NASA Technical Reports Server (NTRS)
Musen, P.
1973-01-01
The method of expansion of the satellite's perturbations, as caused by the oceanic tides, into Fourier series is discussed. The coefficients of the expansion are purely numerical and peculiar to each particular satellite. Such a method is termed as semi-analytical in celestial mechanics. Gaussian form of the differential equations for variation of elements, with the right hand sides averaged over the orbit of the satellite, is convenient to use with the semi-analytical expansion.
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.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
NASA Astrophysics Data System (ADS)
Jameel, A. F.; Ismail, Ahmad Izani Md
2014-07-01
In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The effectiveness of the algorithm is demonstrated by solving nonlinear second order fuzzy Riccati equation. The results indicate that the method is very effective and simple to apply.
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.
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.
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)
Cui, Zhenshan; Chen, Wen; Sui, Dashan; Liu, Juan
2013-05-01
A pass planning method for multi-pass and multi-hit stretching of heavy forgings is proposed, which composes of a semi-analytical procedure and a degrees-reduced finite element code. The semi-analytical procedure is based on a kinematically admissible velocity and Markov variational principle, and can be applied to roughly calculate the deformed shape and working force for stretch forging process for work-piece which has vertical and lateral symmetrical lines in cross-section. Meanwhile, in order to obtain the distributions of metal flow, temperature, strain and stress in detail, a degrees-reduced thermo-mechanical coupled rigid finite element code is developed. In this code, the instantaneous deformation zone is specially extracted from the total domain and simulated for metal flow, while the total domain is used to simulate the evolution of thermal field. Taking the semi-analytical method as a solver, the pass planning procedure for stretch forging is developed, and the degrees-reduced finite element code is used as a supplement to check the rationality of the planed pass schedule. An example is implemented to demonstrate the application of the proposed technique.
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 Astrophysics Data System (ADS)
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
Cao, Le; Wei, Bing
2014-08-25
Finite-difference time-domain (FDTD) algorithm with a new method of plane wave excitation is used to investigate the RCS (Radar Cross Section) characteristics of targets over layered half space. Compare with the traditional excitation plane wave method, the calculation memory and time requirement is greatly decreased. The FDTD calculation is performed with a plane wave incidence, and the RCS of far field is obtained by extrapolating the currently calculated data on the output boundary. However, methods available for extrapolating have to evaluate the half space Green function. In this paper, a new method which avoids using the complex and time-consuming half space Green function is proposed. Numerical results show that this method is in good agreement with classic algorithm and it can be used in the fast calculation of scattering and radiation of targets over layered half space.
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.
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-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.
Two-dimensional physically based semi-analytical model of source/drain series resistance in MOSFETs
NASA Astrophysics Data System (ADS)
He, Pei; Ke, Daoming; Hu, Pengfei
2016-01-01
In this study, a two-dimensional physically based semi-analytical model of source/drain series resistance in MOSFETs is developed, in which only one parameter needs to be extracted by measurement and the extracted parameter can be repeatedly used when the structure size of the source or drain is changed. The model at the first time separates the resistance into two independent parameters that multiply each other. One is the extracted parameter that is only related to the resistivity. The other one is calculated by the expressions obtained by using the semi-analytical method and Eigen function expansion method, and is only related to the structure size of the source or drain area. The model provides a new approach to solve the resistance problem and matches well with simulation results. It can be used easily to estimate the resistance when the device structure changes in device design.
Roll levelling semi-analytical model for process optimization
NASA Astrophysics Data System (ADS)
Silvestre, E.; Garcia, D.; Galdos, L.; Saenz de Argandoña, E.; Mendiguren, J.
2016-08-01
Roll levelling is a primary manufacturing process used to remove residual stresses and imperfections of metal strips in order to make them suitable for subsequent forming operations. In the last years the importance of this process has been evidenced with the apparition of Ultra High Strength Steels with strength > 900 MPa. The optimal setting of the machine as well as a robust machine design has become critical for the correct processing of these materials. Finite Element Method (FEM) analysis is the widely used technique for both aspects. However, in this case, the FEM simulation times are above the admissible ones in both machine development and process optimization. In the present work, a semi-analytical model based on a discrete bending theory is presented. This model is able to calculate the critical levelling parameters i.e. force, plastification rate, residual stresses in a few seconds. First the semi-analytical model is presented. Next, some experimental industrial cases are analyzed by both the semi-analytical model and the conventional FEM model. Finally, results and computation times of both methods are compared.
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)
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-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.
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
High resolution semi-analytical three dimensional linear motions for tension leg platforms
Mullarkey, T.P.; McNamara, J.F. |
1995-12-31
Previous work by the authors has resulted in very accurate semi-analytical solutions for the three-dimensional linear hydrodynamics of submerged pontoons, floating columns and combinations of these solutions for the analysis of structures such as the ISSC TLP. The present paper is an extension of the semi-analytical approach to establishing the linear motions of the ISSC TLP including the effects of the tethers. A major advantage of the approach is that response functions may be computed accurately at an arbitrarily high resolution due to the inherent geometric and computational simplicity of the semi-analytical solution scheme. Therefore, the solution serves as a benchmark for the evaluation of results generated using panel methods, and this is illustrated by comparisons with the scatter obtained with available results in the literature.
Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation
NASA Astrophysics Data System (ADS)
Rosenwaks, Salman; Barmashenko, Boris D.; Waichman, Karol
2014-02-01
The feasibility of operating diode pumped alkali lasers (DPALs) with supersonic expansion of the gaseous laser mixture, consisting of alkali atoms, He atoms and (frequently) hydrocarbon molecules, is explored. Taking into account fluid dynamics and kinetic processes, both semi-analytical and three-dimensional (3D) computational fluid dynamics (CFD) modeling of supersonic DPALs is reported. Using the semi-analytical model, the operation of supersonic DPALs is compared with that measured and modeled in subsonic lasers for both Cs and K. The maximum power of supersonic Cs and K lasers is found to be higher than that of subsonic lasers with the same resonator and alkali density at the laser inlet by 25% and 70%, respectively. Using the 3D CFD model, the flow pattern and spatial distributions of the pump and laser intensities in the resonator are calculated for Cs DPALs. Comparison between the semi-analytical and 3D CFD models for Cs shows that the latter predicts much larger maximum achievable laser power than the former. These results indicate that for scaling-up the power of DPALs, supersonic expansion should be considered.
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.
Ultrasonic elastic modes in solid bars: an application of the plane wave expansion method.
Manzanares-Martinez, Betsabe; Ramos-Mendieta, Felipe; Baltazar, Arturo
2010-06-01
Ultrasonic elastic modes in solid bars are investigated theoretically and experimentally using the plane wave expansion method to calculate the dispersion curves k=k(omega) for longitudinal, torsional, and flexural waves. The plane wave extension method allows to consider rods of circular and square cross sections. The technique, which has received attention in the study of photonic and phononic crystals, is adapted in order to identify the various types of modes. Results are compared with predictions from semi-analytical models. The numerical approximation is validated with the experimental determination of the time-frequency dispersion curves. The technique based on the plane wave expansion method presented here could be a numerical alternative used to determine the wave propagation and modal vibration with high precision in structures like bars and cylinders. Practical applications of this study could include the inspection of long-span engineering systems with bar or cylinder like characteristics.
Semi-analytic technique for analyzing mode-locked lasers
Usechak, N.G.; Agrawal, G.P.
2005-03-21
A semi-analytic tool is developed for investigating pulse dynamics in mode-locked lasers. It provides a set of rate equations for pulse energy, width, and chirp, whose solutions predict how these pulse parameters evolve from one round trip to the next and how they approach their final steady-state values. An actively mode-locked laser is investigated using this technique and the results are in excellent agreement with numerical simulations and previous analytical studies.
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.
NASA Astrophysics Data System (ADS)
Monkewitz, Peter; Nagib, Hassan
2003-11-01
A semi-analytical procedure, based on matched asymptotic expansion techniques, is used to represent by a single composite expansion a number of mean-velocity data sets from laboratory and numerical (DNS) experiments covering a range of Re_τ from 100 to 530,000. The process reveals the importance of the logarithmic representation in the overlap region of these wall bounded flows and sheds some light on the reasons for the different values of the Kármán constant proposed in the literature. From the semi-analytical representation, the scalings for the value and location of the Reynolds stress maximum are extracted. Furthermore, an expression for the dependence of skin friction on Reynolds number is obtained. Finally, the need for additional well instrumented experiments and higher Reynolds number DNS will be discussed.
NASA Astrophysics Data System (ADS)
Xu, Hui-Fang; Dai, Yue-Hua; Xu, Jian-Bin; Li, Ning; Yang, Jin; Zheng, Chang-Yong
2015-05-01
A semi-analytical subthreshold surface potential model for double-doping polysilicon gate (DDPG) MOSFETs is presented. By introducing two rectangular sources located in the gate insulator and the channel-depleted region, the two-dimensional (2D) Poisson equations are solved using a semi-analytical method combined with an eigenfunction expansion method. Expressions for the potentials are obtained as special functions of infinite series expressions. A subthreshold drain current is proposed on the basis of the potential profile, and it accounts for the carriers’ drift diffusion and thermionic emission theory. The advantage of this work is that the two-dimensional treatment of the gate insulator region has resulted in physical consistency across a dielectric boundary. The proposed model not only offers physical insight into device physics but also provides the basic designing guideline for DDPG MOSFETs, enabling the designer to optimize the device in accordance with the application. Very good agreement for both the subthreshold surface potential and drain current is observed between the model calculations and the simulated results.
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.
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.
Chen, Jun; Quan, Wenting; Cui, Tingwei
2015-01-01
In this study, two sample semi-analytical algorithms and one new unified multi-band semi-analytical algorithm (UMSA) for estimating chlorophyll-a (Chla) concentration were constructed by specifying optimal wavelengths. The three sample semi-analytical algorithms, including the three-band semi-analytical algorithm (TSA), four-band semi-analytical algorithm (FSA), and UMSA algorithm, were calibrated and validated by the dataset collected in the Yellow River Estuary between September 1 and 10, 2009. By comparing of the accuracy of assessment of TSA, FSA, and UMSA algorithms, it was found that the UMSA algorithm had a superior performance in comparison with the two other algorithms, TSA and FSA. Using the UMSA algorithm in retrieving Chla concentration in the Yellow River Estuary decreased by 25.54% NRMSE (normalized root mean square error) when compared with the FSA algorithm, and 29.66% NRMSE in comparison with the TSA algorithm. These are very significant improvements upon previous methods. Additionally, the study revealed that the TSA and FSA algorithms are merely more specific forms of the UMSA algorithm. Owing to the special form of the UMSA algorithm, if the same bands were used for both the TSA and UMSA algorithms or FSA and UMSA algorithms, the UMSA algorithm would theoretically produce superior results in comparison with the TSA and FSA algorithms. Thus, good results may also be produced if the UMSA algorithm were to be applied for predicting Chla concentration for datasets of Gitelson et al. (2008) and Le et al. (2009).
Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers
NASA Astrophysics Data System (ADS)
Samani, Nozar; Sedghi, Mohammad M.
2015-03-01
Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head-constant head wedge, constant head-barrier wedge and barrier-barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.
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.
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.
A semi-analytic dynamical friction model for cored galaxies
NASA Astrophysics Data System (ADS)
Petts, J. A.; Read, J. I.; Gualandris, A.
2016-11-01
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 our semi-analytic model from previous work, 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.
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.
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.
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.
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
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.
Semi-analytical models of hydroelastic sloshing impact in tanks of liquefied natural gas vessels.
Ten, I; Malenica, Š; Korobkin, A
2011-07-28
The present paper deals with the methods for the evaluation of the hydroelastic interactions that appear during the violent sloshing impacts inside the tanks of liquefied natural gas carriers. The complexity of both the fluid flow and the structural behaviour (containment system and ship structure) does not allow for a fully consistent direct approach according to the present state of the art. Several simplifications are thus necessary in order to isolate the most dominant physical aspects and to treat them properly. In this paper, choice was made of semi-analytical modelling for the hydrodynamic part and finite-element modelling for the structural part. Depending on the impact type, different hydrodynamic models are proposed, and the basic principles of hydroelastic coupling are clearly described and validated with respect to the accuracy and convergence of the numerical results.
Semi-analytical models of hydroelastic sloshing impact in tanks of liquefied natural gas vessels.
Ten, I; Malenica, Š; Korobkin, A
2011-07-28
The present paper deals with the methods for the evaluation of the hydroelastic interactions that appear during the violent sloshing impacts inside the tanks of liquefied natural gas carriers. The complexity of both the fluid flow and the structural behaviour (containment system and ship structure) does not allow for a fully consistent direct approach according to the present state of the art. Several simplifications are thus necessary in order to isolate the most dominant physical aspects and to treat them properly. In this paper, choice was made of semi-analytical modelling for the hydrodynamic part and finite-element modelling for the structural part. Depending on the impact type, different hydrodynamic models are proposed, and the basic principles of hydroelastic coupling are clearly described and validated with respect to the accuracy and convergence of the numerical results. PMID:21690141
The Multi-SAG project: filling the MultiDark simulations with semi-analytic galaxies
NASA Astrophysics Data System (ADS)
Vega-Martínez, C. A.; Cora, S. A.; Padilla, N. D.; Muñoz Arancibia, A. M.; Orsi, A. A.; Ruiz, A. N.
2016-08-01
The semi-analytical model sag is a code of galaxy formation and evolution which is applied to halo catalogs and merger trees extracted from cosmological -body simulations of dark matter. This contribution describes the project of constructing a catalog of simulated galaxies by adapting and applying the model sag over two dark matter simulations of the spanish MultiDark Project publicly available. Those simulations have particles, each, in boxes with sizes of 1000 Mpc and 400 Mpc respectively with Planck cosmological parameters. They cover a large range of masses and have halo mass resolutions of , therefore each simulation is able to produce more than 150 millions of simulated galaxies. A detailed description of the method is explained, and the first statistical results are shown.
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.
Development of new hole expansion testing method
NASA Astrophysics Data System (ADS)
Kim, Hyunok; Shang, Jianhui; Beam, Kevin; Samant, Anoop; Hoschouer, Cliff; Dykeman, Jim
2016-08-01
This paper introduces a new hole expansion (HE) testing method that could be more relevant to the edge cracking problem observed in stamping advanced high strength steel (AHSS). The new testing method adopted a large hole diameter of 75 mm compared to the standard hole diameter of 10 mm. An inline monitoring system was developed to visually monitor the hole edge cracking during the test and synchronize the load-displacement data with the recorded video for capturing the initial crack. A new hole expansion testing method was found to be effective in evaluating the edge cracking by considering the effects of material properties and trimming methods. It showed a much larger difference, up to 11%, of the HE ratio between DP980 and TRIP780 compared to the standard HE testing method giving less than a 2% difference.
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.
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)
Bertone, Serena; Stoehr, Felix; White, Simon D. M.
2005-06-01
We present a semi-analytic treatment of galactic winds within high-resolution, large-scale cosmological N-body simulations of a Λ cold dark matter (ΛCDM) universe. The evolution of winds is investigated by following the expansion of supernova-driven superbubbles around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52h-1Mpc and mean density close to the mean density of the universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao. Results are presented for the volume filling factor and the mass fraction of the intergalactic medium (IGM) affected by winds, and their dependence on the model parameters is carefully investigated. The mass-loading efficiency of bubbles is a key factor to determine the evolution of winds and their global impact on the IGM: the higher the mass loading, the later the IGM is enriched with metals. Galaxies with 109 < M* < 1010Msolar are responsible for most of the metals ejected into the IGM at z= 3, while galaxies with M* < 109Msolargive a non-negligible contribution only at higher redshifts, when larger galaxies have not yet assembled. We find a higher mean IGM metallicity than Lyα forest observations suggest, and we argue that the discrepancy may be explained by the high temperatures of a large fraction of the metals in winds, which may not leave detectable imprints in absorption in the Lyα forest.
Gravity field error analysis for pendulum formations by a semi-analytical approach
NASA Astrophysics Data System (ADS)
Li, Huishu; Reubelt, Tilo; Antoni, Markus; Sneeuw, Nico
2016-10-01
Many geoscience disciplines push for ever 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 compared to uc(Grace). One possibility to increase the sensitivity and isotropy by adding cross-track information is a pair of satellites flying in a pendulum formation. This formation contains two satellites which have different ascending nodes and arguments of latitude, but have the same orbital height and inclination. In this study, the semi-analytical approach for efficient pre-mission error assessment is presented, and the transfer coefficients of range, range-rate and range-acceleration gravitational perturbations are derived analytically for the pendulum formation considering a set of opening angles. The new challenge is the time variations of the opening angle and the range, leading to temporally variable transfer coefficients. This is solved by Fourier expansion of the sine/cosine of the opening angle and the central angle. The transfer coefficients are further applied to assess the error patterns which are caused by different orbital parameters. The simulation results indicate that a significant improvement in accuracy and isotropy is obtained for small and medium initial opening angles of single polar pendulums, compared to uc(Grace). The optimal initial opening angles are 45° and 15° for accuracy and isotropy, respectively. For a Bender configuration, which is constituted by a polar uc(Grace) and an inclined pendulum in this paper, the behaviour of results is dependent on the inclination (prograde vs. retrograde) and on the relative baseline orientation (left or right leading). The simulation for a sun-synchronous orbit shows better results for the left leading case.
NASA Astrophysics Data System (ADS)
Munekane, H.
2005-10-01
We developed a semi-analytical method to evaluate the effect of the second-order ionospheric correction on GPS positioning. This method is based on the semi-analytical positioning error simulation method developed by Geiger and Santerre in which, assuming the continuous distribution of the satellites, a normal equation is formed to estimate the positioning error taking all the contributions of the ranging error by the visible satellites into account. Our method successfully reproduced the averaged time-series of three IGS sites which is comparable to the rigorous simulation. We then evaluated the effect of the ionospheric error on the determination of the reference frame. We evaluated the additional Helmert parameters that are required for the ionospheric effect. We found that the ionospheric effect can lead to annual scale changes of 0.1 ppb, with an offset of 1.8 mm and a semi-annual oscillation of 1 mm in the z-direction. However, these values are too small to explain the current deviations between the GPS-derived reference frame and the ITRF reference frame. Next, we estimated the apparent scale changes due to the ionospheric error in the GEONET coordinate time-series in Japan. We could qualitatively reproduce the observed semi-annual scale changes peaking at the equinoxes and having asymmetrical amplitudes between the vernal and autumnal equinoxes.
Semi-analytical model of arrayed waveguide grating in SOI using Gaussian beam approximation.
Sidharth, R; Das, B K
2015-03-10
The arrayed waveguide grating structure can be used as an important component in high-speed CMOS optical interconnects in silicon-on-insulator (SOI) platform. However, the performance of such device is found to be extremely sensitive to the fabrication-related errors in defining the critical features. In the absence of an appropriate analytical model, one needs to rely on numerical computation to analyze the device characteristics and fabrication tolerances. Because compact design of such a device structure has foot-print ∼mm^{2} and the smallest features can be as small as ∼500 nm×220 nm (waveguide cross section), it demands a huge computational budget to optimize the design parameters. A semi-analytical model using Gaussian beam approximation of guided mode profiles has been developed to analyze the output spectrum of arrayed waveguide grating and to estimate the phase errors due to waveguide inhomogeneities. This model has been validated with existing numerical methods and published experimental results. It has been observed that a probabilistic waveguide width variations of ΔW∼5 nm can cause a cross-talk degradation of about 40 dB (25 dB) for a device (operating at λ∼1550 nm) fabricated on SOI substrate with 220 nm (2 μm) device layer thickness.
Synthetic aperture imaging using a semi-analytic model for the transmit beams
NASA Astrophysics Data System (ADS)
Hansen, Jens M.; Nikolov, Svetoslav I.
2015-03-01
Many modern high-end scanners use some form for coherent synthesis of image lines by combining beams acquired with different transmissions, such as retrospective dynamic transmit focusing (Acuson / Siemens), nSIGHT (Philips), and Zone imaging (Zonare). There are two major strategies described in the literature to uniformly focus both transmit and receive beams throughout the field of view - using virtual sources, and by applying spatial matched filtration. The virtual source model is precise, when the transmit is either strongly focused (f-number ~ 1, 2) or images are formed using circular or spherical waves. The spatial matched filtration can be used also with weakly focused transmissions, but requires the measurement and storage of the response of point targets within the limits of the transmit beam. This paper presents a semi-analytic model for the transmitted field, which can be applied to synthetic transmit imaging. The model is more precise than the virtual source concept, does not require the measurement of the transmit field as matched filtration methods do, and can be applied to both strongly and weakly focused transmissions. Furthermore, the model is applicable to tissue harmonic and contrast enhanced ultrasound imaging. The paper presents the development of the model using the principles of diffraction, and its validation using computer simulations and measurements on a phantom. Finally, the model is demonstrated for synthetic aperture tissue harmonic in-vivo imaging.
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.
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 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.
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.
Analytical and Semi-Analytical Tools for the Design of Oscillatory Pumping Tests.
Cardiff, Michael; Barrash, Warren
2015-01-01
Oscillatory pumping tests-in which flow is varied in a periodic fashion-provide a method for understanding aquifer heterogeneity that is complementary to strategies such as slug testing and constant-rate pumping tests. During oscillatory testing, pressure data collected at non-pumping wells can be processed to extract metrics, such as signal amplitude and phase lag, from a time series. These metrics are robust against common sensor problems (including drift and noise) and have been shown to provide information about aquifer heterogeneity. Field implementations of oscillatory pumping tests for characterization, however, are not common and thus there are few guidelines for their design and implementation. Here, we use available analytical solutions from the literature to develop design guidelines for oscillatory pumping tests, while considering practical field constraints. We present two key analytical results for design and analysis of oscillatory pumping tests. First, we provide methods for choosing testing frequencies and flow rates which maximize the signal amplitude that can be expected at a distance from an oscillating pumping well, given design constraints such as maximum/minimum oscillator frequency and maximum volume cycled. Preliminary data from field testing helps to validate the methodology. Second, we develop a semi-analytical method for computing the sensitivity of oscillatory signals to spatially distributed aquifer flow parameters. This method can be quickly applied to understand the "sensed" extent of an aquifer at a given testing frequency. Both results can be applied given only bulk aquifer parameter estimates, and can help to optimize design of oscillatory pumping test campaigns. PMID:25535805
Structural Properties of Spherical Galaxies: a Semi-Analytical Approach
NASA Astrophysics Data System (ADS)
Simonneau, E.; Prada, F.
