Equation for the melting curve of solids under high pressure

International Nuclear Information System (INIS)

Boguslavskii, Yu.Ya.

1982-01-01

Simon's equation of the melting curve is obtained using the Clausius-Clapeyron equation in the linear approximation of the pressure dependence of the melting entropy and the volume change at the melting point. The constants in Simon's equation are calculated in this approximation for the alkali metals Li, Na, K, Rb, Cs and also for hydrogen, H 2 , and argon. It is shown that one can obtain the constants of Simon's equation in a pressure range which is wider than the region of the thermodynamical validity of Simon's equation by averaging the values of the constants determined in different points of the melting curves. The constants obtained by this manner agree well with the experimental data. (author)

Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

International Nuclear Information System (INIS)

Kraloua, B.; Hennad, A.

2008-01-01

The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

New fundamental equations of thermodynamics for systems in chemical equilibrium at a specified partial pressure of a reactant and the standard transformed formation properties of reactants

International Nuclear Information System (INIS)

Alberty, R.A.; Oppenheim, I.

1993-01-01

When temperature, pressure, and the partial pressure of a reactant are fixed, the criterion of chemical equilibrium can be expressed in terms of the transformed Gibbs energy G' that is obtained by using a Legendre transform involving the chemical potential of the reactant that is fixed. For reactions of ideal gases, the most natural variables to use in the fundamental equation are T, P', and P B , where P' is the partial pressure of the reactants other than the one that is fixed and P B is the partial pressure of the reactant that is fixed. The fundamental equation for G' yields the expression for the transformed entropy S', and a transformed enthalpy can be defined by the additional Legendre transform H'=G'+TS'. This leads to an additional form of the fundamental equation. The calculation of transformed thermodynamic properties and equilibrium compositions is discussed for a simple system and for a general multireaction system. The change, in a reaction, of the binding of the reactant that is at a specified pressure can be calculated using one of the six Maxwell equations of the fundamental equation in G'

Pressure drop calculation using a one-dimensional mathematical model for two-phase flow through an orifice

DEFF Research Database (Denmark)

Petkov, K.P.; Puton, M; Madsen, Søren Peder

2014-01-01

are accounted for through both friction and acceleration as in a conventional formulation. However, in this analysis the acceleration term is both attributed geometrical effects through the area change and fluid dynamic effects through the expansion of the two-phase flow. The comparison of numerical...... is a one dimensional formulation in space and the equations incorporates the change in tubes and orifice diameter as formulated in (S. Madsen et.al., Dynamic Modeling of Phase Crossings in Two-Phase Flow, Communications in Computational Physics 12 (4), 1129-1147). The pressure changes in the flow...

Equations of states for an ionic liquid under high pressure: A molecular dynamics simulation study

International Nuclear Information System (INIS)

Ribeiro, Mauro C.C.; Pádua, Agílio A.H.; Gomes, Margarida F.C.

2014-01-01

Highlights: • We compare different equation of states, EoS, for an ionic liquid under high pressure. • Molecular dynamics, MD, simulations have been used to evaluate the best EoS. • MD simulations show that a group contribution model can be extrapolated to P ∼ 1.0 GPa. • A perturbed hard-sphere EoS also fits the densities calculated by MD simulations. - Abstract: The high-pressure dependence of density given by empirical equation of states (EoS) for the ionic liquid 1-butyl-3-methylimidazolium trifluoromethanesulfonate (or triflate), [C 4 C 1 im][TfO], is compared with results obtained by molecular dynamics (MD) simulations. Two EoS proposed for [C 4 C 1 im][TfO] in the pressure range of tens of MPa, which give very different densities when extrapolated to pressures beyond the original experiments, are compared with a group contribution model (GCM). The MD simulations provide support that one of the empirical EoS and the GCM is valid in the pressure range of hundreds of MPa. As an alternative to these EoS that are based on modified Tait equations, it is shown that a perturbed hard-sphere EoS based on the Carnahan–Starling–van der Waals equation also fits the densities calculated by MD simulations of [C 4 C 1 im][TfO] up to ∼1.0 GPa

Six-Degree-of-Freedom Sensor Fish Design: Governing Equations and Motion Modeling

Energy Technology Data Exchange (ETDEWEB)

Deng, Zhiqun; Richmond, Marshall C.; Simmons, Carver S.; Carlson, Thomas J.

2004-08-19

The Sensor Fish device is being used at Northwest hydropower projects to better understand the conditions fish experience during passage through hydroturbines and other dam bypass alternatives. Since its initial development in 1997, the Sensor Fish has undergone numerous design changes to improve its function and extend the range of its use. The most recent Sensor Fish design, the three degree of freedom (3DOF) device, has been used successfully to characterize the environment fish experience when passing through turbines, in spill, or in engineered fish bypass facilities at dams. Pacific Northwest National Laboratory (PNNL) is in the process of redesigning the current 3DOF Sensor Fish device package to improve its field performance. Rate gyros will be added to the new six degree of freedom (6DOF) device so that it will be possible to observe the six linear and angular accelerations of the Sensor Fish as it passes the dam. Before the 6DOF Sensor Fish device can be developed and deployed, governing equations of motion must be developed in order to understand the design implications of instrument selection and placement within the body of the device. In this report, we describe a fairly general formulation for the coordinate systems, equations of motion, force and moment relationships necessary to simulate the 6DOF movement of an underwater body. Some simplifications are made by considering the Sensor Fish device to be a rigid, axisymmetric body. The equations of motion are written in the body-fixed frame of reference. Transformations between the body-fixed and interial reference frames are performed using a formulation based on quaternions. Force and moment relationships specific to the Sensor Fish body are currently not available. However, examples of the trajectory simulations using the 6DOF equations are presented using existing low and high-Reynolds number force and moment correlations. Animation files for the test cases are provided in an attached CD. The next

EQUATIONS FOR GAS RELEASING PROCESS FROM PRESSURIZED VESSELS IN ODH EVALUATION

International Nuclear Information System (INIS)

JIA, L.X.; WANG, L.

2001-01-01

IN THE EVALUATION OF ODH, THE CALCULATION OF THE SPILL RATE FROM THE PRESSURIZED VESSEL IS THE CENTRAL TASK. THE ACCURACY OF THE ENGINEERING ESTIMATION BECOMES ONE OF THE SAFETY DESIGN ISSUES. THIS PAPER SUMMARIZES THE EQUATIONS FOR THE OXYGEN CONCENTRATION CALCULATION IN DIFFERENT CASES, AND DISCUSSES THE EQUATIONS FOR THE GAS RELEASE PROCESS CALCULATION BOTH FOR THE HIGH-PRESSURE GAS TANK AND THE LOW-TEMPERATURE LIQUID CONTAINER

Six-degree-of-freedom Sensor Fish design - Governing equations and motion modeling

Energy Technology Data Exchange (ETDEWEB)

Zeng, D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Richmond, M. C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Simmons, C. S. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Carlson, T. J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

2004-07-01

The Sensor Fish device is being used at Northwest hydropower projects to better understand the conditions fish experience during passage through hydro turbines and other dam bypass alternatives. Since its initial development in 1997, the Sensor Fish has undergone numerous design changes to improve its function and extend the range of its use. The most recent Sensor Fish design, the three degree of freedom (3DOF) device, has been used successfully to characterize the environment fish experience when passing through turbines, in spill, or in engineered fish bypass facilities at dams. Pacific Northwest National Laboratory (PNNL) is in the process of redesigning the current 3DOF Sensor Fish device package to improve its field performance. Rate gyros will be added to the new six degree of freedom (6DOF) device so that it will be possible to observe the six linear and angular accelerations of the Sensor Fish as it passes the dam. Before the 6DOF Sensor Fish device can be developed and deployed, governing equations of motion must be developed in order to understand the design implications of instrument selection and placement within the body of the device. The report describes a fairly general formulation for the coordinate systems, equations of motion, force and moment relationships necessary to simulate the 6DOF movement of an underwater body.

Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity

International Nuclear Information System (INIS)

Yepez, Jeffrey

2006-01-01

Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory

Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence

CERN Document Server

Jenkins, Elizabeth E; Trott, Michael

2013-01-01

We calculate the order \\lambda, \\lambda^2 and \\lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \\lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.

Modelling of anisotropic compact stars of embedding class one

Energy Technology Data Exchange (ETDEWEB)

Bhar, Piyali [Government General Degree College, Department of Mathematics, Singur, Hooghly, West Bengal (India); Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, U.P. (India); Manna, Tuhina [St. Xavier' s College, Department of Commerce (Evening), Kolkata, West Bengal (India)

2016-10-15

In the present article, we have constructed static anisotropic compact star models of Einstein field equations for the spherical symmetric metric of embedding class one. By assuming the particular form of the metric function ν, we have solved the Einstein field equations for anisotropic matter distribution. The anisotropic models represent the realistic compact objects such as SAX J 1808.4-3658 (SS1), Her X-1, Vela X-12, PSR J1614-2230 and Cen X-3. We have reported our results in details for the compact star Her X-1 on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, TOV equation and red-shift etc. Along with these, we have also discussed about the stability of the compact star models. Finally we made a comparison between our anisotropic stars with the realistic objects on the key aspects as central density, central pressure, compactness and surface red-shift. (orig.)

Modelling of microwave sustained capillary plasma columns at atmospheric pressure

International Nuclear Information System (INIS)

Pencheva, M; Petrova, Ts; Benova, E; Zhelyazkov, I

2006-01-01

In this work we present a model of argon microwave sustained discharge at high pressure (1 atm), which includes two self-consistently linked parts - electrodynamic and kinetic ones. The model is based on a steady-state Boltzmann equation in an effective field approximation coupled with a collisional-radiative model for high-pressure argon discharge numerically solved together with Maxwell's equation for an azimuthally symmetric TM surface wave and wave energy balance equation. It is applied for the purpose of theoretical description of the discharge in a stationary state. The phase diagram, the electron energy distribution function as well as the dependences of the electron and heavy particles densities and the mean input power per electron on the electron number density and wave number are presented

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

Science.gov (United States)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and

Development of a polynomial nodal model to the multigroup transport equation in one dimension

International Nuclear Information System (INIS)

Feiz, M.

1986-01-01

A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

Science.gov (United States)

Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.

2014-01-01

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

Pressure correction schemes for compressible flows: application to baro-tropic Navier-Stokes equations and to drift-flux model; Methodes de correction de pression pour les ecoulements compressibles: application aux equations de Navier-Stokes barotropes et au modele de derive

Energy Technology Data Exchange (ETDEWEB)

Gastaldo, L

2007-11-15

We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they

A Brief Review on the Baer-Nunziato type Multi-pressure Multi-fluid Models

International Nuclear Information System (INIS)

Lee, Sang Yong; Park, Chan Eok; Lee, Gyu Cheon

2010-01-01

Single pressure two-fluid flow equations have complex characteristics. This causes ill-posedness problem. Even though some authors show that the numerical solutions are well behaved if the number of mesh points is sufficiently small, the stability of the solution is always challenged. There have been several attempts to overcome these problems. Multi-pressure multi-fluid models are one of them. Among them, Baer and Nunziato (BN) derived an interesting two-fluid model. BN model has independent phase pressures. It is closed by inserting volume fraction evolution equation. In this paper, several aspects of the BN type model will be reviewed and some suggestion for the future study will be made

One-dimensional model of inertial pumping

Science.gov (United States)

Kornilovitch, Pavel E.; Govyadinov, Alexander N.; Markel, David P.; Torniainen, Erik D.

2013-02-01

A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location.

Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

International Nuclear Information System (INIS)

Ng, Felix S.L.

2016-01-01

We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

Some thoughts on the pressure integration requirements of the Navier–Stokes equations

International Nuclear Information System (INIS)

Saad, Tony; Majdalani, Joseph

2012-01-01

The Navier–Stokes formulation represents a uniquely challenging system of partial differential equations that continues to influence modern applied science and engineering. In its simplest form, the system can be used to prescribe the motion of a viscous incompressible fluid with constant properties. It consists of four equations in three-dimensional space that account for both the kinematic and dynamic conditions that a fluid element senses. In this work, we investigate the pressure integration rules and restrictions that affect the resolution of the scalar pressure field. We begin our analysis by exploring the integration properties of Euler's equations in two dimensions while making use of Clairaut's theorem on the commutativity of mixed partial derivatives. We then extend our findings to three-dimensional space. This process gives rise to a theorem and four corollaries that help to clarify the conditions needed to obtain exact or asymptotic solutions for the pressure distribution. Consequently, we identify the fundamental conditions under which the Navier–Stokes equations can be properly integrated to arrive at an analytic expression for the pressure field, namely, one that is continuous and twice differentiable. In closing, several configurations are used to test the theorem and showcase its connection with the pressure formulation. These include potential flows for which the pressure can be obtained unconditionally, and inviscid rotational motions of the Taylor–Culick type with and without headwall injection. (paper)

Thermodynamic inconsistency of the modified Saha equation at high pressures

International Nuclear Information System (INIS)

Sweeney, M.A.

1978-01-01

The inclusion of a pressure ionization term in the Saha equation violates the thermodynamic Maxwell identities if corresponding changes are not made to the expressions for entropy and pressure. It is demonstrated that the usual application of the Rouse and Stewart-Pyatt modesl suffers from this limitation. Negative values of the adiabatic gradient in the degenerate dwarf models of Boehm and Straka are explained in terms of this thermodynamic inconsistency

Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

Science.gov (United States)

Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

2016-08-01

Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.

Electromagnetic-field equations in the six-dimensional space-time R6

International Nuclear Information System (INIS)

Teli, M.T.; Palaskar, D.

1984-01-01

Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts

Nonlinear Modeling and Analysis of Pressure Wave inside CEUP Fuel Pipeline

Directory of Open Access Journals (Sweden)

Qaisar Hayat

2014-01-01

Full Text Available Operating conditions dependent large pressure variations are one of the working characteristics of combination electronic unit pump (CEUP fuel injection system for diesel engines. We propose a precise and accurate nonlinear numerical model of pressure inside HP fuel pipeline of CEUP using wave equation (WE including both viscous and frequency dependent frictions. We have proved that developed hyperbolic approximation gives more realistic description of pressure wave as compared to classical viscous damped wave equation. Frictional effects of various frequencies on pressure wave have been averaged out across valid frequencies to represent the combined effect of all frequencies on pressure wave. Dynamic variations of key fuel properties including density, acoustic wave speed, and bulk modulus with varying pressures have also been incorporated. Based on developed model we present analysis on effect of fuel pipeline length on pressure wave propagation and variation of key fuel properties with both conventional diesel and alternate fuel rapeseed methyl ester (RME for CEUP pipeline.

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Modular differential equations for torus one-point functions

International Nuclear Information System (INIS)

Gaberdiel, Matthias R; Lang, Samuel

2009-01-01

It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions

Equation of state of the one- and three-dimensional Bose-Bose gases

Science.gov (United States)

Chiquillo, Emerson

2018-06-01

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the interspecies coupling constants.

The hyper-Kaehler supersymmetric sigma-model in six dimensions

International Nuclear Information System (INIS)

Sierra, G.; Townsend, P.K.

1983-01-01

The maximally supersymmetric, hyper-Kaehler, sigma-model is given in six-dimensional superfield form. The hyper-Kaehler condition follows from the requirements that the equations of motion be derivable from an action. (orig.)

One-dimensional transient unequal velocity two-phase flow by the method of characteristics

International Nuclear Information System (INIS)

Rasouli, F.

1981-01-01

An understanding of two-phase flow is important when one is analyzing the accidental loss of coolant or when analyzing industrial processes. If a pipe in the steam generator of a nuclear reactor breaks, the flow will remain critical (or choked) for almost the entire blowdown. For this reason the knowledge of the two-phase maximum (critical) flow rate is important. A six-equation model--consisting of two continuity equations, two energy equations, a mixture momentum equation, and a constitutive relative velocity equation--is solved numerically by the method of characteristics for one-dimensional, transient, two-phase flow systems. The analysis is also extended to the special case of transient critical flow. The six-equation model is used to study the flow of a nonequilibrium sodium-argon system in a horizontal tube in which the nonequilibrium sodium-argon system in a horizontal tube in which the critical flow condition is at the entrance. A four-equation model is used to study the pressure-pulse propagation rate in an isothermal air-water system, and the results that are found are compared with the experimental data. Proper initial and boundary conditions are obtained for the blowdown problem. The energy and mass exchange relations are evaluated by comparing the model predictions with results of void-fraction and heat-transfer experiments. A simplified two-equation model is obtained for the special case of two incompressible phases. This model is used in the preliminary analysis of batch sedimentation. It is also used to predict the shock formation in the gas-solid fluidized bed

Hamiltonian derivation of the nonhydrostatic pressure-coordinate model

Science.gov (United States)

Salmon, Rick; Smith, Leslie M.

1994-07-01

In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.

One-equation near-wall turbulence modeling with the aid of direct simulation data

Science.gov (United States)

Rodi, W.; Mansour, N. N.; Michelassi, V.

1993-01-01

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

I. A model for the magnetic equation of state of liquid 3He. II. An induced interaction model for a two-component Fermi liquid

International Nuclear Information System (INIS)

Sanchez-Castro, C.R.

1988-01-01

This dissertation is divided in six chapters. Chapter 1 is an introduction to the rest of the dissertation. In it, the author presents the different models for the magnetic equation state of liquid 3 He, a derivation of the induced interaction equations for a one component Fermi liquid, and discuss the basic hamiltonian describing the heavy fermion compounds. In Chapter 2 and Chapter 3, he presents a complete discussion of the thermodynamics and Landau theory of a spin polarized Fermi liquid. A phenomenological model is then developed to predict the polarization dependence of the longitudinal Landau parameters in liquid 3 He. This model predicts a new magnetic equation of state and the possibility of liquid 3 He being 'nearly metamagnetic' at high pressures. Chapter 4 contains a microscopic calculation of the magnetic field dependence of the Landau parameters in a strongly correlated Fermi system using the induced interaction model. The system he studied consists of a single component Fermi liquid with parabolic energy bands, and a large on-site repulsive interaction. In Chapter 5, he presents a complete discussion of the Landau theory of a two component Fermi liquid. Then, he generalizes the induced interaction equations to calculate Landau parameters and scattering amplitudes for an arbitrary, spin polarized, two component Fermi liquid. The resulting equations are used to study a model for the heavy fermion Fermi liquid state: a two band electronic system with an antiferromagnetic interaction between the two bands. Chapter 6 contains the concluding remarks of the dissertation

Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

International Nuclear Information System (INIS)

Krolikowski, W.

1983-01-01

A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

Science.gov (United States)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

A one-step method for modelling longitudinal data with differential equations.

Science.gov (United States)

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

The Schroedinger-Newton equation as model of self-gravitating quantum systems

International Nuclear Information System (INIS)

Grossardt, Andre

2013-01-01

The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

Differential Equations Models to Study Quorum Sensing.

Science.gov (United States)

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

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

Application of a Lorentz transformation in six dimensions to an extension of dirac equation

International Nuclear Information System (INIS)

Sabry, A.A.

2000-01-01

On applying a six dimensional Lorentz transformation (by adding three time components to the usual 3 space components) a covariant extended Dirac equation in this six dimensional space is suggested. From the free field solution of the extended equation we obtained four solutions for E , the first component of energy which depends on very big masses M and M 0 . The observed masses of the leptons and their corresponding neutrinos satisfying the same free field equation, can then be obtained on using second quantisation procedures on the field operators

One-way spatial integration of hyperbolic equations

Science.gov (United States)

Towne, Aaron; Colonius, Tim

2015-11-01

In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.

Modeling the dynamic response of pressures in a distributed helium refrigeration system

International Nuclear Information System (INIS)

Brubaker, J.C.

1997-12-01

A mathematical model is created of the dynamic response of pressures caused by flow inputs to an existing distributed helium refrigeration system. The dynamic system studied consists of the suction and discharge pressure headers and compressor portions of the refrigeration system used to cool the superconducting magnets of the Tevatron accelerator at the Fermi National Accelerator Laboratory. The modeling method involves identifying the system from data recorded during a series of controlled tests, with effort made to detect locational differences in pressure response around the four mile accelerator circumference. A review of the fluid mechanics associated with the system indicates linear time invariant models are suitable for the identification, particularly since the governing equations of one dimensional fluid flow are approximated by linear differential equations. An outline of the experimental design and the data acquisition system are given, followed by a detailed description of the modeling, which utilized the Matlab programming language and associated System Identification Toolbox. Two representations of the system are presented. One, a black box model, provides a multi-input, multi-output description assembled from the results of single input step function testing. This description indicates definite variation in pressure response with distance from the flow input location, and also suggests subtle differences in response with the input location itself. A second system representation is proposed which details the relation between continuous flow changes and pressure response, and provides explanation of a previously unappreciated pressure feedback internal to the system

Modeling the dynamic response of pressures in a distributed helium refrigeration system

Energy Technology Data Exchange (ETDEWEB)

Brubaker, John Carl [Illinois Inst. of Technology, Chicago, IL (United States)

1997-12-01

A mathematical model is created of the dynamic response of pressures caused by flow inputs to an existing distributed helium refrigeration system. The dynamic system studied consists of the suction and discharge pressure headers and compressor portions of the refrigeration system used to cool the superconducting magnets of the Tevatron accelerator at the Fermi National Accelerator Laboratory. The modeling method involves identifying the system from data recorded during a series of controlled tests, with effort made to detect locational differences in pressure response around the four mile accelerator circumference. A review of the fluid mechanics associated with the system indicates linear time invariant models are suitable for the identification, particularly since the governing equations of one dimensional fluid flow are approximated by linear differential equations. An outline of the experimental design and the data acquisition system are given, followed by a detailed description of the modeling, which utilized the Matlab programming language and associated System Identification Toolbox. Two representations of the system are presented. One, a black box model, provides a multi-input, multi-output description assembled from the results of single input step function testing. This description indicates definite variation in pressure response with distance from the flow input location, and also suggests subtle differences in response with the input location itself. A second system representation is proposed which details the relation between continuous flow changes and pressure response, and provides explanation of a previously unappreciated pressure feedback internal to the system.

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

Science.gov (United States)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Numerical solution of conservation equations in the transient model for the system thermal - hydraulics in the Korsar computer code

International Nuclear Information System (INIS)

Yudov, Y.V.

2001-01-01

The functional part of the KORSAR computer code is based on the computational unit for the reactor system thermal-hydraulics and other thermal power systems with water cooling. The two-phase flow dynamics of the thermal-hydraulic network is modelled by KORSAR in one-dimensional two-fluid (non-equilibrium and nonhomogeneous) approximation with the same pressure of both phases. Each phase is characterized by parameters averaged over the channel sections, and described by the conservation equations for mass, energy and momentum. The KORSAR computer code relies upon a novel approach to mathematical modelling of two-phase dispersed-annular flows. This approach allows a two-fluid model to differentiate the effects of the liquid film and droplets in the gas core on the flow characteristics. A semi-implicit numerical scheme has been chosen for deriving discrete analogs the conservation equations in KORSAR. In the semi-implicit numerical scheme, solution of finite-difference equations is reduced to the problem of determining the pressure field at a new time level. For the one-channel case, the pressure field is found from the solution of a system of linear algebraic equations by using the tri-diagonal matrix method. In the branched network calculation, the matrix of coefficients in the equations describing the pressure field is no longer tri-diagonal but has a sparseness structure. In this case, the system of linear equations for the pressure field can be solved with any of the known classical methods. Such an approach is implemented in the existing best-estimate thermal-hydraulic computer codes (TRAC, RELAP5, etc.) For the KORSAR computer code, we have developed a new non-iterative method for calculating the pressure field in the network of any topology. This method is based on the tri-diagonal matrix method and performs well when solving the thermal-hydraulic network problems. (author)

Engineering Model of High Pressure Moist Air

Directory of Open Access Journals (Sweden)

Hyhlík Tomáš

2017-01-01

Full Text Available The article deals with the moist air equation of state. There are equations of state discussed in the article, i.e. the model of an ideal mixture of ideal gases, the model of an ideal mixture of real gases and the model based on the virial equation of state. The evaluation of sound speed based on the ideal mixture concept is mentioned. The sound speed calculated by the model of an ideal mixture of ideal gases is compared with the sound speed calculated by using the model based on the concept of an ideal mixture of real gases. The comparison of enthalpy end entropy based on the model of an ideal mixture of ideal gases and the model of an ideal mixture of real gases is performed. It is shown that the model of an ideal mixture of real gases deviates from the model of an ideal mixture of ideal gases only in the case of high pressure. An impossibility of the definition of partial pressure in the mixture of real gases is discussed, where the virial equation of state is used.

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

NARCIS (Netherlands)

van Duijn, C. J.; Mitra, K.; Pop, I. S.

2018-01-01

The Richards equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the

One-Dimensional Modelling of Internal Ballistics

Science.gov (United States)

Monreal-González, G.; Otón-Martínez, R. A.; Velasco, F. J. S.; García-Cascáles, J. R.; Ramírez-Fernández, F. J.

2017-10-01

A one-dimensional model is introduced in this paper for problems of internal ballistics involving solid propellant combustion. First, the work presents the physical approach and equations adopted. Closure relationships accounting for the physical phenomena taking place during combustion (interfacial friction, interfacial heat transfer, combustion) are deeply discussed. Secondly, the numerical method proposed is presented. Finally, numerical results provided by this code (UXGun) are compared with results of experimental tests and with the outcome from a well-known zero-dimensional code. The model provides successful results in firing tests of artillery guns, predicting with good accuracy the maximum pressure in the chamber and muzzle velocity what highlights its capabilities as prediction/design tool for internal ballistics.

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

Science.gov (United States)

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Modeling liquid-vapor equilibria with an equation of state taking into account dipolar interactions and association by hydrogen bonding

International Nuclear Information System (INIS)

Perfetti, E.

2006-11-01

Modelling fluid-rock interactions as well as mixing and unmixing phenomena in geological processes requires robust equations of state (EOS) which must be applicable to systems containing water, gases over a broad range of temperatures and pressures. Cubic equations of state based on the Van der Waals theory (e. g. Soave-Redlich-Kwong or Peng-Robinson) allow simple modelling from the critical parameters of the studied fluid components. However, the accuracy of such equations becomes poor when water is a major component of the fluid since neither association trough hydrogen bonding nor dipolar interactions are accounted for. The Helmholtz energy of a fluid may be written as the sum of different energetic contributions by factorization of partition function. The model developed in this thesis for the pure H 2 O and H 2 S considers three contributions. The first contribution represents the reference Van der Waals fluid which is modelled by the SRK cubic EOS. The second contribution accounts for association through hydrogen bonding and is modelled by a term derived from Cubic Plus Association (CPA) theory. The third contribution corresponds to the dipolar interactions and is modelled by the Mean Spherical Approximation (MSA) theory. The resulting CPAMSA equation has six adjustable parameters, which three represent physical terms whose values are close to their experimental counterpart. This equation results in a better reproduction of the thermodynamic properties of pure water than obtained using the classical CPA equation along the vapour-liquid equilibrium. In addition, extrapolation to higher temperatures and pressure is satisfactory. Similarly, taking into account dipolar interactions together with the SRK cubic equation of state for calculating molar volume of H 2 S as a function of pressure and temperature results in a significant improvement compared to the SRK equation alone. Simple mixing rules between dipolar molecules are proposed to model the H 2 O-H 2 S

Relativistic one-boson-exchange model for the nucleon-nucleon interaction

International Nuclear Information System (INIS)

Gross, F.; Van Orden, J.W.; Holinde, K.

