumption is correct and the fluorophore is a single species, the fluorescence lifetime can be determined by a set of measurements of temporal point-spread function of the excitation light and fluorescence at two different concentrations of the fluorophore. This method is not dependent on the heterogeneity of the optical properties of the medium as well as the geometry of the excitation-detection on an arbitrary shape of the sample. The algorithm was validated by an indocyanine green fluorescence in phantom measurements and demonstrated by an in vivo measurement.

Identification and control of structures in space

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Quinn, R. D.; Norris, M. A.

1984-01-01

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

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.

On the joint bimodality of temperature and moisture near stratocumulus cloud tops

NASA Technical Reports Server (NTRS)

Randall, D. A.

1983-01-01

The observed distributions of the thermodynamic variables near stratocumulus top are highly bimodal. Two simple models of sub-grid fractional cloudiness motivated by this observed bimodality are examined. In both models, certain low order moments of two independent, moist-conservative thermodynamic variables are assumed to be known. The first model is based on the assumption of two discrete populations of parcels: a warm-day population and a cool-moist population. If only the first and second moments are assumed to be known, the number of unknowns exceeds the number of independent equations. If the third moments are assumed to be known as well, the number of independent equations exceeds the number of unknowns. The second model is based on the assumption of a continuous joint bimodal distribution of parcels, obtained as the weighted sum of two binormal distributions. For this model, the third moments are used to obtain 9 independent nonlinear algebraic equations in 11 unknowns. Two additional equations are needed to determine the covariance within the two subpopulations. In case these two internal covariance vanish, the system of equations can be solved analytically.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Bianchi type-I universe in Lyra manifold with quadratic equation of state

NASA Astrophysics Data System (ADS)

Şen, R.; Aygün, S.

2017-02-01

In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = ap(t)2 - ρ(t). Where α ≠0 is an important constant. Cosmic pressure, density and displacement vector (β2) are related with α constant. In this study β2 is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of Halford, Pradhan and Singh, Aygün et al., Agarwal et al., Yadav and Haque as well as SN Ia observations.

A new perspective on Quantum Finance using the Black-Scholes pricing model

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2007-03-01

Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money.

On the time-splitting scheme used in the Princeton Ocean Model

NASA Astrophysics Data System (ADS)

Kamenkovich, V. M.; Nechaev, D. A.

2009-05-01

The analysis of the time-splitting procedure implemented in the Princeton Ocean Model (POM) is presented. The time-splitting procedure uses different time steps to describe the evolution of interacting fast and slow propagating modes. In the general case the exact separation of the fast and slow modes is not possible. The main idea of the analyzed procedure is to split the system of primitive equations into two systems of equations for interacting external and internal modes. By definition, the internal mode varies slowly and the crux of the problem is to determine the proper filter, which excludes the fast component of the external mode variables in the relevant equations. The objective of this paper is to examine properties of the POM time-splitting procedure applied to equations governing the simplest linear non-rotating two-layer model of constant depth. The simplicity of the model makes it possible to study these properties analytically. First, the time-split system of differential equations is examined for two types of the determination of the slow component based on an asymptotic approach or time-averaging. Second, the differential-difference scheme is developed and some criteria of its stability are discussed for centered, forward, or backward time-averaging of the external mode variables. Finally, the stability of the POM time-splitting schemes with centered and forward time-averaging is analyzed. The effect of the Asselin filter on solutions of the considered schemes is studied. It is assumed that questions arising in the analysis of the simplest model are inherent in the general model as well.

Equations for calculating the properties of dissociated steam

NASA Astrophysics Data System (ADS)

Aminov, R. Z.; Gudym, A. A.

2017-08-01

The equations of state for dissociated steam have been developed in the temperature and pressure ranges of 1250-2300 K and 0.01-10.00 MPa for calculating thermodynamic processes in thermal power units operating on high-temperature steam. These equations are based on the property tables for dissociated steam derived at a reference temperature of 0 K. It is assumed that the initial substance is steam, the dissociation of which—in accordance with the most likely chemical reactions—results in formation of molecules of hydrogen, oxygen, steam, hydroxyl, and atoms of oxygen and hydrogen. Differential thermodynamic correlations, considering a change in the chemical potential and the composition of the mixture, during the steam dissociation are used. A reference temperature of 0.01°C used in the calculation of parameters of nondissociated steam has been adopted to predict processes in thermal power units without matching the reference temperatures and to account for transformation of dissociated steam into its usual form for which there is the international system of equations with the water triple point of 0.01°C taken as the reference. In the investigated region, the deviation of dissociated steam properties from those of nondissociated steam, which increases with decreasing the pressure or increasing the temperature, was determined. For a pressure of 0.02 MPa and a temperature of 2200 K, these deviations are 512 kJ/kg for the enthalpy, 0.2574 kJ/(kg K) for the entropy, and 3.431 kJ/(kg K) for the heat capacity at constant pressure. The maximum deviation of the dissociated steam properties calculated by the developed equations from the handbook values that these equations are based on does not exceed 0.03-0.05%.

Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters

NASA Astrophysics Data System (ADS)

Panaseti, Pandelitsa; Damianou, Yiolanda; Georgiou, Georgios C.; Housiadas, Kostas D.

2018-03-01

The lubrication flow of a Herschel-Bulkley fluid in a symmetric long channel of varying width, 2h(x), is modeled extending the approach proposed by Fusi et al. ["Pressure-driven lubrication flow of a Bingham fluid in a channel: A novel approach," J. Non-Newtonian Fluid Mech. 221, 66-75 (2015)] for a Bingham plastic. Moreover, both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order depends only on x and the semi-width of the unyielded core is found to be given by σ(x) = -(1 + 1/n)h(x) + C, where n is the power-law exponent and the constant C depends on the Bingham number and the consistency-index and yield-stress growth numbers. Hence, in a channel of constant width, the width of the unyielded core is also constant, despite the pressure dependence of the yield stress, and the pressure distribution is not affected by the yield-stress function. With the present model, the pressure is calculated numerically solving an integro-differential equation and then the position of the yield surface and the two velocity components are computed using analytical expressions. Some analytical solutions are also derived for channels of constant and linearly varying widths. The lubrication solutions for other geometries are calculated numerically. The implications of the pressure-dependence of the material parameters and the limitations of the method are discussed.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Cosmology with Strong-lensing Systems

NASA Astrophysics Data System (ADS)

Cao, Shuo; Biesiada, Marek; Gavazzi, Raphaël; Piórkowska, Aleksandra; Zhu, Zong-Hong

2015-06-01

In this paper, we assemble a catalog of 118 strong gravitational lensing systems from the Sloan Lens ACS Survey, BOSS emission-line lens survey, Lens Structure and Dynamics, and Strong Lensing Legacy Survey and use them to constrain the cosmic equation of state. In particular, we consider two cases of dark energy phenomenology: the XCDM model, where dark energy is modeled by a fluid with constant w equation-of-state parameter, and in the Chevalier-Polarski-Linder (CPL) parameterization, where w is allowed to evolve with redshift, w(z)={{w}0}+{{w}1}\\frac{z}{1 + z} . We assume spherically symmetric mass distribution in lensing galaxies, but we relax the rigid assumption of the SIS model in favor of a more general power-law index γ, also allowing it to evolve with redshifts γ (z). Our results for the XCDM cosmology show agreement with values (concerning both w and γ parameters) obtained by other authors. We go further and constrain the CPL parameters jointly with γ (z). The resulting confidence regions for the parameters are much better than those obtained with a similar method in the past. They are also showing a trend of being complementary to the Type Ia supernova data. Our analysis demonstrates that strong gravitational lensing systems can be used to probe cosmological parameters like the cosmic equation of state for dark energy. Moreover, they have a potential to judge whether the cosmic equation of state evolved with time or not.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

PubMed Central

Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George

2015-01-01

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874

Compact Representations of Extended Causal Models

DTIC Science & Technology

2012-10-01

get a yet more compact representation by assuming that, by default , it is typical for the variables to obey the structural equations. Finally, in...Halpern and Hitchcock (2011), is to incorporate considerations about about defaults , typicality, and normality. “Normality” and its cognates (“normal...atypical to violate it. 17 Variables typically obey the structural equations. Thus, it is often far more efficient to assume this holds by default

Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows

NASA Technical Reports Server (NTRS)

Rubesin, Morris W.

1990-01-01

Forms of extra-compressibility terms that result from use of Favre averaging of the turbulence transport equations for kinetic energy and dissipation are derived. These forms introduce three new modeling constants, a polytropic coefficient that defines the interrelationships of the pressure, density, and enthalpy fluctuations and two constants in the dissipation equation that account for the non-zero pressure-dilitation and mean pressure gradients.

Integrated Sachs-Wolfe effect from the cross correlation of WMAP 3year and the NRAO VLA sky survey data: New results and constraints on dark energy

NASA Astrophysics Data System (ADS)

Pietrobon, Davide; Balbi, Amedeo; Marinucci, Domenico

2006-08-01

We cross correlate the new 3 year Wilkinson Microwave Anistropy Probe (WMAP) cosmic microwave background data with the NRAO VLA Sky Survey radio galaxy data and find further evidence of late integrated Sachs-Wolfe (ISW) effect taking place at late times in cosmic history. Our detection makes use of a novel statistical method (P. Baldi, G. Kerkyacharian, D. Marinucci, and D. Picard, math.ST/0606154 and P. Baldi, G. Kerkyacharian, D. Marinucci, D. Picard, math.ST/0606599) based on a new construction of spherical wavelets, called needlets. The null hypothesis (no ISW) is excluded at more than 99.7% confidence. When we compare the measured cross correlation with the theoretical predictions of standard, flat cosmological models with a generalized dark energy component parameterized by its density, ΩDE, equation of state w and speed of sound cs2, we find 0.3≤ΩDE≤0.8 at 95% C.L., independently of cs2 and w. If dark energy is assumed to be a cosmological constant (w=-1), the bound on density shrinks to 0.41≤ΩDE≤0.79. Models without dark energy are excluded at more than 4σ. The bounds on w depend rather strongly on the assumed value of cs2. We find that models with more negative equation of state (such as phantom models) are a worse fit to the data in the case cs2=1 than in the case cs2=0.

Extending the Constant Coefficient Solution Technique to Variable Coefficient Ordinary Differential Equations

ERIC Educational Resources Information Center

Mohammed, Ahmed; Zeleke, Aklilu

2015-01-01

We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

On Gravitational Effects in the Schrödinger Equation

NASA Astrophysics Data System (ADS)

Pollock, M. D.

2014-04-01

The Schrödinger equation for a particle of rest mass and electrical charge interacting with a four-vector potential can be derived as the non-relativistic limit of the Klein-Gordon equation for the wave function , where and , or equivalently from the one-dimensional action for the corresponding point particle in the semi-classical approximation , both methods yielding the equation in Minkowski space-time , where and . We show that these two methods generally yield equations that differ in a curved background space-time , although they coincide when if is replaced by the effective mass in both the Klein-Gordon action and , allowing for non-minimal coupling to the gravitational field, where is the Ricci scalar and is a constant. In this case , where and , the correctness of the gravitational contribution to the potential having been verified to linear order in the thermal-neutron beam interferometry experiment due to Colella et al. Setting and regarding as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space-time. Conservation of probability and electrical current requires both electromagnetic gauge and space-time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div, where and . The quantum-cosmological Schrödinger (Wheeler-DeWitt) equation is also discussed in the -dimensional mini-superspace idealization, with particular regard to the vacuum potential and the characteristics of the ground state, assuming a gravitational Lagrangian which contains higher-derivative terms up to order . For the heterotic superstring theory , consists of an infinite series in , where is the Regge slope parameter, and in the perturbative approximation , is positive semi-definite for . The maximally symmetric ground state satisfying the field equations is Minkowski space for and anti-de Sitter space for.

A Method of Implementing Cutoff Conditions for Saturn V Lunar Missions Out of Earth Parking Orbit Assuming a Continuous Ground Launch Window

NASA Technical Reports Server (NTRS)

Cooper, F. D.

1965-01-01

A method of implementing Saturn V lunar missions from an earth parking orbit is presented. The ground launch window is assumed continuous over a four and one-half hour period. The iterative guidance scheme combined with a set of auxiliary equations that define suitable S-IVB cutoff conditions, is the approach taken. The four inputs to the equations that define cutoff conditions are represented as simple third-degree polynomials as a function of ignition time. Errors at lunar arrival caused by the separate and combined effects of the guidance equations, cutoff conditions, hypersurface errors, and input representations are shown. Vehicle performance variations and parking orbit injection errors are included as perturbations. Appendix I explains how aim vectors were computed for the cutoff equations. Appendix II presents all guidance equations and related implementation procedures. Appendix III gives the derivation of the auxiliary cutoff equations. No error at lunar arrival was large enough to require a midcourse correction greater than one meter per second assuming a transfer time of three days and the midcourse correction occurs five hours after injection. Since this result is insignificant when compared to expected hardware errors, the implementation procedures presented are adequate to define cutoff conditions for Saturn V lunar missions.

Numerical solutions of the complete Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hassan, H. A.

1993-01-01

The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.

Limitations on the applicability of FODO lattices for electron cooling

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

Bertsche, K.J.

1997-09-01

Assuming a KV beam distribution (a uniform distribution over an elliptical region of transverse phase space), the beam envelop equations are shown, where X and Y are the transverse beam sizes, {kappa} is the lens strength, K is the generalized beam perveance, and {epsilon} is the beam emittance. If we further assume operation in a space-charge dominated regime, the right most term can be ignored in each equation. In this case, particle flow will be laminar, and the above equations not only describe the envelope of the beam, but also the trajectory of the outermost particles.

Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

DTIC Science & Technology

2011-04-01

L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

The effect of magnetohydrodynamic nano fluid flow through porous cylinder

NASA Astrophysics Data System (ADS)

Widodo, Basuki; Arif, Didik Khusnul; Aryany, Deviana; Asiyah, Nur; Widjajati, Farida Agustini; Kamiran

2017-08-01

This paper concerns about the analysis of the effect of magnetohydrodynamic nano fluid flow through horizontal porous cylinder on steady and incompressible condition. Fluid flow is assumed opposite gravity and induced by magnet field. Porous cylinder is assumed had the same depth of porous and was not absorptive. The First thing to do in this research is to build the model of fluid flow to obtain dimentional governing equations. The dimentional governing equations are consist of continuity equation, momentum equation, and energy equation. Furthermore, the dimensional governing equations are converted to non-dimensional governing equation by using non-dimensional parameters and variables. Then, the non-dimensional governing equations are transformed into similarity equations using stream function and solved using Keller-Box method. The result of numerical solution further is obtained by taking variation of magnetic parameter, Prandtl number, porosity parameter, and volume fraction. The numerical results show that velocity profiles increase and temperature profiles decrease when both of the magnetic and the porosity parameter increase. However, the velocity profiles decrease and the temperature profiles increase when both of the magnetic and the porosity parameter increase.

Derivation of equations of motion for multi-blade rotors employing coupled modes and including high twist capability

NASA Technical Reports Server (NTRS)

Sopher, R.

1975-01-01

The equations of motion are derived for a multiblade rotor. A high twist capability and coupled flatwise-edgewise assumed normal modes are employed instead of uncoupled flatwise - edgewise assumed normal models. The torsion mode is uncoupled. Support system models, consisting of complete helicopters in free flight, or grounded flexible supports, arbitrary rotor-induced inflow, and arbitrary vertical gust models are also used.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

ERIC Educational Resources Information Center

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

Documentation of a numerical code for the simulation of variable density ground-water flow in three dimensions

USGS Publications Warehouse

Kuiper, L.K.

1985-01-01

A numerical code is documented for the simulation of variable density time dependent groundwater flow in three dimensions. The groundwater density, although variable with distance, is assumed to be constant in time. The Integrated Finite Difference grid elements in the code follow the geologic strata in the modeled area. If appropriate, the determination of hydraulic head in confining beds can be deleted to decrease computation time. The strongly implicit procedure (SIP), successive over-relaxation (SOR), and eight different preconditioned conjugate gradient (PCG) methods are used to solve the approximating equations. The use of the computer program that performs the calculations in the numerical code is emphasized. Detailed instructions are given for using the computer program, including input data formats. An example simulation and the Fortran listing of the program are included. (USGS)

Self-consistent electrostatic potential due to trapped plasma in the magnetosphere

NASA Technical Reports Server (NTRS)

Miller, Ronald H.; Khazanov, George V.

1993-01-01

A steady state solution for the self-consistent electrostatic potential due to a plasma confined in a magnetic flux tube is considered. A steady state distribution function is constructed for the trapped particles from the constants of the motion, in the absence of waves and collisions. Using Liouville's theorem, the particle density along the geomagnetic field is determined and found to depend on the local magnetic field, self-consistent electric potential, and the equatorial plasma distribution function. A hot anisotropic magnetospheric plasma in steady state is modeled by a bi-Maxwellian at the equator. The self-consistent electric potential along the magnetic field is calculated assuming quasineutrality, and the potential drop is found to be approximately equal to the average kinetic energy of the equatorially trapped plasma. The potential is compared with that obtained by Alfven and Faelthammar (1963).

A fast numerical method for ideal fluid flow in domains with multiple stirrers

NASA Astrophysics Data System (ADS)

Nasser, Mohamed M. S.; Green, Christopher C.

2018-03-01

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

A new model of arterial hemodynamics.

PubMed

Branzan, M; Sundri, G

1983-01-01

The determination of arterial blood flow parameters on the basis of ultrasound investigation requires a new hydrodynamic model of arterial circulation. Unlike previous research (Womersley, Bergel) considering the arterial pressure of its gradients to be known, the present model uses blood flow velocity and arterial radius magnitude easily obtained by ultrasound (Doppler effect). Processing these data requires the thorough analysis of rheological characteristics of blood flow and of arterial wall behaviour (elastic deformability). It has been assumed that: a) blood is a homogeneous and isotropic fluid; b) the artery has a cylindrical symmetry of a circular cross-section at any time moment; c) the pressure in the artery cross-section is constant. Because arterial dynamics has an undulatory character the Fourier analysis of the modified Navier-Stokes equations has been used. Finally, a simplified relation for blood pressure determination has been obtained.

Numerical simulation of nanofluids based on power-law fluids with flow and heat transfer

NASA Astrophysics Data System (ADS)

Li, Lin; Jiang, Yongyue; Chen, Aixin

2017-04-01

In this paper, we investigate the heat transfer of nanofluids based on power-law fluids and movement of nanoparticles with the effect of thermophoresis in a rotating circular groove. The velocity of circular groove rotating is a constant and the temperature on the wall is kept to be zero all the time which is different from the temperature of nanofluids in the initial time. The effects of thermophoresis and Brownian diffusion are considered in temperature and concentration equations, and it is assumed that the thermal conductivity of nanofluids is a function of concentration of nanoparticles. Based on numerical results, it can be found that nanofluids improve the process of heat transfer than base fluids in a rotating circular groove. The enhancement of heat transfer increases as the power law index of base fluids decreases.

HZETRN: A heavy ion/nucleon transport code for space radiations

NASA Technical Reports Server (NTRS)

Wilson, John W.; Chun, Sang Y.; Badavi, Forooz F.; Townsend, Lawrence W.; Lamkin, Stanley L.

