A two-dimensional, semi-analytic expansion method for nodal calculations
Palmtag, S.P.
1995-08-01
Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure.
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
NASA Astrophysics Data System (ADS)
Camporeale, E.; Hogan, E. A.; MacDonald, E. A.
2015-04-01
We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979 American Institute of Aeronautics, Astronautics Conf. vol 1), Korsun and Tverdokhlebova (1997 33rd Joint Prop. Conf. (Seattle, WA) AIAA-97-3065), and Ashkenazy and Fruchtman (2001 27th Int. Electric Propulsion Conf. (Pasadena, CA)). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.
Study on Two Methods for Nonlinear Force-Free Extrapolation Based on Semi-Analytical Field
NASA Astrophysics Data System (ADS)
Liu, S.; Zhang, H. Q.; Su, J. T.; Song, M. T.
2011-03-01
In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai ( Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. ( Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.
A semi-analytical numerical method for fast metamaterial absorber design
NASA Astrophysics Data System (ADS)
Song, Y. C.; Ding, J.; Guo, C. J.
2015-09-01
In this paper, a semi-analytical numerical approach utilizing a novel non-grounded model and interpolation technique is introduced to design the frequency selective surface (FSS) based metamaterial absorbers (MAs) with dramatically reduced time consumption. Different from commonly used trial-and-error technology, our method mainly utilize the numerically computed FSS layer impedance with slow-varying feature in the vicinity of operating frequency. The introduced non-grounded model establishes the quantitative relationship between geometry parameters and equivalent lumped circuit components in conventional transmission line (TL) model with reasonable accuracy. The interpolation technique, on the other hand, promises a relative sparse parameter sweep. The detailed design flow as well as analytical explanation with carefully deduced expressions is presented. With the purpose of validating the proposed method and analytical models, a MA with slotted patches is designed through both the semi-analytical numerical approach and the trial-and-error method, where an over 2300 times acceleration is observed. Additionally, results from the analytical computation and full wave simulation agree well with each other.
Dynamic buckling analysis of delaminated composite plates using semi-analytical finite strip method
NASA Astrophysics Data System (ADS)
Ovesy, H. R.; Totounferoush, A.; Ghannadpour, S. A. M.
2015-05-01
The delamination phenomena can become of paramount importance when the design of the composite plates is concerned. In the current study, the effect of through-the-width delamination on dynamic buckling behavior of a composite plate is studied by implementing semi-analytical finite strip method. In this method, the energy and work integrations are computed analytically due to the implementation of trigonometric functions. Moreover, the method can lead to converged results with comparatively small number of degrees of freedom. These features have made the method quite efficient. To account for delamination effects, displacement field is enriched by adding appropriate terms. Also, the penetration of the delamination surfaces is prevented by incorporating an appropriate contact scheme into the time response analysis. Some selected results are validated against those available in the literature.
Towards in-vivo K-edge imaging using a new semi-analytical calibration method
NASA Astrophysics Data System (ADS)
Schirra, Carsten; Thran, Axel; Daerr, Heiner; Roessl, Ewald; Proksa, Roland
2014-03-01
Flat field calibration methods are commonly used in computed tomography (CT) to correct for system imperfections. Unfortunately, they cannot be applied in energy-resolving CT when using bow-tie filters owing to spectral distortions imprinted by the filter. This work presents a novel semi-analytical calibration method for photon-counting spectral CT systems, which is applicable with a bow-tie filter in place and efficiently compensates pile-up effects at fourfold increased photon flux compared to a previously published method without degradation of image quality. The achieved reduction of the scan time enabled the first K-edge imaging in-vivo. The method employs a calibration measurement with a set of flat sheets of only a single absorber material and utilizes an analytical model to predict the expected photon counts, taking into account factors such as x-ray spectrum and detector response. From the ratios of the measured x-ray intensities and the corresponding simulated photon counts, a look-up table is generated. By use of this look-up table, measured photon-counts can be corrected yielding data in line with the analytical model. The corrected data show low pixel-to-pixel variations and pile-up effects are mitigated. Consequently, operations like material decomposition based on the same analytical model yield accurate results. The method was validated on a experimental spectral CT system equipped with a bow-tie filter in a phantom experiment and an in-vivo animal study. The level of artifacts in the resulting images is considerably lower than in images generated with a previously published method. First in-vivo K-edge images of a rabbit selectively depict vessel occlusion by an ytterbium-based thermoresponsive polymer.
NASA Astrophysics Data System (ADS)
RoyChoudhury, Raja; RoyChoudhury, Arundhati
2011-02-01
This paper presents a semi analytical formulation of modal properties of a non linear optical fiber having Kerr non linearity with a three parameter approximation of fundamental modal field. The minimization of core parameter ( U) which involves Kerr nonlinearity through the non-stationary expression of propagation constant, is carried out by Nelder-Mead Simplex method of non linear unconstrained minimization, suitable for problems with non-smooth functions as the method does not require any derivative information. Use of three parameters in modal approximation and implementation of Simplex methods enables our semi analytical description to be an alternative way having less computational burden for calculation of modal parameters than full numerical methods.
NASA Astrophysics Data System (ADS)
Zhou, R.; Zhan, H.
2015-12-01
With the consideration of advection, dispersion, adsorption and first order decay in the fracture and rock matrix in a single fracture model, a new semi-analytical solution is derived using the Mobile-Immobile Method. It can be used to estimate the concentration at any location at any time precisely within the fracture and rock matrix. Most fractures found underground are filled with the conglomerate, sand, clay and other kinds of possible porous media. The existence of those filling ingredients leads to the isolated pore space within the fracture, which is also called immobile zone. Certain assumptions have be made: the diffusion is the only way that the contamination travels from the fracture to the matrix as the large permeability difference between them; the diffusive transport is dominant in the rock matrix while the advective-dispersive transport plays the major role in the fracture. Experimental data have been collected from literatures to compare the performance of this semi-analytical solution from the classical analytical solution. The comparison shows that the semi-analytical solution simulates it better when the mobile zone percentage is limited. Also, the effects of matrix diffusion, dispersivity and Darcy velocity in the fracture, fracture aperture, first order mass transfer rate and mobile zone percentage on solute transport are demonstrated through the sensitivity analysis, concentration profiles and breakthrough curves. By modifying the boundary conditions and adding an advection term in the rock matrix governing equation, this model can be extended to a two-layer solute transport model.
NASA Astrophysics Data System (ADS)
Moster, Benjamin P.; Macciò, Andrea V.; Somerville, Rachel S.
2014-01-01
We present a new approach to study galaxy evolution in a cosmological context. We combine cosmological merger trees and semi-analytic models of galaxy formation to provide the initial conditions for multimerger hydrodynamic simulations. In this way, we exploit the advantages of merger simulations (high resolution and inclusion of the gas physics) and semi-analytic models (cosmological background and low computational cost), and integrate them to create a novel tool. This approach allows us to study the evolution of various galaxy properties, including the treatment of the hot gaseous halo from which gas cools and accretes on to the central disc, which has been neglected in many previous studies. This method shows several advantages over other methods. As only the particles in the regions of interest are included, the run time is much shorter than in traditional cosmological simulations, leading to greater computational efficiency. Using cosmological simulations, we show that multiple mergers are expected to be more common than sequences of isolated mergers, and therefore studies of galaxy mergers should take this into account. In this pilot study, we present our method and illustrate the results of simulating 10 Milky Way-like galaxies since z = 1. We find good agreement with observations for the total stellar masses, star formation rates, cold gas fractions and disc scalelength parameters. We expect that this novel numerical approach will be very useful for pursuing a number of questions pertaining to the transformation of galaxy internal structure through cosmic time.
NASA Astrophysics Data System (ADS)
Chen, Jeng-Tzong; Lee, Jia-Wei
2013-09-01
In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.
Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method
NASA Astrophysics Data System (ADS)
Jabbari, Azizeh; Kheiri, Hossein; Bekir, Ahmet
2015-03-01
In this work, we present a dynamic behavior of the avian-human influenza epidemic model by using efficient computational algorithm, namely the multistage differential transform method(MsDTM). The MsDTM is used here as an algorithm for approximating the solutions of the avian-human influenza epidemic model in a sequence of time intervals. In order to show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method (RK4M) and differential transform method(DTM) solutions. It is shown that the MsDTM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RK4M.
Comparison of optimization methods for the hyperspectral semi-analytical model
NASA Astrophysics Data System (ADS)
Du, KePing; Xi, Ying; Sun, LiRan; Zhang, Xuegang
2009-01-01
During recent years, more and more efforts have been focused on developing new models based on ocean optics theory to retrieve water's bio-geo-chemical parameters or inherent optical properties (IOPs) from either ocean color imagery or in situ measurements. Basically, these models are sophisticated, and hard to invert directly, look up table (LUT) technique or optimization methods are employed to retrieve the unknown parameters, e.g., chlorophyll concentration, CDOM absorption, etc. Many researches prefer to use time-consuming global optimization methods, e.g., genetic or evolutionary algorithm, etc. In this study, different optimization methods, smooth nonlinear optimization (NLP), global optimization (GO), nonsmooth optimization (NSP), are compared based on the sophisticated hyper-spectral semianalytical (SA) algorithm developed by Lee et al., retrieval accuracy and performance are evaluated. It is found that retrieval accuracy don't have much difference, the performance difference, however, is much larger, NLP works very well for the SA model. For a given model, it is better to analyze the model is linear, nonlinear or nonsmooth category problem, sometimes, convex also need to be determined, or linearize some nonsmooth problem caused by if decision, then select the corresponding category optimization methods. Initial values selection is a big issue for optimization, the simple statistical models (e.g., OC2 or OC4) are used to retrieve the unknowns as initial values.
A semi-analytical method for heat sweep calculations in fractured reservoirs
Pruess, K.; Wu, Y.S.
1988-01-01
An analytical approximation is developed for purely conductive heat transfer from impermeable blocks of rock to fluids sweeping past the rocks in fractures. The method was incorporated into a multi-phase fluid and heat flow simulator. Comparison with exact analytical solutions and with simulations using a multiple interacting continua approach shows very good accuracy, with no increase in computing time compared to porous medium simulations.
A semi-analytical method for heat sweep calculations in fractured reservoirs
Pruess, K.; Wu, Y.S.
1988-01-01
An analytical approximation is developed for purely conductive heat transfer from impermeable blocks of rock to fluids sweeping past the rocks in fractures. The method was incorporated into a multi-phase fluid and heat flow simulator. Comparison with exact analytical solutions and with simulations using a multiple interacting continua approach shows very good accuracy, with no increase in computing time compared to porous medium simulations. 14 refs., 3 figs., 5 tabs.
NASA Astrophysics Data System (ADS)
Nguyen, K. L.; Treyssède, F.; Hazard, C.
2015-05-01
Among the numerous techniques of non-destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes becomes necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.
NASA Astrophysics Data System (ADS)
Wailliez, Sébastien E.
2014-03-01
In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180° transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.
NASA Astrophysics Data System (ADS)
Wang, R.; Kuempel, H.
2003-12-01
From poroelasticity theory we know that fluid diffusion will induce matrix deformation and vice versa. In practice, well known phenomena for such coupled processes are, for example, occurrence of seismo-tectonically induced groundwater fluctuations, land subsidence as a result of fluid extraction from subsurface reservoirs, production-induced surface strain near the vicinity of wells, reservoir- or injection-induced seismicity. Modeling of deformation and pore-pressure data that have been observed near the surface can help to image the dynamics and to assess the hydraulic properties of subsurface aquifers. We here present a semi-analytical Haskell propagator method to fully handle linear poroelastic problems in a multilayered half-space. Our method is a powerful tool for various reasons: (1) It is faster than traditional numerical schemes when respective discretization of the object region is chosen and solutions are sought for single locations only; (2) a problem is easily formulated, as only a set of five poroelastic parameters per layer plus the layers' thicknesses need to be specified; (3) the method is highly flexible, as forcing functions of point injection, single force (e.g., surface loading), double couple dislocation (earthquakes), etc. may be readily incorporated; (4) the so-called loss-of-precision problem of the original propagator algorithm has been fully overcome using the orthonormalization technique. The effectiveness of the new tool has been demonstrated by modeling pump-induced near-surface tilt data obtained at a test site near Sopron in western Hungary. The results show that the hydraulic diffusivity of the shallow subsurface aquifer can be assessed with an accuracy better than half an order of magnitude, if other elastic parameters and the geometry (depth and thickness) of the water-bearing formations are sufficiently known from, for example, bore-log records. Moreover, the present method can be applied to model induced seismicity based on the
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
NASA Technical Reports Server (NTRS)
Chaudhuri, Reaz A.; Seide, Paul
1987-01-01
An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.
NASA Astrophysics Data System (ADS)
Liang, Xu; Wang, Zhenyu; Wang, Lizhong; Izzuddin, Bassam A.; Liu, Guohua
2015-02-01
Functionally graded (FG) plates are of current interest and are widely used in a variety of applications including deep sea exploration and naval/marine and coastal engineering, despite the fact that there has, to date, been little research undertaken on the subject. In order to remedy the situation, an analytical method to investigate the elastic dynamic responses of FG plates to underwater shock is proposed here, their material properties varying by the same exponential law along the thickness direction. Taylor's one dimensional fluid solid interaction (FSI) model is extended to fit a three dimensional model suitable for FG plates. The extended FSI model and Laplace transform are integrated into the state space method, with the transient solution in the time domain being obtained by using the numerical inversion of the Laplace transform. The solutions of the total forces acting throughout the front and back faces in the time domain are derived for the first time. The present method is validated by comparing it with the results of other methods and experiments found in the relevant literature. The influence of the boundary conditions at the backside of the plate and FG parameters on front and back side pressures, cavitations, displacements, stresses and total forces acting throughout the faces are then investigated, with the time progression of the cavitation areas of air-backed plates and water-backed plates being investigated in detail. The method proposed in this paper may prove useful for the future three-dimensional assessment of the response of FG structures when FSI effects are taken into consideration. It is hoped that the results will lead to a full understanding of the mechanism of the interaction between fluid and an FG plate, and that they can be used as benchmark solutions in further research.
NASA Technical Reports Server (NTRS)
Yang, Charles; Sun, Wenjun; Tomblin, John S.; Smeltzer, Stanley S., III
2007-01-01
A semi-analytical method for determining the strain energy release rate due to a prescribed interface crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rate of the crack is determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUS. The results determined using the analytical method correlated well with the results from the finite element analyses.
NASA Astrophysics Data System (ADS)
Shannon, Andrew; Mustill, Alexander J.; Wyatt, Mark
2015-03-01
Dust grains migrating under Poynting-Robertson drag may be trapped in mean-motion resonances with planets. Such resonantly trapped grains are observed in the Solar system. In extrasolar systems, the exozodiacal light produced by dust grains is expected to be a major obstacle to future missions attempting to directly image terrestrial planets. The patterns made by resonantly trapped dust, however, can be used to infer the presence of planets, and the properties of those planets, if the capture and evolution of the grains can be modelled. This has been done with N-body methods, but such methods are computationally expensive, limiting their usefulness when considering large, slowly evolving grains, and for extrasolar systems with unknown planets and parent bodies, where the possible parameter space for investigation is large. In this work, we present a semi-analytic method for calculating the capture and evolution of dust grains in resonance, which can be orders of magnitude faster than N-body methods. We calibrate the model against N-body simulations, finding excellent agreement for Earth to Neptune mass planets, for a variety of grain sizes, initial eccentricities, and initial semimajor axes. We then apply the model to observations of dust resonantly trapped by the Earth. We find that resonantly trapped, asteroidally produced grains naturally produce the `trailing blob' structure in the zodiacal cloud, while to match the intensity of the blob, most of the cloud must be composed of cometary grains, which owing to their high eccentricity are not captured, but produce a smooth disc.
NASA Astrophysics Data System (ADS)
LaForce, T.; Ennis-King, J.; Paterson, L.
2015-12-01
Reservoir cooling near the wellbore is expected when fluids are injected into a reservoir or aquifer in CO2 storage, enhanced oil or gas recovery, enhanced geothermal systems, and water injection for disposal. Ignoring thermal effects near the well can lead to under-prediction of changes in reservoir pressure and stress due to competition between increased pressure and contraction of the rock in the cooled near-well region. In this work a previously developed semi-analytical model for immiscible, nonisothermal fluid injection is generalised to include partitioning of components between two phases. Advection-dominated radial flow is assumed so that the coupled two-phase flow and thermal conservation laws can be solved analytically. The temperature and saturation profiles are used to find the increase in reservoir pressure, tangential, and radial stress near the wellbore in a semi-analytical, forward-coupled model. Saturation, temperature, pressure, and stress profiles are found for parameters representative of several CO2 storage demonstration projects around the world. General results on maximum injection rates vs depth for common reservoir parameters are also presented. Prior to drilling an injection well there is often little information about the properties that will determine the injection rate that can be achieved without exceeding fracture pressure, yet injection rate and pressure are key parameters in well design and placement decisions. Analytical solutions to simplified models such as these can quickly provide order of magnitude estimates for flow and stress near the well based on a range of likely parameters.
Semi-analytic valuation of stock loans with finite maturity
NASA Astrophysics Data System (ADS)
Lu, Xiaoping; Putri, Endah R. M.
2015-10-01
In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.
SAGE: Semi-Analytic Galaxy Evolution
NASA Astrophysics Data System (ADS)
Croton, Darren J.; Stevens, Adam R. H.; Tonini, Chiara; Garel, Thibault; Bernyk, Maksym; Bibiano, Antonio; Hodkinson, Luke; Mutch, Simon J.; Poole, Gregory B.; Shattow, Genevieve M.
2016-01-01
SAGE (Semi-Analytic Galaxy Evolution) models galaxy formation in a cosmological context. SAGE has been rebuilt to be modular and customizable. The model runs on any dark matter cosmological N-body simulation whose trees are organized in a supported format and contain a minimum set of basic halo properties.
Semi-analytical modelling of piezoelectric excitation of guided waves
NASA Astrophysics Data System (ADS)
Kalkowski, Michał K.; Rustighi, Emiliano; Waters, Timothy P.
2015-03-01
Piezoelectric elements are a key component of modern non-destructive testing (NDT) and structural health monitoring (SHM) systems and play a significant role in many other areas involving dynamic interaction with the structure such as energy harvesting, active control, power ultrasonics or removal of surface accretions using structural waves. In this paper we present a wave-based technique for modelling waveguides equipped with piezoelectric actuators in which there is no need for common simplifications regarding their dynamic behaviour or mutual interaction with the structure. The proposed approach is based on the semi-analytical finite element (SAFE) method. We developed a new piezoelectric semi-analytical element and employed the analytical wave approach to model the distributed electric excitation and scattering of the waves at discontinuities. The model is successfully validated against an experiment on a beam-like waveguide with emulated anechoic terminations.
A 2-D semi-analytical model of double-gate tunnel field-effect transistor
NASA Astrophysics Data System (ADS)
Huifang, Xu; Yuehua, Dai; Ning, Li; Jianbin, Xu
2015-05-01
A 2-D semi-analytical model of double gate (DG) tunneling field-effect transistor (TFET) is proposed. By aid of introducing two rectangular sources located in the gate dielectric layer and the channel, the 2-D Poisson equation is solved by using a semi-analytical method combined with an eigenfunction expansion method. The expression of the surface potential is obtained, which is a special function for the infinite series expressions. The influence of the mobile charges on the potential profile is taken into account in the proposed model. On the basis of the potential profile, the shortest tunneling length and the average electrical field can be derived, and the drain current is then constructed by using Kane's model. In particular, the changes of the tunneling parameters Ak and Bk influenced by the drain—source voltage are also incorporated in the predicted model. The proposed model shows a good agreement with TCAD simulation results under different drain—source voltages, silicon film thicknesses, gate dielectric layer thicknesses, and gate dielectric layer constants. Therefore, it is useful to optimize the DG TFET and this provides a physical insight for circuit level design. Project supported by the National Natural Science Foundation of China (No. 61376106) and the Graduate Innovation Fund of Anhui University.
Gravity Field Recovery from the Cartwheel Formation by the Semi-analytical Approach
NASA Astrophysics Data System (ADS)
Li, Huishu; Reubelt, Tilo; Antoni, Markus; Sneeuw, Nico; Zhong, Min; Zhou, Zebing
2016-04-01
Past and current gravimetric satellite missions have contributed drastically to our knowledge of the Earth's gravity field. Nevertheless, several geoscience disciplines push for even higher requirements on accuracy, homogeneity and time- and space-resolution of the Earth's gravity field. Apart from better instruments or new observables, alternative satellite formations could improve the signal and error structure. With respect to other methods, one significant advantage of the semi-analytical approach is its effective pre-mission error assessment for gravity field missions. The semi-analytical approach builds a linear analytical relationship between the Fourier spectrum of the observables and the spherical harmonic spectrum of the gravity field. The spectral link between observables and gravity field parameters is given by the transfer coefficients, which constitutes the observation model. In connection with a stochastic model, it can be used for pre-mission error assessment of gravity field mission. The cartwheel formation is formed by two satellites on elliptic orbits in the same plane. The time dependent ranging will be considered in the transfer coefficients via convolution including the series expansion of the eccentricity functions. The transfer coefficients are applied to assess the error patterns, which are caused by different orientation of the cartwheel for range-rate and range acceleration. This work will present the isotropy and magnitude of the formal errors of the gravity field coefficients, for different orientations of the cartwheel.
NASA Astrophysics Data System (ADS)
Stübbe, Oliver
2015-03-01
Optical interconnects on printed circuit board level are a promising choice to support high bandwidth for short distance interconnects. These interconnects consists of highly multimode step index waveguides with rectangular core cross sections. Therefore ray tracing is an excellent method to determine the optical path parameters, e.g. optical power, ray path lengths and local ray directions. Based on these parameters the step response, the transient transfer function and the coupling behavior can be calculated. Classical ray tracing methods calculates the optical path parameters of each ray by successively computing internal reflections until a termination condition is reached. Therefore the computing time depends on the number of internal reflections. If the optical waveguide consists of cascaded straight and curved segments, e. g. point-to-point interconnects, one can use the analytic ray tracing method to determine the optical path parameters. The whole path parameters of each ray are determined by one analytical computation. The computing time depends on the number of segments. The analytic ray tracing method is unusable to determine ray path parameters of segments with varying core cross sections, e.g. tapers, crossings, splitters and combiners.
NASA Astrophysics Data System (ADS)
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler–Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
NASA Astrophysics Data System (ADS)
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler–Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
Semi-Analytic Reconstruction of Flux in Finite Volume Formulations
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
2006-01-01
Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.
Semi-analytic computation of the driven fields in right circular cylindrical microwave applicators
Nelson, E.M.; Kares, R.J.; Stringfield, R.M.
1995-05-01
A semi-analytic technique for computing the driven fields in a pillbox microwave applicator composed of concentric right circular cylinders (e.g., load, tube and air regions) is described. The fields are driven by idealized apertures on the cavity wall. A modal expansion of the driven fields provides insight about thermal energy deposition in the load.
Semi-analytical computation of displacement in linear viscoelastic materials
NASA Astrophysics Data System (ADS)
Spinu, S.; Gradinaru, D.
2015-11-01
Prediction of mechanical contact performance based on elastic models is not accurate in case of viscoelastic materials; however, a closed-form description of the viscoelastic contact has yet to be found. This paper aims to advance a semi-analytical method for computation of displacement induced in viscoelastic materials by arbitrary surface tractions, as a prerequisite to a semi-analytical solution for the viscoelastic contact problem. The newly advanced model is expected to provide greater generality, allowing for arbitrary contact geometry and / or arbitrary loading history. While time-independent equations in the purely elastic model can be treated numerically by imposing a spatial discretization only, a viscoelastic constitutive law requires supplementary temporal discretization capable of simulating the memory effect specific to viscoelastic materials. By deriving new influence coefficients, computation of displacement induced in a viscoelastic material by a known but otherwise arbitrary history of surface tractions can be achieved via superposition authorized by the Boltzmann superposition theory applicable in the frame of linear viscoelasticity.
NASA Astrophysics Data System (ADS)
Riggs, Lloyd Stephen
In this work the transient currents induced on an arbitrary system of thin linear scatterers by an electromagnetic plane wave are solved by using an electric field integral equation (EFIE) formulation. The transient analysis is carried out using the singularity expansion method (SEM). The general analysis developed here is useful for assessing the vulnerability of military aircraft to a nuclear generated electromagnetic pulse (EMP). It is also useful as a modal synthesis tool in the analysis and design of frequency selective surfaces (FSS). SEM parameters for a variety of thin cylindrical geometries have been computed. Specifically, SEM poles, modes, coupling coefficients, and transient currents are given for the two and three element planar array. Poles and modes for planar arrays with a larger number (as many as eight) of identical equally spaced elements are also considered. SEM pole-mode results are given for identical parallel elements with ends located at the vertices of a regular N-agon. Pole-mode patterns are found for symmetric (and slightly perturbed) single junction N-arm elements and for the five junction Jerusalem cross. The Jerusalem cross element has been used extensively in FSS.
Semi-analytic approach for electromagnetic problems of large arrays structures
NASA Astrophysics Data System (ADS)
Rostami-Angas, Masoud
There are limited electromagnetic problems which have closed form analytic solutions. Most of the real-world electromagnetic problems like electromagnetic scattering, electromagnetic radiation, waveguide modeling, etc., are not analytically calculable, because of the multitude of irregular geometries found in actual devices. Numerical computational techniques can be used as alternative method to overcome the inability of deriving closed form solutions of Maxwell's equations under various constitutive relations of media, and boundary conditions. This makes computational electromagnetics important in microwave, RF and photonic areas. Care must be taken into choosing the right method; otherwise the wrong method can either yield incorrect results, or results which take excessively long or demand great computational resources. Moreover, there are important electromagnetic problems for which numerical method solutions are challenging, if not impossible. Large non-periodic array of dipoles and multilayer spheres are examples of those problems. Some of these problems, because of their specific geometries and characteristics, can be modeled accurately and efficiently by applying Discrete Dipole Approximation (DDA), multipole expansion and translation addition theorem. The usual solution approach is to model the electromagnetic fields, or other unknowns, using multipole expansions, truncate appropriately the infinite summations, apply the boundary conditions, and then solve the resulting matrix problem by numerical methods. Because the approach contains both of analytic methods and numerical matrix solvers, it can be considered as a semi-analytic approach. The first chapter briefly describes the electromagnetic problems and semi-analytic approaches of this thesis. In the second chapter, a large array of molecular aggregates is investigated with the goal of solving the multiscale problem of a large array of molecules to explore its optical behaviors. Quantum electrodynamics
A semi-analytical approach to molecular dynamics
NASA Astrophysics Data System (ADS)
Michels, Dominik L.; Desbrun, Mathieu
2015-12-01
Despite numerous computational advances over the last few decades, molecular dynamics still favors explicit (and thus easily-parallelizable) time integrators for large scale numerical simulation. As a consequence, computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size. In this paper, we present a semi-analytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes. By efficiently approximating the exact integration of the strong (harmonic) forces of covalent bonds through matrix functions, far improved stability with respect to time step size is achieved without sacrificing the explicit, symplectic, time-reversible, or fine-grained parallelizable nature of the integration scheme. We demonstrate the efficiency and scalability of our integrator on simulations ranging from DNA strand unbinding and protein folding to nanotube resonators.
Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables
NASA Technical Reports Server (NTRS)
Fenyes, Peter A.; Lust, Robert V.
1989-01-01
Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.
Research on bathymetry estimation by Worldview-2 based with the semi-analytical model
NASA Astrophysics Data System (ADS)
Sheng, L.; Bai, J.; Zhou, G.-W.; Zhao, Y.; Li, Y.-C.
2015-04-01
South Sea Islands of China are far away from the mainland, the reefs takes more than 95% of south sea, and most reefs scatter over interested dispute sensitive area. Thus, the methods of obtaining the reefs bathymetry accurately are urgent to be developed. Common used method, including sonar, airborne laser and remote sensing estimation, are limited by the long distance, large area and sensitive location. Remote sensing data provides an effective way for bathymetry estimation without touching over large area, by the relationship between spectrum information and bathymetry. Aimed at the water quality of the south sea of China, our paper develops a bathymetry estimation method without measured water depth. Firstly the semi-analytical optimization model of the theoretical interpretation models has been studied based on the genetic algorithm to optimize the model. Meanwhile, OpenMP parallel computing algorithm has been introduced to greatly increase the speed of the semi-analytical optimization model. One island of south sea in China is selected as our study area, the measured water depth are used to evaluate the accuracy of bathymetry estimation from Worldview-2 multispectral images. The results show that: the semi-analytical optimization model based on genetic algorithm has good results in our study area;the accuracy of estimated bathymetry in the 0-20 meters shallow water area is accepted.Semi-analytical optimization model based on genetic algorithm solves the problem of the bathymetry estimation without water depth measurement. Generally, our paper provides a new bathymetry estimation method for the sensitive reefs far away from mainland.
NASA Astrophysics Data System (ADS)
Caire, François; Prémel, Denis; Granet, Gérard
2013-11-01
Semi-analytical models developed at Cea List for the simulation of Eddy current non-destructive testing are currently based on the volume integral equation formalism. This method is very effective for canonical geometries such as planes or cylinders since the analytical expressions of Green's dyads are known. This approach requires three steps: the computation of the quasi-static fields induced by the probe in the workpiece without flaw, the determination of the interaction between the primary field and the defect and finally, the calculation of the response of the eddy current sensor, resulting from this interaction. In order to generalize this approach to more complex configurations, in this paper, we focus on the first step: the computation of quasi-static fields induced by an eddy current probe in a conductor with a rough surface. The semi-analytical model we generalize here is based on Maxwell's equations, written in a non-orthogonal coordinate system resulting in the writing of the boundary conditions at the interface by using a simple analytical expression. Starting from the second-order vector-potential formalism dedicated to non-orthogonal curvilinear coordinate systems, two scalar potentials are expressed as a modal expansion, satisfying the outgoing wave condition. Finally, the coefficients of the modal expansion are determined by applying boundary conditions at the complex interface. First numerical results, obtained considering a specific configuration, are compared to other Finite Element data. Contribution to the Topical Issue "Numelec 2012", Edited by Adel Razek.
Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions
NASA Astrophysics Data System (ADS)
Alharthi, M. R.; Marchant, T. R.; Nelson, M. I.
2016-06-01
Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations.
A semi-analytical solution for saltwater intrusion with a very narrow transition zone
NASA Astrophysics Data System (ADS)
Younes, Anis; Fahs, Marwan
2014-03-01
The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b = 0.1). Finding a stable semi-analytical solution for small values of b is challenging due to the low convergence of the corresponding nonlinear system. In this work, an accurate semi-analytical solution is developed in the case of a very narrow transition zone corresponding to b = 0.005. About 6,330 terms are used in the Fourier series to accurately represent the solution. The resolution of the corresponding highly nonlinear system is made possible by the modified Powell hybrid algorithm due to the analytical evaluation of the Jacobian, which drastically reduces the computational time. The new test problem is also investigated numerically using different numerical methods and different mesh sizes to show its high worthiness, compared to the standard Henry problem, for benchmarking density driven flow codes.
NASA Astrophysics Data System (ADS)
Hua, Chengyun; Minnich, Austin J.
2015-05-01
Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.
Hua, Chengyun; Minnich, Austin J.
2015-05-07
Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.
Sussing merger trees: the impact of halo merger trees on galaxy properties in a semi-analytic model
NASA Astrophysics Data System (ADS)
Lee, Jaehyun; Yi, Sukyoung K.; Elahi, Pascal J.; Thomas, Peter A.; Pearce, Frazer R.; Behroozi, Peter; Han, Jiaxin; Helly, John; Jung, Intae; Knebe, Alexander; Mao, Yao-Yuan; Onions, Julian; Rodriguez-Gomez, Vicente; Schneider, Aurel; Srisawat, Chaichalit; Tweed, Dylan
2014-12-01
A halo merger tree forms the essential backbone of a semi-analytic model for galaxy formation and evolution. Recent studies have pointed out that extracting merger trees from numerical simulations of structure formation is non-trivial; different tree building algorithms can give differing merger histories. These differences should be carefully understood before merger trees are used as input for models of galaxy formation. We investigate the impact of different halo merger trees on a semi-analytic model. We find that the z = 0 galaxy properties in our model show differences between trees when using a common parameter set. The star formation history of the universe and the properties of satellite galaxies can show marked differences between trees with different construction methods. Independently calibrating the semi-analytic model for each tree can reduce the discrepancies between the z = 0 global galaxy properties, at the cost of increasing the differences in the evolutionary histories of galaxies. Furthermore, the underlying physics implied can vary, resulting in key quantities such as the supernova feedback efficiency differing by factors of 2. Such a change alters the regimes where star formation is primarily suppressed by supernovae. Therefore, halo merger trees extracted from a common halo catalogue using different, but reliable, algorithms can result in a difference in the semi-analytic model. Given the uncertainties in galaxy formation physics, however, these differences may not necessarily be viewed as significant.
Semi-Analytical Approches to Variable Density Flows.
NASA Astrophysics Data System (ADS)
Telyakovskiy, A. S.; Wheatcraft, S. W.
2005-12-01
A few classical problems are known in the theory of variable density flows: Henry's, Elder's and Yusa's problems. A very limited number of analytical solutions are known for these problems. The goal of this work is to obtain new analytical/semi-analytical solutions that would provide insights into the nature of these problems. Also, it would allow more efficient testing of numerical codes that can be used for many applications. Today these codes are tested only against an extremely limited number of known solutions. So such solutions will be extremely useful to the groundwater hydrology community. Sea water ntrusion, the most important of variable density flow problems, is a very big problem in the world today, with a significant portion of the world's population living within 50 km of the world's oceans.
Calibration of Semi-analytic Models of Galaxy Formation Using Particle Swarm Optimization
NASA Astrophysics Data System (ADS)
Ruiz, Andrés N.; Cora, Sofía A.; Padilla, Nelson D.; Domínguez, Mariano J.; Vega-Martínez, Cristian A.; Tecce, Tomás E.; Orsi, Álvaro; Yaryura, Yamila; García Lambas, Diego; Gargiulo, Ignacio D.; Muñoz Arancibia, Alejandra M.
2015-03-01
We present a fast and accurate method to select an optimal set of parameters in semi-analytic models of galaxy formation and evolution (SAMs). Our approach compares the results of a model against a set of observables applying a stochastic technique called Particle Swarm Optimization (PSO), a self-learning algorithm for localizing regions of maximum likelihood in multidimensional spaces that outperforms traditional sampling methods in terms of computational cost. We apply the PSO technique to the SAG semi-analytic model combined with merger trees extracted from a standard Lambda Cold Dark Matter N-body simulation. The calibration is performed using a combination of observed galaxy properties as constraints, including the local stellar mass function and the black hole to bulge mass relation. We test the ability of the PSO algorithm to find the best set of free parameters of the model by comparing the results with those obtained using a MCMC exploration. Both methods find the same maximum likelihood region, however, the PSO method requires one order of magnitude fewer evaluations. This new approach allows a fast estimation of the best-fitting parameter set in multidimensional spaces, providing a practical tool to test the consequences of including other astrophysical processes in SAMs.
NASA Astrophysics Data System (ADS)
Zhang, Yao-Ming; Gu, Yan; Chen, Jeng-Tzong
2011-05-01
For a long time, most of the current numerical methods, including the finite element method, have not been efficient to analyze stress fields of very thin structures, such as the problems of thin coatings and their interfacial/internal mechanics. In this paper, the boundary element method for 2-D elastostatic problems is studied for the analysis of multi-coating systems. The nearly singular integrals, which is the primary obstacle associated with the BEM formulations, are dealt with efficiently by using a semi-analytical algorithm. The proposed semi-analytical integral formulas, compared with current analytical methods in the BEM literature, are suitable for high-order geometry elements when nearly singular integrals need to be calculated. Owing to the employment of the curved surface elements, only a small number of elements need to be divided along the boundary, and high accuracy can be achieved without increasing more computational efforts. For the test problems studied, very promising results are obtained when the thickness of coated layers is in the orders of 10-6-10-9, which is sufficient for modeling most coated systems in the micro- or nano-scales.
Multipole expansion method for supernova neutrino oscillations
Duan, Huaiyu; Shalgar, Shashank E-mail: shashankshalgar@unm.edu
2014-10-01
We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis.
A semi-analytical guidance algorithm for autonomous landing
NASA Astrophysics Data System (ADS)
Lunghi, Paolo; Lavagna, Michèle; Armellin, Roberto
2015-06-01
One of the main challenges posed by the next space systems generation is the high level of autonomy they will require. Hazard Detection and Avoidance is a key technology in this context. An adaptive guidance algorithm for landing that updates the trajectory to the surface by means of an optimal control problem solving is here presented. A semi-analytical approach is proposed. The trajectory is expressed in a polynomial form of minimum order to satisfy a set of boundary constraints derived from initial and final states and attitude requirements. By imposing boundary conditions, a fully determined guidance profile is obtained, function of a restricted set of parameters. The guidance computation is reduced to the determination of these parameters in order to satisfy path constraints and other additional constraints not implicitly satisfied by the polynomial formulation. The algorithm is applied to two different scenarios, a lunar landing and an asteroidal landing, to highlight its general validity. An extensive Monte Carlo test campaign is conducted to verify the versatility of the algorithm in realistic cases, by the introduction of attitude control systems, thrust modulation, and navigation errors. The proposed approach proved to be flexible and accurate, granting a precision of a few meters at touchdown.
Machine learning and cosmological simulations - I. Semi-analytical models
NASA Astrophysics Data System (ADS)
Kamdar, Harshil M.; Turk, Matthew J.; Brunner, Robert J.
2016-01-01
We present a new exploratory framework to model galaxy formation and evolution in a hierarchical Universe by using machine learning (ML). Our motivations are two-fold: (1) presenting a new, promising technique to study galaxy formation, and (2) quantitatively analysing the extent of the influence of dark matter halo properties on galaxies in the backdrop of semi-analytical models (SAMs). We use the influential Millennium Simulation and the corresponding Munich SAM to train and test various sophisticated ML algorithms (k-Nearest Neighbors, decision trees, random forests, and extremely randomized trees). By using only essential dark matter halo physical properties for haloes of M > 1012 M⊙ and a partial merger tree, our model predicts the hot gas mass, cold gas mass, bulge mass, total stellar mass, black hole mass and cooling radius at z = 0 for each central galaxy in a dark matter halo for the Millennium run. Our results provide a unique and powerful phenomenological framework to explore the galaxy-halo connection that is built upon SAMs and demonstrably place ML as a promising and a computationally efficient tool to study small-scale structure formation.
A semi-analytic dynamical friction model for cored galaxies
NASA Astrophysics Data System (ADS)
Petts, J. A.; Read, J. I.; Gualandris, A.
2016-08-01
We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts et al. (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc ≪ 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.
Semi-analytic galaxy formation in coupled dark energy cosmologies
NASA Astrophysics Data System (ADS)
Fontanot, Fabio; Baldi, Marco; Springel, Volker; Bianchi, Davide
2015-09-01
Among the possible alternatives to the standard cosmological model (ΛCDM), coupled dark energy models postulate that dark energy (DE), seen as a dynamical scalar field, may interact with dark matter (DM), giving rise to a `fifth-force', felt by DM particles only. In this paper, we study the impact of these cosmologies on the statistical properties of galaxy populations by combining high-resolution numerical simulations with semi-analytic models (SAMs) of galaxy formation and evolution. New features have been implemented in the reference SAM in order to have it run self-consistently and calibrated on these cosmological simulations. They include an appropriate modification of the mass-temperature relation and of the baryon fraction in DM haloes, due to the different virial scalings and to the gravitational bias, respectively. Our results show that the predictions of our coupled-DE SAM do not differ significantly from theoretical predictions obtained with standard SAMs applied to a reference Λ cold dark matter (ΛCDM) simulation, implying that the statistical properties of galaxies provide only a weak probe for these alternative cosmological models. On the other hand, we show that both galaxy bias and the galaxy pairwise velocity distribution are sensitive to coupled DE models: this implies that these probes might be successfully applied to disentangle among quintessence, f(R)-gravity and coupled DE models.
A semi-analytic model of magnetized liner inertial fusion
McBride, Ryan D.; Slutz, Stephen A.
2015-05-15
Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized α-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.
Star formation in Herschel's Monsters versus semi-analytic models
NASA Astrophysics Data System (ADS)
Gruppioni, C.; Calura, F.; Pozzi, F.; Delvecchio, I.; Berta, S.; De Lucia, G.; Fontanot, F.; Franceschini, A.; Marchetti, L.; Menci, N.; Monaco, P.; Vaccari, M.
2015-08-01
We present a direct comparison between the observed star formation rate functions (SFRFs) and the state-of-the-art predictions of semi-analytic models (SAMs) of galaxy formation and evolution. We use the PACS Evolutionary Probe Survey and Herschel Multi-tiered Extragalactic Survey data sets in the COSMOS and GOODS-South fields, combined with broad-band photometry from UV to sub-mm, to obtain total (IR+UV) instantaneous star formation rates (SFRs) for individual Herschel galaxies up to z ˜ 4, subtracted of possible active galactic nucleus (AGN) contamination. The comparison with model predictions shows that SAMs broadly reproduce the observed SFRFs up to z ˜ 2, when the observational errors on the SFR are taken into account. However, all the models seem to underpredict the bright end of the SFRF at z ≳ 2. The cause of this underprediction could lie in an improper modelling of several model ingredients, like too strong (AGN or stellar) feedback in the brighter objects or too low fallback of gas, caused by weak feedback and outflows at earlier epochs.
NASA Astrophysics Data System (ADS)
Reverdy, Frédéric; Mahaut, Steve; Dominguez, Nicolas; Dubois, Philippe
2015-03-01
Carbon Fiber reinforced composites are increasingly used in structural parts in the aeronautics industry, as they allow to reduce the weight of aircrafts while maintaining high mechanical performances. However, such structures can be complicated to inspect due to their complex geometries and complex composite properties, leading to highly heterogeneous and anisotropic materials. Different potential damages and manufacturing flaws related to these parts are to be detected: porosities, ply waviness, delaminations after impact. Ultrasonic inspection, which is commonly used to test the full volume of composite panels, thus has to cope with both complex wave propagation (within anisotropic parts whose crystallographic orientation varies according to the layers structure) and flaw interaction (local distortion of plies such as ply waviness, small pores, structural noise due to periodicity patterns…). Developing NDT procedures for those parts therefore requires simulation tools to help for understanding those phenomena, and to optimize probes and techniques. Within the CIVA multi-techniques platform, CEA-LIST has developed semi-analytical tools for ultrasonic techniques, which have the advantages of high computational efficiency (fast calculations), but with limited range of application due to some hypothesis (for instance, homogenization approaches which don't allow to take account of structural noise). On the other hand, numerical methods such as finite element (FEM) or finite difference in time domain (FDTD) are more suitable to compute ultrasonic wave propagation and defect scattering in complex materials such as composite but require more computational efforts. Hybrid methods couple semi-analytical solutions and numerical computations in limited spatial domains to handle complex cases with high computation performances. In CIVA we have integrated a hybrid model that combines the semi-analytical methods developed at CEA to FDTD codes developed at Airbus Group
Semi-analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending
NASA Astrophysics Data System (ADS)
Lü, C. F.; Huang, Z. Y.; Chen, W. Q.
2007-07-01
Elasticity solutions for free vibration of angle-ply laminates subjected to cylindrical bending are obtained using a newly developed semi-analytical approach. The thickness domain is solved analytically using the transfer matrix method based on the state space concept, while the in-plane domain is solved approximately via the technique of differential quadrature. The present method is applicable to arbitrarily thick laminates and for treating arbitrary edge conditions. The method is verified by comparisons with the exact solutions of Pagano's problem. Effects of variation of ply angle on the vibration properties of laminates are investigated; mode shape switching is observed when ply angle varies. Numerical results for fully clamped thick laminates are presented for future references.
A semi-analytical model for semiconductor solar cells
NASA Astrophysics Data System (ADS)
Ding, D.; Johnson, S. R.; Yu, S.-Q.; Wu, S.-N.; Zhang, Y.-H.
2011-12-01
A semi-analytical model is constructed for single- and multi-junction solar cells. This model incorporates the key performance aspects of practical devices, including nonradiative recombination, photon recycling within a given junction, spontaneous emission coupling between junctions, and non-step-like absorptance and emittance with below-bandgap tail absorption. Four typical planar structures with the combinations of a smooth/textured top surface and an absorbing/reflecting substrate (or backside surface) are investigated, through which the extracted power and four types of fundamental loss mechanisms, transmission, thermalization, spatial-relaxation, and recombination loss are analyzed for both single- and multi-junction solar cells. The below-bandgap tail absorption increases the short-circuit current but decreases the output and open-circuit voltage. Using a straightforward formulism this model provides the initial design parameters and the achievable efficiencies for both single- and multiple-junction solar cells over a wide range of material quality. The achievable efficiency limits calculated using the best reported materials and AM1.5 G one sun for GaAs and Si single-junction solar cells are, respectively, 27.4 and 21.1% for semiconductor slabs with a flat surface and a non-reflecting index-matched absorbing substrate, and 30.8 and 26.4% for semiconductor slabs with a textured surface and an ideal 100% reflecting backside surface. Two important design rules for both single- and multi-junction solar cells are established: i) the optimal junction thickness decreases and the optimal bandgap energy increases when nonradiative recombination increases; and ii) the optimal junction thickness increases and the optimal bandgap energy decreases for higher solar concentrations.
NASA Astrophysics Data System (ADS)
Guo, Kongming; Jiang, Jun; Xu, Yalan
2016-09-01
In this paper, a simple but accurate semi-analytical method to approximate probability density function of stochastic closed curve attractors is proposed. The expression of distribution applies to systems with strong nonlinearities, while only weak noise condition is needed. With the understanding that additive noise does not change the longitudinal distribution of the attractors, the high-dimensional probability density distribution is decomposed into two low-dimensional distributions: the longitudinal and the transverse probability density distributions. The longitudinal distribution can be calculated from the deterministic systems, while the probability density in the transverse direction of the curve can be approximated by the stochastic sensitivity function method. The effectiveness of this approach is verified by comparing the expression of distribution with the results of Monte Carlo numerical simulations in several planar systems.
Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH
NASA Astrophysics Data System (ADS)
Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.
2014-03-01
This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k-ɛ turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction.
A semi-analytical solution for slug tests in an unconfined aquifer considering unsaturated flow
NASA Astrophysics Data System (ADS)
Sun, Hongbing
2016-01-01
A semi-analytical solution considering the vertical unsaturated flow is developed for groundwater flow in response to a slug test in an unconfined aquifer in Laplace space. The new solution incorporates the effects of partial penetrating, anisotropy, vertical unsaturated flow, and a moving water table boundary. Compared to the Kansas Geological Survey (KGS) model, the new solution can significantly improve the fittings of the modeled to the measured hydraulic heads at the late stage of slug tests in an unconfined aquifer, particularly when the slug well has a partially submerged screen and moisture drainage above the water table is significant. The radial hydraulic conductivities estimated with the new solution are comparable to those from the KGS, Bouwer and Rice, and Hvorslev methods. In addition, the new solution also can be used to examine the vertical conductivity, specific storage, specific yield, and the moisture retention parameters in an unconfined aquifer based on slug test data.
A new semi-analytical solution for inertial waves in a rectangular parallelepiped
NASA Astrophysics Data System (ADS)
Nurijanyan, S.; Bokhove, O.; Maas, L. R. M.
2013-12-01
A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane, the two dimensional solution is constructed via superposition of "inertial" analogs of surface Poincaré and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincaré waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor ["Tidal oscillations in gulfs and basins," Proc. London Math. Soc., Ser. 2 XX, 148-181 (1921)], Rao ["Free gravitational oscillations in rotating rectangular basins," J. Fluid Mech. 25, 523-555 (1966)] and also, for inertial waves, by Maas ["On the amphidromic structure of inertial waves in a rectangular parallelepiped," Fluid Dyn. Res. 33, 373-401 (2003)] upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas. In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.
A semi-analytic theory for the motion of a close-earth artificial satellite with drag
NASA Technical Reports Server (NTRS)
Liu, J. J. F.; Alford, R. L.
1979-01-01
A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Sumit; Tsang, Yvonne W.
2008-10-01
Flowing fluid temperature logging (FFTL) has recently been proposed as a method to locate flowing fractures. We argue that FFTL, backed up by data from high-precision distributed temperature sensors, can be a useful tool in locating flowing fractures and in estimating the transport properties of unsaturated fractured rocks. We have developed the theoretical background needed to analyze data from FFTL. In this article, we present a simplified conceptualization of FFTL in unsaturated fractured rock and develop a semi-analytical solution for spatial and temporal variations of pressure and temperature inside a borehole in response to an applied perturbation (pumping of air from the borehole). We compare the semi-analytical solution with predictions from the TOUGH2 numerical simulator. On the basis of the semi-analytical solution, we propose a method to estimate the permeability of the fracture continuum surrounding the borehole. Using this proposed method, we estimated the effective fracture continuum permeability of the unsaturated rock hosting the Drift Scale Test (DST) at Yucca Mountain, Nevada. Our estimate compares well with previous independent estimates for fracture permeability of the DST host rock. The conceptual model of FFTL presented in this article is based on the assumptions of single-phase flow, convection-only heat transfer, and negligible change in system state of the rock formation. In a sequel article, we extend the conceptual model to evaluate some of these assumptions. In that paper, we also perform inverse modeling of FFTL data to estimate, in addition to permeability, other transport parameters (such as porosity and thermal conductivity) of unsaturated fractured rocks.
A SEMI-ANALYTIC FORMULATION FOR RELATIVISTIC BLAST WAVES WITH A LONG-LIVED REVERSE SHOCK
Uhm, Z. Lucas
2011-06-01
This paper performs a semi-analytic study of relativistic blast waves in the context of gamma-ray bursts. Although commonly used in a wide range of analytical and numerical studies, the equation of state (EOS) with a constant adiabatic index is a poor approximation for relativistic hydrodynamics. Adopting a more realistic EOS with a variable adiabatic index, we present a simple form of jump conditions for relativistic hydrodynamical shocks. Then we describe in detail our technique of modeling a very general class of GRB blast waves with a long-lived reverse shock. Our technique admits an arbitrary radial stratification of the ejecta and ambient medium. We use two different methods to find dynamics of the blast wave: (1) customary pressure balance across the blast wave and (2) the 'mechanical model'. Using a simple example model, we demonstrate that the two methods yield significantly different dynamical evolutions of the blast wave. We show that the pressure balance does not satisfy the energy conservation for an adiabatic blast wave while the mechanical model does. We also compare two sets of afterglow light curves obtained with the two different methods.
NASA Astrophysics Data System (ADS)
Guo, B.; Matteo, E. N.; Elliot, T. R.; Nogues, J. P.; Deng, H.; Fitts, J. P.; Pollak, M.; Bielicki, J.; Wilson, E.; Celia, M. A.; Peters, C. A.
2011-12-01
Using the semi-analytical ELSA model, wellbore leakage risk is estimated for CO2 injection into either the Mt. Simon or St. Peter formations, which are part of the Michigan Sedimentary Basin that lies beneath Ottawa County, MI. ELSA is a vertically integrated subsurface modeling tool that can be used to simulate both supercritical CO2 plume distribution/migration and pressure- induced brine displacement during CO2 injection. A composite 3D subsurface domain was constructed for the ELSA simulations based on estimated permeabilities for formation layers, as well as GIS databases containing subsurface stratigraphy, active and inactive and inactive wells, and potential interactions with subsurface activities. These activities include potable aquifers, oil and gas reservoirs, and waste injection sites, which represent potential liabilities if encountered by brine or supercritical CO2 displaced from the injection formation. Overall, the 3D subsurface domain encompasses an area of 1500 km2 to a depth of 2 km and contains over 3,000 wells. The permeabilities for abandoned wells are derived from a ranking system based on available well data including historical records and well logs. This distribution is then randomly sampled in Monte Carlo simulations that are used to generate a probability map for subsurface interferences or atmospheric release resulting from leakage of CO2 and /or brine from the injection formation. This method serves as the basis for comparative testing between various scenarios for injection, as well as for comparing the relative risk of leakage between injection formations or storage sites.
Allan, Mathew G; Hamilton, David P; Hicks, Brendan; Brabyn, Lars
2015-06-01
The concentration of chlorophyll a (chl a; as a proxy for phytoplankton biomass) provides an indication of the water quality and ecosystem health of lakes. An automated image processing method for Landsat images was used to derive chl a concentrations in 12 Rotorua lakes of North Island, New Zealand, with widely varying trophic status. Semi-analytical and empirical models were used to process 137 Landsat 7 Enhanced Thematic Mapper (ETM+) images using records from 1999 to 2013. Atmospheric correction used radiative transfer modelling, with atmospheric conditions prescribed with Moderate Resolution Imaging Spectroradiometer (MODIS) Terra and AIRS data. The best-performing semi-analytical and empirical equations resulted in similar levels of variation explained (r (2) = 0.68 for both equations) and root-mean-square error (RMSE = 10.69 and 10.43 μg L(-1), respectively) between observed and estimated chl a. However, the symbolic regression algorithm performed better for chl a concentrations <5 μg L(-1). Our Landsat-based algorithms provide a valuable method for synoptic assessments of chl a across the 12 lakes in this region. They also provide a basis for assessing changes in chl a individual lakes through time. Our methods provide a basis for cost-effective hindcasting of lake trophic status at a regional scale, informing on spatial variability of chl a within and between lakes. PMID:25986777
NASA Technical Reports Server (NTRS)
Zumwalt, Kenneth W.; El-Sayed, Mohamed E. M.
1990-01-01
This paper presents an analytical approach for incorporating design sensitivity calculations directly into the finite element analysis. The formulation depends on the implicit differentiation approach and requires few additional calculations to obtain the design sensitivity derivatives. In order to evaluate this approach, it is compared with the semi-analytical approach which is based on commonly used finite difference formulations. Both approaches are implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the accuracy and robustness of the developed analytical approach compared to the semi-analytical approach, some test cases using different structural and continuum element types are presented.