2004-04-01
Since the distribution of light measured along any galactocentric radius of an elliptical galaxy has the same functional form exp[-R1/n] (Sérsic profile) for almost all galaxies, and since this profile is the Abel integral of the luminous density, it looks worth-while to seek the way to derive the latter from the former. We propose in this paper a ''discrete ordinate'' method, which yields, for any value of n > 1, an explicit expression for the luminous density, ρL(r), that can be evaluated numerically to any required degree of precision. Once we have obtained such an expresion for the spatial density, ρL(r), we can compute straightforwardly the mass distribution, M(r), the potential, φ(r), and the velocity dispersions, σs2 (r), in space and on the observational plane, σp2(R).
Semi-analytic stellar structure in scalar-tensor gravity
NASA Astrophysics Data System (ADS)
Horbatsch, M. W.; Burgess, C. P.
2011-08-01
Precision tests of gravity can be used to constrain the properties of hypothetical very light scalar fields, but these tests depend crucially on how macroscopic astrophysical objects couple to the new scalar field. We study the equations of stellar structure using scalar-tensor gravity, with the goal of seeing how stellar properties depend on assumptions made about the scalar coupling at a microscopic level. In order to make the study relatively easy for different assumptions about microscopic couplings, we develop quasi-analytic approximate methods for solving the stellar-structure equations rather than simply integrating them numerically. (The approximation involved assumes the dimensionless scalar coupling at the stellar center is weak, and we compare our results with numerical integration in order to establish its domain of validity.) We illustrate these methods by applying them to Brans-Dicke scalars, and their generalization in which the scalar-matter coupling slowly runs — or `walks' — as a function of the scalar field: a(phi) simeq as+bsphi. (Such couplings can arise in extra-dimensional applications, for instance.) The four observable parameters that characterize the fields external to a spherically symmetric star are the stellar radius, R, mass, M, scalar `charge', Q, and the scalar's asymptotic value, phi∞. These are subject to two relations because of the matching to the interior solution, generalizing the usual mass-radius, M(R), relation of General Relativity. Since phi∞ is common to different stars in a given region (such as a binary pulsar), all quantities can be computed locally in terms of the stellar masses. We identify how these relations depend on the microscopic scalar couplings, agreeing with earlier workers when comparisons are possible. Explicit analytical solutions are obtained for the instructive toy model of constant-density stars, whose properties we compare to more realistic equations of state for neutron star models.
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
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
Recent advances in semi-analytical scattering models for NDT simulation
NASA Astrophysics Data System (ADS)
Darmon, M.; Chatillon, S.; Mahaut, S.; Calmon, P.; Fradkin, L. J.; Zernov, V.
2011-01-01
For several years, CEA-LIST and partners have been developing ultrasonic simulation tools with the aim of modelling non-destructive evaluation. The existing ultrasonic modules allow us to simulate fully real ultrasonic inspection scenarios in a range of applications which requires the computation of the propagated beam, as well as its interaction with flaws. To fulfil requirements of an intensive use (for parametric studies), the choice has been made to adopt mainly analytical approximate or exact methods to model the scattering of ultrasound by flaws. The applied analytical theories (Kirchhoff and Born approximations, GTD, SOV...) were already described in previous GDR communication. Over the years, this "semi-analytical" approach has been enriched by adaptations and improvements of the existing models or by new models, in order to extend the applicability of the simulation tools. This paper is devoted to the following recent advances performed in the framework of this approach: The SOV method based on the exact analytical model for the scattering from a cylindrical cavity has been extended in 3D to account for field variations along the cylinder. This new 3D model leads to an improvement in simulation of small side-drilled holes. Concerning the geometrical theories of diffraction (GTD), subroutines for calculation of the 2D wedge diffraction coefficients (for bulk or Rayleigh incident waves) have been developed by the Waves and Fields Group and uniform corrections (UAT and UTD) are under investigation. Modelling of the contribution of the head wave and creeping wave to the echoes arising from a wedge. Numerous experimental validations of the developed models are provided. New possibilities offered by these new developments are emphasized.
NASA Astrophysics Data System (ADS)
Mayrhofer, Arno; Rogers, Benedict D.; Violeau, Damien; Ferrand, Martin
2013-11-01
Semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in smoothed particle hydrodynamics (SPH) for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as a form of "turbulence", is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusion term as well as the wall boundary condition. In order to validate the theoretical constructs numerical experiments are performed showing that the present volume flux term yields results with an error 5 orders of magnitude smaller then previous methods while the Robin boundary conditions are imposed correctly with an error depending on the order of the approximation. Furthermore, the proposed modifications for free-surface flows improve the behavior at the intersection of free surface and wall as well as prevent free-surface detachment when using the volume diffusion term. Finally, this paper is concluded by a simulation of a dam break over a wedge demonstrating the improvements proposed in this paper.
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.
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.
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
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
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.
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
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.
Hilpert, Markus
2010-07-15
The displacement of a gas by a liquid in both horizontal and inclined capillary tubes where the tube inlet is connected to a liquid reservoir of constant pressure can be described by the Lucas-Washburn theory. One can also use the Lucas-Washburn theory to model the reverse flow, that is, liquid withdrawal, even though the latter case has received relatively little attention. In this paper, we derive analytical solutions for the travel time of the gas-liquid interface as a function of interface velocity. The interface position can be obtained by numerically integrating the numerically inverted interface velocity. Therefore we refer to these solutions as (semi)-analytical. We neglect inertial forces. However, we account for a dynamic contact angle where the nondimensional non-equilibrium Young force depends on the capillary number in the form of either a power law or a power series. We explore the entire nondimensional parameter space. The analytical solutions allow us to show that five different liquid withdrawal scenarios may occur that differ in the direction of flow and the sign of the acceleration of the gas-liquid interface: horizontal, upward, steady-state downward, accelerating downward, and decelerating downward flow. In the last case, the liquid is withdrawn from the tube either completely or partially. The (semi)-analytical solutions are also valid within the limit where the contact angle is constant.
[Retrieve phycocyanin concentrations based on semi-analytical model in the Dianchi Lake, China].
Yin, Bin; Lü, Heng; Li, Yun-Mei; Wu, Chuan-Qing; Zhu, Li; Wang, Yan-Fei
2011-02-01
Phycocyanin (PC) in the blue-green algae is usually used to detective the quantity of the blue-green algae, because of its special absorption at band 620 nm. A semi-analytical model retrieving phycocyanin concentrations is been built, based on a nested semi-empirical band ratio algorithm, using the data sets collected in September 19 and September 20, 2009 from Dianchi Lake. The empirical relationship between the specific absorption coefficient at band 620 nm [a(PC)* (620)] and the absorption coefficient at band 620 nm [a(PC) (620)] reduces the impact of the variability of a(PC)* (620) in the model built by Simis. The new semi-analytical model is proved well done in retrieving phycocyanin concentrations and has a mean relative error (MRE) 21.63% by the dataset collected on December 1, 2009 from Dianchi Lake. The model error analysis prove that the main reason of the error is caused by the component and concentrations of pigments changing seasonally in the blue-green algae.
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).
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
Homentcovschi, Dorel; Miles, Ronald N
2012-02-01
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.
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.
NASA Astrophysics Data System (ADS)
Jaurigue, Lina; Pimenov, Alexander; Rachinskii, Dmitrii; Schöll, Eckehard; Lüdge, Kathy; Vladimirov, Andrei G.
2015-11-01
We study the effect of delayed coherent optical feedback on the pulse timing jitter in passively-mode-locked semiconductor lasers with the help of a semi-analytical method which we develop to calculate the timing fluctuations in these lasers. Through the proposed method physical insights into the feedback dependence of the timing jitter are gained and the greatly reduced computation times allow for the investigation of the dependence of timing fluctuations over greater parameter domains. We show that resonant feedback leads to a reduction in the timing jitter and that a frequency-pulling region forms about the main resonances, within which a timing jitter reduction is observed. The width of these frequency-pulling regions increases linearly with short feedback delay times. We derive an analytic expression for the timing jitter, which predicts a monotonic decrease in the timing jitter for resonant feedback of increasing delay lengths, when timing jitter effects are fully separated from amplitude jitter effects. For long feedback cavities the decrease in timing jitter scales approximately as 1 /τ with increasing feedback delay time τ . This behavior is not related to the stability of the system but is instead due to the influence of the noise, on the timing jitter, being reduced since the solution space is larger for increasing τ .
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
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.
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.
Constraining the last 7 billion years of galaxy evolution in semi-analytic models
NASA Astrophysics Data System (ADS)
Mutch, Simon J.; Poole, Gregory B.; Croton, Darren J.
2013-01-01
We investigate the ability of the Croton et al. semi-analytic model to reproduce the evolution of observed galaxies across the final 7 billion years of cosmic history. Using Monte Carlo Markov Chain techniques we explore the available parameter space to produce a model which attempts to achieve a statistically accurate fit to the observed stellar mass function at z = 0 and z ≈ 0.8, as well as the local black hole-bulge relation. We find that in order to be successful we are required to push supernova feedback efficiencies to extreme limits which are, in some cases, unjustified by current observations. This leads us to the conclusion that the current model may be incomplete. Using the posterior probability distributions provided by our fitting, as well as the qualitative details of our produced stellar mass functions, we suggest that any future model improvements must act to preferentially bolster star formation efficiency in the most massive haloes at high redshift.
Galaxy Number Counts Applied to a Semi-Analytic Galaxy Model in the Millennium Run Simulation
NASA Astrophysics Data System (ADS)
Bucklein, Brian; Moody, J. W.; Hintz, E. G.
2010-01-01
The Millennium Run simulation used more than 10 billion particles to trace the evolution of the dark matter distribution in a ΛCDM cosmology in a cubic region of the Universe over 2 billion light-years on a side. This data was used by Croton et al. as the basis of a semi-analytic galaxy model, allowing the region to be populated with more than 9 million galaxies brighter than Mr = -17.4. We visually analyze this galaxy catalog searching for significant voids and then apply galaxy number count (GNC) analysis to the lines-of-sight to these voids. Using Wolf plots, we investigate whether GNC analysis would allow us to locate voids within the sample without the need to first find them visually.
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
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.