1992-01-01

Nucleon-nucleon data below 300-MeV laboratory energy are described by a manifestly covariant wave equation in which one of the intermediate nucleons is restricted to its mass shell. Antisymmetrization of the kernel yields an equation in which the two nucleons are treated in an exactly symmetric manner, and in which all amplitudes satisfy the Pauli principle exactly. The kernel is modeled by the sum of one boson exchanges, and four models, all of which fit the data very well (χ 2 congruent 3 per data point) are discussed. Two models require the exchange of only the π, σ, ρ, and ω, but also require an admixture of γ 5 coupling for the pion, while two other models restrict the pion coupling to pure γ 5 γ μ , but require the exchange of six mesons, including the η, and a light scalar-isovector meson referred to as σ 1 . Deuteron wave functions resulting from these models are obtained. The singularities and relativistic effects which are a part of this approach are discussed, and a complete development of the theory is presented

Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

Science.gov (United States)

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

2018-03-01

In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

Comparison of various state equations for approximation and extrapolation of experimental hydrogen molar volumes in wide temperature and pressure intervals

International Nuclear Information System (INIS)

Didyk, A.Yu.; Altynov, V.A.; Wisniewski, R.

2009-01-01

The numerical analysis of practically all existing formulae such as expansion series, Tait, logarithm, Van der Waals and virial equations for interpolation of experimental molar volumes versus high pressure was carried out. One can conclude that extrapolating dependences of molar volumes versus pressure and temperature can be valid. It was shown that virial equations can be used for fitting experimental data at relatively low pressures P<3 kbar too in distinction to other equations. Direct solving of a linear equation of the third order relatively to volume using extrapolated virial coefficients allows us to obtain good agreement between existing experimental data for high pressure and calculated values

New Models for Velocity/Pressure-Gradient Correlations in Turbulent Boundary Layers

Science.gov (United States)

Poroseva, Svetlana; Murman, Scott

2014-11-01

To improve the performance of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, one has to improve the accuracy of models for three physical processes: turbulent diffusion, interaction of turbulent pressure and velocity fluctuation fields, and dissipative processes. The accuracy of modeling the turbulent diffusion depends on the order of a statistical closure chosen as a basis for a RANS model. When the Gram-Charlier series expansions for the velocity correlations are used to close the set of RANS equations, no assumption on Gaussian turbulence is invoked and no unknown model coefficients are introduced into the modeled equations. In such a way, this closure procedure reduces the modeling uncertainty of fourth-order RANS (FORANS) closures. Experimental and direct numerical simulation data confirmed the validity of using the Gram-Charlier series expansions in various flows including boundary layers. We will address modeling the velocity/pressure-gradient correlations. New linear models will be introduced for the second- and higher-order correlations applicable to two-dimensional incompressible wall-bounded flows. Results of models' validation with DNS data in a channel flow and in a zero-pressure gradient boundary layer over a flat plate will be demonstrated. A part of the material is based upon work supported by NASA under award NNX12AJ61A.

Newtonian hydrodynamic equations with relativistic pressure and velocity

Energy Technology Data Exchange (ETDEWEB)

Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)

2016-07-01

We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.

Observation of non-chemical equilibrium effect on Ar-CO2-H2 thermal plasma model by changing pressure

International Nuclear Information System (INIS)

Al-Mamun, Sharif Abdullah; Tanaka, Yasunori; Uesugi, Yoshihiko

2009-01-01

The authors developed a two-dimensional one-temperature chemical non-equilibrium (1T-NCE) model of Ar-CO 2 -H 2 inductively coupled thermal plasmas (ICTP) to investigate the effect of pressure variation. The basic concept of one-temperature model is the assumption and treatment of the same energy conservation equation for electrons and heavy particles. The energy conservation equations consider reaction heat effects and energy transfer among the species produced as well as enthalpy flow resulting from diffusion. Assuming twenty two (22) different particles in this model and by solving mass conservation equations for each particle, considering diffusion, convection and net production terms resulting from hundred and ninety eight (198) chemical reactions, chemical non-equilibrium effects were taken into account. Transport and thermodynamic properties of Ar-CO 2 -H 2 thermal plasmas were self-consistently calculated using the first-order approximation of the Chapman-Enskog method. Finally results obtained at atmospheric pressure (760 Torr) and at reduced pressure (500, 300 Torr) were compared with results from one-temperature chemical equilibrium (1T-CE) model. And of course, this comparison supported discussion of chemical non-equilibrium effects in the inductively coupled thermal plasmas (ICTP).

An improved nucleate boiling design equation

International Nuclear Information System (INIS)

Basu, D.K.; Pinder, K.L.

1976-01-01

The effect of varying ΔT, the primary variable, on the value of heat transfer coefficient (h) in nucleate boiling is discussed. The three-parameter quadratic equation, h=P 1 + P 2 (ΔT) + P 3 (ΔT) 2 (where the constants, P 1 ,P 2 ,P 3 are functions of pressure, liquid properties and surface properties of the heater) is suggested. Ten sets of data at atmospheric pressure from six different workers and two more sets for pressure variation have been tested. The above quadratic equation fits the experimental data better than the existing two-parameter power relation, h=C(ΔT)sup(n) (where C is constant). The values of the three coeffcients in the quadratic equations are dependent on pressure, liquid properties and surface properties. A generalized empirical equation has been derived, which fits the selected pressure data well. (author)

Equation of state of liquid Indium under high pressure

Directory of Open Access Journals (Sweden)

Huaming Li

2015-09-01

Full Text Available We apply an equation of state of a power law form to liquid Indium to study its thermodynamic properties under high temperature and high pressure. Molar volume of molten indium is calculated along the isothermal line at 710K within good precision as compared with the experimental data in an externally heated diamond anvil cell. Bulk modulus, thermal expansion and internal pressure are obtained for isothermal compression. Other thermodynamic properties are also calculated along the fitted high pressure melting line. While our results suggest that the power law form may be a better choice for the equation of state of liquids, these detailed predictions are yet to be confirmed by further experiment.

Dirac equation and optical wave propagation in one dimension

Energy Technology Data Exchange (ETDEWEB)

Gonzalez, Gabriel [Catedras CONACYT, Universidad Autonoma de San Luis Potosi (Mexico); Coordinacion para la Innovacion y la Aplicacion de la Ciencia y la Tecnologia, Universidad Autonoma de San Luis Potosi (Mexico)

2018-02-15

We show that the propagation of transverse electric (TE) polarized waves in one-dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be generated in an optical set-up by controlling the refractive index landscape, where TE-polarized waves mimic the Dirac particles and the soliton field can be tuned by adjusting the refractive index. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Effect of disjoining pressure in a thin film equation with non-uniform forcing

KAUST Repository

MOULTON, D. E.; LEGA, J.

2013-01-01

We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations

Laser driven shock wave experiments for equation of state studies at megabar pressures

CERN Document Server

Pant, H C; Senecha, V K; Bandyopadhyay, S; Rai, V N; Khare, P; Bhat, R K; Gupta, N K; Godwal, B K

2002-01-01

We present the results from laser driven shock wave experiments for equation of state (EOS) studies of gold metal. An Nd:YAG laser chain (2 J, 1.06 mu m wavelength, 200 ps pulse FWHM) is used to generate shocks in planar Al foils and Al + Au layered targets. The EOS of gold in the pressure range of 9-13 Mbar is obtained using the impedance matching technique. The numerical simulations performed using the one-dimensional radiation hydrodynamic code support the experimental results. The present experimental data show remarkable agreement with the existing standard EOS models and with other experimental data obtained independently using laser driven shock wave experiments.

Laser driven shock wave experiments for equation of state studies at megabar pressures

International Nuclear Information System (INIS)

Pant, H C; Shukla, M; Senecha, V K; Bandyopadhyay, S; Rai, V N; Khare, P; Bhat, R K; Gupta, N K; Godwal, B K

2002-01-01

We present the results from laser driven shock wave experiments for equation of state (EOS) studies of gold metal. An Nd:YAG laser chain (2 J, 1.06 μm wavelength, 200 ps pulse FWHM) is used to generate shocks in planar Al foils and Al + Au layered targets. The EOS of gold in the pressure range of 9-13 Mbar is obtained using the impedance matching technique. The numerical simulations performed using the one-dimensional radiation hydrodynamic code support the experimental results. The present experimental data show remarkable agreement with the existing standard EOS models and with other experimental data obtained independently using laser driven shock wave experiments

An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

International Nuclear Information System (INIS)

Fujita, Y.

2001-01-01

In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

The Laguerre finite difference one-way equation solver

Science.gov (United States)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Equations for predicting biomass of six introduced tree species, island of Hawaii

Science.gov (United States)

Thomas H. Schukrt; Robert F. Strand; Thomas G. Cole; Katharine E. McDuffie

1988-01-01

Regression equations to predict total and stem-only above-ground dry biomass for six species (Acacia melanoxylon, Albizio falcataria, Eucalyptus globulus, E. grandis, E. robusta, and E. urophylla) were developed by felling and measuring 2- to 6-year-old...

One and one-half dimensional model of the EBT reactor

International Nuclear Information System (INIS)

Klein, H.H.; Bathke, C.G.

1979-01-01

A one-dimensional, time-dependent model is described for plasma particle and energy transport and alpha particle transport coupled with magnetic field evolution in a geometry appropriate to EBT. The transport equations used are derived from exact moments of the Boltzmann equation, and the magnetic field is calculated from Faraday's and Ampere's laws. The set of transport equations is closed by incorporating into them transport coefficiencents derived from the appropriate kinetic equation. Also included in the model is a Fokker-Planck calculation of the alpha particle slowing down and resultant plasma heating

Hybrid equation/agent-based model of ischemia-induced hyperemia and pressure ulcer formation predicts greater propensity to ulcerate in subjects with spinal cord injury.

Directory of Open Access Journals (Sweden)

Alexey Solovyev

Full Text Available Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI. People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation.

Mathematical Modelling of Intraretinal Oxygen Partial Pressure

African Journals Online (AJOL)

Erah

The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.

One dimensional reactor core model

International Nuclear Information System (INIS)

Kostadinov, V.; Stritar, A.; Radovo, M.; Mavko, B.

1984-01-01

The one dimensional model of neutron dynamic in reactor core was developed. The core was divided in several axial nodes. The one group neutron diffusion equation for each node is solved. Feedback affects of fuel and water temperatures is calculated. The influence of xenon, boron and control rods is included in cross section calculations for each node. The system of equations is solved implicitly. The model is used in basic principle Training Simulator of NPP Krsko. (author)

Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

KAUST Repository

Davit, Y.

2012-07-26

In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.

Pressurizer model for Embalse nuclear power plant

International Nuclear Information System (INIS)

Parkansky, D.G.; Bedrossian, G.C.

1993-01-01

Since the models normally used for he simulation of eventual accidents at the Embalse nuclear power plant with the FIREBIRD III code did not work satisfactorily when the pressurizer becomes empty of liquid, a new model was developed. This report presents the governing equations as well as the calculation technique, for which a computer program was made. An example of application is also presented. The results show that this new model can easily solve the problem of lack of liquid in the pressurizer, as it lets the fluid enter and exit freely, according to the pressure transient at the reactor outlet headers. (author)

Boltzmann equations for a binary one-dimensional ideal gas.

Science.gov (United States)

Boozer, A D

2011-09-01

We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

International Nuclear Information System (INIS)

Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

2009-01-01

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

Reference equation for prediction of a total distance during six-minute walk test using Indonesian anthropometrics.

Science.gov (United States)

Nusdwinuringtyas, Nury; Widjajalaksmi; Yunus, Faisal; Alwi, Idrus

2014-04-01

to develop a reference equation for prediction of the total distance walk using Indonesian anthropometrics of sedentary healthy subjects. Subsequently, the prediction obtained was compared to those calculated by the Caucasian-based Enright prediction equation. the cross-sectional study was conducted among 123 healthy Indonesian adults with sedentary life style (58 male and 65 female subjects in an age range between 18 and 50 years). Heart rate was recorded using Polar with expectation in the sub-maximal zone (120-170 beats per minute). The subjects performed two six-minute walk tests, the first one on a 15-meter track according to the protocol developed by the investigator. The second walk was carried out on Biodex®gait trainer as gold standard. an average total distance of 547±54.24 m was found, not significantly different from the gold standard of 544.72±54.11 m (p>0.05). Multiple regression analysis was performed to develop the new equation. the reference equation for prediction of the total distance using Indonesian anthropometrics is more applicable in Indonesia.

Revised predictive equations for salt intrusion modelling in estuaries

NARCIS (Netherlands)

Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.

2015-01-01

For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion

Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory

CERN Multimedia

CERN. Geneva

2015-01-01

The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.

One-Dimensional Contact Mode Interdigitated Center of Pressure Sensor (CMIPS)

Science.gov (United States)

Xu, Tian-Bing; Kang, Jinho; Park, Cheol; Harrison, Joycelyn S.; Guerreiro, Nelson M.; Hubbard, James E.

2009-01-01

A one dimensional contact mode interdigitated center of pressure sensor (CMIPS) has been developed. The experimental study demonstrated that the CMIPS has the capability to measure the overall pressure as well as the center of pressure in one dimension, simultaneously. A theoretical model for the CMIPS is established here based on the equivalent circuit of the configuration of the CMIPS as well as the material properties of the sensor. The experimental results match well with theoretical modeling predictions. A system mapped with two or more pieces of the CMIPS can be used to obtain information from the pressure distribution in multi-dimensions.

One-dimensional adiabatic model of waterhammer; Endodimenzionalni adiabatni model vodnega udara

Energy Technology Data Exchange (ETDEWEB)

Bizjak, S [Institut Jozef Stefan, Ljubljana (Yugoslavia)

1984-07-01

Program WH was developed to calculate transient pressure and velocities in hydraulic networks. It is based on one-dimensional approximation of conservation laws of mass and momentum. the energy equation is ignored which means that heat transfer effects are no included. When calculating the velocity of pressure wave, compressibility of liquid, elasticity of pipe and possible minimal presence of gas in bubble or dissolved form are included. (author)

Partially integrable nonlinear equations with one higher symmetry

International Nuclear Information System (INIS)

Mikhailov, A V; Novikov, V S; Wang, J P

2005-01-01

In this letter, we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function. (letter to the editor)

Equation of states and phonons at high pressure of intermediate valence compound TmTe

International Nuclear Information System (INIS)

Jha, Prafulla K.; Sanyal, Sankar P.

1997-01-01

The study of equation of states and pressure dependence of the phonon frequencies of the compound TmTe have been performed by using a simple interatomic potential approach in the frame work of rigid ion model. The compressibility study confirms that below 2 GPa the valence of the Tm is 2+ while there is a valence transition from Tm 2+ to Tm 3+ above 2 GPa. The phonon frequencies of TmTe increases as pressure is increased. (author)

Fast pressure-correction method for incompressible Navier-Stokes equations in curvilinear coordinates

Science.gov (United States)

Aithal, Abhiram; Ferrante, Antonino

2017-11-01

In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.

SharePoint 2010 Six-in-One

CERN Document Server

Geier, Chris; Bertram, Becky

2011-01-01

A team of SharePoint authorities addresses the six most essential areas of SharePoint 2010. SharePoint enables Web sites to host shared workspaces and is a leading solution for Enterprise Content Management. This book serves as one-stop shopping for concise coverage on six key areas that you need to know in order to get up and running with SharePoint 2010 quickly. After an introduction to the new features of SharePoint 2010, the author team of SharePoint experts walk you through branding and customization, workflow, business connectivity services, social networking and tools, the search functi

Development and validation of bubble breakup and coalescence constitutive models for the one-group interfacial area transport equation

International Nuclear Information System (INIS)

Pellacani, Filippo

2012-01-01

A local mechanistic model for bubble coalescence and breakup for the one-group interfacial area transport equation has been developed, in agreement and within the limits of the current understanding, based on an exhaustive survey of the theory and of the state of the art models for bubble dynamics simulation. The new model has been tested using the commercial 3D CFD code ANSYS CFX. Upward adiabatic turbulent air-water bubbly flow has been simulated and the results have been compared with the data obtained in the experimental facility PUMA. The range of the experimental data available spans between 0.5 to 2 m/s liquid velocity and 5 to 15 % volume fraction. For the implementation of the models, both the monodispersed and the interfacial area transport equation approaches have been used. The first one to perform a detailed analysis of the forces and models to reproduce the dynamic of the dispersed phase adequately and to be used in the next phases of the work. Also two different bubble induced turbulence models have been tested to consider the effect of the presence of the gas phase on the turbulence of the liquid phase. The interfacial area transport equation has been successfully implemented into the CFD code and the state of the art breakup and coalescence models have been used for simulation. The limitations of the actual theory have been shown and a new bubble interactions model has been developed. The simulations showed that a considerable improvement is achieved if compared to the state of the art closure models. Limits in the implementation derive from the actual understanding and formulation of the bubbly dynamics. A strong dependency on the interfacial non-drag force models and coefficients have been shown. More experimental and theory work needs to be done in this field to increase the prediction capability of the simulation tools regarding the distribution of the phases along the pipe radius.

A porous medium approach for the fluid structure interaction modelling of a water pressurized nuclear reactor core fuel assemblies: simulation and experimentation

International Nuclear Information System (INIS)

Ricciardi, G.

2008-10-01

The designing of a pressurized water reactor core subjected to seismic loading, is a major concern of the nuclear industry. We propose, in this PhD report, to establish the global behaviour equations of the core, in term of a porous medium. Local equations of fluid and structure are space averaged on a control volume, thus we define an equivalent fluid and an equivalent structure, of which unknowns are defined on the whole space. The non-linear fuel assemblies behaviour is modelled by a visco-elastic constitutive law. The fluid-structure coupling is accounted for by a body force, the expression of that force is based on empirical formula of fluid forces acting on a tube subject to an axial flow. The resulting equations are solved using a finite element method. A validation of the model, on three experimental device, is proposed. The first one presents two fuel assemblies subjected to axial flow. One of the two fuel assemblies is deviated from its position of equilibrium and released, while the other is at rest. The second one presents a six assemblies row, immersed in water, placed on a shaking table that can simulate seismic loading. Finally, the last one presents nine fuel assemblies network, arranged in a three by three, subject to an axial flow. The displacement of the central fuel assembly is imposed. The simulations are in agreement with the experiments, the model reproduces the influence of the flow of fluid on the dynamics and coupling of the fuel assemblies. (author)

A Multi-Phase Equation of State and Strength Model for Tin

International Nuclear Information System (INIS)

Cox, G. A.

2006-01-01

This paper considers a multi-phase equation of state and a multi-phase strength model for tin in the β, γ and liquid phases. At a phase transition there are changes in volume, energy, and properties of a material that should be included in an accurate model. The strength model will also be affected by a solid-solid phase transition. For many materials there is a lack of experimental data for strength at high pressures making the derivation of strength parameters for some phases difficult. In the case of tin there are longitudinal sound speed data on the Hugoniot available that have been used here in conjunction with a multi-phase equation of state to derive strength parameters for the γ phase, a phase which does not exist at room temperature and pressure

Global model of instabilities in low-pressure inductively coupled chlorine plasmas

Science.gov (United States)

Despiau-Pujo, Emilie; Chabert, Pascal

2009-10-01

Experimental studies have shown that low-pressure inductive discharges operating with electronegative gases are subject to instabilities near the transition between capacitive (E) and inductive (H) modes. A global model, consisting of two particle balance equations and one energy balance equation, has been previously proposed to describe the instability mechanism in SF6/ArSF6 [1]. This model, which agrees qualitatively well with experimental observations, leaves significant quantitative differences. In this paper, the model is revisited with Cl2 as the feedstock gas. An alternative treatment of the inductive power deposition is evaluated and chlorine chemistry is included. Old and new models are systematically compared. The alternative inductive coupling description slightly modifies the results. The effect of gas chemistry is even more pronounced. The instability window is smaller in pressure and larger in absorbed power, the frequency is higher and the amplitudes of oscillations are reduced. The feedstock gas is weakly dissociated ( 16%) and Cl2^+ is the dominant positive ion, which is consistent with the moderate electron density during the instability cycle. [1] M.A. Lieberman, A.J. Lichtenberg, and A.M. Marakhtanov, Appl. Phys. Lett. 75 (1999) 3617

Evaluation of Different Dose-Response Models for High Hydrostatic Pressure Inactivation of Microorganisms

Directory of Open Access Journals (Sweden)

Sencer Buzrul

2017-09-01

Full Text Available Modeling of microbial inactivation by high hydrostatic pressure (HHP requires a plot of the log microbial count or survival ratio versus time data under a constant pressure and temperature. However, at low pressure and temperature values, very long holding times are needed to obtain measurable inactivation. Since the time has a significant effect on the cost of HHP processing it may be reasonable to fix the time at an appropriate value and quantify the inactivation with respect to pressure. Such a plot is called dose-response curve and it may be more beneficial than the traditional inactivation modeling since short holding times with different pressure values can be selected and used for the modeling of HHP inactivation. For this purpose, 49 dose-response curves (with at least 4 log10 reduction and ≥5 data points including the atmospheric pressure value (P = 0.1 MPa, and with holding time ≤10 min for HHP inactivation of microorganisms obtained from published studies were fitted with four different models, namely the Discrete model, Shoulder model, Fermi equation, and Weibull model, and the pressure value needed for 5 log10 (P5 inactivation was calculated for all the models above. The Shoulder model and Fermi equation produced exactly the same parameter and P5 values, while the Discrete model produced similar or sometimes the exact same parameter values as the Fermi equation. The Weibull model produced the worst fit (had the lowest adjusted determination coefficient (R2adj and highest mean square error (MSE values, while the Fermi equation had the best fit (the highest R2adj and lowest MSE values. Parameters of the models and also P5 values of each model can be useful for the further experimental design of HHP processing and also for the comparison of the pressure resistance of different microorganisms. Further experiments can be done to verify the P5 values at given conditions. The procedure given in this study can also be extended for

From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

Science.gov (United States)

Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios

2017-08-01

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.

Equation of state experiments and theory relevant to planetary modelling

International Nuclear Information System (INIS)

Ross, M.; Graboske, H.C. Jr.; Nellis, W.J.

1981-01-01

In recent years there have been a number of static and shockwave experiments on the properties of planetary materials. The highest pressure measurements, and the ones most relevant to planetary modelling, have been obtained by shock compression. Of particular interest to the Jovian group are results for H 2 , H 2 O, CH 4 and NH 3 . Although the properties of metallic hydrogen have not been measured, they have been the subject of extensive calculations. In addition recent shock wave experiments on iron report to have detected melting under Earth core conditions. From this data theoretical models have been developed for computing the equations of state of materials used in planetary studies. A compelling feature that has followed from the use of improved material properties is a simplification in the planetary models. (author)

Development and validation of constitutive equation of HBS irradiation swelling considering hydrostatic pressure

International Nuclear Information System (INIS)

Gao Lijun; Jiang Shengyao; Yu Jiyang; Chen Bingde; Xiao Zhong

2014-01-01

The mechanism of hydrostatic pressure affecting the irradiation swelling of UO_2 high burnup structure was analyzed. Three basic assumptions used to develop the constitutive equation of irradiation swelling were made accordingly. It is concluded that hydrostatic pressure imposes an important impact on irradiation swelling mainly through compressing the UO_2 high burnup structure pores. Based on the already developed correlation of the irradiation swelling of UO_2 high burnup structure, pore shrinkage due to the application of hydrostatic pressure and thus the reduction of irradiation swelling of UO_2 high burnup structure were determined quantitatively, and the constitutive equation of irradiation swelling of UO_2 high burnup structure considering the hydrostatic pressure was constructed successfully. The constitutive equation is validated using available irradiation swelling data of UO_2 high burnup structure, which demonstrates its reasonability. (authors)

Modeling vapor liquid equilibrium of ionic liquids + gas binary systems at high pressure with cubic equations of state

Directory of Open Access Journals (Sweden)

A. C. D. Freitas

2013-03-01

Full Text Available Ionic liquids (IL have been described as novel environmentally benign solvents because of their remarkable characteristics. Numerous applications of these solvents continue to grow at an exponential rate. In this work, high pressure vapor liquid equilibria for 17 different IL + gas binary systems were modeled at different temperatures with Peng-Robinson (PR and Soave-Redlich-Kwong (SRK equations of state, combined with the van der Waals mixing rule with two binary interaction parameters (vdW-2. The experimental data were taken from the literature. The optimum binary interaction parameters were estimated by minimization of an objective function based on the average absolute relative deviation of liquid and vapor phases, using the modified Simplex algorithm. The solubilities of all gases studied in this work decrease as the temperature increases and increase with increasing pressure. The correlated results were highly satisfactory, with average absolute relative deviations of 2.10% and 2.25% for PR-vdW-2 and SRK-vdW-2, respectively.

On petroleum fluid characterization with the PC-SAFT equation of state

DEFF Research Database (Denmark)

Liang, Xiaodong; Yan, Wei; Thomsen, Kaj

2014-01-01

The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has shown promising results for describing complex phase behaviors and high pressure properties of various systems. It has been proposed as an alternative to the classical cubic equations of state in the petroleum...... industry. It is, however, far from a simple task to develop a sophisticated oil characterization method for the PC-SAFT EOS. In this work, in order to answer some fundamental questions of developing new characterization methods for PC-SAFT, six methods are proposed to estimate the model parameters...

Computer simulation of the thermal pressure in solids and the equation of state

International Nuclear Information System (INIS)

Welch, D.O.; Dienes, G.J.; Paskin, A.