1991-01-01

The galactic heavy ion transport code (GCRTRN) and the nucleon transport code (BRYNTRN) are integrated into a code package (HZETRN). The code package is computer efficient and capable of operating in an engineering design environment for manned deep space mission studies. The nuclear data set used by the code is discussed including current limitations. Although the heavy ion nuclear cross sections are assumed constant, the nucleon-nuclear cross sections of BRYNTRN with full energy dependence are used. The relation of the final code to the Boltzmann equation is discussed in the context of simplifying assumptions. Error generation and propagation is discussed, and comparison is made with simplified analytic solutions to test numerical accuracy of the final results. A brief discussion of biological issues and their impact on fundamental developments in shielding technology is given.

The lateral/directional stability characteristics of a four-propeller tilt-wing V/STOL model in low-speed steep descent. M.S. Thesis - Princeton Univ., N.J.

NASA Technical Reports Server (NTRS)

Dicarlo, D. J.

1971-01-01

Lateral-directional dynamic stability derivatives are presented for a O.1-scale model of the XC-142A tilt-wing transport. The tests involved various descending flight conditions achieved at constant speed and wing incidence by varying the vehicle angle of attack. The propeller blade angle and the speed were also changed in the steepest descent case. The experimental data were analyzed assuming that the dynamic motions of the vehicle may be described by linearized equations, with the lateral-directional characteristics of the full-scale aircraft also presented and discussed. Results from this experimental investigation indicated that the full-scale aircraft would have a stable lateral-directional motion in level flight, with the dynamic motion becoming less stable as the descent angle was increased.

Tensile stress-strain behavior of boron/aluminum laminates

NASA Technical Reports Server (NTRS)

Sova, J. A.; Poe, C. C., Jr.

1978-01-01

The tensile stress-strain behavior of five types of boron/aluminum laminates was investigated. Longitudinal and transverse stress-strain curves were obtained for monotonic loading to failure and for three cycles of loading to successively higher load levels. The laminate strengths predicted by assuming that the zero deg plies failed first correlated well with the experimental results. The stress-strain curves for all the boron/aluminum laminates were nonlinear except at very small strains. Within the small linear regions, elastic constants calculated from laminate theory corresponded to those obtained experimentally to within 10 to 20 percent. A limited amount of cyclic loading did not affect the ultimate strength and strain for the boron/aluminum laminates. The laminates, however, exhibited a permanent strain on unloading. The Ramberg-Osgood equation was fitted to the stress-strain curves to obtain average curves for the various laminates.

X-ray Reflected Spectra from Accretion Disk Models. I. Constant Density Atmospheres

NASA Technical Reports Server (NTRS)

Garcia, Javier; Kallman, Timothy R.

2009-01-01

We present new models for illuminated accretion disks, their structure and reprocessed emission. We consider the effects of incident X-rays on the surface of an accretion disk by solving simultaneously the equations of radiative transfer, energy balance and ionization equilibrium over a large range of column densities. We assume plane-parallel geometry and azimuthal symmetry, such that each calculation corresponds to a ring at a given distance from the central object. Our models include recent and complete atomic data for K-shell of the iron and oxygen isonuclear sequences. We examine the effect on the spectrum of fluorescent Ka line emission and absorption in the emitted spectrum. We also explore the dependence of the spectrum on the strength of the incident X-rays and other input parameters, and discuss the importance of Comptonization on the emitted spectrum.

Reliable and accurate extraction of Hamaker constants from surface force measurements.

PubMed

Miklavcic, S J

2018-08-15

A simple and accurate closed-form expression for the Hamaker constant that best represents experimental surface force data is presented. Numerical comparisons are made with the current standard least squares approach, which falsely assumes error-free separation measurements, and a nonlinear version assuming independent measurements of force and separation are subject to error. The comparisons demonstrate that not only is the proposed formula easily implemented it is also considerably more accurate. This option is appropriate for any value of Hamaker constant, high or low, and certainly for any interacting system exhibiting an inverse square distance dependent van der Waals force. Copyright © 2018 Elsevier Inc. All rights reserved.

Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

ERIC Educational Resources Information Center

Moses, Tim; Liu, Jinghua

2011-01-01

In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT).

PubMed

Biswas, M E; Chatzis, I; Ioannidis, M A; Chen, P

2005-06-01

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)

Inverse construction of the ΛLTB model from a distance-redshift relation

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

Tokutake, Masato; Yoo, Chul-Moon, E-mail: tokutake@gravity.phys.nagoya-u.ac.jp, E-mail: yoo@gravity.phys.nagoya-u.ac.jp

2016-10-01

Spherically symmetric dust universe models with a positive cosmological constant Λ, known as Λ-Lemaȋtre-Tolman-Bondi (ΛLTB) models, are considered. We report a method to construct the ΛLTB model from a given distance-redshift relation observed at the symmetry center. The spherical inhomogeneity is assumed to be composed of growing modes. We derive a set of ordinary differential equations for three functions of the redshift, which specify the spherical inhomogeneity. Once a distance-redshift relation is given, with careful treatment of possible singular points, we can uniquely determine the model by solving the differential equations for each value of Λ. As a demonstration, wemore » fix the distance-redshift relation as that of the flat ΛCDM model with (Ω{sup dis}{sub m0}, Ω{sup dis}{sub Λ0})=(0.3,0.7), where Ω{sup dis}{sub m0} and Ω{sup dis}{sub Λ0} are the normalized matter density and the cosmological constant, respectively. Then, we construct the ΛLTB model for several values of Ω{sub Λ0}:=Λ/(3 H {sub 0}{sup 2}), where H {sub 0} is the present Hubble parameter observed at the symmetry center. We obtain void (over dense) structure around the symmetry center for Ω{sub Λ0} < Ω{sup dis}{sub Λ0}(Ω{sub Λ0} > Ω{sup dis}{sub Λ0}). We show the relation between the ratio Ω{sub Λ0}/Ω{sup dis}{sub Λ0} and the amplitude of the inhomogeneity.« less

A simple thermodynamic model useful for calculating gas solubilities in water/brine/hydrocarbon mixtures from 0 to 250 C and 1 to 150 bars

NASA Astrophysics Data System (ADS)

Perez, R. J.; Shevalier, M.; Hutcheon, I.

2004-05-01

Gas solubility is of considerable interest, not only for the theoretical understanding of vapor-liquid equilibria, but also due to extensive applications in combined geochemical, engineering, and environmental problems, such as greenhouse gas sequestration. Reliable models for gas solubility calculations in salt waters and hydrocarbons are also valuable when evaluating fluid inclusions saturated with gas components. We have modeled the solubility of methane, ethane, hydrogen, carbon dioxide, hydrogen sulfide, and five other gases in a water-brine-hydrocarbon system by solving a non-linear system of equations composed by modified Henry's Law Constants (HLC), gas fugacities, and assuming binary mixtures. HLCs are a function of pressure, temperature, brine salinity, and hydrocarbon density. Experimental data of vapor pressures and mutual solubilities of binary mixtures provide the basis for the calibration of the proposed model. It is demonstrated that, by using the Setchenow equation, only a relatively simple modification of the pure water model is required to assess the solubility of gases in brine solutions. Henry's Law constants for gases in hydrocarbons are derived using regular solution theory and Ostwald coefficients available from the literature. We present a set of two-parameter polynomial expressions, which allow simple computation and formulation of the model. Our calculations show that solubility predictions using modified HLCs are acceptable within 0 to 250 C, 1 to 150 bars, salinity up to 5 molar, and gas concentrations up to 4 molar. Our model is currently being used in the IEA Weyburn CO2 monitoring and storage project.

Dynamics of viscous cosmologies in the full Israel-Stewart formalism

NASA Astrophysics Data System (ADS)

Lepe, Samuel; Otalora, Giovanni; Saavedra, Joel

2017-07-01

A detailed dynamical analysis for a bulk viscosity model in the full Israel-Stewart formalism for a spatially flat Friedmann-Robertson-Walker universe is performed. In our study we have considered the total cosmic fluid constituted by radiation, dark matter, and dark energy. The dark matter fluid is treated as an imperfect fluid which has a bulk viscosity that depends on its energy density in the usual form ξ (ρm)=ξ0ρm1 /2, whereas the other components are assumed to behave as perfect fluids with constant equation of state parameter. We show that the thermal history of the Universe is reproduced provided that the viscous coefficient satisfies the condition ξ0≪1 , either for a zero or a suitable nonzero coupling between dark energy and viscous dark matter. In this case, the final attractor is a dark-energy-dominated, accelerating universe, with an effective equation of state parameter in the quintessence-like, cosmological constant-like, or phantom-like regime, in agreement with observations. As our main result, we show that in order to obtain a viable cosmological evolution and at the same time alleviating the cosmological coincidence problem via the mechanism of scaling solution, an explicit interaction between dark energy and viscous dark matter seems inevitable. This result is consistent with the well-known fact that models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. Furthermore, by insisting on above, we show that in the present context a phantom nature of this interacting dark energy fluid is also favored.

Stability of Rigidly Rotating Relativistic Stars with Soft Equations of State against Gravitational Collapse

NASA Astrophysics Data System (ADS)

Shibata, Masaru

2004-04-01

We study secular stability against a quasi-radial oscillation for rigidly rotating stars with soft equations of state in general relativity. The polytropic equations of state with polytropic index n between 3 and 3.05 are adopted for modeling the rotating stars. The stability is determined in terms of the turning-point method. It is found that (1) for n>~3.04, all the rigidly rotating stars are unstable against the quasi-radial oscillation and (2) for n>~3.01, the nondimensional angular momentum parameter q≡cJ/GM2 (where J, M, G, and c denote the angular momentum, the gravitational mass, the gravitational constant, and the speed of light, respectively) for all marginally stable rotating stars is larger than unity. A semianalytic calculation is also performed, and good agreement with the numerical results is confirmed. The final outcome after axisymmetric gravitational collapse of rigidly rotating and marginally stable massive stars with q>1 is predicted, assuming that the rest-mass distribution as a function of the specific angular momentum is preserved and that the pressure never halt the collapse. It is found that even for 1~2.5, the significant angular momentum will prevent the direct formation of a black hole.

Extended lattice Boltzmann scheme for droplet combustion.

PubMed

Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

2017-05-01

The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

Electric analog of three-dimensional flow to wells and its application to unconfined aquifers

USGS Publications Warehouse

Stallman, Robert W.

1963-01-01

Electric-analog design criteria are established from the differential equations of ground-water flow for analyzing pumping-test data. A convenient analog design was obtained by transforming the cylindrical equation of flow to a rectilinear form. The design criteria were applied in the construction of an electric analog, which was used for studying pumping-test data collected near Grand Island, Nebr. Data analysis indicated (1) vertical flow components near pumping wells in unconfined aquifers may be much more significant in the control of water-table decline than radial flow components for as much as a day of pumping; (2) the specific yield during the first few minutes of pumping appears to be a very small fraction of that observed after pumping for more than 1 day; and (3) estimates of specific yield made from model studies seem much more sensitive to variations in assumed flow conditions than are estimates of permeability. Analysis of pumping-test data where vertical flow components are important requires that the degree of anisotropy be known. A procedure for computing anisotropy directly from drawdowns observed at five points was developed. Results obtained in the analog study emphasize the futility of calculating unconfined aquifer properties from pumping tests of short duration by means of equations based on the assumptions that vertical flow components are negligible and specific yield is constant.

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

Earthquake triggering by transient and static deformations

USGS Publications Warehouse

Gomberg, J.; Beeler, N.M.; Blanpied, M.L.; Bodin, P.

1998-01-01

Observational evidence for both static and transient near-field and far-field triggered seismicity are explained in terms of a frictional instability model, based on a single degree of freedom spring-slider system and rate- and state-dependent frictional constitutive equations. In this study a triggered earthquake is one whose failure time has been advanced by ??t (clock advance) due to a stress perturbation. Triggering stress perturbations considered include square-wave transients and step functions, analogous to seismic waves and coseismic static stress changes, respectively. Perturbations are superimposed on a constant background stressing rate which represents the tectonic stressing rate. The normal stress is assumed to be constant. Approximate, closed-form solutions of the rate-and-state equations are derived for these triggering and background loads, building on the work of Dieterich [1992, 1994]. These solutions can be used to simulate the effects of static and transient stresses as a function of amplitude, onset time t0, and in the case of square waves, duration. The accuracies of the approximate closed-form solutions are also evaluated with respect to the full numerical solution and t0. The approximate solutions underpredict the full solutions, although the difference decreases as t0, approaches the end of the earthquake cycle. The relationship between ??t and t0 differs for transient and static loads: a static stress step imposed late in the cycle causes less clock advance than an equal step imposed earlier, whereas a later applied transient causes greater clock advance than an equal one imposed earlier. For equal ??t, transient amplitudes must be greater than static loads by factors of several tens to hundreds depending on t0. We show that the rate-and-state model requires that the total slip at failure is a constant, regardless of the loading history. Thus a static load applied early in the cycle, or a transient applied at any time, reduces the stress at the initiation of failure, whereas static loads that are applied sufficiently late raise it. Rate-and-state friction predictions differ markedly from those based on Coulomb failure stress changes (??CFS) in which ??t equals the amplitude of the static stress change divided by the background stressing rate. The ??CFS model assumes a stress failure threshold, while the rate-and-state equations require a slip failure threshold. The complete rale-and-state equations predict larger ??t than the ??CFS model does for static stress steps at small t0, and smaller ??t than the ??CFS model for stress steps at large t0. The ??CFS model predicts nonzero ??t only for transient loads that raise the stress to failure stress levels during the transient. In contrast, the rate-and-state model predicts nonzero ??t for smaller loads, and triggered failure may occur well after the transient is finished. We consider heuristically the effects of triggering on a population of faults, as these effects might be evident in seismicity data. Triggering is manifest as an initial increase in seismicity rate that may be followed by a quiescence or by a return to the background rate. Available seismicity data are insufficient to discriminate whether triggered earthquakes are "new" or clock advanced. However, if triggering indeed results from advancing the failure time of inevitable earthquakes, then our modeling suggests that a quiescence always follows transient triggering and that the duration of increased seismicity also cannot exceed the duration of a triggering transient load. Quiescence follows static triggering only if the population of available faults is finite.

Nonquaternary Cholinesterase Reactivators.

DTIC Science & Technology

1982-08-30

c, a plot (not shown) of pKa versus Hammet substituent constant (a )42 is also linear and conforms p to equation (5) pKa - (7.63 ±0.02) - (.63 ±0.05...dissociates to the active oximate form, we have defined an effective bimolecular reactivation rate constant as in equation (6) keff ’ kb [1 + antilog(pKa...type 1 compounds generally exhibit low activity as reactivators. In terms of keff values [see equation (6)] for reactivation of ethyl methylphosphonyl

Stability analysis for acoustic wave propagation in tilted TI media by finite differences

NASA Astrophysics Data System (ADS)

Bakker, Peter M.; Duveneck, Eric

2011-05-01

Several papers in recent years have reported instabilities in P-wave modelling, based on an acoustic approximation, for inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media). In particular, instabilities tend to occur if the axis of symmetry varies rapidly in combination with strong contrasts of medium parameters, which is typically the case at the foot of a steeply dipping salt flank. In a recent paper, we have proposed and demonstrated a P-wave modelling approach for TTI media, based on rotated stress and strain tensors, in which the wave equations reduce to a coupled set of two second-order partial differential equations for two scalar stress components: a normal component along the variable axis of symmetry and a lateral component of stress in the plane perpendicular to that axis. Spatially constant density is assumed in this approach. A numerical discretization scheme was proposed which uses discrete second-derivative operators for the non-mixed second-order derivatives in the wave equations, and combined first-derivative operators for the mixed second-order derivatives. This paper provides a complete and rigorous stability analysis, assuming a uniformly sampled grid. Although the spatial discretization operator for the TTI acoustic wave equation is not self-adjoint, this operator still defines a complete basis of eigenfunctions of the solution space, provided that the solution space is somewhat restricted at locations where the medium is elliptically anisotropic. First, a stability analysis is given for a discretization scheme, which is purely based on first-derivative operators. It is shown that the coefficients of the central difference operators should satisfy certain conditions. In view of numerical artefacts, such a discretization scheme is not attractive, and the non-mixed second-order derivatives of the wave equation are discretized directly by second-derivative operators. It is shown that this modification preserves stability, provided that the central difference operators of the second-order derivatives dominate over the twice applied operators of the first-order derivatives. In practice, it turns out that this is almost the case. Stability of the desired discretization scheme is enforced by slightly weighting down the mixed second-order derivatives in the wave equation. This has a minor, practically negligible, effect on the kinematics of wave propagation. Finally, it is shown that non-reflecting boundary conditions, enforced by applying a taper at the boundaries of the grid, do not harm the stability of the discretization scheme.

Strange stars in f(R,Script T) gravity

NASA Astrophysics Data System (ADS)

Deb, Debabrata; Rahaman, Farook; Ray, Saibal; Guha, B. K.

2018-03-01

In this article we try to present spherically symmetric isotropic strange star model under the framework of f(R,Script T) theory of gravity. To this end, we consider that the Lagrangian density is a linear function of the Ricci scalar R and the trace of the energy momentum tensor Script T given as f(R,Script T)=R+2χ Script T. We also assume that the quark matter distribution is governed by the simplest form of the MIT bag model equation of state (EOS) as p=1/3(ρ‑4B), where B is the bag constant. We have obtained an exact solution of the modified form of the Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of f(R,Script T) gravity theory and have studied the dependence of different physical properties, viz., the total mass, radius, energy density and pressure for the chosen values of χ. Further, to examine physical acceptability of the proposed stellar model, we have conducted different tests in detail, viz., the energy conditions, modified TOV equation, mass-radius relation, causality condition etc. We have precisely explained the effects arising due to the coupling of the matter and geometry on the compact stellar system. For a chosen value of the bag constant, we have predicted numerical values of the different physical parameters in tabular form for the different strange star candidates. It is found that as the factor χ decreases the strange star candidates become gradually massive and larger in size with less dense stellar configuration. However, when χ increases the stars shrink gradually and become less massive to turn into a more compact stellar system. Hence for χ>0 our proposed model is suitable to explain the ultra-dense compact stars well within the observational limits and for χ<0 case allows to represent the recent massive pulsars and super-Chandrasekhar stars. For χ=0 we retrieve as usual the standard results of the general relativity (GR).

Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface

NASA Astrophysics Data System (ADS)

Coons, Marc P.; Herbert, John M.

2018-06-01

Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ɛ. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ɛ(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F-(aq), Cl-(aq), neat liquid water, and the hydrated electron, although errors for Li+(aq) and Na+(aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.

Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface.