NASA Astrophysics Data System (ADS)
Setty, Srinivas J.; Cefola, Paul J.; Montenbruck, Oliver; Fiedler, Hauke
2016-05-01
Catalog maintenance for Space Situational Awareness (SSA) demands an accurate and computationally lean orbit propagation and orbit determination technique to cope with the ever increasing number of observed space objects. As an alternative to established numerical and analytical methods, we investigate the accuracy and computational load of the Draper Semi-analytical Satellite Theory (DSST). The standalone version of the DSST was enhanced with additional perturbation models to improve its recovery of short periodic motion. The accuracy of DSST is, for the first time, compared to a numerical propagator with fidelity force models for a comprehensive grid of low, medium, and high altitude orbits with varying eccentricity and different inclinations. Furthermore, the run-time of both propagators is compared as a function of propagation arc, output step size and gravity field order to assess its performance for a full range of relevant use cases. For use in orbit determination, a robust performance of DSST is demonstrated even in the case of sparse observations, which is most sensitive to mismodeled short periodic perturbations. Overall, DSST is shown to exhibit adequate accuracy at favorable computational speed for the full set of orbits that need to be considered in space surveillance. Along with the inherent benefits of a semi-analytical orbit representation, DSST provides an attractive alternative to the more common numerical orbit propagation techniques.
A Semi-Analytical Orbit Propagator Program for Highly Elliptical Orbits
NASA Astrophysics Data System (ADS)
Lara, M.; San-Juan, J. F.; Hautesserres, D.
2016-05-01
A semi-analytical orbit propagator to study the long-term evolution of spacecraft in Highly Elliptical Orbits is presented. The perturbation model taken into account includes the gravitational effects produced by the first nine zonal harmonics and the main tesseral harmonics affecting to the 2:1 resonance, which has an impact on Molniya orbit-types, of Earth's gravitational potential, the mass-point approximation for third body perturbations, which on ly include the Legendre polynomial of second order for the sun and the polynomials from second order to sixth order for the moon, solar radiation pressure and atmospheric drag. Hamiltonian formalism is used to model the forces of gravitational nature so as to avoid time-dependence issues the problem is formulated in the extended phase space. The solar radiation pressure is modeled as a potential and included in the Hamiltonian, whereas the atmospheric drag is added as a generalized force. The semi-analytical theory is developed using perturbation techniques based on Lie transforms. Deprit's perturbation algorithm is applied up to the second order of the second zonal harmonics, J2, including Kozay-type terms in the mean elements Hamiltonian to get "centered" elements. The transformation is developed in closed-form of the eccentricity except for tesseral resonances and the coupling between J_2 and the moon's disturbing effects are neglected. This paper describes the semi-analytical theory, the semi-analytical orbit propagator program and some of the numerical validations.
Comparison of a semi-analytic and a CFD model uranium combustion to experimental data.
Clarksean, R.
1998-04-01
Two numerical models were developed and compared for the analysis of uranium combustion and ignition in a furnace. Both a semi-analytical solution and a computational fluid dynamics (CFD) numerical solution were obtained. Prediction of uranium oxidation rates is important for fuel storage applications, fuel processing, and the development of spent fuel metal waste forms. The semi-analytical model was based on heat transfer correlations, a semi-analytical model of flow over a flat surface, and simple radiative heat transfer from the material surface. The CFD model numerically determined the flowfield over the object of interest, calculated the heat and mass transfer to the material of interest, and calculated the radiative heat exchange of the material with the furnace. The semi-analytical model is much less detailed than the CFD model, but yields reasonable results and assists in understanding the physical process. Short computation times allowed the analyst to study numerous scenarios. The CFD model had significantly longer run times, was found to have some physical limitations that were not easily modified, but was better able to yield details of the heat and mass transfer and flow field once code limitations were overcome.
A semi-analytic model for localized variable charge dust acoustic waves
Tribeche, Mouloud; Gougam, Leila Ait; Aoutou, Kamal
2006-09-15
A semi-analytic model for nonlinear variable charge dust acoustic waves is outlined. It is shown that rarefactive variable charge dust acoustic solitons involving cusped density humps can exist. The effects of dust dynamics as well as equilibrium dust charge on these nonlinear localized structures are briefly discussed.
A Bayesian approach to the semi-analytic model of galaxy formation
NASA Astrophysics Data System (ADS)
Lu, Yu
It is believed that a wide range of physical processes conspire to shape the observed galaxy population but it remains unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality and large uncertainties in the model, the parametric problem of galaxy formation can be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this thesis, I present a newly developed method to build SAM upon the framework of Bayesian inference. I show that, aided by advanced Markov-Chain Monte-Carlo algorithms, the method has the power to efficiently combine information from diverse data sources, rigorously establish confidence bounds on model parameters, and provide powerful probability-based methods for hypothesis test. Using various data sets (stellar mass function, conditional stellar mass function, K-band luminosity function, and cold gas mass functions) of galaxies in the local Universe, I carry out a series of Bayesian model inferences. The results show that SAM contains huge degeneracies among its parameters, indicating that some of the conclusions drawn previously with the conventional approach may not be truly valid but need to be revisited by the Bayesian approach. Second, some of the degeneracy of the model can be broken by adopting multiple data sets that constrain different aspects of the galaxy population. Third, the inferences reveal that model has challenge to simultaneously explain some important observational results, suggesting that some key physics governing the evolution of star formation and feedback may still be missing from the model. These analyses show clearly that the Bayesian inference based SAM can be used to perform systematic and statistically
NASA Astrophysics Data System (ADS)
Cardiff, Michael; Liu, Xiaoyi; Kitanidis, Peter K.; Parker, Jack; Kim, Ungtae
2010-04-01
Dense non-aqueous phase liquid (DNAPL) spills represent a potential long-term source of aquifer contamination, and successful low-cost remediation may require a combination of both plume management and source treatment. In addition, substantial uncertainty exists in many of the parameters that control field-scale behavior of DNAPL sources and plumes. For these reasons, cost optimization of DNAPL cleanup needs to consider multiple treatment options and their associated costs while also gauging the influence of prediction uncertainty on expected costs. In this paper, we present a management methodology for field-scale DNAPL source and plume management under uncertainty. Using probabilistic methods, historical data and prior information are combined to produce a set of equally likely realizations of true field conditions (i.e., parameter sets). These parameter sets are then used in a simulation-optimization framework to produce DNAPL cleanup solutions that have the lowest possible expected net present value (ENPV) cost and that are suitably cautious in the presence of high uncertainty. For simulation, we utilize a fast-running semi-analytic field-scale model of DNAPL source and plume evolution that also approximates the effects of remedial actions. The degree of model prediction uncertainty is gauged using a restricted maximum likelihood method, which helps to produce suitably cautious remediation strategies. We test our methodology on a synthetic field-scale problem with multiple source architectures, for which source zone thermal treatment and electron donor injection are considered as remedial actions. The lowest cost solution found utilizes a combination of source and plume remediation methods, and is able to successfully meet remediation constraints for a majority of possible scenarios. Comparisons with deterministic optimization results show that not taking into account uncertainty can result in optimization strategies that are not aggressive enough and result
Density-functional expansion methods: Grand challenges
Giese, Timothy J.; York, Darrin M.
2016-01-01
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian. PMID:27293378
Hodgson, Norman; Caprara, Andrea
2016-07-01
Temperature profiles in pumped solid-state laser disks are generally calculated numerically by using finite-element programs to solve the heat conduction equation in the disk and the heat spreader. Analytical expressions exist for the longitudinal temperature profile in the case of an infinitely thick heat spreader or in the limit of zero thickness of the disk. We are presenting a simplified, semi-analytical method to calculate the three-dimensional temperature profiles for any disk or heat spreader dimensions by solving the heat conduction equation using Hankel transforms. This method allows for straightforward optimization of the cooling properties of heat-sink-mounted solid-state and semiconductor disk lasers. PMID:27409198
Mukhopadhyay, Sumit; Tsang, Yvonne W.
2008-08-01
Flowing fluid temperature logging (FFTL) has been recently proposed as a method to locate flowing fractures. We argue that FFTL, backed up by data from high-precision distributed temperature sensors, can be a useful tool in locating flowing fractures and in estimating the transport properties of unsaturated fractured rocks. We have developed the theoretical background needed to analyze data from FFTL. In this paper, we present a simplified conceptualization of FFTL in unsaturated fractured rock, and develop a semianalytical solution for spatial and temporal variations of pressure and temperature inside a borehole in response to an applied perturbation (pumping of air from the borehole). We compare the semi-analytical solution with predictions from the TOUGH2 numerical simulator. Based on the semi-analytical solution, we propose a method to estimate the permeability of the fracture continuum surrounding the borehole. Using this proposed method, we estimated the effective fracture continuum permeability of the unsaturated rock hosting the Drift Scale Test (DST) at Yucca Mountain, Nevada. Our estimate compares well with previous independent estimates for fracture permeability of the DST host rock. The conceptual model of FFTL presented in this paper is based on the assumptions of single-phase flow, convection-only heat transfer, and negligible change in system state of the rock formation. In a sequel paper [Mukhopadhyay et al., 2008], we extend the conceptual model to evaluate some of these assumptions. We also perform inverse modeling of FFTL data to estimate, in addition to permeability, other transport parameters (such as porosity and thermal conductivity) of unsaturated fractured rocks.
Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi
2014-01-01
Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582
NASA Astrophysics Data System (ADS)
Cody, B. M.; Gonzalez-Nicolas, A.; Bau, D. A.
2011-12-01
Carbon capture and storage (CCS) has been proposed as a method of reducing global carbon dioxide (CO2) emissions. Although CCS has the potential to greatly retard greenhouse gas loading to the atmosphere while cleaner, more sustainable energy solutions are developed, there is a possibility that sequestered CO2 may leak and intrude into and adversely affect groundwater resources. It has been reported [1] that, while CO2 intrusion typically does not directly threaten underground drinking water resources, it may cause secondary effects, such as the mobilization of hazardous inorganic constituents present in aquifer minerals and changes in pH values. These risks must be fully understood and minimized before CCS project implementation. Combined management of project resources and leakage risk is crucial for the implementation of CCS. In this work, we present a method of: (a) minimizing the total CCS cost, the summation of major project costs with the cost associated with CO2 leakage; and (b) maximizing the mass of injected CO2, for a given proposed sequestration site. Optimization decision variables include the number of CO2 injection wells, injection rates, and injection well locations. The capital and operational costs of injection wells are directly related to injection well depth, location, injection flow rate, and injection duration. The cost of leakage is directly related to the mass of CO2 leaked through weak areas, such as abandoned oil wells, in the cap rock layers overlying the injected formation. Additional constraints on fluid overpressure caused by CO2 injection are imposed to maintain predefined effective stress levels that prevent cap rock fracturing. Here, both mass leakage and fluid overpressure are estimated using two semi-analytical models based upon work by [2,3]. A multi-objective evolutionary algorithm coupled with these semi-analytical leakage flow models is used to determine Pareto-optimal trade-off sets giving minimum total cost vs. maximum mass
Method of assembling a thermal expansion compensator
NASA Technical Reports Server (NTRS)
Determan, William (Inventor); Matejczyk, Daniel Edward (Inventor)
2012-01-01
A thermal expansion compensator is provided and includes a first electrode structure having a first surface, a second electrode structure having a second surface facing the first surface and an elastic element bonded to the first and second surfaces and including a conductive element by which the first and second electrode structures electrically and/or thermally communicate, the conductive element having a length that is not substantially longer than a distance between the first and second surfaces.
Lu, Yu; Wechsler, Risa H.; Somerville, Rachel S.; Croton, Darren; Porter, Lauren; Primack, Joel; Moody, Chris; Behroozi, Peter S.; Ferguson, Henry C.; Koo, David C.; Guo, Yicheng; Finlator, Kristian; Castellano, Marco; Sommariva, Veronica E-mail: rwechsler@stanford.edu
2014-11-10
We compare the predictions of three independently developed semi-analytic galaxy formation models (SAMs) that are being used to aid in the interpretation of results from the CANDELS survey. These models are each applied to the same set of halo merger trees extracted from the 'Bolshoi' high-resolution cosmological N-body simulation and are carefully tuned to match the local galaxy stellar mass function using the powerful method of Bayesian Inference coupled with Markov Chain Monte Carlo or by hand. The comparisons reveal that in spite of the significantly different parameterizations for star formation and feedback processes, the three models yield qualitatively similar predictions for the assembly histories of galaxy stellar mass and star formation over cosmic time. Comparing SAM predictions with existing estimates of the stellar mass function from z = 0-8, we show that the SAMs generally require strong outflows to suppress star formation in low-mass halos to match the present-day stellar mass function, as is the present common wisdom. However, all of the models considered produce predictions for the star formation rates (SFRs) and metallicities of low-mass galaxies that are inconsistent with existing data. The predictions for metallicity-stellar mass relations and their evolution clearly diverge between the models. We suggest that large differences in the metallicity relations and small differences in the stellar mass assembly histories of model galaxies stem from different assumptions for the outflow mass-loading factor produced by feedback. Importantly, while more accurate observational measurements for stellar mass, SFR and metallicity of galaxies at 1 < z < 5 will discriminate between models, the discrepancies between the constrained models and existing data of these observables have already revealed challenging problems in understanding star formation and its feedback in galaxy formation. The three sets of models are being used to construct catalogs of mock
Series Expansion of Functions with He's Homotopy Perturbation Method
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2012-01-01
Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…
Homentcovschi, Dorel; Miles, Ronald N.
2012-01-01
The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient. PMID:22352491
Laurien, E.
2012-07-01
Within the Generation IV International Forum the Supercritical Water Reactor is investigated. For its core design and safety analysis the efficient prediction of flow and heat transfer parameters such as the wall-shear stress and the heat-transfer coefficient for pipe and channel flows is needed. For circular pipe flows a numerical model based on the one-dimensional conservation equations of mass, momentum end energy in the radial direction is presented, referred to as a 'semi-analytical' method. An accurate, high-order numerical method is employed to evaluate previously derived analytical solutions of the governing equations. Flow turbulence is modeled using the algebraic approach of Prandtl/van-Karman, including a model for the buffer layer. The influence of wall roughness is taken into account by a new modified numerical damping function of the turbulence model. The thermo-hydraulic properties of water are implemented according to the international standard of 1997. This method has the potential to be used within a sub-channel analysis code and as wall-functions for CFD codes to predict the wall shear stress and the wall temperature. The present study presents a validation of the method with comparison of model results with experiments and multi-dimensional computational (CFD) studies in a wide range of flow parameters. The focus is laid on forced convection flows related to reactor design and near-design conditions. It is found, that the method can accurately predict the wall temperature even under deterioration conditions as they occur in the selected experiments (Yamagata el al. 1972 at 24.5 MPa, Ornatski et al. 1971 at 25.5 and Swenson et al. 1963 at 22.75 MPa). Comparison of the friction coefficient under high heat flux conditions including significant viscosity and density reductions near the wall with various correlations for the hydraulic resistance will be presented; the best agreement is achieve with the correlation of Pioro et al. 2004. It is
SWIM: A Semi-Analytical Ocean Color Inversion Algorithm for Optically Shallow Waters
NASA Technical Reports Server (NTRS)
McKinna, Lachlan I. W.; Werdell, P. Jeremy; Fearns, Peter R. C. S.; Weeks, Scarla J.; Reichstetter, Martina; Franz, Bryan A.; Shea, Donald M.; Feldman, Gene C.
2014-01-01
Ocean color remote sensing provides synoptic-scale, near-daily observations of marine inherent optical properties (IOPs). Whilst contemporary ocean color algorithms are known to perform well in deep oceanic waters, they have difficulty operating in optically clear, shallow marine environments where light reflected from the seafloor contributes to the water-leaving radiance. The effect of benthic reflectance in optically shallow waters is known to adversely affect algorithms developed for optically deep waters [1, 2]. Whilst adapted versions of optically deep ocean color algorithms have been applied to optically shallow regions with reasonable success [3], there is presently no approach that directly corrects for bottom reflectance using existing knowledge of bathymetry and benthic albedo.To address the issue of optically shallow waters, we have developed a semi-analytical ocean color inversion algorithm: the Shallow Water Inversion Model (SWIM). SWIM uses existing bathymetry and a derived benthic albedo map to correct for bottom reflectance using the semi-analytical model of Lee et al [4]. The algorithm was incorporated into the NASA Ocean Biology Processing Groups L2GEN program and tested in optically shallow waters of the Great Barrier Reef, Australia. In-lieu of readily available in situ matchup data, we present a comparison between SWIM and two contemporary ocean color algorithms, the Generalized Inherent Optical Property Algorithm (GIOP) and the Quasi-Analytical Algorithm (QAA).
A semi-analytical study of positive corona discharge in wire-plane electrode configuration
NASA Astrophysics Data System (ADS)
Yanallah, K.; Pontiga, F.; Chen, J. H.
2013-08-01
Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.
IRP methods for Environmental Impact Statements of utility expansion plans
Cavallo, J.D.; Hemphill, R.C.; Veselka, T.D.
1992-10-01
Most large electric utilities and a growing number of gas utilities in the United States are using a planning method -- Integrated Resource Planning (IRP) - which incorporates demand-side management (DSM) programs whenever the marginal cost of the DSM programs are lower than the marginal cost of supply-side expansion options. Argonne National Laboratory has applied the IRP method in its socio-economic analysis of an Environmental Impact Statement (EIS) of power marketing for a system of electric utilities in the mountain and western regions of the United States. Applying the IRP methods provides valuable information to the participants in an EIS process involving capacity expansion of an electric or gas utility. The major challenges of applying the IRP method within an EIS are the time consuming and costly task of developing a least cost expansion path for each altemative, the detailed quantification of environmental damages associated with capacity expansion, and the explicit inclusion of societal-impacts to the region.
IRP methods for Environmental Impact Statements of utility expansion plans
Cavallo, J.D.; Hemphill, R.C.; Veselka, T.D.
1992-01-01
Most large electric utilities and a growing number of gas utilities in the United States are using a planning method -- Integrated Resource Planning (IRP) - which incorporates demand-side management (DSM) programs whenever the marginal cost of the DSM programs are lower than the marginal cost of supply-side expansion options. Argonne National Laboratory has applied the IRP method in its socio-economic analysis of an Environmental Impact Statement (EIS) of power marketing for a system of electric utilities in the mountain and western regions of the United States. Applying the IRP methods provides valuable information to the participants in an EIS process involving capacity expansion of an electric or gas utility. The major challenges of applying the IRP method within an EIS are the time consuming and costly task of developing a least cost expansion path for each altemative, the detailed quantification of environmental damages associated with capacity expansion, and the explicit inclusion of societal-impacts to the region.
NASA Astrophysics Data System (ADS)
Askari, Amir R.; Tahani, Masoud
2016-05-01
The objective of the present paper is to determine pull-in parameters (pull-in voltage and its corresponding displacement) of nano/micro-beams with clamped-clamped, clamped-free, clamped-hinged and hinged-hinged boundary conditions, when they are subjected to the electrostatics and van der Waals (vdW) attractions. The governing non-linear boundary value equation of equilibrium is derived, non-dimensionalized and reduced to an algebraic equation, which describes the position of the maximum deflection of the beam, utilizing the Galerkin decomposition method. The equation which governs on the stability condition of the system is also obtained by differentiating the reduced equilibrium equation with respect to the maximum deflection of the beam. These two equations are solved simultaneously to determine pull-in parameters. Closed-form solutions are provided for cases under electrical loading and vdW attraction alone. The combined effect of both electrostatic and vdW loadings are also investigated using the homotopy perturbation method (HPM). It is found that the present semi-analytical findings are in excellent agreement with those obtained numerically. In addition, it is observed that the present semi-analytical approach can provide results which agree better with available three-dimensional finite element simulations as well as those obtained by nonlinear finite element method than other available analytical or semi-analytical findings in the literature. Non-dimensional electrostatic and vdW parameters, which are defined in the text, are plotted versus each other at pull-in condition. It is found that there exists a linear relationship between these two parameters at pull-in condition. Using this fact, pull-in voltage, detachment length and minimum allowable gap of electrostatically actuated nano/micro-beams are determined explicitly through some closed-form expressions.
NASA Astrophysics Data System (ADS)
Xu, Wenfu; She, Yu; Xu, Yangsheng
2014-12-01
Redundant space manipulators, including Space Station Remote Manipulator System (SSRMS), Special Purpose Dexterous Manipulator (SPDM) and European Robotic Arm (ERA), have been playing important roles in the construction and maintenance of International Space Station (ISS). They all have 7 revolute joints arranged in similar configurations, and are referred to as SSRMS-type manipulators. When a joint is locked in an arbitrary position due to some failures, a 7R manipulator degrades to a 6R manipulator. Without a spherical wrist or three consecutive parallel joints, the inverse kinematics of the 6R manipulator is very complex. In this paper, we propose effective methods to resolve the inverse kinematics for different cases of any joint locked in an arbitrary position. Firstly, configuration characteristics of the SSRMS-type redundant manipulators are analyzed. Then, an existing of closed-form inverse kinematics is discussed for locking different joints. Secondly, D-H frames and corresponding D-H parameters of the new 6-DOF manipulator formed by locking a joint in an arbitrary position are re-constructed. A unified table is then created to describe the kinematics for all possible cases of single joint locking failure. Thirdly, completely analytical and semi-analytical methods are presented to solve the inverse kinematics equations, and the former is used for locking joint 1, 2, 6 or 7 while the latter for locking joint 3, 4 or 5. Finally, typical cases for single joint locking are studied. The results verify the proposed methods.
Simon, Laurent; Ospina, Juan
2016-07-25
Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. PMID:27286637
Exploring magnetized liner inertial fusion with a semi-analytic model
McBride, Ryan D.; Slutz, Stephen A.; Vesey, Roger A.; Gomez, Matthew R.; Sefkow, Adam B.; Hansen, Stephanie B.; Knapp, Patrick F.; Schmit, Paul F.; Geissel, Matthias; Harvey-Thompson, Adam James; et al
2016-01-01
In this study, we explore magnetized liner inertial fusion (MagLIF) [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] using a semi-analytic model [R. D. McBride and S. A. Slutz, Phys. Plasmas 22, 052708 (2015)]. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories [M. R. Gomez et al., Phys. Rev. Lett. 113,more » 155003 (2014)]; (d) highlight the experimental challenges presently facing the MagLIF program; and (e) demonstrate how increases to the preheat energy, fuel density, axial magnetic field, and drive current could affect future MagLIF performance.« less
Exploring magnetized liner inertial fusion with a semi-analytic model
McBride, Ryan D.; Slutz, Stephen A.; Vesey, Roger A.; Gomez, Matthew R.; Sefkow, Adam B.; Hansen, Stephanie B.; Knapp, Patrick F.; Schmit, Paul F.; Geissel, Matthias; Harvey-Thompson, Adam James; Jennings, Christopher Ashley; Harding, Eric C.; Awe, Thomas James; Rovang, Dean C.; Hahn, Kelly D.; Martin, Matthew R.; Cochrane, Kyle R.; Peterson, Kyle J.; Rochau, Gregory A.; Porter, John L.; Stygar, William A.; Campbell, Edward Michael; Nakhleh, Charles W.; Herrmann, Mark C.; Cuneo, Michael E.; Sinars, Daniel B.
2016-01-01
In this study, we explore magnetized liner inertial fusion (MagLIF) [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] using a semi-analytic model [R. D. McBride and S. A. Slutz, Phys. Plasmas 22, 052708 (2015)]. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]; (d) highlight the experimental challenges presently facing the MagLIF program; and (e) demonstrate how increases to the preheat energy, fuel density, axial magnetic field, and drive current could affect future MagLIF performance.
The evolution of individual galaxies in numerical simulations and semi-analytic models
NASA Astrophysics Data System (ADS)
Cohen, Yotam; Somerville, Rachel S.; Brooks, Alyson; Christensen, Charlotte; Ahmed, Sheehan
2016-01-01
We compare results from high-resolution cosmological hydrodynamic zoom simulations with those from a semi-analytic model (SAM) of galaxy formation. We present a detailed comparison of the histories of baryonic, morphological, and structural properties as well as key observational scaling relations as predicted by both simulation and SAM. Our sample consists of more than a dozen galaxies with halo masses ranging from Mvir ˜ (10^10 - 10^12) Msun at z = 0. In order to make direct comparisons, we run the SAM within halo merger trees extracted from the simulation output snapshots, and produced using the ROCKSTAR halo finder/merger tree code. We also present a new tool used to visualize the merger histories of dark matter halos in 3D space using the open-source, data analysis application ParaView.
A semi-analytical model for exploring Galilean satellites formation from a massive disk
NASA Astrophysics Data System (ADS)
Miguel, Yamila; Ida, Shigeru
2016-03-01
A better knowledge of jovian satellites' origins will bring light on the environment that surrounded Jupiter during its formation and can help us to understand the characteristics of this unique satellite system. We developed a semi-analytical model to investigate Jupiter's regular satellite formation and present the results of our population synthesis calculations. We performed simulations adopting a massive, static, low-viscosity circumplanetary disk model, in agreement with a current study of magnetorotational instability in a circum-planetary disk. We find that the high gas density leads to very rapid migration of satellitesimals due to gas drag and type II migration of satellites in a faster disk-dominated mode. A large concentration of solids, large building blocks and longer type II migration time-scales favor formation and survival of large satellites. However, bodies as massive as Ganymede and those located far away from Jupiter, such as Callisto, are difficult to form with this scenario.
Exploring magnetized liner inertial fusion with a semi-analytic model
NASA Astrophysics Data System (ADS)
McBride, R. D.; Slutz, S. A.; Vesey, R. A.; Gomez, M. R.; Sefkow, A. B.; Hansen, S. B.; Knapp, P. F.; Schmit, P. F.; Geissel, M.; Harvey-Thompson, A. J.; Jennings, C. A.; Harding, E. C.; Awe, T. J.; Rovang, D. C.; Hahn, K. D.; Martin, M. R.; Cochrane, K. R.; Peterson, K. J.; Rochau, G. A.; Porter, J. L.; Stygar, W. A.; Campbell, E. M.; Nakhleh, C. W.; Herrmann, M. C.; Cuneo, M. E.; Sinars, D. B.
2016-01-01
In this paper, we explore magnetized liner inertial fusion (MagLIF) [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] using a semi-analytic model [R. D. McBride and S. A. Slutz, Phys. Plasmas 22, 052708 (2015)]. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]; (d) highlight the experimental challenges presently facing the MagLIF program; and (e) demonstrate how increases to the preheat energy, fuel density, axial magnetic field, and drive current could affect future MagLIF performance.
Semi-analytical modeling of acoustic beam divergence in homogeneous anisotropic half-spaces.
Kono, Naoyuki; Hirose, Sohichi
2016-02-01
Beam divergences of acoustical fields in semi-infinite homogeneous anisotropic media are calculated based on a semi-analytical model. The model for a plane source in a semi-infinite homogeneous anisotropic medium is proposed as an extended model for a point source in an infinite medium. Beam divergences propagating along crystallographic axes 〈100〉, 〈110〉, and 〈111〉 in a cubic crystal, a single crystalline Ni-based alloy, are measured and compared to calculation results for verifying the model. The contribution of beam divergence attenuation to the total attenuation for propagating in anisotropic polycrystalline materials is quantitatively evaluated in isolation from scattering attenuation effects. PMID:26508085
A Semi-Analytical Model for Short Range Dispersion From Ground Sources
NASA Astrophysics Data System (ADS)
Gavze, E.; Fattal, E.; Reichman, R.