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 Rapid Distortion Theory modified turbulence spectra for semi-analytical airfoil noise prediction
NASA Astrophysics Data System (ADS)
Santana, Leandro D.; Christophe, Julien; Schram, Christophe; Desmet, Wim
2016-11-01
This paper proposes an implementation of the Rapid Distortion Theory, for the prediction of the noise resulting from the interaction of an airfoil with incoming turbulence. In the framework of the semi-analytical modeling strategy known as Amiet's theory, this interaction mechanism is treated in a linearized form where the airfoil thickness, camber and angle of attack are assumed negligible, leading to a frozen turbulence description of the incident gust. Important semi-analytical developments have been proposed in the literature to improve the modeling of the gust-airfoil interaction accounting for parallel and skewed gusts, non-rectangular linearized airfoil shapes or blade tip effects. This work is rather focused on the investigation of the distortion of turbulence that occurs in the vicinity of the airfoil leading edge, compared with Rapid Distortion Theory, where main results are briefly reminded in this paper. The main contribution of this work is a detailed experimental investigation of the evolution of turbulent quantities relevant to noise production, performed in the close vicinity of the airfoil leading edge subjected to grid turbulence, by means of stereoscopic Particle Image Velocimetry measurements. The results indicate that the distortion effects are concentrated in a narrow region close to the stagnation point of the leading edge, with dimension of the order of its radius of curvature. Additionally, it is shown that the turbulence intensity grows significantly as the flow approaches the airfoil leading-edge. Based on those results, a modified turbulence spectrum is proposed to describe the incoming turbulence in Amiet's theory. The sound predictions show a significantly better match with acoustic measurements than using the original turbulence model.
NASA Astrophysics Data System (ADS)
Ostiguy, Pierre-Claude; Quaegebeur, Nicolas; Bilodeau, Maxime; Masson, Patrice
2015-03-01
In Structural Health Monitoring (SHM), classical imaging techniques rely on the use of analytical formulations to predict the propagation and interaction of guided waves generated using piezoceramic (PZT) transducers. For the implementation of advanced imaging approaches on composites structures, analytical formulations need to consider (1) the dependency of phase velocity and damping as a function of angle (2) the steering effect on guided wave propagation caused by the anisotropy of the structure and (3) the full transducer dynamics. In this paper, the analytical modeling of guided waves generation by a circular PZT and propagation on composite structures is investigated. This work, based on previous work from the authors, is intended to extend a semi- analytical formulation from isotropic to transversely isotropic plate-like structures. The formulation considers the dependency of the interfacial shear stress under the PZT as a function of radius, angular frequency and orientation on the composite structure. Validation is conducted for a unidirectional transversely isotropic structure with a bonded circular PZT of 10 mm in diameter. Amplitude curves and time domain signals of the A0 and S0 modes obtained from the proposed formulation and the classical pin-force model are first compared to Finite Element Model simulations. Experimental validation is then conducted using a 3D laser Doppler vibrometer for a non- principal direction on the composite. The results show the interest of considering a semi-analytical formulation for which the transducer dynamics where the shear stress distribution under the transducer is considered in order to reproduce more precisely the generation of guided waves on composite structures.
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.
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.
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.
Improved fake mode free plane wave expansion method.
Jiang, Bin; Zhou, Wenjun; Chen, Wei; Liu, Anjin; Zheng, Wanhua
2011-08-01
We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.
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
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.
The star formation and AGN luminosity relation: predictions from a semi-analytical model
NASA Astrophysics Data System (ADS)
Gutcke, Thales A.; Fanidakis, Nikos; Macciò, Andrea V.; Lacey, Cedric
2015-08-01
In a universe where active galactic nucleus (AGN) feedback regulates star formation in massive galaxies, a strong correlation between these two quantities is expected. If the gas causing star formation is also responsible for feeding the central black hole, then a positive correlation is expected. If powerful AGNs are responsible for the star formation quenching, then a negative correlation is expected. Observations so far have mainly found a mild correlation or no correlation at all [i.e. a flat relation between star formation rate (SFR) and AGN luminosity], raising questions about the whole paradigm of `AGN feedback'. In this paper, we report the predictions of the GALFORM semi-analytical model, which has a very strong coupling between AGN activity and quenching of star formation. The predicted SFR-AGN luminosity correlation appears negative in the low AGN luminosity regime, where AGN feedback acts, but becomes strongly positive in the regime of the brightest AGN. Our predictions reproduce reasonably well recent observations by Rosario et al., yet there is some discrepancy in the normalization of the correlation at low luminosities and high redshifts. Though this regime could be strongly influenced by observational biases, we argue that the disagreement could be ascribed to the fact that GALFORM neglects AGN variability effects. Interestingly, the galaxies that dominate the regime where the observations imply a weak correlation are massive early-type galaxies that are subject to AGN feedback. Nevertheless, these galaxies retain high enough molecular hydrogen contents to maintain relatively high SFRs and strong infrared emission.
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.
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.
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-analytical solution for simulating contaminant transport subject to chain-decay reactions.
Sudicky, Edward A; Hwang, Hyoun-Tae; Illman, Walter A; Wu, Yu-Shu; Kool, Jan B; Huyakorn, Peter
2013-01-01
We present a set of new, semi-analytical solutions to simulate three-dimensional contaminant transport subject to first-order chain-decay reactions. The aquifer is assumed to be areally semi-infinite, but finite in thickness. The analytical solution can treat the transformation of contaminants into daughter products, leading to decay chains consisting of multiple contaminant species and various reaction pathways. The solution in its current form is capable of accounting for up to seven species and four decay levels. The complex pathways are represented by means of first-order decay and production terms, while branching ratios account for decay stoichiometry. Besides advection, dispersion, bio-chemical or radioactive decay and daughter product formation, the model also accounts for sorption of contaminants on the aquifer solid phase with each species having a different retardation factor. First-type contaminant boundary conditions are utilized at the source (x=0 m) and can be either constant-in-time for each species, or the concentration can be allowed to undergo first-order decay. The solutions are obtained by exponential Fourier, Fourier cosine and Laplace transforms. Limiting forms of the solutions can be obtained in closed form, but we evaluate the general solutions by numerically inverting the analytical solutions in exponential Fourier and Laplace transform spaces. Various cases are generated and the solutions are verified against the HydroGeoSphere numerical model.
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.
Density-functional expansion methods: Generalization of the auxiliary basis
Giese, Timothy J.; York, Darrin M.
2011-01-01
The formulation of density-functional expansion methods is extended to treat the second and higher-order terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the self-consistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis. PMID:21599040
A semi-analytical model for the prediction of underwater noise from offshore pile driving
NASA Astrophysics Data System (ADS)
Tsouvalas, A.; Metrikine, A. V.
2013-06-01
Underwater noise from offshore pile driving gained considerable attention in recent years mainly due to the large scale construction of offshore wind farms. The most common foundation type of a wind turbine is a monopile, upon which the wind tower rests. The pile is driven into place with the help of hydraulic hammers. During the hammering of the pile, high levels of noise are generated which are known to produce deleterious effects on both mammals and fish. In this work, a linear semi-analytical model is developed for predicting the levels of underwater noise for a wide range of system parameters. The model incorporates all major parts of the system. The hydraulic hammer is substituted by an external force, the pile is described as a thin circular cylindrical shell, the water is modelled as a compressible fluid and the water-saturated seabed is defined by distributed springs and dashpots in all directions. The solution of the coupled vibroacoustic problem is based on the representation of the response of the complete system on the modal basis of the in vacuo shell structure. The influence that the inter-modal coupling, the choice of the soil parameters and the acoustic impedance of the seabed have on the generated noise levels is studied in the frequency domain. Strong and weak points of the present model are discussed on the basis of a comparison with a set of available experimental data. The obtained results show the capability of the model to predict the underwater noise levels both qualitatively and quantitatively.
Galaxies in the EAGLE hydrodynamical simulation and in the Durham and Munich semi-analytical models
NASA Astrophysics Data System (ADS)
Guo, Quan; Gonzalez-Perez, Violeta; Guo, Qi; Schaller, Matthieu; Furlong, Michelle; Bower, Richard G.; Cole, Shaun; Crain, Robert A.; Frenk, Carlos S.; Helly, John C.; Lacey, Cedric G.; Lagos, Claudia del P.; Mitchell, Peter; Schaye, Joop; Theuns, Tom
2016-10-01
We compare global predictions from the EAGLE hydrodynamical simulation, and two semi-analytic (SA) models of galaxy formation, L-GALAXIES and GALFORM. All three models include the key physical processes for the formation and evolution of galaxies and their parameters are calibrated against a small number of observables at z ≈ 0. The two SA models have been applied to merger trees constructed from the EAGLE dark matter only simulation. We find that at z ≤ 2, both the galaxy stellar mass functions for stellar masses M* < 1010.5 M⊙ and the median specific star formation rates (sSFRs) in the three models agree to better than 0.4 dex. The evolution of the sSFR predicted by the three models closely follows the mass assembly history of dark matter haloes. In both EAGLE and L-GALAXIES there are more central passive galaxies with M* < 109.5 M⊙ than in GALFORM. This difference is related to galaxies that have entered and then left a larger halo and which are treated as satellites in GALFORM. In the range 0 < z < 1, the slope of the evolution of the star formation rate density in EAGLE is a factor of ≈1.5 steeper than for the two SA models. The median sizes for galaxies with M* > 109.5 M⊙ differ in some instances by an order of magnitude, while the stellar mass-size relation in EAGLE is a factor of ≈2 tighter than for the two SA models. Our results suggest the need for a revision of how SA models treat the effect of baryonic self-gravity on the underlying dark matter. The treatment of gas flows in the models needs to be revised based on detailed comparison with observations to understand in particular the evolution of the stellar mass-metallicity relation.
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.
The dynamics of double slab subduction from numerical and semi-analytic models
NASA Astrophysics Data System (ADS)
Holt, A.; Royden, L.; Becker, T. W.
2015-12-01
Regional interactions between multiple subducting slabs have been proposed to explain enigmatic slab kinematics in a number of subduction zones, a pertinent example being the rapid pre-collisional plate convergence of India and Eurasia. However, dynamically consistent 3-D numerical models of double subduction have yet to be explored, and so the physics of such double slab systems remain poorly understood. Here we build on the comparison of a fully numerical finite element model (CitcomCU) and a time-dependent semi-analytic subduction models (FAST) presented for single subduction systems (Royden et. al., 2015 AGU Fall Abstract) to explore how subducting slab kinematics, particularly trench and plate motions, can be affected by the presence of an additional slab, with all of the possible slab dip direction permutations. A second subducting slab gives rise to a more complex dynamic pressure and mantle flow fields, and an additional slab pull force that is transmitted across the subduction zone interface. While the general relationships among plate velocity, trench velocity, asthenospheric pressure drop, and plate coupling modes are similar to those observed for the single slab case, we find that multiple subducting slabs can interact with each other and indeed induce slab kinematics that deviate significantly from those observed for the equivalent single slab models. References Jagoutz, O., Royden, L. H., Holt, A. F. & Becker, T. W., 2015, Nature Geo., 8, 10.1038/NGEO2418. Moresi, L. N. & Gurnis, M., 1996, Earth Planet. Sci. Lett., 138, 15-28. Royden, L. H. & Husson, L., 2006, Geophys. J. Int. 167, 881-905. Zhong, S., 2006, J. Geophys. Res., 111, doi: 10.1029/2005JB003972.