PubMed

Coons, Marc P; Herbert, John M

2018-06-14

Widely used continuum solvation models for electronic structure calculations, including popular polarizable continuum models (PCMs), usually assume that the continuum environment is isotropic and characterized by a scalar dielectric constant, ε. This assumption is invalid at a liquid/vapor interface or any other anisotropic solvation environment. To address such scenarios, we introduce a more general formalism based on solution of Poisson's equation for a spatially varying dielectric function, ε(r). Inspired by nonequilibrium versions of PCMs, we develop a similar formalism within the context of Poisson's equation that includes the out-of-equilibrium dielectric response that accompanies a sudden change in the electron density of the solute, such as that which occurs in a vertical ionization process. A multigrid solver for Poisson's equation is developed to accommodate the large spatial grids necessary to discretize the three-dimensional electron density. We apply this methodology to compute vertical ionization energies (VIEs) of various solutes at the air/water interface and compare them to VIEs computed in bulk water, finding only very small differences between the two environments. VIEs computed using approximately two solvation shells of explicit water molecules are in excellent agreement with experiment for F - (aq), Cl - (aq), neat liquid water, and the hydrated electron, although errors for Li + (aq) and Na + (aq) are somewhat larger. Nonequilibrium corrections modify VIEs by up to 1.2 eV, relative to models based only on the static dielectric constant, and are therefore essential to obtain agreement with experiment. Given that the experiments (liquid microjet photoelectron spectroscopy) may be more sensitive to solutes situated at the air/water interface as compared to those in bulk water, our calculations provide some confidence that these experiments can indeed be interpreted as measurements of VIEs in bulk water.

The Thomas-Fermi model in the theory of systems of charged particles above the surface of liquid dielectrics

NASA Astrophysics Data System (ADS)

Lytvtnenko, D. M.; Slyusarenko, Yu. V.; Kirdin, A. I.

2012-10-01

A consistent theory of equilibrium states of same sign charges above the surface of liquid dielectric film located on solid substrate in the presence of external attracting constant electric field is proposed. The approach to the development of the theory is based on the Thomas-Fermi model generalized to the systems under consideration and on the variational principle. The using of self-consistent field model allows formulating a theory containing no adjustable constants. In the framework of the variational principle we obtain the self-consistency equations for the parameters describing the system: the distribution function of charges above the liquid dielectric surface, the electrostatic field potentials in all regions of the system and the surface profile of the liquid dielectric. The self-consistency equations are used to describe the phase transition associated with the formation of spatially periodic structures in the system of charges on liquid dielectric surface. Assuming the non-degeneracy of the gas of charges above the surface of liquid dielectric film the solutions of the self-consistency equations near the critical point are obtained. In the case of the symmetric phase we obtain the expressions for the potentials and electric fields in all regions of the studied system. The distribution of the charges above the surface of liquid dielectric film for the symmetric phase is derived. The system parameters of the phase transition to nonsymmetric phase - the states with a spatially periodic ordering are obtained. We derive the expression determining the period of two-dimensional lattice as a function of physical parameters of the problem - the temperature, the external attractive electric field, the number of electrons per unit of the flat surface area of the liquid dielectric, the density of the dielectric, its surface tension and permittivity, and the permittivity of the solid substrate. The possibility of generalizing the developed theory in the case of degenerate gas of like-charged particles above the liquid dielectric surface is discussed.

A General Linear Method for Equating with Small Samples

ERIC Educational Resources Information Center

Albano, Anthony D.

2015-01-01

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

Universality of P - V criticality in horizon thermodynamics

NASA Astrophysics Data System (ADS)

Hansen, Devin; Kubizňák, David; Mann, Robert B.

2017-01-01

We study P - V criticality of black holes in Lovelock gravities in the context of horizon thermodynamics. The corresponding first law of horizon thermodynamics emerges as one of the Einstein-Lovelock equations and assumes the universal (independent of matter content) form δ E = T δ S - P δ V , where P is identified with the total pressure of all matter in the spacetime (including a cosmological constant Λ if present). We compare this approach to recent advances in extended phase space thermodynamics of asymptotically AdS black holes where the `standard' first law of black hole thermodynamics is extended to include a pressure-volume term, where the pressure is entirely due to the (variable) cosmological constant. We show that both approaches are quite different in interpretation. Provided there is sufficient non-linearity in the gravitational sector, we find that horizon thermodynamics admits the same interesting black hole phase behaviour seen in the extended case, such as a Hawking-Page transition, Van der Waals like behaviour, and the presence of a triple point. We also formulate the Smarr formula in horizon thermodynamics and discuss the interpretation of the quantity E appearing in the horizon first law.

Calculating tracer currents through narrow ion channels: Beyond the independent particle model.

PubMed

Coalson, Rob D; Jasnow, David

2018-06-01

Discrete state models of single-file ion permeation through a narrow ion channel pore are employed to analyze the ratio of forward to backward tracer current. Conditions under which the well-known Ussing formula for this ratio hold are explored in systems where ions do not move independently through the channel. Building detailed balance into the rate constants for the model in such a way that under equilibrium conditions (equal rate of forward vs. backward permeation events) the Nernst Equation is satisfied, it is found that in a model where only one ion can occupy the channel at a time, the Ussing formula is always obeyed for any number of binding sites, reservoir concentrations of the ions and electric potential difference across the membrane which the ion channel spans, independent of the internal details of the permeation pathway. However, numerical analysis demonstrates that when multiple ions can occupy the channel at once, the nonequilibrium forward/backward tracer flux ratio deviates from the prediction of the Ussing model. Assuming an appropriate effective potential experienced by ions in the channel, we provide explicit formulae for the rate constants in these models. © 2018 IOP Publishing Ltd.

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.

How things fall apart: understanding the nature of internalizing through its relationship with impairment.

PubMed

Markon, Kristian E

2010-08-01

The literature suggests that internalizing psychopathology relates to impairment incrementally and gradually. However, the form of this relationship has not been characterized. This form is critical to understanding internalizing psychopathology, as it is possible that internalizing may accelerate in effect at some level of severity, defining a natural boundary of abnormality. Here, a novel method-semiparametric structural equation modeling-was used to model the relationship between internalizing and impairment in a sample of 8,580 individuals from the 2000 British Office for National Statistics Survey of Psychiatric Morbidity, a large, population-representative study of psychopathology. This method allows one to model relationships between latent internalizing and impairment without assuming any particular form a priori and to compare models in which the relationship is constant and linear. Results suggest that the relationship between internalizing and impairment is in fact linear and constant across the entire range of internalizing variation and that it is impossible to nonarbitrarily define a specific level of internalizing beyond which consequences suddenly become catastrophic in nature. Results demonstrate the phenomenological continuity of internalizing psychopathology, highlight the importance of impairment as well as symptoms, and have clear implications for defining mental disorder. Copyright 2010 APA, all rights reserved

Comparison between solar wind latitude distribution derived from Lyman-alpha observations and Ulysses measurements

NASA Technical Reports Server (NTRS)

Quemarais, E.; Lallement, R.; Bertaux, J. L.; Sandel, B. R.

1995-01-01

The all-sky interplanetary Lyman-alpha pattern is sensitive to the latitude distribution of the solar wind because of destruction of neutral H by charge-exchange with solar wind protons. Lyman-alpha intensities recorded by Prognoz 5 and 6 in 1976 in a few parts of the sky were demonstrating a decrease of solar wind mass flux by about 30 % from equator to pole, when assuming a sinusoidal variation of this mass flux (harmonic distribution). A new analysis with a discrete variation with latitude has shown a decrease from 0 to 30 deg and then a plateau of constant mass flux up to the pole. This distribution bears a striking resemblance with Ulysses in-situ measurements, showing a clear similarity at 19 years interval. The Ulysses measurements were then used as a model input to calculate an all-sky Lyman-alpha pattern, either with a discrete model or with a harmonic solar wind variation with the same Ulysses equator-to-pole variation. There are conspicuous differences between the two Lyman-alpha patterns, in particular in the downwind region which are discussed in the context of future all-sky measurements with SWAN experiment on SOHO.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations

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

Madanu, Sushma B.; Barbel, Stanley I.; Ward, Thomas

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude ofmore » vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.« less

Investigation of energy dissipation due to contact angle hysteresis in capillary effect

NASA Astrophysics Data System (ADS)

Athukorallage, Bhagya; Iyer, Ram

2016-06-01

Capillary action or Capillarity is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to, external forces like gravity. Three effects contribute to capillary action, namely, adhesion of the liquid to the walls of the confining solid; meniscus formation; and low Reynolds number fluid flow. We investigate the dissipation of energy during one cycle of capillary action, when the liquid volume inside a capillary tube first increases and subsequently decreases while assuming quasi-static motion. The quasi-static assumption allows us to focus on the wetting phenomenon of the solid wall by the liquid and the formation of the meniscus. It is well known that the motion of a liquid on an non-ideal surface involves the expenditure of energy due to contact angle hysteresis. In this paper, we derive the equations for the menisci and the flow rules for the change of the contact angles for a liquid column in a capillary tube at a constant temperature and volume by minimizing the Helmholtz free energy using calculus of variations. We describe the numerical solution of these equations and present results from computations for the case of a capillary tube with 1 mm diameter.

Phase retrieval with tunable phase transfer function based on the transport of intensity equation

NASA Astrophysics Data System (ADS)

Martinez-Carranza, J.; Stepien, P.; Kozacki, T.

2017-06-01

Recovering phase information with Deterministic approaches as the Transport of Intensity Equation (TIE) has recently emerged as an alternative tool to the interferometric techniques because it is experimentally easy to implement and provides fast and accurate results. Moreover, the potential of employing partially coherent illumination (PCI) in such techniques allow obtaining high quality phase reconstructions providing that the estimation of the corresponding Phase Transfer Function (PTF) is carried out correctly. Hence, accurate estimation of the PTF requires that the physical properties of the optical system are well known. Typically, these parameters are assumed constant in all the set of measurements, which might not be optimal. In this work, we proposed the use of an amplitude Spatial Light Modulator (aSLM) for tuning the degree of coherence of the optical system. The aSLM will be placed at the Fourier plane of the optical system, and then, band pass filters will be displayed. This methodology will perform amplitude modulation of the propagated field and as a result, the state of coherence of the optical system can be modified. Theoretical and experimental results that validate our proposed technique will be shown.

Modeling the effect of water on mantle rheology

NASA Technical Reports Server (NTRS)

Bounama, CH.; Franck, S.

1994-01-01

To study the thermal history of the Earth we use a parameterized model of mantle convection. This model includes a mathematical description of de- and regassing processes of water from the Earth's mantle. The rates of this processes are considered to be directly proportional to the seafloor spreading rate. The kinematic viscosity of the mantle depends on the temperature/pressure as well as on the volatile content. Dissolved volatiles such as water weaken the minerals by reducing their activation energy for solid state creep. Karato and Toriumi showed a power law dependence between creep rate and water fugacity derived from experimental results. Therefore, we use such flow parameters of diffusion creep in olivine under wet and dry conditions to calculate the mantle viscosity as a function of the water content. Because the creep rate is proportional to the concentration of water-related point deflects we assume that the water fugacity is proportional to the water weight fraction. An equation for the steady-state strain rate under wet conditions is established. To assess the unknown constant K in this equation, we use flow law parameters given by Karato and Wu as well as the results of McGovern and Schubert.

Exact analytical formulae for linearly distributed vortex and source sheets in uence computation in 2D vortex methods

NASA Astrophysics Data System (ADS)

Kuzmina, K. S.; Marchevsky, I. K.; Ryatina, E. P.

2017-11-01

We consider the methodology of numerical schemes development for two-dimensional vortex method. We describe two different approaches to deriving integral equation for unknown vortex sheet intensity. We simulate the velocity of the surface line of an airfoil as the influence of attached vortex and source sheets. We consider a polygonal approximation of the airfoil and assume intensity distributions of free and attached vortex sheets and attached source sheet to be approximated with piecewise constant or piecewise linear (continuous or discontinuous) functions. We describe several specific numerical schemes that provide different accuracy and have a different computational cost. The study shows that a Galerkin-type approach to solving boundary integral equation requires computing several integrals and double integrals over the panels. We obtain exact analytical formulae for all the necessary integrals, which makes it possible to raise significantly the accuracy of vortex sheet intensity computation and improve the quality of velocity and vorticity field representation, especially in proximity to the surface line of the airfoil. All the formulae are written down in the invariant form and depend only on the geometric relationship between the positions of the beginnings and ends of the panels.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates

NASA Astrophysics Data System (ADS)

Shah, Zahir; Islam, Saeed; Gul, Taza; Bonyah, Ebenezer; Altaf Khan, Muhammad

2018-06-01

The current research aims to examine the combined effect of magnetic and electric field on micropolar nanofluid between two parallel plates in a rotating system. The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid has been assumed in steady state. The rudimentary governing equations have been changed to a set of differential nonlinear and coupled equations using suitable similarity variables. An optimal approach has been used to acquire the solution of the modelled problems. The convergence of the method has been shown numerically. The impact of the Skin friction on velocity profile, Nusslet number on temperature profile and Sherwood number on concentration profile have been studied. The influences of the Hall currents, rotation, Brownian motion and thermophoresis analysis of micropolar nanofluid have been mainly focused in this work. Moreover, for comprehension the physical presentation of the embedded parameters that is, coupling parameter N1 , viscosity parameter Re , spin gradient viscosity parameter N2 , rotating parameter Kr , Micropolar fluid constant N3 , magnetic parameter M , Prandtl number Pr , Thermophoretic parameter Nt , Brownian motion parameter Nb , and Schmidt number Sc have been plotted and deliberated graphically.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Cosmological Constant: A Lesson from Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Finazzi, Stefano; Liberati, Stefano; Sindoni, Lorenzo

2012-02-01

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.

Cosmological constant: a lesson from Bose-Einstein condensates.

PubMed

Finazzi, Stefano; Liberati, Stefano; Sindoni, Lorenzo

2012-02-17

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms. [in early star atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Kunasz, P. B.

1978-01-01

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Current interactions from the one-form sector of nonlinear higher-spin equations

NASA Astrophysics Data System (ADS)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

Finite element analysis of notch behavior using a state variable constitutive equation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.

1985-01-01

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Fragmentation of a Filamentary Cloud Permeated by a Perpendicular Magnetic Field

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

Hanawa, Tomoyuki; Kudoh, Takahiro; Tomisaka, Kohji

We examine the linear stability of an isothermal filamentary cloud permeated by a perpendicular magnetic field. Our model cloud is assumed to be supported by gas pressure against self-gravity in the unperturbed state. For simplicity, the density distribution is assumed to be symmetric around the axis. Also for simplicity, the initial magnetic field is assumed to be uniform, and turbulence is not taken into account. The perturbation equation is formulated to be an eigenvalue problem. The growth rate is obtained as a function of the wavenumber for fragmentation along the axis and the magnetic field strength. The growth rate dependsmore » critically on the outer boundary. If the displacement vanishes in regions very far from the cloud axis (fixed boundary), cloud fragmentation is suppressed by a moderate magnetic field, which means the plasma beta is below 1.67 on the cloud axis. If the displacement is constant along the magnetic field in regions very far from the cloud, the cloud is unstable even when the magnetic field is infinitely strong. The cloud is deformed by circulation in the plane perpendicular to the magnetic field. The unstable mode is not likely to induce dynamical collapse, since it is excited even when the whole cloud is magnetically subcritical. For both boundary conditions, the magnetic field increases the wavelength of the most unstable mode. We find that the magnetic force suppresses compression perpendicular to the magnetic field especially in regions of low density.« less

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

A transport equation for the scalar dissipation in reacting flows with variable density: First results

NASA Technical Reports Server (NTRS)

Mantel, T.

1993-01-01

Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

PubMed

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

PubMed Central

Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M.

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach. PMID:23564972

The Modelling of Axially Translating Flexible Beams

NASA Astrophysics Data System (ADS)

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

1996-04-01

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

The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations.

NASA Technical Reports Server (NTRS)

Cooke, K. L.; Meyer, K. R.

1966-01-01

Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution

HO + CO reaction rates and H/D kinetic isotope effects: master equation models with ab initio SCTST rate constants.

PubMed

Weston, Ralph E; Nguyen, Thanh Lam; Stanton, John F; Barker, John R

2013-02-07

Ab initio microcanonical rate constants were computed using Semi-Classical Transition State Theory (SCTST) and used in two master equation formulations (1D, depending on active energy with centrifugal corrections, and 2D, depending on total energy and angular momentum) to compute temperature-dependent rate constants for the title reactions using a potential energy surface obtained by sophisticated ab initio calculations. The 2D master equation was used at the P = 0 and P = ∞ limits, while the 1D master equation with centrifugal corrections and an empirical energy transfer parameter could be used over the entire pressure range. Rate constants were computed for 75 K ≤ T ≤ 2500 K and 0 ≤ [He] ≤ 10(23) cm(-3). For all temperatures and pressures important for combustion and for the terrestrial atmosphere, the agreement with the experimental rate constants is very good, but at very high pressures and T ≤ 200 K, the theoretical rate constants are significantly smaller than the experimental values. This effect is possibly due to the presence in the experiments of dimers and prereactive complexes, which were not included in the model calculations. The computed H/D kinetic isotope effects are in acceptable agreement with experimental data, which show considerable scatter. Overall, the agreement between experimental and theoretical H/D kinetic isotope effects is much better than in previous work, and an assumption of non-RRKM behavior does not appear to be needed to reproduce experimental observations.

Numerical analysis of flows of rarefied gases in long channels with octagonal cross section shapes

NASA Astrophysics Data System (ADS)

Szalmas, L.

2014-12-01

Isothermal, pressure driven rarefied gas flows through long channels with octagonal cross section shapes are analyzed computationally. The capillary is between inlet and outlet reservoirs. The cross section is constant along the axial direction. The boundary condition at the solid-gas interface is assumed to be diffuse reflection. Since the channel is long, the gaseous velocity is small compared to the average molecular speed. Consequently, a linearized description can be used. The flow is described by the linearized Bhatnagar-Gross-Krook kinetic model. The solution of the problem is divided into two stages. First, the local flow field is determined by assuming the local pressure gradient. Secondly, the global flow behavior is deduced by the consideration of the conservation of the mass along the axis of the capillary. The kinetic equation is solved by the discrete velocity method on the cross section. Both spatial and velocity spaces are discretized. A body fitted rectangular grid is used for the spatial space. Near the boundary, first-order, while in the interior part of the flow domain, second-order finite-differences are applied to approximate the spatial derivatives. This combination results into an efficient and straightforward numerical treatment. The velocity space is represented by a Gauss-Legendre quadrature. The kinetic equation is solved in an iterative manner. The local dimensionless flow rate is calculated and tabulated for a wide range of the gaseous rarefaction for octagonal cross sections with various geometrical parameters. It exhibits the Knudsen minimum phenomenon. The flow rates in the octagonal channel are compared to those through capillaries with circular and square cross sections. Typical velocity profiles are also shown. The mass flow rate and the distribution of the pressure are determined and presented for global pressure driven flows.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

PubMed Central

Koehl, Patrice; Delarue, Marc

2010-01-01

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Van der Waals equation of state revisited: importance of the dispersion correction.

PubMed

de Visser, Sam P

2011-04-28

One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

Gradient estimates on the weighted p-Laplace heat equation

NASA Astrophysics Data System (ADS)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

PubMed

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

Release from or through a wax matrix system. I. Basic release properties of the wax matrix system.

PubMed

Yonezawa, Y; Ishida, S; Sunada, H

2001-11-01

Release properties from a wax matrix tablet was examined. To obtain basic release properties, the wax matrix tablet was prepared from a physical mixture of drug and wax powder (hydrogenated caster oil) at a fixed mixing ratio. Properties of release from the single flat-faced surface or curved side surface of the wax matrix tablet were examined. The applicability of the square-root time law and of Higuchi equations was confirmed. The release rate constant obtained as g/min(1/2) changed with the release direction. However, the release rate constant obtained as g/cm2 x min(1/2) was almost the same. Hence it was suggested that the release property was almost the same and the wax matrix structure was uniform independent of release surface or direction at a fixed mixing ratio. However, these equations could not explain the entire release process. The applicability of a semilogarithmic equation was not as good compared with the square-root time law or Higuchi equation. However, it was revealed that the semilogarithmic equation was available to simulate the entire release process, even though the fit was somewhat poor. Hence it was suggested that the semilogarithmic equation was sufficient to describe the release process. The release rate constant was varied with release direction. However, these release rate constants were expressed by a function of the effective surface area and initial amount, independent of the release direction.