1976-01-01

The equation of state of solids was investigated with molecular dynamics techniques by obtaining the pressure as a function of temperature over a wide range of compressions. Data were obtained for fcc crystals with Lennard--Jones interactions and for bcc crystals with Morse interactions. The results were analyzed in terms of the Mie--Gruneisen equation of state. The Gruneisen constant at zero temperature is found to be essentially that obtained from the volume dependence of the mean-squared lattice vibration frequency, and its temperature dependence can be approximated well with a self-consistent cell model. Calculated results are compared with experimental data for argon along the melting line

Work-Family Conflict and Psychological Well-Being: Stability and Cross-Lagged Relations within One- and Six-Year Follow-Ups

Science.gov (United States)

Rantanen, Johanna; Kinnunen, Ulla; Feldt, Taru; Pulkkinen, Lea

2008-01-01

The rank-order stability and cross-lagged relations between work-to-family conflict (WFC), family-to-work conflict (FWC), and psychological well-being were examined in two longitudinal studies with full two-wave panel designs. In Study 1 (n = 365), the time lag was one year, and in Study 2 (n = 153), six years. The Structural Equation Modeling…

Six-axis multi-anvil press for high-pressure, high-temperature neutron diffraction experiments

Energy Technology Data Exchange (ETDEWEB)

Sano-Furukawa, A., E-mail: sano.asami@jaea.go.jp; Hattori, T. [Quantum Beam Science Center, Japan Atomic Energy Agency, Ibaraki 319-1195 (Japan); J-PARC Center, Japan Atomic Energy Agency, Ibaraki 319-1195 (Japan); Arima, H. [Institute for Materials Research, Tohoku University, Sendai 980-8577 (Japan); Yamada, A. [The University of Shiga Prefecture, Shiga 522-8533 (Japan); Tabata, S.; Kondo, M.; Nakamura, A. [Sumitomo Heavy Industries Co., Ltd., Ehime 792-0001 (Japan); Kagi, H.; Yagi, T. [Geochemical Research Center, Graduate School of Science, The University of Tokyo, Tokyo 113-0033 (Japan)

2014-11-15

We developed a six-axis multi-anvil press, ATSUHIME, for high-pressure and high-temperature in situ time-of-flight neutron powder diffraction experiments. The press has six orthogonally oriented hydraulic rams that operate individually to compress a cubic sample assembly. Experiments indicate that the press can generate pressures up to 9.3 GPa and temperatures up to 2000 K using a 6-6-type cell assembly, with available sample volume of about 50 mm{sup 3}. Using a 6-8-type cell assembly, the available conditions expand to 16 GPa and 1273 K. Because the six-axis press has no guide blocks, there is sufficient space around the sample to use the aperture for diffraction and place an incident slit, radial collimators, and a neutron imaging camera close to the sample. Combination of the six-axis press and the collimation devices realized high-quality diffraction pattern with no contamination from the heater or the sample container surrounding the sample. This press constitutes a new tool for using neutron diffraction to study the structures of crystals and liquids under high pressures and temperatures.

Limitations of demand- and pressure-driven modeling for large deficient networks

Science.gov (United States)

Braun, Mathias; Piller, Olivier; Deuerlein, Jochen; Mortazavi, Iraj

2017-10-01

The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that may not be tackled correctly by current models. This paper will take a closer look at the two modeling paradigms given by demand- and pressure-driven modeling. The basic equations are introduced and parallels are drawn with the optimization formulations from electrical engineering. These formulations guarantee the existence and uniqueness of the solution. One of the central questions of the French and German research project ResiWater is the investigation of the network resilience in the case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits, we talk about deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand- and pressure-driven models.

Analysis of one-dimensional nonequilibrium two-phase flow using control volume method

International Nuclear Information System (INIS)

Minato, Akihiko; Naitoh, Masanori

1987-01-01

A one-dimensional numerical analysis model was developed for prediction of rapid flow transient behavior involving boiling. This model was based on six conservation equations of time averaged parameters of gas and liquid behavior. These equations were solved by using a control volume method with an explicit time integration. This model did not use staggered mesh scheme, which had been commonly used in two-phase flow analysis. Because void fraction and velocity of each phase were defined at the same location in the present model, effects of void fraction on phase velocity calculation were treated directly without interpolation. Though non-staggered mesh scheme was liable to cause numerical instability with zigzag pressure field, stability was achieved by employing the Godunov method. In order to verify the present analytical model, Edwards' pipe blow down and Zaloudek's initially subcooled critical two-phase flow experiments were analyzed. Stable solutions were obtained for rarefaction wave propagation with boiling and transient two-phase flow behavior in a broken pipe by using this model. (author)

A first course in structural equation modeling

CERN Document Server

Raykov, Tenko

2012-01-01

In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...

Melting-pressure and density equations of 3He at temperatures from 0.001 to 30 K

International Nuclear Information System (INIS)

Huang Yonghua; Chen Guobang

2005-01-01

Nonsegmented equations for melting pressure and density at temperatures from 0.001 K to 30 K have been developed to fit the reference data. The maximum and average deviations between the melting pressure equation and the totaling 298 reference data are 2.17% and 0.218%, respectively. For the density equations, the average deviations are 0.236% for the liquid side and 0.218% for the solid side. Both the melting pressure curve and melting density curves predicted by the submitted equations approach their minimums at about 0.315 K

Effect of disjoining pressure in a thin film equation with non-uniform forcing

KAUST Repository

MOULTON, D. E.

2013-08-02

We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotic expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions. Copyright © Cambridge University Press 2013.

Periodic solutions for one dimensional wave equation with bounded nonlinearity

Science.gov (United States)

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.

Modeling of microstructure evolution of magnesium alloy during the high pressure die casting process

International Nuclear Information System (INIS)

Wu Mengwu; Xiong Shoumei

2012-01-01

Two important microstructure characteristics of high pressure die cast magnesium alloy are the externally solidified crystals (ESCs) and the fully divorced eutectic which form at the filling stage of the shot sleeve and at the last stage of solidification in the die cavity, respectively. Both of them have a significant influence on the mechanical properties and performance of magnesium alloy die castings. In the present paper, a numerical model based on the cellular automaton (CA) method was developed to simulate the microstructure evolution of magnesium alloy during cold-chamber high pressure die casting (HPDC) process. Modeling of dendritic growth of magnesium alloy with six-fold symmetry was achieved by defining a special neighbourhood configuration and calculating of the growth kinetics from complete solution of the transport equations. Special attention was paid to establish a nucleation model considering both of the nucleation of externally solidified crystals in the shot sleeve and the massive nucleation in the die cavity. Meanwhile, simulation of the formation of fully divorced eutectic was also taken into account in the present CA model. Validation was performed and the capability of the present model was addressed by comparing the simulated results with those obtained by experiments.

The mediating role of Internet addiction in depression, social anxiety, and psychosocial well-being among adolescents in six Asian countries: a structural equation modelling approach.

Science.gov (United States)

Lai, C M; Mak, K K; Watanabe, H; Jeong, J; Kim, D; Bahar, N; Ramos, M; Chen, S H; Cheng, C

2015-09-01

This study examines the associations of Internet addiction with social anxiety, depression, and psychosocial well-being among Asian adolescents. A self-medication model conceptualizing Internet addiction as a mediating role in relating depression and social anxiety to negative psychosocial well-being was tested. A cross-sectional survey. In the Asian Adolescent Risk Behavior Survey (AARBS), 5366 adolescents aged 12-18 years from six Asian countries (China, Hong Kong, Japan, South Korea, Malaysia, and Philippines) completed a questionnaire with items of the Internet Addiction Test (IAT), Social Anxiety Scale for Adolescents (SAS-A), Center for Epidemiological Studies Depression Scale (CESD), Self-Rated Health of the Nation Outcome Scales for Children and Adolescents (HoNOSCA-SR) in the 2012-2013 school year. Structural equation modelling was used to examine the mediating role of Internet addiction in depression, social anxiety, and subjective psychosocial well-being. Significant differences on the scores of IAT, SAS-A, CESD, and HoNOSCA-SR across the six countries were found. The proposed self-medication model of Internet addiction received satisfactory goodness-of-fit with data of all countries. After the path from social anxiety to Internet addiction had been discarded in the revised model, there was a significant improvement of the goodness-of-fit in the models for Japan, South Korea, and the Philippines. Depression and social anxiety reciprocally influenced, whereas depression associated with poorer psychosocial well-being directly and indirectly through Internet addiction in all six countries. Internet addiction mediated the association between social anxiety and poor psychosocial well-being in China, Hong Kong, and Malaysia. Copyright © 2015 The Royal Society for Public Health. Published by Elsevier Ltd. All rights reserved.

Using PIV to determine relative pressures in a stenotic phantom under steady flow based on the pressure-poisson equation.

Science.gov (United States)

Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A

2010-01-01

Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.

Modeling and simulation of pressurizer dynamic process in PWR nuclear power plant

International Nuclear Information System (INIS)

Ma Jin; Liu Changliang; Li Shu'na

2010-01-01

By analysis of the actual operating characteristics of pressurizer in pressurized water reactor (PWR) nuclear power plant and based on some reasonable simplification and basic assumptions, the quality and energy conservation equations about pressurizer' s steam zone and the liquid zone are set up. The purpose of this paper is to build a pressurizer model of two imbalance districts. Water level and pressure control system of pressurizer is formed though model encapsulation. Dynamic simulation curves of main parameters are also shown. At last, comparisons between the theoretical analysis and simulation results show that the pressurizer model of two imbalance districts is reasonable. (authors)

Equation of state for neutron matter in the Quark Compound Bag model

Science.gov (United States)

Krivoruchenko, M. I.

2017-11-01

The equation of state for neutron matter is derived in the framework of the Quark Compound Bag model, in which the nucleon-nucleon interaction is generated by the s-channel exchange of six-quark Jaffe-Low primitives.

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

REDUCING REJECTION/REWORK IN PRESSURE DIE CASTING PROCESS BY APPLICATION OF DMAIC METHODOLOGY OF SIX SIGMA

Directory of Open Access Journals (Sweden)

Javedhusen Malek

2015-12-01

Full Text Available In today's ever-changing customer driven market, industries are needed to improve their products and processes to satisfy customer requirements. The Six Sigma approach has set a new paradigm of business excellence. Six Sigma as a process driven improvement methodology has been adopted successfully by many industries. From the review of various literatures, it is revealed that Six Sigma is well adopted in large scale enterprise but having less evidence of adoption in Indian SMEs. This paper is focused on providing path to Indian SMEs for initiating Six Sigma approach in their industries. The paper discusses the real life case where Six Sigma has been successfully applied at one of the Indian small-scale unit to improve rejection/rework rate in manufacturing products by pressure die casting process. This paper describes phase wise application of all the phases of define-measure-analyse-improve-control (DMAIC which also shows impact of Six Sigma in quality improvement.

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

CERN Document Server

Bleher, P M

2005-01-01

The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...

Gas-evolution oscillators. 10. A model based on a delay equation

Energy Technology Data Exchange (ETDEWEB)

Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)

1992-09-17

This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.

Gas-evolution oscillators. 10. A model based on a delay equation

International Nuclear Information System (INIS)

Bar-Eli, K.; Noyes, R.M.

1992-01-01

This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas

Differential equation models for sharp threshold dynamics.

Science.gov (United States)

Schramm, Harrison C; Dimitrov, Nedialko B

2014-01-01

We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

Science.gov (United States)

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

Directory of Open Access Journals (Sweden)

Narcisa Apreutesei

2014-05-01

Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

Remarks for one-dimensional fractional equations

Directory of Open Access Journals (Sweden)

Massimiliano Ferrara

2014-01-01

Full Text Available In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.

Validity of one-repetition maximum predictive equations in men with spinal cord injury.

Science.gov (United States)

Ribeiro Neto, F; Guanais, P; Dornelas, E; Coutinho, A C B; Costa, R R G

2017-10-01

Cross-sectional study. The study aimed (a) to test the cross-validation of current one-repetition maximum (1RM) predictive equations in men with spinal cord injury (SCI); (b) to compare the current 1RM predictive equations to a newly developed equation based on the 4- to 12-repetition maximum test (4-12RM). SARAH Rehabilitation Hospital Network, Brasilia, Brazil. Forty-five men aged 28.0 years with SCI between C6 and L2 causing complete motor impairment were enrolled in the study. Volunteers were tested, in a random order, in 1RM test or 4-12RM with 2-3 interval days. Multiple regression analysis was used to generate an equation for predicting 1RM. There were no significant differences between 1RM test and the current predictive equations. ICC values were significant and were classified as excellent for all current predictive equations. The predictive equation of Lombardi presented the best Bland-Altman results (0.5 kg and 12.8 kg for mean difference and interval range around the differences, respectively). The two created equation models for 1RM demonstrated the same and a high adjusted R 2 (0.971, Ppredictive equations are accurate to assess individuals with SCI at the bench press exercise. However, the predictive equation of Lombardi presented the best associated cross-validity results. A specific 1RM prediction equation was also elaborated for individuals with SCI. The created equation should be tested in order to verify whether it presents better accuracy than the current ones.

Validation of the activity expansion method with ultrahigh pressure shock equations of state

Science.gov (United States)

Rogers, Forrest J.; Young, David A.

1997-11-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter.

The one-dimensional Gross-Pitaevskii equation and its some excitation states

Energy Technology Data Exchange (ETDEWEB)

Prayitno, T. B., E-mail: trunk-002@yahoo.com [Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun no. 10, Jakarta, 13220 (Indonesia)

2015-04-16

We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.

Partial differential equations methods, applications and theories

CERN Document Server

Hattori, Harumi

2013-01-01

This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...

Modelling of pressure tube Quench using PDETWO

International Nuclear Information System (INIS)

Parlatan, Y.; Lei, Q.M.; Kwee, M.

2004-01-01

Transient two-dimensional heat conduction calculations have been carried out to determine the time-dependent temperature distribution in an overheated pressure tube during quenching with water. The purpose of the calculations is to provide input for evaluation of thermal (secondary) stresses in the pressure tube due to quench. The quench phenomenon in pressure tubes could occur in several hypothetical accident scenarios, including incidents involving intermittent buoyancy-induced flow during outages. In these scenarios, there will be two (radial and axial) or three dimensional temperature gradients, resulting in thermal stresses in the pressure tube, as the water front reaches and starts to cool down the hot pressure tube. The transient, two-dimensional heat conduction equation in the pressure tube during quench is solved using a FORTRAN package called PDETWO, available in the open literature for solving time-dependent coupled systems of non-linear partial differential equations over a two-dimensional rectangular region. This routine is based on finite difference solution of coupled, non-linear partial differential equations. Temperature gradient in the circumferential gradient is neglected for conservatism and convenience. The advancing water front is not modelled explicitly, and assumed to be at a uniform temperature and moving at a constant velocity inferred from experimental data. For outer surface and both ends of the pressure tube in the axial direction, a zero-heat flux boundary condition is assumed, while for the inner surface a moving water-quench front is assumed by appropriately varying the fluid temperature and the heat transfer coefficient. The pressure tube is assumed to be at a uniform temperature of 400 o C initially, to represent conditions expected during an intermittent buoyancy-influenced flow scenario. The results confirm the expectations that axial temperature gradients and associated heat fluxes are small in comparison with those in the

Stochastic higher spin six vertex model and Macdonald measures

Science.gov (United States)

Borodin, Alexei

2018-02-01

We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.

AMPTRACT: an algebraic model for computing pressure tube circumferential and steam temperature transients under stratified channel coolant conditions

International Nuclear Information System (INIS)

Gulshani, P.; So, C.B.

1986-10-01

In a number of postulated accident scenarios in a CANDU reactor, some of the horizontal fuel channels are predicted to experience periods of stratified channel coolant condition which can lead to a circumferential temperature gradient around the pressure tube. To study pressure tube strain and integrity under stratified flow channel conditions, it is, necessary to determine the pressure tube circumferential temperature distribution. This paper presents an algebraic model, called AMPTRACT (Algebraic Model for Pressure Tube TRAnsient Circumferential Temperature), developed to give the transient temperature distribution in a closed form. AMPTRACT models the following modes of heat transfer: radiation from the outermost elements to the pressure tube and from the pressure to calandria tube, convection between the fuel elements and the pressure tube and superheated steam, and circumferential conduction from the exposed to submerged part of the pressure tube. An iterative procedure is used to solve the mass and energy equations in closed form for axial steam and fuel-sheath transient temperature distributions. The one-dimensional conduction equation is then solved to obtain the pressure tube circumferential transient temperature distribution in a cosine series expansion. In the limit of large times and in the absence of convection and radiation to the calandria tube, the predicted pressure tube temperature distribution reduces identically to a parabolic profile. In this limit, however, radiation cannot be ignored because the temperatures are generally high. Convection and radiation tend to flatten the parabolic distribution

Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

KAUST Repository

Davit, Y.; Wood, B. D.; Debenest, G.; Quintard, M.

2012-01-01

In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time

Loop equations for multi-cut matrix models

International Nuclear Information System (INIS)

Akemann, G.

1995-03-01

The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)

A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

International Nuclear Information System (INIS)

Angelo, P.M.; Riela, G.

1981-01-01

We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

Science.gov (United States)

Chu, Weiqi; Li, Xiantao

2018-01-01

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

A One-Dimensional Wave Equation with White Noise Boundary Condition

International Nuclear Information System (INIS)

Kim, Jong Uhn

2006-01-01

We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one work which investigated the initial-boundary value problem for a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations

On the Schroedinger equation for the minisuperspace models

International Nuclear Information System (INIS)

Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

2000-01-01

We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator

Modeling High Frequency Semiconductor Devices Using Maxwell's Equations

National Research Council Canada - National Science Library

El-Ghazaly, Samier

1999-01-01

.... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...

Integral model of linear momentum for one-dimensional two-phase flows

International Nuclear Information System (INIS)

Kuznetsov, Yu.A.; Sabaev, E.F.

1976-01-01

''An integrated momentum model'' obtained by Meyer-Rose and widely applicable in calculations of dynamics of the thermal power systems is generalized for a case of flow of a vapour-liquid mixture with phase creep and pressure variation in the heated channel. Pressure distribution along the channel length is shown for a number of cases to be negligible. The obtained equations are found as well applicable in case pressure greatly though slowly varies in the system

A general analytical approach to the one-group, one-dimensional transport equation

International Nuclear Information System (INIS)

Barichello, L.B.; Vilhena, M.T.

1993-01-01

The main feature of the presented approach to solve the neutron transport equation consists in the application of the Laplace transform to the discrete ordinates equations, which yields a linear system of order N to be solved (LTS N method). In this paper this system is solved analytically and the inversion is performed using the Heaviside expansion technique. The general formulation achieved by this procedure is then applied to homogeneous and heterogeneous one-group slab-geometry problems. (orig.) [de

Validation of the activity expansion method with ultrahigh pressure shock equations of state

International Nuclear Information System (INIS)

Rogers, F.J.; Young, D.A.

1997-01-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. copyright 1997 The American Physical Society

Validation of the activity expansion method with ultrahigh pressure shock equations of state

Energy Technology Data Exchange (ETDEWEB)

Rogers, F.J.; Young, D.A. [Physics Department, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)

1997-11-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}

Isothermal equation of state of a lithium fluoride single crystal

Energy Technology Data Exchange (ETDEWEB)

Kim, K.Y.

1975-01-01

An isothermal equation of state of a LiF single crystal was determined from length change measurements of the specimen as a function of hydrostatic pressure up to approximately 7 kbars at 28 to 41/sup 0/C. The length change was measured with an accuracy of approximately 500 A by using a Fabry Perot type He--Ne laser interferometer for a 1-m long specimen at temperatures constant to less than 0.002/sup 0/C. Several two- and three-parameter equations of state were used in analyzing the measured pressure-volume data. The computer fit for each equation of state determines not only the value of its parameters but also the standard deviations associated with them and one dependent variable, either pressure or volume. With the parameters determined, the equations of state are extrapolated to approximately 5 megabars in order to see discrepancies. Using the Born model of ionic solids, two equations of state were derived both from a power law potential and from an exponential form for the repulsive energy of alkali metal halides and used to fit the pressure-volume data of a LiF single crystal. They are also extrapolated to approximately 5 megabars. The Birch's two-parameter equation and the Grover, Getting, and Kennedy equation are indistinguishable from the two equations of state derived from the Born model for pressures approximately equal to or less than 800 kbars within +-20 kbars. The above four equations of state also fit closely the Pagannone and Drickamer static compression data, the Christian shock wave data, and the Kormer et al. shock wave data. The isothermal bulk modulus and its first pressure derivative at atmospheric pressure and 28.83/sup 0/C are 664.5 +- 0.5 kbars and 5.40 +- 0.18, respectively, in close agreement with those values ultrasonically measured by R. A. Miller and C. S. Smith. (auth)

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

Science.gov (United States)

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Generalized enthalpy model of a high-pressure shift freezing process

KAUST Repository

Smith, N. A. S.

2012-05-02

High-pressure freezing processes are a novel emerging technology in food processing, offering significant improvements to the quality of frozen foods. To be able to simulate plateau times and thermal history under different conditions, in this work, we present a generalized enthalpy model of the high-pressure shift freezing process. The model includes the effects of pressure on conservation of enthalpy and incorporates the freezing point depression of non-dilute food samples. In addition, the significant heat-transfer effects of convection in the pressurizing medium are accounted for by solving the two-dimensional Navier-Stokes equations. We run the model for several numerical tests where the food sample is agar gel, and find good agreement with experimental data from the literature. © 2012 The Royal Society.

The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state

International Nuclear Information System (INIS)

Philipse, A; Vrij, A

2011-01-01

The thermodynamic equilibrium between charged colloids and an electrolyte reservoir is named after Frederic Donnan who first published on it one century ago (Donnan 1911 Z. Electrochem. 17 572). One of the intriguing features of the Donnan equilibrium is the ensuing osmotic equation of state which is a nonlinear one, even when both colloids and ions obey Van 't Hoff's ideal osmotic pressure law. The Donnan equation of state, nevertheless, is internally consistent; we demonstrate it to be a rigorous consequence of the phenomenological thermodynamics of a neutral bulk suspension equilibrating with an infinite salt reservoir. Our proof is based on an exact thermodynamic relation between osmotic pressure and salt adsorption which, when applied to ideal ions, does indeed entail the Donnan equation of state. Our derivation also shows that, contrary to what is often assumed, the Donnan equilibrium does not require ideality of the colloids: the Donnan model merely evaluates the osmotic pressure of homogeneously distributed ions, in excess of the pressure exerted by an arbitrary reference fluid of uncharged colloids. We also conclude that results from the phenomenological Donnan model coincide with predictions from statistical thermodynamics in the limit of weakly charged, point-like colloids.

The reservoir model: a differential equation model of psychological regulation.

Science.gov (United States)

Deboeck, Pascal R; Bergeman, C S

2013-06-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Mathematical model of one-man air revitalization system

Science.gov (United States)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

A stochastic-bayesian model for the fracture probability of PWR pressure vessels

Energy Technology Data Exchange (ETDEWEB)

Francisco, Alexandre S.; Duran, Jorge Alberto R., E-mail: afrancisco@metal.eeimvr.uff.br, E-mail: duran@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Dept. de Engenharia Mecanica

2013-07-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)

A stochastic-bayesian model for the fracture probability of PWR pressure vessels

International Nuclear Information System (INIS)

Francisco, Alexandre S.; Duran, Jorge Alberto R.

2013-01-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)

Auxiliary matrices for the six-vertex model at q sup N = 1 and a geometric interpretation of its symmetries

CERN Document Server

Korff, C

2003-01-01

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U sub q (s-tilde l-tilde sub 2) at q sup N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra pa...

A thermodynamically consistent model for granular-fluid mixtures considering pore pressure evolution and hypoplastic behavior

Science.gov (United States)

Hess, Julian; Wang, Yongqi

2016-11-01

A new mixture model for granular-fluid flows, which is thermodynamically consistent with the entropy principle, is presented. The extra pore pressure described by a pressure diffusion equation and the hypoplastic material behavior obeying a transport equation are taken into account. The model is applied to granular-fluid flows, using a closing assumption in conjunction with the dynamic fluid pressure to describe the pressure-like residual unknowns, hereby overcoming previous uncertainties in the modeling process. Besides the thermodynamically consistent modeling, numerical simulations are carried out and demonstrate physically reasonable results, including simple shear flow in order to investigate the vertical distribution of the physical quantities, and a mixture flow down an inclined plane by means of the depth-integrated model. Results presented give insight in the ability of the deduced model to capture the key characteristics of granular-fluid flows. We acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) for this work within the Project Number WA 2610/3-1.

Eight equation model for arbitrary shaped pipe conveying fluid

International Nuclear Information System (INIS)

Gale, J.; Tiselj, I.

2006-01-01

Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)

Basic studies for the solution of the criticality equation: two groups of energy and one dimension

International Nuclear Information System (INIS)

Britto Aghina, L.O. de.

1994-12-01

This work collects six basic studies for the numerical solution of the criticality equation for thermal reactors. Use is made of the diffusion theory for two groups of energy and one dimension, applicable to bare reactors, bare equivalent, infinite bare equivalent and reflected reactors. These studies were written in Mathcad 4.0/WIN programming, a practical form for use by the researchers and operators working with the Argonaut Reactor at the Instituto de Engenharia Nuclear (IEN). (author). 11 refs, 20 figs, 8 tabs

Generalized heat-transport equations: parabolic and hyperbolic models

Science.gov (United States)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

CERN Document Server

Dixon, Lance J.; Henn, Johannes M.

2011-01-01

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\\tilde\\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\\\mathcal{N}=4$ super-Yang-Mills theory, $\\Omega^{(1)}$ and $\\Omega^{(2)}$. The derivative of $\\Omega^{(2)}$ with respect to one of the conformal invariants yields $\\tilde\\Phi_6$, while another first-order differential operator applied to $\\tilde\\Phi_6$ yields $\\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\\\mathcal{N}=4$ super-Yang-Mills.

Modeling of high-pressure generation using the laser colliding foil technique

Energy Technology Data Exchange (ETDEWEB)

Fabbro, R.; Faral, B.; Virmont, J.; Cottet, F.; Romain, J.P.

1989-03-01

An analytical model describing the collision of two foils is presented and applied to the collision of laser-accelerated foils. Numerical simulations have been made to verify this model and to compare its results in the case of laser-accelerated foils. Scaling laws relating the different parameters (shock pressure, laser intensity, target material, etc.) have been established. The application of this technique to high-pressure equation of state experiments is then discussed.

Modeling of high-pressure generation using the laser colliding foil technique

International Nuclear Information System (INIS)

Fabbro, R.; Faral, B.; Virmont, J.; Cottet, F.; Romain, J.P.