Improved Fermi operator expansion methods for fast electronic structure calculations
NASA Astrophysics Data System (ADS)
Liang, WanZhen; Saravanan, Chandra; Shao, Yihan; Baer, Roi; Bell, Alexis T.; Head-Gordon, Martin
2003-08-01
Linear scaling algorithms based on Fermi operator expansions (FOE) have been considered significantly slower than other alternative approaches in evaluating the density matrix in Kohn-Sham density functional theory, despite their attractive simplicity. In this work, two new improvements to the FOE method are introduced. First, novel fast summation methods are employed to evaluate a matrix polynomial or Chebyshev matrix polynomial with matrix multiplications totalling roughly twice the square root of the degree of the polynomial. Second, six different representations of the Fermi operators are compared to assess the smallest possible degree of polynomial expansion for a given target precision. The optimal choice appears to be the complementary error function. Together, these advances make the FOE method competitive with the best existing alternatives.
Modal characteristics of a simplified brake rotor model using semi-analytical Rayleigh Ritz method
NASA Astrophysics Data System (ADS)
Zhang, F.; Cheng, L.; Yam, L. H.; Zhou, L. M.
2006-10-01
Emphasis of this paper is given to the modal characteristics of a brake rotor which is utilized in automotive disc brake system. The brake rotor is modeled as a combined structure comprising an annular plate connected to a segment of cylindrical shell by distributed artificial springs. Modal analysis shows the existence of three types of modes for the combined structure, depending on the involvement of each substructure. A decomposition technique is proposed, allowing each mode of the combined structure to be decomposed into a linear combination of the individual substructure modes. It is shown that the decomposition coefficients provide a direct and systematic means to carry out modal classification and quantification.
Comparison of methods for improving the 1/N expansion
NASA Astrophysics Data System (ADS)
Varshni, Y. P.
1989-08-01
The recently proposed method by Papp [Phys. Rev. A 36, 3550 (1987); 38, 2158 (1988)] for determining the shift parameter in the shifted 1/N expansion method has been applied in three approximations to calculate the eigenenergies for the static screened Coulomb potential (SSCP) and Lennard-Jones 12-6 potential. The results are compared with those obtained by the method of Imbo et al. [Phys. Rev. D 29, 1669 (1984)] and the exact values. For the SSCP, comparison is also made with the results obtained by two methods proposed by Doren and Herschbach [Phys. Rev. A 34, 2654 (1986); 34, 2665 (1986)].
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.
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.
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.
Lens array fabrication method with volume expansion property of PDMS
NASA Astrophysics Data System (ADS)
Jang, WonJae; Kim, Junoh; Lee, Muyoung; Lee, Jooho; Bang, Yousung; Won, Yong Hyub
2016-03-01
Conventionally, poly (dimethylsiloxane) lens array is fabricated by replica molding. In this paper, we describe simple method for fabricating lens array with expanding property of PDMS. The PDMS substrate is prepared by spin coating on cleaned glass. After spin coating PDMS, substrate is treated with O2 plasma to promote adhesion between PDMS substrate and photoresist pattern on it. Positive photoresist az-4330 and AZ 430K developer is used for patterning on PDMS. General photolithography process is used to patterning. Then patterned PDMS substrate is dipped to 1- Bromododecane bath. During this process, patterned photoresist work as a barrier and prevent blocked PDMS substrate from reaction with 1-Bromododecane. Unblocked part of PDMS directly react with 1-Bromododecane and results in expanded PDMS volume. The expansion of PDMS is depends on absorbed 1-Bromododecane volume, dipping time and ratio of block to open area. The focal length of lens array is controlled by those PDMS expansion factors. Scale of patterned photoresist determine a diameter of each lens. The expansion occurs symmetrically at center of unblocked PDMS and 1-Bromododecane interface. As a result, the PDMS lens array is achieved by this process.
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
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.
Zimmerman, R.W.; Bodvarsson, G.S.
1992-04-01
A semi-analytical dual-porosity simulator for unsaturated flow in fractured rock masses has been developed. Fluid flow between the fracture network and the matrix blocks is described by analytical expressions that have been derived from approximate solutions to the imbibition equation. These expressions have been programmed into the unsaturated flow simulator, TOUGH, as a source/sink term. Flow processes are then simulated using only fracture elements in the computational grid. The modified code is used to simulate flow along single fractures, and infiltration into pervasively fractured formations.
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.
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.
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Li, Cheng; Jing, Y. P.; Kauffmann, Guinevere; Börner, Gerhard; Kang, Xi; Wang, Lan
2007-04-01
By comparing semi-analytic galaxy catalogues with data from the Sloan Digital Sky Survey (SDSS), we show that current galaxy formation models reproduce qualitatively the dependence of galaxy clustering and pairwise peculiar velocities on luminosity, but some subtle discrepancies with the data still remain. The comparisons are carried out by constructing a large set of mock galaxy redshift surveys that have the same selection function as the SDSS Data Release Four (DR4). The mock surveys are based on two sets of semi-analytic catalogues presented by Croton et al. and Kang et al. From the mock catalogues, we measure the redshift-space projected two-point correlation function wp(rp), the power spectrum P(k) and the pairwise velocity dispersion (PVD) in Fourier space σ12(k) and in configuration space σ12(rp), for galaxies in different luminosity intervals. We then compare these theoretical predictions with the measurements derived from the SDSS DR4. On large scales and for galaxies brighter than L*, both sets of mock catalogues agree well with the data. For fainter galaxies, however, both models predict stronger clustering and higher pairwise velocities than observed. We demonstrate that this problem can be resolved if the fraction of faint satellite galaxies in massive haloes is reduced by ~30 per cent compared to the model predictions. A direct look into the model galaxy catalogues reveals that a significant fraction (15 per cent) of faint galaxies (-18 < M0.1r - 5 log10h < -17) reside in haloes with Mvir > 1013 Msolar, and this population is predominantly red in colour. These faint red galaxies are responsible for the high PVD values of low-luminosity galaxies on small scales.
Chaikovskaya, Ludmila I; Zege, Eleonora P; Katsev, Iosif L; Hirschberger, Markus; Oppel, Ulrich G
2009-01-20
Quite recently, a semi-analytical approach to the sounding of multiply scattering media (clouds, seawaters) using multiple-field-of-view and CCD lidars with polarization devices was developed. The angular distributions of polarized components of the lidar returns from multiply scattering media computed on the basis of this theory using the small-angle approximation are presented and discussed. The semi-analytical nature of the solution makes the computation procedure faster. The obtained data are compared with results provided by the most advanced Monte Carlo algorithms for simulation of modern lidar performance. The good agreement between data provided by the semi-analytical approach and Monte Carlo computations assures one that these approaches can serve as a reliable theoretical base for interpretation and inversion of cloud lidar sounding data obtained with polarized lidars, including polarized multiple-field-of-view and CCD lidars.
Semi-analytical calculation of all magnetic values of a superconducting toric storage
Caron, J.P.; Sargos, F.M.; Rezzoug, A.; Leveque, J.; Netter, D.
1995-05-01
For particular applications, the design of systems composed of several superconducting coils needs good accuracy in calculations. Using analytical methods involving elliptic integrals, themselves calculated using the A.G.M. method, all electromagnetic values can be evaluated with a good precision. An application to a superconducting toroidal core illustrates this study.
High-quality, semi-analytical volume rendering for AMR data.
Marchesin, Stéphane; Colin de Verdière, Guillaume
2009-01-01
This paper presents a pipeline for high quality volume rendering of adaptive mesh refinement (AMR) datasets. We introduce a new method allowing high quality visualization of hexahedral cells in this context; this method avoids artifacts like discontinuities in the isosurfaces. To achieve this, we choose the number and placement of sampling points over the cast rays according to the analytical properties of the reconstructed signal inside each cell. We extend our method to handle volume shading of such cells. We propose an interpolation scheme that guarantees continuity between adjacent cells of different AMR levels. We introduce an efficient hybrid CPU-GPU mesh traversal technique. We present an implementation of our AMR visualization method on current graphics hardware, and show results demonstrating both the quality and performance of our method.
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.
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
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-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)
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)
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.
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)
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
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.
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.
Soares Dos Santos, Marco P; Ferreira, Jorge A F; Simões, José A O; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P
2016-01-04
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.
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)
Merson, Alexander I.; Baugh, Carlton M.; Helly, John C.; Gonzalez-Perez, Violeta; Cole, Shaun; Bielby, Richard; Norberg, Peder; Frenk, Carlos S.; Benson, Andrew J.; Bower, Richard G.; Lacey, Cedric G.; Lagos, Claudia del P.
2013-02-01
We introduce a method for constructing end-to-end mock galaxy catalogues using a semi-analytical model of galaxy formation, applied to the halo merger trees extracted from a cosmological N-body simulation. The mocks that we construct are lightcone catalogues, in which a galaxy is placed according to the epoch at which it first enters the past lightcone of the observer, and incorporate the evolution of galaxy properties with cosmic time. We determine the position between the snapshot outputs at which a galaxy enters the observer's lightcone by interpolation. As an application, we consider the effectiveness of the BzK colour selection technique, which was designed to isolate galaxies in the redshift interval 1.4 < z < 2.5. The mock catalogue is in reasonable agreement with the observed number counts of all BzK galaxies, as well as with the observed counts of the subsample of BzKs that are star-forming galaxies. We predict that over 75 per cent of the model galaxies with KAB ≤ 23, and 1.4 < z < 2.5, are selected by the BzK technique. Interloper galaxies, outside the intended redshift range, are predicted to dominate bright samples of BzK galaxies (i.e. with KAB ≤ 21). Fainter K-band cuts are necessary to reduce the predicted interloper fraction. We also show that shallow B-band photometry can lead to confusion in classifying BzK galaxies as being star forming or passively evolving. Overall, we conclude that the BzK colour selection technique is capable of providing a sample of galaxies that is representative of the 1.4 < z < 2.5 galaxy population.
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.
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.
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.
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.
Analysis for the convergence problem of the plane-wave expansion method for photonic crystals.
Shen, Linfang; He, Sailing
2002-05-01
The convergence feature of two types of plane-wave expansion methods commonly used for photonic crystals is analyzed. It is shown that the reason for the slow convergence of these plane-wave expansion methods is not the slow convergence of the Fourier series for the permittivity profile of the photonic crystal but the inappropriate formulation of the eigenproblem. A new formulation of the eigenproblem is presented to improve the convergence in the one-dimensional case.
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.