The evolution of human phenotypic plasticity: age and nutritional status at maturity.

PubMed

Gage, Timothy B

2003-08-01

Several evolutionary optimal models of human plasticity in age and nutritional status at reproductive maturation are proposed and their dynamics examined. These models differ from previously published models because fertility is not assumed to be a function of body size or nutritional status. Further, the models are based on explicitly human demographic patterns, that is, model human life-tables, model human fertility tables, and, a nutrient flow-based model of maternal nutritional status. Infant survival (instead of fertility as in previous models) is assumed to be a function of maternal nutritional status. Two basic models are examined. In the first the cost of reproduction is assumed to be a constant proportion of total nutrient flow. In the second the cost of reproduction is constant for each birth. The constant proportion model predicts a negative slope of age and nutritional status at maturation. The constant cost per birth model predicts a positive slope of age and nutritional status at maturation. Either model can account for the secular decline in menarche observed over the last several centuries in Europe. A search of the growth literature failed to find definitive empirical documentation of human phenotypic plasticity in age and nutritional status at maturation. Most research strategies confound genetics with phenotypic plasticity. The one study that reports secular trends suggests a marginally insignificant, but positive slope. This view tends to support the constant cost per birth model.

Analytical Prediction of Lower Leg Injury in a Vehicular Mine Blast Event

DTIC Science & Technology

2010-01-01

the spring constant of the tibia is nearly arbitrary; the spring constant of the boot assumes a hard ethylene propylene diene monomer ( EPDM ) rubber ...the sole of the boot. The significantly lower spring constant of the EPDM rubber in the sole compared to the bone structures greatly diminished the

CYBERSUSY A new mechanism for supersymmetry breaking in models like the Supersymmetric Standard Model (SSM):

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

Dixon, John A.

2010-02-10

The SUSY breaking in Cybersusy is proportional to the VEV that breaks the gauge symmetry SU(2)xU(1) down to U(1), and it is rather specific to models like the SSM. Assuming full breaking, as explained below, for the leptons, Cybersusy predicts a spectrum of SUSY breaking that is in accord with experimental results so far. In particular, for the choice of parameters below, Cybersusy predicts that the lowest mass superpartner for the charged leptons is a charged vector boson lepton (the Velectron), which has a mass of 316 Gev. The Selectron has a mass of 771 Gev for that choice ofmore » parameters. The theory also leads to a zero cosmological constant after SUSY breaking. The mechanism generates equations that restrict models like the SSM. This version of this paper incorporates recent results and changes discovered subsequent to the talk.« less

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1982-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Stresses in adhesively bonded joints: A closed form solution. [plate theory

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1980-01-01

The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

PubMed Central

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, L. F.

2013-01-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. PMID:24204236

Resonance treatment using pin-based pointwise energy slowing-down method

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

Choi, Sooyoung, E-mail: csy0321@unist.ac.kr; Lee, Changho, E-mail: clee@anl.gov; Lee, Deokjung, E-mail: deokjung@unist.ac.kr

A new resonance self-shielding method using a pointwise energy solution has been developed to overcome the drawbacks of the equivalence theory. The equivalence theory uses a crude resonance scattering source approximation, and assumes a spatially constant scattering source distribution inside a fuel pellet. These two assumptions cause a significant error, in that they overestimate the multi-group effective cross sections, especially for {sup 238}U. The new resonance self-shielding method solves pointwise energy slowing-down equations with a sub-divided fuel rod. The method adopts a shadowing effect correction factor and fictitious moderator material to model a realistic pointwise energy solution. The slowing-down solutionmore » is used to generate the multi-group cross section. With various light water reactor problems, it was demonstrated that the new resonance self-shielding method significantly improved accuracy in the reactor parameter calculation with no compromise in computation time, compared to the equivalence theory.« less

The reconstruction of tachyon inflationary potentials

NASA Astrophysics Data System (ADS)

Fei, Qin; Gong, Yungui; Lin, Jiong; Yi, Zhu

2017-08-01

We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of e-folds before the end of inflation. Using the relation between the observables like ns and r with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter wre during reheating is a constant. Depending on the model parameters and the value of wre, the constraints on Nre and Tre are different. As ns increases, the allowed reheating epoch becomes longer for wre=-1/3, 0 and 1/6 while the allowed reheating epoch becomes shorter for wre=2/3.

Interpretation of the Hubble diagram in a nonhomogeneous universe

NASA Astrophysics Data System (ADS)

Fleury, Pierre; Dupuy, Hélène; Uzan, Jean-Philippe

2013-06-01

In the standard cosmological framework, the Hubble diagram is interpreted by assuming that the light emitted by standard candles propagates in a spatially homogeneous and isotropic spacetime. However, the light from “point sources”—such as supernovae—probes the Universe on scales where the homogeneity principle is no longer valid. Inhomogeneities are expected to induce a bias and a dispersion of the Hubble diagram. This is investigated by considering a Swiss-cheese cosmological model, which (1) is an exact solution of the Einstein field equations, (2) is strongly inhomogeneous on small scales, but (3) has the same expansion history as a strictly homogeneous and isotropic universe. By simulating Hubble diagrams in such models, we quantify the influence of inhomogeneities on the measurement of the cosmological parameters. Though significant in general, the effects reduce drastically for a universe dominated by the cosmological constant.

A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation

NASA Astrophysics Data System (ADS)

Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C.

2018-02-01

We investigate the idealized mathematical model of single scatter in PET for a detector system possessing excellent energy resolution. The model has the form of integral transforms estimating the distribution of photons undergoing a single Compton scattering with a certain angle. The total single scatter is interpreted as the volume integral over scatter points that constitute a rotation body with a football shape, while single scattering with a certain angle is evaluated as the surface integral over the boundary of the rotation body. The equations for total and sample single scatter calculations are derived using a single scatter simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion provided that the attenuation map is assumed to be constant. The results of the numerical experiments are presented.

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-06-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Corruption: Taking into account the psychological mimicry of officials

NASA Astrophysics Data System (ADS)

Kolesin, Igor; Malafeyev, Oleg; Andreeva, Mariia; Ivanukovich, Georgiy

2017-07-01

A mathematical model of corruption with regard to psychological mimicry in the administrative apparatus with three forms of corruption is constructed. It is assumed that the change of officials forms of corruption is due to situational factors, and anti-corruption laws imply the change of the dominant form. Form's changing is modeled by the system of four differential equations (including groups of corrupt officials), describing the number of groups. The speed of the transition from group to group is expressed through the frequency of meetings. The controlling influence is expressed through the force of anticorruption laws. Two cases are discussed: strictly constant and variable (depending on the scope of one or another form). The equilibrium states that allow to specify the dominant form and investigate its stability, depending on the parameters of the psychological mimicry and rigor of anti-corruption laws are found and discussed.

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

NASA Astrophysics Data System (ADS)

Meerson, Baruch

2015-05-01

Suppose that a point-like steady source at x = 0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with mean \\bar{N} predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N. We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N.

Laser Doppler velocimeter system simulation for sensing aircraft wake vortices

NASA Technical Reports Server (NTRS)

Thomson, J. A. L.; Meng, J. C. S.

1974-01-01

A hydrodynamic model of aircraft vortex wakes in an irregular wind shear field near the ground is developed and used as a basis for modeling the characteristics of a laser Doppler detection and vortex location system. The trailing vortex sheet and the wind shear are represented by discrete free vortices distributed over a two-dimensional grid. The time dependent hydrodynamic equations are solved by direct numerical integration in the Boussinesq approximation. The ground boundary is simulated by images, and fast Fourier Transform techniques are used to evaluate the vorticity stream function. The atmospheric turbulence was simulated by constructing specific realizations at time equal to zero, assuming that Kolmogoroff's law applies, and that the dissipation rate is constant throughout the flow field. The response of a simulated laser Doppler velocimeter is analyzed by simulating the signal return from the flow field as sensed by a simulation of the optical/electronic system.

Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

NASA Astrophysics Data System (ADS)

Rizov, V.

2016-03-01

Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

Coalescing colony model: Mean-field, scaling, and geometry

NASA Astrophysics Data System (ADS)

Carra, Giulia; Mallick, Kirone; Barthelemy, Marc

2017-12-01

We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth, and is also of great interest for modeling urban sprawl. Assuming the primary colony to be always circular of radius r (t ) and the emission rate proportional to r (t) θ , where θ >0 , we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ , and compare our results with numerical simulations. We then critically test the validity of the circular approximation for the colony shape and show that it is sound for a constant emission rate (θ =0 ). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony cannot be discarded, thus modifying the scaling exponents.

A power-law coupled three-form dark energy model

NASA Astrophysics Data System (ADS)

Yao, Yan-Hong; Yan, Yang-Jie; Meng, Xin-He

2018-02-01

We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter Ω _{m0} and the present three-form field κ X0 gives stringent constraints on the coupling constant, - 0.017< λ <0.047 (2σ confidence level), by which we present the model's applicable parameter range.

Prediction of flyover jet noise spectra from static tests

NASA Astrophysics Data System (ADS)

Michel, U.; Michalke, A.

A scaling law for predicting the overall flyover noise of a single stream shock-free circular jet from static experiments is outlined. It is valid for isothermal and hot jets. It assumes that the jet flow and turbulence field are axially stretched in flight. Effects of the boundary layer within the nozzle and along the engine nacelle are neglected. The scaling laws for the power spectral density and spectra with constant relative bandwidth can be derived. In order to compare static and inflight directivities, the far field point relative to the source position must be denoted by the emission angle and the wave normal distance. From the solution of the convective Lighthill equation in a coordinate system fixed to the jet nozzle (wind tunnel case), the power spectral density of sound pressure at a given frequency is found. Predictions for Aerotrain compare well with measured values.

Tikekar superdense stars in electric fields

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-04-01

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t=constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter K and the electric field intensity parameter α. Consequently, it is possible to find exact solutions in terms of elementary functions, namely, polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [J. Math. Phys. 31, 2454 (1990)] when K=-7 and α=0. Our class of charged spheroidal models generalize the uncharged isotropic Maharaj and Leach solutions [J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

Thermodynamic properties derived from the free volume model of liquids

NASA Technical Reports Server (NTRS)

Miller, R. I.

1974-01-01

An equation of state and expressions for the isothermal compressibility, thermal expansion coefficient, heat capacity, and entropy of liquids have been derived from the free volume model partition function suggested by Turnbull. The simple definition of the free volume is used, and it is assumed that the specific volume is directly related to the cube of the intermolecular separation by a proportionality factor which is found to be a function of temperature and pressure as well as specific volume. When values of the proportionality factor are calculated from experimental data for real liquids, it is found to be approximately constant over ranges of temperature and pressure which correspond to the dense liquid phase. This result provides a single-parameter method for calculating dense liquid thermodynamic properties and is consistent with the fact that the free volume model is designed to describe liquids near the solidification point.

Review of Jones-Wilkins-Lee equation of state

NASA Astrophysics Data System (ADS)

Baudin, G.; Serradeill, R.

The JWL EOS is widely used in different forms (two, three terms) according to the level of accuracy in the pressure-volume domain that applications need. The foundations of the relationship chosen to represent the reference curve, Chapman-Jouguet (CJ) isentrope, can be found assuming that the DP expansion isentrope issued from the CJ point is very nearly coincident with the Crussard curve in the pressure-material velocity plane. Its mathematical expression, using an appropriate relationship between shock velocity and material velocity leads to the exponential terms of the JWL EOS. It well validates the pressure-volume relationship chosen to represent the reference curves for DP. Nevertheless, the assumption of constant Gruneisen coefficient and heat capacity in the EOS thermal part remains the more restrictive assumption. A new derivation of JWL EOS is proposed, using a less restrictive assumption for the Gruneisen coefficient suggested by W.C. Davis to represent both large expansions and near-CJ states.

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-03-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

STEADY-STATE MODEL OF SOLAR WIND ELECTRONS REVISITED

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

Yoon, Peter H.; Kim, Sunjung; Choe, G. S., E-mail: yoonp@umd.edu

2015-10-20

In a recent paper, Kim et al. put forth a steady-state model for the solar wind electrons. The model assumed local equilibrium between the halo electrons, characterized by an intermediate energy range, and the whistler-range fluctuations. The basic wave–particle interaction is assumed to be the cyclotron resonance. Similarly, it was assumed that a dynamical steady state is established between the highly energetic superhalo electrons and high-frequency Langmuir fluctuations. Comparisons with the measured solar wind electron velocity distribution function (VDF) during quiet times were also made, and reasonable agreements were obtained. In such a model, however, only the steady-state solution for themore » Fokker–Planck type of electron particle kinetic equation was considered. The present paper complements the previous analysis by considering both the steady-state particle and wave kinetic equations. It is shown that the model halo and superhalo electron VDFs, as well as the assumed wave intensity spectra for the whistler and Langmuir fluctuations, approximately satisfy the quasi-linear wave kinetic equations in an approximate sense, thus further validating the local equilibrium model constructed in the paper by Kim et al.« less

Papain hydrolysis of X-phenyl-N-methanesulfonyl glycinates: a quantitative structure-activity relationship and molecular graphics analysis.

PubMed

Carotti, A; Smith, R N; Wong, S; Hansch, C; Blaney, J M; Langridge, R

1984-02-15

The hydrolysis of 32 X-phenyl-N-methanesulfonyl glycinates by papain was investigated. It was found that the variation in the Michaelis constants could be rationalized by the following correlation equation: log 1/Km = 0.61 pi '3 + 0.46 MR4 + 0.55 sigma + 2.00 with a correlation coefficient of 0.945. In this expression, pi '3 is the hydrophobic constant for the more lipophilic of the two possible meta substituents, MR4 is the molar refractivity of 4-substituents, and sigma is the Hammett constant summed for all substituents. Using this equation, we designed, synthesized, and successfully predicted Km for a new congener intended to maximize binding (1/Km). The interactions involved in enzyme-substrate binding, as characterized by the correlation equation, are interpreted using a computer-constructed color three-dimensional-graphics molecular model of the enzyme active site. The nonenzymatic hydrolysis (both acid and basic) of phenyl hippurates yield rate constants which are well correlated by Hammett equations; however, log k for both acid and alkaline hydrolysis are not linearly related to log 1/Km or log kcat/Km.

A theory for the retrieval of virtual temperature from winds, radiances and the equations of fluid dynamics

NASA Technical Reports Server (NTRS)

Tzvi, G. C.

1986-01-01

A technique to deduce the virtual temperature from the combined use of the equations of fluid dynamics, observed wind and observed radiances is described. The wind information could come from ground-based sensitivity very high frequency (VHF) Doppler radars and/or from space-borne Doppler lidars. The radiometers are also assumed to be either space-borne and/or ground-based. From traditional radiometric techniques the vertical structure of the temperature can be estimated only crudely. While it has been known for quite some time that the virtual temperature could be deduced from wind information only, such techniques had to assume the infallibility of certain diagnostic relations. The proposed technique is an extension of the Gal-Chen technique. It is assumed that due to modeling uncertainties the equations of fluid dynamics are satisfied only in the least square sense. The retrieved temperature, however, is constrained to reproduce the observed radiances. It is shown that the combined use of the three sources of information (wind, radiances and fluid dynamical equations) can result in a unique determination of the vertical temperature structure with spatial and temporal resolution comparable to that of the observed wind.

Indriect Measurement Of Nitrogen In A Mult-Component Natural Gas By Heating The Gas

DOEpatents

Morrow, Thomas B.; Behring, II, Kendricks A.

2004-06-22

Methods of indirectly measuring the nitrogen concentration in a natural gas by heating the gas. In two embodiments, the heating energy is correlated to the speed of sound in the gas, the diluent concentrations in the gas, and constant values, resulting in a model equation. Regression analysis is used to calculate the constant values, which can then be substituted into the model equation. If the diluent concentrations other than nitrogen (typically carbon dioxide) are known, the model equation can be solved for the nitrogen concentration.

All-optical computation system for solving differential equations based on optical intensity differentiator.

PubMed

Tan, Sisi; Wu, Zhao; Lei, Lei; Hu, Shoujin; Dong, Jianji; Zhang, Xinliang

2013-03-25

We propose and experimentally demonstrate an all-optical differentiator-based computation system used for solving constant-coefficient first-order linear ordinary differential equations. It consists of an all-optical intensity differentiator and a wavelength converter, both based on a semiconductor optical amplifier (SOA) and an optical filter (OF). The equation is solved for various values of the constant-coefficient and two considered input waveforms, namely, super-Gaussian and Gaussian signals. An excellent agreement between the numerical simulation and the experimental results is obtained.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Estimation of total body water from bioelectrical impedance spectroscopy in oncology outpatients receiving radiotherapy and agreement with three prediction equations.

PubMed

Isenring, E; Colombo, M; Cross, G; Kellett, E; Swaney, L

2009-02-01

Bioelectrical impedance spectroscopy (BIS) may be more accurate in determining total body water (TBW) than bioelectrical impedance analysis (BIA). The present study compared the agreement between three TBW prediction equations developed using BIA and BIS-derived TBW in oncology outpatients. A cross-sectional, observational study was conducted in 37 outpatients receiving radiotherapy (27 males/10 females, aged 68.3 +/- 10.2 years). TBW was estimated by BIS (TBW(BIS)) and three BIA TBW prediction equations (TBW(ca-u): underweight cancer patients; TBW(ca-n): normal-weight cancer patients; and TBW(rad): patients receiving radiotherapy). Bland-Altman analyses determined agreement between methods. BIS-derived TBW using new resistivity constants was calculated. The mean +/- SD of TBW estimated by BIS was 39.8 +/- 8.3 L, which was significantly different from the prediction equations; TBW(rad) 35.1 +/- 7.9 L, TBW(ca-u) 33.1 +/- 7.5 L and TBW(ca-n) 32.3 +/- 7.3 L, (P < 0.001). Using new resistivity constants, TBW was 36.2 +/- 8.1 L but this still differed from the equations (P < 0.001). Bias between TBW(BIS) and that predicted by the equations was in the range 4.7-7.4 L or 1.1-3.9 L using new resistivity constants. TBW estimated by BIS cannot be directly compared with oncology-specific BIA equations, suggesting that BIS cannot be used at the group level in outpatients receiving radiotherapy. There was a reduced bias with BIS using new resistivity constants; however, further research should determine any advantage of BIS over BIA in this population.