1989-01-01

An analytical model describing the collision of two foils is presented and applied to the collision of laser-accelerated foils. Numerical simulations have been made to verify this model and to compare its results in the case of laser-accelerated foils. Scaling laws relating the different parameters (shock pressure, laser intensity, target material, etc.) have been established. The application of this technique to high-pressure equation of state experiments is then discussed

Application of the cubic-plus-association equation of state to mixtures with polar chemicals and high pressures

DEFF Research Database (Denmark)

Folas, Georgios; Kontogeorgis, Georgios; Michelsen, Michael Locht

2006-01-01

was given to low pressures and liquid-liquid equilibria. In this work, CPA is applied to two classes of mixtures containing polar chemicals for which high-pressure data are available: acetone-containing systems and dimethyl ether mixtures. They are of both scientific and industrial importance. Moreover, CPA......The cubic-plus-association (CPA) equation of state has been previously applied to vapor-liquid, liquid-liquid, and solid-liquid equilibria of mixtures containing associating compounds (water, alcohols, glycols, acids, amines). Although some high-pressure applications have been presented, emphasis...... to conventional models such as MHV2. Very good results are also obtained for multicomponent vapor-liquid-liquid equilibria for mixtures containing gases, water, and dimethyl ether. Finally, it is shown that high-pressure SLE can be predicted based on interaction parameters obtained from low-pressure SLE data....

Transient modelling of a natural circulation loop under variable pressure

International Nuclear Information System (INIS)

Vianna, Andre L.B.; Faccini, Jose L.H.; Su, Jian; Instituto de Engenharia Nuclear

2017-01-01

The objective of the present work is to model the transient operation of a natural circulation loop, which is one-tenth scale in height to a typical Passive Residual Heat Removal system (PRHR) of an Advanced Pressurized Water Nuclear Reactor and was designed to meet the single and two-phase flow similarity criteria to it. The loop consists of a core barrel with electrically heated rods, upper and lower plena interconnected by hot and cold pipe legs to a seven-tube shell heat exchanger of countercurrent design, and an expansion tank with a descending tube. A long transient characterized the loop operation, during which a phenomenon of self-pressurization, without self-regulation of the pressure, was experimentally observed. This represented a unique situation, named natural circulation under variable pressure (NCVP). The self-pressurization was originated in the air trapped in the expansion tank and compressed by the loop water dilatation, as it heated up during each experiment. The mathematical model, initially oriented to the single-phase flow, included the heat capacity of the structure and employed a cubic polynomial approximation for the density, in the buoyancy term calculation. The heater was modelled taking into account the different heat capacities of the heating elements and the heater walls. The heat exchanger was modelled considering the coolant heating, during the heat exchanging process. The self-pressurization was modelled as an isentropic compression of a perfect gas. The whole model was computationally implemented via a set of finite difference equations. The corresponding computational algorithm of solution was of the explicit, marching type, as for the time discretization, in an upwind scheme, regarding the space discretization. The computational program was implemented in MATLAB. Several experiments were carried out in the natural circulation loop, having the coolant flow rate and the heating power as control parameters. The variables used in the

Transient modelling of a natural circulation loop under variable pressure

Energy Technology Data Exchange (ETDEWEB)

Vianna, Andre L.B.; Faccini, Jose L.H.; Su, Jian, E-mail: avianna@nuclear.ufrj.br, E-mail: sujian@nuclear.ufrj.br, E-mail: faccini@ien.gov.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil). Lab. de Termo-Hidraulica Experimental

2017-07-01

The objective of the present work is to model the transient operation of a natural circulation loop, which is one-tenth scale in height to a typical Passive Residual Heat Removal system (PRHR) of an Advanced Pressurized Water Nuclear Reactor and was designed to meet the single and two-phase flow similarity criteria to it. The loop consists of a core barrel with electrically heated rods, upper and lower plena interconnected by hot and cold pipe legs to a seven-tube shell heat exchanger of countercurrent design, and an expansion tank with a descending tube. A long transient characterized the loop operation, during which a phenomenon of self-pressurization, without self-regulation of the pressure, was experimentally observed. This represented a unique situation, named natural circulation under variable pressure (NCVP). The self-pressurization was originated in the air trapped in the expansion tank and compressed by the loop water dilatation, as it heated up during each experiment. The mathematical model, initially oriented to the single-phase flow, included the heat capacity of the structure and employed a cubic polynomial approximation for the density, in the buoyancy term calculation. The heater was modelled taking into account the different heat capacities of the heating elements and the heater walls. The heat exchanger was modelled considering the coolant heating, during the heat exchanging process. The self-pressurization was modelled as an isentropic compression of a perfect gas. The whole model was computationally implemented via a set of finite difference equations. The corresponding computational algorithm of solution was of the explicit, marching type, as for the time discretization, in an upwind scheme, regarding the space discretization. The computational program was implemented in MATLAB. Several experiments were carried out in the natural circulation loop, having the coolant flow rate and the heating power as control parameters. The variables used in the

Application of stability enhancing minimum interfacial pressure force model for MARS

Energy Technology Data Exchange (ETDEWEB)

Lee, Won Jae; Lim, Ho Gon; Kim, Kyung Doo; Ha, Kwi Seok

2001-04-01

For thermal-hydraulic modeling of two-phase flow systems, two-fluid model, which assumes that the pressures of liquid, vapor and interface are identical, a so-called single-pressure model, is commonly used in codes for nuclear reactor safety analyses. Typical two-phase model with single pressure assumption possesses complex characteristics that result in system being ill-posed. As a result, typical single pressure model may cause the unbounded growth of instabilities. In order to overcome the ill-posedness of single-pressure two-fluid model, a hyperbolic equation system has been developed by introducing an interfacial pressure force into single pressure two-fluid model. The potential impact of the present model on the stability of finite difference solution has been examined by Von-Neumann stability analysis. The obvious improvement in numerical stability has been found when a semi-implicit time advancement scheme is used. Numerical experiments using the pilot code were also performed for the conceptual problems. It was found that the result was consistent with numerical stability test. The new model was implemented to MARS using Two-step approach. Through the conceptual stability test problems and benchmark problems, the applicability of the new model was verified.

Application of stability enhancing minimum interfacial pressure force model for MARS

International Nuclear Information System (INIS)

Lee, Won Jae; Lim, Ho Gon; Kim, Kyung Doo; Ha, Kwi Seok

2001-04-01

For thermal-hydraulic modeling of two-phase flow systems, two-fluid model, which assumes that the pressures of liquid, vapor and interface are identical, a so-called single-pressure model, is commonly used in codes for nuclear reactor safety analyses. Typical two-phase model with single pressure assumption possesses complex characteristics that result in system being ill-posed. As a result, typical single pressure model may cause the unbounded growth of instabilities. In order to overcome the ill-posedness of single-pressure two-fluid model, a hyperbolic equation system has been developed by introducing an interfacial pressure force into single pressure two-fluid model. The potential impact of the present model on the stability of finite difference solution has been examined by Von-Neumann stability analysis. The obvious improvement in numerical stability has been found when a semi-implicit time advancement scheme is used. Numerical experiments using the pilot code were also performed for the conceptual problems. It was found that the result was consistent with numerical stability test. The new model was implemented to MARS using Two-step approach. Through the conceptual stability test problems and benchmark problems, the applicability of the new model was verified

Turbulent Spot Pressure Fluctuation Wave Packet Model

Energy Technology Data Exchange (ETDEWEB)

Dechant, Lawrence J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-05-01

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler, closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.

A Novel Interpretation for Arterial Pulse Pressure Amplification in Health and Disease

Directory of Open Access Journals (Sweden)

Manuel R. Alfonso

2018-01-01

Full Text Available Arterial pressure waves have been described in one dimension using several approaches, such as lumped (Windkessel or distributed (using Navier-Stokes equations models. An alternative approach consists of modeling blood pressure waves using a Korteweg-de Vries (KdV equation and representing pressure waves as combinations of solitons. This model captures many key features of wave propagation in the systemic network and, in particular, pulse pressure amplification (PPA, which is a mechanical biomarker of cardiovascular risk. The main objective of this work is to compare the propagation dynamics described by a KdV equation in a human-like arterial tree using acquired pressure waves. Furthermore, we analyzed the ability of our model to reproduce induced elastic changes in PPA due to different pathological conditions. To this end, numerical simulations were performed using acquired central pressure signals from different subject groups (young, adults, and hypertensive as input and then comparing the output of the model with measured radial artery pressure waveforms. Pathological conditions were modeled as changes in arterial elasticity (E. Numerical results showed that the model was able to propagate acquired pressure waveforms and to reproduce PPA variations as a consequence of elastic changes. Calculated elasticity for each group was in accordance with the existing literature.

Simplified local density model for adsorption over large pressure ranges

International Nuclear Information System (INIS)

Rangarajan, B.; Lira, C.T.; Subramanian, R.

1995-01-01

Physical adsorption of high-pressure fluids onto solids is of interest in the transportation and storage of fuel and radioactive gases; the separation and purification of lower hydrocarbons; solid-phase extractions; adsorbent regenerations using supercritical fluids; supercritical fluid chromatography; and critical point drying. A mean-field model is developed that superimposes the fluid-solid potential on a fluid equation of state to predict adsorption on a flat wall from vapor, liquid, and supercritical phases. A van der Waals-type equation of state is used to represent the fluid phase, and is simplified with a local density approximation for calculating the configurational energy of the inhomogeneous fluid. The simplified local density approximation makes the model tractable for routine calculations over wide pressure ranges. The model is capable of prediction of Type 2 and 3 subcritical isotherms for adsorption on a flat wall, and shows the characteristic cusplike behavior and crossovers seen experimentally near the fluid critical point

Evaluation of atmospheric-pressure change in tornado using Fujita model

International Nuclear Information System (INIS)

Shimizu, Juntaro; Ohtsubo, Shunsuke

2017-01-01

Evaluation of the atmospheric-pressure change (APC) in a tornado is necessary to assess the integrity of nuclear-related facilities. The Rankine model has been most frequently used to theoretically calculate the APC in a tornado. The result, however, is considered to be overly conservative because the Rankine model wind speed at the ground is larger than that in reality. On the other hand, the wind speed of the Fujita model is closer to that of actual tornadoes but is expressed by more complicated algebraic equations than that in the Rankine model. Also, because it is impossible to analytically derive the APC equation using the Fujita model, numerical computation is required. A previous study employed the finite element method (FEM) for such a purpose. However, a general-purpose FEM code often requires complicated input parameters. In order to conduct parametric studies to evaluate the integrity of facilities in various cases of tornadoes, the finite-difference method code “TORPEC”, which is specialized to analyze the APC, was developed as a convenient design tool. TORPEC is based on Poisson’s equation derived from the Navier-Stokes equation. It also runs on widely available technical calculation software such as Microsoft"® Excel VBA or MATLAB"®. Taking advantage of such convenience, various calculations have been conducted to reveal the characteristics of APC as functions of the maximum tangential wind speed, axial position and tornado radius. TORPEC is used as a benchmark in the existing paper. The case study results obtained by TORPEC show a constant ratio of the pressure drop of the Fujita model against the Rankine model. This factor can be used to derive the Fujita model result from the Rankine model result without FEM analysis. (author)

Non-Equilibrium Turbulence and Two-Equation Modeling

Science.gov (United States)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Prediction of pressure between packers of staged fracturing pipe strings in high-pressure deep wells and its application

Directory of Open Access Journals (Sweden)

Fuxiang Zhang

2015-03-01

Full Text Available Addressing to the deteriorated load conditions of working string and packers caused by annular pressure drop between packers during the staged stimulation of high-pressure deep well, one 2D temperature field transient prediction model for borehole under injecting conditions which considers such influences as friction heat, convection heat exchange was set up, based on energy conservation principle and borehole heat transfer theory. By means of analyzing the influences of borehole temperature and pressure changes on the annular volume between packers, and in combination with borehole temperature transient prediction model, annular fluid PVT equations of state, radial deformation model of tubing and formation transient seepage equation, a typical high-pressure deep well inter-packer annular pressure prediction model was established. Taking a high-pressure gas well in Tarim Oilfield for example, the inter-packer annular pressure prediction was conducted, on which, the mechanical analysis on packers and working strings was carried out. The analysis results show that although the pipe string is safe in the viewpoint of conventional design methods, it is still susceptible to failure after the annular pressure drop between packers was taken into consideration. Such factor should be fully considered in the design of staged stimulation pipe strings, and this prediction model provides new thoughts for the optimal design of high-pressure deep well staged stimulation pipe strings.

Equation-of-State Modeling of Phase Equilibria in Petroleum Fluids

DEFF Research Database (Denmark)

Jørgensen, Marianne

1996-01-01

The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters. A comphr......The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters....... A comphrensive study of pseudoization procedures is presented. It is concluded that the compared methods exhibit results of comparable accuracy, and that six to eight pseudocomponents are needed for optimal representation of petroleum fluids.Finally, it is investigated how well the EOS can represent the VLLE...

Nonaligned shocks for discrete velocity models of the Boltzmann equation

Directory of Open Access Journals (Sweden)

J. M. Greenberg

1991-05-01

Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

Solution-diffusion with defects model for pressure-assisted forward osmosis

KAUST Repository

Duan, Jintang

2014-11-01

An osmosis transport model is presented that combines the standard internal and external concentration polarization equations in the forward osmosis (FO) field with the selective layer transport equations first proposed by Sherwood in 1967. The Sherwood model describes water flux as the sum of a solute-selective, diffusive component driven by the sum of osmotic pressure and hydraulic pressure differences, and a nonselective, convective component driven by hydraulic pressure difference only. This solution-diffusion with defects (SDWD) model and the solution-diffusion (SD) model were compared against data collected using polyamide thin-film-composite (PA-TFC) and integrally-skinned asymmetric cellulose triacetate (CTA) membranes, evaluated in various configurations. When tested with pure water on the porous support side and 1.5. M (π=72.7. bar) sodium chloride solution on the selective layer side, applying 1.25. bar of hydraulic pressure to the porous support side increased water flux by an order of magnitude for PA-TFC membranes, but had negligible effect on CTA membrane flux. These large flux variations can be explained by the SDWD model, but not the SD model. To confirm the existence of defects, a PA-TFC membrane was coated with a uniform, highly water-permeable, nonselective polymer. After coating to block convection through defects, the influence of hydraulic pressure on water flux through this membrane essentially disappeared. Water flux through these defects is low (<1% of total water flux for PA-TFC membranes) and of little consequence in practical FO or reverse osmosis (RO) applications. But in pressure-assisted forward osmosis (PAFO) or pressure-retarded osmosis (PRO), convective transport through defects affects the solute concentration difference across the membrane selective layer, increasing or decreasing water flux through defect-free regions. The presence of defects may explain why membrane power density in PRO is lower than that predicted based on

Right ventricular pressure elevated in one-kidney, one clip Goldblatt hypertensive rats.

Science.gov (United States)

Ketabchi, Farzaneh; Bajoovand, Shirin; Adlband, Mojtaba; Naseh, Maryam; Nekooeian, Ali A; Mashghoolozekr, Elaheh

2017-01-01

Both renal and respiratory diseases are common with high mortality rate around the world. This study was the first to compare effects of two kidneys, one clip (2K1C) and one-kidney, one clip (1K1C) Goldblatt hypertension on right ventricular pressure during normal condition and mechanical ventilation with hypoxia gas. Male Sprague-Dawley rats were subjected to control, 2K1C, or 1K1C groups. Twenty-eight days after the first surgery, animals were anesthetized, and femoral artery and vein, and right ventricle cannulated. Systemic arterial pressure and right ventricular systolic pressures (RVSP) were recorded during ventilation the animals with normoxic or hypoxic gas. RVSP in the 1K1C group was significantly more than the control and 2K1C groups during baseline conditions and ventilation the animals with hypoxic gas. Administration of antioxidant Trolox increased RVSP in the 1K1C and control groups compared with their baselines. Furthermore, there was no alteration in RVSP during hypoxia in the presence of Trolox. This study indicated that RVSP only increased after 28 days induction of 1K1C but not 2K1C model. In addition, it seems that the response to hypoxic gas and antioxidants in 1K1C is more than 2K1C. These data also suggest that effects of 1K1C may partially be related to reactive oxygen species (ROS) pathways.

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

Science.gov (United States)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

Science.gov (United States)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

Energy Technology Data Exchange (ETDEWEB)

Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

2017-07-01

In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)

A Multi-Fidelity Surrogate Model for the Equation of State for Mixtures of Real Gases

Science.gov (United States)

Ouellet, Frederick; Park, Chanyoung; Koneru, Rahul; Balachandar, S.; Rollin, Bertrand

2017-11-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the products of detonated explosives must be treated as real gases while the ideal gas equation of state is used for the ambient air. As the products expand outward, they mix with the air and create a region where both state equations must be satisfied. One of the most accurate, yet expensive, methods to handle this problem is an algorithm that iterates between both state equations until both pressure and thermal equilibrium are achieved inside of each computational cell. This work creates a multi-fidelity surrogate model to replace this process. This is achieved by using a Kriging model to produce a curve fit which interpolates selected data from the iterative algorithm. The surrogate is optimized for computing speed and model accuracy by varying the number of sampling points chosen to construct the model. The performance of the surrogate with respect to the iterative method is tested in simulations using a finite volume code. The model's computational speed and accuracy are analyzed to show the benefits of this novel approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Cockburn, S. P.; Gallucci, D.; Proukakis, N. P.

2011-01-01

The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al.[Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al.[Phys. Rev. Lett. 100, 090402 (2008)] and the density fluctuation data reported by Armijo et al.[Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose and implement a quasi-one-dimensional extension to the one-dimensional stochastic Gross-Pitaevskii equation for the low-energy, axial modes, while atoms in excited transverse modes are treated as independent ideal Bose gases.

High Temperature, high pressure equation of state density correlations and viscosity correlations

Energy Technology Data Exchange (ETDEWEB)

Tapriyal, D.; Enick, R.; McHugh, M.; Gamwo, I.; Morreale, B.

2012-07-31

Global increase in oil demand and depleting reserves has derived a need to find new oil resources. To find these untapped reservoirs, oil companies are exploring various remote and harsh locations such as deep waters in Gulf of Mexico, remote arctic regions, unexplored deep deserts, etc. Further, the depth of new oil/gas wells being drilled has increased considerably to tap these new resources. With the increase in the well depth, the bottomhole temperature and pressure are also increasing to extreme values (i.e. up to 500 F and 35,000 psi). The density and viscosity of natural gas and crude oil at reservoir conditions are critical fundamental properties required for accurate assessment of the amount of recoverable petroleum within a reservoir and the modeling of the flow of these fluids within the porous media. These properties are also used to design appropriate drilling and production equipment such as blow out preventers, risers, etc. With the present state of art, there is no accurate database for these fluid properties at extreme conditions. As we have begun to expand this experimental database it has become apparent that there are neither equations of state for density or transport models for viscosity that can be used to predict these fundamental properties of multi-component hydrocarbon mixtures over a wide range of temperature and pressure. Presently, oil companies are using correlations based on lower temperature and pressure databases that exhibit an unsatisfactory predictive capability at extreme conditions (e.g. as great as {+-} 50%). From the perspective of these oil companies that are committed to safely producing these resources, accurately predicting flow rates, and assuring the integrity of the flow, the absence of an extensive experimental database at extreme conditions and models capable of predicting these properties over an extremely wide range of temperature and pressure (including extreme conditions) makes their task even more daunting.

Modelling equation of knee force during instep kicking using ...

African Journals Online (AJOL)

This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...

QCD corrections to neutron electric dipole moment from dimension-six four-quark operators

Energy Technology Data Exchange (ETDEWEB)

Hisano, Junji, E-mail: hisano@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); IPMU, TODIAS, University of Tokyo, Kashiwa 277-8568 (Japan); Tsumura, Koji, E-mail: ko2@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China); Yang, Masaki J.S., E-mail: yang@eken.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)

2012-07-18

In this Letter, the renormalization-group equations for the (flavor-conserving) CP-violating interaction are derived up to the dimension six, including all the four-quark operators, at one-loop level. We apply them to the models with the neutral scalar boson or the color-octet scalar boson which have CP-violating Yukawa interactions with quarks, and discuss the neutron electric dipole moment in these models.

High temperature and high pressure equation of state of gold

International Nuclear Information System (INIS)

Matsui, Masanori

2010-01-01

High-temperature and high-pressure equation of state (EOS) of Au has been developed using measured data from shock compression up to 240 GPa, volume thermal expansion between 100 and 1300 K and 0 GPa, and temperature dependence of bulk modulus at 0 GPa from ultrasonic measurements. The lattice thermal pressures at high temperatures have been estimated based on the Mie-Grueneisen-Debye type treatment with the Vinet isothermal EOS. The contribution of electronic thermal pressure at high temperatures, which is relatively insignificant for Au, has also been included here. The optimized EOS parameters are K' 0T = 6.0 and q = 1.6 with fixed K 0T = 167 GPa, γ 0 = 2.97, and Θ 0 = 170 K from previous investigations. We propose the present EOS to be used as a reliable pressure standard for static experiments up to 3000K and 300 GPa.

An introductory model of a one-piston engine

International Nuclear Information System (INIS)

GlarIa, Jaime; Wendler, Thomas; Goodwin, Graham

2005-01-01

Reciprocating internal combustion engine models have the antithetical goals of accurately describing complex nonlinear behaviour and being simple enough for such purposes as automatic control and online diagnosis. A one-piston four-stroke engine is modelled here by recursively stating simple physical equations. To do that, the domestic ideas of domination and dependence are called as methodological tools for modelling, since they hand out necessary and sufficient equations with few manoeuvres, allocate simulations with the same characteristic and, hopefully, provide a fine way to understanding. The resulting model reveals both steady cycles and transient behaviour

Modelling of FCC (Fluid Catalytic Cracking) risers with six lumps; Modelo de elevadores de Unidades de Craqueamento Catalitico com cinetica de seis classes

Energy Technology Data Exchange (ETDEWEB)

Baldessar, Fabio; Negrao, Cezar O. Ribeiro; Palu, Claudia [Centro Federal de Educacao Tecnologica do Parana (CEFET-PR), Curitiba, PR (Brazil)

2004-07-01

The current work presents a mathematical model of an ascendant flow vertical reactor (riser) of a Fluid Catalytic Cracking Unit. The two-phase flow (gas-solid) and the cracking reactions are admitted one-dimensional and steady state. Mass, momentum and energy conservation equations are considered for each phase (solid and gas). A six-lump kinetic model is employed to evaluate gasoil, gasoline, GLP, fuel gas, light cycle oil and coke fractions. The model results are compared to experimental values from a pilot plant and to another model found in the literature. The results are in good agreement, showing the model has great potential. (author)

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

Prediction equations for spirometry in four- to six-year-old children.

Science.gov (United States)

França, Danielle Corrêa; Camargos, Paulo Augusto Moreira; Jones, Marcus Herbert; Martins, Jocimar Avelar; Vieira, Bruna da Silva Pinto Pinheiro; Colosimo, Enrico Antônio; de Mendonça, Karla Morganna Pereira Pinto; Borja, Raíssa de Oliveira; Britto, Raquel Rodrigues; Parreira, Verônica Franco

2016-01-01

To generate prediction equations for spirometry in 4- to 6-year-old children. Forced vital capacity, forced expiratory volume in 0.5s, forced expiratory volume in one second, peak expiratory flow, and forced expiratory flow at 25-75% of the forced vital capacity were assessed in 195 healthy children residing in the town of Sete Lagoas, state of Minas Gerais, Southeastern Brazil. The least mean squares method was used to derive the prediction equations. The level of significance was established as p<0.05. Overall, 85% of the children succeeded in performing the spirometric maneuvers. In the prediction equation, height was the single predictor of the spirometric variables as follows: forced vital capacity=exponential [(-2.255)+(0.022×height)], forced expiratory volume in 0.5s=exponential [(-2.288)+(0.019×height)], forced expiratory volume in one second=exponential [(-2.767)+(0.026×height)], peak expiratory flow=exponential [(-2.908)+(0.019×height)], and forced expiratory flow at 25-75% of the forced vital capacity=exponential [(-1.404)+(0.016×height)]. Neither age nor weight influenced the regression equations. No significant differences in the predicted values for boys and girls were observed. The predicted values obtained in the present study are comparable to those reported for preschoolers from both Brazil and other countries. Copyright © 2016 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.

Polarization Insensitive One-to-Six WDM Multicasting in a Silicon Nanowire

DEFF Research Database (Denmark)

Pu, Minhao; Hu, Hao; Peucheret, Christophe

2012-01-01

We present polarization insensitive one-to-six WDM multicasting based on nondegenerate four-wave mixing in a silicon nanowire with angled-pump scheme. Bit-error rate measurements are performed and error-free operation is achieved.......We present polarization insensitive one-to-six WDM multicasting based on nondegenerate four-wave mixing in a silicon nanowire with angled-pump scheme. Bit-error rate measurements are performed and error-free operation is achieved....

New equation of state model for hydrodynamic applications

Energy Technology Data Exchange (ETDEWEB)

Young, D.A.; Barbee, T.W. III; Rogers, F.J.

1997-07-01

Two new theoretical methods for computing the equation of state of hot, dense matter are discussed.The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.

New equation of state models for hydrodynamic applications

Science.gov (United States)

Young, David A.; Barbee, Troy W.; Rogers, Forrest J.

1998-07-01

Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, Johan H. L.; Folmer, Henk

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A structural equation approach to models with spatial dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A path analysis model for explaining unsafe behavior in workplaces: the effect of perceived work pressure.

Science.gov (United States)

Ghasemi, Fakhradin; Kalatpour, Omid; Moghimbeigi, Abbas; Mohhamadfam, Iraj

2018-06-01

Unsafe behavior is closely related to occupational accidents. Work pressure is one the main factors affecting employees' behavior. The aim of the present study was to provide a path analysis model for explaining how work pressure affects safety behavior. Using a self-administered questionnaire, six variables supposed to affect safety employees' behavior were measured. The path analysis model was constructed based on several hypotheses. The goodness of fit of the model was assessed using both absolute and comparative fit indices. Work pressure was determined not to influence safety behavior directly. However, it negatively influenced other variables. Group attitude and personal attitude toward safety were the main factors mediating the effect of work pressure on safety behavior. Among the variables investigated in the present study, group attitude, personal attitude and work pressure had the strongest effects on safety behavior. Managers should consider that in order to improve employees' safety behavior, work pressure should be reduced to a reasonable level, and concurrently a supportive environment, which ensures a positive group attitude toward safety, should be provided. Replication of the study is recommended.

Perfect fluid cosmological Universes: One equation of state and the ...

Indian Academy of Sciences (India)

Anadijiban Das

2018-01-04

Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...