Three-Dimensional Simulation of Scalp Soft Tissue Expansion Using Finite Element Method
Guan, Qiu; Du, Xiaochen; Shao, Yan; Lin, Lili; Chen, Shengyong
2014-01-01
Scalp soft tissue expansion is one of the key medical techniques to generate new skin tissue for correcting various abnormalities and defects of skin in plastic surgery. Therefore, it is very important to work out the appropriate approach to evaluate the increase of expanded scalp area and to predict the shape, size, number, and placement of the expander. A novel method using finite element model is proposed to solve large deformation of scalp expansion in this paper. And the procedure to implement the scalp tissue expansion with finite element method is also described in detail. The three-dimensional simulation results show that the proposed method is effective, and the analysis of simulation experiment shows that the volume and area of the expansion scalp can be accurately calculated and the quantity, location, and size of the expander can also be predicted successfully with the proposed model. PMID:25110514
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
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)
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
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
Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method
NASA Astrophysics Data System (ADS)
Sedighi, Hamid M.; Shirazi, Kourosh H.
2013-04-01
This paper presents a new asymptotic procedure to predict the nonlinear vibrational behavior of micro-beams pre-deformed by an electric field. The nonlinear equation of motion includes both even and odd nonlinearities. A powerful analytical method called Parameter Expansion Method (PEM) is employed to obtain the approximated solution and frequency-amplitude relationship. It is demonstrated that the first two terms in series expansions are sufficient to produce an acceptable solution of mentioned system. The obtained results from numerical methods verify the soundness of the analytical procedure. Finally, the influences of basic parameters on pull-in instability and natural frequency are investigated.
NASA Astrophysics Data System (ADS)
Álvarez, Gabriel; Martínez Alonso, Luis; Medina, Elena
2011-07-01
We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.
"Flypaper technique" a modified expansion method for preparation of postage stamp autografts.
Lee, Su-Shin; Lin, Tsai-Ming; Chen, Yi-Hui; Lin, Sin-Daw; Lai, Chung-Sheng
2005-09-01
The gold standard for management of extensive burn has been early excision, temporary allografting and final autografting. However, "lack of donor skin" is a challenge condition when autografting in the treatment of extensive burns. Designing an efficient and easy to apply expansion method may improve burn care quality and shorten the hospital stay period. From December 1998 to May 2004, we have performed fly paper technique postage stamp skin autografting for eight major burn patients in the Kaohsiung Medical University Hospital. By using a quick cutting plate, chessboard tray and petrolatum gauze, the skin islands can be uniformly located and correctly oriented on gauze. Then, the gauze with skin islands was grafted on to the wound. The wound healing time depends on the size of skin islands and expansion ratio. This method allows true expansion ratio up to nine times. The average wound healing times are 27.2 days for six times expansion and 34 days for nine times expansion. However, the burn scar needs further compression therapy to improve the cosmetic result. In comparison with the mesh technique, the skin islands are independent of each other, any dislodgement of a skin island will not interfere with the surrounding skin squares. When compared with the modified Meek technique, this method also offers rapid wound reepithilization but with lower cost. This flypaper technique is worthy of consideration in dealing with the extensive burns.
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
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.
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.
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
An In Vitro Intact Globe Expansion Method for Evaluation of Cross-linking Treatments
Mattson, Matthew S.; Huynh, Joyce; Wiseman, Meredith; Coassin, Marco; Kornfield, Julia A.; Schwartz, Daniel M.
2010-01-01
Purpose. To measure the tissue mechanical response to elevated intraocular pressure (IOP) using intact globe expansion of rabbit eyes. This method examined rabbit kit (2–3 weeks old) eyes as a model for weakened tissue and evaluated riboflavin/UVA and glyceraldehyde cross-linking treatments. Methods. The ocular shape of enucleated eyes was photographed during a 24-hour period while a controlled IOP was imposed (either low IOP = 22 mm Hg or high IOP = 85 mm Hg). Untreated controls consisted of kit eyes tested at both low- and high IOP and adult eyes tested at high IOP. Treated kit eyes (dextran controls, riboflavin/UVA treatment of the cornea, and glyceraldehyde treatment of the entire globe) were tested at high IOP. Results. Low IOP elicited negligible creep of the sclera and very gradual creep of the cornea. In contrast, high IOP induced up to an 8% strain in the sclera and a 15% strain in the cornea of rabbit kit eyes. The expansion of adult eyes was less than one third that of kit eyes at the same, high IOP. Riboflavin/UVA treatment of corneas reduced expansion compared with that in both dextran-treated and untreated control corneas. Glyceraldehyde treatment prevented expansion of the cornea and sclera. Conclusions. The intact globe expansion method (GEM) imposes a loading geometry comparable to in vivo conditions and can quantify changes in mechanical stability as a function of testing conditions (e.g., IOP, tissue maturation, and therapeutic cross-linking) with small sample sizes and small variability. Rabbit kit eyes provide a model of weak tissue suitable for screening treatments that strengthen the cornea and sclera. PMID:20071684
Huberts, W; Donders, W P; Delhaas, T; van de Vosse, F N
2014-12-01
Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space. PMID:25377937
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.
Rood, A.S.
1992-03-01
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 1 and Track 2 assessment of Comprehensive Environmental Response, Compensation and Liability Act (CERCLA) sites identified as low probability hazard at the Idaho National Engineering Laboratory (DOE, 1991). The code calculates the limiting soil concentration such that 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 for transient mass flux input.
Rood, A.S.
1992-03-01
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 1 and Track 2 assessment of Comprehensive Environmental Response, Compensation and Liability Act (CERCLA) sites identified as low probability hazard at the Idaho National Engineering Laboratory (DOE, 1991). The code calculates the limiting soil concentration such that 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 for transient mass flux input.
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.
NASA Astrophysics Data System (ADS)
Oogi, Taira; Enoki, Motohiro; Ishiyama, Tomoaki; Kobayashi, Masakazu A. R.; Makiya, Ryu; Nagashima, Masahiro
We investigate clustering properties of quasars using a new version of our semi-analytic model of galaxy and quasar formation with state-of-the-art cosmological N-body simulations (Ishiyama et al. 2015; Oogi et al. 2015). We assume that a major merger of galaxies triggers quasar activity. We find that the quasar bias does not depend significantly on the quasar luminosity, similar to observed trends. This result reflects the fact that quasars with a fixed luminosity have various Eddington ratios and thus have various host halo masses that primarily determine the quasar bias. The quasar bias increases with redshift, which is in qualitative agreement with observations. Our bias value is lower than the observed values at high redshifts, implying that we need some mechanisms that make quasars inactive in low-mass haloes and/or that make them more active in high-mass haloes.
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.
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 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.
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)
Parrott, T. L.
1973-01-01
An improved method for the design of expansion-chamber mufflers is described and applied to the task of reducing exhaust noise generated by a helicopter. The method is an improvement of standard transmission-line theory in that it accounts for the effect of the mean exhaust-gas flow on the acoustic-transmission properties of a muffler system, including the termination boundary condition. The method has been computerized, and the computer program includes an optimization procedure that adjusts muffler component lengths to achieve a minimum specified desired transmission loss over a specified frequency range. A printout of the program is included together with a user-oriented description.
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
NASA Astrophysics Data System (ADS)
De Micheli, Enrico; Viano, Giovanni Alberto
2013-04-01
We present a simple and fast algorithm for the computation of the Gegenbauer transform, which is known to be very useful in the development of spectral methods for the numerical solution of ordinary and partial differential equations of physical interest. We prove that the coefficients of the expansion of a function f(x) in Gegenbauer (also known as ultraspherical) polynomials coincide with the Fourier coefficients of a suitable integral transform of the function f(x). This allows to compute N Gegenbauer coefficients in O(Nlog2N) operations by means of a single Fast Fourier Transform of the integral transform of f(x). We also show that the inverse Gegenbauer transform is expressible as the Abel-type transform of a suitable Fourier series. This fact produces a novel algorithm for the fast evaluation of Gegenbauer expansions.
An Improved (G'/G)-expansion Method for Solving Nonlinear PDEs in Mathematical Physics
NASA Astrophysics Data System (ADS)
Zayed, Elsayed M. E.; Al-Joudi, Shorog
2010-09-01
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.
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.
Eigenfunction-expansion method for solving the quantum-wire problem: Formulation
NASA Astrophysics Data System (ADS)
Baraff, G. A.; Gershoni, D.
1991-02-01
We present a method of formulating the multiband-envelope-function equations for a quantum structure whose internal interfaces are perpendicular planes. The method can be used for quantum wells, quantum wires, or quantum dots (one-, two-, or three-dimensional confinement of the electronic wave function), as well as for periodic repetitions (superlattices) of these elementary structures. The technique used is expansion of the multiband envelope functions in a Fourier series for each of the coordinates x, y, and z. Special attention is paid to formulating interface-matching conditions that impose Hermiticity on the resulting systems of equations. This demand leads to the usual condition that the normal component of the current must be continuous across each internal interface. The method we have devised is similar to the one used by Altarelli for the quantum-well problem in that it leads to a secular equation that is solved by diagonalizing an energy-independent matrix. It differs in that here, the envelope functions are expanded in smooth continuous functions using the same expansion coefficients in all regions of the structure. Using this method, one can now calculate the optical absorption, its frequency, and polarization dependence, with the same amount of detail that has previously been possible only for confinement in one dimension, namely, in the quantum well and one-dimensional superlattice.
NASA Astrophysics Data System (ADS)
Ganguly, Pranabendu; Biswas, Juran Chandra; Lahiri, Samir Kumar
Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO3 curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.
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)
Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li
2016-02-01
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037
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
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 spectral element method for fluid dynamics - Laminar flow in a channel expansion
NASA Technical Reports Server (NTRS)
Patera, A. T.
1984-01-01
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
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.
NASA Astrophysics Data System (ADS)
Sedghi, Mohammad Mahdi; Samani, Nozar; Sleep, Brent
2009-06-01
The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471-80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.
Borgia, Alessandro; Zheng, Wenwei; Buholzer, Karin; Borgia, Madeleine B; Schüler, Anja; Hofmann, Hagen; Soranno, Andrea; Nettels, Daniel; Gast, Klaus; Grishaev, Alexander; Best, Robert B; Schuler, Benjamin
2016-09-14
There has been a long-standing controversy regarding the effect of chemical denaturants on the dimensions of unfolded and intrinsically disordered proteins: A wide range of experimental techniques suggest that polypeptide chains expand with increasing denaturant concentration, but several studies using small-angle X-ray scattering (SAXS) have reported no such increase of the radius of gyration (Rg). This inconsistency challenges our current understanding of the mechanism of chemical denaturants, which are widely employed to investigate protein folding and stability. Here, we use a combination of single-molecule Förster resonance energy transfer (FRET), SAXS, dynamic light scattering (DLS), and two-focus fluorescence correlation spectroscopy (2f-FCS) to characterize the denaturant dependence of the unfolded state of the spectrin domain R17 and the intrinsically disordered protein ACTR in two different denaturants. Standard analysis of the primary data clearly indicates an expansion of the unfolded state with increasing denaturant concentration irrespective of the protein, denaturant, or experimental method used. This is the first case in which SAXS and FRET have yielded even qualitatively consistent results regarding expansion in denaturant when applied to the same proteins. To more directly illustrate this self-consistency, we used both SAXS and FRET data in a Bayesian procedure to refine structural ensembles representative of the observed unfolded state. This analysis demonstrates that both of these experimental probes are compatible with a common ensemble of protein configurations for each denaturant concentration. Furthermore, the resulting ensembles reproduce the trend of increasing hydrodynamic radius with denaturant concentration obtained by 2f-FCS and DLS. We were thus able to reconcile the results from all four experimental techniques quantitatively, to obtain a comprehensive structural picture of denaturant-induced unfolded state expansion, and to
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a
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)
Govindaraju, Rao S.; Corradini, Corrado; Morbidelli, Renato
2006-01-01
A semi-analytical model for the estimate of expected areal-average infiltration rate at hillslope scale is presented. It accounts for spatial heterogeneity of the saturated hydraulic conductivity, Ks, and rainfall rate, r. The Ks field is characterized by a lognormal probability density function while the rainfall rate r is represented by a uniform distribution between two extreme values. The model formulation relies upon the use of cumulative infiltration as the independent variable which is then expressed as a function of an expected time for use in practical applications. The solution is applicable for those ranges of r and Ks that allow for neglecting the infiltration of surface water running downslope into pervious soils (run-on process). The model was tested by comparisons with Monte Carlo simulations carried out for a variety of coefficients of variation of r and Ks over a clay loam soil and a sandy loam soil. The model was found to be very reliable both with coupled spatial variability of r and Ks and when only one variable is characterized by spatial heterogeneity while the other is uniform.