Thermodiffusion in concentrated ferrofluids: A review and current experimental and numerical results on non-magnetic thermodiffusion

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

Sprenger, Lisa, E-mail: Lisa.Sprenger@tu-dresden.de; Lange, Adrian; Odenbach, Stefan

2013-12-15

Ferrofluids are colloidal suspensions consisting of magnetic nanoparticles dispersed in a carrier liquid. Their thermodiffusive behaviour is rather strong compared to molecular binary mixtures, leading to a Soret coefficient (S{sub T}) of 0.16 K{sup −1}. Former experiments with dilute magnetic fluids have been done with thermogravitational columns or horizontal thermodiffusion cells by different research groups. Considering the horizontal thermodiffusion cell, a former analytical approach has been used to solve the phenomenological diffusion equation in one dimension assuming a constant concentration gradient over the cell's height. The current experimental work is based on the horizontal separation cell and emphasises the comparison ofmore » the concentration development in different concentrated magnetic fluids and at different temperature gradients. The ferrofluid investigated is the kerosene-based EMG905 (Ferrotec) to be compared with the APG513A (Ferrotec), both containing magnetite nanoparticles. The experiments prove that the separation process linearly depends on the temperature gradient and that a constant concentration gradient develops in the setup due to the separation. Analytical one dimensional and numerical three dimensional approaches to solve the diffusion equation are derived to be compared with the solution used so far for dilute fluids to see if formerly made assumptions also hold for higher concentrated fluids. Both, the analytical and numerical solutions, either in a phenomenological or a thermodynamic description, are able to reproduce the separation signal gained from the experiments. The Soret coefficient can then be determined to 0.184 K{sup −1} in the analytical case and 0.29 K{sup −1} in the numerical case. Former theoretical approaches for dilute magnetic fluids underestimate the strength of the separation in the case of a concentrated ferrofluid.« less

Probing dark energy via galaxy cluster outskirts

NASA Astrophysics Data System (ADS)

Morandi, Andrea; Sun, Ming

2016-04-01

We present a Bayesian approach to combine Planck data and the X-ray physical properties of the intracluster medium in the virialization region of a sample of 320 galaxy clusters (0.056 < z < 1.24, kT ≳ 3 keV) observed with Chandra. We exploited the high level of similarity of the emission measure in the cluster outskirts as cosmology proxy. The cosmological parameters are thus constrained assuming that the emission measure profiles at different redshift are weakly self-similar, that is their shape is universal, explicitly allowing for temperature and redshift dependence of the gas fraction. This cosmological test, in combination with Planck+SNIa data, allows us to put a tight constraint on the dark energy models. For a constant-w model, we have w = -1.010 ± 0.030 and Ωm = 0.311 ± 0.014, while for a time-evolving equation of state of dark energy w(z) we have Ωm = 0.308 ± 0.017, w0 = -0.993 ± 0.046 and wa = -0.123 ± 0.400. Constraints on the cosmology are further improved by adding priors on the gas fraction evolution from hydrodynamic simulations. Current data favour the cosmological constant with w ≡ -1, with no evidence for dynamic dark energy. We checked that our method is robust towards different sources of systematics, including background modelling, outlier measurements, selection effects, inhomogeneities of the gas distribution and cosmic filaments. We also provided for the first time constraints on which definition of cluster boundary radius is more tenable, namely based on a fixed overdensity with respect to the critical density of the Universe. This novel cosmological test has the capacity to provide a generational leap forward in our understanding of the equation of state of dark energy.

A piecewise mass-spring-damper model of the human breast.

PubMed

Cai, Yiqing; Chen, Lihua; Yu, Winnie; Zhou, Jie; Wan, Frances; Suh, Minyoung; Chow, Daniel Hung-Kay

2018-01-23

Previous models to predict breast movement whilst performing physical activities have, erroneously, assumed uniform elasticity within the breast. Consequently, the predicted displacements have not yet been satisfactorily validated. In this study, real time motion capture of the natural vibrations of a breast that followed, after raising and allowing it to fall freely, revealed an obvious difference in the vibration characteristics above and below the static equilibrium position. This implied that the elastic and viscous damping properties of a breast could vary under extension or compression. Therefore, a new piecewise mass-spring-damper model of a breast was developed with theoretical equations to derive values for its spring constants and damping coefficients from free-falling breast experiments. The effective breast mass was estimated from the breast volume extracted from a 3D body scanned image. The derived spring constant (k a  = 73.5 N m -1 ) above the static equilibrium position was significantly smaller than that below it (k b  = 658 N m -1 ), whereas the respective damping coefficients were similar (c a  = 1.83 N s m -1 , c b  = 2.07 N s m -1 ). These values were used to predict the nipple displacement during bare-breasted running for validation. The predicted and experimental results had a 2.6% or less root-mean-square-error of the theoretical and experimental amplitudes, so the piecewise mass-spring-damper model and equations were considered to have been successfully validated. This provides a theoretical basis for further research into the dynamic, nonlinear viscoelastic properties of different breasts and the prediction of external forces for the necessary breast support during different sports activities. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dependence of cancer cell adhesion kinetics on integrin ligand surface density measured by a high-throughput label-free resonant waveguide grating biosensor.

PubMed

Orgovan, Norbert; Peter, Beatrix; Bősze, Szilvia; Ramsden, Jeremy J; Szabó, Bálint; Horvath, Robert

2014-02-07

A novel high-throughput label-free resonant waveguide grating (RWG) imager biosensor, the Epic® BenchTop (BT), was utilized to determine the dependence of cell spreading kinetics on the average surface density (v(RGD)) of integrin ligand RGD-motifs. v(RGD) was tuned over four orders of magnitude by co-adsorbing the biologically inactive PLL-g-PEG and the RGD-functionalized PLL-g-PEG-RGD synthetic copolymers from their mixed solutions onto the sensor surface. Using highly adherent human cervical tumor (HeLa) cells as a model system, cell adhesion kinetic data of unprecedented quality were obtained. Spreading kinetics were fitted with the logistic equation to obtain the spreading rate constant (r) and the maximum biosensor response (Δλmax), which is assumed to be directly proportional to the maximum spread contact area (Amax). r was found to be independent of the surface density of integrin ligands. In contrast, Δλmax increased with increasing RGD surface density until saturation at high densities. Interpreting the latter behavior with a simple kinetic mass action model, a 2D dissociation constant of 1753 ± 243 μm(-2) (corresponding to a 3D dissociation constant of ~30 μM) was obtained for the binding between RGD-specific integrins embedded in the cell membrane and PLL-g-PEG-RGD. All of these results were obtained completely noninvasively without using any labels.

Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation

NASA Astrophysics Data System (ADS)

Blumenthal, Benjamin J.; Zhan, Hongbin

2016-08-01

We have derived a rapidly computed analytical solution for drawdown caused by a partially or fully penetrating directional wellbore (vertical, horizontal, or slant) via Green's function method. The mathematical model assumes an anisotropic, homogeneous, confined, box-shaped aquifer. Any dimension of the box can have one of six possible boundary conditions: 1) both sides no-flux; 2) one side no-flux - one side constant-head; 3) both sides constant-head; 4) one side no-flux; 5) one side constant-head; 6) free boundary conditions. The solution has been optimized for rapid computation via Poisson Resummation, derivation of convergence rates, and numerical optimization of integration techniques. Upon application of the Poisson Resummation method, we were able to derive two sets of solutions with inverse convergence rates, namely an early-time rapidly convergent series (solution-A) and a late-time rapidly convergent series (solution-B). From this work we were able to link Green's function method (solution-B) back to image well theory (solution-A). We then derived an equation defining when the convergence rate between solution-A and solution-B is the same, which we termed the switch time. Utilizing the more rapidly convergent solution at the appropriate time, we obtained rapid convergence at all times. We have also shown that one may simplify each of the three infinite series for the three-dimensional solution to 11 terms and still maintain a maximum relative error of less than 10-14.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

PubMed

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Cosmology with a stiff matter era

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2015-11-01

We consider the possibility that the Universe is made of a dark fluid described by a quadratic equation of state P =K ρ2 , where ρ is the rest-mass density and K is a constant. The energy density ɛ =ρ c2+K ρ2 is the sum of two terms: a rest-mass term ρ c2 that mimics "dark matter" (P =0 ) and an internal energy term u =K ρ2=P that mimics a "stiff fluid" (P =ɛ ) in which the speed of sound is equal to the speed of light. In the early universe, the internal energy dominates and the dark fluid behaves as a stiff fluid (P ˜ɛ , ɛ ∝a-6). In the late universe, the rest-mass energy dominates and the dark fluid behaves as pressureless dark matter (P ≃0 , ɛ ∝a-3). We provide a simple analytical solution of the Friedmann equations for a universe undergoing a stiff matter era, a dark matter era, and a dark energy era due to the cosmological constant. This analytical solution generalizes the Einstein-de Sitter solution describing the dark matter era, and the Λ CDM model describing the dark matter era and the dark energy era. Historically, the possibility of a primordial stiff matter era first appeared in the cosmological model of Zel'dovich where the primordial universe is assumed to be made of a cold gas of baryons. A primordial stiff matter era also occurs in recent cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the internal energy of the dark fluid mimicking stiff matter is positive, the primordial universe is singular like in the standard big bang theory. It expands from an initial state with a vanishing scale factor and an infinite density. We consider the possibility that the internal energy of the dark fluid is negative (while, of course, its total energy density is positive), so that it mimics anti-stiff matter. This happens, for example, when the BECs have an attractive self-interaction with a negative scattering length. In that case, the primordial universe is nonsingular and bouncing like in loop quantum cosmology. At t =0 , the scale factor is finite and the energy density is equal to zero. The universe first has a phantom behavior where the energy density increases with the scale factor, then a normal behavior where the energy density decreases with the scale factor. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the Universe asymptotically reaches a de Sitter regime where the scale factor increases exponentially rapidly with time. This can account for the accelerating expansion of the Universe that we observe at present. When the cosmological constant is negative (anti-de Sitter), the evolution of the Universe is cyclic. Therefore, depending on the sign of the internal energy of the dark fluid and on the sign of the cosmological constant, we obtain analytical solutions of the Friedmann equations describing singular and nonsingular expanding, bouncing, or cyclic universes.

[Comparison of three stand-level biomass estimation methods].

PubMed

Dong, Li Hu; Li, Feng Ri

2016-12-01

At present, the forest biomass methods of regional scale attract most of attention of the researchers, and developing the stand-level biomass model is popular. Based on the forestry inventory data of larch plantation (Larix olgensis) in Jilin Province, we used non-linear seemly unrelated regression (NSUR) to estimate the parameters in two additive system of stand-level biomass equations, i.e., stand-level biomass equations including the stand variables and stand biomass equations including the biomass expansion factor (i.e., Model system 1 and Model system 2), listed the constant biomass expansion factor for larch plantation and compared the prediction accuracy of three stand-level biomass estimation methods. The results indicated that for two additive system of biomass equations, the adjusted coefficient of determination (R a 2 ) of the total and stem equations was more than 0.95, the root mean squared error (RMSE), the mean prediction error (MPE) and the mean absolute error (MAE) were smaller. The branch and foliage biomass equations were worse than total and stem biomass equations, and the adjusted coefficient of determination (R a 2 ) was less than 0.95. The prediction accuracy of a constant biomass expansion factor was relatively lower than the prediction accuracy of Model system 1 and Model system 2. Overall, although stand-level biomass equation including the biomass expansion factor belonged to the volume-derived biomass estimation method, and was different from the stand biomass equations including stand variables in essence, but the obtained prediction accuracy of the two methods was similar. The constant biomass expansion factor had the lower prediction accuracy, and was inappropriate. In addition, in order to make the model parameter estimation more effective, the established stand-level biomass equations should consider the additivity in a system of all tree component biomass and total biomass equations.

Indirect Measurement Of Nitrogen In A Multi-Component Gas By Measuring The Speed Of Sound At Two States Of The Gas.

DOEpatents

Morrow, Thomas B.; Behring, II, Kendricks A.

2004-10-12

A methods of indirectly measuring the nitrogen concentration in a gas mixture. The molecular weight of the gas is modeled as a function of the speed of sound in the gas, the diluent concentrations in the gas, and constant values, resulting in a model equation. Regression analysis is used to calculate the constant values, which can then be substituted into the model equation. If the speed of sound in the gas is measured at two states and diluent concentrations other than nitrogen (typically carbon dioxide) are known, two equations for molecular weight can be equated and solved for the nitrogen concentration in the gas mixture.

The impact of viscosity on the combined heat, mass and momentum transfer in laminar liquid falling films

NASA Astrophysics Data System (ADS)

Mittermaier, M.; Ziegler, F.

2018-04-01

In this article we present a model describing a laminar film flow over a vertical isothermal plate whilst heat and mass transfer is occurring. We focus on a formulation where most common assumptions, such as constant property data and constant film thickness, have been cancelled. The hydrodynamic model results in longitudinal and transversal velocity components and their evolution in the entrance region. Heat and mass transfer occurs simultaneously and is modelled with respect to release of differential heat of solution as well as heat flow due to interdiffusion. The numerical solution is obtained by utilising a Newton-Raphson method to solve the finite difference formulation of the governing equations. Mass transfer across the film affects the development of both longitudinal and transversal velocity components. The hydrodynamics are modelled using a boundary layer approximation of the Navier-Stokes equations. The significance of simplifications on the hydrodynamic model are illustrated and discussed using a fully developed velocity profile (Nusselt flow) and a plug flow at the inlet for comparison. Even if a Nusselt profile is assumed, it develops further since mass is absorbed or desorbed. It is found that the onset of absorption occurs at shorter flow length when applying a plug flow at the inlet. If the film is initially in equilibrium, this results in a 9.3% increase in absorbed mass over a length of 0.03 m as compared with the Nusselt flow. A fluid with a viscosity five times the one of lithium bromide solution but sharing comparable properties apart from that, leads to lower overall heat and mass transfer rates. If the respective fluids are saturated at the inlet, the accumulated mass flux absorbed by lithium bromide solution is 2.2 times higher than the one absorbed by a high viscous fluid. However, when a plug flow is applied and the fluid is sub-cooled, ab initio the absorbed mass flux is slightly higher for a high viscous fluid. Assuming a sub-cooling of 3 K at the inlet, lithium bromide solution now only performs around 11% better as compared with a high viscous fluid over the considered length of 0.03 m. The code may be downloaded from: https://github.com/mittermaier/hmt.

Selection of Common Items as an Unrecognized Source of Variability in Test Equating: A Bootstrap Approximation Assuming Random Sampling of Common Items

ERIC Educational Resources Information Center

Michaelides, Michalis P.; Haertel, Edward H.

2014-01-01

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally…

Cosmological constant implementing Mach principle in general relativity

NASA Astrophysics Data System (ADS)

Namavarian, Nadereh; Farhoudi, Mehrdad

2016-10-01

We consider the fact that noticing on the operational meaning of the physical concepts played an impetus role in the appearance of general relativity (GR). Thus, we have paid more attention to the operational definition of the gravitational coupling constant in this theory as a dimensional constant which is gained through an experiment. However, as all available experiments just provide the value of this constant locally, this coupling constant can operationally be meaningful only in a local area. Regarding this point, to obtain an extension of GR for the large scale, we replace it by a conformal invariant model and then, reduce this model to a theory for the cosmological scale via breaking down the conformal symmetry through singling out a specific conformal frame which is characterized by the large scale characteristics of the universe. Finally, we come to the same field equations that historically were proposed by Einstein for the cosmological scale (GR plus the cosmological constant) as the result of his endeavor for making GR consistent with the Mach principle. However, we declare that the obtained field equations in this alternative approach do not carry the problem of the field equations proposed by Einstein for being consistent with Mach's principle (i.e., the existence of de Sitter solution), and can also be considered compatible with this principle in the Sciama view.

g-Jitter Mixed Convective Slip Flow of Nanofluid past a Permeable Stretching Sheet Embedded in a Darcian Porous Media with Variable Viscosity

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Amin, Norsarahaida S.

2014-01-01

The unsteady two-dimensional laminar g-Jitter mixed convective boundary layer flow of Cu-water and Al2O3-water nanofluids past a permeable stretching sheet in a Darcian porous is studied by using an implicit finite difference numerical method with quasi-linearization technique. It is assumed that the plate is subjected to velocity and thermal slip boundary conditions. We have considered temperature dependent viscosity. The governing boundary layer equations are converted into non-similar equations using suitable transformations, before being solved numerically. The transport equations have been shown to be controlled by a number of parameters including viscosity parameter, Darcy number, nanoparticle volume fraction, Prandtl number, velocity slip, thermal slip, suction/injection and mixed convection parameters. The dimensionless velocity and temperature profiles as well as friction factor and heat transfer rates are presented graphically and discussed. It is found that the velocity reduces with velocity slip parameter for both nanofluids for fluid with both constant and variable properties. It is further found that the skin friction decreases with both Darcy number and momentum slip parameter while it increases with viscosity variation parameter. The surface temperature increases as the dimensionless time increases for both nanofluids. Nusselt numbers increase with mixed convection parameter and Darcy numbers and decreases with the momentum slip. Excellent agreement is found between the numerical results of the present paper with published results. PMID:24927277

Thermal Analysis of a Carbon Fiber Rope Barrier for Use in the Reusable Solid Rocket Motor Nozzle Joint-2

NASA Technical Reports Server (NTRS)

Clayton, J. Louie

2002-01-01

This study provides development and verification of analysis methods used to assess performance of a carbon fiber rope (CFR) thermal barrier system that is currently being qualified for use in Reusable Solid Rocket Motor (RSRM) nozzle joint-2. Modeled geometry for flow calculations considers the joint to be vented with the porous CFR barriers placed in the 'open' assembly gap. Model development is based on a 1-D volume filling approach where flow resistances (assembly gap and CFRs) are defined by serially connected internal flow and the porous media 'Darcy' relationships. Combustion gas flow rates are computed using the volume filling code by assuming a lumped distribution total joint fill volume on a per linear circumferential inch basis. Gas compressibility, friction and heat transfer are included in the modeling. Gas-to-wall heat transfer is simulated by concurrent solution of the compressible flow equations and a large thermal 2-D finite element (FE) conduction grid. The derived numerical technique loosely couples the FE conduction matrix with the compressible gas flow equations. Free constants that appear in the governing equations are calibrated by parametric model comparison to hot fire subscale test results. The calibrated model is then used to make full-scale motor predictions using RSRM aft dome environments. Model results indicate that CFR thermal barrier systems will provide a thermally benign and controlled pressurization environment for the RSRM nozzle joint-2 primary seal activation.

Thermal Analysis of a Carbon Fiber Rope Barrier for Use in the Reusable Solid Rocket Motor Nozzle Joint-2

NASA Technical Reports Server (NTRS)

Clayton, J. Louie; Phelps, Lisa (Technical Monitor)

2001-01-01

This study provides for development and verification of analysis methods used to assess performance of a carbon fiber rope (CFR) thermal barrier system that is currently being qualified for use in Reusable Solid Rocket Motor (RSRM) nozzle joint-2. Modeled geometry for flow calculations considers the joint to be vented with the porous CFR barriers placed in the "open' assembly gap. Model development is based on a 1-D volume filling approach where flow resistances (assembly gap and CFRs) are defined by serially connected internal flow and the porous media "Darcy" relationships. Combustion gas flow rates are computed using the volume filling code by assuming a lumped distribution total joint fill volume on a per linear circumferential inch basis. Gas compressibility, friction and heat transfer are included in the modeling. Gas-to-wall heat transfer is simulated by concurrent solution of the compressible flow equations and a large thermal 2-D finite element (FE) conduction grid. The derived numerical technique loosely couples the FE conduction matrix with the compressible gas flow equations, Free constants that appear in the governing equations are calibrated by parametric model comparison to hot fire subscale test results. The calibrated model is then used to make full-scale motor predictions using RSRM aft dome environments. Model results indicate that CFR thermal barrier systems will provide a thermally benign and controlled pressurization environment for the RSRM nozzle joint-2 primary seal activation.