The lattice Boltzmann model for the second-order Benjamin–Ono equations

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

A sigmoidal fit for pressure-volume curves of idiopathic pulmonary fibrosis patients on mechanical ventilation: clinical implications

Directory of Open Access Journals (Sweden)

Juliana C. Ferreira

2011-01-01

Full Text Available OBJECTIVE: Respiratory pressure-volume curves fitted to exponential equations have been used to assess disease severity and prognosis in spontaneously breathing patients with idiopathic pulmonary fibrosis. Sigmoidal equations have been used to fit pressure-volume curves for mechanically ventilated patients but not for idiopathic pulmonary fibrosis patients. We compared a sigmoidal model and an exponential model to fit pressure-volume curves from mechanically ventilated patients with idiopathic pulmonary fibrosis. METHODS: Six idiopathic pulmonary fibrosis patients and five controls underwent inflation pressure-volume curves using the constant-flow technique during general anesthesia prior to open lung biopsy or thymectomy. We identified the lower and upper inflection points and fit the curves with an exponential equation, V = A-B.e-k.P, and a sigmoid equation, V = a+b/(1+e-(P-c/d. RESULTS: The mean lower inflection point for idiopathic pulmonary fibrosis patients was significantly higher (10.5 ± 5.7 cm H2O than that of controls (3.6 ± 2.4 cm H2O. The sigmoidal equation fit the pressure-volume curves of the fibrotic and control patients well, but the exponential equation fit the data well only when points below 50% of the inspiratory capacity were excluded. CONCLUSION: The elevated lower inflection point and the sigmoidal shape of the pressure-volume curves suggest that respiratory system compliance is decreased close to end-expiratory lung volume in idiopathic pulmonary fibrosis patients under general anesthesia and mechanical ventilation. The sigmoidal fit was superior to the exponential fit for inflation pressure-volume curves of anesthetized patients with idiopathic pulmonary fibrosis and could be useful for guiding mechanical ventilation during general anesthesia in this condition.

The Pressure-Volume-Temperature Equation of State of Iron-Rich (Mg,Fe)O

Science.gov (United States)

Wicks, J. K.; Jackson, J. M.; Zhuravlev, K. K.; Prakapenka, V.

2012-12-01

Seismic observations near the base of the core-mantle boundary (CMB) have detected 5-20 km thick patches in which the seismic wave velocities are reduced by up to 30%. These ultra-low velocity zones (ULVZs) have been interpreted as aggregates of partially molten material (e.g. Williams and Garnero 1996, Hernlund and Jellinek, 2010) or as solid, iron-enriched residues (e.g. Knittle and Jeanloz, 1991; Mao et al., 2006; Wicks et al., 2010), typically based on proposed sources of velocity reduction. The stabilities of these structure types have been explored through dynamic models that have assembled a relationship between ULVZ stability and density (Hernlund and Tackley, 2007; Bower et al., 2010). Now, to constrain the chemistry of ULVZs, more information is needed on the relationship between density and sound velocity of candidate phases. Recently, we have shown that the characteristically low sound speeds of ULVZs can be produced by small amounts of iron-rich (Mg,Fe)O, which is likely to be found in iron-rich assemblages based on current partitioning studies (eg. Sakai et al., 2010; Tange et al., 2009). We determined the Debye velocity (VD) of (Mg.1657Fe.84)O using nuclear resonant inelastic x-ray scattering (NRIXS), and calculated the seismically relevant compressional (VP) and shear (VS) wave velocities up to 120 GPa using an equation of state of a similar composition (Wicks et al., 2010). These densities and sound velocities, in turn, are consistent with reasonable morphologies of modeled solid ULVZs (Bower et al., 2011). To increase the accuracy of density and sound velocity predictions, measurements must be made at elevated temperatures to correctly predict the properties of iron-rich (Mg,Fe)O at mantle conditions. In this study, we present the pressure-volume-temperature equation of state of (Mg.0657Fe.94)O measured up to pressures of 120 GPa and temperatures of 2000 K. Volume was measured with x-ray diffraction at beamline 13-ID-D of the Advanced Photon

Comparison of six different models describing survival of mammalian cells after irradiation

International Nuclear Information System (INIS)

Sontag, W.

1990-01-01

Six different cell-survival models have been compared. All models are based on the similar assumption that irradiated cells are able to exist in one of three states. S A is the state of a totally repaired cell, in state S C the cell contains lethal lesions and in state S b the cell contains potentially lethal lesions i.e. those which either can be repaired or converted into lethal lesions. The differences between the six models lie in the different mathematical relationships between the three states. To test the six models, six different sets of experimental data were used which describe cell survival at different repair times after irradiation with sparsely ionizing irradiation. In order to compare the models, a goodness-of-fit function was used. The differences between the six models were tested by use of the nonparametric Mann-Whitney two sample test. Based on the 95% confidence limit, this required separation into three groups. (orig.)

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT DOI: http://dx.doi.org/10.22342/jme.7.1.2814.19-30

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

Science.gov (United States)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

Science.gov (United States)

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

Simulation of shock-induced bubble collapse using a four-equation model

Science.gov (United States)

Goncalves, E.; Hoarau, Y.; Zeidan, D.

2018-02-01

This paper presents a numerical study of the interaction between a planar incident shock wave with a cylindrical gas bubble. Simulations are performed using an inviscid compressible one-fluid solver based upon three conservation laws for the mixture variables, namely mass, momentum, and total energy along with a supplementary transport equation for the volume fraction of the gas phase. The study focuses on the maximum pressure generated by the bubble collapse. The influence of the strength of the incident shock is investigated. A law for the maximum pressure function of the Mach number of the incident shock is proposed.

Modelling conjugation with stochastic differential equations

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

2010-01-01

Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

Consistent three-equation model for thin films

Science.gov (United States)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Comparison of Perturbed Pathways in Two Different Cell Models for Parkinson's Disease with Structural Equation Model.

Science.gov (United States)

Pepe, Daniele; Do, Jin Hwan

2015-12-16

Increasing evidence indicates that different morphological types of cell death coexist in the brain of patients with Parkinson's disease (PD), but the molecular explanation for this is still under investigation. In this study, we identified perturbed pathways in two different cell models for PD through the following procedures: (1) enrichment pathway analysis with differentially expressed genes and the Reactome pathway database, and (2) construction of the shortest path model for the enriched pathway and detection of significant shortest path model with fitting time-course microarray data of each PD cell model to structural equation model. Two PD cell models constructed by the same neurotoxin showed different perturbed pathways. That is, one showed perturbation of three Reactome pathways, including cellular senescence, chromatin modifying enzymes, and chromatin organization, while six modules within metabolism pathway represented perturbation in the other. This suggests that the activation of common upstream cell death pathways in PD may result in various down-stream processes, which might be associated with different morphological types of cell death. In addition, our results might provide molecular clues for coexistence of different morphological types of cell death in PD patients.

Thermodynamic properties by Equation of state of liquid sodium under pressure

Science.gov (United States)

Li, Huaming; Sun, Yongli; Zhang, Xiaoxiao; Li, Mo

Isothermal bulk modulus, molar volume and speed of sound of molten sodium are calculated through an equation of state of a power law form within good precision as compared with the experimental data. The calculated internal energy data show the minimum along the isothermal lines as the previous result but with slightly larger values. The calculated values of isobaric heat capacity show the unexpected minimum in the isothermal compression. The temperature and pressure derivative of various thermodynamic quantities in liquid Sodium are derived. It is discussed about the contribution from entropy to the temperature and pressure derivative of isothermal bulk modulus. The expressions for acoustical parameter and nonlinearity parameter are obtained based on thermodynamic relations from the equation of state. Both parameters for liquid Sodium are calculated under high pressure along the isothermal lines by using the available thermodynamic data and numeric derivations. By comparison with the results from experimental measurements and quasi-thermodynamic theory, the calculated values are found to be very close at melting point at ambient condition. Furthermore, several other thermodynamic quantities are also presented. Scientific Research Starting Foundation from Taiyuan university of Technology, Shanxi Provincial government (``100-talents program''), China Scholarship Council and National Natural Science Foundation of China (NSFC) under Grant No. 11204200.

Random matrices and the six-vertex model

CERN Document Server

Bleher, Pavel

2013-01-01

This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wa...

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.

xRage Equation of State

Energy Technology Data Exchange (ETDEWEB)

Grove, John W. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-08-16

The xRage code supports a variety of hydrodynamic equation of state (EOS) models. In practice these are generally accessed in the executing code via a pressure-temperature based table look up. This document will describe the various models supported by these codes and provide details on the algorithms used to evaluate the equation of state.

One-boson exchange model in the Tobocman-Chulick formalism

International Nuclear Information System (INIS)

Chulick, G.S.

1988-01-01

An alternative method to the standard techniques of field theory for the derivation of few-body dynamical equations is presented here. This new formalism gives rise to a set of coupled, three-dimensional, relativistic equations which represent one or more (coupled channel) nuclear interactive processes. The particles represented by these equations are dressed and/or are composite, with mass and vertex renormalization done in a simple, straightforward manner. The n-boson Tamm-Dancoff approximation is then used to restrict to a reasonable amount the number of coupled equations to be solved. In the one-boson Tamm-Dancoff approximation, the formalism gives rise to relativistic One-Boson Exchange time-ordered perturbation theory: i.e., the basic Bonn potential. Moreover, the formalism gives the Bonn potential a firmer theoretical basis, with physical particles, and with mass and vertex renormalization systematically taken into account. The formalism was tested numerically at two levels. First, it was tested for the simple model of elastic scalar NN scattering via the exchange of a single scalar boson. The resultant phase shifts, when compared to those for the Bethe-Salpeter equation and several of its three-dimensional reductions for the same model, were found to be reasonable. Next, the formalism was tested for the same model expanded to include non-elastic NN scattering processes. Even though the resultant scattering cross-sections were not compatible to the empirical scattering cross-sections, it was possible to discern what must be included in the model to obtain qualitative agreement

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

Science.gov (United States)

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

Science.gov (United States)

Appelo, C. A. J.; Parkhurst, D. L.; Post, V. E. A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich-Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson-Kirkham-Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye-Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich-Rosenfeld equation were fitted by least-squares on measured solution densities. The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng-Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The coefficients for the

Three-dimensional wave-induced current model equations and radiation stresses

Science.gov (United States)

Xia, Hua-yong

2017-08-01

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

New equation of state models for hydrodynamic applications

Energy Technology Data Exchange (ETDEWEB)

Young, D.A.; Barbee, T.W. III; Rogers, F.J. [Physics Department, Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)

1998-07-01

Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations. {copyright} {ital 1998 American Institute of Physics.}

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

Science.gov (United States)

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

A model for the calculation of vent clearing transients in pressure suppression systems

International Nuclear Information System (INIS)

Brosche, D.

1975-01-01

For the layout of a pressure suppression system of a light water cooled reactor (boiling water reactor) it is important to know the time dependent behavior of the vent clearing transient after a loss-of-coolant accident for two main reasons: time of the end of the vent clearing transient influences strongly the pressure and temperature maxima in the drywell and wetwell. Time-dependent behavior of the vent clearing transient influences pressure loads in the condensation pool of the wetwell and therefore pressure induced stresses to the structure. The time-dependent behavior of the water masses in the vent pipes and wetwell are described by the basic equations for a nonstationary incompressible friction flow: momentum equation, continuity equation and a correlation for the variation of the state of the gas volume in the wetwell above the water level. After many algebraic operations and integrations along the flow path, a single ordinary nonlinear differential equation for the variations of the water levels in the vent pipes and wetwell is obtained. Therefore the time-dependent velocities and accelerations of the water levels and the moment of the end clearing transient are known. The time-dependent pressure behavior in the drywell, geometrical conditions, initial submergence depth of the vent pipes and different friction and pressure loss factors are presented. The theoretical model has been tested at corresponding experiments performed at a full scale 1/48 segment of the Humboldt Bay pressure suppression containment in the USA and at the pressure suppression containment at the Marviken nuclear power station in Sweden. All these comparisons have shown good agreement between theory and experiment

Application of high-power lasers to equation-of-state research at ultrahigh pressures

International Nuclear Information System (INIS)

Trainor, R.J.; Graboske, H.C.; Long, K.S.; Shaner, J.W.

1978-01-01

The application of high-power pulsed lasers to ultrahigh pressure equation-of-state (EOS) experiments is discussed. It is shown that pressures along the principal Hugoniot between 1 and 10 TPa can be produced with existing lasers used for inertial-confinement fusion research. The relevance of measurements in this pressure regime to improving our understanding of condensed matter physics is also discussed. New experimental techniques as well as potential experimental problems are described, and EOS experiments on the Janus and Argus laser systems are proposed

Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model

DEFF Research Database (Denmark)

Mogensen, Kristian; Stenby, Erling Halfdan; Banerjee, Srilekha

1999-01-01

In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU-time. Each nonlinear system requires...

An integrodifferential Dirac equation with quantized charge in one space dimension

International Nuclear Information System (INIS)

Ranada, A.F.

1985-01-01

An integrodifferential Dirac equation in one space dimension is proposed, such that there is a close correspondence between its solutions and a subset of those of the sine-Gordon equation. It has solitonic solutions, quantized charge and positive definite energy density, so that it can be considered a spinorial version of sine-Gordon. Accordingly, it could be named the sine-Dirac equation. (orig.)

An improved model to predict nonuniform deformation of Zr-2.5 Nb pressure tubes

International Nuclear Information System (INIS)

Lei, Q.M.; Fan, H.Z.

1997-01-01

Present circular pressure-tube ballooning models in most fuel channel codes assume that the pressure tube remains circular during ballooning. This model provides adequate predictions of pressure-tube ballooning behaviour when the pressure tube (PT) and the calandria tube (CT) are concentric and when a small (<100 degrees C) top-to-bottom circumferential temperature gradient is present on the pressure tube. However, nonconcentric ballooning is expected to occur under certain postulated CANDU (CANada Deuterium Uranium) accident conditions. This circular geometry assumption prevents the model from accurately predicting nonuniform pressure-tube straining and local PT/CT contact when the pressure tube is subjected to a large circumferential temperature gradient and consequently deforms in a noncircular pattern. This paper describes an improved model that predicts noncircular pressure-tube deformation. Use of this model (once fully validated) will reduce uncertainties in the prediction of pressure-tube ballooning during a postulated loss-of-coolant accident (LOCA) in a CANDU reactor. The noncircular deformation model considers a ring or cross-section of a pressure tube with unit axial length to calculate deformation in the radial and circumferential directions. The model keeps track of the thinning of the pressure-tube wall as well as the shape deviation from a reference circle. Such deviation is expressed in a cosine Fourier series for the lateral symmetry case. The coefficients of the series for the first m terms are calculated by solving a set of algebraic equations at each time step. The model also takes into account the effects of pressure-tube sag or bow on ballooning, using an input value of the offset distance between the centre of the calandria tube and the initial centre of the pressure tube for determining the position radius of the pressure tube. One significant improvement realized in using the noncircular deformation model is a more accurate prediction in

Rupture tests with reactor pressure vessel head models

International Nuclear Information System (INIS)

Talja, H.; Keinaenen, H.; Hosio, E.; Pankakoski, P.H.; Rahka, K.

2003-01-01

In the LISSAC project (LImit Strains in Severe ACcidents), partly funded by the EC Nuclear Fission and Safety Programme within the 5th Framework programme, an extensive experimental and computational research programme is conducted to study the stress state and size dependence of ultimate failure strains. The results are aimed especially to make the assessment of severe accident cases more realistic. For the experiments in the LISSAC project a block of material of the German Biblis C reactor pressure vessel was available. As part of the project, eight reactor pressure vessel head models from this material (22 NiMoCr 3 7) were tested up to rupture at VTT. The specimens were provided by Forschungszentrum Karlsruhe (FzK). These tests were performed under quasistatic pressure load at room temperature. Two specimens sizes were tested and in half of the tests the specimens contain holes describing the control rod penetrations of an actual reactor pressure vessel head. These specimens were equipped with an aluminium liner. All six tests with the smaller specimen size were conducted successfully. In the test with the large specimen with holes, the behaviour of the aluminium liner material proved to differ from those of the smaller ones. As a consequence the experiment ended at the failure of the liner. The specimen without holes yielded results that were in very good agreement with those from the small specimens. (author)

[Pressure sores unit--a one year study].

Science.gov (United States)

Jaul, E

2001-10-01

The phenomenon of pressure sores in the elderly patient often requires an alternative management policy to that of the standard treatment. In general, the therapeutic approach to pressure sores in the elderly should be different to that in younger patients. This modification is due to the accompanying comorbidity so often associated with aging. Due to accompanying illnesses, the aging population is at high risk and more predisposed to the development of pressure sores. The importance of the establishment of a unit for pressure sores arises from the specific geriatric team approach to the patient and the need to focus carefully on the pressure sores. The management of this special Pressure Sores Unit with a permanent capable staff requires skilled treatment, both localized and systemic, since pressure sores are very often a result of systemic failure or an indication of a terminal condition in the elderly patient. Over six months we followed-up on the number and location of the pressure sores in 47 patients in addition to other functional and nutritional parameters, in order to investigate any connection between the pressure sores and nutritional parameters. The results of the study indicate that the nutritional state of the patients admitted for pressure sores was very poor. Two thirds of the patients suffered from either dementia or stroke, and 90 percent were bedridden, incontinent and enterally fed. Despite the poor general condition of the patient, the study shows improvement in the pressure sores with a reduction from an average of 2.8 to 1.8 pressure sores per patient. The improvement in the pressure sore located on the legs was three times greater than those located in the pelvic area. By the end of the study, 50% of the patients had died, 33% of the original patients who were still in the unit showed improvement in the pressure sores and 15% were discharged showing complete recovery from the sores. No significant correlation was found between changes in the

One-dimensional energy flow model for poroelastic material

International Nuclear Information System (INIS)

Kim, Jung Soo; Kang, Yeon June

2009-01-01

This paper presents a one-dimensional energy flow model to investigate the energy behavior for poroelastic media coupled with acoustical media. The proposed energy flow model is expressed by an independent energy governing equation that is classified into each wave component propagating in poroelastic media. The energy governing equation is derived using the General Energetic Method (GEM). To facilitate a comparison with the classical solution based on the conventional displacement-base formulation, approximate solutions of energy density and intensity are obtained. Furthermore, the limitations and usability of the proposed energy flow model for poroelastic media are described.

Modeling thermophysical properties of food under high pressure.

Science.gov (United States)

Otero, L; Guignon, B; Aparicio, C; Sanz, P D

2010-04-01

A set of well-known generic models to predict the thermophysical properties of food from its composition at atmospheric conditions was adapted to work at any pressure. The suitability of the models was assessed using data from the literature for four different food products, namely tomato paste, potato, pork, and cod. When the composition of the product considered was not known, an alternative was proposed if some thermal data at atmospheric conditions were available. Since knowledge on the initial freezing point and ice content of food are essential for the correct prediction of its thermal properties, models for obtaining these properties under pressure were also included. Our results showed that good predictions under pressure, accurate enough for most engineering calculations can be made, either from composition data or using known thermal data of the food considered at atmospheric conditions. All the equations and coefficients needed to construct the models are given throughout the text, thus readers can compose their own routines. However, these routines can also be downloaded free at http://www.if.csic.es/programas/ifiform.htm as executable programs running in Windows.

Effect of cavitation in high-pressure direct injection

Science.gov (United States)

Aboulhasanzadeh, Bahman; Johnsen, Eric

2015-11-01

As we move toward higher pressures for Gasoline Direct Injection and Diesel Direct Injection, cavitation has become an important issue. To better understand the effect of cavitation on the nozzle flow and primary atomization, we use a high-order accurate Discontinuous Galerkin approach using multi-GPU parallelism to simulate the compressible flow inside and outside the nozzle. Phase change is included using the six-equations model. We investigate the effect of nozzle geometry on cavitation inside the injector and on primary atomization outside the nozzle.

Pressure wave propagation in sodium loop

International Nuclear Information System (INIS)

Botelho, D.A.

1989-01-01

A study was done on the pressure wave propagation within the pipes and mixture vessel of a termohydraulic loop for thermal shock with sodium. It was used the characteristic method to solve the one-dimensional continuity and momentum equations. The numerical model includes the pipes and the effects of valves and other accidents on pressure losses. The study was based on designer informations and engineering tables. It was evaluated the pressure wave sizes, parametrically as a function of the draining valve closure times. (author) [pt

On the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Sani, R.L.; Gresho, P.M.; Lee, R.L.

1979-01-01

The spurious pressures and acceptable velocities generated when using certain combinations of velocity and pressure approximations in a Galerkin finite element discretization of the primitive variable form of the incompressible Navier-Stokes equations are analyzed both theoretically and numerically for grids composed of quadrilateral finite elements. Schemes for obtaining usable pressure fields from the spurious numerical results are presented for certain cases

Slave equations for spin models

International Nuclear Information System (INIS)

Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

1992-01-01

We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

TBA equations for excited states in the sine-Gordon model

International Nuclear Information System (INIS)

Balog, Janos; Hegedus, Arpad

2004-01-01

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found

On the viability of rank-six superstring models

International Nuclear Information System (INIS)

Campbell, B.A.; Olive, K.A.; Reiss, D.B.

1988-01-01

We consider the possibility of breaking a rank-six superstring model to the rank-four standard model. In particular, we point out the difficulties in generating two vacuum expectation values for the two standard model singlets contained in the 27 of E 6 . Although one expectation value is compatible with low energy phenomenology, a vev for ν c is problematic because of the absence of large neutrino masses and/or flavor changing neutral currents. We show that even simple models containing extra fields from incomplete multiplets or E 6 singlets do not resolve these problems. (orig.)

The 12-foot pressure wind tunnel restoration project model support systems

Science.gov (United States)

Sasaki, Glen E.

1992-01-01

The 12 Foot Pressure Wind Tunnel is a variable density, low turbulence wind tunnel that operates at subsonic speeds, and up to six atmospheres total pressure. The restoration of this facility is of critical importance to the future of the U.S. aerospace industry. As part of this project, several state of the art model support systems are furnished to provide an optimal balance between aerodynamic and operational efficiency parameters. Two model support systems, the Rear Strut Model Support, and the High Angle of Attack Model Support are discussed. This paper covers design parameters, constraints, development, description, and component selection.

Diffusion with space memory modelled with distributed order space fractional differential equations

Directory of Open Access Journals (Sweden)

M. Caputo

2003-06-01

Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.

Six Sigma Driven Enterprise Model Transformation

Directory of Open Access Journals (Sweden)

Raymond Vella

2009-10-01

Full Text Available Enterprise architecture methods provide a structured system to understand enterprise activities. However, existing enterprise modelling methodologies take static views of the enterprise and do not naturally lead to a path of improvement during enterprise model transformation. This paper discusses the need for a methodology to facilitate changes for improvement in an enterprise. The six sigma methodology is proposed as the tool to facilitate progressive and continual Enterprise Model Transformation to allow businesses to adapt to meet increased customer expectation and global competition. An alignment of six sigma with phases of GERAM life cycle is described with inclusion of Critical-To-Satisfaction (CTS requirements. The synergies of combining the two methodologies are presented in an effort to provide a more culturally embedded framework for Enterprise Model Transformation that builds on the success of six sigma.

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

Science.gov (United States)

Appelo, C.A.J.; Parkhurst, David L.; Post, V.E.A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich–Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson–Kirkham–Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye–Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich–Rosenfeld equation were fitted by least-squares on measured solution densities.The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng–Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The

Modeling of Natural Self-Pressurized Circulation Circuits

International Nuclear Information System (INIS)

Zanocco, Pablo; Gimenez, Marcelo; Delmastro, Dario

2003-01-01

In this work, HUARPE code models for self-pressurized two-phase natural convection systems are improved.A drift-flux model is included, allowing the modeling of the relative velocity between phases.The model of steam dome structures is improved, with a thermal resistance scheme, in order to model the material thermal conductivity.This allows improving thermal losses modeling and structures dynamic.'Shape functions' are implemented based on analytic solutions for pressure derivative and density in each node, which allows less diffusive solving schemes, more appropriate for analyzing cases involving density waves phenomena.Finally, pressure evolutions during a pressurization transient are analyzed, comparing the new models and the previous version results.These results are also checked against RELAP code ones, obtained with different dome nodalizations. Moreover, modeling problems are analyzed for each case

From the hypergeometric differential equation to a non-linear Schrödinger one

International Nuclear Information System (INIS)

Plastino, A.; Rocca, M.C.

2015-01-01

We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Optimal level of continuous positive airway pressure: auto-adjusting titration versus titration with a predictive equation.

Science.gov (United States)

Choi, Ji Ho; Jun, Young Joon; Oh, Jeong In; Jung, Jong Yoon; Hwang, Gyu Ho; Kwon, Soon Young; Lee, Heung Man; Kim, Tae Hoon; Lee, Sang Hag; Lee, Seung Hoon

2013-05-01

The aims of the present study were twofold. We sought to compare two methods of titrating the level of continuous positive airway pressure (CPAP) - auto-adjusting titration and titration using a predictive equation - with full-night manual titration used as the benchmark. We also investigated the reliability of the two methods in patients with obstructive sleep apnea syndrome (OSAS). Twenty consecutive adult patients with OSAS who had successful, full-night manual and auto-adjusting CPAP titration participated in this study. The titration pressure level was calculated with a previously developed predictive equation based on body mass index and apnea-hypopnea index. The mean titration pressure levels obtained with the manual, auto-adjusting, and predictive equation methods were 9.0 +/- 3.6, 9.4 +/- 3.0, and 8.1 +/- 1.6 cm H2O,respectively. There was a significant difference in the concordance within the range of +/- 2 cm H2O (p = 0.019) between both the auto-adjusting titration and the titration using the predictive equation compared to the full-night manual titration. However, there was no significant difference in the concordance within the range of +/- 1 cm H2O (p > 0.999). When compared to full-night manual titration as the standard method, auto-adjusting titration appears to be more reliable than using a predictive equation for determining the optimal CPAP level in patients with OSAS.

Fluid-structure interactions in one-dimensional linear cases

International Nuclear Information System (INIS)

Schumann, U.

1979-01-01

The interaction of pressure waves in a pipe with an elastic endwall (piston) is analyzed using a linear ('acoustic') model. Two transient and two periodic cases are investigated. In the transient cases the motions are initiated by either a sudden pressure drop at the opeen end (breaking membrane) or by a sudden release of the piston from a non-equilibrium position ('snapback'); in the latter case the other end of the pipe is closed. In the periodic cases harmonic oscillations of the piston and the fluid are investigated with the other end of the pipe being either closed or open (kept at constant pressure). The problem is characterized by three non-dimensional numbers (e.g.: Mach-, Strouhal-, and an interaction-number). The solution of the wave equation for the pressure accounting for the coupling to the structure can be reduced analytically to the problem of integrating one ordinary differential equation of second order in time. This differential equation in turn can be integrated analytically at least for a certain time period. At later times this ordinary differential equation is integrated numerically. For the periodic cases eigenvalue-problems arise with an infinite number of solutions. The first few eigensolutions are given. (orig./RW) [de

A quantum relativistic integrable model as the continuous limit of the six-vertex model

International Nuclear Information System (INIS)

Zhou, Y.K.