2014-12-01
A semi-analytical model for dispersion of passive scalars from ground sources up to distances of a few hundred meters is presented. Most widely used analytical models are Gaussian models which assume both a uniform wind field and homogeneous turbulence. These assumptions are not valid when ground sources are involved since both the wind and the turbulence depend on height. The model presented here is free of these two assumptions. The formulation of the vertical dispersion is based on approximating the vertical profiles of the wind and the the vertical diffusion coefficient, based on Monin Obukhov Similarity Theory, as power laws. One advantage of this approach is that it allows for non Gaussian vertical profiles of the concentration which better fit the experimental data. For the lateral dispersion the model still assumes a Gaussian form. A system of equations was developed to compute the cloud width. This system of equations is based on an analytical solution of a Langevin equation which takes into account the non-homogeneity of the wind and the turbulence in the vertical direction. The model was tested against two field experiments. Comparison with a Gaussian model showed that it performed much better in predicting both the integrated cross wind ground concentration and the cloud width. Analytical, or semi-analytical models are useful as they are simple to use and require only a short computation time, compared, for example, to Lagrangian Stochastic Models. The presented model is very efficient from the computational point of view. As such it is suitable for cases in which repeated computations of the concentration field are required, as for example in risk assessments and in the inverse problem of source determination.
Fast radiative transfer of dust reprocessing in semi-analytic models with artificial neural networks
NASA Astrophysics Data System (ADS)
Silva, Laura; Fontanot, Fabio; Granato, Gian Luigi
2012-06-01
A serious concern for semi-analytical galaxy formation models, aiming to simulate multiwavelength surveys and to thoroughly explore the model parameter space, is the extremely time-consuming numerical solution of the radiative transfer of stellar radiation through dusty media. To overcome this problem, we have implemented an artificial neural network (ANN) algorithm in the radiative transfer code GRASIL, in order to significantly speed up the computation of the infrared (IR) spectral energy distribution (SED). The ANN we have implemented is of general use, in that its input neurons are defined as those quantities effectively determining the shape of the IR SED. Therefore, the training of the ANN can be performed with any model and then applied to other models. We made a blind test to check the algorithm, by applying a net trained with a standard chemical evolution model (i.e. CHE_EVO) to a mock catalogue extracted from the semi-analytic model MORGANA, and compared galaxy counts and evolution of the luminosity functions in several near-IR to sub-millimetre (sub-mm) bands, and also the spectral differences for a large subset of randomly extracted models. The ANN is able to excellently approximate the full computation, but with a gain in CPU time by ˜2 orders of magnitude. It is only advisable that the training covers reasonably well the range of values of the input neurons in the application. Indeed in the sub-mm at high redshift, a tiny fraction of models with some sensible input neurons out of the range of the trained net cause wrong answer by the ANN. These are extreme starbursting models with high optical depths, favourably selected by sub-mm observations, and are difficult to predict a priori.
NASA Astrophysics Data System (ADS)
Mahdavi, Ali; Seyyedian, Hamid
2014-05-01
This study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.
NASA Astrophysics Data System (ADS)
de Leo, Andrea Matteo; Contento, Alessandro; Di Egidio, Angelo
2015-09-01
A model of linear, internally constrained shell with single, constant curvature is used to describe the behaviour of existing structures, such as barrel shells. A linear, elastic, isotropic material is considered. Observing that in the shell two families of mono-dimensional interacting beams can be recognized: straight longitudinal beams and transversal arches, a non-conventional semi-analytical approximate solution, which uses the method of separation of variables, is proposed. By using an integral procedure, reduced differential, ordinary equations, capable of describing the behaviour of the shell, are obtained. Both linear static behaviour and longitudinal buckling of the shell are investigated. The approximate solution proposed leads to results that match those of a finite element model and permits to give a description of shells similar to that of beams on elastic soil. With regard to the linear static behaviour of the shell, a "short" and a "long" characterization is proposed and original graphical abaci are obtained with the purpose of facilitating the classification. An extensive study is then performed in order to analyse the buckling of the shells.
Thermal expansion method for lining tantalum alloy tubing with tungsten
NASA Technical Reports Server (NTRS)
Watson, G. K.; Whittenberger, J. D.; Mattson, W. F.
1973-01-01
A differential-thermal expansion method was developed to line T-111 (tantalum - 8 percent tungsten - 2 percent hafnium) tubing with a tungsten diffusion barrier as part of a fuel element fabrication study for a space power nuclear reactor concept. This method uses a steel mandrel, which has a larger thermal expansion than T-111, to force the tungsten against the inside of the T-111 tube. Variables investigated include lining temperature, initial assembly gas size, and tube length. Linear integrity increased with increasing lining temperature and decreasing gap size. The method should have more general applicability where cylinders must be lined with a thin layer of a second material.
A semi-analytic evaluation of the effect of second-order ionosphere term on GPS positioning
NASA Astrophysics Data System (ADS)
Munekane, H.
2005-05-01
We developed a method to evaluate the effect of the second-order ionosphere term on GPS positioning. The method is based on the semi-analytic positioning error simulation method developed by Geiger (1988), which assumes the continuous distribution of the GPS satellites and maps the ranging error to the positioning error using the normal equation. We expanded the method to incorporate the satellite positioning error due to the second-order ionospheric term, which is estimated in a similar manner as the site positioning error, assuming the continuous distribution of the ground tracking stations instead of the continuous satellite distribution in the case of the site positioning error estimation. The method is first applied to simulate the positioning errors on three IGS sites (BAHR, COCO, GALA) which were investigated in Kedar et al. (2002) by analyzing the observed GPS data using the GIPSY software with the correction for second-order ionospheric term. We considered three cases, namely, 1) without satellite positioning error, 2) with satellite positioning error, and 3) with satellite positioning error whose spatial average of each component is corrected for. The third case corresponds to the situation where there are other observations available such as SLR and the center of the mass of the GPS satellite network is corrected properly. For the first case, we found that our method reproduced the positioning errors observed at these stations as well as Kedar et al. (2002). For the second case, however, we found that the positioning error is almost canceled. For the third case, we found that the error is reproduced as well as in the first case, though the spatial distribution of the error is different. These results indicate that 1) the semi-analytic method developed in this paper is accurate enough to simulate the position error due to the second-order ionospheric term, and 2) the satellite positioning error due to the second-order ionospheric term may have significant
VizieR Online Data Catalog: Metal enrichment in semi-analytical model (Cousin+, 2016)
NASA Astrophysics Data System (ADS)
Cousin, M.; Buat, V.; Boissier, S.; Bethermin, M.; Roehlly, Y. Genois M.
2016-04-01
The repository contains outputs from the different models: - m1: Classical (only hot gas) isotropic accretion scenario + Standard Shmidt Kennicutt law - m2: Bimodal accretion (cold streams) + Standard Shmidt Kennicutt law - m3: Classical (only hot gas) isotropic accretion scenario + ad-hoc non-star forming gas reservoir - m4: Bimodal accretion (cold streams) + ad-hoc non-star forming gas reservoir For each model of these models dada are saved in eGalICS_m*.fits file. All these fits-formated files are compatible with the TOPCAT software available on: http://www.star.bris.ac.uk/~mbt/topcat/ We also provide, for each Initial Mass Function available, a set of two fits-formated files associated to the chemodynamical library presented in the paper. For these two files, data are available for all metallicity bins used. - masslossrates_IMF.fits: The instantaneous total ejecta rate associated to a SSP for the six different main-ISM elements. - SNratesIMF.fits: The total SN rate (SNII+SNIa [nb/Gyr]) associated to a SSP, individual contribution of SNII and SNIa are also given. These files are available for four different IMFs: Salpeter+55 (1955ApJ...121..161S), Chabrier+03 (2003PASP..115..763C), Kroupa+93 (2001MNRAS.322..231K) and Scalo+98 (1998ASPC..142..201S. Both ejecta rates and SN rates are computed for the complete list of stellar ages provided in the BC03 spectra library. They are saved in fits-formated files and structured with different extensions corresponding to the different initial stellar metallicity bins. We finally provide the median star formation history, the median gas accretion history and the metal enrichment histories associated to our MW-sisters sample: MWsistershistories.dat If you used data associated to eGalICS semi-analytic model, please cite the following paper: Cousin et al., 2015A&A...575A..33C, "Toward a new modelling of gas flows in a semi-analytical model of galaxy formation and evolution" (3 data files).
A semi-analytical model for predicting water quality from an aquifer storage and recovery system
NASA Astrophysics Data System (ADS)
Sedighi, Ali; Klammler, Harald; Brown, Chris; Hatfield, Kirk
2006-10-01
SummaryAquifer storage and recovery (ASR) involves the injection of freshwater in an aquifer through wells for the purpose of creating a subsurface water supply that is recovered at a later time, often using the same wells, to meet seasonal, long-term, emergency, or other demands. In this paper a numerically efficient semi-analytical model is developed for predicting the quality of water recovered by an ASR system given data on the qualities of ambient and injected waters, hydraulic properties of the aquifer, ambient hydraulic gradient, and system operations. It is assumed the ASR well is installed in a stratified aquifer such that the semi-analytical ASR model (SASRM) simulates the fate of water injected under steady-state conditions into each stratum. It is also assumed that a sharp and mobile interface separates injected water from ambient groundwater such that in situ mixing of water within and between strata does not occur. SASRM assigns particles to define the location the interface in all strata and then follows the migration of these particles under ambient and induced flow conditions. During water recovery, the transient location of the interface is simulated in each stratum and this information is used to quantify the fractions of ambient and injected water extracted at the well-head and the quality of water recovered. To mimic the effects of dispersion, a Latin Hypercube sampling strategy is used to assign hydraulic conductivities according to a predefined probability distribution to the layers of a conceptually stratified aquifer. The volumetric fraction of water received or delivered from any given lithologic unit is assumed proportional to the transmissivity of the stratum normalized to the total aquifer transmissivity interrogated by the ASR well. SARSM is numerically verified against MT3DMS and then calibrated and validated using field data from an ASR system located in Boynton Beach, FL. The field demonstration shows SASRM is capable of predicting
Sussing Merger Trees: The Impact of Halo Merger Trees on Galaxy Properties in a Semi-Analytic Model
NASA Astrophysics Data System (ADS)
Lee, Jaehyun; Yi, Sukyoung
2015-01-01
Halo merger trees are essential backbones of a semi-analytic model for galaxy formation and evolution. Recent studies have pointed out that extracting merger trees from numerical simulations of structure formation using different tree building algorithms can give differing merger histories. To understand the uncertainties developed from these differences in galaxy formation models, we investigate the impact of different halo merger trees on galaxy properties in a semi-analytic model. We find that the galaxy properties in our model differ between trees when using a common parameter set. The star formation history and the number density of galaxies show marked differences between trees with different construction algorithms. The semi-analytic model can be calibrated for each tree to reduce the discrepancies between the z=0 global galaxy properties, at the cost of increasing the differences in the evolutionary histories of galaxies. The calibration is carries out by adjusting key quantities such as the supernova feedback efficiency differing by factor of 2. Such a change affects the regimes where star formation is primarily suppressed by supernovae. Therefore, halo merger trees extracted from a common halo catalogue using different, but reliable, algorithms can result in a difference in the semi-analytic model. Given the uncertainties in galaxy formation physics, however, these differences may not be viewed as significant.
Thermal expansion of composites: Methods and results. [large space structures
NASA Technical Reports Server (NTRS)
Bowles, D. E.; Tenney, D. R.
1981-01-01
The factors controlling the dimensional stability of various components of large space structures were investigated. Cyclic, thermal and mechanical loading were identified as the primary controlling factors of the dimensional stability of cables. For organic matrix composites, such as graphite-epoxy, it was found that these factors include moisture desorption in the space environment, thermal expansion as the structure moves from the sunlight to shadow in its orbit, mechanical loading, and microyielding of the material caused by microcracking of the matrix material. The major focus was placed on the thermal expansion of composites and in particular the development and testing of a method for its measurement.
Experiences using DAKOTA stochastic expansion methods in computational simulations.
Templeton, Jeremy Alan; Ruthruff, Joseph R.
2012-01-01
Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.
Integrand reduction of one-loop scattering amplitudes through Laurent series expansion
NASA Astrophysics Data System (ADS)
Mastrolia, Pierpaolo; Mirabella, Edoardo; Peraro, Tiziano
2012-06-01
We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is known a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.
Semi-analytic modeling and simulation of magnetized liner inertial fusion
NASA Astrophysics Data System (ADS)
McBride, R. D.; Slutz, S. A.; Hansen, S. B.
2013-10-01
Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) pre-heat of the fuel; (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, and internal magnetic pressure and heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) deuterium-deuterium and deuterium-tritium primary fusion reactions; and (9) magnetized alpha-particle heating. We will first show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper. We will then use this model to illustrate the MagLIF parameter space, energetics, and efficiencies, and to show the experimental challenges that we will likely be facing as we begin testing MagLIF using the infrastructure presently available at the Z facility. Finally, we will demonstrate how this scenario could likely change as various facility upgrades are made over the next three to five years and beyond. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Exploring magnetized liner inertial fusion with a semi-analytic model
NASA Astrophysics Data System (ADS)
McBride, R. D.; Slutz, S. A.; Sinars, D. B.; Vesey, R. A.; Gomez, M. R.; Sefkow, A. B.; Hansen, S. B.; Cochrane, K. R.; Schmit, P. F.; Knapp, P. F.; Geissel, M.; Harvey-Thompson, A. J.; Jennings, C. A.; Martin, M. R.; Awe, T. J.; Rovang, D. C.; Lamppa, D. C.; Peterson, K. J.; Rochau, G. A.; Porter, J. L.; Stygar, W. A.; Cuneo, M. E.
2015-11-01
In this presentation, we explore magnetized liner inertial fusion (MagLIF) using a semi-analytic model. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories; (d) highlight the experimental challenges presently facing the MagLIF program (as MagLIF is first being tested using the infrastructure presently available at the Z pulsed-power facility); and (e) demonstrate how these challenges could change as various system upgrades are made to the Z facility over the next three to five years and beyond. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
A Semi-Analytic Study of Feedback Processes and Metallicity Profiles in Disc Galaxies
NASA Astrophysics Data System (ADS)
Sandford, Nathan Ross; Lu, Yu
2016-01-01
The metallicity gradients of disc galaxies contain valuable information about the physics governing their formation and evolution. The observed metallicity profiles have negative gradients that are steeper at high redshifts, indicating an inside-out formation of disc galaxies. We improve on our semi-analytic galaxy formation model (Lu, Mo & Wechsler 2015) by incorporating the radial distribution of metals into the model. With the improved model, we explore how feedback scenarios affect metallicity gradients. The model features 3 feedback scenarios: An Ejective (EJ) model, which includes ejective supernova (SN) feedback, a PRe-Heating (PR) model, which assumes that the intergalactic medium is preheated, preventing it from collapsing onto galaxies, and a Re-Incorporation (RI) model, which also includes strong outflows but allows ejected gas to re-accrete onto the galaxies. We compare the models with observations from Ho et al. (2015) and find that while all models struggle to match the observed metallicity gradient-stellar mass relationship, the PR model predicts metallicity gradients that best match observations. We also find that the RI model predicts a flat gradient because its outflow and re-accretion replenish the disc uniformly with newly accreted enriched gas, erasing the mark of inside-out formation. Our findings suggest feedback plays a key role in shaping the metallicity gradients of disc galaxies and require more detailed theoretical modeling to understand them.
Semi-Analytic Galaxy Evolution (SAGE): Model Calibration and Basic Results
NASA Astrophysics Data System (ADS)
Croton, Darren J.; Stevens, Adam R. H.; Tonini, Chiara; Garel, Thibault; Bernyk, Maksym; Bibiano, Antonio; Hodkinson, Luke; Mutch, Simon J.; Poole, Gregory B.; Shattow, Genevieve M.
2016-02-01
This paper describes a new publicly available codebase for modeling galaxy formation in a cosmological context, the “Semi-Analytic Galaxy Evolution” model, or sage for short.5 sage is a significant update to the 2006 model of Croton et al. and has been rebuilt to be modular and customizable. The model will run on any N-body simulation whose trees are organized in a supported format and contain a minimum set of basic halo properties. In this work, we present the baryonic prescriptions implemented in sage to describe the formation and evolution of galaxies, and their calibration for three N-body simulations: Millennium, Bolshoi, and GiggleZ. Updated physics include the following: gas accretion, ejection due to feedback, and reincorporation via the galactic fountain; a new gas cooling-radio mode active galactic nucleus (AGN) heating cycle; AGN feedback in the quasar mode; a new treatment of gas in satellite galaxies; and galaxy mergers, disruption, and the build-up of intra-cluster stars. Throughout, we show the results of a common default parameterization on each simulation, with a focus on the local galaxy population.
A Bayesian approach to the semi-analytic model of galaxy formation: methodology
NASA Astrophysics Data System (ADS)
Lu, Yu; Mo, H. J.; Weinberg, Martin D.; Katz, Neal
2011-09-01
We believe that a wide range of physical processes conspire to shape the observed galaxy population, but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multidimensional parametrizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference-based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper, we develop a SAM in the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov chain Monte Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterize galaxy formation in the current Λ cold dark matter cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.
Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system
NASA Astrophysics Data System (ADS)
Sedghi, Mohammad M.; Samani, Nozar
2015-09-01
Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.
NASA Astrophysics Data System (ADS)
Stevens, Adam R. H.; Croton, Darren J.; Mutch, Simon J.
2016-06-01
We present the new semi-analytic model of galaxy evolution, DARK SAGE, a heavily modified version of the publicly available SAGE code. The model is designed for detailed evolution of galactic discs. We evolve discs in a series of annuli with fixed specific angular momentum, which allows us to make predictions for the radial and angular-momentum structure of galaxies. Most physical processes, including all channels of star formation and associated feedback, are performed in these annuli. We present the surface density profiles of our model spiral galaxies, both as a function of radius and specific angular momentum, and find the discs naturally build a pseduobulge-like component. Our main results are focussed on predictions relating to the integrated mass-specific angular momentum relation of stellar discs. The model produces a distinct sequence between these properties in remarkable agreement with recent observational literature. We investigate the impact Toomre disc instabilities have on shaping this sequence and find they are crucial for regulating both the mass and spin of discs. Without instabilities, high-mass discs would be systematically deficient in specific angular momentum by a factor of ˜2.5, with increased scatter. Instabilities also appear to drive the direction in which the mass-spin sequence of spiral galaxy discs evolves. With them, we find galaxies of fixed mass have higher specific angular momentum at later epochs.
NASA Astrophysics Data System (ADS)
Stevens, Adam R. H.; Croton, Darren J.; Mutch, Simon J.
2016-09-01
We present the new semi-analytic model of galaxy evolution, DARK SAGE, a heavily modified version of the publicly available SAGE code. The model is designed for detailed evolution of galactic discs. We evolve discs in a series of annuli with fixed specific angular momentum, which allows us to make predictions for the radial and angular-momentum structure of galaxies. Most physical processes, including all channels of star formation and associated feedback, are performed in these annuli. We present the surface density profiles of our model spiral galaxies, both as a function of radius and specific angular momentum, and find that the discs naturally build a pseudo-bulge-like component. Our main results are focused on predictions relating to the integrated mass-specific angular momentum relation of stellar discs. The model produces a distinct sequence between these properties in remarkable agreement with recent observational literature. We investigate the impact Toomre disc instabilities have on shaping this sequence and find they are crucial for regulating both the mass and spin of discs. Without instabilities, high-mass discs would be systematically deficient in specific angular momentum by a factor of ˜2.5, with increased scatter. Instabilities also appear to drive the direction in which the mass-spin sequence of spiral galaxy discs evolves. With them, we find galaxies of fixed mass have higher specific angular momentum at later epochs.
NASA Astrophysics Data System (ADS)
Charbonneau, A. M.; Novakowski, K. S.; Ross, N.
2004-05-01
In fractured rock environments, the process of matrix diffusion strongly influences the persistence of groundwater contamination. Biofilm growth, which occurs naturally in fractured rock, can have a significant effect on the solute transport properties of the matrix, and thus the mobility of contaminants in the system. A semi-analytical model that accounts for the presence of a biofilm has been developed from a solution of the advection-dispersion equation for solute transport in radial coordinates. The model is intended to aid in simulating radial diffusion experiments. It describes solute transport by diffusion from a cylindrical reservoir into a layered medium of finite diameter. The model accounts for linear adsorption and decay in each layer, as well as the periodic addition and/or removal of fluid of known solute concentration from the reservoir. The boundary value problem is solved using the Laplace transform method and Crout's method of LU Decomposition, and numerically inverted using the De Hoog algorithm. According to a sensitivity analysis, compared to the no-biofilm case, diffusion of conservative tracers is most sensitive to the depth of penetration of the biofilm into the matrix, as well as the effective porosity and diffusion coefficient of that penetrated zone. The model developed in this study has been used to interpret the results of diffusion experiments undertaken to investigate mass transport into intact rock samples in the presence of a biofilm and to assign average mass transport parameters to the system. Laboratory data demonstrates that the presence of a biofilm acts to limit diffusive transfer between a discrete fracture and the matrix.
NASA Astrophysics Data System (ADS)
Choudhury, Raja Roy; Choudhury, Arundhati Roy; Ghose, Mrinal Kanti
2013-09-01
To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder-Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder-Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.
Star formation in semi-analytic galaxy formation models with multiphase gas
NASA Astrophysics Data System (ADS)
Somerville, Rachel S.; Popping, Gergö; Trager, Scott C.
2015-11-01
We implement physically motivated recipes for partitioning cold gas into different phases (atomic, molecular, and ionized) in galaxies within semi-analytic models of galaxy formation based on cosmological merger trees. We then model the conversion of molecular gas into stars using empirical recipes motivated by recent observations. We explore the impact of these new recipes on the evolution of fundamental galaxy properties such as stellar mass, star formation rate (SFR), and gas and stellar phase metallicity. We present predictions for stellar mass functions, stellar mass versus SFR relations, and cold gas phase and stellar mass-metallicity relations for our fiducial models, from redshift z ˜ 6 to the present day. In addition we present predictions for the global SFR, mass assembly history, and cosmic enrichment history. We find that the predicted stellar properties of galaxies (stellar mass, SFR, metallicity) are remarkably insensitive to the details of the recipes used for partitioning gas into H I and H2. We see significant sensitivity to the recipes for H2 formation only in very low mass haloes (M_h ≲ 10^{10.5} M_{⊙}), which host galaxies with stellar masses m_* ≲ 10^8 M_{⊙}. The properties of low-mass galaxies are also quite insensitive to the details of the recipe used for converting H2 into stars, while the formation epoch of massive galaxies does depend on this significantly. We argue that this behaviour can be interpreted within the framework of a simple equilibrium model for galaxy evolution, in which the conversion of cold gas into stars is balanced on average by inflows and outflows.
Satellite galaxies in semi-analytic models of galaxy formation with sterile neutrino dark matter
NASA Astrophysics Data System (ADS)
Lovell, Mark R.; Bose, Sownak; Boyarsky, Alexey; Cole, Shaun; Frenk, Carlos S.; Gonzalez-Perez, Violeta; Kennedy, Rachel; Ruchayskiy, Oleg; Smith, Alex
2016-09-01
The sterile neutrino is a viable dark matter candidate that can be produced in the early Universe via non-equilibrium processes, and would therefore possess a highly non-thermal spectrum of primordial velocities. In this paper we analyse the process of structure formation with this class of dark matter particles. To this end we construct primordial dark matter power spectra as a function of the lepton asymmetry, L6, that is present in the primordial plasma and leads to resonant sterile neutrino production. We compare these power spectra with those of thermally produced dark matter particles and show that resonantly produced sterile neutrinos are much colder than their thermal relic counterparts. We also demonstrate that the shape of these power spectra is not determined by the free-streaming scale alone. We then use the power spectra as an input for semi-analytic models of galaxy formation in order to predict the number of luminous satellite galaxies in a Milky Way-like halo. By assuming that the mass of the Milky Way halo must be no more than 2 × 1012 M⊙ (the adopted upper bound based on current astronomical observations) we are able to constrain the value of L6 for Ms ≤ 8 keV. We also show that the range of L6 that is in best agreement with the 3.5 keV line (if produced by decays of 7 keV sterile neutrino) requires that the Milky Way halo has a mass no smaller than 1.5 × 1012 M⊙. Finally, we compare the power spectra obtained by direct integration of the Boltzmann equations for a non-resonantly produced sterile neutrino with the fitting formula of Viel et al. and find that the latter significantly underestimates the power amplitude on scales relevant to satellite galaxies.
Satellite galaxies in semi-analytic models of galaxy formation with sterile neutrino dark matter
NASA Astrophysics Data System (ADS)
Lovell, Mark R.; Bose, Sownak; Boyarsky, Alexey; Cole, Shaun; Frenk, Carlos S.; Gonzalez-Perez, Violeta; Kennedy, Rachel; Ruchayskiy, Oleg; Smith, Alex
2016-06-01
The sterile neutrino is a viable dark matter candidate that can be produced in the early Universe via non-equilibrium processes, and would therefore possess a highly non-thermal spectrum of primordial velocities. In this paper we analyse the process of structure formation with this class of dark matter particles. To this end we construct primordial dark matter power spectra as a function of the lepton asymmetry, L6, that is present in the primordial plasma and leads to resonant sterile neutrino production. We compare these power spectra with those of thermally produced dark matter particles and show that resonantly produced sterile neutrinos are much colder than their thermal relic counterparts. We also demonstrate that the shape of these power spectra are not determined by the free-streaming scale alone. We then use the power spectra as an input for semi-analytic models of galaxy formation in order to predict the number of luminous satellite galaxies in a Milky Way-like halo. By assuming that the mass of the Milky Way halo must be no more than 2 × 1012M⊙ (the adopted upper bound based on current astronomical observations) we are able to constrain the value of L6 for Ms ≤ 8 keV. We also show that the range of L6 that is in best agreement with the 3.5 keV line (if produced by decays of 7 keV sterile neutrino) requires that the Milky Way halo has a mass no smaller than 1.5 × 1012M⊙. Finally, we compare the power spectra obtained by direct integration of the Boltzmann equations for a non-resonantly produced sterile neutrino with the fitting formula of Viel et al. (2005) and find that the latter significantly underestimates the power amplitude on scales relevant to satellite galaxies.
Mesler, Robert A.; Pihlstroem, Ylva M.
2013-09-01
We perform calorimetry on the bright gamma-ray burst GRB 030329 by fitting simultaneously the broadband radio afterglow and the observed afterglow image size to a semi-analytic MHD and afterglow emission model. Our semi-analytic method is valid in both the relativistic and non-relativistic regimes, and incorporates a model of the interstellar scintillation that substantially effects the broadband afterglow below 10 GHz. The model is fitted to archival measurements of the afterglow flux from 1 day to 8.3 yr after the burst. Values for the initial burst parameters are determined and the nature of the circumburst medium is explored. Additionally, direct measurements of the lateral expansion rate of the radio afterglow image size allow us to estimate the initial Lorentz factor of the jet.