ZMOTTO- MODELING THE INTERNAL COMBUSTION ENGINE

NASA Technical Reports Server (NTRS)

Zeleznik, F. J.

1994-01-01

The ZMOTTO program was developed to model mathematically a spark-ignited internal combustion engine. ZMOTTO is a large, general purpose program whose calculations can be established at five levels of sophistication. These five models range from an ideal cycle requiring only thermodynamic properties, to a very complex representation demanding full combustion kinetics, transport properties, and poppet valve flow characteristics. ZMOTTO is a flexible and computationally economical program based on a system of ordinary differential equations for cylinder-averaged properties. The calculations assume that heat transfer is expressed in terms of a heat transfer coefficient and that the cylinder average of kinetic plus potential energies remains constant. During combustion, the pressures of burned and unburned gases are assumed equal and their heat transfer areas are assumed proportional to their respective mass fractions. Even the simplest ZMOTTO model provides for residual gas effects, spark advance, exhaust gas recirculation, supercharging, and throttling. In the more complex models, 1) finite rate chemistry replaces equilibrium chemistry in descriptions of both the flame and the burned gases, 2) poppet valve formulas represent fluid flow instead of a zero pressure drop flow, and 3) flame propagation is modeled by mass burning equations instead of as an instantaneous process. Input to ZMOTTO is determined by the model chosen. Thermodynamic data is required for all models. Transport properties and chemical kinetics data are required only as the model complexity grows. Other input includes engine geometry, working fluid composition, operating characteristics, and intake/exhaust data. ZMOTTO accommodates a broad spectrum of reactants. The program will calculate many Otto cycle performance parameters for a number of consecutive cycles (a cycle being an interval of 720 crankangle degrees). A typical case will have a number of initial ideal cycles and progress through levels of nonideal cycles. ZMOTTO has restart capabilities and permits multicycle calculations with parameters varying from cycle to cycle. ZMOTTO is written in FORTRAN IV (IBM Level H) but has also been compiled with IBM VSFORTRAN (1977 standard). It was developed on an IBM 3033 under the TSS operating system and has also been implemented under MVS. Approximately 412K of 8 bit bytes of central memory are required in a nonpaging environment. ZMOTTO was developed in 1985.

Effect of rock rheology on fluid leak- off during hydraulic fracturing

NASA Astrophysics Data System (ADS)

Yarushina, V. M.; Bercovici, D.; Oristaglio, M. L.

2012-04-01

In this communication, we evaluate the effect of rock rheology on fluid leak­off during hydraulic fracturing of reservoirs. Fluid leak-off in hydraulic fracturing is often nonlinear. The simple linear model developed by Carter (1957) for flow of fracturing fluid into a reservoir has three different regions in the fractured zone: a filter cake on the fracture face, formed by solid additives from the fracturing fluid; a filtrate zone affected by invasion of the fracturing fluid; and a reservoir zone with the original formation fluid. The width of each zone, as well as its permeability and pressure drop, is assumed to remain constant. Physical intuition suggests some straightforward corrections to this classical theory to take into account the pressure dependence of permeability, the compressibility or non-Newtonian rheology of fracturing fluid, and the radial (versus linear) geometry of fluid leak­off from the borehole. All of these refinements, however, still assume that the reservoir rock adjacent to the fracture face is non­deformable. Although the effect of poroelastic stress changes on leak-off is usually thought to be negligible, at the very high fluid pressures used in hydraulic fracturing, where the stresses exceed the rock strength, elastic rheology may not be the best choice. For example, calculations show that perfectly elastic rock formations do not undergo the degree of compaction typically seen in sedimentary basins. Therefore, pseudo-elastic or elastoplastic models are used to fit observed porosity profiles with depth. Starting from balance equations for mass and momentum for fluid and rock, we derive a hydraulic flow equation coupled with a porosity equation describing rock compaction. The result resembles a pressure diffusion equation with the total compressibility being a sum of fluid, rock and pore-space compressibilities. With linear elastic rheology, the bulk formation compressibility is dominated by fluid compressibility. But the possibility of permanent, time-independent (plastic) rock deformation significantly increases the pore space compressibility (compaction), which becomes a leading term in the total compressibility. Inclusion of rock and fluid compressibilities in the model can explain both linear and nonlinear leak­off. In particular, inclusion of rock compaction and decompaction may be important for description of naturally fractured and tight gas reservoirs for which very strong dependence of permeability on porosity has been reported. Carter R.D. Derivation of the general equation for estimating the extent of the fractured area. Appendix I of "Optimum fluid characteristics for fracture extension", Drilling and Production Practice, G.C. Howard and C.R.Fast, New York, New York, USA, American Petroleum Institute (1957), 261-269.

A Comparative Analysis of Reynolds-Averaged Navier-Stokes Model Predictions for Rayleigh-Taylor Instability and Mixing with Constant and Complex Accelerations

NASA Astrophysics Data System (ADS)

Schilling, Oleg

2016-11-01

Two-, three- and four-equation, single-velocity, multicomponent Reynolds-averaged Navier-Stokes (RANS) models, based on the turbulent kinetic energy dissipation rate or lengthscale, are used to simulate At = 0 . 5 Rayleigh-Taylor turbulent mixing with constant and complex accelerations. The constant acceleration case is inspired by the Cabot and Cook (2006) DNS, and the complex acceleration cases are inspired by the unstable/stable and unstable/neutral cases simulated using DNS (Livescu, Wei & Petersen 2011) and the unstable/stable/unstable case simulated using ILES (Ramaprabhu, Karkhanis & Lawrie 2013). The four-equation models couple equations for the mass flux a and negative density-specific volume correlation b to the K- ɛ or K- L equations, while the three-equation models use a two-fluid algebraic closure for b. The lengthscale-based models are also applied with no buoyancy production in the L equation to explore the consequences of neglecting this term. Predicted mixing widths, turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify similarities and differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

On parasupersymmetric oscillators and relativistic vector mesons in constant magnetic fields

NASA Technical Reports Server (NTRS)

Debergh, Nathalie; Beckers, Jules

1995-01-01

Johnson-Lippmann considerations on oscillators and their connection with the minimal coupling schemes are visited in order to introduce a new Sakata-Taketani equation describing vector mesons in interaction with a constant magnetic field. This new proposal, based on a specific parasupersymmetric oscillator-like system, is characterized by real energies as opposed to previously pointed out relativistic equations corresponding to this interacting context.

Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

ERIC Educational Resources Information Center

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

A numerical study of granular dam-break flow

NASA Astrophysics Data System (ADS)

Pophet, N.; Rébillout, L.; Ozeren, Y.; Altinakar, M.

2017-12-01

Accurate prediction of granular flow behavior is essential to optimize mitigation measures for hazardous natural granular flows such as landslides, debris flows and tailings-dam break flows. So far, most successful models for these types of flows focus on either pure granular flows or flows of saturated grain-fluid mixtures by employing a constant friction model or more complex rheological models. These saturated models often produce non-physical result when they are applied to simulate flows of partially saturated mixtures. Therefore, more advanced models are needed. A numerical model was developed for granular flow employing a constant friction and μ(I) rheology (Jop et al., J. Fluid Mech. 2005) coupled with a groundwater flow model for seepage flow. The granular flow is simulated by solving a mixture model using Finite Volume Method (FVM). The Volume-of-Fluid (VOF) technique is used to capture the free surface motion. The constant friction and μ(I) rheological models are incorporated in the mixture model. The seepage flow is modeled by solving Richards equation. A framework is developed to couple these two solvers in OpenFOAM. The model was validated and tested by reproducing laboratory experiments of partially and fully channelized dam-break flows of dry and initially saturated granular material. To obtain appropriate parameters for rheological models, a series of simulations with different sets of rheological parameters is performed. The simulation results obtained from constant friction and μ(I) rheological models are compared with laboratory experiments for granular free surface interface, front position and velocity field during the flows. The numerical predictions indicate that the proposed model is promising in predicting dynamics of the flow and deposition process. The proposed model may provide more reliable insight than the previous assumed saturated mixture model, when saturated and partially saturated portions of granular mixture co-exist.

Master Equation Analysis of Thermal and Nonthermal Microwave Effects.

PubMed

Ma, Jianyi

2016-10-11

Master equation is a successful model to describe the conventional heating reaction, it is expanded to capture the "microwave effect" in this work. The work equation of "microwave effect" included master equation presents the direct heating, indirect heating, and nonthermal effect about the microwave field. The modified master equation provides a clear physics picture to the nonthermal microwave effect: (1) The absorption and the emission of the microwave, which is dominated by the transition dipole moment between two corresponding states and the intensity of the microwave field, provides a new path to change the reaction rate constants. (2) In the strong microwave field, the distribution of internal states of the molecules will deviate from the equilibrium distribution, and the system temperature defined in the conventional heating reaction is no longer available. According to the general form of "microwave effect" included master equation, a two states model for unimolecular dissociation is proposed and is used to discuss the microwave nonthermal effect particularly. The average rate constants can be increased up to 2400 times for some given cases without the temperature changed in the two states model. Additionally, the simulation of a model system was executed using our State Specified Master Equation package. Three important conclusions can be obtained in present work: (1) A reasonable definition of the nonthermal microwave effect is given in the work equation of "microwave effect" included master equation. (2) Nonthermal microwave effect possibly exists theoretically. (3) The reaction rate constants perhaps can be changed obviously by the microwave field for the non-RRKM and the mode-specified reactions.

Dynamics of Geometrically Nonlinear Elastic Nonthin Anisotropic Shells of Variable Thickness

NASA Astrophysics Data System (ADS)

Marchuk, M. V.; Tuchapskii, R. I.

2017-11-01

A theory of dynamic elastic geometrically nonlinear deformation of nonthin anisotropic shells with variable thickness is constructed. Shells are assumed asymmetric about the reference surface. Functions are expanded into Legendre series. The basic equations are written in a coordinate system aligned with the lines of curvature of the reference surface. The equations of motion and appropriate boundary conditions are obtained using the Hamilton-Ostrogradsky variational principle. The change in metric across the thickness is taken into account. The theory assumes that the refinement process is regular and allows deriving equations including products of terms of Legendre series of unknown functions of arbitrary order. The behavior of a square metallic plate acted upon by a pressure pulse distributed over its face is studied.

Wake excited in plasma by an ultrarelativistic pointlike bunch

DOE PAGES

Stupakov, G.; Breizman, B.; Khudik, V.; ...

2016-10-05

We study propagation of a relativistic electron bunch through a cold plasma assuming that the transverse and longitudinal dimensions of the bunch are much smaller than the plasma collisionless skin depth. Treating the bunch as a point charge and assuming that its charge is small, we derive a simplified system of equations for the plasma electrons and show that, through a simple rescaling of variables, the bunch charge can be eliminated from the equations. The equations demonstrate an ion cavity formed behind the driver. They are solved numerically and the scaling of the cavity parameters with the driver charge ismore » obtained. As a result, a numerical solution for the case of a positively charged driver is also found.« less

QED Based Calculation of the Fine Structure Constant

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

Lestone, John Paul

2016-10-13

Quantum electrodynamics is complex and its associated mathematics can appear overwhelming for those not trained in this field. Here, semi-classical approaches are used to obtain a more intuitive feel for what causes electrostatics, and the anomalous magnetic moment of the electron. These intuitive arguments lead to a possible answer to the question of the nature of charge. Virtual photons, with a reduced wavelength of λ, are assumed to interact with isolated electrons with a cross section of πλ 2. This interaction is assumed to generate time-reversed virtual photons that are capable of seeking out and interacting with other electrons. Thismore » exchange of virtual photons between particles is assumed to generate and define the strength of electromagnetism. With the inclusion of near-field effects the model presented here gives a fine structure constant of ~1/137 and an anomalous magnetic moment of the electron of ~0.00116. These calculations support the possibility that near-field corrections are the key to understanding the numerical value of the dimensionless fine structure constant.« less

Optimal determination of the elastic constants of composite materials from ultrasonic wave-speed measurements

NASA Astrophysics Data System (ADS)

Castagnède, Bernard; Jenkins, James T.; Sachse, Wolfgang; Baste, Stéphane

1990-03-01

A method is described to optimally determine the elastic constants of anisotropic solids from wave-speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree-three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double-iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Oscillation Amplitude Growth for a Decelerating Object with Constant Pitch Damping

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Queen, Eric M.; Litton, Daniel

2006-01-01

The equations governing the deceleration and oscillation of a blunt body moving along a planar trajectory are re-expressed in the form of the Euler-Cauchy equation. An analytic solution of this equation describes the oscillation amplitude growth and frequency dilation with time for a statically stable decelerating body with constant pitch damping. The oscillation histories for several constant pitch damping values, predicted by the solution of the Euler-Cauchy equation are compared to POST six degree-of-freedom (6-DoF) trajectory simulations. The simulations use simplified aerodynamic coefficients matching the Euler-Cauchy approximations. Agreement between the model predictions and simulation results are excellent. Euler-Cauchy curves are also fit through nonlinear 6-DoF simulations and ballistic range data to identify static stability and pitch damping coefficients. The model os shown to closely fit through the data points and capture the behavior of the blunt body observed in simulation and experiment. The extracted coefficients are in reasonable agreement with higher fidelity, nonlinear parameter identification results. Finally, a nondimensional version of the Euler-Cauchy equation is presented and shown to be a simple and effective tool for designing dynamically scaled experiments for decelerating blunt capsule flight.

Binding Energies of Proton-Bound Dimers of Imidazole and n-Acetylalanine Methyl Ester Obtained by Blackbody Infrared Radiative Dissociation

PubMed Central

Jockusch, Rebecca A.; Williams*, Evan R.

2005-01-01

The dissociation kinetics of protonated n-acetyl-L-alanine methyl ester dimer (AcAlaMEd), imidazole dimer, and their cross dimer were measured using blackbody infrared radiative dissociation (BIRD). Master equation modeling of these data was used to extract threshold dissociation energies (Eo) for the dimers. Values of 1.18 ± 0.06, 1.11 ± 0.04, and 1.12 ± 0.08 eV were obtained for AcAlaMEd, imidazole dimer, and the cross dimer, respectively. Assuming that the reverse activation barrier for dissociation of the ion–molecule complex is negligible, the value of Eo can be compared to the dissociation enthalpy (ΔHd°) from HPMS data. The Eo values obtained for the imidazole dimer and the cross dimer are in agreement with HPMS values; the value for AcAlaMEd is somewhat lower. Radiative rate constants used in the master equation modeling were determined using transition dipole moments calculated at the semiempirical (AM1) level for all dimers and compared to ab initio (RHF/3-21G*) calculations where possible. To reproduce the experimentally measured dissociation rates using master equation modeling, it was necessary to multiply semiempirical transition dipole moments by a factor between 2 and 3. Values for transition dipole moments from the ab initio calculations could be used for two of the dimers but appear to be too low for AcAlaMEd. These results demonstrate that BIRD, in combination with master equation modeling, can be used to determine threshold dissociation energies for intermediate size ions that are in neither the truncated Boltzmann nor the rapid energy exchange limit. PMID:16604163

Extrinsic and intrinsic index finger muscle attachments in an OpenSim upper-extremity model.

PubMed

Lee, Jong Hwa; Asakawa, Deanna S; Dennerlein, Jack T; Jindrich, Devin L

2015-04-01

Musculoskeletal models allow estimation of muscle function during complex tasks. We used objective methods to determine possible attachment locations for index finger muscles in an OpenSim upper-extremity model. Data-driven optimization algorithms, Simulated Annealing and Hook-Jeeves, estimated tendon locations crossing the metacarpophalangeal (MCP), proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints by minimizing the difference between model-estimated and experimentally-measured moment arms. Sensitivity analysis revealed that multiple sets of muscle attachments with similar optimized moment arms are possible, requiring additional assumptions or data to select a single set of values. The most smooth muscle paths were assumed to be biologically reasonable. Estimated tendon attachments resulted in variance accounted for (VAF) between calculated moment arms and measured values of 78% for flex/extension and 81% for ab/adduction at the MCP joint. VAF averaged 67% at the PIP joint and 54% at the DIP joint. VAF values at PIP and DIP joints partially reflected the constant moment arms reported for muscles about these joints. However, all moment arm values found through optimization were non-linear and non-constant. Relationships between moment arms and joint angles were best described with quadratic equations for tendons at the PIP and DIP joints.

Fine-structure constant constraints on dark energy. II. Extending the parameter space

NASA Astrophysics Data System (ADS)

Martins, C. J. A. P.; Pinho, A. M. M.; Carreira, P.; Gusart, A.; López, J.; Rocha, C. I. S. A.

2016-01-01

Astrophysical tests of the stability of fundamental couplings, such as the fine-structure constant α , are a powerful probe of new physics. Recently these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, were used to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, ζ , to the electromagnetic sector) the α variation. One caveat of these analyses was that it was based on fiducial models where the dark energy equation of state was described by a single parameter (effectively its present day value, w0). Here we relax this assumption and study broader dark energy model classes, including the Chevallier-Polarski-Linder and early dark energy parametrizations. Even in these extended cases we find that the current data constrains the coupling ζ at the 1 0-6 level and w0 to a few percent (marginalizing over other parameters), thus confirming the robustness of earlier analyses. On the other hand, the additional parameters are typically not well constrained. We also highlight the implications of our results for constraints on violations of the weak equivalence principle and improvements to be expected from forthcoming measurements with high-resolution ultrastable spectrographs.

Self-consistent average-atom scheme for electronic structure of hot and dense plasmas of mixture.

PubMed

Yuan, Jianmin

2002-10-01

An average-atom model is proposed to treat the electronic structures of hot and dense plasmas of mixture. It is assumed that the electron density consists of two parts. The first one is a uniform distribution with a constant value, which is equal to the electron density at the boundaries between the atoms. The second one is the total electron density minus the first constant distribution. The volume of each kind of atom is proportional to the sum of the charges of the second electron part and of the nucleus within each atomic sphere. By this way, one can make sure that electrical neutrality is satisfied within each atomic sphere. Because the integration of the electron charge within each atom needs the size of that atom in advance, the calculation is carried out in a usual self-consistent way. The occupation numbers of electron on the orbitals of each kind of atom are determined by the Fermi-Dirac distribution with the same chemical potential for all kinds of atoms. The wave functions and the orbital energies are calculated with the Dirac-Slater equations. As examples, the electronic structures of the mixture of Au and Cd, water (H2O), and CO2 at a few temperatures and densities are presented.

Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient.

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.

A moment-convergence method for stochastic analysis of biochemical reaction networks.

PubMed

Zhang, Jiajun; Nie, Qing; Zhou, Tianshou

2016-05-21

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Phase transitions in neutron star equation of state induced by the delta resonances matter

NASA Astrophysics Data System (ADS)

T, Oliveira J. C.; Rodrigues, H.; Duarte, S. B.

2016-04-01

In the present work we determine the equation of state and the population of baryons and leptons, and also we discuss the implication of changes in the baryon-meson coupling constants to the formation of delta matter in the stellar medium. And also in this work the phase transition is explored with respect to the domain of the delta-mesons coupling constants.