1992-01-01

The six-vertex model in two-dimensional statistical mechanics is used to construct the L-matrix of a one-dimensional quantum relativistic integrable model through a continuous limit. This is the first step to extend the method used earlier by the author to construct quantum completely integrable systems from other well-known two-dimensional vertex models. (orig.)

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

Science.gov (United States)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

Model-based setting of inspiratory pressure and respiratory rate in pressure-controlled ventilation

International Nuclear Information System (INIS)

Schranz, C; Möller, K; Becher, T; Schädler, D; Weiler, N

2014-01-01

Mechanical ventilation carries the risk of ventilator-induced-lung-injury (VILI). To minimize the risk of VILI, ventilator settings should be adapted to the individual patient properties. Mathematical models of respiratory mechanics are able to capture the individual physiological condition and can be used to derive personalized ventilator settings. This paper presents model-based calculations of inspiration pressure (p I ), inspiration and expiration time (t I , t E ) in pressure-controlled ventilation (PCV) and a retrospective evaluation of its results in a group of mechanically ventilated patients. Incorporating the identified first order model of respiratory mechanics in the basic equation of alveolar ventilation yielded a nonlinear relation between ventilation parameters during PCV. Given this patient-specific relation, optimized settings in terms of minimal p I and adequate t E can be obtained. We then retrospectively analyzed data from 16 ICU patients with mixed pathologies, whose ventilation had been previously optimized by ICU physicians with the goal of minimization of inspiration pressure, and compared the algorithm's ‘optimized’ settings to the settings that had been chosen by the physicians. The presented algorithm visualizes the patient-specific relations between inspiration pressure and inspiration time. The algorithm's calculated results highly correlate to the physician's ventilation settings with r = 0.975 for the inspiration pressure, and r = 0.902 for the inspiration time. The nonlinear patient-specific relations of ventilation parameters become transparent and support the determination of individualized ventilator settings according to therapeutic goals. Thus, the algorithm is feasible for a variety of ventilated ICU patients and has the potential of improving lung-protective ventilation by minimizing inspiratory pressures and by helping to avoid the build-up of clinically significant intrinsic positive end

Model-based setting of inspiratory pressure and respiratory rate in pressure-controlled ventilation.

Science.gov (United States)

Schranz, C; Becher, T; Schädler, D; Weiler, N; Möller, K

2014-03-01

Mechanical ventilation carries the risk of ventilator-induced-lung-injury (VILI). To minimize the risk of VILI, ventilator settings should be adapted to the individual patient properties. Mathematical models of respiratory mechanics are able to capture the individual physiological condition and can be used to derive personalized ventilator settings. This paper presents model-based calculations of inspiration pressure (pI), inspiration and expiration time (tI, tE) in pressure-controlled ventilation (PCV) and a retrospective evaluation of its results in a group of mechanically ventilated patients. Incorporating the identified first order model of respiratory mechanics in the basic equation of alveolar ventilation yielded a nonlinear relation between ventilation parameters during PCV. Given this patient-specific relation, optimized settings in terms of minimal pI and adequate tE can be obtained. We then retrospectively analyzed data from 16 ICU patients with mixed pathologies, whose ventilation had been previously optimized by ICU physicians with the goal of minimization of inspiration pressure, and compared the algorithm's 'optimized' settings to the settings that had been chosen by the physicians. The presented algorithm visualizes the patient-specific relations between inspiration pressure and inspiration time. The algorithm's calculated results highly correlate to the physician's ventilation settings with r = 0.975 for the inspiration pressure, and r = 0.902 for the inspiration time. The nonlinear patient-specific relations of ventilation parameters become transparent and support the determination of individualized ventilator settings according to therapeutic goals. Thus, the algorithm is feasible for a variety of ventilated ICU patients and has the potential of improving lung-protective ventilation by minimizing inspiratory pressures and by helping to avoid the build-up of clinically significant intrinsic positive end-expiratory pressure.

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

International Nuclear Information System (INIS)

Yomba, Emmanuel; Kofane, Timoleon Crepin

2003-01-01

The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

Some properties of matter at very HTGH temperatures and high pressures (equations of state, opacity); Quelques proprietes de la matiere aux tres hautes temperatures et fortes pressions (equation d'etat, opacite)

Energy Technology Data Exchange (ETDEWEB)

Gervat, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-06-15

The Thomas-Fermi equations which' are zero-order approximations of the Hartree-Fock equations, make it possible to study some aspects of the behaviour of matter at high pressures. In the first chapter is considered the calculation of 1 values which do not require the Schroedinger equation to be solved. The values of the quantum and exchange corrections give the zone of validity of the theory. For each R and T pair it is possible to calculate the energy and the pressure. For the calculation of the energy 'it has been necessary, in the region close to the nucleus where the corrections diverge, to replace the density given by the Thomas-Fermi theory by that deduced from the wave-functions which, in the small region, are very similar to that of a hydrogen atom of charge z. The calculation of the degree of ionization is particularly simple and does not require the Saha equations to be solved. Besides the distribution of electrons in the r space it is simple to determine the distribution according to the quantum number I, and this for each value of the R, T pair. In the second chapter, the introduction of the, Thomas and Fermi potential into the Schroedinger equation makes it possible to obtain the energy spectrum of a perfect isolated atom supposed to represent an average atom of the hot, compressed matter. The changes in the levels with increasing temperature and pressure can be deduced from this. It is particular easy with this model to interpret the phenomenon of ionization caused by pressure. A knowledge of the wave functions makes it possible to calculate the transition probabilities which, coupled with the occupation probabilities, lead to the opacity coefficients. Only the bound-free and free-free transitions have been considered but these latter include, because of the properties of the model used, a large part of bound-bound or band-band transitions. Finally, the use of the Thomas-Fermi potential for the calculation of bands is particularly suitable for

One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma

Science.gov (United States)

Chaplin, Vernon H.; Bellan, Paul M.

2015-12-01

A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak ne≳ 5 ×1019 m-3 ) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density ne(z ,t ) and temperature Te(z ,t ) , and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excited state manifolds are calculated to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at pA r=30 -60 mTorr . We present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency antenna.

A lattice Boltzmann model for the Burgers-Fisher equation.

Science.gov (United States)

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Models of genus one curves

OpenAIRE

Sadek, Mohammad

2010-01-01

In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or complete intersections of two quadrics in P3. By minimising such a curve we mean making the invariants associated to its defining equations as small as possible using a suitable change of coordinates. We study the non-uniqueness of minimisations of the genus one curves des...

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

International Nuclear Information System (INIS)

Yang Pei; Li Zhibin; Chen Yong

2010-01-01

In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)

On singularity formation of a 3D model for incompressible Navier–Stokes equations

OpenAIRE

Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu

2012-01-01

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...

Numerical instability of time-discretized one-point kinetic equations

International Nuclear Information System (INIS)

Hashimoto, Kengo; Ikeda, Hideaki; Takeda, Toshikazu

2000-01-01

The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank-Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank-Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula

Tensor formulation of the model equations on strong conservation form for an incompressible flow in general coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....

Pressure broadening and pressure shift of diatomic iodine at 675 nm

Science.gov (United States)

Wolf, Erich N.

Doppler-limited, steady-state, linear absorption spectra of 127 I2 (diatomic iodine) near 675 nm were recorded with an internally-referenced wavelength modulation spectrometer, built around a free-running diode laser using phase-sensitive detection, and capable of exceeding the signal-to-noise limit imposed by the 12-bit data acquisition system. Observed I2 lines were accounted for by published spectroscopic constants. Pressure broadening and pressure shift coefficients were determined respectively from the line-widths and line-center shifts as a function of buffer gas pressure, which were determined from nonlinear regression analysis of observed line shapes against a Gaussian-Lorentzian convolution line shape model. This model included a linear superposition of the I2 hyperfine structure based on changes in the nuclear electric quadrupole coupling constant. Room temperature (292 K) values of these coefficients were determined for six unblended I 2 lines in the region 14,817.95 to 14,819.45 cm-1 for each of the following buffer gases: the atoms He, Ne, Ar, Kr, and Xe; and the molecules H2, D2, N2, CO2, N2O, air, and H2O. These coefficients were also determined at one additional temperature (388 K) for He and CO2, and at two additional temperatures (348 and 388 K) for Ar. Elastic collision cross-sections were determined for all pressure broadening coefficients in this region. Room temperature values of these coefficients were also determined for several low-J I2 lines in the region 14,946.17 to 14,850.29 cm-1 for Ar. A line shape model, obtained from a first-order perturbation solution of the time-dependent Schrodinger equation for randomly occurring interactions between a two-level system and a buffer gas treated as step-function potentials, reveals a relationship between the ratio of pressure broadening to pressure shift coefficients and a change in the wave function phase-factor, interpreted as reflecting the "cause and effect" of state-changing events in the

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

Science.gov (United States)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Convergence of the Stochastic Six-Vertex Model to the ASEP

Energy Technology Data Exchange (ETDEWEB)

Aggarwal, Amol, E-mail: amolaggarwal@g.harvard.edu [Harvard University Cambridge (United States)

2017-06-15

In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.

SGS Modeling of the Internal Energy Equation in LES of Supersonic Channel Flow

Science.gov (United States)

Raghunath, Sriram; Brereton, Giles

2011-11-01

DNS of fully-developed turbulent supersonic channel flows (Reτ = 190) at up to Mach 3 indicate that the turbulent heat fluxes depend only weakly on Mach number, while the viscous dissipation and pressure dilatation do so strongly. Moreover, pressure dilatation makes a significant contribution to the internal energy budget at Mach 3 and higher. The balance between these terms is critical to determining the temperature (and so molecular viscosity) from the internal energy equation and so, in LES of these flows, it is essential to use accurate SGS models for the viscous dissipation and the pressure dilatation. In this talk, we present LES results for supersonic channel flow, using SGS models for these terms that are based on the resolved-scale dilatation, an inverse timescale, and SGS momentum fluxes, which intrinsically represent this Mach number effect.

THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE

Directory of Open Access Journals (Sweden)

K. O. Soroka

2015-06-01

Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods

Introduction to turbulence modelling: Applications of Reynolds Averaged Navier Stokes Equations (RANSE) to engineering problems

International Nuclear Information System (INIS)

Laurence, D.

1997-01-01

The k-ε model and Reynolds stress transport model are set out in a few words. Limitations of models are shown, particularly for turbulence generation in the turbulent viscosity context, and, more generally, the uncertainties and miscellaneous changes made to the dissipation equation. The performances of models are then compared, using results of the three latest ERCOFTA/IAHR workshops. It is shown that algebraic constraints which can be derived exactly by assuming asymptotic limits (rapid distortion, homogeneous shear at infinite time, 2D turbulence) have inhibited a better tuning of the models for real life flow where these limits are not encountered. A more pragmatic approach could be taken by allowing the constants to be functions of invariant parameters. But these functions, making the models non-linear, can lead to bifurcations or instability. One essential parameter is the distance to the wall, which recent models have tried to eliminate, although this parameter appears indirectly through the Poisson equation for the fluctuating pressure. A possible indirect model is the elliptic relaxation. Progress was recently achieved in near-wall low Re modelling, but these advances do not always result in benefits to industry since only the 'wall function' approaches can be used in the high Re, 3D flows that we need to study. With the knowledge gained from near-wall modelling, it might be profitable to revisit the 'wall functions' devised 20 years ago. (author)

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

International Nuclear Information System (INIS)

Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

2013-01-01

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

A new exact anisotropic solution of embedding class one

Energy Technology Data Exchange (ETDEWEB)

Maurya, S.K.; Smitha, T.T. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad (India); Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

2016-07-15

We have presented a new anisotropic solution of Einstein's field equations for compact-star models. Einstein's field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor (Δ) by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor (Δ). The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2). (orig.)

Auxiliary matrices for the six-vertex model at qN = 1 and a geometric interpretation of its symmetries

International Nuclear Information System (INIS)

Korff, Christian

2003-01-01

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U q (s-tilde l-tilde 2 ) at q N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged centre Z of the algebra U q (s-tilde l-tilde 2 ) at q N = 1. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a hypersurface Spec Z subset of C 4 which remains invariant under the action of an infinite-dimensional group G of analytic transformations, called the quantum coadjoint action

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Estimates of the eigenvalues of operator arising in swelling pressure model

International Nuclear Information System (INIS)

Kanguzhin, Baltabek; Zhapsarbayeva, Lyailya

2016-01-01

Swelling pressures from materials confined by structures can cause structural deformations and instability. Due to the complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic spectral problem based on the Euler-elastic beam theory and some simplistic swelling pressure model. In this work estimates of the eigenvalues of some initial/boundary value problem for nonlinear Euler-elastic beam equation are obtained.

One-dimensional model for QCD at high energy

International Nuclear Information System (INIS)

Iancu, E.; Santana Amaral, J.T. de; Soyez, G.; Triantafyllopoulos, D.N.

2007-01-01

We propose a stochastic particle model in (1+1) dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of pomeron loops. The model evolves via non-linear particle splitting, with a non-local splitting rate which is constrained by boost-invariance and multiple scattering. The splitting rate saturates at high density, so like the gluon emission rate in the JIMWLK evolution. In the mean field approximation obtained by ignoring fluctuations, the model exhibits the hallmarks of the BK equation, namely a BFKL-like evolution at low density, the formation of a traveling wave, and geometric scaling. In the full evolution including fluctuations, the geometric scaling is washed out at high energy and replaced by diffusive scaling. It is likely that the model belongs to the universality class of the reaction-diffusion process. The analysis of the model sheds new light on the pomeron loops equations in QCD and their possible improvements

Application of the B-Determining Equations Method to One Problem of Free Turbulence

Directory of Open Access Journals (Sweden)

Oleg V. Kaptsov

2012-10-01

Full Text Available A three-dimensional model of the far turbulent wake behind a self-propelled body in a passively stratified medium is considered. The model is reduced to a system of ordinary differential equations by a similarity reduction and the B-determining equations method. The system of ordinary differential equations satisfying natural boundary conditions is solved numerically. The solutions obtained here are in close agreement with experimental data.

Self-pressurization analysis of the natural circulation integral nuclear reactor using a new dynamic model

Directory of Open Access Journals (Sweden)

Ali Farsoon Pilehvar

2018-06-01

Full Text Available Self-pressurization analysis of the natural circulation integral nuclear reactor through a new dynamic model is studied. Unlike conventional pressurized water reactors, this reactor type controls the system pressure using saturated coolant water in the steam dome at the top of the pressure vessel. Self-pressurization model is developed based on conservation of mass, volume, and energy by predicting the condensation that occurs in the steam dome and the flashing inside the chimney using the partial differential equation. A simple but functional model is adopted for the steam generator. The obtained results indicate that the variable measurement is consistent with design data and that this new model is able to predict the dynamics of the reactor in different situations. It is revealed that flashing and condensation power are in direct relation with the stability of the system pressure, without which pressure convergence cannot be established. Keywords: Condensation Power, Flashing Phenomenon, Natural Circulation, Self-Pressurization, Small Modular Reactor

Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals?

DEFF Research Database (Denmark)

Privat, Romain; Gani, Rafiqul; Jaubert, Jean-Noël

2010-01-01

The PC-SAFT equation of state is a very popular and promising model for fluids that employs a complicated pressure-explicit mathematical function (and can therefore not be solved analytically at a specified pressure and temperature, contrary to classical cubic equations). In this work, we...... demonstrate that in case of pure fluids, the PC-SAFT equation may exhibit up to five different volume-roots whereas cubic equations give at the most three volume-roots (and yet, only one or two volume roots have real significance). The consequence of this strongly atypical behaviour is the existence of two...... different fluid-fluid coexistence lines (the vapour pressure-curve and an additional liquid-liquid equilibrium curve) and two critical points for a same pure component, which is obviously physically inconsistent. In addition to n-alkanes, nearly sixty very common pure components (branched alkanes...

Light radiation pressure upon a wrinkled membrane – parametrization of an optically orthotropic model

Science.gov (United States)

Nerovny, N. A.; Zimin, V. N.

2018-04-01

In this paper, the problem of representing the light pressure force upon the surface of a thin wrinkled film is discussed. The common source of wrinkles is the shear deformation of the membrane sample. The optical model of such a membrane is assumed to be optically orthotropic and an analytic equation for infinitesimal light pressure force is written. A linear regression model in the case of wrinkle geometry, where a surface element can have different optical parameters, is constructed and the Bayesian approach is used to calculate the parameters of this model.

Relaxation and Numerical Approximation of a Two-Fluid Two-Pressure Diphasic Model

International Nuclear Information System (INIS)

Ambroso, A.; Chalons, Ch.; Galie, Th.; Chalons, Ch.; Coquel, F.; Coquel, F.

2009-01-01

This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach. (authors)

Predictive equations for lumbar spine loads in load-dependent asymmetric one- and two-handed lifting activities.

Science.gov (United States)

Arjmand, N; Plamondon, A; Shirazi-Adl, A; Parnianpour, M; Larivière, C

2012-07-01

Asymmetric lifting activities are associated with low back pain. A finite element biomechanical model is used to estimate spinal loads during one- and two-handed asymmetric static lifting activities. Model input variables are thorax flexion angle, load magnitude as well as load sagittal and lateral positions while response variables are L4-L5 and L5-S1 disc compression and shear forces. A number of levels are considered for each input variable and all their possible combinations are introduced into the model. Robust yet user-friendly predictive equations that relate model responses to its inputs are established. Predictive equations with adequate goodness-of-fit (R(2) ranged from ~94% to 99%, P≤0.001) that relate spinal loads to task (input) variables are established. Contour plots are used to identify combinations of task variable levels that yield spine loads beyond the recommended limits. The effect of uncertainties in the measurements of asymmetry-related inputs on spinal loads is studied. A number of issues regarding the NIOSH asymmetry multiplier are discussed and it is concluded that this multiplier should depend on the trunk posture and be defined in terms of the load vertical and horizontal positions. Due to an imprecise adjustment of the handled load magnitude this multiplier inadequately controls the biomechanical loading of the spine. Ergonomists and bioengineers, faced with the dilemma of using either complex but more accurate models on one hand or less accurate but simple models on the other hand, have hereby easy-to-use predictive equations that quantify spinal loads under various occupational tasks. Copyright © 2011 Elsevier Ltd. All rights reserved.

Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method

KAUST Repository

Louaked, Mohammed; Seloula, Nour; Trabelsi, Saber

2017-01-01

In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017

Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method

KAUST Repository

Louaked, Mohammed

2017-07-20

In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017

Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

International Nuclear Information System (INIS)

Bourdon, A; Pasko, V P; Liu, N Y; Celestin, S; Segur, P; Marode, E

2007-01-01

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP 3 ) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by Segur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 O 2 O 2 is the partial pressure of molecular oxygen in air in units of Torr ( p O 2 = 150 Torr) at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP 3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of

Structural equation modeling methods and applications

CERN Document Server

Wang, Jichuan

2012-01-01

A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a

Structural Equation Modeling (SEM) for Satisfaction and Dissatisfaction Ratings; Multiple Group Invariance Analysis across Scales with Different Response Format

Science.gov (United States)

Mazaheri, Mehrdad; Theuns, Peter

2009-01-01

The current study evaluates three hypothesized models on subjective well-being, comprising life domain ratings (LDR), overall satisfaction with life (OSWL), and overall dissatisfaction with life (ODWL), using structural equation modeling (SEM). A sample of 1,310 volunteering students, randomly assigned to six conditions, rated their overall life…

Structure and osmotic pressure of ionic microgel dispersions

Energy Technology Data Exchange (ETDEWEB)

Hedrick, Mary M. [Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050 (United States); Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108-6050 (United States); Chung, Jun Kyung; Denton, Alan R., E-mail: alan.denton@ndsu.edu [Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050 (United States)

2015-01-21

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions.

Structure and osmotic pressure of ionic microgel dispersions

International Nuclear Information System (INIS)

Hedrick, Mary M.; Chung, Jun Kyung; Denton, Alan R.

2015-01-01

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels—soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model’s limits in predicting osmotic pressures of salty dispersions

Reservoir pressure evolution model during exploration drilling

Directory of Open Access Journals (Sweden)

Korotaev B. A.

2017-03-01

Full Text Available Based on the analysis of laboratory studies and literature data the method for estimating reservoir pressure in exploratory drilling has been proposed, it allows identify zones of abnormal reservoir pressure in the presence of seismic data on reservoir location depths. This method of assessment is based on developed at the end of the XX century methods using d- and σ-exponentials taking into account the mechanical drilling speed, rotor speed, bit load and its diameter, lithological constant and degree of rocks' compaction, mud density and "regional density". It is known that in exploratory drilling pulsation of pressure at the wellhead is observed. Such pulsation is a consequence of transferring reservoir pressure through clay. In the paper the mechanism for transferring pressure to the bottomhole as well as the behaviour of the clay layer during transmission of excess pressure has been described. A laboratory installation has been built, it has been used for modelling pressure propagation to the bottomhole of the well through a layer of clay. The bulge of the clay layer is established for 215.9 mm bottomhole diameter. Functional correlation of pressure propagation through the layer of clay has been determined and a reaction of the top clay layer has been shown to have bulge with a height of 25 mm. A pressure distribution scheme (balance has been developed, which takes into account the distance from layers with abnormal pressure to the bottomhole. A balance equation for reservoir pressure evaluation has been derived including well depth, distance from bottomhole to the top of the formation with abnormal pressure and density of clay.

Experimental study and modelling of pressure losses during reflooding of a debris beds

International Nuclear Information System (INIS)

Clavier, Remi

2015-01-01

This work deals with single and two-phase flow pressure losses in porous media. The aim is to improve understanding and modeling of momentum transfer inside particle beds, in relation with nuclear safety issues concerning the reflooding of debris beds during severe nuclear accidents. Indeed, the degradation of the core during such accidents can lead to the collapse of the fuel assemblies, and to the formation of a debris bed, which can be described as a hot porous medium. This thesis is included in a nuclear safety research project on coolability of debris beds during reflooding sequences. An experimental study of single and two-phase cold-flow pressure losses in particle beds is proposed. The geometrical characteristics of the debris and the hydrodynamic conditions are representative of the real case, in terms of granulometry, particle shapes, and flow velocities. The new data constitute an important contribution. In particular, they contain pressure losses and void fraction measurements in two-phase air-water flows with non-zero liquid Reynolds numbers, which did not exist before. Predictive models for pressure losses in single and two-phase flow through particle beds have been established from experimental data. Their structures are based on macroscopic equations obtained from the volume averaging of local conservation equations. Single-phase flow pressure losses can be described by a Darcy-Forchheimer law with a quadratic correction, in terms of filtration velocity, with a better-than-10 % precision. Numerical study of single-phase flows through porous media shows that this correlation is valid for disordered smooth particle beds. Two-phase flow pressure losses are described using a generalized Darcy-Forchheimer structure, involving inertial and cross flow terms. A new model is proposed and compared to the experimental data and to the usual models used in severe accident simulation codes. (author)

A pressure drop model for PWR grids

Energy Technology Data Exchange (ETDEWEB)

Oh, Dong Seok; In, Wang Ki; Bang, Je Geon; Jung, Youn Ho; Chun, Tae Hyun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1999-12-31

A pressure drop model for the PWR grids with and without mixing device is proposed at single phase based on the fluid mechanistic approach. Total pressure loss is expressed in additive way for form and frictional losses. The general friction factor correlations and form drag coefficients available in the open literatures are used to the model. As the results, the model shows better predictions than the existing ones for the non-mixing grids, and reasonable agreements with the available experimental data for mixing grids. Therefore it is concluded that the proposed model for pressure drop can provide sufficiently good approximation for grid optimization and design calculation in advanced grid development. 7 refs., 3 figs., 3 tabs. (Author)

A pressure drop model for PWR grids

Energy Technology Data Exchange (ETDEWEB)

Oh, Dong Seok; In, Wang Ki; Bang, Je Geon; Jung, Youn Ho; Chun, Tae Hyun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

A pressure drop model for the PWR grids with and without mixing device is proposed at single phase based on the fluid mechanistic approach. Total pressure loss is expressed in additive way for form and frictional losses. The general friction factor correlations and form drag coefficients available in the open literatures are used to the model. As the results, the model shows better predictions than the existing ones for the non-mixing grids, and reasonable agreements with the available experimental data for mixing grids. Therefore it is concluded that the proposed model for pressure drop can provide sufficiently good approximation for grid optimization and design calculation in advanced grid development. 7 refs., 3 figs., 3 tabs. (Author)

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

International Nuclear Information System (INIS)

Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

2015-01-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

The one-parameter-model - a constitutive equation applied to a heat resistant alloy

International Nuclear Information System (INIS)

Schwarze, E.; Schuster, H.; Nickel, H.

1992-01-01

In the present work a constitutive model earlier developed and used to predict experimental results of hot tests and fatigue tests from creep experiments of metallic materials were modified to comply with the properties of a high temperature resistant material. The improved model accounts for the properties of a material developing a density and a structure of dislocation lines which are capable of interactions with particles (carbides) from a second phase. The time and temperature dependent evolution of the carbide structure has been described by an equation which explains the formation of seeds as well as their growths (Ostwald ripening). The extended model was applied to Incoloy 800H which is known to develop a carbide structure. Therefore hot tensile and fatigue tests, creep and relaxation experiments using the heats ADU and BAK (KFA specifications) at temperature between 800deg C and 900deg C were performed including both solution treated specimens and specimens heat treated for 10, 100 and 1000 hours. As compared with the results from tensile tests where the carbide structures play a subordinated role, alternately, these structures have a decisive influence on the creep properties of specimens during the primary creep phase, i.e. low stresses and high temperatures. (orig.) [de

A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

DEFF Research Database (Denmark)

Banijamali, Babak

model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

Development of a system dynamics model based on Six Sigma methodology

Directory of Open Access Journals (Sweden)

José Jovani Cardiel Ortega

2017-01-01

Full Text Available A dynamic model to analyze the complexity associated with the manufacturing systems and to improve the performance of the process through the Six Sigma philosophy is proposed. The research focuses on the implementation of the system dynamics tool to comply with each of the phases of the DMAIC methodology. In the first phase, define, the problem is articulated, collecting data, selecting the variables, and representing them in a mental map that helps build the dynamic hypothesis. In the second phase, measure, model is formulated, equations are developed, and Forrester diagram is developed to carry out the simulation. In the third phase, analyze, the simulation results are studied. For the fourth phase, improving, the model is validated through a sensitivity analysis. Finally, in control phase, operation policies are proposed. This paper presents the development of a dynamic model of the system of knitted textile production knitted developed; the implementation was done in a textile company in southern Guanajuato. The results show an improvement in the process performance by increasing the level of sigma allowing the validation of the proposed approach.