NASA Astrophysics Data System (ADS)
Oogi, Taira; Enoki, Motohiro; Ishiyama, Tomoaki; Kobayashi, Masakazu; Makiya, Ryu; Nagashima, Masahiro
2015-08-01
We construct a new version of the Numerical Galaxy Catalog (Nagashima et al. 2005, Enoki et al. 2014), a semi-analytic model of galaxy formation, with state-of-the-art cosmological N-body simulations which are carried on the K computer. The minimum dark halo mass of our simulations is ~1010 Msun, and the box sizes are larger than 560 Mpc/h, and the largest simulation consists of 81923 (550 billion) dark matter particles in a box of 1.12 Gpc/h (Ishiyama et al. 2015). The model includes both galaxy and quasar formations based on the hierarchical structure formation scenario. This model enables us to investigate the large-scale quasar clustering and its evolution from z~5 to z=0 for less luminous quasars as well as more luminous quasars.In this talk, we present the evolution of the quasar host halo mass distribution, the cross-correlation function of quasars and galaxies, and the quasar bias, and compare these results with current observations. Furthermore, we will show an observational strategy to determine the model prescriptions of quasar formation including their parameters.
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
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
Edee, Kofi; Guizal, Brahim
2013-04-01
In this paper we present an extension of the modal method by Gegenbauer expansion (MMGE) [J. Opt. Soc. Am. A28, 2006 (2011)], [Progress Electromagn. Res.133, 17 (2013)] to the study of nonperiodic problems. The nonperiodicity is introduced through the perfectly matched layers (PMLs) concept, which can be introduced in an equivalent way either by a change of coordinates or by the use of a uniaxial anisotropic medium. These PMLs can generate strong irregularities of the electromagnetic fields that can significantly alter the convergence and stability of the numerical scheme. This is the case, e.g., for the famous Fourier modal method, especially when using complex stretching coordinates. In this work, it will be shown that the MMGE equipped with PMLs is a robust approach because of its natural immunity against spurious modes. PMID:23595322
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.
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.
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
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM.
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM. PMID:21979505
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.
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.
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
Orr, Leigh-Ann; Mulholland, Anthony J; O'Leary, Richard L; Hayward, Gordon
2008-12-01
Periodic composite ultrasonic transducers offer many advantages but the periodic pillar architecture can give rise to unwanted modes of vibration which interfere with the piston like motion of the fundamental thickness mode. In this paper, viscoelastic loss is incorporated into a three-dimensional plane wave expansion model (PWE) of these transducers. A comparison with experimental and finite element data is conducted and a design to damp out these lateral modes is investigated. Scaling and regularisation techniques are introduced to the PWE method to reduce ill-conditioning in the large matrices which can arise. The identification of the modes of vibration is aided by examining profiles of the displacements, electrical potential and Poynting vector. The dispersive behaviour of a 2-2 composite transducer with high shear attenuation in the passive phase is examined. The model shows that the use of a high shear attenuation filler material improves the frequency band gap surrounding the fundamental thickness mode.
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.
Introducing the Pietarinen expansion method into the single-channel pole extraction problem
NASA Astrophysics Data System (ADS)
Švarc, Alfred; Hadžimehmedović, Mirza; Osmanović, Hedim; Stahov, Jugoslav; Tiator, Lothar; Workman, Ron L.
2013-09-01
We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the nonsingular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the nonsingular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by the quality of the fit. The method is tested in two ways: on a toy model constructed from two known poles, various background terms, and two physical cuts, and on several sets of realistic πN elastic energy-dependent partial-wave amplitudes (GWU/SAID [Arndt , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.74.045205 74, 045205 (2006); Workman , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.86.035202 86, 035202 (2012)], and Dubna-Mainz-Taipei [Chen , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.76.035206 76, 035206 (2007); Tiator , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.82.055203 82, 055203 (2010)]). We show that the method is robust and confident using up to three Pietarinen series, and is particularly convenient in fits to amplitudes, such as single-energy solutions, coming more directly from experiment: cases where the analytic structure of the regular part is a priori unknown.
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
Lesage, Jonathan C; Bond, Jill V; Sinclair, Anthony N
2014-09-01
The problem of elastic wave propagation in an infinite bar of arbitrary cross section is studied via a generalized version of the Fourier expansion collocation method. In the current formulation, the exact three dimensional solution to Navier's equation in cylindrical coordinates is used to obtain the boundary traction vector as a periodic, piecewise continuous/differentiable function of the angular coordinate. Traction free conditions are then met by setting the Fourier coefficients of the boundary traction vector to zero without approximating the bounding surface by multi-sided polygons as in the method presented by Nagaya. The method is derived for a general cross section with no axial planes of symmetry. Using the general formulation it is shown that the symmetric and asymmetric modes decouple for cross sections having one axial plane of symmetry. An efficient algorithm for computing dispersion curves based on the current method is presented and used to obtain the fundamental longitudinal and flexural wave speeds for a bar of elliptical cross section. The results are compared to those obtained by previous researchers using exact and approximate treatments.
Three-Body Coulomb Functions in the Hyperspherical Adiabatic Expansion Method
NASA Astrophysics Data System (ADS)
Garrido, E.; Kievsky, A.; Viviani, M.
2016-10-01
In this work we describe a numerical method devised to compute continuum three-body wave functions. The method is implemented using the hyperspherical adiabatic expansion for the three-body wave function imposing a box boundary condition. The continuum energy spectrum results discretized and, for specific quantum number values, all the possible incoming and outgoing channels are simultaneously computed. For a given energy, the hyperradial continuum functions form a matrix whose ij-term refers to specific incoming and outgoing channels. When applied to three-body systems interacting only through the Coulomb potential, this method provides the adiabatic representation of the regular three-body Coulomb wave function. The computation of the irregular Coulomb wave function representation is also discussed. These regular and irregular Coulomb functions can be used to extract the {S} -matrix for those reactions where, together with some short-range potential, the Coulomb interaction is also present. The method is illustrated in the case of the 3→ 3 process of three alpha particles.
NASA Astrophysics Data System (ADS)
Reveillere, A. R.; Rohmer, J. R.
2012-04-01
Deep saline aquifers are currently considered for CO2 storage in different places of the world. Many of these aquifers are located in sedimentary basins that have experienced a past oil and gas prospection and / or production, which has left a quantity of wells with sometimes undetermined plugging history. Despite a careful site selection, a remaining risk of leakage outside the storage reservoir cannot be excluded, and potential leakage pathways have to be reviewed. Existing semi-analytical models can estimate the leakage flow rate of brine, possibly followed by CO2, from the storage aquifer to an overlying one (cf. publications by Nordbotten and co-authors, 2004-2009). These models use a time discretization, but do not use any spatial grid. They are consequently very computationally efficient but require considering homogeneous horizontal aquifer models with uniform properties. In addition, several authors have proposed a definition of the "Area of Review" of CO2 storage sites as the area where the pressure changes due to the injection can drive the reservoir brine up to a shallower aquifer. This approach relies on a static equilibrium of the denser brine replacing a lighter one, which implies supposing that the wellbore does not present any cement plug or any element that can slow down the leakage. In the present study, we combine these two approaches by developing a semi-analytical model able to consider the dynamic brine flow from the storage reservoir to an overlying aquifer through a vertical conduit. That leak is composed of an open wellbore and a porous column, whose characteristics are representative of degraded cements of an abandoned well. During the leakage, the saline brine coming from the storage reservoir progressively fills in the leak and replaces the original fluid, which was less saline and therefore less dense. The model computes the transient leakage rate, the progressive filling of the leak and several pressures variations. For a given
NASA Astrophysics Data System (ADS)
Tang, Liling; Cheng, Li; Ji, Hongli; Qiu, Jinhao
2016-07-01
Acoustics Black Hole (ABH) effect shows promising features for potential vibration control and energy harvesting applications. The phenomenon occurs in a structure with diminishing thickness which gradually reduces the phase velocity of flexural waves. The coupling between the tailored ABH structure and the damping layer used to compensate for the adverse effect of the unavoidable truncation is critical and has not been well apprehended by the existing models. This paper presents a semi-analytical model to analyze an Euler-Bernoulli beam with embedded ABH feature and its full coupling with the damping layers coated over its surface. By decomposing the transverse displacement field of the beam over the basis of a set of Mexican hat wavelets, the extremalization of the Hamiltonian via Lagrange's equation yields a set of linear equations, which can be solved for structural responses. Highly consistent with the FEM and experimental results, numerical simulations demonstrate that the proposed wavelet-based model is particularly suitable to characterize the ABH-induced drastic wavelength fluctuation phenomenon. The ABH feature as well as the effect of the wedge truncation and that of the damping layers on the vibration response of the beam is analyzed. It is shown that the mass of the damping layers needs particular attention when their thickness is comparable to that of the ABH wedge around the tip area. Due to its modular and energy-based feature, the proposed framework offers a general platform allowing embodiment of other control or energy harvesting elements into the model to guide ABH structural design for various applications.
Hu, Renyu; Demory, Brice-Olivier; Seager, Sara; Lewis, Nikole; Showman, Adam P.
2015-03-20
Kepler has detected numerous exoplanet transits by measuring stellar light in a single visible-wavelength band. In addition to detection, the precise photometry provides phase curves of exoplanets, which can be used to study the dynamic processes on these planets. However, the interpretation of these observations can be complicated by the fact that visible-wavelength phase curves can represent both thermal emission and scattering from the planets. Here we present a semi-analytical model framework that can be applied to study Kepler and future visible-wavelength phase curve observations of exoplanets. The model efficiently computes reflection and thermal emission components for both rocky and gaseous planets, considering both homogeneous and inhomogeneous surfaces or atmospheres. We analyze the phase curves of the gaseous planet Kepler- 7 b and the rocky planet Kepler- 10 b using the model. In general, we find that a hot exoplanet’s visible-wavelength phase curve having a significant phase offset can usually be explained by two classes of solutions: one class requires a thermal hot spot shifted to one side of the substellar point, and the other class requires reflective clouds concentrated on the same side of the substellar point. Particularly for Kepler- 7 b, reflective clouds located on the west side of the substellar point can best explain its phase curve. The reflectivity of the clear part of the atmosphere should be less than 7% and that of the cloudy part should be greater than 80%, and the cloud boundary should be located at 11° ± 3° to the west of the substellar point. We suggest single-band photometry surveys could yield valuable information on exoplanet atmospheres and surfaces.