Semi-analytic modeling of FWM noise in dispersion-managed DWDM systems with DQPSK/DPSK/OOK channels
NASA Astrophysics Data System (ADS)
Du, Jianxin; Teng, Zhiyu; Shen, Ninghang
2016-01-01
Semi-analytic models are developed to deterministically calculate the variances of degenerate and non-degenerate four-wave-mixing (FWM) noises for dispersion-managed dense wavelength division multiplexing (DWDM) systems with pure and mixed differential quadrature-phase-shift keying (DQPSK)/differential phase-shift keying (DPSK)/on-off-keying (OOK) channels. The semi-analytic models include various important propagation effects for exact numerical results. The novel dispersion map used here for dispersion management is composed of effective-area-enlarged positive dispersion fiber (EE-PDF), dispersion slope and dispersion compensating fiber (SCDCF) and nonzero dispersion-shifted fiber (NZ-DSF). It is numerically validated with the new models that, under the condition that all channels have the same average launch powers and baud rates, the impact of FWM noise for mixed DQPSK/OOK channels are more severe than that for pure DQPSK and mixed DQPSK/DPSK channels. It is also shown that the FWM efficiency is strongly dependent on the peak power of launched optical pulse for a large number of channels, as can be mainly attributed to the quasi-linear evolution of pulse shapes in pump channels induced by cross-phase modulation (XPM). Compared with some commercial optical-fiber transmission simulators, massive time-consuming can be avoided by using the newly derived semi-analytic models when transmission performances of such DWDM systems are numerically optimized and evaluated.
A general moment expansion method for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Ale, Angelique; Kirk, Paul; Stumpf, Michael P. H.
2013-05-01
Moment approximation methods are gaining increasing attention for their use in the approximation of the stochastic kinetics of chemical reaction systems. In this paper we derive a general moment expansion method for any type of propensities and which allows expansion up to any number of moments. For some chemical reaction systems, more than two moments are necessary to describe the dynamic properties of the system, which the linear noise approximation is unable to provide. Moreover, also for systems for which the mean does not have a strong dependence on higher order moments, moment approximation methods give information about higher order moments of the underlying probability distribution. We demonstrate the method using a dimerisation reaction, Michaelis-Menten kinetics and a model of an oscillating p53 system. We show that for the dimerisation reaction and Michaelis-Menten enzyme kinetics system higher order moments have limited influence on the estimation of the mean, while for the p53 system, the solution for the mean can require several moments to converge to the average obtained from many stochastic simulations. We also find that agreement between lower order moments does not guarantee that higher moments will agree. Compared to stochastic simulations, our approach is numerically highly efficient at capturing the behaviour of stochastic systems in terms of the average and higher moments, and we provide expressions for the computational cost for different system sizes and orders of approximation. We show how the moment expansion method can be employed to efficiently quantify parameter sensitivity. Finally we investigate the effects of using too few moments on parameter estimation, and provide guidance on how to estimate if the distribution can be accurately approximated using only a few moments.
A field expansions method for scattering by periodic multilayered media.
Malcolm, Alison; Nicholls, David P
2011-04-01
The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate. PMID:21476635
Damped Lyα absorption systems in semi-analytic models with multiphase gas
NASA Astrophysics Data System (ADS)
Berry, Michael; Somerville, Rachel S.; Haas, Marcel R.; Gawiser, Eric; Maller, Ariyeh; Popping, Gergö; Trager, Scott C.
2014-06-01
We investigate the properties of damped Lyman α absorption systems (DLAs) in semi-analytic models of galaxy formation, including new modelling of the partitioning of cold gas into atomic, molecular, and ionized phases, and a star formation recipe based on the density of molecular gas. We use three approaches for partitioning gas into atomic and molecular constituents: a pressure-based recipe and metallicity-based recipes with fixed and varying ultraviolet (UV) radiation fields. We identify DLAs by adopting an assumed gas density profile for galactic discs and passing lines of sight through our simulations to compute H I column densities. We find that models with `standard' gas radial profiles - computed assuming that the average specific angular momentum of the gas disc is equal to that of the host dark matter halo - fail to reproduce the observed column density distribution of DLAs, regardless of the assumed gas partitioning. These models also fail to reproduce the distribution of velocity widths Δv of low-ionization state metal systems, overproducing low-Δv relative to high-Δv systems. Models with `extended' radial gas profiles - corresponding to gas discs with higher specific angular momentum, or gas in an alternate extended configuration - are able to reproduce quite well the column density distribution of absorbers over the column density range 19 < log NH I < 22.5 in the redshift range 2 < z < 3.5. The model with pressure-based gas partitioning and the metallicity-based recipe with a varying UV radiation field also reproduce the observed line density of DLAs, H I gas density, and Δv distribution at z < 3 well. However all of the models investigated here underproduce DLAs and the H I gas density at z > 3. This may indicate that DLAs at high redshift arise from a different physical phenomenon, such as outflows or filaments. If this is the case, the flatness in the number of DLAs and H I gas density over the redshift interval 0 < z < 5 may be due to a
NASA Astrophysics Data System (ADS)
Lian, Zengju
2016-07-01
We study the electrostatic pair interaction between two nonuniformly like-charged colloidal spheres trapped in an air-water interface. Under the linear Poisson-Boltzmann approximation, a general form of the electrostatic potential for the system is shown in terms of multipole expansions. After combining the translation-rotation transform of the coordinates with the numerical multipoint collection, we give a semi-analytical result of the electrostatic pair interaction between the colloids. The pair interaction changes quantitatively or even qualitatively with different distributions of the surface charges on the particles. Because of the anisotropic distribution of the surface charge and the asymmetric dielectric medium, the dipole moment of the ion cloud associating with the particle orients diagonally to the air-water interface with an angle α. When the angle is large, the colloids interact repulsively, while they attract each other when the angle is small. The attractive colloids may be "Janus-like" charged and be arranged with some specific configurations. Whatever the repulsions or the attractions, they all decay asymptotically ∝1/d3 (d is the center-center distance of the particles) which is consistent with our general acknowledge. The calculation results also provide an insight of the effect of the ion concentration, particle size, and the total charge of the particle on the pair interaction between the particles.
Lian, Zengju
2016-07-01
We study the electrostatic pair interaction between two nonuniformly like-charged colloidal spheres trapped in an air-water interface. Under the linear Poisson-Boltzmann approximation, a general form of the electrostatic potential for the system is shown in terms of multipole expansions. After combining the translation-rotation transform of the coordinates with the numerical multipoint collection, we give a semi-analytical result of the electrostatic pair interaction between the colloids. The pair interaction changes quantitatively or even qualitatively with different distributions of the surface charges on the particles. Because of the anisotropic distribution of the surface charge and the asymmetric dielectric medium, the dipole moment of the ion cloud associating with the particle orients diagonally to the air-water interface with an angle α. When the angle is large, the colloids interact repulsively, while they attract each other when the angle is small. The attractive colloids may be "Janus-like" charged and be arranged with some specific configurations. Whatever the repulsions or the attractions, they all decay asymptotically ∝1/d(3) (d is the center-center distance of the particles) which is consistent with our general acknowledge. The calculation results also provide an insight of the effect of the ion concentration, particle size, and the total charge of the particle on the pair interaction between the particles. PMID:27394119
Spittel, Ron; Bartelt, Harmut; Schmidt, Markus A
2014-05-19
We present a highly efficient semi-analytical and straightforward-to-implement model for the determination of plasmonic band edges of metallic nanowire arrays inside photonic crystal fibers. The model relies on the approximation of the hexagonal unit cell by a circle and using particular boundary conditions, showing an accurate agreement with finite element simulations. The model reduces simulation time by a factor of 100, thus representing an efficient tool for structure design. It further allows the calculation of all relevant modes in the system by slight changes of the entries in a 4 × 4 matrix. PMID:24921296
Chen, Jun; D'Sa, Eurico; Cui, Tingwei; Zhang, Xunhua
2013-06-01
A simple semi-analytical model to estimate total suspended sediment matter (3S) was established for estimating TSM concentrations in Changjiang River Estuary. The results indicate that 3S model with near-infrared wavelengths provide good estimates of TSM concentrations in the study region. Furthermore, the applicability of 3S model was evaluated using an independent data set taken from Oujiang river estuary during September 2012. The results indicate that providing an available atmospheric correction scheme for satellite imagery, the 3S model could be used for quantitative monitoring of TSM concentration in coastal waters, even though local bio-optical information is still needed to reinitialize the model. PMID:23736555
Razzaghi, D; Hajiesmaeilbaigi, F; Ruzbehani, M
2012-08-31
Possible effects of amplified spontaneous emission on output pulse characteristics of a Q-switched laser are discussed within the framework of a semi-analytical approach. It is shown that output energy decreases almost exponentially with average path length of the spontaneously emitted photons which in turn depends on geometrical specification and active medium properties as well as on optical finishing of the surfaces (for solid-state lasers). Optimal coupling dependence on the average path length is also investigated and shown to increase with average path length increment. (control of laser radiation parameters)
NASA Astrophysics Data System (ADS)
Jones, S.; Hunt, H.
2009-08-01
Ground vibration due to underground railways is a significant source of disturbance for people living or working near the subways. The numerical models used to predict vibration levels have inherent uncertainty which must be understood to give confidence in the predictions. A semi-analytical approach is developed herein to investigate the effect of soil layering on the surface vibration of a halfspace where both soil properties and layer inclination angles are varied. The study suggests that both material properties and inclination angle of the layers have significant effect (± 10dB) on the surface vibration response.
A collisionless plasma thruster plume expansion model
NASA Astrophysics Data System (ADS)
Merino, Mario; Cichocki, Filippo; Ahedo, Eduardo
2015-06-01
A two-fluid model of the unmagnetized, collisionless far region expansion of the plasma plume for gridded ion thrusters and Hall effect thrusters is presented. The model is integrated into two semi-analytical solutions valid in the hypersonic case. These solutions are discussed and compared against the results from the (exact) method of characteristics; the relative errors in density and velocity increase slowly axially and radially and are of the order of 10-2-10-3 in the cases studied. The plasma density, ion flux and ambipolar electric field are investigated. A sensitivity analysis of the problem parameters and initial conditions is carried out in order to characterize the far plume divergence angle in the range of interest for space electric propulsion. A qualitative discussion of the physics of the secondary plasma plume is also provided.
NASA Astrophysics Data System (ADS)
Sahoo, S.; Saha Ray, S.
2016-04-01
In the present paper, we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics; namely time fractional modified KdV equation by using (G‧ / G)-expansion method and improved (G‧ / G)-expansion method. As a result, new types of exact analytical solutions are obtained.
NASA Astrophysics Data System (ADS)
Liang, Xu; Wang, Zhenyu; Wang, Lizhong; Liu, Guohua
2014-06-01
The three-dimensional transient analysis of functionally graded annular plates with arbitrary boundary conditions is carried out in this paper. The material properties of the FGM plate are assumed to vary smoothly in an exponential law along the thickness direction. The plate is assumed to rest on a two parameter viscoelastic foundation. A semi-analytical method, which integrates the state space method (SSM), Laplace transform and its inversion, as well as the one-dimensional differential quadrature method (DQM), is proposed to obtain the transient response of the plate. The state space method is used to obtain the analytical solution in the thickness direction. The differential quadrature method is employed to approximate the solution in the radial direction. The Laplace transform and the numerical inversion are used to obtain the solution in time domain. Numerical results show a good agreement between the response histories obtained by the present method and finite element method. The effects of the boundary conditions at the edges, the material graded index, the Winkler and shearing layer elastic coefficients, and the damping coefficient are studied. Numerical examples show that the peak response decreases as the material graded index, the Winkler and shearing layer elastic coefficients, and the damping coefficient increase. The results obtained in this paper can serve as benchmark data in further research.
A Multipole Expansion Method for Analyzing Lightning Field Changes
NASA Technical Reports Server (NTRS)
Koshak, William J.; Krider, E. Philip; Murphy, Martin J.
1998-01-01
Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q-model) or a point dipole (the P-model). The Q-model has 4 unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P-model has 6 unknown parameters and describes many intracloud (IC) discharges. In this paper, we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a 3-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer simulated sources and on natural lightning at the NASA Kennedy Space Center and USAF Eastern Range.
A Multipole Expansion Method for Analyzing Lightning Field Changes
NASA Technical Reports Server (NTRS)
Koshak, William J.; Krider, E. Philip; Murphy, Martin J.
1999-01-01
Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.
NASA Astrophysics Data System (ADS)
Atteia, O.; Höhener, P.
2012-09-01
The aim of this work was to extend and to validate the flux tube-mixed instantaneous and kinetics superposition sequence approach (FT-MIKSS) to reaction chains of degrading species. Existing analytical solutions for the reactive transport of chains of decaying solutes were embedded in the flux-tube approach in order to conceive a semi-analytical model that allows fast parameter fitting. The model was applied for chloroethenes undergoing reductive dechlorination and oxidation in homogeneous and heterogeneous aquifers with sorption. The results from the semi-analytical model were compared to results from three numerical models (RT3D, PH3TD, PHAST). All models were validated in a homogeneous domain with an existing analytical solution. In heterogeneous domains, we found significant differences between the four models. FT-MIKSS gave intermediate results for all modelled cases. Results were obtained almost instantaneously, whereas other models had calculation times of up to several hours. Chloroethene plumes and redox conditions at the Plattsburgh field site were realistically modelled by FT-MIKSS, although results differed somewhat from those of PHT3D and PHAST. It is concluded that it may be tedious to obtain correct modelling results in heterogeneous media with degradation chain reactions and that the comparison of two different models may be useful. FT-MIKSS is a valuable tool for fast parameter fitting at field sites and should be used in the preparation of longer model runs with other numerical models.
NASA Astrophysics Data System (ADS)
Pozdniakov, Sergey P.; Wang, Ping; Lekhov, Mikhail V.
2016-09-01
The well-known Hvorslev (1951) formula was developed to estimate soil permeability using single-well slug tests and has been widely applied to determine riverbed hydraulic conductivity using in situ standpipe permeameter tests. Here, we further develop a general solution of the Hvorslev (1951) formula that accounts for flow in a bounded medium and assumes that the bottom of the river is a prescribed head boundary. The superposition of real and imaginary disk sources is used to obtain a semi-analytical expression of the total hydraulic resistance of the flow in and out of the pipe. As a result, we obtained a simple semi-analytical expression for the resistance, which represents a generalization of the Hvorslev (1951). The obtained expression is benchmarked against a finite-element numerical model of 2-D flow (in r-z coordinates) in an anisotropic medium. The results exhibit good agreement between the simulated and estimated riverbed hydraulic conductivity values. Furthermore, a set of simulations for layered, stochastically heterogeneous riverbed sediments was conducted and processed using the proposed expression to demonstrate the potential associated with measuring vertical heterogeneity in bottom sediments using a series of standpipe permeameter tests with different lengths of pipe inserted into the riverbed sediments.
A semi-analytic approach to the self-induced motion of vortex sheets
NASA Technical Reports Server (NTRS)
Schwartz, L. W.
1981-01-01
The rolling-up of the trailing vortex sheet produced by a wing of finite span is calculated as a series expansion in time. For a vorticity distribution corresponding to a wing with cusped tips, the shape of the sheet is found by summing the series using Pade approximants. The sheet remains analytic for some time but ultimately develops an exponential spiral at the tips. The centroid of vorticity is conserved to high accuracy.
A semi-analytic approach to the self induced motion of vortex sheets
NASA Technical Reports Server (NTRS)
Schwartz, L. W.
1980-01-01
The rolling up of the trailing vortex sheet produced by a wing of finite span was calculated as a series expansion in time. For a vorticity distribution corresponding to a wing with cusped tips, the shape of the sheet was found by summing the series using Pade approximants. The sheet remains analytic for some time but ultimately develops an exponential spiral at the tips. The centroid of vorticity was conserved to high accuracy.
Smit, Hans Harmen; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita
2013-01-01
Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance. PMID:24039700
Harmen Smit, Hans; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita
2013-01-01
Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance. PMID:24039700
A new semi-analytical treatment of the effect of supernovae on ULIRG spectral energy distributions
NASA Astrophysics Data System (ADS)
Jenner, Clare Elizabeth
This work presents a method for generating synthetic spectra of Ultra-Luminous Infrared Galaxies (ULIRGS) using AGN, HII region and supernovae source functions. The AGN element represents the far-infrared contribution to the ULIRG spectrum from an energetic central engine. It is modelled using a quasar source embedded in an axi-symmetric dusty torus. The radiative transfer of flux (RT) is then simulated and the AGN emergent spectral energy distributions (SEDs) generated. The HII region solution is then developed. A stellar evolutionary synthesis code is used to generate instantaneous burst (ISB) source functions which decay in time. The evolution of the gas and dust density in a spherically-symmetric, dense GMC, under the influence of a time-dependent ionizing source flux, is derived. Having irradiated the dust distribution with the source cluster SED, the RT is calculated and the HII region SEDs obtained. The impact of supernovae energy on a GMC already ionized by stellar flux is then considered. Using the standard pressure-driven expansion model of e.g., Weaver et al. (1977) the radial evolution of a superbubble expanding under the influence of a continuous super novae energy function is derived. The superbubble is modelled in both an adiabatic rapid expansion phase and in an isothermal momentum-conserving phase. As the superbubble expands, upstream gas is swept into a thin shell trapped on its surface and the gas density enhancement is modelled using simple shock physics. Having generated expressions for the evolution of the shell gas temperature, it is linked to the dust density via a temperature dependent condensation factor. Finally expressions are developed to quantify the evolution of the optical depth along a line of sight. It is found that the star formation efficiency (SFE) has a profound effect on the radial evolution of the optical depth distributions in GMCs generating marked differences in behaviour between and high and low SFEs. Low SFE models have
Conservation laws and a new expansion method for sixth order Boussinesq equation
NASA Astrophysics Data System (ADS)
Yokuş, Asıf; Kaya, Doǧan
2015-09-01
In this study, we analyze the conservation laws of a sixth order Boussinesq equation by using variational derivative. We get sixth order Boussinesq equation's traveling wave solutions with (1/G) -expansion method which we constitute newly by being inspired with (G/G) -expansion method which is suggested in [1]. We investigate conservation laws of the analytical solutions which we obtained by the new constructed method. The analytical solution's conductions which we get according to new expansion method are given graphically.
Globus, Noemie; Levinson, Amir
2014-11-20
We construct a semi-analytic model for magnetohydrodynamic (MHD) flows in Kerr geometry that incorporates energy loading via neutrino annihilation on magnetic field lines threading the horizon. We compute the structure of the double-flow established in the magnetisphere for a wide range of energy injection rates and identify the different operation regimes. At low injection rates, the outflow is powered by the spinning black hole via the Blandford-Znajek mechanism, whereas at high injection rates, it is driven by the pressure of the plasma deposited on magnetic field lines. In the intermediate regime, both processes contribute to the outflow formation. The parameter that quantifies the load is the ratio of the net power injected below the stagnation radius and the maximum power that can be extracted magnetically from the black hole.
Mahnama, Ali; Ghorbaniasl, Ghader; Allaei, S Mehdi Vaez; Nourbakhsh, Ahmad
2014-10-01
Reducing size of the particles to the nanoscale range gives them new physicochemical properties. Several experiments have shown cytotoxic effects for different kinds of engineered nanoparticles (ENP). In-vitro cell culture assays are widely utilized by researchers to evaluate cytotoxic effects of the ENPs. The present paper deals with the "In vitro Sedimentation, Diffusion and Dosimetry (ISDD)" model. This mathematical model uses an advection-diffusion equation with specific assumptions and coefficients to estimate the dose of the particles delivered to the cells monolayer in the culture medium. In the present work, utilizing the generalized integral transform technique (GITT), a semi-analytical solution is developed for the ISDD model. The parameters affecting the ISDD predictions are integrated into two dimensionless numbers, Pe and τ. The Pe number shows the ratio of the convective to the diffusive mass transport rates and τ is a dimensionless time parameter. The quality of the results for an extensive range of Pe and τ numbers is surveyed through application of the developed formula to two series of test cases. A comparison of the results with those obtained from numerical methods shows deviations in the numerical results at high Pe numbers. Applying the developed formula, ISDD predictions for a wide practical range of Pe and τ numbers are calculated and plotted in two- and three-dimensional plots. The curves and formula obtained in this study facilitate the achievement of ISDD predictions with higher accuracies and capabilities for verification of the results. PMID:25064483
Solution of a nonlinear time-delay model in biology via semi-analytical approaches
NASA Astrophysics Data System (ADS)
Dehghan, Mehdi; Salehi, Rezvan
2010-07-01
The delay logistic equations have been extensively used as models in biology and other sciences, with particular emphasis on population dynamics. In this work, the variational iteration and Adomian decomposition methods are applied to solve the delay logistic equation. The variational iteration method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. On the other hand, the Adomian decomposition method approximates the solution as an infinite series and usually converges to the accurate solution. Moreover, these techniques reduce the volume of calculations because they have no need of discretization of the variables, linearization or small perturbations. Illustrative examples are included to demonstrate the validity and applicability of the presented methods.
An Economical Semi-Analytical Orbit Theory for Retarded Satellite Motion About an Oblate Planet
NASA Technical Reports Server (NTRS)
Gordon, R. A.
1980-01-01
Brouwer and Brouwer-Lyddanes' use of the Von Zeipel-Delaunay method is employed to develop an efficient analytical orbit theory suitable for microcomputers. A succinctly simple pseudo-phenomenologically conceptualized algorithm is introduced which accurately and economically synthesizes modeling of drag effects. The method epitomizes and manifests effortless efficient computer mechanization. Simulated trajectory data is employed to illustrate the theory's ability to accurately accommodate oblateness and drag effects for microcomputer ground based or onboard predicted orbital representation. Real tracking data is used to demonstrate that the theory's orbit determination and orbit prediction capabilities are favorably adaptable to and are comparable with results obtained utilizing complex definitive Cowell method solutions on satellites experiencing significant drag effects.
Lee, Plato C.; Parks, Eric K.; Moran, Brian J
2003-12-31
An innovative (and yet simple) dosimetric model is proposed that provides a semi-analytical solution to the total activity-volume relationship in ultrasound-guided transperineal prostate implant. This dosimetric model is based on 4 simple assumptions. First, the prostate target volume is approximated as a sphere. Second, the urethra is presumed to transverse through the center of the prostate target volume. Third, peripheral loading is applied as the seed-loading technique. Fourth, as the major innovation of the proposed model, the radial dose function of the Iodine-125 {sup 125}I seed is forced to fit a simple power function of the distance r. Pursuant to the third assumption, the peripherally-loaded seeds also define a spherical volume defined as the loading volume w. Also pursuant to the fourth assumption, the radial dose function is expressed as 1.139*r{sup -0.474} for r = 1.5 to 2.5 cm. Thereafter, a simple analytical power-law equation, A = 1.630* w{sup 0.825}, for the relationship between the total activity A in mCi and the loading volume w in cc is derived for {sup 125}I monotherapy. Isodose plans for loading volumes corresponding to r = 1.5, 1.8, 2.2, and 2.5 cm were performed. The maximal isodose coverage volume {sub max}V100 was calculated for each case and was found to be on the average 65% larger than the loading volume w. Matching prostate target volume V to the loading volume w therefore yields a generous implant (with a margin of approximately 3.3 mm). Conversely, matching the prostate target volume V to the {sub max}V100 yields a tight implant (with 0.0 mm or no margin). Matching the prostate target volume V to a midpoint between the loading volume w and {sub max}V100 yields a moderate implant (with approximately 1- to 2-mm margin). Three individual equations are derived for each type of implants: A = 1.630* V{sup 0.825}, A = 1.288* V{sup 0.825}, or A = 1.078 V{sup 0.825} for generous, tight, or moderate implants, respectively. Patient data at the
NASA Astrophysics Data System (ADS)
Jia, Pin; Cheng, Linsong; Huang, Shijun; Wu, Yonghui
2016-06-01
This paper presents a semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete fracture model. The small-scale fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the fracture network characteristics while keeping the computational work manageable. For example, the large-scale fracture network may have complex geometry and varying conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in fractured reservoir with multi-scale fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale fracture network linear flow, bilinear flow, small-scale fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale fracture network behaves as if it only drains in the small-scale fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale fracture network linear flow are predominantly determined by the dimensionless large-scale fracture conductivity. And low dimensionless fracture conductivity will generate large pressure drops in the large-scale fractures surrounding the wellbore. With
NASA Astrophysics Data System (ADS)
Pandey, P.; De Ridder, K.; van Lipzig, N.
2009-04-01
Clouds play a very important role in the Earth's climate system, as they form an intermediate layer between Sun and the Earth. Satellite remote sensing systems are the only means to provide information about clouds on large scales. The geostationary satellite, Meteosat Second Generation (MSG) has onboard an imaging radiometer, the Spinning Enhanced Visible and Infrared Imager (SEVIRI). SEVIRI is a 12 channel imager, with 11 channels observing the earth's full disk with a temporal resolution of 15 min and spatial resolution of 3 km at nadir, and a high resolution visible (HRV) channel. The visible channels (0.6 µm and 0.81 µm) and near infrared channel (1.6µm) of SEVIRI are being used to retrieve the cloud optical thickness (COT). The study domain is over Europe covering the region between 35°N - 70°N and 10°W - 30°E. SEVIRI level 1.5 images over this domain are being acquired from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) archive. The processing of this imagery, involves a number of steps before estimating the COT. The steps involved in pre-processing are as follows. First, the digital count number is acquired from the imagery. Image geo-coding is performed in order to relate the pixel positions to the corresponding longitude and latitude. Solar zenith angle is determined as a function of latitude and time. The radiometric conversion is done using the values of offsets and slopes of each band. The values of radiance obtained are then used to calculate the reflectance for channels in the visible spectrum using the information of solar zenith angle. An attempt is made to estimate the COT from the observed radiances. A semi analytical algorithm [Kokhanovsky et al., 2003] is implemented for the estimation of cloud optical thickness from the visible spectrum of light intensity reflected from clouds. The asymptotical solution of the radiative transfer equation, for clouds with large optical thickness, is the basis of
Improved semi-analytic algorithms for finding the flux from a cylindrical source
Wallace, O.J.
1992-12-31
Hand calculation methods for radiation shielding problems continue to be useful for scoping studies, for checking the results from sophisticated computer simulations and in teaching shielding personnel. This paper presents two algorithms which give improved results for hand calculations of the flux at a lateral detector point from a cylindrical source with an intervening slab shield parallel to the cylinder axis. The first algorithm improves the accuracy of the approximate flux flux formula of Ono and Tsuro so that results are always conservative and within a factor of two. The second algorithm uses the first algorithm and the principle of superposition of sources to give a new approximate method for finding the flux at a detector point outside the axial and radial extensions of a cylindrical source. A table of error ratios for this algorithm versus an exact calculation for a wide range of geometry parameters is also given. There is no other hand calculation method for the geometric configuration of the second algorithm available in the literature.