Differential equations in airplane mechanics

NASA Technical Reports Server (NTRS)

Carleman, M T

1922-01-01

In the following report, we will first draw some conclusions of purely theoretical interest, from the general equations of motion. At the end, we will consider the motion of an airplane, with the engine dead and with the assumption that the angle of attack remains constant. Thus we arrive at a simple result, which can be rendered practically utilizable for determining the trajectory of an airplane descending at a constant steering angle.

Determination of kinetic and equilibrium parameters of the batch adsorption of Mn(II), Co(II), Ni(II) and Cu(II) from aqueous solution by black carrot (Daucus carota L.) residues.

PubMed

Güzel, Fuat; Yakut, Hakan; Topal, Giray

2008-05-30

In this study, the effect of temperature on the adsorption of Mn(II), Ni(II), Co(II) and Cu(II) from aqueous solution by modified carrot residues (MCR) was investigated. The equilibrium contact times of adsorption process for each heavy metals-MCR systems were determined. Kinetic data obtained for each heavy metal by MCR at different temperatures were applied to the Lagergren equation, and adsorption rate constants (kads) at these temperatures were determined. These rate constants related to the adsorption of heavy metal by MCR were applied to the Arrhenius equation, and activation energies (Ea) were determined. In addition, the isotherms for adsorption of each heavy metal by MCR at different temperatures were also determined. These isothermal data were applied to linear forms of isotherm equations that they fit the Langmuir adsorption isotherm, and the Langmuir constants (qm and b) were calculated. b constants determined at different temperatures were applied to thermodynamic equations, and thermodynamic parameters such as enthalpy (Delta H), free energy (Delta G), and entropy (Delta S) were calculated and these values show that adsorption of heavy metal on MCR was an endothermic process and process of adsorption was favoured at high temperatures.

Periodic solutions for one dimensional wave equation with bounded nonlinearity

NASA Astrophysics Data System (ADS)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

Quantitative relations between fishing mortality, spawning stress mortality and biomass growth rate (computed with numerical model FISHMO)

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

Laevastu, T.

1983-01-01

The effects of fishing on a given species biomass have been quantitatively evaluated. A constant recruitment is assumed in this study, but the evaluation can be computed on any known age distribution of exploitable biomass. Fishing mortality is assumed to be constant with age; however, spawning stress mortality increases with age. When fishing (mortality) increases, the spawning stress mortality decreases relative to total and exploitable biomasses. These changes are quantitatively shown for two species from the Bering Sea - walleye pollock, Theragra chalcogramma, and yellowfin sole, Limanda aspera.

A neutral functional differential equation of Lurie type. [on asymptotic stability of feedback control

NASA Technical Reports Server (NTRS)

Chukwu, E. N.

1980-01-01

The problem of Lurie is posed for systems described by a functional differential equation of neutral type. Sufficient conditions are obtained for absolute stability for the controlled system if it is assumed that the uncontrolled plant equation is uniformly asymptotically stable. Both the direct and indirect control cases are treated.

Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

PubMed

Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

2011-08-01

We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds.

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer.

PubMed

Keh, Huan J; Ding, Jau M

2003-07-15

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.

General solution for diffusion-controlled dissolution of spherical particles. 1. Theory.

PubMed

Wang, J; Flanagan, D R

1999-07-01

Three classical particle dissolution rate expressions are commonly used to interpret particle dissolution rate phenomena. Our analysis shows that an assumption used in the derivation of the traditional cube-root law may not be accurate under all conditions for diffusion-controlled particle dissolution. Mathematical analysis shows that the three classical particle dissolution rate expressions are approximate solutions to a general diffusion layer model. The cube-root law is most appropriate when particle size is much larger than the diffusion layer thickness, the two-thirds-root expression applies when the particle size is much smaller than the diffusion layer thickness. The square-root expression is intermediate between these two models. A general solution to the diffusion layer model for monodispersed spherical particles dissolution was derived for sink and nonsink conditions. Constant diffusion layer thickness was assumed in the derivation. Simulated dissolution data showed that the ratio between particle size and diffusion layer thickness (a0/h) is an important factor in controlling the shape of particle dissolution profiles. A new semiempirical general particle dissolution equation is also discussed which encompasses the three classical particle dissolution expressions. The success of the general equation in explaining limitations of traditional particle dissolution expressions demonstrates the usefulness of the general diffusion layer model.

Transient competitive complexation in biological kinetic isotope fractionation explains non-steady isotopic effects: Theory and application to denitrification in soils

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

Maggi, F.M.; Riley, W.J.

2009-06-01

The theoretical formulation of biological kinetic reactions in isotopic applications often assume first-order or Michaelis-Menten-Monod kinetics under the quasi-steady-state assumption to simplify the system kinetics. However, isotopic e ects have the same order of magnitude as the potential error introduced by these simpli cations. Both formulations lead to a constant fractionation factor which may yield incorrect estimations of the isotopic effect and a misleading interpretation of the isotopic signature of a reaction. We have analyzed the isotopic signature of denitri cation in biogeochemical soil systems by Menyailo and Hungate [2006], where high {sup 15}N{sub 2}O enrichment during N{sub 2}O productionmore » and inverse isotope fractionation during N{sub 2}O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with the quasi-steady-state Michaelis-Menten-Monod kinetics. When the quasi-steady-state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observations and aided in interpretation of experimental isotopic signatures. These results may imply a substantial revision in using the Rayleigh equation for interpretation of isotopic signatures and in modeling biological kinetic isotope fractionation with first-order kinetics or quasi-steady-state Michaelis-Menten-Monod kinetics.« less

Is there a relationship between elderly suicide rates and educational attainment? A cross-national study.

PubMed

Shah, Ajit; Chatterjee, Santanu

2008-11-01

Suicides are associated with both high and low levels of intelligence and educational attainment in both individual-level and aggregate-level studies, but this has been rarely studied in the elderly. A cross-national study examining the relationship between elderly suicide rates (y-axis) and educational attainment (x-axis) was undertaken with the 'a priori' hypothesis that the relationship would be curvilinear and follow a U-shaped curve with the quadratic equation Y = A + BX + CX(2), where A, B and C are constants. Data on suicide rates for both sexes in the age-bands 65-74 years and 75+ years, and the Education Index (a proxy measure of educational attainment) were ascertained from the World Health Organisation and the United Nations websites, respectively. The main finding was the predicted curvilinear relationship between suicide rates, in both sexes in both the elderly age-bands, and the Education Index fitting the quadratic equation Y = A + BX + CX(2). Given the cross-sectional study design, a causal relationship cannot be assumed. The impact of educational attainment on elderly suicide rates may occur through interaction with other factors, mediation of the effects of other factors, or by its effects being mediated by other factors, and require further study.

State relations for a two-phase mixture of reacting explosives and applications

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

Kubota, Shiro; Saburi, Tei; Ogata, Yuji

2007-10-15

To assess the assumptions behind the two phase mixture rule for reacting explosives, the shock-to-detonation transition process was calculated for high explosives using a finite difference method. An ignition and growth model and the Jones-Wilkins-Lee (JWL) equations of state were employed. The simple mixture rule assumes that the reacting explosive is a simple mixture of the reactant and product components. Four different assumptions, such as that of thermal equilibrium and isotropy, were adopted to calculate the pressure. The main purpose of this paper is to present the answer to the question of why the numerical results of shock-initiation are insensitivemore » to the assumptions adopted. The equations of state for reactants and products were assessed by considering plots of the specific internal energy E and specific volume V. If the slopes of the constant-pressure lines for both components in the E-V plane are almost the same, it is demonstrated that the numerical results are insensitive to the assumptions adopted. We have found that the relation for the specific volumes of the two components can be approximately expressed by a single curve of the specific volume of the reactant vs that of the products. We discuss this relationship in terms of the results of the numerical simulation. (author)« less

Balance-Equation Approach to Nonuniform Electron Transport in Nonparabolic Semiconductors

NASA Astrophysics Data System (ADS)

Cao, Juncheng; Lei, Xiaolin

1998-10-01

On the basis of the Lei-Ting balance-equation transport theory recently developed for nonparabolic energy band, we propose a hydrodynamic approach to the spatially inhomogeneous electron transport in semiconductor devices. In the present approach, the momentum and energy collision terms are expressed by two nonlinear functions, the frictional acceleration and energy-loss rate, which give a detailed scattering-process-level description of nonstationary and nonlocal charge transport in the system. This approach allows one to calculate selfconsistently the transport parameters within the model itself based on the primary material data (band structure, deformation potential constant, etc.), thus it minimizes the uncertainty associated with the use of some empirical relations for transport coefficients. As a demonstration of the approach, we have carried out a numerical calculation for a submicrometer Si n^+nn^+ diode by assuming an isotropic Kane-type energy band. The results for electron velocity and energy, obtained at much less computing cost than the Monte-Carlo (MC) method, are in good agreement with MC prediction. The influence of heat-flow term on electron transport behaviour, especially on velocity overshoot, is also investigated. The project supported by National Natural Science Foundation of China, National and Shanghai Municipal Commission of Science and Technology, and the Shanghai Foundation for Research and Development of Applied Materials

Modeling electronegative plasma discharge

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

Lichtenberg, A.J.; Lieberman, M.A.

Macroscopic analytic models for a three-component electronegative gas discharge are developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is derived. The discharge consists of an electronegative core and electropositive edges. The electron density in the core is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to a constant mobility transport model of an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane r.f. driven oxygen plasma for p = 50 mTorr and n{sub eo}=more » 2.4 x 10{sup 15} m{sup -3}. The ratio {alpha}{sub o} of central negative ion density to electron density, and the electron temperature T{sub e}, found in the simulation, are in reasonable agreement with the values calculated from the model. The model is extended to: (1) low pressures, where a variable mobility model is used in the electropositive edge region; and (2) high {alpha}{sub o} in which the edge region disappears. The inclusion of a second positive ion species, which can be very important in describing electronegative discharges used for materials processing, is a possible extension of the model.« less

Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

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…

A near-wall four-equation turbulence model for compressible boundary layers

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1992-01-01

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Time constant determination for electrical equivalent of biological cells

NASA Astrophysics Data System (ADS)

Dubey, Ashutosh Kumar; Dutta-Gupta, Shourya; Kumar, Ravi; Tewari, Abhishek; Basu, Bikramjit

2009-04-01

The electric field interactions with biological cells are of significant interest in various biophysical and biomedical applications. In order to study such important aspect, it is necessary to evaluate the time constant in order to estimate the response time of living cells in the electric field (E-field). In the present study, the time constant is evaluated by considering the hypothesis of electrical analog of spherical shaped cells and assuming realistic values for capacitance and resistivity properties of cell/nuclear membrane, cytoplasm, and nucleus. In addition, the resistance of cytoplasm and nucleoplasm was computed based on simple geometrical considerations. Importantly, the analysis on the basis of first principles shows that the average values of time constant would be around 2-3 μs, assuming the theoretical capacitance values and the analytically computed resistance values. The implication of our analytical solution has been discussed in reference to the cellular adaptation processes such as atrophy/hypertrophy as well as the variation in electrical transport properties of cellular membrane/cytoplasm/nuclear membrane/nucleoplasm.

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Constraining the 40K decay constant with 87Rb-87Sr - 40K-40Ca chronometer intercomparison

NASA Astrophysics Data System (ADS)

Naumenko-Dèzes, Maria O.; Nägler, Thomas F.; Mezger, Klaus; Villa, Igor M.

2018-01-01

A literature survey reveals that the K-Ar chronometer gives ages that are ca. 1% younger than U-Pb ages. This offset is generally attributed to an inaccurate 40K decay constant. Three geological samples selected from a shortlist of eight with known U-Pb ages were investigated using detailed petrological methods and subsequently the Rb-Sr and K-Ca chronometers in order (a) to evaluate if they meet the requirement of a geological history reflecting a ;point-like; event (i.e. isochronous formation and subsequent ideal closure of chronometers) and (b) to narrow down the systematic uncertainty on the 40K decay constant by investigating the metrologically traceable K-Ca decay branch. Lepidolite of the Rubikon pegmatite, Namibia, was dated with Rb-Sr at 504.7 ± 4.2 Ma and the phlogopite and apatite from the Phalaborwa carbonatite complex, South Africa, yielded a Rb-Sr age of 2058.9 ± 5.2 Ma. Both Rb-Sr ages agree with published U-Pb ages. The Rb-Sr age of the late Archean Siilinjärvi carbonatite, Finland, records a later regional metamorphic event at 1869 ± 10 Ma. Only the samples from the Phalaborwa complex represent a ;point-like; magmatic event and meet all the criteria to make them suitable for the 40K decay constant intercalibration. The Phalaborwa K-Ca isochron has a slope of 1.878 ± 0.012. Forcing the K-Ca isochron to coincide with the U-Pb and Rb-Sr ages gives one equation with two unknowns. Assuming that the branching ratio of the K-Ca branch, BCa, lies in the interval (k = 2) of all published references, 0.8925 < BCa < 0.8963, then the most reliable uncertainty interval (k = 2) for the total 40K decay constant, λtot, is calculated as 5.484 × 10-10 a-1 < λtot < 5.498 × 10-10 a-1. This confirms that the currently used IUGS recommendation is inaccurate.

Evaluating growth assumptions using diameter or radial increments in natural even-aged longleaf pine

Treesearch

John C. Gilbert; Ralph S. Meldahl; Jyoti N. Rayamajhi; John S. Kush

2010-01-01

When using increment cores to predict future growth, one often assumes future growth is identical to past growth for individual trees. Once this assumption is accepted, a decision has to be made between which growth estimate should be used, constant diameter growth or constant basal area growth. Often, the assumption of constant diameter growth is used due to the ease...

Rail-to-rail differential input amplification stage with main and surrogate differential pairs

DOEpatents

Britton, Jr., Charles Lanier; Smith, Stephen Fulton

2007-03-06

An operational amplifier input stage provides a symmetrical rail-to-rail input common-mode voltage without turning off either pair of complementary differential input transistors. Secondary, or surrogate, transistor pairs assume the function of the complementary differential transistors. The circuit also maintains essentially constant transconductance, constant slew rate, and constant signal-path supply current as it provides rail-to-rail operation.

Supplemental Analysis on Compressed Sensing Based Interior Tomography

PubMed Central

Yu, Hengyong; Yang, Jiansheng; Jiang, Ming; Wang, Ge

2010-01-01

Recently, in the compressed sensing framework we proved that an interior ROI can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant. In the proofs, we implicitly utilized the property that if an artifact image assumes a constant value within the ROI then this constant must be zero. Here we prove this property in the space of square integrable functions. PMID:19717891

Determination of elastic constants of a generally orthotropic plate by modal analysis

NASA Astrophysics Data System (ADS)

Lai, T. C.; Lau, T. C.

1993-01-01

This paper describes a method of finding the elastic constants of a generally orthotropic composite thin plate through modal analysis based on a Rayleigh-Ritz formulation. The natural frequencies and mode shapes for a plate with free-free boundary conditions are obtained with chirp excitation. Based on the eigenvalue equation and the constitutive equations of the plate, an iteration scheme is derived using the experimentally determined natural frequencies to arrive at a set of converged values for the elastic constants. Four sets of experimental data are required for the four independent constants: namely the two Young's moduli E1 and E2, the in-plane shear modulus G12, and one Poisson's ratio nu12. The other Poisson's ratio nu21 can then be determined from the relationship among the constants. Comparison with static test results indicate good agreement. Choosing the right combinations of natural modes together with a set of reasonable initial estimates for the constants to start the iteration has been found to be crucial in achieving convergence.

Modeling Frequency Fluctuations in Surface Contaminated Crystal Resonators

DTIC Science & Technology

1990-07-23

resonator cannot be described by cubic polynomial equations. (Cubic polynomial equations are used in the quartz resonator industry to describe frequency...frequency M = 28 ( nitrogen ), fluctuations- are studied. Our study is motivated by the the rate of-arrival ro of nitrogen molecules at a contami...the pressure If the product Qf 0 is constant, as is usually the case, then gradually. Extra care must be taken to keep constant all their spectral

Numerical simulation of solitary waves on deep water with constant vorticity

NASA Astrophysics Data System (ADS)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Holographic dark energy with varying gravitational constant in Hořava-Lifshitz cosmology

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

Setare, M.R.; Jamil, Mubasher, E-mail: rezakord@ipm.ir, E-mail: mjamil@camp.nust.edu.pk

2010-02-01

We investigate the holographic dark energy scenario with a varying gravitational constant in a flat background in the context of Hořava-Lifshitz gravity. We extract the exact differential equation determining the evolution of the dark energy density parameter, which includes G variation term. Also we discuss a cosmological implication of our work by evaluating the dark energy equation of state for low redshifts containing varying G corrections.

Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation.

PubMed

Akhmediev, Nail; Ankiewicz, Adrian

2011-04-01

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.

Recursion Operators and Bi-Hamiltonian Structures in Multidimensions II,

DTIC Science & Technology

1986-07-01

a Symmifetry (1.2). For example the Kadomtsev - Petviashvili (KP) equation and the Davey-Stewartson (DS) equation admit two such hierarchies of...Degasperis, Nuovo Cimento, 398, 1 (1977). [16] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation ...these equations possess infinitely many time dependent symmetries and constants of motion. The master symmetries T for these equations are simply derived

Hierarchical coarse-graining model for photosystem II including electron and excitation-energy transfer processes.

PubMed

Matsuoka, Takeshi; Tanaka, Shigenori; Ebina, Kuniyoshi

2014-03-01

We propose a hierarchical reduction scheme to cope with coupled rate equations that describe the dynamics of multi-time-scale photosynthetic reactions. To numerically solve nonlinear dynamical equations containing a wide temporal range of rate constants, we first study a prototypical three-variable model. Using a separation of the time scale of rate constants combined with identified slow variables as (quasi-)conserved quantities in the fast process, we achieve a coarse-graining of the dynamical equations reduced to those at a slower time scale. By iteratively employing this reduction method, the coarse-graining of broadly multi-scale dynamical equations can be performed in a hierarchical manner. We then apply this scheme to the reaction dynamics analysis of a simplified model for an illuminated photosystem II, which involves many processes of electron and excitation-energy transfers with a wide range of rate constants. We thus confirm a good agreement between the coarse-grained and fully (finely) integrated results for the population dynamics. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Alternative supply specifications and estimates of regional supply and demand for stumpage.

Treesearch

Kent P. Connaughton; David H. Jackson; Gerard A. Majerus

1988-01-01

Four plausible sets of stumpage supply and demand equations were developed and estimated; the demand equation was the same for each set, although the supply equation differed. The supply specifications varied from the model of regional excess demand in which National Forest harvest levels were assumed fixed to a more realistic model in which the harvest on the National...

Transverse vibrations of wood-based products : equations and considerations

Treesearch

Joseph F. Murphy

2011-01-01

Four equations are presented to determine bending stiffness using transverse vibration. These equations are used for constant cross-section products, panels, rectangular cross-section products, and logs with and without taper. Practical considerations for their use are discussed and concluding remarks are included.