Study of pressure-volume relationships and higher derivatives of bulk modulus based on generalized equations of state

International Nuclear Information System (INIS)

Kushwah, S.S.; Shrivastava, H.C.; Singh, K.S.

2007-01-01

We have generalized the pressure-volume (P-V) relationships using simple polynomial and logarithmic expansions so as to make them consistent with the infinite pressure extrapolation according to the model of Stacey. The formulations are used to evaluate P-V relationships and pressure derivatives of bulk modulus upto third order (K', K'' and K''') for the earth core material taking input parameters based on the seismological data. The results based on the equations of state (EOS) generalized in the present study are found to yield good agreement with the Stacey EOS. The generalized logarithmic EOS due to Poirier and Tarantola deviates substantially from the seismic values for P, K and K'. The generalized Rydberg EOS gives almost identical results with the Birch-Murnaghan third-order EOS. Both of them yield deviations from the seismic data, which are in opposite direction as compared to those found from the generalized Poirier-Tarantola logarithmic EOS

The linearized pressure Poisson equation for global instability analysis of incompressible flows

Science.gov (United States)

Theofilis, Vassilis

2017-12-01

The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

Convective heat transport of high-pressure flows inside active, thick walled-tubes with isothermal outer surfaces: usage of Nusselt correlation equations for an inactive, thin walled-tube

Energy Technology Data Exchange (ETDEWEB)

Campo, Antonio [Idaho State Univ., Nuclear Engineering Dept., Pocatello, ID (United States); Sanchez, Alejo [Universidad de los Andes, Depto. de Ingenieria Mecanica, Merida (Venezuela)

1998-03-01

A semi-analytical analysis was conducted for the prediction of the mean bulk- and interface temperatures of gaseous and liquid fluids moving laminarly at high pressures inside thick-walled metallic tubes. The outer surfaces of the tubes are isothermal. The central goal of this article is to critically examine the thermal response of this kind of in-tube flows utilizing two versions of the 1-D lumped model: one is differential-numerical while the other is differential-algebraic. For the former, the local Nusselt number characterizing an inactive, isothermal tube was taken from correlation equations reported in the heat transfer literature. For the latter, a streamwise-mean Nusselt number associated with an active, isothermal tube was taken from standard correlation equations that appear in text-books on basic heat transfer. For the two different versions of the 1-D lumped model tested, the computed results consistently demonstrate that the differential-algebraic, provides accurate estimates of both the mean bulk- and the interface temperatures when compared with those temperature results computed with formal 2-D differential models. (author)

A discussion of hyperbolicity in CATHENA 4. Virtual mass and phase-to-interface pressure differences

International Nuclear Information System (INIS)

Aydemir, Nusret U.

2012-01-01

It is well known that the one-dimensional equations of motion for two-phase flow are non-hyperbolic. Non-hyperbolicity can lead to numerical instabilities, destroying the solution. However, researchers in the last few decades were able to show that inclusion of virtual mass and/or phase-to-interface pressure differences in the momentum equations successfully render the equations of motion hyperbolic. In the present paper, the effect of including virtual mass and phase-to-interface pressure terms in the momentum equations on the hyperbolicity of the two-phase model in the CATHENA 4 code is discussed. The study is motivated by the fact that the inclusion of either model has been shown in the open literature to lead to a hyperbolic system separately. However, no known study exists that examine hyperbolicity in the presence of both these terms in the momentum equations. In this work, both terms are considered in the model equations simultaneously and their implications on the hyperbolicity of the two-phase model are discussed. Specifically, it is shown that in the case of mixed flow, there is a distinct region of non-hyperbolicity that developers need to be aware of when their equations include both the virtual mass and the phase-to-interface terms. Selecting the coefficients of phase-to-interface pressure difference terms properly ensures that the equations are hyperbolic for a wide range of conditions. (orig.)

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

Science.gov (United States)

Nestler, Steffen

2014-05-01

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

Meta-analysis a structural equation modeling approach

CERN Document Server

Cheung, Mike W-L

2015-01-01

Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo

High pressure generation by laser driven shock waves: application to equation of state measurement; Generation de hautes pressions par choc laser: application a la mesure d'equations d'etat

Energy Technology Data Exchange (ETDEWEB)

Benuzzi, A

1997-12-15

This work is dedicated to shock waves and their applications to the study of the equation of state of compressed matter.This document is divided into 6 chapters: 1) laser-produced plasmas and abrasion processes, 2) shock waves and the equation of state, 3) relative measuring of the equation of state, 4) comparison between direct and indirect drive to compress the target, 5) the measurement of a new parameter: the shock temperature, and 6) control and measurement of the pre-heating phase. In this work we have reached relevant results, we have shown for the first time the possibility of generating shock waves of very high quality in terms of spatial distribution, time dependence and of negligible pre-heating phase with direct laser radiation. We have shown that the shock pressure stays unchanged as time passes for targets whose thickness is over 10 {mu}m. A relative measurement of the equation of state has been performed through the simultaneous measurement of the velocity of shock waves passing through 2 different media. The great efficiency of the direct drive has allowed us to produce pressures up to 40 Mbar. An absolute measurement of the equation of state requires the measurement of 2 parameters, we have then performed the measurement of the colour temperature of an aluminium target submitted to laser shocks. A simple model has been developed to infer the shock temperature from the colour temperature. The last important result is the assessment of the temperature of the pre-heating phase that is necessary to know the media in which the shock wave propagates. The comparison of the measured values of the reflectivity of the back side of the target with the computed values given by an adequate simulation has allowed us to deduce the evolution of the temperature of the pre-heating phase. (A.C.)

Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

Energy Technology Data Exchange (ETDEWEB)

Gregoire, O

2008-07-01

In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

COMPARATIVE EFFICIENCIES STUDY OF SLOT MODEL AND MOUSE MODEL IN PRESSURISED PIPE FLOW

Directory of Open Access Journals (Sweden)

Saroj K. Pandit

2014-01-01

Full Text Available The flow in sewers is unsteady and variable between free-surfac e to full pipe pressurized flow. Sewers are designed on the basis of free surf ace flow (gravity flow however they may carry pressurized flow. Preissmann Slot concep t is widely used numerical approach in unsteady free surface-pressurized flow as it provides the advantage of using free surface flow as a single type flow. Slo t concept uses the Saint- Venant’s equations as a basic equation for one-dimensional unst eady free surface flow. This paper includes two different numerical models using Saint Venant’s equations. The Saint Venant’s e quations of continuity and momen tum are solved by the Method of Characteristics and presented in forms for direct substitution into FORTRAN programming for numerical analysis in the first model. The MOUSE model carries out computation of unsteady flows which is founde d on an implicit, finite difference numerical solut ion of the basic one dimension al Saint Venant’s equations of free surface flow. The simulation results are comp ared to analyze the nature and degree of errors for further improvement.

Anisotropic charged physical models with generalized polytropic equation of state

Energy Technology Data Exchange (ETDEWEB)

Nasim, A.; Azam, M. [University of Education, Division of Science and Technology, Lahore (Pakistan)

2018-01-15

In this paper, we found the exact solutions of Einstein-Maxwell equations with generalized polytropic equation of state (GPEoS). For this, we consider spherically symmetric object with charged anisotropic matter distribution. We rewrite the field equations into simple form through transformation introduced by Durgapal (Phys Rev D 27:328, 1983) and solve these equations analytically. For the physically acceptability of these solutions, we plot physical quantities like energy density, anisotropy, speed of sound, tangential and radial pressure. We found that all solutions fulfill the required physical conditions. It is concluded that all our results are reduced to the case of anisotropic charged matter distribution with linear, quadratic as well as polytropic equation of state. (orig.)

Axial mercury segregation in direct current operated low-pressure argon-mercury gas discharge: Part II. Model

International Nuclear Information System (INIS)

Gielen, John W A M; Groot, Simon de; Dijk, Jan van; Mullen, Joost J A M van der

2004-01-01

In a previous paper we had presented experimental results on mercury segregation due to cataphoresis in direct current operated low-pressure argon-mercury gas discharges. In this paper, we present our model to describe cataphoretic segregation in argon (or another noble gas)-mercury discharges. The model is based on the balance equations for mass and momentum and includes electrophoresis effects of electrons on mercury. Good agreement is found between the experimental results and model calculations. The model confirms our experimental observation that the mercury vapour pressure gradient depends on the local mercury vapour pressure. Furthermore, the model predicts the reversal of the direction of the transport of mercury under certain conditions (the phenomenon known as retrograde cataphoresis)

Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

Science.gov (United States)

Hong, Sehee; Kim, Soyoung

2018-01-01

There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.

A transient one-dimensional numerical model for kinetic Stirling engine

International Nuclear Information System (INIS)

Wang, Kai; Dubey, Swapnil; Choo, Fook Hoong; Duan, Fei

2016-01-01

Highlights: • A non-equilibrium thermal mode with considering loses is adopted in Stirling engine. • Good agreements are achieved for predicting various critical system parameters. • Differences between helium and hydrogen systems are highlighted and analyzed. • Pressure drop of helium system is much larger and more sensitive to frequency. - Abstract: A third-order numerical model based on one-dimensional computational fluid dynamics is developed for kinetic Stirling engines. Various loss mechanisms in Stirling engines, including gas spring hysteresis loss, shuttle loss, appendix displacer gap loss, gas leakage loss, finite speed loss, piston friction loss, pressure drop loss, heat conduction loss, mechanical loss and imperfect heat transfer, are considered and embedded into the basic control equations. The non-equilibrium thermal model is adopted for the regenerator to capture the oscillating features of the gas and solid temperatures. To improve the numerical stability and accuracy, the implicit second-order time difference scheme and the second-order upwind scheme are adopted for discretizing the time differential terms and convective terms, respectively. Experimental validations are then conducted on a beta-type Stirling engine with the extensive experimental data for diverse working conditions. The results show that the developed model has better accuracies than the previous second-order models. Good agreements are achieved for predicting various critical system parameters, including pressure-volume diagram, indicated power, brake power, indicated efficiency, brake efficiency and mechanical efficiency. In particular, both the experiments and simulations show that the Stirling engine charged with helium tends to have much lower optimal working frequencies and poorer performances compared to the hydrogen system. Based on the analyses of the losses, it reveals that the pressure drop in the flow channels plays a critical role in shaping the different

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

Science.gov (United States)

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.

Theoretical-experimental modelling of the momentum equation for PWR reactor steam generators

International Nuclear Information System (INIS)

Rodrigues, L.A.H.

1994-01-01

A mathematical model in steady-state conditions of the momentum equation at the secondary side of a vertical U-tube steam generator with recirculation is presented. The U-tube test section was the 150 bar - Circuito Termoidraulico Experimental - CTE-150. This facility is a Experimental Thermal-hydraulic Circuit and operates at the same conditions (pressure and temperature) of a typical PWR reactor. A comparison between the Homogeneous and Separate Flow models was done. those models were verified and compared with experimental data for several operational conditions. The results show that the model fits very well the experimental data and seems to be appropriate to study water recirculation of a steam generator secondary side. (author)

Line pressure effects on differential pressure measurements

International Nuclear Information System (INIS)

Neff, G.G.; Evans, R.P.

1982-01-01

The performance of differential pressure transducers in experimental pressurized water reactor (PWR) systems was evaluated. Transient differential pressure measurements made using a simple calibration proportionality relating differential pressure to output voltage could have large measurement uncertainties. A more sophisticated calibration equation was derived to incorporate the effects of zero shifts and sensitivity shifts as pressure in the pressure sensing line changes with time. A comparison made between the original calibration proportionality equation and the derived compensation equation indicates that potential measurement uncertainties can be reduced

Structural Equation Model Trees

Science.gov (United States)

Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

2013-01-01

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation

Directory of Open Access Journals (Sweden)

Huei Chu Weng

2013-09-01

Full Text Available Despite a long research history, theoretical predictions for the material properties as well as the flow fields and characteristics of magnetic fluids were not well consistent with the experimental data. The lack of a universally accepted magnetization equation for accurately modeling hydrodynamics of magnetic fluids/nanofluids is particularly a major issue. In this paper, we give an overview on the continuum theory and test the six well-known models via comparisons with magnetoviscosity measurements to make clear the magnetization relaxation due to the rotation of magnetic particles and see how well they make predictions on the basis of numerical calculations. Results reveal that the ML model leads to unexplainable behavior. Moreover, the WC model with a ‘relaxation rate’ modification is found to reproduce the predictions of the MRSh model, which agree well with experimental data. The revised WC model (WCC should therefore be preferred.

On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of pressure filtration

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Frid, H.; Karlsen, K.H.

2002-07-01

We consider a free boundary problem of a quasilinear strongly degenerate parabolic equation arising from a model of pressure filtration of flocculated suspensions. We provide definitions of generalized solutions of the free boundary problem in the framework of L2 divergence-measure fields. The formulation of boundary conditions is based on a Gauss-Green theorem for divergence-measure fields on bounded domains with Lipschitz deformable boundaries and avoids referring to traces of the solution. This allows to consider generalized solutions from a larger class than BV. Thus it is not necessary to derive the usual uniform estimates on spatial and time derivatives of the solutions of the corresponding regularized problem requires in the BV approach. We first prove existence and uniqueness of the solution of the regularized parabolic free boundary problem and then apply the vanishing viscosity method to prove existence of a generalized solution to the degenerate free boundary problem. (author)

Modelling of SOEC-FT reactor: Pressure effects on methanation process

International Nuclear Information System (INIS)

Chen, Bin; Xu, Haoran; Ni, Meng

2017-01-01

Highlights: • Numerical study on combined SOEC-FT reactor in pressurized condition. • Effects of operating pressure on co-electrolysis and CH_4 production are studied. • The lower limit temperature of the FT section is dependent on the operating pressure. • The CH_4 production can be improved at higher voltage due to the current increase. • Effects of higher exchange current density is predicted at different temperature. - Abstract: In this paper a numerical model is developed for a novel reactor combining a Solid Oxide Electrolyzer Cell (SOEC) section with a Fischer Tropsch like section for methane production under pressurized & temperature-gradient condition. Governing equations for mass, momentum, charge transport are solved with Finite Element Method. The chemical reaction kinetics of reversible water gas shift reaction and reversible methanation reaction in Ni/YSZ cathode are fully considered. The model is validated by comparing simulation results with experimental data. Parametric simulations are conducted to understand the physical-chemical processes in the reactor with a focus on the pressure effect. It is predicted that the optimal operating pressure is around 3 bar, beyond which the CH_4 conversion ratio (2.5 times enhanced than 1 bar operating) cannot be further increased. It is also found that it is feasible to operate the pressurized SOEC at a lower temperature for CH_4 production with improved catalyst activity.

Dynamical System Analysis of Reynolds Stress Closure Equations

Science.gov (United States)

Girimaji, Sharath S.

1997-01-01

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Dynamics of single-bubble sonoluminescence. An alternative approach to the Rayleigh-Plesset equation

Science.gov (United States)

de Barros, Ana L. F.; Nogueira, Álvaro L. M. A.; Paschoal, Ricardo C.; Portes, Dirceu, Jr.; Rodrigues, Hilario

2018-03-01

Sonoluminescence is the phenomenon in which acoustic energy is (partially) transformed into light as a bubble of gas collapses inside a liquid medium. One particular model used to explain the motion of the bubble’s wall forced by acoustic pressure is expressed by the Rayleigh-Plesset equation, which can be obtained from the Navier-Stokes equation. In this article, we describe an alternative approach to derive the Rayleigh-Plesset equation based on Lagrangian mechanics. This work is addressed mainly to undergraduate students and teachers. It requires knowledge of calculus and of many concepts from various fields of physics at the intermediate level.

A variational model of disjoining pressure: Liquid film on a nonplanar surface

Energy Technology Data Exchange (ETDEWEB)

Silin, D.; Virnovsky, G.

2009-06-01

Variational methods have been successfully used in modelling thin liquid films in numerous theoretical studies of wettability. In this paper, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmgoltz free energy functional depends both on the disjoining pressure isotherm and the shape of the solid surface. The augmented Young-Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A number of solutions describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait technique describes the entire variety of mathematically feasible solutions. It turns out that a periodic solution, which would describe wave-like wetting films, does not satisfy the Jacobi's condition of the classical calculus of variations. Therefore, such a solution is nonphysical. The roughness of the solid surface significantly affects liquid film stability. AYLE solutions suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space and the curvature is positive.

High Temperature, High Pressure Equation of State: Solidification of Hydrocarbons and Measurement of Krytox Oil Using Rolling-Ball Viscometer Validation

Energy Technology Data Exchange (ETDEWEB)

Gamwo, Isaac K. [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States); Burgess, Ward [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States); Tapriyal, Deepak [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States)

2014-10-03

The global consumption of oil and gas continues to rise and has led to the search and recovery of petroleum sources from reservoirs exhibiting increasingly high-temperature, high-pressure conditions. For example, ultra-deep petroleum formations found at depths of approximately 5 km or more, can exhibit pressure and temperature values as high as 240 MPa (35,000 psi) and 533 K (260°C). The hydrocarbons produced from these ultra-deep formations experience significant decreases in temperature and pressure from reservoir to platform conditions. Hence, it is highly desirable to develop accurate equation of state models (EOS) and fluid properties databases that covers the entire temperature and pressure ranges associated with this process to promote the efficient, safe, and environmentally responsible production from these reservoirs at extreme conditions. Currently available databases and EOS models are generally limited to approximately 69 MPa and do not correlate accurately when extrapolated to the extreme environments associated with ultra-deep reservoirs where temperatures can reach as high as 533 K and pressures up to 240 MPa. Despite recent exploration and production of petroleum from ultra-deep formations, there are major gaps in the databases for pure and mixture density and viscosity of hydrocarbons. These are the most important fluid properties that enable accurate booking of reserves as well as the design of size and equipment to safely bring these fluids to the platform. The overall objective of this project is to develop methodologies to provide crude oil thermodynamic and transport properties—including density, viscosity, and phase composition— at extreme temperature and pressure conditions. The knowledge of these crude oil properties reduces uncertainties associated with deep drilling and promotes safer and reliable access to domestic energy resources. This report is an extension of work reported in our first Technical Report Series (TRS) released

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

Quasi-exact solvability of the one-dimensional Holstein model

International Nuclear Information System (INIS)

Pan Feng; Dai Lianrong; Draayer, J P

2006-01-01

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is solved by using a Bethe ansatz in analogue to that for the one-dimensional spinless Fermi-Hubbard model. Excitation energies and the corresponding wavefunctions of the model are determined by a set of partial differential equations. It is shown that the model is, at least, quasi-exactly solvable for the two-site case, when the phonon frequency, the electron-phonon coupling strength and the hopping integral satisfy certain relations. As examples, some quasi-exact solutions of the model for the two-site case are derived. (letter to the editor)

Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

Directory of Open Access Journals (Sweden)

Nakao Hayashi

2004-04-01

Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

Science.gov (United States)

Mapakshi, N. K.; Chang, J.; Nakshatrala, K. B.

2018-04-01

Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do not satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart-Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. A series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select

Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling

NARCIS (Netherlands)

Hesan, R.; Ghorbani, A.; Dignum, M.V.

2014-01-01

In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we

Will learning to solve one-step equations pose a challenge to 8th grade students?

Science.gov (United States)

Ngu, Bing Hiong; Phan, Huy P.

2017-08-01

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. Element interactivity arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features (e.g. negative pronumeral) poses additional challenge to master equation solving skills. In an experiment, 41 8th grade students (girls = 16, boys = 25) sat for a pre-test, attended a session about equation solving, completed an acquisition phase which constituted the main intervention and were tested again in a post-test. The results showed that at post-test, students performed better on one-step equations tapping low rather than high element interactivity knowledge. In addition, students performed better on those one-step equations that contained no special features. Thus, both the degree of element interactivity and the operation with special features affect the challenge posed to 8th grade students on learning how to solve one-step equations.

The effect of KZK1 pressure equation on the sonoluminescence in water and fat tissues

Science.gov (United States)

Gheshlaghi, M.; Sadighi-Bonabi, R.; Ghadirifar, A.

2015-09-01

The effect of the produced light flashes from sonoluminescence (SL) on the fat tissue and water is studied. By using KZK equation as an essential equation for calculating the thermal source in bio-liquids, the effective bubble parameters in quasi-adiabatic model are calculated and compared in these systems. It is noticed that the temperature and the intensity for fat tissue are about 30% and 38% less than the ones for water respectively. These results are almost in good agreement with the only experimental measurement denoting less SL temperature in bio-liquids which present more suitable condition for using SL in such applications.

Solvation quantities from a COSMO-RS equation of state

International Nuclear Information System (INIS)

Panayiotou, C.; Tsivintzelis, I.; Aslanidou, D.; Hatzimanikatis, V.

2015-01-01

Highlights: • Extension of the successful COSMO-RS model to an equation-of-state model. • Two scaling constants, obtained from atom-specific contributions. • Overall estimation of the solvation quantities and contributions. - Abstract: This work focuses on the extension of the successful COSMO-RS model of mixtures into an equation-of-state model of fluids and its application for the estimation of solvation/hydration quantities of a variety of chemical substances. These quantities include free-energies, enthalpies and entropies of hydration as well as the separate contributions to each of them. Emphasis is given on the estimation of contributions from the conformational changes of solutes upon solvation and the associated restructuring of solvent in its immediate neighborhood. COSMO-RS is a quantum-mechanics based group/segment contribution model in which the Quasi-Chemical (QC) approach is used for the description of the non-random distribution of interacting segments in the system. Thus, the equation-of-state development is done through such a QC framework. The new model will not need any adjustable parameters for the strong specific interactions, such as hydrogen bonds, since they will be provided by the quantum-mechanics based cosmo-files – a key feature of COSMO-RS model. It will need, however, one volumetric and one energy parameter per fluid, which are scaling constants or molecular descriptors of the fluid and are obtained from rather easily available data such as densities, boiling points, vapor pressures, heats of vaporization or second virial coefficients. The performance and the potential of the new equation-of-state model to become a fully predictive model are critically discussed

Radiological diagnosis of pulmonary sequestration: review of six cases, including one bilateral

International Nuclear Information System (INIS)

Brito Pacheco, E.M. de; Cazerta, N.M.G.; Marins, J.L.C.; Prando, A.

1989-01-01

Radiological diagnosis of pulmonary sequestration: review of six cases, including one bilateral. Pulmonary sequestration is an uncommon disorder consisting of aberrant pulmonary tissue that has no normal connection with the bronchial tree or with the pulmonary arteries, but is supplied by a systemic artery which usually arises from the aorta. Six cases of pulmonary sequestration are presented and the radiological manifestation of this rare congenital disorder are discussed. These sequestrations were intralobar/unilateral in four patients, extralobar/unilateral in one and extralobar/bilateral in the other patient. Special attention is given to the extremely uncommon bilateral sequestration. To our knowledge only four cases of this form of disease has been described in the literature. (author) [pt

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

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

Science.gov (United States)

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Physical Limitations of Empirical Field Models: Force Balance and Plasma Pressure

International Nuclear Information System (INIS)

Sorin Zaharia; Cheng, C.Z.

2002-01-01

In this paper, we study whether the magnetic field of the T96 empirical model can be in force balance with an isotropic plasma pressure distribution. Using the field of T96, we obtain values for the pressure P by solving a Poisson-type equation (gradient) 2 P = (gradient) · (J x B) in the equatorial plane, and 1-D profiles on the Sun-Earth axis by integrating (gradient)P = J x B. We work in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials. Our results lead to the conclusion that the T96 model field cannot be in equilibrium with an isotropic pressure. We also analyze in detail the computation of Birkeland currents using the Vasyliunas relation and the T96 field, which yields unphysical results, again indicating the lack of force balance in the empirical model. The underlying reason for the force imbalance is likely the fact that the derivatives of the least-square fitted model B are not accurate predictions of the actual magnetospheric field derivatives. Finally, we discuss a possible solution to the problem of lack of force balance in empirical field models

About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models

OpenAIRE

De La Sen, M.

2008-01-01

Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called ...

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

Science.gov (United States)

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

Homotopy analysis solutions of point kinetics equations with one delayed precursor group

International Nuclear Information System (INIS)

Zhu Qian; Luo Lei; Chen Zhiyun; Li Haofeng

2010-01-01

Homotopy analysis method is proposed to obtain series solutions of nonlinear differential equations. Homotopy analysis method was applied for the point kinetics equations with one delayed precursor group. Analytic solutions were obtained using homotopy analysis method, and the algorithm was analysed. The results show that the algorithm computation time and precision agree with the engineering requirements. (authors)

Effects of pressure anisotropy on plasma transport

International Nuclear Information System (INIS)

Zawaideh, E.; Najmabadi, F.; Conn, R.W.

1986-03-01

In a recent paper a new set of generalized two-field equations is derived which describes plasma transport along the field lines of a space and time dependent magnetic field. These equations are valid for collisional to weakly collisional plasmas; they reduce to the conventional fluid equations of Braginskii for highly collisional plasmas. An important feature of these equations is that the anisotropy in the ion pressure is explicitly included. In this paper, these generalized transport equations are applied to a model problem of plasma flow through a magnetic mirror field. The profiles of the plasma parameters (density, flow speed, and pressures) are numerically calculated for plasma in different collisionality regimes. These profiles are explained by examining the competing terms in the transport equation. The pressure anisotropy is found to profoundly impact the plasma flow behavior. As a result, the new generalized equations predict flow behavior more accurately than the conventional transport equations. A large density and pressure drop is predicted as the flow passes through a magnetic mirror. Further, the new equations uniquely predict oscillations in the density profile, an effect missing in results from the conventional equations

On one model problem for the reaction-diffusion-advection equation

Science.gov (United States)

Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.

2017-09-01

The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.

One-dimensional two-phase thermal hydraulics (ENSTA course)

International Nuclear Information System (INIS)

Olive, J.