This presentation will provide a conceptual preview of an Area of Review (AoR) tool being developed by EPA’s Office of Research and Development that applies analytic and semi-analytical mathematical solutions to elucidate potential risks associated with geologic sequestration of ...
Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres
NASA Astrophysics Data System (ADS)
Jafari Fesharaki, J.; Loghman, A.; Yazdipoor, M.; Golabi, S.
2014-02-01
By using a method of successive elastic solution, the time-dependent creep behavior of a functionally graded hollow sphere under thermomechanical loads has been investigated. Based on volume percentage, the mechanical and thermal properties of material, except for the Poisson's ratio, are assumed to be radially dependent. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are temperature-, stress- and time-dependent. Using the Prandtl-Reuss relations and Sherby's law, histories of stresses and strains are presented from their initial elastic values at zero time up to 30 years after loading. The results show that the creep stresses and strains change with time and material inhomogeneity has influence on thermomechanical creep behavior. The aim of this work was to understand the effect of creep behavior on a functionally graded hollow sphere subjected to thermomechanical load.
Semi-analytic approach to analyze single well tracer tests TR-44
Antunez, E.U.
1984-08-01
Residual oil saturation is one of the most important parameters to be considered when analyzing a prospective field for enhanced oil recovery. Traditionally, residual oil saturation has been estimated from cores or well logs. These methods have a small radius of investigation, evaluating saturations in a region close to the wellbore. This region is often affected by injection or production operations. Single well tracer tests have proven to be a better alternative to estimate residual oil saturation since they cover a substantially larger volume of the reservoir, and thus measure a more representative residual oil saturation of the target formation. The method consists of the injection of a reactive tracer that is soluble in oil and water. This tracer slowly hydrolyzes forming a secondary tracer as a product of an irreversible chemical reaction. After injection, the well is shut in to allow the formation of a detectable amount of secondary tracer, which is soluble only in water. When the well is open to production, each tracer arrives to the well at different times. From the separation between the concentration peaks, residual oil saturation is estimated. However, the determination of the residual oil saturation through the analysis of single well tracer test production data, in the past, has required: 1) the use of finite difference simulators, 2) five fitting parameters and 3) considerable man-computer interaction time. In addition finite difference simulators give results that are affected by numerical dispersion. This, and the fitting parameters, add uncertainty to the uniqueness of the solution. In this work, a new approach is presented. The test is analyzed. 28 references, 70 figures, 7 tables.
NASA Astrophysics Data System (ADS)
Lapucci, Chiara; Ampolo Rella, Marina; Brandini, Carlo; Ganzin, Nicolas; Gozzini, Bernardo; Maselli, Fabio; Massi, Luca; Nuccio, Caterina; Ortolani, Alberto; Trees, Charles
2012-01-01
The estimation of chlorophyll concentration in marine waters is fundamental for a number of scientific and practical purposes. Standard ocean color algorithms applicable to moderate resolution imaging spectroradiometer (MODIS) imagery, such as OC3M and MedOC3, are known to overestimate chlorophyll concentration ([CHL]) in Mediterranean oligotrophic waters. The performances of these algorithms are currently evaluated together with two relatively new algorithms, OC5 and SAM_LT, which make use of more of the spectral information of MODIS data. This evaluation exercise has been carried out using in situ data collected in the North Tyrrhenian and Ligurian Seas during three recent oceanographic campaigns. The four algorithms perform differently in Case 1 and Case 2 waters defined following global and local classification criteria. In particular, the mentioned [CHL] overestimation of OC3M and MedOC3 is not evident for typical Case 1 waters; this overestimation is instead significant in intermediate and Case 2 waters. OC5 and SAM_LT are less sensitive to this problem, and are generally more accurate in Case 2 waters. These results are finally interpreted and discussed in light of a possible operational utilization of the [CHL] estimation methods.
Semi-analytical emission model for diffusion flame, rich/lean and premixed lean combustors
NASA Astrophysics Data System (ADS)
Rizk, N. K.; Mongia, H. C.
1995-04-01
To enhance gas turbine combustor performance and emissions characteristics, better design methods need to be developed. In the present investigation, an emission model that simulates a detailed chemical kinetic scheme has been developed to provide the rate of reactions of the parent fuel, an intermediate hydrocarbon compound, CO, and H2. The intermediate fuel has variable carbon and hydrogen contents depending on operating conditions, that were selected in the development effort to simulate actual operation of rich/lean, diffusion flame, and lean combustor concepts. The developed reaction rate expressions address also the limited reaction rates that may occur in the near-wall regions of the combustor due to the admittance of radial air jets and cooling air in these regions. The validation effort included the application of the developed model to a combustor simulated by a multiple-reactor arrangement. The results indicate the accurate duplication of the calculations obtained from the detailed kinetic scheme using the developed model. This illustrates the great potential of using such a unified approach to guide the design of various types of combustor to meet the more stringent emissions and performance requirements of next-generation gas turbine engines.
A semi-analytical study on helical springs made of shape memory polymer
NASA Astrophysics Data System (ADS)
Baghani, M.; Naghdabadi, R.; Arghavani, J.
2012-04-01
In this paper, the responses of shape memory polymer (SMP) helical springs under axial force are studied both analytically and numerically. In the analytical solution, we first derive the response of a cylindrical tube under torsional loadings. This solution can be used for helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of the mean coil radius to the cross sectional radius (spring index) and also small pitch angles. Making use of this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with circular cross section. The 3D phenomenological constitutive model recently proposed for SMPs is also reduced to the 1D shear case. Thus, an analytical solution for the torsional response of SMP tubes in a full cycle of stress-free strain recovery is derived. In addition, the curvature effect is added to the formulation and the SMP helical spring is analyzed using the exact solution presented for torsion of curved SMP tubes. In this modified solution, the effect of the direct shear force is also considered. In the numerical analysis, the 3D constitutive equations are implemented in a finite element program and a full cycle of stress-free strain recovery of an SMP (extension or compression) helical spring is simulated. Analytical and numerical results are compared and it is shown that the analytical solution gives accurate stress distributions in the cross section of the helical SMP spring besides the global load-deflection response. Some case studies are presented to show the validity of the presented analytical method.
NASA Astrophysics Data System (ADS)
Jumper, Kevin; Fisher, Robert
2012-03-01
Type Ia supernovae are astronomical events in which a white dwarf, the cold remnant of a star that has exhausted its hydrogen fuel, detonates and briefly produces an explosion brighter than most galaxies. Many researchers think that they could occur as the white dwarf approaches a critical mass of 1.4 solar masses by accreting matter from a companion main sequence star, a scenario that is referred to as the single-degenerate channel. Assuming such a progenitor, we construct a semi-analytic model of the propagation of a flame bubble ignited at a single off-center point within the white dwarf. The bubble then rises under the influences of buoyancy and drag, burning the surrounding fuel material in a process called deflagration. We contrast the behavior of the deflagration phase in the presence of a physically high Reynolds number regime with the low Reynolds number regimes inherent to three-dimensional simulations, which are a consequence of numerical viscosity. Our work may help validate three-dimensional deflagration results over a range of initial conditions.
Soares dos Santos, Marco P.; Ferreira, Jorge A. F.; Simões, José A. O.; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P.
2016-01-01
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters. PMID:26725842
NASA Astrophysics Data System (ADS)
Dorval, Vincent; Leymarie, Nicolas; Chatillon, Sylvain
2016-02-01
Semi-analytical models are often used for computationally efficient ultrasonic simulations. They typically apply plane-wave or quasi plane-wave approximations to the ultrasonic fields at the location of flaws in order to calculate diffraction coefficients. In favorable cases, the plane-wave approximations used for echo computations in the Civa software yield satisfying results. However, it can lead to inaccuracies in unfavorable cases, such as for wide probe apertures, outside of the focal region, or for beam-splitting or distortion due to irregular geometries. This communication presents an improved model, implemented in a development version of the software. The new approach describes the ultrasonic field as a sum of rays and applies the plane-wave approximation to each ray instead of the entire field. It significantly improves the accuracy of echo computations. However, it implies that the diffraction is calculated for each pair of incident and diffracted rays instead of being calculated only once: a specific algorithm has been developed in order to avoid a significant increase in computation times. Benefits of the new approach are illustrated by comparing its results and computation times to those of the former plane-wave model in several cases of interest. They are also compared to those of a coupled finite element model (Civa-Athena).
NASA Astrophysics Data System (ADS)
Soares Dos Santos, Marco P.; Ferreira, Jorge A. F.; Simões, José A. O.; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P.
2016-01-01
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters.
Soares Dos Santos, Marco P; Ferreira, Jorge A F; Simões, José A O; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P
2016-01-01
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters. PMID:26725842
NASA Astrophysics Data System (ADS)
Marin, Esteban B.; Tran, Hieu V.; Kobyakov, Andrey
2016-07-01
Three-dimensional finite element analysis of physical-contact, multi-fiber optical connector was used to characterize fiber-to-fiber contact and support the development and validation of a semi-analytical model (SAM) for the contact force. This contact behavior is determined by the elastic deformation of the system components (ferrule, fibers, and bonding adhesive) and the classical Hertzian contact at the fiber tips - effects that ultimately define the axial compliance of the system. Two 3-D finite element models for a 12-fiber connector are constructed to study the contact of two connectors, and the specific numerical simulations are carried out to generate input data to SAM, confirm the main assumptions made in its development, and numerically validate the predictions for the contact force. These simulations mainly consider non-uniform fiber height profiles and different end-face fiber tip geometries characterized by their radius of curvature. The numerically validated SAM is then used to study some performance aspects of multi-fiber connectors as related to the required contact force, namely, finding fiber height profiles that require minimum contact force and evaluating the throughput of polishing processes assuming a target contact force. Predictions are supported by Monte Carlo simulations and associated with current profile geometry metrics.
Analysis of loss mechanisms in InGaN solar cells using a semi-analytical model
NASA Astrophysics Data System (ADS)
Huang, Xuanqi; Fu, Houqiang; Chen, Hong; Lu, Zhijian; Ding, Ding; Zhao, Yuji
2016-06-01
InGaN semiconductors are promising candidates for high-efficiency next-generation thin film solar cells. In this work, we study the photovoltaic performance of single-junction and two-junction InGaN solar cells using a semi-analytical model. We analyze the major loss mechanisms in InGaN solar cell including transmission loss, thermalization loss, spatial relaxation loss, and recombination loss. We find that transmission loss plays a major role for InGaN solar cells due to the large bandgaps of III-nitride materials. Among the recombination losses, Shockley-Read-Hall recombination loss is the dominant process. Compared to other III-V photovoltaic materials, we discovered that the emittance of InGaN solar cells is strongly impacted by Urbach tail energy. For two- and multi-junction InGaN solar cells, we discover that the current matching condition results in a limited range of top-junction bandgaps. This theoretical work provides detailed guidance for the design of high-performance InGaN solar cells.
NASA Astrophysics Data System (ADS)
Shattow, Genevieve M.; Croton, Darren J.; Bibiano, Antonio
2015-07-01
With the installation of the Cosmic Origins Spectrograph on the Hubble Space Telescope, measurements of the metal content of the low-redshift intergalactic medium (IGM) are now available. Using a new grid-based model for diffuse gas coupled to the SAGE semi-analytic model of galaxy formation, we examine the impact of supernova feedback on the pollution of the IGM. We consider different assumptions for the reheating and ejection of gas by supernovae and their dependence on galaxy circular velocity and gas surface density. Where metals are present, we find the most likely metallicity to be -1.5
NASA Astrophysics Data System (ADS)
LaForce, T.; Mijić, A.; Ennis-King, J.; Paterson, L.
2014-11-01
In this work semi-analytical solutions for saturation, temperature, pressure and in situ reservoir stress are found for immiscible nonisothermal injection into a radial porous medium. A model for advection-dominated, nonisothermal, two-phase flow from a previous work is used to estimate the reservoir pressure and stress that result from injection of cold CO2. Flow is assumed to be one-dimensional and purely advective, while temperature has radial advection in the reservoir and transverse diffusion into the surrounding media. A simplified thermal solution is developed to allow for easier analysis of the reservoir stress. Two pressure models are presented, one which requires numerical integration of the pressure in the two-phase region, and one which is fully analytical, but simplifies the pressure profile. Two models are used to calculate reservoir stress, one which uses the full pressure and temperature profiles and must be numerically integrated, and one which uses the simplified models and has a closed-form analytical solution. The resulting radial and tangential (hoop) stress profiles in the reservoir are compared and it is shown that the simplified model is adequate for estimating the reservoir stresses. The impact of outer boundary conditions on reservoir pressure and stresses is also explored.
NASA Astrophysics Data System (ADS)
Halloran, Landon J. S.; Roshan, Hamid; Rau, Gabriel C.; Andersen, Martin S.
2016-03-01
A novel semi-analytical model for the calculation of water saturation levels in the near subsurface using passive temperature measurements is derived. The amplitude and phase of dominant natural diel temperature variations are exploited, although the solution is general so that a cyclical temperature signal of any period could be used. The model is based on the first-principles advection-conduction-dispersion equation, which is fully general for porous media. It requires a single independent soil moisture estimate, but directly considers the spatially variable saturation dependency of thermal conductivity which has been avoided in previous studies. An established empirical model for the thermal conductivity of variably saturated porous media is incorporated and two solutions for saturation are derived. Using data from numerical models, a spatially sequential implementation of one of these solutions is shown to predict the vertical saturation profile to within 2% for a hydraulically stable case and to within the saturation range observed over a single day for percolation rates up to 10 cm/day. The developed model and methodology can aid in the analysis of archived temperature data from the vadose zone and will serve as a powerful tool in future heat-tracing experiments in variably saturated conditions.
A semi-analytic power balance model for low (L) to high (H) mode transition power threshold
Singh, R.; Jhang, Hogun; Kaw, P. K.; Diamond, P. H.; Nordman, H.; Bourdelle, C.
2014-06-15
We present a semi-analytic model for low (L) to high (H) mode transition power threshold (P{sub th}). Two main assumptions are made in our study. First, high poloidal mode number drift resistive ballooning modes (high-m DRBM) are assumed to be the dominant turbulence driver in a narrow edge region near to last closed flux surface. Second, the pre-transition edge profile and turbulent diffusivity at the narrow edge region pertain to turbulent equipartition. An edge power balance relation is derived by calculating the dissipated power flux through both turbulent conduction and convection, and radiation in the edge region. P{sub th} is obtained by imposing the turbulence quench rule due to sheared E × B rotation. Evaluation of P{sub th} shows a good agreement with experimental results in existing machines. Increase of P{sub th} at low density (i.e., the existence of roll-over density in P{sub th} vs. density) is shown to originate from the longer scale length of the density profile than that of the temperature profile.
Razani, A.; Shahinpoor, M. . Dept. of Mechanical Engineering); Hingorani-Norenberg, S.L. )
1990-01-01
Recent experiments with Titanium Subhydride Potassium Perchlorate burning under a zero-volume firing condition have shown that compaction occurs ahead of the burn front. A multiphase flow model can be used to obtain the pressure-time history. However, the number of assumptions on parameters and models must be made to obtain a solution. In this work a semi-analytical model is developed to determine the pressure-time history based on the measured burning front velocity. There are experimental evidence that the burning velocity is a slowly varying function of compaction. It is assumed that the burning particles have a given size distribution and they burn parallel to their outer surface. The burning rate is assumed to be pressure dependent. The penetration of gaseous combustion products into the pores ahead of the burn front and the compaction of the charge can be included by introducing suitable pressure dependent parameters. The formulation of the problem results in an integro-differential equation for the pressure-time history of gaseous combustion products in the close system. This equation is solved numerically to obtain the pressure. A parametric study is performed to find the sensitivity of pressure to different parameters. 15 refs., 5 figs.
NASA Astrophysics Data System (ADS)
Berry, Michael; Somerville, Rachel S.; Gawiser, Eric; Maller, Ariyeh H.; Popping, Gergö; Trager, Scott C.
2016-05-01
We investigate predictions from semi-analytic cosmological models of galaxy formation for the properties of star-forming galaxies (SFGs) and damped Ly α absorption systems (DLAS), and the relationship between these two populations. Our models reproduce fairly well the observed distributions of redshift, stellar mass, star formation rate (SFR), and dust extinction for z ˜ 2 SFGs. We predict that DLA hosts span a broad range of properties, with broad and relatively flat distributions of stellar and halo mass, SFR, and luminosity. The photometric colours of DLA host galaxies trace the colours of galaxies with similar luminosities, but the majority are much fainter than the limits of most existing surveys of SFGs. Generally, DLA host galaxies and SFGs at z = 2 follow similar trends between stellar mass, DLA cross-section, cold gas fraction, SFR, metallicity, and dust extinction as the global population of galaxies with the same stellar mass. Since DLAS select galaxies with larger cold gas masses, they tend to have larger cold gas fractions, lower metallicities, higher SFRs, and less dust extinction than galaxies at the same stellar mass. Our models reproduce the observed relations between impact parameter, column density, and metallicity, suggesting that the sizes of the gas discs giving rise to DLAS in our models are roughly correct. We find that molecular fractions and SFRs are in general significantly lower at the location of the DLA line of sight than the galaxy-averaged value.
NASA Astrophysics Data System (ADS)
Suk, Heejun
2016-08-01
This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.
NASA Astrophysics Data System (ADS)
Makiya, Ryu; Enoki, Motohiro; Ishiyama, Tomoaki; Kobayashi, Masakazu A. R.; Nagashima, Masahiro; Okamoto, Takashi; Okoshi, Katsuya; Oogi, Taira; Shirakata, Hikari
2016-04-01
We present a new cosmological galaxy formation model, ν2GC, as an updated version of our previous model νGC. We adopt the so-called "semi-analytic" approach, in which the formation history of dark matter halos is computed by N-body simulations, while the baryon physics such as gas cooling, star formation, and supernova feedback are simply modeled by phenomenological equations. Major updates of the model are as follows: (1) the merger trees of dark matter halos are constructed in state-of-the-art N-body simulations, (2) we introduce the formation and evolution process of supermassive black holes and the suppression of gas cooling due to active galactic nucleus (AGN) activity, (3) we include heating of the intergalactic gas by the cosmic UV background, and (4) we tune some free parameters related to the astrophysical processes using a Markov chain Monte Carlo method. Our N-body simulations of dark matter halos have unprecedented box size and mass resolution (the largest simulation contains 550 billion particles in a 1.12 Gpc h-1 box), enabling the study of much smaller and rarer objects. The model was tuned to fit the luminosity functions of local galaxies and mass function of neutral hydrogen. Local observations, such as the Tully-Fisher relation, the size-magnitude relation of spiral galaxies, and the scaling relation between the bulge mass and black hole mass were well reproduced by the model. Moreover, the model also reproduced well the cosmic star formation history and redshift evolution of rest-frame K-band luminosity functions. The numerical catalog of the simulated galaxies and AGNs is publicly available on the web.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
NASA Astrophysics Data System (ADS)
Kase, Yuki; Yamashita, Haruo; Sakama, Makoto; Mizota, Manabu; Maeda, Yoshikazu; Tameshige, Yuji; Murayama, Shigeyuki
2015-08-01
In the development of an external radiotherapy treatment planning system, the output factor (OPF) is an important value for the monitor unit calculations. We developed a proton OPF calculation model with consideration for the collimator aperture edge to account for the dependence of the OPF on the collimator aperture and distance in proton beam therapy. Five parameters in the model were obtained by fitting with OPFs measured by a pinpoint chamber with the circular radiation fields of various field radii and collimator distances. The OPF model calculation using the fitted model parameters could explain the measurement results to within 1.6% error in typical proton treatment beams with 6- and 12 cm SOBP widths through a range shifter and a circular aperture more than 10.6 mm in radius. The calibration depth dependences of the model parameters were approximated by linear or quadratic functions. The semi-analytical OPF model calculation was tested with various MLC aperture shapes that included circles of various sizes as well as a rectangle, parallelogram, and L-shape for an intermediate proton treatment beam condition. The pre-calculated OPFs agreed well with the measured values, to within 2.7% error up to 620 mm in the collimator distance, though the maximum difference was 5.1% in the case of the largest collimator distance of 740 mm. The OPF calculation model would allow more accurate monitor unit calculations for therapeutic proton beams within the expected range of collimator conditions in clinical use.
NASA Astrophysics Data System (ADS)
Bandilla, K.; Kraemer, S. R.
2009-12-01
Injection of carbon dioxide into deep saline formations is seen as one possible technology for mitigating carbon emissions from utilities. The safety of the sequestered carbon dioxide is the focus of many studies with leakage through faults or abandoned wells as some of the main failure mechanisms. The focus of this study is on the displacement of resident brine and the resulting changes in pressure due to the injection of large volumes of super-critical phase carbon dioxide into the subsurface. The movement of brine becomes important if it travels vertically and reaches an existing or potential underground source of drinking water where an increase in salt content may threaten the viability of the drinking water source. Vertical displacement of brine may occur slowly through confining layers, or more rapidly through faults and abandoned wells. This presentation compares several (semi-) analytic solutions to determine their applicability to the problem of brine pressurization and displacement. The goal is to find ranges of formation parameters (e.g., formation seal conductivity, distance to lateral boundary, … ) for which simplifying assumption are justifiable Each simplification in the conceptual model (e.g., neglecting the lateral boundary turns a bounded domain into an infinite one) leads to a simpler (semi-) analytic solution. The process involves a solution hierarchy from the most complex solution down to the basic Theis solution. A software tool-kit implementing several (semi-) analytic solutions was developed for this study to facilitate the comparison of the solutions.
Modular application of an integration by fractional expansion method to multiloop Feynman diagrams
Gonzalez, Ivan; Schmidt, Ivan
2008-10-15
We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically correspond to recursive constructions of bubble type diagrams. The main idea is to reduce these subgraphs, replacing them by their equivalent multiregion expansion. One of the main advantages of this integration technique is that it allows one to reduce massive cases with the same degree of difficulty as in the massless case.
Towards a new modelling of gas flows in a semi-analytical model of galaxy formation and evolution
NASA Astrophysics Data System (ADS)
Cousin, M.; Lagache, G.; Bethermin, M.; Guiderdoni, B.
2015-03-01
We present an extended version of the semi-analytical model, GalICS. Like its predecessor, eGalICS applies a post-treatment of the baryonic physics on pre-computed dark-matter merger trees extracted from an N-body simulation. We review all the mechanisms that affect, at any given time, the formation and evolution of a galaxy in its host dark-matter halo. We mainly focus on the gas cycle from the smooth cosmological accretion to feedback processes. To follow this cycle with a high accuracy, we introduce some novel prescriptions: i) a smooth baryonic accretion with two phases: a cold mode and a hot mode built on the continuous dark-matter accretion. In parallel to this smooth accretion, we implement the standard photoionisation modelling to reduce the input gas flow on the smallest structures. ii) a complete monitoring of the hot gas phase. We compute the evolution of the core density, the mean temperature and the instantaneous escape fraction of the hot atmosphere by considering that the hot gas is in hydrostatic equilibrium in the dark-matter potential well, and by applying a principle of conservation of energy on the treatment of gas accretion, supernovae and super massive black hole feedback iii) a new treatment for disc instabilities based on the formation, the migration and the disruption of giant clumps. The migration of such clumps in gas-rich galaxies allows to form pseudo-bulges. The different processes in the gas cycle act on different time scales, and we thus build an adaptive time-step scheme to solve the evolution equations. The model presented here is compared in detail to the observations of stellar-mass functions, star formation rates, and luminosity functions, in a companion paper. Model outputs are available at the CDS. Model outputs are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/575/A33
NASA Astrophysics Data System (ADS)
Deleflie, Florent; Rossi, Alessandro; Portmann, Christophe; Métris, Gilles; Barlier, François
2011-03-01
This paper aims at investigating the stability over 150 years of a very large number of trajectories in the Medium Earth Orbit (MEO) region, near the orbits devoted to radionavigation such as the Global Navigation Satellite Systems (GNSS like GPS, Glonass, Galileo, COMPASS).The stability is characterized by the long term evolution of the eccentricity, and a stable orbit will be defined by initial conditions not inducing through gravitational perturbations a high difference between the perigee and apogee altitudes over a 150 years (for keeping as low as possible the collision risk with operational orbits).The initial conditions of motion used for our tests cover a wide range of semi-major axes and inclinations, regularly sampled, so as to describe as exhaustively as possible the gravitational perturbations acting on the space debris population in these regions.In this study, we pay particular attention to the dynamical properties which can make the orbits eccentricity becoming very large, due to effects induced by the non-spherical shape of the Earth, and the luni-solar attraction, with an amplitude governed by the satellite inclination, as well. We show that even if apogee and perigee variations must be limited to less than 300 km (corresponding to a maximum allowed eccentricity growth of 0.01), there are some cases where the eccentricity growth can rise up to the order of 0.7 over a few decades.The paper is organized such as follows. We begin with the general and historical background of the study. We then give some detail about the semi-analytical modelling than we will propagate with about 36,000 various initial conditions over 150 years. These simulations are based on a parallelized code which works on a “Grid” with about 60,000 CPUs available, ensuring reasonable integration times. First interpretations are then addressed, from an analytical point of view, searching for combinations of angles and initial conditions inducing very long periodic terms in the
A Perturbation Expansion Method to Study Highly Correlated Spins
Anda, E. V.; Chiappe, G.; Busser, Carlos A; Davidovich, M. A.; Martins, G. B.; Heidrich-Meisner, F.; Dagotto, Elbio R
2009-01-01
This paper proposes a new numerical algorithm to study dynamical spin dependent properties of local highly correlated structures. The method consists in diagonalizing a finite cluster containing the many-body terms of the Hamil- tonian and embedding it into the rest of the system, the Em- bedding Cluster Approximation (ECA), combined with Wil- son s ideas of logarithmic discretization of the representa- tion of the Hamiltonian, the Logarithm Discretization Em- bedded Cluster Approximation (LDECA). The physics as- sociated to a dot and a side-coupled double dot connected to leads are discussed in detail.
On the Model and Solution Methods for Multi-Facility Capacity Expansion Problem
NASA Astrophysics Data System (ADS)
Magori, Hideki; Yokoyama, Ryuichi
Capacity expansion problem is a hard combinatorial problem to solve because it must treat many scheduling subproblems within a multi-facility framework. It is classified into a category of general Investment & Operation planning problems. This paper presents a basic model for a certain class of capacity expansion problem applicable to the generation expansion problem in power systems, and proposes several mathematical methods for the model. In the field of Operational Research, Dynamic Programming (DP) has been the most popular method under multistage dynamic environments. It is however made clear in the paper that the model cannot be exactly solved by standard DPs. Consequently, another representative methods such as Lagrangian Relaxation, Branch-and-Bound and Heuristics are also tailored as alternatives for DP and compared with each other. Computational experiments by all proposed methods yielded promising suboptima with quality guarantee, among others Branch-and-Bound and Lagrangian Relaxation methods are recommended as suitable ones for the model.
Breakup of three particles within the adiabatic expansion method
NASA Astrophysics Data System (ADS)
Garrido, E.; Kievsky, A.; Viviani, M.
2014-07-01
General expressions for the breakup cross sections in the laboratory frame for 1+2 reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The S matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe 1+2 processes, there are particular configurations in the breakup channel (for example, those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations.