Measurement and Interpretation of Flow Stress Data for the Simulation of Metal-Forming Processes

DTIC Science & Technology

2010-01-01

fitting constants that differ in each equation): Ludwik Equation: c)εb(aσ += , (29) Voce Equation: )]εcexp([1*a][baσ −−−+= (30) Swift...stress at low strains (ɘ.2) and to overestimate the stress for high strains. For heavily prestrained materials, c ~ 1. The Voce and Swift equations tend

The rate constant of a quantum-diffusion-controlled bimolecular reaction

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

A quantum-mechanical equation is derived in the tight-bond approximation which describes the motion and chemical interaction of a pair of species A and B when their displacement in the matrix is caused by tunnelling. Within the framework of the discrete model of random walks, definitions are given of the probability and rate constant of a reaction A + B → P (products) proceeding in a condensed medium. A method is suggested for calculating the rate constant of a quantum-diffusion-controlled bimolecular reaction. By this method, an expression is obtained for the rate constant in the stationary spherically symmetrical case. An equation for the density matrix is also proposed which describes the motion and chemical interaction of a pair of species when the quantum and classical diffusion are competitive.

Stability and bifurcation analysis of a generalized scalar delay differential equation.

PubMed

Bhalekar, Sachin

2016-08-01

This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

NASA Astrophysics Data System (ADS)

Kassem, M.

2006-03-01

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.

SU-E-I-95: Personalized Radiography Technical Parameters for Each Patient and Exam

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

Soares, F; Camozzato, T; Kahl, G

Purpose: To determine exact electrical parameters (kV, mAs) a radiological technologist shall use taking account the exam and patient's structure, with guarantee of minimum dose and adequate quality image. Methods: A patient's absorbed dose equation was developed by means of Entrance Skin Dose (ESD), irradiated area and patient width for specific anatomy. ESD is calculated from a developed equation, where entrance surface air-KERMA and backscatter factor are included, with air-to-skin coefficient conversion. We developed specific Lambert-Beer attenuation equations derived from mass energy-absorption coefficients data for skin, fat, and muscle and bone as one tissue. Anatomy tissue thickness distribution at centralmore » X-ray location in anteroposterior incidence for hand and chest, was estimate by discounting constant skin and bone thickness from patient measured width, assuming the result as muscle and fat. A clinical research at a big hospital were executed when real parameters (kV, mAs, filtration, ripple) used by technologists were combined with the image quality and patient's data: anatomy width, height and weight. A correlation among the best images acquired and electrical parameters used were confronted with patient's data and dose estimation. The best combinations were used as gold standards. Results: For each anatomy, two equations were developed to calculate voltage (kV) and exposure (mAs) to reproduce and interpolate the gold standards. Patient is measured and data are input into equations, giving radiological technologists the right set of electrical parameters for that specific exam. Conclusion: This work indicates that radiological technologist can personalize the exact electrical parameters for each patient exam, instead of using standard values. It also guarantee that patients under or over-sized measures will receive the right dose for the best image. It will stop wrong empiric adjusts technologists do when examining a non-standard patient and reduce probability of radiography retaken because of over or under exposition.« less

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α -stable noise

NASA Astrophysics Data System (ADS)

Noetel, Joerg; Sokolov, Igor M.; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α -stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τϕ, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t ≫τϕ , is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α-stable noise.

PubMed

Noetel, Joerg; Sokolov, Igor M; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α-stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τ_{ϕ}, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t≫τ_{ϕ}, is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Modeling the expenditure and reconstitution of work capacity above critical power.

PubMed

Skiba, Philip Friere; Chidnok, Weerapong; Vanhatalo, Anni; Jones, Andrew M

2012-08-01

The critical power (CP) model includes two constants: the CP and the W' [P = (W' / t) + CP]. The W' is the finite work capacity available above CP. Power output above CP results in depletion of the W' complete depletion of the W' results in exhaustion. Monitoring the W' may be valuable to athletes during training and competition. Our purpose was to develop a function describing the dynamic state of the W' during intermittent exercise. After determination of V˙O(2max), CP, and W', seven subjects completed four separate exercise tests on a cycle ergometer on different days. Each protocol comprised a set of intervals: 60 s at a severe power output, followed by 30-s recovery at a lower prescribed power output. The intervals were repeated until exhaustion. These data were entered into a continuous equation predicting balance of W' remaining, assuming exponential reconstitution of the W'. The time constant was varied by an iterative process until the remaining modeled W' = 0 at the point of exhaustion. The time constants of W' recharge were negatively correlated with the difference between sub-CP recovery power and CP. The relationship was best fit by an exponential (r = 0.77). The model-predicted W' balance correlated with the temporal course of the rise in V˙O(2) (r = 0.82-0.96). The model accurately predicted exhaustion of the W' in a competitive cyclist during a road race. We have developed a function to track the dynamic state of the W' during intermittent exercise. This may have important implications for the planning and real-time monitoring of athletic performance.

Scene-based nonuniformity correction using local constant statistics.

PubMed

Zhang, Chao; Zhao, Wenyi

2008-06-01

In scene-based nonuniformity correction, the statistical approach assumes all possible values of the true-scene pixel are seen at each pixel location. This global-constant-statistics assumption does not distinguish fixed pattern noise from spatial variations in the average image. This often causes the "ghosting" artifacts in the corrected images since the existing spatial variations are treated as noises. We introduce a new statistical method to reduce the ghosting artifacts. Our method proposes a local-constant statistics that assumes that the temporal signal distribution is not constant at each pixel but is locally true. This considers statistically a constant distribution in a local region around each pixel but uneven distribution in a larger scale. Under the assumption that the fixed pattern noise concentrates in a higher spatial-frequency domain than the distribution variation, we apply a wavelet method to the gain and offset image of the noise and separate out the pattern noise from the spatial variations in the temporal distribution of the scene. We compare the results to the global-constant-statistics method using a clean sequence with large artificial pattern noises. We also apply the method to a challenging CCD video sequence and a LWIR sequence to show how effective it is in reducing noise and the ghosting artifacts.

Modeling Heterogeneous Variance-Covariance Components in Two-Level Models

ERIC Educational Resources Information Center

Leckie, George; French, Robert; Charlton, Chris; Browne, William

2014-01-01

Applications of multilevel models to continuous outcomes nearly always assume constant residual variance and constant random effects variances and covariances. However, modeling heterogeneity of variance can prove a useful indicator of model misspecification, and in some educational and behavioral studies, it may even be of direct substantive…

Numerical study of active control of mixing in electro-osmotic flows by temperature difference using lattice Boltzmann methods.

PubMed

Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M

2013-10-01

In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. Copyright © 2013 Elsevier Inc. All rights reserved.

A Novel Non-Intrusive Method to Resolve the Thermal-Dome-Effect of Pyranometers: Radiometric Calibration and Implications

NASA Technical Reports Server (NTRS)

Ji, Qiang; Tsay, Si-Chee; Lau, K. M.; Hansell, R. A.; Butler, J. J.; Cooper, J. W.

2011-01-01

Traditionally the calibration equation for pyranometers assumes that the measured solar irradiance is solely proportional to the thermopile's output voltage; therefore only a single calibration factor is derived. This causes additional measurement uncertainties because it does not capture sufficient information to correctly account for a pyranometer's thermal effect. In our updated calibration equation, temperatures from the pyranometer's dome and case are incorporated to describe the instrument's thermal behavior, and a new set of calibration constants are determined, thereby reducing measurement uncertainties. In this paper, we demonstrate why a pyranometer's uncertainty using the traditional calibration equation is always larger than a-few-percent, but with the new approach can become much less than 1% after the thermal issue is resolved. The highlighted calibration results are based on NIST-traceable light sources under controlled laboratory conditions. The significance of the new approach lends itself to not only avoiding the uncertainty caused by a pyranometer's thermal effect but also the opportunity to better isolate and characterize other instrumental artifacts, such as angular response and non-linearity of the thermopile, to further reduce additional uncertainties. We also discuss some of the implications, including an example of how the thermal issue can potentially impact climate studies by evaluating aerosol's direct-radiative effect using field measurements with and without considering the pyranometer's thermal effect. The results of radiative transfer model simulation show that a pyranometer's thermal effect on solar irradiance measurements at the surface can be translated into a significant alteration of the calculated distribution of solar energy inside the column atmosphere.

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

NASA Astrophysics Data System (ADS)

Pu, Shi; Roy, Victor; Rezzolla, Luciano; Rischke, Dirk H.

2016-04-01

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility χm and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with χm>0 ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with χm<0 ), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time τ with a power law ˜τ-a, two distinct solutions can be found depending on the values of a and χm. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.

A Novel Nonintrusive Method to Resolve the Thermal Dome Effect of Pyranometers: Radiometric Calibration and Implications

NASA Technical Reports Server (NTRS)

Ji. Q.; Tsay, S.-C.; Lau, K. M.; Hansell, R. A.; Butler, J. J.; Cooper, J. W.

2011-01-01

Traditionally the calibration equation for pyranometers assumes that the measured solar irradiance is solely proportional to the thermopile s output voltage; therefore, only a single calibration factor is derived. This causes additional measurement uncertainties because it does not capture sufficient information to correctly account for a pyranometer s thermal effect. In our updated calibration equation, temperatures from the pyranometer's dome and case are incorporated to describe the instrument's thermal behavior, and a new set of calibration constants are determined, thereby reducing measurement uncertainties. In this paper, we demonstrate why a pyranometer's uncertainty using the traditional calibration equation is always larger than a few percent, but with the new approach can become much less than 1% after the thermal issue is resolved. The highlighted calibration results are based on NIST traceable light sources under controlled laboratory conditions. The significance of the new approach lends itself to not only avoiding the uncertainty caused by a pyranometer's thermal effect but also the opportunity to better isolate and characterize other instrumental artifacts, such as angular response and nonlinearity of the thermopile, to further reduce additional uncertainties. We also discuss some of the implications, including an example of how the thermal issue can potentially impact climate studies by evaluating aerosol s direct radiative effect using field measurements with and without considering the pyranometer s thermal effect. The results of radiative transfer model simulation show that a pyranometer s thermal effect on solar irradiance measurements at the surface can be translated into a significant alteration of the calculated distribution of solar energy inside the column atmosphere.

Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

ERIC Educational Resources Information Center

Tolle, John

2011-01-01

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

Convective drying of osmo-dehydrated apple slices: kinetics and spatial behavior of effective mass diffusivity and moisture content

NASA Astrophysics Data System (ADS)

de Farias Aires, Juarez Everton; da Silva, Wilton Pereira; de Almeida Farias Aires, Kalina Lígia Cavalcante; da Silva Júnior, Aluízio Freire; da Silva e Silva, Cleide Maria Diniz Pereira

2018-04-01

The main objective of this study is the presentation of a numerical model of liquid diffusion for the description of the convective drying of apple slices submitted to pretreatment of osmotic dehydration able of predicting the spatial distribution of effective mass diffusivity values in apple slabs. Two models that use numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with the boundary condition of third kind were proposed to describe drying. The first one does not consider the shrinkage of the product and assumes that the process parameters remain constant along the convective drying. The second one considers the shrinkage of the product and assumes that the effective mass diffusivity of water varies according to the local value of the water content in the apple samples. Process parameters were estimated from experimental data through an optimizer coupled to the numerical solutions. The osmotic pretreatment did not reduce the drying time in relation to the fresh fruits when the drying temperature was equal to 40 °C. The use of the temperature of 60 °C led to a reduction in the drying time. The model that considers the variations in the dimensions of the product and the variation in the effective mass diffusivity proved to be more adequate to describe the process.

Gravity Scaling of a Power Reactor Water Shield

NASA Technical Reports Server (NTRS)

Reid, Robert S.; Pearson, J. Boise

2008-01-01

Water based reactor shielding is being considered as an affordable option for use on initial lunar surface power systems. Heat dissipation in the shield from nuclear sources must be rejected by an auxiliary thermal hydraulic cooling system. The mechanism for transferring heat through the shield is natural convection between the core surface and an array of thermosyphon radiator elements. Natural convection in a 100 kWt lunar surface reactor shield design has been previously evaluated at lower power levels (Pearson, 2007). The current baseline assumes that 5.5 kW are dissipated in the water shield, the preponderance on the core surface, but with some volumetric heating in the naturally circulating water as well. This power is rejected by a radiator located above the shield with a surface temperature of 370 K. A similarity analysis on a water-based reactor shield is presented examining the effect of gravity on free convection between a radiation shield inner vessel and a radiation shield outer vessel boundaries. Two approaches established similarity: 1) direct scaling of Rayleigh number equates gravity-surface heat flux products, 2) temperature difference between the wall and thermal boundary layer held constant on Earth and the Moon. Nussult number for natural convection (laminar and turbulent) is assumed of form Nu = CRa(sup n). These combined results estimate similarity conditions under Earth and Lunar gravities. The influence of reduced gravity on the performance of thermosyphon heat pipes is also examined.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Hyperthermia with implanted electrodes.

PubMed

Brezovich, I A; Young, J H

1981-01-01

A general solution is given for the steady state form of the heat conduction equation applied to a simple tumor model which is imagined as being heated by means of electrical currents flowing between metallic electrodes. The model assumes a homogeneous tumor with no bloodflow. The solution for the special case of constant temperature and potential at the surface of the heated volume is examined in detail. The solution shows that there exists, independent of the particular tumor and electrode geometry, a close relationship between the steady state temperature distribution and the electrical potential. Among the more important implications of this relationship are that equipotential surfaces within the heated volume are also isothermal surfaces and that no areas of excessive heat at or near any sharp edges or corners of the electrodes should develop, despite the high electric field intensity. Based on the theory, a procedure is outlined which might greatly facilitate the determination of temperature distributions in phantoms. Finally, the usefulness and the limitations of the theoretical models in clinical hyperthermia are discussed.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Particle creation and non-equilibrium thermodynamical prescription of dark fluids for universe bounded by an event horizon

NASA Astrophysics Data System (ADS)

Saha, Subhajit; Biswas, Atreyee; Chakraborty, Subenoy

2015-03-01

In the present work, flat FRW model of the universe is considered to be an isolated open thermodynamical system where non-equilibrium prescription has been studied using the mechanism of particle creation. In the perspective of recent observational evidences, the matter distribution in the universe is assumed to be dominated by dark matter and dark energy. The dark matter is chosen as dust while for dark energy, the following choices are considered: (i) Perfect fluid with constant equation of state and (ii) Holographic dark energy. In both the cases, the validity of generalized second law of thermodynamics (GSLT) which states that the total entropy of the fluid as well as that of the horizon should not decrease with the evolution of the universe, has been examined graphically for universe bounded by the event horizon. It is found that GSLT holds in both the cases with some restrictions on the interacting coupling parameter.

SME filter approach to multiple target tracking with false and missing measurements

NASA Astrophysics Data System (ADS)

Lee, Yong J.; Kamen, Edward W.

1993-10-01

The symmetric measurement equation (SME) filter for track maintenance in multiple target tracking is extended to the general case when there are an arbitrary unknown number of false and missing position measurements in the measurement set at any time point. It is assumed that the number N of targets is known a priori and that the target motions consist of random perturbations of constant-velocity trajectories. The key idea in the paper is to generate a new measurement vector from sums-of-products of the elements of 'feasible' N-element data vectors that pass a thresholding operation in the sums-of-products framework. Via this construction, the data association problem is completely avoided, and in addition, there is no need to identify which target measurements may correspond to false returns or which target measurements may be missing. A computer simulation of SME filter performance is given, including a comparison with the associated filter (a benchmark) and the joint probabilistic data association (JPDA) filter.

Some constraints on levels of shear stress in the crust from observations and theory.

USGS Publications Warehouse

McGarr, A.

1980-01-01

In situ stress determinations in North America, southern Africa, and Australia indicate that on the average the maximum shear stress increases linearly with depth to at least 5.1 km measured in soft rock, such as shale and sandstone, and to 3.7 km in hard rock, including granite and quartzite. Regression lines fitted to the data yield gradients of 3.8 MPa/km and 6.6 MPa/km for soft and hard rock, respectively. Generally, the maximum shear stress in compressional states of stress for which the least principal stress is oriented near vertically is substantially greater than in extensional stress regimes, with the greatest principal stress in a vertical direction. The equations of equilibrium and compatibility can be used to provide functional constrains on the state of stress. If the stress is assumed to vary only with depth z in a given region, then all nonzero components must have the form A + Bz, where A and B are constants which generally differ for the various components. - Author

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1983-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

Optimization of Fish Protection System to Increase Technosphere Safety

NASA Astrophysics Data System (ADS)

Khetsuriani, E. D.; Fesenko, L. N.; Larin, D. S.

2017-11-01

The article is concerned with field study data. Drawing upon prior information and considering structural features of fish protection devices, we decided to conduct experimental research while changing three parameters: process pressure PCT, stream velocity Vp and washer nozzle inclination angle αc. The variability intervals of examined factors are shown in the Table 1. The conicity angle was assumed as a constant one. The box design B3 was chosen as a baseline being close to D-optimal designs in its statistical characteristics. The number of device rotations and its fish fry protection efficiency were accepted as the output functions of optimization. The numerical values of regression coefficients of quadratic equations describing the behavior of optimization functions Y1 and Y2 and their formulaic errors were calculated upon the test results in accordance with the planning matrix. The adequacy or inadequacy of the obtained quadratic regression model is judged via checking the condition whether Fexp ≤ Ftheor.

Effects of increased inspired oxygen concentration on tissue oxygenation: theoretical considerations.

PubMed

Lumb, Andrew B; Nair, Sindhu

2010-03-01

Breathing increased fractional oxygen concentration (FiO2) is recommended for the treatment of tissue ischaemia. The theoretical benefits of increasing FiO2 on tissue oxygenation were evaluated using standard physiological equations. Assuming constant oxygen consumption by tissues throughout the length of a capillary, the oxygen content at 20 arbitrary points along a capillary was calculated. Using mathematical representations of the haemoglobin dissociation curve and an iterative approach to include the dissolved oxygen component of oxygen content, the oxygen partial pressure (PO2) profile along a capillary was estimated. High FiO2 concentrations cause large increases in PO2 at the arteriolar end of capillaries but these large PO2 values, caused by the extra dissolved oxygen, rapidly decline along the capillary. At the venular end of the capillary (the area of tissue most likely to be hypoxic), breathing oxygen causes only a modest improvement in PO2. Increasing FiO2 to treat tissue hypoxia has clear benefits, but a multimodal approach to management is required.

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

NASA Astrophysics Data System (ADS)

Akai, Takashi; Bijeljic, Branko; Blunt, Martin J.

2018-06-01

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas-Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.

Thermal stability analysis of the fine structure of solar prominences

NASA Technical Reports Server (NTRS)

Demoulin, Pascal; Malherbe, Jean-Marie; Schmieder, Brigitte; Raadu, Mickael A.

1986-01-01

The linear thermal stability of a 2D periodic structure (alternatively hot and cold) in a uniform magnetic field is analyzed. The energy equation includes wave heating (assumed proportional to density), radiative cooling and both conduction parallel and orthogonal to magnetic lines. The equilibrium is perturbed at constant gas pressure. With parallel conduction only, it is found to be unstable when the length scale 1// is greater than 45 Mn. In that case, orthogonal conduction becomes important and stabilizes the structure when the length scale is smaller than 5 km. On the other hand, when the length scale is greater than 5 km, the thermal equilibrium is unstable, and the corresponding time scale is about 10,000 s: this result may be compared to observations showing that the lifetime of the fine structure of solar prominences is about one hour; consequently, our computations suggest that the size of the unresolved threads could be of the order of 10 km only.