1995-11-01

This course is part of the ENSTA 3rd year thermal hydraulics program (nuclear power option). Its purpose is to provide the theoretical basis and main physical notions pertaining to two-phase flow, mainly focussed on water-steam flows. The introduction describes the physical specificities of these flows, emphasizing their complexity. The mathematical bases are then presented (partial derivative equations), leading to a one-dimensional type, simplified description. Balances drawn up for a pipe length volume are used to introduce the mass conservation. motion and energy equations for each phase. Various postulates used to simplify two-phase models are presented, culminating in homogeneous model definitions and equations, several common examples of which are given. The model is then applied to the calculation of pressure drops in two-phase flows. This involves presenting the models most frequently used to represent pressure drops by friction or due to pipe irregularities, without giving details (numerical values of parameters). This chapter terminates with a brief description of static and dynamic instabilities in two-phase flows. Finally, heat transfer conditions frequently encountered in liquid-steam flows are described, still in the context of a 1D model. This chapter notably includes reference to under-saturated boiling conditions and the various forms of DNB. The empirical heat transfer laws are not discussed in detail. Additional material is appended, some of which is in the form of corrected exercises. (author). 6 appends

One-velocity neutron diffusion calculations based on a two-group reactor model

Energy Technology Data Exchange (ETDEWEB)

Bingulac, S; Radanovic, L; Lazarevic, B; Matausek, M; Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

Many processes in reactor physics are described by the energy dependent neutron diffusion equations which for many practical purposes can often be reduced to one-dimensional two-group equations. Though such two-group models are satisfactory from the standpoint of accuracy, they require rather extensive computations which are usually iterative and involve the use of digital computers. In many applications, however, and particularly in dynamic analyses, where the studies are performed on analogue computers, it is preferable to avoid iterative calculations. The usual practice in such situations is to resort to one group models, which allow the solution to be expressed analytically. However, the loss in accuracy is rather great particularly when several media of different properties are involved. This paper describes a procedure by which the solution of the two-group neutron diffusion. equations can be expressed analytically in the form which, from the computational standpoint, is as simple as the one-group model, but retains the accuracy of the two-group treatment. In describing the procedure, the case of a multi-region nuclear reactor of cylindrical geometry is treated, but the method applied and the results obtained are of more general application. Another approach in approximate solution of diffusion equations, suggested by Galanin is applicable only in special ideal cases.

Macroscopic balance equations for two-phase flow models

International Nuclear Information System (INIS)

Hughes, E.D.

1979-01-01

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

One-dimensional integral equations for a system of three identical particles in the boundary condition models and the possibility of changing the off-shell behaviour of the two-particle t-matrix

International Nuclear Information System (INIS)

Efimov, V.N.; Schulz, H.

1976-01-01

It is shown that in the framework of the boundary condition models (BCM) for the two-particle interaction the Schroedinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle t-matrix and therefore to simulate three particle effects. (Auth.)

Equations-of-motion treatment of pairing correlations: Seniority-one states

International Nuclear Information System (INIS)

Andreozzi, F.; Covello, A.; Gargano, A.; Porrino, A.

1988-01-01

In prior work we have developed an equations-of-motion method for treating seniority-one states in pairing-force theory. Here we present a new and simpler version of that method. Some numerical applications to Sn isotopes show its considerable practical value

Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

International Nuclear Information System (INIS)

Alvarez-Estrada, R.F.

1979-01-01

A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow

Energy Technology Data Exchange (ETDEWEB)

Munkejord, Svend Tollak

2006-05-11

This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than

A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship

Energy Technology Data Exchange (ETDEWEB)

Dahle, H K; Celia, M A; Hassanizadeh, S M; Karlsen, K H

2002-07-01

New theories suggest that the relationship between capillary pressure and saturation should be enhanced by a dynamic term that is proportional to the time rate of change of saturation. This so-called dynamic capillary pressure formulation is supported by laboratory experiments, and can be included in various forms of the governing equations for two-phase flow in porous media. An extended model of two-phase flow in porous media may be developed based on fractional flow curves and a total pressure - saturation description that includes the dynamic capillary pressure terms. A dimensionless form of the resulting equation set provides an ideal tool to study the relative importance of the dynamic capillary pressure effect. This equation provides a rich set of mathematical research questions, and numerical solutions to the equation provide insights into the behavior of two-phase immiscible flow. For typical two-phase flow systems, dynamic capillary pressure acts to retard infiltration fronts, with responses dependent on system parameters including boundary conditions. Recent theoretical work suggests that the traditional algebraic relationship between capillary pressure and saturation may be inadequate. Instead, a so-called dynamic capillary pressure formulation is needed, where capillary pressure is defined as a thermodynamic variable, and the difference between phase pressures is only equal to the capillary pressure at equilibrium. Under dynamic conditions, the disequilibrium between phase-pressure differences and the capillary pressure is taken to be proportional to the time rate of change of saturation. A recent study by Hassanizadeh et al. presents experimental evidence, culled from the literature, to support this claim. Numerical simulations using dynamic pore-scale network models and upscaling also support the claim. Hassanizadeh et al. also presented numerical solutions for an enhanced version of Richards' equation that included the dynamic terms. A preliminary

Introduction to computation and modeling for differential equations

CERN Document Server

Edsberg, Lennart

2008-01-01

An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

New Indicated Mean Effective Pressure (IMEP) model for predicting crankshaft movement

International Nuclear Information System (INIS)

Omran, Rabih; Younes, Rafic; Champoussin, Jean-Claude; Outbib, Rachid

2011-01-01

Highlights: → IMEP is essential to estimate the indicated torque in internal combustion engine. → We proposed model which describes the IMEP-Low pressure and the IMEP-High pressure. → We studied the evolution of the IMEP with respect to the engine's variables. → We deduced the variables of influence that can be used to develop the models. → The IMEP model is compared to transient experimental New European Driving Cycle. - Abstract: Indicated Mean Effective Pressure models (IMEP) are essential to estimate the indicated torque in internal combustion engine; they also provide important information about the mechanical efficiency of the engine thermodynamic cycle which describes the conversion of the fuel combustion energy into mechanical work. In the past, many researches were made to improve the IMEP prediction and measurement techniques at different engine operating conditions. In this paper, we proposed a detailed IMEP model which separately describes the IMEP-Low pressure and the IMEP-High pressure of a modern diesel engine; the IMEP is the direct subtraction result between these two variables. We firstly studied the evolution of the IMEP HP and IMEP LP with respect to the engine's variables and then we deduced the variables of influence and the form of the equations that can be used to develop the models. Finally, the models' coefficients were determined based on experimental data collected on a steady state test bench and using the least square regression method. In addition, the IMEP HP model results were compared to transient experimental data collected on a chassis dynamometer test bench; the model results are in excellent agreement with the experimental data.

Parallelization of pressure equation solver for incompressible N-S equations

International Nuclear Information System (INIS)

Ichihara, Kiyoshi; Yokokawa, Mitsuo; Kaburaki, Hideo.

1996-03-01

A pressure equation solver in a code for 3-dimensional incompressible flow analysis has been parallelized by using red-black SOR method and PCG method on Fujitsu VPP500, a vector parallel computer with distributed memory. For the comparison of scalability, the solver using the red-black SOR method has been also parallelized on the Intel Paragon, a scalar parallel computer with a distributed memory. The scalability of the red-black SOR method on both VPP500 and Paragon was lost, when number of processor elements was increased. The reason of non-scalability on both systems is increasing communication time between processor elements. In addition, the parallelization by DO-loop division makes the vectorizing efficiency lower on VPP500. For an effective implementation on VPP500, a large scale problem which holds very long vectorized DO-loops in the parallel program should be solved. PCG method with red-black SOR method applied to incomplete LU factorization (red-black PCG) has more iteration steps than normal PCG method with forward and backward substitution, in spite of same number of the floating point operations in a DO-loop of incomplete LU factorization. The parallelized red-black PCG method has less merits than the parallelized red-black SOR method when the computational region has fewer grids, because the low vectorization efficiency is obtained in red-black PCG method. (author)

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

Science.gov (United States)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

System transient analysis code development for low pressure and low power

International Nuclear Information System (INIS)

Kim, Hee Cheol

1998-02-01

A real time reactor system analysis code, ARTIST, based on drift flux model has been developed to investigate the transient system behavior under low pressure, low flow and low power conditions with noncondensable gas present in the system. The governing equations of the ARTIST code consist of three mass continuity equations (steam, liquid and noncondensable), two energy equations (gas and mixture) and one momentum equation (mixture) constituted with the drift flux model. The capability of ARTIST in predicting two-phase flow void distribution in the system has been validated against experimental data. The results of the ARTIST axial void distribution at low pressure and low flow, are far better than the results of both the homogeneous model of TASS code and the two-fluid model of RELAP5/MOD3 code. Also, RELAP5/MOD3 calculation shows the large amplitude of void fraction oscillations at low pressure. These results imply that interfacial momentum transfer terms in the two-fluid model formulation should be carefully constituted, especially for the low pressure condition due to the big density differences between steam and water. Thermal-hydraulic state solution scheme is developed when noncondensable gas exists. Numerical consistency and convergence of obtaining equilibrium state is tested with the ideal problems for various situations including very low partial pressure conditions. Calculated thermal-hydraulic state for each test shows consistent and expected behaviour. A new multi-layer back propagation network algorithm for calculating the departure from nucleate boiling ratio (DNBR) is developed and adopted in ARTIST code in order to have real-time DNBR evaluation by eliminating the tandem procedure of the transient DNBR calculation. The algorithm trained by different patterns generated by latin hypercube sampling method on the performance space is tested for the randomly sampled untrained data and the transient DNBR data. The uncertainty of the algorithm is

Analysis of bilinear relation of a six-vertex model

International Nuclear Information System (INIS)

Korepin, V.E.

1982-01-01

A problem of calculating all matrices of T(μ) monodromy satisfying certain commutation relations for the six-vertex model matrix is considered. The paper presents full description of all accurate L-operators (all monodromy-matrices per one lattice step). It is noted that the a/d function has the simpliest form for L operators, and the corresponding A, B, C, D operators act transitively in rather narrow subspace of the constructed space

Fitting ARMA Time Series by Structural Equation Models.

Science.gov (United States)

van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

A porous medium approach for the fluid structure interaction modelling of a water pressurized nuclear reactor core fuel assemblies: simulation and experimentation; Une approche milieu poreux pour la modeisation de l'interaction fluide-structure des assemblages combustibles dans un coeur de reacteur a eau pressurisee: simulation et experimentation

Energy Technology Data Exchange (ETDEWEB)

Ricciardi, G.

2008-10-15

The designing of a pressurized water reactor core subjected to seismic loading, is a major concern of the nuclear industry. We propose, in this PhD report, to establish the global behaviour equations of the core, in term of a porous medium. Local equations of fluid and structure are space averaged on a control volume, thus we define an equivalent fluid and an equivalent structure, of which unknowns are defined on the whole space. The non-linear fuel assemblies behaviour is modelled by a visco-elastic constitutive law. The fluid-structure coupling is accounted for by a body force, the expression of that force is based on empirical formula of fluid forces acting on a tube subject to an axial flow. The resulting equations are solved using a finite element method. A validation of the model, on three experimental device, is proposed. The first one presents two fuel assemblies subjected to axial flow. One of the two fuel assemblies is deviated from its position of equilibrium and released, while the other is at rest. The second one presents a six assemblies row, immersed in water, placed on a shaking table that can simulate seismic loading. Finally, the last one presents nine fuel assemblies network, arranged in a three by three, subject to an axial flow. The displacement of the central fuel assembly is imposed. The simulations are in agreement with the experiments, the model reproduces the influence of the flow of fluid on the dynamics and coupling of the fuel assemblies. (author)

Validity of the modified Reynolds equation for incompressible active lubrication

DEFF Research Database (Denmark)

Cerda Varela, Alejandro Javier; Santos, Ilmar

2016-01-01

The modified Reynolds equation for active lubrication has been the cornerstone around which the theoretical investigations regarding actively lubricated bearings have evolved over the years. Introduced originally in 1994, it enables to calculate in a simplified manner the bearing pressure field...... as a function of servovalve controlled pressurized oil injection. This article deals with a preliminary critical review of the simplificatory assumptions that are introduced into the modified Reynolds equation in order to model the phenomena taking place in the interface between the injection nozzle...... and the bearing clearance. The analysis is performed by means of direct comparison of the results of the modified Reynolds equation model versus benchmark CFD calculations, applied to a geometry representative of the system analyzed. The results show that the modified Reynolds equation mathematical simplicity...

Electrolyte CPA equation of state for very high temperature and pressure reservoir and basin applications

Science.gov (United States)

Courtial, Xavier; Ferrando, Nicolas; de Hemptinne, Jean-Charles; Mougin, Pascal

2014-10-01

In this work, an electrolyte version of the Cubic Plus Association (eCPA) equation of state has been adapted to systems containing CH4, CO2, H2O and NaCl (up to 5 molal) at pressures up to 200 MPa and temperatures up to 773 K for salt-free systems and 573 K for salt-containing systems. Its purpose is to represent the phase behavior (including salting-out effect and critical point) and the phase densities in a range of temperature and pressure encountered in deep reservoirs and basins. The goal of the parameterization proposed is not to reach a very high accuracy for phase equilibrium and volumetric properties, but rather to develop a semi-predictive approach to model the phase and volumetric behavior of this system while allowing an easy extension to other compounds. Without salt, predictions for pure component vapor pressures and liquid molar volumes present an average absolute deviation (AAD) lower than 3% compared to experimental reference values. The pure component molar volumes out of saturation show an AAD lower than 4%. The highest deviations in densities are observed as expected in the vicinity of the critical coordinates of pure water and this effect increases when gases or salts are added to the system. For each binary system, CH4 + CO2, CH4 + H2O and CO2 + H2O, binary interaction parameters have been fitted to correctly represent the shape of the fluid phase envelopes (including all critical points) in the entire temperature and pressure range considered (219 K to 633 K and up to 250 MPa). The methane concentration in both phases of the CH4 + CO2 binary system is represented with an AAD lower than 9%. The methane solubility in water is represented within 16% and 8% for the methane content of the vapor. The CO2 solubility in water is within 26%, while the CO2 in the vapor phase shows an average deviation of 12%. All molar volumes are represented with an AAD lower than 3%. The few VLE experimental data for the CH4 + CO2 + H2O ternary system are fairly well

Impact of a Diagnostic Pressure Equation Constraint on Tornadic Supercell Thunderstorm Forecasts Initialized Using 3DVAR Radar Data Assimilation

Directory of Open Access Journals (Sweden)

Guoqing Ge

2013-01-01

Full Text Available A diagnostic pressure equation constraint has been incorporated into a storm-scale three-dimensional variational (3DVAR data assimilation system. This diagnostic pressure equation constraint (DPEC is aimed to improve dynamic consistency among different model variables so as to produce better data assimilation results and improve the subsequent forecasts. Ge et al. (2012 described the development of DPEC and testing of it with idealized experiments. DPEC was also applied to a real supercell case, but only radial velocity was assimilated. In this paper, DPEC is further applied to two real tornadic supercell thunderstorm cases, where both radial velocity and radar reflectivity data are assimilated. The impact of DPEC on radar data assimilation is examined mainly based on the storm forecasts. It is found that the experiments using DPEC generally predict higher low-level vertical vorticity than the experiments not using DPEC near the time of observed tornadoes. Therefore, it is concluded that the use of DPEC improves the forecast of mesocyclone rotation within supercell thunderstorms. The experiments using different weighting coefficients generate similar results. This suggests that DPEC is not very sensitive to the weighting coefficients.

Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review

Energy Technology Data Exchange (ETDEWEB)

Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.

1978-10-01

We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.

Modeling liquid-vapor equilibria with an equation of state taking into account dipolar interactions and association by hydrogen bonding; Modelisation des proprietes PVTX des fluides du systeme H{sub 2}O-gaz prenant en compte l'association par liaisons hydrogenes et les interactions dipolaires

Energy Technology Data Exchange (ETDEWEB)

Perfetti, E

2006-11-15

Modelling fluid-rock interactions as well as mixing and unmixing phenomena in geological processes requires robust equations of state (EOS) which must be applicable to systems containing water, gases over a broad range of temperatures and pressures. Cubic equations of state based on the Van der Waals theory (e. g. Soave-Redlich-Kwong or Peng-Robinson) allow simple modelling from the critical parameters of the studied fluid components. However, the accuracy of such equations becomes poor when water is a major component of the fluid since neither association trough hydrogen bonding nor dipolar interactions are accounted for. The Helmholtz energy of a fluid may be written as the sum of different energetic contributions by factorization of partition function. The model developed in this thesis for the pure H{sub 2}O and H{sub 2}S considers three contributions. The first contribution represents the reference Van der Waals fluid which is modelled by the SRK cubic EOS. The second contribution accounts for association through hydrogen bonding and is modelled by a term derived from Cubic Plus Association (CPA) theory. The third contribution corresponds to the dipolar interactions and is modelled by the Mean Spherical Approximation (MSA) theory. The resulting CPAMSA equation has six adjustable parameters, which three represent physical terms whose values are close to their experimental counterpart. This equation results in a better reproduction of the thermodynamic properties of pure water than obtained using the classical CPA equation along the vapour-liquid equilibrium. In addition, extrapolation to higher temperatures and pressure is satisfactory. Similarly, taking into account dipolar interactions together with the SRK cubic equation of state for calculating molar volume of H{sub 2}S as a function of pressure and temperature results in a significant improvement compared to the SRK equation alone. Simple mixing rules between dipolar molecules are proposed to model the H

Using of Structural Equation Modeling Techniques in Cognitive Levels Validation

Directory of Open Access Journals (Sweden)

Natalija Curkovic

2012-10-01

Full Text Available When constructing knowledge tests, cognitive level is usually one of the dimensions comprising the test specifications with each item assigned to measure a particular level. Recently used taxonomies of the cognitive levels most often represent some modification of the original Bloom’s taxonomy. There are many concerns in current literature about existence of predefined cognitive levels. The aim of this article is to investigate can structural equation modeling techniques confirm existence of different cognitive levels. For the purpose of the research, a Croatian final high-school Mathematics exam was used (N = 9626. Confirmatory factor analysis and structural regression modeling were used to test three different models. Structural equation modeling techniques did not support existence of different cognitive levels in this case. There is more than one possible explanation for that finding. Some other techniques that take into account nonlinear behaviour of the items as well as qualitative techniques might be more useful for the purpose of the cognitive levels validation. Furthermore, it seems that cognitive levels were not efficient descriptors of the items and so improvements are needed in describing the cognitive skills measured by items.

Numerical study of a mathematical model of internal erosion of soil

Science.gov (United States)

Sibin, A.

2017-10-01

The process of internal erosion in a three-phase saturated soil is studied. A mathematical model describing the process consists of the equations of mass conservation, Darcy’s law and equation for capillary pressure. The original system of equations is reduced to a system of three equations for porosity, pressure and water saturation. Obtained equation for the water saturation is degenerate. The degenerate problem in an one-dimensional domain is solved numerically using the finite-difference method.

Six-vertex model and Schramm-Loewner evolution

Science.gov (United States)

Kenyon, Richard; Miller, Jason; Sheffield, Scott; Wilson, David B.

2017-05-01

Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SL E κ, Schramm-Loewner evolution with parameter κ , where 4 <κ ≤12 +8 √{2 } . For square ice, κ =12 . At the "free-fermion point" of the six-vertex model, κ =8 +4 √{3 } . These unusual values lie outside the classical interval 2 ≤κ ≤8 .

Equations of state and melting curve of boron carbide in the high-pressure range of shock compression

Energy Technology Data Exchange (ETDEWEB)

Molodets, A. M., E-mail: molodets@icp.ac.ru; Golyshev, A. A.; Shakhrai, D. V. [Russian Academy of Sciences, Institute for Problems in Chemical Physics (Russian Federation)

2017-03-15

We have constructed the equations of state for crystalline boron carbide B{sub 11}C (C–B–C) and its melt under high dynamic and static pressures. A kink on the shock adiabat for boron carbide has been revealed in the pressure range near 100 GPa, and the melting curve with negative curvature in the pressure range 0–120 GPa has been calculated. The results have been used for interpreting the kinks on the shock adiabat for boron carbide in the pressure range of 0–400 GPa.

Structural Equation Modeling with Lisrel: An Initial Vision

OpenAIRE

Naresh K Malhotra; Evandro Luiz Lopes; Ricardo Teixeira Veiga

2014-01-01

LISREL is considered one of the most robust software packages for Structural Equation Modeling with covariance matrices, while it is also considered complex and difficult to use. In this special issue of the Brazilian Journal of Marketing, we aim to present the main functions of LISREL, its features and, through a didactic example, reduce the perceived difficulty of using it. We also provide helpful guidelines to properly using this technique.

Linear causal modeling with structural equations

CERN Document Server

Mulaik, Stanley A

2009-01-01

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

Genome-wide association study identifies six new loci influencing pulse pressure and mean arterial pressure

Science.gov (United States)

Wain, Louise V; Verwoert, Germaine C; O’Reilly, Paul F; Shi, Gang; Johnson, Toby; Johnson, Andrew D; Bochud, Murielle; Rice, Kenneth M; Henneman, Peter; Smith, Albert V; Ehret, Georg B; Amin, Najaf; Larson, Martin G; Mooser, Vincent; Hadley, David; Dörr, Marcus; Bis, Joshua C; Aspelund, Thor; Esko, Tõnu; Janssens, A Cecile JW; Zhao, Jing Hua; Heath, Simon; Laan, Maris; Fu, Jingyuan; Pistis, Giorgio; Luan, Jian’an; Arora, Pankaj; Lucas, Gavin; Pirastu, Nicola; Pichler, Irene; Jackson, Anne U; Webster, Rebecca J; Zhang, Feng; Peden, John F; Schmidt, Helena; Tanaka, Toshiko; Campbell, Harry; Igl, Wilmar; Milaneschi, Yuri; Hotteng, Jouke-Jan; Vitart, Veronique; Chasman, Daniel I; Trompet, Stella; Bragg-Gresham, Jennifer L; Alizadeh, Behrooz Z; Chambers, John C; Guo, Xiuqing; Lehtimäki, Terho; Kühnel, Brigitte; Lopez, Lorna M; Polašek, Ozren; Boban, Mladen; Nelson, Christopher P; Morrison, Alanna C; Pihur, Vasyl; Ganesh, Santhi K; Hofman, Albert; Kundu, Suman; Mattace-Raso, Francesco US; Rivadeneira, Fernando; Sijbrands, Eric JG; Uitterlinden, Andre G; Hwang, Shih-Jen; Vasan, Ramachandran S; Wang, Thomas J; Bergmann, Sven; Vollenweider, Peter; Waeber, Gérard; Laitinen, Jaana; Pouta, Anneli; Zitting, Paavo; McArdle, Wendy L; Kroemer, Heyo K; Völker, Uwe; Völzke, Henry; Glazer, Nicole L; Taylor, Kent D; Harris, Tamara B; Alavere, Helene; Haller, Toomas; Keis, Aime; Tammesoo, Mari-Liis; Aulchenko, Yurii; Barroso, Inês; Khaw, Kay-Tee; Galan, Pilar; Hercberg, Serge; Lathrop, Mark; Eyheramendy, Susana; Org, Elin; Sõber, Siim; Lu, Xiaowen; Nolte, Ilja M; Penninx, Brenda W; Corre, Tanguy; Masciullo, Corrado; Sala, Cinzia; Groop, Leif; Voight, Benjamin F; Melander, Olle; O’Donnell, Christopher J; Salomaa, Veikko; d’Adamo, Adamo Pio; Fabretto, Antonella; Faletra, Flavio; Ulivi, Sheila; Del Greco, M Fabiola; Facheris, Maurizio; Collins, Francis S; Bergman, Richard N; Beilby, John P; Hung, Joseph; Musk, A William; Mangino, Massimo; Shin, So-Youn; Soranzo, Nicole; Watkins, Hugh; Goel, Anuj; Hamsten, Anders; Gider, Pierre; Loitfelder, Marisa; Zeginigg, Marion; Hernandez, Dena; Najjar, Samer S; Navarro, Pau; Wild, Sarah H; Corsi, Anna Maria; Singleton, Andrew; de Geus, Eco JC; Willemsen, Gonneke; Parker, Alex N; Rose, Lynda M; Buckley, Brendan; Stott, David; Orru, Marco; Uda, Manuela; van der Klauw, Melanie M; Zhang, Weihua; Li, Xinzhong; Scott, James; Chen, Yii-Der Ida; Burke, Gregory L; Kähönen, Mika; Viikari, Jorma; Döring, Angela; Meitinger, Thomas; Davies, Gail; Starr, John M; Emilsson, Valur; Plump, Andrew; Lindeman, Jan H; ’t Hoen, Peter AC; König, Inke R; Felix, Janine F; Clarke, Robert; Hopewell, Jemma C; Ongen, Halit; Breteler, Monique; Debette, Stéphanie; DeStefano, Anita L; Fornage, Myriam; Mitchell, Gary F; Smith, Nicholas L; Holm, Hilma; Stefansson, Kari; Thorleifsson, Gudmar; Thorsteinsdottir, Unnur; Samani, Nilesh J; Preuss, Michael; Rudan, Igor; Hayward, Caroline; Deary, Ian J; Wichmann, H-Erich; Raitakari, Olli T; Palmas, Walter; Kooner, Jaspal S; Stolk, Ronald P; Jukema, J Wouter; Wright, Alan F; Boomsma, Dorret I; Bandinelli, Stefania; Gyllensten, Ulf B; Wilson, James F; Ferrucci, Luigi; Schmidt, Reinhold; Farrall, Martin; Spector, Tim D; Palmer, Lyle J; Tuomilehto, Jaakko; Pfeufer, Arne; Gasparini, Paolo; Siscovick, David; Altshuler, David; Loos, Ruth JF; Toniolo, Daniela; Snieder, Harold; Gieger, Christian; Meneton, Pierre; Wareham, Nicholas J; Oostra, Ben A; Metspalu, Andres; Launer, Lenore; Rettig, Rainer; Strachan, David P; Beckmann, Jacques S; Witteman, Jacqueline CM; Erdmann, Jeanette; van Dijk, Ko Willems; Boerwinkle, Eric; Boehnke, Michael; Ridker, Paul M; Jarvelin, Marjo-Riitta; Chakravarti, Aravinda; Abecasis, Goncalo R; Gudnason, Vilmundur; Newton-Cheh, Christopher; Levy, Daniel; Munroe, Patricia B; Psaty, Bruce M; Caulfield, Mark J; Rao, Dabeeru C

2012-01-01

Numerous genetic loci influence systolic blood pressure (SBP) and diastolic blood pressure (DBP) in Europeans 1-3. We now report genome-wide association studies of pulse pressure (PP) and mean arterial pressure (MAP). In discovery (N=74,064) and follow-up studies (N=48,607), we identified at genome-wide significance (P= 2.7×10-8 to P=2.3×10-13) four novel PP loci (at 4q12 near CHIC2/PDGFRAI, 7q22.3 near PIK3CG, 8q24.12 in NOV, 11q24.3 near ADAMTS-8), two novel MAP loci (3p21.31 in MAP4, 10q25.3 near ADRB1) and one locus associated with both traits (2q24.3 near FIGN) which has recently been associated with SBP in east Asians. For three of the novel PP signals, the estimated effect for SBP was opposite to that for DBP, in contrast to the majority of common SBP- and DBP-associated variants which show concordant effects on both traits. These findings indicate novel genetic mechanisms underlying blood pressure variation, including pathways that may differentially influence SBP and DBP. PMID:21909110

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