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring. PMID:22346672
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring. PMID:22346672
NASA Astrophysics Data System (ADS)
Romeo, A. D.; Kang, Xi; Contini, E.; Sommer-Larsen, J.; Fassbender, R.; Napolitano, N. R.; Antonuccio-Delogu, V.; Gavignaud, I.
2015-09-01
Context. By means of our own cosmological-hydrodynamical simulation (SIM) and semi-analytical model (SAM), we studied galaxy population properties in clusters and groups, spanning over ten different bands from the ultraviolet to the near-infrared (NIR), and their evolution since redshift z = 2. Aims: We compare our results in terms of red/blue galaxy fractions and of the luminous-to-faint ratio (LFR) on the red sequence (RS) with recent observational data reaching beyond z = 1.5. Methods: Different selection criteria were tested to retrieve the galaxies that effectively belong to the RS: either by their quiescence degree measured from their specific star formation rate (sSFR; the so-called "dead sequence"), or by their position in a colour-colour plane, which is also a function of sSFR. In both cases, the colour cut and the lower limit magnitude thresholds were let to evolve with redshift so that they would follow the natural shift of the characteristic luminosity in the luminosity function (LF). Results: We find that the Butcher-Oemler effect is wavelength-dependent, with the fraction of blue galaxies increasing more steeply in optical-optical than in NIR-optical colours. Moreover, a steep trend in the blue fraction can only be reproduced when an optically fixed luminosity-selected sample is chosen, while the trend flattens when selecting samples by stellar mass or by an evolving magnitude limit. We also find that the RS-LFR behaviour, highly debated in the literature, is strongly dependent on the galaxy selection function: in particular, the very mild evolution that is recovered when using a mass-selected galaxy sample agrees with values reported for some of the highest redshift-confirmed (proto)clusters. For differences that are attributable to environments, we find that normal groups and (to a lesser extent) cluster outskirts present the highest values of both the star-forming fraction and LFR at low z, while fossil groups and cluster cores have the lowest
Computation of determinant expansion coefficients within the graphically contracted function method.
Gidofalvi, G.; Shepard, R.; Chemical Sciences and Engineering Division
2009-11-30
Most electronic structure methods express the wavefunction as an expansion of N-electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems.
Computation of determinant expansion coefficients within the graphically contracted function method.
Gidofalvi, Gergely; Shepard, Ron
2009-11-30
Most electronic structure methods express the wavefunction as an expansion of N-electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems. PMID:19360796
Modeling laser beam diffraction and propagation by the mode-expansion method.
Snyder, James J
2007-08-01
In the mode-expansion method for modeling propagation of a diffracted beam, the beam at the aperture can be expanded as a weighted set of orthogonal modes. The parameters of the expansion modes are chosen to maximize the weighting coefficient of the lowest-order mode. As the beam propagates, its field distribution can be reconstructed from the set of weighting coefficients and the Gouy phase of the lowest-order mode. We have developed a simple procedure to implement the mode-expansion method for propagation through an arbitrary ABCD matrix, and we have demonstrated that it is accurate in comparison with direct calculations of diffraction integrals and much faster. PMID:17676115
Chateau, M; Planas, C S
1995-01-01
Orthodontic goniometry applied to expansion cases treated by P. Planas method (neuro-occlusal rehabilitation) demonstrates considerable bimaxillary transverse expansion (crown and apices). Maximal expansion of 10 mm was noted for mandibular apices with a mean of 5.8 mm. Maximal expansion of 11.5 mm was noted for maxillary apices with a mean of 8.11 mm. Results were stable, some being controlled more than eight years out of retention. PMID:8611485
Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set
NASA Technical Reports Server (NTRS)
Carder, Kendall L.; Hawes, Steve K.; Lee, Zhongping
1997-01-01
A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged
NASA Astrophysics Data System (ADS)
Ali Akbar, M.; Norhashidah, Hj. Mohd. Ali; E. M. E., Zayed
2012-02-01
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G'/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.
ERIC Educational Resources Information Center
Greenberg, Jane
2001-01-01
Explores what might be the optimal query expansion (QE) processing method with semantically coded thesauri. Examines whether QE via semantically coded thesauri terminology is more effective in the "automatic" or "interactive" processing environment. Results revealed that synonyms and partial synonyms and narrower terms are "generally good"…
Gonzalez, Ivan; Schmidt, Ivan
2009-06-15
A modular application of the integration by fractional expansion method for evaluating Feynman diagrams is extended to diagrams that contain loop triangle subdiagrams in their geometry. The technique is based in the replacement of this module or subdiagram by its corresponding multiregion expansion (MRE), which in turn is obtained from Schwinger's parametric representation of the diagram. The result is a topological reduction, transforming the triangular loop into an equivalent vertex, which simplifies the search for the MRE of the complete diagram. This procedure has important advantages with respect to considering the parametric representation of the whole diagram: the obtained MRE is reduced, and the resulting hypergeometric series tends to have smaller multiplicity.
A novel hybrid Neumann expansion method for stochastic analysis of mistuned bladed discs
NASA Astrophysics Data System (ADS)
Yuan, Jie; Allegri, Giuliano; Scarpa, Fabrizio; Patsias, Sophoclis; Rajasekaran, Ramesh
2016-05-01
The paper presents a novel hybrid method to enhance the computational efficiency of matrix inversions during the stochastic analysis of mistuned bladed disc systems. The method is based on the use of stochastic Neumann expansion in the frequency domain, coupled with a matrix factorization in the neighbourhood of the resonant frequencies. The number of the expansion terms is used as an indicator to select the matrix inversion technique to be used, without introducing any additional computational cost. The proposed method is validated using two case studies, where the dynamics an aero-engine bladed disc is modelled first using a lumped parameter approach and then with high-fidelity finite element analysis. The frequency responses of the blades are evaluated according to different mistuning patterns via stiffness or mass perturbations under the excitation provided by the engine orders. Results from standard matrix factorization methods are used to benchmark the responses obtained from the proposed hybrid method. Unlike classic Neumann expansion methods, the new technique can effectively update the inversion of an uncertain matrix with no convergence problems during Monte Carlo simulations. The novel hybrid method is more computationally efficient than standard techniques, with no accuracy loss.
Miocchi, P.; Lanzoni, B.; Ferraro, F. R.; Dalessandro, E.; Alessandrini, E.; Vesperini, E.
2015-01-20
We present semi-analytical models and simplified N-body simulations with 10{sup 4} particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of blue straggler stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of N-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over time regardless of the initial concentration of the system. In spite of noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages, the distribution becomes monotonic. These results are in agreement with the observations. Also, the shape of the peak and the location of the minimum (which, in most of cases, is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary.
NASA Astrophysics Data System (ADS)
Hurlbatt, A.; O’Connell, D.; Gans, T.
2016-08-01
Analytical and numerical models allow investigation of complicated discharge phenomena and the interplay that makes plasmas such a complex environment. Global models are quick to implement and can have almost negligible computation cost, but provide only bulk or spatially averaged values. Full fluid models take longer to develop, and can take days to solve, but provide accurate spatio-temporal profiles of the whole plasma. The work presented here details a different type of model, analytically similar to fluid models, but computationally closer to a global model, and able to give spatially resolved solutions for the challenging environment of electronegative plasmas. Included are non-isothermal electrons, gas heating, and coupled neutral dynamics. Solutions are reached in seconds to minutes, and spatial profiles are given for densities, fluxes, and temperatures. This allows the semi-analytical model to fill the gap that exists between global and full fluid models, extending the tools available to researchers. The semi-analytical model can perform broad parameter sweeps that are not practical with more computationally expensive models, as well as exposing non-trivial trends that global models cannot capture. Examples are given for a low pressure oxygen CCP. Excellent agreement is shown with a full fluid model, and comparisons are drawn with the corresponding global model.
NASA Astrophysics Data System (ADS)
Trillon, Adrien; Deneuville, François; Prémel, Denis; Djafa, Steve; Pichon, Lionel
2014-02-01
This communication presents a semi-analytical model based on BEM formalism for computing MFL flaw responses. MFL 2D configurations have been already simulated in the linear case taking into account the complex shape of the magnetizing circuit surrounding the pipe to be inspected. In this paper, the 3D problem is considered, but, in a first step, in order to be able to solve the non-linear problem, we assume that each ferromagnetic part can be divided in a finite number of polyhedral cells of complex shapes, assuming that the relative magnetic permeability is constant inside each cell. The nonlinear magnetosattic problem may be tackled as a finite number of successive 3D linear problems: the unknowns of the problem being the values of the surface magnetic charge density, in this case, the scalar potential of single layer charge on all the facets of each cell. By assuming that the unknowns are piecewise constant on all the facets of each cell, the kernels derived from integral equations can be analytically evaluated. The implemented semi-analytical model reveals itself to be very effective. Some simulated data are presented for some specific configurations before solving truly NDT MFL configurations.
NASA Astrophysics Data System (ADS)
Han, Jong Goo; Park, Tae Hee; Moon, Yong Ho; Eom, Il Kyu
2016-03-01
We propose an efficient Markov feature extraction method for color image splicing detection. The maximum value among the various directional difference values in the discrete cosine transform domain of three color channels is used to choose the Markov features. We show that the discriminability for slicing detection is increased through the maximization process from the point of view of the Kullback-Leibler divergence. In addition, we present a threshold expansion and Markov state decomposition algorithm. Threshold expansion reduces the information loss caused by the coefficient thresholding that is used to restrict the number of Markov features. To compensate the increased number of features due to the threshold expansion, we propose an even-odd Markov state decomposition algorithm. A fixed number of features, regardless of the difference directions, color channels and test datasets, are used in the proposed algorithm. We introduce three kinds of Markov feature vectors. The number of Markov features for splicing detection used in this paper is relatively small compared to the conventional methods, and our method does not require additional feature reduction algorithms. Through experimental simulations, we demonstrate that the proposed method achieves high performance in splicing detection.
NASA Astrophysics Data System (ADS)
Arbuzov, A. B.; Awramik, M.; Czakon, M.; Freitas, A.; Grünewald, M. W.; Mönig, K.; Riemann, S.; Riemann, T.
2006-05-01
ZFITTER is a Fortran program for the calculation of fermion pair production and radiative corrections at high energy ee colliders; it is also suitable for other applications where electroweak radiative corrections appear. ZFITTER is based on a semi-analytical approach to the calculation of radiative corrections in the Standard Model. We present a summary of new features of the ZFITTER program version 6.42 compared to version 6.21. The most important additions are: (i) some higher-order QED corrections to fermion pair production, (ii) electroweak one-loop corrections to atomic parity violation, (iii) electroweak one-loop corrections to νν production, (iv) electroweak two-loop corrections to the W boson mass and the effective weak mixing angle. Program summaryTitle of program:ZFITTER version 6.42 (18 May 2005) Catalogue identifier:ADMJ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADMJ_v2_0 Authors of original program: D. Bardin, P. Christova, M. Jack, L. Kalinovskaya, A. Olshevski, S. Riemann, T. Riemann Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference for ZFITTER version 6.21: D. Bardin et al., Comput. Phys. Comm. 133 (2001) 229-395 Operating system:UNIX/LINUX, program tested under, e.g., HP-UX and PC/Linux Programming language used:FORTRAN 77 High speed storage required: <2 MB No. of lines in distributed program, including test data, etc.:29 164 No. of bytes in distributed program, including test data, etc.:185 824 Distribution format:tar.gz Does the new version supersede the previous version:Yes Nature of the physical problem: Fermion pair production is an important reaction for precision tests of the Standard Model, at LEP/SLC and future linear colliders at higher energies. For this purpose, QED, electroweak and QCD radiative corrections have to be calculated with high precision, including higher order effects. Multi parameter fits used to extract model parameters from experimental measurements
NASA Astrophysics Data System (ADS)
Kovalchuk, Valery I.
2014-11-01
In this paper, a method has been developed to solve three-particle Faddeev equations in the configuration space making use of a series expansion in hyperspherical harmonics. The following parameters of the bound state of triton and helium-3 nuclei have been calculated: the binding energies, the weights of symmetric and mixed-symmetry components of the wave function, the magnetic moments, and the charge radii.
Some Remarks on the Riccati Equation Expansion Method for Variable Separation of Nonlinear Models
NASA Astrophysics Data System (ADS)
Zhang, Yu-Peng; Dai, Chao-Qing
2015-10-01
Based on the Riccati equation expansion method, 11 kinds of variable separation solutions with different forms of (2+1)-dimensional modified Korteweg-de Vries equation are obtained. The following two remarks on the Riccati equation expansion method for variable separation are made: (i) a remark on the equivalence of different solutions constructed by the Riccati equation expansion method. From analysis, we find that these seemly independent solutions with different forms actually depend on each other, and they can transform from one to another via some relations. We should avoid arbitrarily asserting so-called "new" solutions; (ii) a remark on the construction of localised excitation based on variable separation solutions. For two or multi-component systems, we must be careful with excitation structures constructed by all components for the same model lest the appearance of some un-physical structures. We hope that these results are helpful to deeply study exact solutions of nonlinear models in physical, engineering and biophysical contexts.
NASA Astrophysics Data System (ADS)
Lu, Wangtao; Qian, Jianliang; Burridge, Robert
2016-05-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation can be viewed as an evolution equation in one of the spatial directions. With such applications in mind, starting from Babich's expansion, we develop a new high-order asymptotic method, which we dub the fast Huygens sweeping method, for solving point-source Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of this method is that we develop a new Eulerian approach to compute the asymptotics, i.e. the traveltime function and amplitude coefficients that arise in Babich's expansion, yielding a locally valid solution, which is accurate close enough to the source. The second novelty is that we utilize the Huygens-Kirchhoff integral to integrate many locally valid wavefields to construct globally valid wavefields. This automatically treats caustics and yields uniformly accurate solutions both near the source and remote from it. The third novelty is that the butterfly algorithm is adapted to accelerate the Huygens-Kirchhoff summation, achieving nearly optimal complexity O (Nlog N), where N is the number of mesh points; the complexity prefactor depends on the desired accuracy and is independent of the frequency. To reduce the storage of the resulting tables of asymptotics in Babich's expansion, we use the multivariable Chebyshev series expansion to compress each table by encoding the information into a small number of coefficients. The new method enjoys the following desired features. First, it precomputes the asymptotics in Babich's expansion, such as traveltime and amplitudes. Second, it takes care of caustics automatically. Third, it can compute the point-source Helmholtz solution for many different sources at many frequencies simultaneously. Fourth, for a specified number of points per wavelength, it can construct the wavefield in nearly optimal complexity in terms
A study of the bending motion in tetratomic molecules by the algebraic operator expansion method.
Larese, Danielle; Caprio, Mark A; Pérez-Bernal, Francisco; Iachello, Francesco
2014-01-01
We study the bending motion in the tetratomic molecules C2H2 (X̃ (1)Σg (+)), C2H2 (Ã (1)Au) trans-S1, C2H2 (Ã (1)A2) cis-S1, and X̃ (1)A1 H2CO. We show that the algebraic operator expansion method with only linear terms comprised of the basic operators is able to describe the main features of the level energies in these molecules in terms of two (linear) or three (trans-bent, cis-bent, and branched) parameters. By including quadratic terms, the rms deviation in comparison with experiment goes down to typically ∼10 cm(-1) over the entire range of energy 0-6000 cm(-1). We determine the parameters by fitting the available data, and from these parameters we construct the algebraic potential functions. Our results are of particular interest in high-energy regions where spectra are very congested and conventional methods, force-field expansions or Dunham-expansions plus perturbations, are difficult to apply. PMID:24410226
Stochastic approach to the generalized Schrödinger equation: A method of eigenfunction expansion.
Tsuchida, Satoshi; Kuratsuji, Hiroshi
2015-05-01
Using a method of eigenfunction expansion, a stochastic equation is developed for the generalized Schrödinger equation with random fluctuations. The wave field ψ is expanded in terms of eigenfunctions: ψ=∑(n)a(n)(t)ϕ(n)(x), with ϕ(n) being the eigenfunction that satisfies the eigenvalue equation H(0)ϕ(n)=λ(n)ϕ(n), where H(0) is the reference "Hamiltonian" conventionally called the "unperturbed" Hamiltonian. The Langevin equation is derived for the expansion coefficient a(n)(t), and it is converted to the Fokker-Planck (FP) equation for a set {a(n)} under the assumption of Gaussian white noise for the fluctuation. This procedure is carried out by a functional integral, in which the functional Jacobian plays a crucial role in determining the form of the FP equation. The analyses are given for the FP equation by adopting several approximate schemes. PMID:26066158
Voss, Clifford I.; Simmons, Craig T.; Robinson, Neville I.
2010-01-01
This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.
Arbuzov, A.B.; Awramik, M.; Czakon, M.; Freitas, A.; Grunewald, M.W.; Monig, K.; Riemann, S.; Riemann, T.; /Dubna, JINR /DESY, Zeuthen /Cracow, INP /Wurzburg U. /Silesia U. /Fermilab /University Coll., Dublin
2005-07-01
ZFITTER is a Fortran program for the calculation of fermion pair production and radiative corrections at high energy e{sup +}e{sup -} colliders; it is also suitable for other applications where electroweak radiative corrections appear. ZFITTER is based on a semi-analytical approach to the calculation of radiative corrections in the Standard Model. They present a summary of new features of the ZFITTER program version 6.42 compared to version 6.21. The most important additions are: (1) some higher-order QED corrections to fermion pair production, (2) electroweak one-loop corrections to atomic parity violation, (3) electroweak one-loop corrections to {bar {nu}}{sub e}{nu}{sub e} production, (4) electroweak two-loop corrections to the W boson mass and the effective weak mixing angle.
Zhou, Quanlin; Birkholzer, Jens T.; Tsang, Chin-Fu
2008-07-15
A number of (semi-)analytical solutions are available to drawdown analysis and leakage estimation of shallow aquifer-aquitard systems. These solutions assume that the systems are laterally infinite. When a large-scale pumping from (or injection into) an aquifer-aquitard system of lower specific storativity occurs, induced pressure perturbation (or hydraulic head drawdown/rise) may reach the lateral boundary of the aquifer. We developed semi-analytical solutions to address the induced pressure perturbation and vertical leakage in a 'laterally bounded' system consisting of an aquifer and an overlying/underlying aquitard. A one-dimensional radial flow equation for the aquifer was coupled with a one-dimensional vertical flow equation for the aquitard, with a no-flow condition imposed on the outer radial boundary. Analytical solutions were obtained for (1) the Laplace-transform hydraulic head drawdown/rise in the aquifer and in the aquitard, (2) the Laplace-transform rate and volume of leakage through the aquifer-aquitard interface integrated up to an arbitrary radial distance, (3) the transformed total leakage rate and volume for the entire interface, and (4) the transformed horizontal flux at any radius. The total leakage rate and volume depend only on the hydrogeologic properties and thicknesses of the aquifer and aquitard, as well as the duration of pumping or injection. It was proven that the total leakage rate and volume are independent of the aquifer's radial extent and wellbore radius. The derived analytical solutions for bounded systems are the generalized solutions of infinite systems. Laplace-transform solutions were numerically inverted to obtain the hydraulic head drawdown/rise, leakage rate, leakage volume, and horizontal flux for given hydrogeologic and geometric conditions of the aquifer-aquitard system, as well as injection/pumping scenarios. Application to a large-scale injection-and-storage problem in a bounded system was demonstrated.
NASA Technical Reports Server (NTRS)
Matsuoka, A.; Babin, M.; Doxaran, D.; Hooker, S. B.; Mitchell, B. G.; Belanger, S.; Bricaud, A.
2014-01-01
The light absorption coefficients of particulate and dissolved materials are the main factors determining the light propagation of the visible part of the spectrum and are, thus, important for developing ocean color algorithms. While these absorption properties have recently been documented by a few studies for the Arctic Ocean [e.g., Matsuoka et al., 2007, 2011; Ben Mustapha et al., 2012], the datasets used in the literature were sparse and individually insufficient to draw a general view of the basin-wide spatial and temporal variations in absorption. To achieve such a task, we built a large absorption database at the pan-Arctic scale by pooling the majority of published datasets and merging new datasets. Our results showed that the total non-water absorption coefficients measured in the Eastern Arctic Ocean (EAO; Siberian side) are significantly higher 74 than in the Western Arctic Ocean (WAO; North American side). This higher absorption is explained 75 by higher concentration of colored dissolved organic matter (CDOM) in watersheds on the Siberian 76 side, which contains a large amount of dissolved organic carbon (DOC) compared to waters off 77 North America. In contrast, the relationship between the phytoplankton absorption (a()) and chlorophyll a (chl a) concentration in the EAO was not significantly different from that in the WAO. Because our semi-analytical CDOM absorption algorithm is based on chl a-specific a() values [Matsuoka et al., 2013], this result indirectly suggests that CDOM absorption can be appropriately erived not only for the WAO but also for the EAO using ocean color data. Derived CDOM absorption values were reasonable compared to in situ measurements. By combining this algorithm with empirical DOC versus CDOM relationships, a semi-analytical algorithm for estimating DOC concentrations for coastal waters at the Pan-Arctic scale is presented and applied to satellite ocean color data.
An Improved ((G'/G))-expansion Method for Solving Nonlinear PDEs in Mathematical Physics
Zayed, Elsayed M. E.; Al-Joudi, Shorog
2010-09-30
In the present article, we construct the traveling wave solutions of the (1+1)-dimensional coupled Hirota-Satsuma-KdV equations and the (1+1)-dimensional variant coupled Boussinesq system of equations by using an improved ((G'/G))-expansion method, where G satisfies the second order linear ordinary differential equation. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
Yang, W.; Wu, H.; Cao, L.
2012-07-01
More and more MOX fuels are used in all over the world in the past several decades. Compared with UO{sub 2} fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for {sup 240}Pu and {sup 242}Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)
Axial expansion methods for solution of the multi-dimensional neutron diffusion equation
Beaklini Filho, J.F.
1984-01-01
The feasibility and practical implementation of axial expansion methods for the solution of the multi-dimensional multigroup neutron diffusion (MGD) equations is investigated. The theoretical examination which is applicable to the general MGD equations in arbitrary geometry includes the derivation of a new weak (reduced) form of the MGD equations by expanding the axial component of the neutron flux in a series of known trial functions and utilizing the Galerkin weighting. A general two-group albedo boundary condition is included in the weak form as a natural boundary condition. The application of different types of trial functions is presented.
NASA Astrophysics Data System (ADS)
Chuang, C.-I.; Nyquist, D. P.; Chen, K.-M.; Drachman, B. C.
1985-10-01
The impulse response of an infinite, perfectly conducting thick cylinder to normally incident, transversely polarized, impulsive plane wave illumination is determined. Spectral-domain analysis based upon the singularity expansion method reveals that this response consists of a discrete series of natural resonance modes (natural frequencies are computed) augmented by a series of continuous-spectrum terms. The resultant late-time response demonstrates the correct 'creeping wave' behavior as predicted by the Fourier synthesis technique, but with far fewer terms required for convergence.
Rapid maxillary expansion effects: An alternative assessment method by means of cone-beam tomography
Melgaço, Camilo Aquino; Columbano, José; Jurach, Estela Maris; Nojima, Matilde da Cunha Gonçalves; Sant'Anna, Eduardo Franzotti; Nojima, Lincoln Issamu
2014-01-01
INTRODUCTION: This study aims to develop a method to assess the changes in palatal and lingual cross-sectional areas in patients submitted to rapid maxillary expansion (RME). METHODS: The sample comprised 31 Class I malocclusion individuals submitted to RME and divided into two groups treated with Haas (17 patients) and Hyrax (14 patients) expanders. Cone-beam computed tomography scans were acquired at T0 (before expansion ) and T1 (six months after screw stabilization). Maxillary and mandibular cross-sectional areas were assessed at first permanent molars and first premolars regions and compared at T0 and T1. Mandibular occlusal area was also analyzed. RESULTS: Maxillary cross-sectional areas increased in 56.18 mm2 and 44.32 mm2 for the posterior and anterior regions. These values were smaller for the mandible, representing augmentation of 40.32 mm2 and 39.91 mm2 for posterior and anterior sections. No differences were found when comparing both expanders. Mandibular occlusal area increased 43.99mm2 and mandibular incisors proclined. Increments of 1.74 mm and 1.7 mm occurred in mandibular intermolar and interpremolar distances. These same distances presented increments of 5.5 mm and 5.57 mm for the maxillary arch. CONCLUSION: Occlusal and cross-sectional areas increased significantly after RME. The method described seems to be reliable and precise to assess intraoral area changes. PMID:25715721
Time-domain incident-field extrapolation technique based on the singularity-expansion method
Klaasen, J.J.
1991-05-01
In this report, a method presented to extrapolate measurements from Nuclear Electromagnetic Pulse (NEMP) assessments directly in the time domain. This method is based on a time-domain extrapolation function which is obtained from the Singularity Expansion Method representation of the measured incident field of the NEMP simulator. Once the time-domain extrapolation function is determined, the responses recorded during an assessment can be extrapolated simply by convolving them with the time domain extrapolation function. It is found that to obtain useful extrapolated responses, the incident field measurements needs to be made minimum phase; otherwise unbounded results can be obtained. Results obtained with this technique are presented, using data from actual assessments.
Method for fabricating an ultra-low expansion mask blank having a crystalline silicon layer
Cardinale, Gregory F.
2002-01-01
A method for fabricating masks for extreme ultraviolet lithography (EUVL) using Ultra-Low Expansion (ULE) substrates and crystalline silicon. ULE substrates are required for the necessary thermal management in EUVL mask blanks, and defect detection and classification have been obtained using crystalline silicon substrate materials. Thus, this method provides the advantages for both the ULE substrate and the crystalline silicon in an Extreme Ultra-Violet (EUV) mask blank. The method is carried out by bonding a crystalline silicon wafer or member to a ULE wafer or substrate and thinning the silicon to produce a 5-10 .mu.m thick crystalline silicon layer on the surface of the ULE substrate. The thinning of the crystalline silicon may be carried out, for example, by chemical mechanical polishing and if necessary or desired, oxidizing the silicon followed by etching to the desired thickness of the silicon.
A Modal Expansion Equilibrium Cycle Perturbation Method for Optimizing High Burnup Fast Reactors
NASA Astrophysics Data System (ADS)
Touran, Nicholas W.
This dissertation develops a simulation tool capable of optimizing advanced nuclear reactors considering the multiobjective nature of their design. An Enhanced Equilibrium Cycle (EEC) method based on the classic equilibrium method is developed to evaluate the response of the equilibrium cycle to changes in the core design. Advances are made in the consideration of burnup-dependent cross sections and dynamic fuel performance (fission gas release, fuel growth, and bond squeeze-out) to allow accuracy in high-burnup reactors such as the Traveling Wave Reactor. EEC is accelerated for design changes near a reference state through a new modal expansion perturbation method that expands arbitrary flux perturbations on a basis of λ-eigenmodes. A code is developed to solve the 3-D, multigroup diffusion equation with an Arnoldi-based solver that determines hundreds of the reference flux harmonics and later uses these harmonics to determine expansion coefficients required to approximate the perturbed flux. The harmonics are only required for the reference state, and many substantial and localized perturbations from this state are shown to be well-approximated with efficient expressions after the reference calculation is performed. The modal expansion method is coupled to EEC to produce the later-in-time response of each design perturbation. Because the code determines the perturbed flux explicitly, a wide variety of core performance metrics may be monitored by working within a recently-developed data management system called the ARMI. Through ARMI, the response of each design perturbation may be evaluated not only for the flux and reactivity, but also for reactivity coefficients, thermal hydraulics parameters, economics, and transient performance. Considering the parameters available, an automated optimization framework is designed and implemented. A non-parametric surrogate model using the Alternating Conditional Expectation (ACE) algorithm is trained with many design
SU-E-J-221: A Novel Expansion Method for MRI Based Target Delineation in Prostate Radiotherapy
Ruiz, B; Feng, Y; Shores, R; Fung, C
2015-06-15
Purpose: To compare a novel bladder/rectum carveout expansion method on MRI delineated prostate to standard CT and expansion based methods for maintaining prostate coverage while providing superior bladder and rectal sparing. Methods: Ten prostate cases were planned to include four trials: MRI vs CT delineated prostate/proximal seminal vesicles, and each image modality compared to both standard expansions (8mm 3D expansion and 5mm posterior, i.e. ∼8mm) and carveout method expansions (5mm 3D expansion, 4mm posterior for GTV-CTV excluding expansion into bladder/rectum followed by additional 5mm 3D expansion to PTV, i.e. ∼1cm). All trials were planned to total dose 7920 cGy via IMRT. Evaluation and comparison was made using the following criteria: QUANTEC constraints for bladder/rectum including analysis of low dose regions, changes in PTV volume, total control points, and maximum hot spot. Results: ∼8mm MRI expansion consistently produced the most optimal plan with lowest total control points and best bladder/rectum sparing. However, this scheme had the smallest prostate (average 22.9% reduction) and subsequent PTV volume, consistent with prior literature. ∼1cm MRI had an average PTV volume comparable to ∼8mm CT at 3.79% difference. Bladder QUANTEC constraints were on average less for the ∼1cm MRI as compared to the ∼8mm CT and observed as statistically significant with 2.64% reduction in V65. Rectal constraints appeared to follow the same trend. Case-by-case analysis showed variation in rectal V30 with MRI delineated prostate being most favorable regardless of expansion type. ∼1cm MRI and ∼8mm CT had comparable plan quality. Conclusion: MRI delineated prostate with standard expansions had the smallest PTV leading to margins that may be too tight. Bladder/rectum carveout expansion method on MRI delineated prostate was found to be superior to standard CT based methods in terms of bladder and rectal sparing while maintaining prostate coverage
Spectral likelihood expansions for Bayesian inference
NASA Astrophysics Data System (ADS)
Nagel, Joseph B.; Sudret, Bruno
2016-03-01
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.
Spherical Harmonic Expansion Method for Coupled Electron-Phonon Boltzmann Transport
NASA Astrophysics Data System (ADS)
Santia, Marco; Albrecht, John
2014-03-01
Thermoelectric transport modeling often relies on independent Boltzmann transport equations (BTEs) for electrons and phonons which work best near equilibrium (linearized) and steady-state. Device design relies heavily on this baseline approximation. Monte Carlo methods can allow for complex physical interactions (e.g., anharmonicity) but their stochastic nature has practical limits. Distribution functions with wide disparities in population (e.g., ratios >108 between majority and minority carriers.[1]) are a computational challenge. We present a coupled BTE solver based on a k-space spherical harmonic expansion (SHE) of the distribution functions and eigenstates of electrons and phonons. The method is deterministic and allows for detailed treatments of scattering processes, yet ameliorates the issues with population disparity within phase space. We set the formalism and examine the accuracy of the SHE for phonon band structures, calculate scattering rates determined within that representation, and compare our preliminary results for distribution statistics in control examples such as thermal conductivity and drift velocity.
Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method
NASA Astrophysics Data System (ADS)
Švarc, Alfred; Hadžimehmedović, Mirza; Osmanović, Hedim; Stahov, Jugoslav; Tiator, Lothar; Workman, Ron L.
2014-06-01
We applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial-wave T matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method is applied to multipole fits generated by the MAID and George Washington University SAID (GWU-SAID) groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from πN elastic data and values cited by the Particle Data Group (PDG). The photoproduction residues provide new information for the electromagnetic current at the pole position, which are independent of background parametrizations, which is not the case for the Breit-Wigner representation. Finally, we present the photodecay amplitudes from the current MAID and SAID solutions at the pole for all four-star nucleon resonances below W =2 GeV.
Application of Gaussian expansion method to nuclear mean-field calculations with deformation
NASA Astrophysics Data System (ADS)
Nakada, H.
2008-08-01
We extensively develop a method of implementing mean-field calculations for deformed nuclei, using the Gaussian expansion method (GEM). This GEM algorithm has the following advantages: (i) it can efficiently describe the energy-dependent asymptotics of the wave functions at large r, (ii) it is applicable to various effective interactions including those with finite ranges, and (iii) the basis parameters are insensitive to nuclide, thereby many nuclei in wide mass range can be handled by a single set of bases. Superposing the spherical GEM bases with feasible truncation for the orbital angular momentum, we obtain deformed single-particle wave-functions to reasonable precision. We apply the new algorithm to the Hartree-Fock and the Hartree-Fock-Bogolyubov calculations of Mg nuclei with the Gogny interaction, by which neck structure of a deformed neutron halo is suggested for 40Mg.
An operator expansion method for computing nonlinear surface waves on a ferrofluid jet
NASA Astrophysics Data System (ADS)
Guyenne, Philippe; Părău, Emilian I.
2016-09-01
We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet-Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illustrate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided.
Zhang, Yongliang; Chen, Yu; Li, David Day-Uei
2016-06-27
Fast deconvolution is an essential step to calibrate instrument responses in big fluorescence lifetime imaging microscopy (FLIM) image analysis. This paper examined a computationally effective least squares deconvolution method based on Laguerre expansion (LSD-LE), recently developed for clinical diagnosis applications, and proposed new criteria for selecting Laguerre basis functions (LBFs) without considering the mutual orthonormalities between LBFs. Compared with the previously reported LSD-LE, the improved LSD-LE allows to use a higher laser repetition rate, reducing the acquisition time per measurement. Moreover, we extended it, for the first time, to analyze bi-exponential fluorescence decays for more general FLIM-FRET applications. The proposed method was tested on both synthesized bi-exponential and realistic FLIM data for studying the endocytosis of gold nanorods in Hek293 cells. Compared with the previously reported constrained LSD-LE, it shows promising results. PMID:27410552
Validation of the activity expansion method with ultrahigh pressure shock equations of state
NASA Astrophysics Data System (ADS)
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.
Calculation of Coherent Synchrotron Radiation Impedance Using the Mode Expansion Method
Stupakov, G.V.; Kotelnikov, I.A.; /Novosibirsk, IYF
2009-12-09
We study an impedance due to coherent synchrotron radiation (CSR) generated by a short bunch of charged particles passing through a dipole magnet of finite length in a vacuum chamber of a given cross section. In our method we decompose the electromagnetic field of the beam over the eigenmodes of the toroidal chamber and derive a system of equations for the expansion coefficients in the series. The general method is further specialized for a toroidal vacuum chamber of a rectangular cross section where the eigenmodes can be computed analytically. We also develop a computer code that calculates the CSR impedance for a toroid of rectangular cross section. Numerical results obtained with the code are presented in the paper.
Feasibility of a wavelet expansion method to treat energy in cell calculations
Van Rooijen, W. F. G.
2012-07-01
This paper discusses the application of the Discrete Wavelet Transform (DWT) for the functional expansion of the energy variable in a cell calculation. The motivation of the work is the desire to obtain a self-shielding methodology in which the treatment of the energy variable in a given material region can be automatically adapted to the complexity of the cross section in that region. Unfortunately, the work presented in this paper shows that it is generally not possible to obtain the desired adaptivity. The most fundamental reason is that in a multi-region system, the energy dependence of the flux in a given material region is a function of the energy dependent cross sections and sources in all material regions through which the neutrons have crossed before entering into the present material. The complexity of the energy dependence of the cross section in a material region is thus not necessarily linked to the energy dependence of the flux in that region. If one sacrifices the objective of adaptivity, then an accurate method can be obtained using the DWT as a functional expansion. However, the resulting system of equations is more complicated than the direct solution of a hyper-fine group calculation. The conclusion is thus that the DWT approach is not very practical. (authors)
Plume expansion of a laser-induced plasma studied with the particle-in-cell method
NASA Astrophysics Data System (ADS)
Ellegaard, O.; Nedelea, T.; Schou, J.; Urbassek, H. M.
2002-09-01
The initial stage of laser-induced plasma plume expansion from a solid in vacuum and the effect of the Coulomb field have been studied. We have performed a one-dimensional numerical calculation by mapping the charge on a computational grid according to the particle-in-cell (PIC) method of Birdsall et al. It is assumed that the particle ablation from a surface with a fixed temperature takes place as a pulse, i.e. within a finite period of time. A number of characteristic quantities for the plasma plume are compared with similar data for expansion of neutrals as well as fluid models: Density profiles n( x, t), velocity distributions of ions u( x, t), distribution functions for velocities F( vx) of ions or electrons as well as the time dependence of kinetic energy Ekin( t) for both type of particles. We found a significant increase in the velocities of the ions at the expense of field potential energy as well as electron energy. We have estimated the time constant for energy transfer between the electrons and the ions. The scaling of these processes is given by a single parameter determined by the Debye length obtained from the electron density in the plasma outside the surface.
NASA Astrophysics Data System (ADS)
LaForce, T.; Ennis-King, J.; Paterson, L.
2014-11-01
This work introduces the derivation and solution of the conservation laws for nonisothermal immiscible two-phase flow in one dimension (1D) with heat loss to surrounding strata. Purely advective flow is assumed so that the method of characteristics can be applied to the fluid flow and thermal equations with an arbitrary relative permeability model. The formulation allows for a wide class of time-dependent models for heat loss into surrounding strata. One-dimensional linear and radial displacements are considered. Thermal losses to the under- and over-burden are modelled using a heat-loss coefficient derived from the classic Lauwerier model. In order to demonstrate the two kinds of solution that may occur, examples are shown for cold methane injection into an aquifer and cold water injection into a natural gas reservoir. Finally the new analytical solutions are compared with two literature models which assume piston-like displacement, and numerical reservoir simulations. The solutions from the proposed model match the thermal profile from the reservoir simulation much better than either of the literature models in the examples considered.
NASA Astrophysics Data System (ADS)
Rozel, A. B.; Golabek, G.; Thielmann, M.; Tackley, P.
2015-12-01
We present a semi analytical model of mantle convection able to predict the grain size profile of the present day Earth. Grain size evolution has been studied with increasing interest over the last decades but its behavior in both mantle and lithosphere remains largely misunderstood due to its non-linearity. Several recent studies suggest that it might play a fundamental role in localization of deformation in the lithosphere but we focus here on the mantle in which we also observe important processes.We propose a 1D compressible thermal convection model based on the equality of advective heat flux and the integral of viscous dissipation in the whole domain. Imposing mass conservation, our model is able to predict all rheological parameters able to produce both present day average surface velocity and lower mantle viscosity. Composite rheologies involving dislocation creep and grain size dependent diffusion creep are considered. The effect of phase transitions on the grain size is also explicitely taken into account. We present the family of solutions for the activation volume and the viscosity jump at the 660 discontinuity according to any initial choice of activation energy. The scaling laws for rheological parameters obtained are compared to self-consistent evolutionary simulations of mantle convection in 2D spherical annulus geometry considering composite rheologies. The transition between diffusion and dislocation creep due to the cooling of the Earth is illustrated in a set of numerical simulations starting from the physical conditions of the Archean.
NASA Astrophysics Data System (ADS)
Chen, Jun; Cui, Tingwei; Qiu, Zhongfeng; Lin, Changsong
2014-07-01
The accurate assessment of total suspended sediment (TSM) concentration in coastal waters by means of remote sensing is quite challenging, due to the optical complexity and significant variability of these waters. In this study, three-band semi-analytical TSM retrieval (TSTM) model with HJ-1A/CCD spectral bands was developed for the retrieval of TSM concentration from turbid coastal waters. This model was calibrated and validated by means of one calibration dataset and three independent validation datasets obtained from three different turbid waters. It was found that the TSTM model may be used to retrieve accurate TSM concentration data from highly turbid waters without the spectral slope of the model requiring further optimization. Finally, the TSM concentration data were quantified from the HJ-1A/CCD images after atmospheric correction using the dark-object subtraction technique. Upon comparing the model-derived and field-measured TSM concentration data, it was observed that the TSTM model produced <29% uncertainty in deriving TSM concentration from the HJ-1A/CCD data. These findings imply that the TSTM model may be used for the quantitative monitoring of TSM concentration in coastal waters, provided that the atmospheric correction scheme for the HJ-1A/CCD imagery is available.
Rood, A.S.
1993-06-01
GWSCREEN was developed for assessment of the groundwater pathway from leaching of radioactive and non radioactive substances from surface or buried sources. The code was designed for implementation in the Track I and Track II assessment of CERCLA (Comprehensive Environmental Response, Compensation and Liability Act) sites identified as low probability hazard at the Idaho National Engineering Laboratory (DOE, 1992). The code calculates the limiting soil concentration such that, after leaching and transport to the aquifer, regulatory contaminant levels in groundwater are not exceeded. The code uses a mass conservation approach to model three processes: contaminant release from a source volume, contaminant transport in the unsaturated zone, and contaminant transport in the saturated zone. The source model considers the sorptive properties and solubility of the contaminant. Transport in the unsaturated zone is described by a plug flow model. Transport in the saturated zone is calculated with a semi-analytical solution to the advection dispersion equation in groundwater. In Version 2.0, GWSCREEN has incorporated an additional source model to calculate the impacts to groundwater resulting from the release to percolation ponds. In addition, transport of radioactive progeny has also been incorporated. GWSCREEN has shown comparable results when compared against other codes using similar algorithms and techniques. This code was designed for assessment and screening of the groundwater pathway when field data is limited. It was not intended to be a predictive tool.
NASA Astrophysics Data System (ADS)
Islam, J.; Zhan, H.
2013-12-01
Study of potential leakage of hazardous liquid waste into deep aquifer or abandoned wells is very important research work in recent days. CO2 sequestration into the brine media is not an exception of that. The saline aquifer is always overlain by a leaky aquitard or seal which may allow the migration of the injected CO2 or any kind of hazardous liquid waste to the upper aquifer through some leaks or fractures. The scope of study includes how the migration through the seal or aquitard causes the pressure change in the upper aquifer because of that injection into the target storage aquifer. Such pressure change is used to infer the leakage pathway location and characteristics of the leak or fractures. In this complex issue both Darcian and non-Darcian flow has been taken care of combindly. The Izbash equation has been used to describe the non-Darcian flow in the aquifer. A semi-analytical solution is obtained in Laplace domain and finally it has been solved numerically. Afterwards different parameters have been evaluated (leak or fracture size, injection rate, conductivity) to see how they directly affect the upper aquifer pressure and leakage rate independently.
NASA Astrophysics Data System (ADS)
Cousin, M.; Buat, V.; Boissier, S.; Bethermin, M.; Roehlly, Y.; Génois, M.
2016-05-01
Context. Gas flows play a fundamental role in galaxy formation and evolution, providing the fuel for the star formation process. These mechanisms leave an imprint in the amount of heavy elements that enrich the interstellar medium. Thus, the analysis of this metallicity signature provides additional constraint on the galaxy formation scenario. Aims: We aim to discriminate between four different galaxy formation models based on two accretion scenarios and two different star formation recipes. We address the impact of a bimodal accretion scenario and a strongly regulated star formation recipe on the metal enrichment process of galaxies. Methods: We present a new extension of the eGalICS model, which allows us to track the metal enrichment process in both stellar populations and in the gas phase. Based on stellar metallicity bins from 0 to 2.5 Z⊙, our new chemodynamical model is applicable for situations ranging from metal-free primordial accretion to very enriched interstellar gas contents. We use this new tool to predict the metallicity evolution of both the stellar populations and gas phase. We compare these predictions with recent observational measurements. We also address the evolution of the gas metallicity with the star formation rate (SFR). We then focus on a sub-sample of Milky Way-like galaxies. We compare both the cosmic stellar mass assembly and the metal enrichment process of such galaxies with observations and detailed chemical evolution models. Results: Our models, based on a strong star formation regulation, allow us to reproduce well the stellar mass to gas-phase metallicity relation observed in the local Universe. The shape of our average stellar mass to stellar metallicity relations is in good agreement with observations. However, we observe a systematic shift towards high masses. Our M⋆ - Zg -SFR relation is in good agreement with recent measurements: our best model predicts a clear dependence with the SFR. Both SFR and metal enrichment
NASA Astrophysics Data System (ADS)
Cousin, M.; Buat, V.; Boissier, S.; Bethermin, M.; Roehlly, Y.; Génois, M.
2016-04-01
Context. Gas flows play a fundamental role in galaxy formation and evolution, providing the fuel for the star formation process. These mechanisms leave an imprint in the amount of heavy elements that enrich the interstellar medium. Thus, the analysis of this metallicity signature provides additional constraint on the galaxy formation scenario. Aims: We aim to discriminate between four different galaxy formation models based on two accretion scenarios and two different star formation recipes. We address the impact of a bimodal accretion scenario and a strongly regulated star formation recipe on the metal enrichment process of galaxies. Methods: We present a new extension of the eGalICS model, which allows us to track the metal enrichment process in both stellar populations and in the gas phase. Based on stellar metallicity bins from 0 to 2.5 Z⊙, our new chemodynamical model is applicable for situations ranging from metal-free primordial accretion to very enriched interstellar gas contents. We use this new tool to predict the metallicity evolution of both the stellar populations and gas phase. We compare these predictions with recent observational measurements. We also address the evolution of the gas metallicity with the star formation rate (SFR). We then focus on a sub-sample of Milky Way-like galaxies. We compare both the cosmic stellar mass assembly and the metal enrichment process of such galaxies with observations and detailed chemical evolution models. Results: Our models, based on a strong star formation regulation, allow us to reproduce well the stellar mass to gas-phase metallicity relation observed in the local Universe. The shape of our average stellar mass to stellar metallicity relations is in good agreement with observations. However, we observe a systematic shift towards high masses. Our M⋆ - Zg -SFR relation is in good agreement with recent measurements: our best model predicts a clear dependence with the SFR. Both SFR and metal enrichment
NASA Astrophysics Data System (ADS)
Sai Venkata Ramana, A.
2016-01-01
In this paper, we have applied the seventh order version of coupling parameter expansion (CPE) method combined with global renormalization group theory (GRGT) to square well fluids of various ranges and have performed the following studies. Firstly, the convergence of the GRGT iteration scheme has been studied. It is observed that the point-wise convergence is non-uniform and slow in the coexistence region away from the critical point. However, the point-wise convergence improved as the critical temperature is approached. Secondly, we have obtained the liquid-vapor phase diagrams (LVPDs) for the square well fluids. The LVPDs obtained using GRGT corrected seventh order CPE are significantly accurate over those obtained from GRGT corrected 1-order thermodynamic perturbation theory (TPT). Also, excessive flatness of LVPDs close to the critical region as observed in GRGT corrected 1-order TPT has not been seen in the LVPDs of present method. Thirdly, the critical exponents have been obtained using present method. The exponents are seen to be of Ising universality class and follow the Rushbrooke and Griffiths equalities qualitatively. Finally, a study of Yang-Yang anomaly has been done using our method. It has been observed that the method predicts the existence of the anomaly but the predictions of the strength of anomaly differed from those of simulations. The reasons for the differences are analyzed.
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko
2014-04-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials. PMID:24827360
Error analysis of the quadratic nodal expansion method in slab geometry
Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.
1994-10-01
As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.
NASA Astrophysics Data System (ADS)
Tang, Chen; Zhang, Junjiang; Sun, Chen; Su, Yonggang; Su, Kai Leung
2015-05-01
Nuclear graphite has been widely used as moderating and reflecting materials. However, due to severe neutron irradiation under high temperature, nuclear graphite is prone to deteriorate, resulting in massive microscopic flaws and even cracks under large stress in the later period of its service life. It is indispensable, therefore, to understand the fracture behavior of nuclear graphite to provide reference to structural integrity and safety analysis of nuclear graphite members in reactors. In this paper, we investigated the fracture expansion in nuclear graphite based on PDE image processing methods. We used the second-order oriented partial differential equations filtering model (SOOPDE) to denoise speckle noise, then used the oriented gradient vector fields for to obtain skeletons. The full-field displacement of fractured nuclear graphite and the location of the crack tip were lastly measured under various loading conditions.
NASA Astrophysics Data System (ADS)
Olsen, Jeppe
2014-07-01
A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 106 coefficients in the CSF basis is obtained from the 150 × 106 coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require.
High order spatial expansion for the method of characteristics applied to 3-D geometries
Naymeh, L.; Masiello, E.; Sanchez, R.
2013-07-01
The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)
Olsen, Jeppe
2014-07-21
A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10{sup 6} coefficients in the CSF basis is obtained from the 150 × 10{sup 6} coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require.
Olsen, Jeppe
2014-07-21
A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10(6) coefficients in the CSF basis is obtained from the 150 × 10(6) coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require. PMID:25053306
Comparing regression methods for the two-stage clonal expansion model of carcinogenesis.
Kaiser, J C; Heidenreich, W F
2004-11-15
In the statistical analysis of cohort data with risk estimation models, both Poisson and individual likelihood regressions are widely used methods of parameter estimation. In this paper, their performance has been tested with the biologically motivated two-stage clonal expansion (TSCE) model of carcinogenesis. To exclude inevitable uncertainties of existing data, cohorts with simple individual exposure history have been created by Monte Carlo simulation. To generate some similar properties of atomic bomb survivors and radon-exposed mine workers, both acute and protracted exposure patterns have been generated. Then the capacity of the two regression methods has been compared to retrieve a priori known model parameters from the simulated cohort data. For simple models with smooth hazard functions, the parameter estimates from both methods come close to their true values. However, for models with strongly discontinuous functions which are generated by the cell mutation process of transformation, the Poisson regression method fails to produce reliable estimates. This behaviour is explained by the construction of class averages during data stratification. Thereby, some indispensable information on the individual exposure history was destroyed. It could not be repaired by countermeasures such as the refinement of Poisson classes or a more adequate choice of Poisson groups. Although this choice might still exist we were unable to discover it. In contrast to this, the individual likelihood regression technique was found to work reliably for all considered versions of the TSCE model. PMID:15490436
NASA Astrophysics Data System (ADS)
Huang, He
In this thesis, I present the results of studies of the structural properties and phase transition of a charge neutral FCC Lattice Gas with Yukawa Interaction and discuss a novel fast calculation algorithm---Accelerated Cartesian Expansion (ACE) method. In the first part of my thesis, I discuss the results of Monte Carlo simulations carried out to understand the finite temperature (phase transition) properties and the ground state structure of a Yukawa Lattice Gas (YLG) model. In this model the ions interact via the potential q iqjexp(-kappar> ij)/rij where qi,j are the charges of the ions located at the lattice sites i and j with position vectors R i and Rj; rij = Ri-Rj, kappa is a measure of the range of the interaction and is called the screening parameter. This model approximates an interesting quaternary system of great current thermoelectric interest called LAST-m, AgSbPbmTem+2. I have also developed rapid calculation methods for the potential energy calculation in a lattice gas system with periodic boundary condition bases on the Ewald summation method and coded the algorithm to compute the energies in MC simulation. Some of the interesting results of the MC simulations are: (i) how the nature and strength of the phase transition depend on the range of interaction (Yukawa screening parameter kappa) (ii) what is the degeneracy of the ground state for different values of the concentration of charges, and (iii) what is the nature of two-stage disordering transition seen for certain values of x. In addition, based on the analysis of the surface energy of different nano-clusters formed near the transition temperature, the solidification process and the rate of production of these nano-clusters have been studied. In the second part of my thesis, we have developed two methods for rapidly computing potentials of the form R-nu. Both these methods are founded on addition theorems based on Taylor expansions. Taylor's series has a couple of inherent advantages: (i) it
Sever, Martin; Krč, Janez; Čampa, Andrej; Topič, Marko
2015-11-30
Finite element method is coupled with Huygens' expansion to determine light intensity distribution of scattered light in solar cells and other optoelectronic devices. The rigorous foundation of the modelling enables calculation of the light intensity distribution at a chosen distance and surface of observation in chosen material in reflection or in transmission for given wavelength of the incident light. The calculation of scattering or anti-reflection properties is not limited to a single textured interface, but can be done above more complex structures with several scattering interfaces or even with particles involved. Both scattering at periodic and at random textures can be efficiently handled with the modelling approach. A procedure for minimisation of the effect of small-area sample, which is considered in the finite element method calculation, is proposed and implemented into the modelling. Angular distribution function, total transmission and total reflection of the scattering interface or structure can be determined using the model. Furthermore, a method for calculation of the haze parameter of reflected or transmitted light is proposed. The modelling approach is applied to periodic and random nano-textured samples for photovoltaic applications, showing good agreement with measured data. PMID:26698803
A NOVEL ENVIRONMENT FRIENDLY METHOD FOR EXPANSION AND MOLDING OF POLYMERIC FOAM
The objective of the project is to develop an environment friendly, novel and efficient alternative process for expansion and molding of polymeric foam. Spherical, expandable polymer beads are prepared from liquid monomer suspended in an aqueous medium, containing an expansion...
Use of advanced particle methods in modeling space propulsion and its supersonic expansions
NASA Astrophysics Data System (ADS)
Borner, Arnaud
This research discusses the use of advanced kinetic particle methods such as Molecular Dynamics (MD) and direct simulation Monte Carlo (DSMC) to model space propulsion systems such as electrospray thrusters and their supersonic expansions. MD simulations are performed to model an electrospray thruster for the ionic liquid (IL) EMIM--BF4 using coarse-grained (CG) potentials. The model is initially featuring a constant electric field applied in the longitudinal direction. Two coarse-grained potentials are compared, and the effective-force CG (EFCG) potential is found to predict the formation of the Taylor cone, the cone-jet, and other extrusion modes for similar electric fields and mass flow rates observed in experiments of a IL fed capillary-tip-extractor system better than the simple CG potential. Later, one-dimensional and fully transient three-dimensional electric fields, the latter solving Poisson's equation to take into account the electric field due to space charge at each timestep, are computed by coupling the MD model to a Poisson solver. It is found that the inhomogeneous electric field as well as that of the IL space-charge improve agreement between modeling and experiment. The boundary conditions (BCs) are found to have a substantial impact on the potential and electric field, and the tip BC is introduced and compared to the two previous BCs, named plate and needle, showing good improvement by reducing unrealistically high radial electric fields generated in the vicinity of the capillary tip. The influence of the different boundary condition models on charged species currents as a function of the mass flow rate is studied, and it is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the MD simulations with the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with
Zhou, S.; Solana, J. R.
2014-12-28
In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients a{sub i} of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients a{sub i} falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25.