NASA Astrophysics Data System (ADS)
Luo, Yu; Kang, Xi; Kauffmann, Guinevere; Fu, Jian
2016-05-01
The quenching of star formation in satellite galaxies is observed over a wide range of dark matter halo masses and galaxy environments. In the recent Guo et al. and Fu et al. semi-analytic + N-body models, the gaseous environment of the satellite galaxy is governed by the properties of the dark matter subhalo in which it resides. This quantity depends of the resolution of the N-body simulation, leading to a divergent fraction of quenched satellites in high- and low-resolution simulations. Here, we incorporate an analytic model to trace the subhaloes below the resolution limit. We demonstrate that we then obtain better converged results between the Millennium I and II simulations, especially for the satellites in the massive haloes (log Mhalo = [14, 15]). We also include a new physical model for the ram-pressure stripping of cold gas in satellite galaxies. However, we find very clear discrepancies with observed trends in quenched satellite galaxy fractions as a function of stellar mass at fixed halo mass. At fixed halo mass, the quenched fraction of satellites does not depend on stellar mass in the models, but increases strongly with mass in the data. In addition to the overprediction of low-mass passive satellites, the models also predict too few quenched central galaxies with low stellar masses, so the problems in reproducing quenched fractions are not purely of environmental origin. Further improvements to the treatment of the gas-physical processes regulating the star formation histories of galaxies are clearly necessary to resolve these problems.
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
Plane wave expansion method used to engineer photonic crystal sensors with high efficiency.
Antos, Roman; Vozda, Vojtech; Veis, Martin
2014-02-10
A photonic crystal waveguide (PhC-WG) was reported to be usable as an optical sensor highly sensitive to various material parameters, which can be detected via changes in transmission through the PhC-WG caused by small changes of the refractive index of the medium filling its holes. To monitor these changes accurately, a precise optical model is required, for which the plane wave expansion (PWE) method is convenient. We here demonstrate the revision of the PWE method by employing the complex Fourier factorization approach, which enables the calculation of dispersion diagrams with fast convergence, i.e., with high precision in relatively short time. The PhC-WG is proposed as a line defect in a hexagonal array of cylindrical holes periodically arranged in bulk silicon, filled with a variable medium. The method of monitoring the refractive index changes is based on observing cutoff wavelengths in the PhC-WG dispersion diagrams. The PWE results are also compared with finite-difference time-domain calculations of transmittance carried out on a PhC-WG with finite dimensions. PMID:24663549
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.
Plane wave expansion method used to engineer photonic crystal sensors with high efficiency.
Antos, Roman; Vozda, Vojtech; Veis, Martin
2014-02-10
A photonic crystal waveguide (PhC-WG) was reported to be usable as an optical sensor highly sensitive to various material parameters, which can be detected via changes in transmission through the PhC-WG caused by small changes of the refractive index of the medium filling its holes. To monitor these changes accurately, a precise optical model is required, for which the plane wave expansion (PWE) method is convenient. We here demonstrate the revision of the PWE method by employing the complex Fourier factorization approach, which enables the calculation of dispersion diagrams with fast convergence, i.e., with high precision in relatively short time. The PhC-WG is proposed as a line defect in a hexagonal array of cylindrical holes periodically arranged in bulk silicon, filled with a variable medium. The method of monitoring the refractive index changes is based on observing cutoff wavelengths in the PhC-WG dispersion diagrams. The PWE results are also compared with finite-difference time-domain calculations of transmittance carried out on a PhC-WG with finite dimensions.
He, Yuejing; Chen, Xuanyang
2014-01-01
Compared with coupled-mode theory (CMT), which is widely used for studies involving optical fiber Bragg gratings (FBGs), the proposed investigation scheme is visualized, diagrammatic, and simple. This method combines the finite element method (FEM) and eigenmode expansion method (EEM). The function of the FEM is to calculate all guided modes that match the boundary conditions of optical fiber waveguides. Moreover, the FEM is used for implementing power propagation for HE11 in optical fiber devices. How the periodic characteristic of FBG causes this novel scheme to be substantially superior to CMT is explained in detail. Regarding current numerical calculation techniques, the scheme proposed in this paper is the only method capable of the 3D design and analysis of large periodic components. Additionally, unlike CMT, in which deviations exist between the designed wavelength λD and the maximal reflection wavelength λmax, the proposed method performs rapid scans of the periods of optical FBG. Therefore, once the operating wavelength is set for the component design, the maximal reflection wavelength of the final products can be accurately limited to that of the original design, such as λ = 1550 nm. Furthermore, a comparison between the period scan plot and the optical spectra plot for FBG indicated an inverse relationship between the periods and wavelengths. Consequently, this property can be used to predict the final FBG spectra before implementing time-consuming calculations. By employing this novel investigation scheme involving a rigorous design procedure, the graphical and simple calculation method reduces the studying time and professional expertise required for researching and applying optical FBG. PMID:24949643
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
NASA Astrophysics Data System (ADS)
Zhou, S.; Solana, J. R.
2014-12-01
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 ai 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 ai 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.
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 ai 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 ai 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.
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.
Numerical divergence effects of equivalence theory in the nodal expansion method
Zika, M.R.; Downar, T.J. )
1993-11-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible.
NASA Astrophysics Data System (ADS)
Wu, Kun; Zhang, Feng; Min, Jinzhong; Yu, Qiu-Run; Wang, Xin-Yue; Ma, Leiming
2016-09-01
The adding method, which could calculate the infrared radiative transfer (IRT) in inhomogeneous atmosphere with multiple layers, has been applied to δ -four-stream discrete-ordinates method (DOM). This scheme is referred as δ -4DDA. However, there is a lack of application for adding method of δ -four-stream spherical harmonic expansion approximation (SHM) to solve infrared radiative transfer through multiple layers. In this paper, the adding method for δ -four-stream SHM (δ -4SDA) will be obtained and the accuracy of it will be evaluated as well. The result of δ -4SDA in an idealized medium with homogeneous optical property is significantly more accurate than that of the adding method for δ -two-stream DOM (δ -2DDA). The relative errors of δ -2DDA can be over 15% in thin optical depths for downward emissivity, while errors of δ -4SDA are bounded by 2%. However, the result of δ -4SDA is slightly less accurate than that of δ -4DDA. In a radiation model with realistic atmospheric profile considering gaseous transmission, the accuracy for heating rate of δ -4SDA is significantly superior than that of δ -2DDA, especially for the cloudy sky. The accuracy for heating rate of δ -4SDA is slightly less accurate than that of δ -4DDA under water cloud conditions, while it is superior than that of δ -4DDA in ice cloud cases. Beside, the computational efficiency of δ -4SDA is higher than that of δ -4DDA.
Improved generalized F-expansion method for the time fractional modified KdV(fmKdV) equation
NASA Astrophysics Data System (ADS)
Sonmezoglu, Abdullah
2016-06-01
In this article, an improved generalized F-expansion method is used for solving the time fractional modified KdV(fmKdV) equation. Using this approach new Jacobi elliptic function solutions are obtained. This method can be suitable for solving other nonlinear fractional differential equations.
Systematic synthesis of CCCCTA-based T-T filters using NAM expansion method
NASA Astrophysics Data System (ADS)
Li, Yongan; Cao, Rui
2016-06-01
In the light of nullor-mirror models for current-controlled current conveyor trans-conductance amplifier (CCCCTA), initiating the admittance matrices of the Tow-Thomas (T-T) filter, three different types of the T-T filter are synthesised by means of the nodal admittance matrix (NAM) expansion method. The type A filter, which employ one CCCCTA, one grounded resistor and two grounded capacitors, has eight different forms, the type B filter, which employ one CCCCTA, two grounded capacitors and a second-generation current-controlled conveyor (CCCII) or an second-generation inverting current-controlled conveyor (ICCCII) or an operational trans-conductance amplifier (OTA), has 64 different forms and the type C filter employing one CCCCTA and two grounded capacitors has eight different forms. In all, 80 voltage-mode/current-mode T-T filter circuits are obtained. Because of using canonic number components, the circuits are highly desirable from the viewpoint of IC fabrication and their parameters can be electronically tuned through tuning bias currents of CCCCTAs. The hand analysis and computer simulation results have been provided to support the synthesis method.
NASA Astrophysics Data System (ADS)
Bitter, Christopher; Mulligan, Gordon F.; Dall'Erba, Sandy
2007-04-01
Hedonic house price models typically impose a constant price structure on housing characteristics throughout an entire market area. However, there is increasing evidence that the marginal prices of many important attributes vary over space, especially within large markets. In this paper, we compare two approaches to examine spatial heterogeneity in housing attribute prices within the Tucson, Arizona housing market: the spatial expansion method and geographically weighted regression (GWR). Our results provide strong evidence that the marginal price of key housing characteristics varies over space. GWR outperforms the spatial expansion method in terms of explanatory power and predictive accuracy.
Linear 3 and 5-step methods using Taylor series expansion for solving special 3rd order ODEs
NASA Astrophysics Data System (ADS)
Rajabi, Marzieh; Ismail, Fudziah; Senu, Norazak
2016-06-01
Some new linear 3 and 5-step methods for solving special third order ordinary differential equations directly are constructed using Taylor's series expansion. A set of test problems are solved using the new method and the results are compared when the problem is reduced to a system of first order ordinary differential equations and then using the existing Runge-Kutta method. The numerical results have clearly shown the advantage and competency of the new methods.
Uncovering compounds by synergy of cluster expansion and high-throughput methods.
Levy, Ohad; Hart, Gus L W; Curtarolo, Stefano
2010-04-01
Predicting from first-principles calculations whether mixed metallic elements phase-separate or form ordered structures is a major challenge of current materials research. It can be partially addressed in cases where experiments suggest the underlying lattice is conserved, using cluster expansion (CE) and a variety of exhaustive evaluation or genetic search algorithms. Evolutionary algorithms have been recently introduced to search for stable off-lattice structures at fixed mixture compositions. The general off-lattice problem is still unsolved. We present an integrated approach of CE and high-throughput ab initio calculations (HT) applicable to the full range of compositions in binary systems where the constituent elements or the intermediate ordered structures have different lattice types. The HT method replaces the search algorithms by direct calculation of a moderate number of naturally occurring prototypes representing all crystal systems and guides CE calculations of derivative structures. This synergy achieves the precision of the CE and the guiding strengths of the HT. Its application to poorly characterized binary Hf systems, believed to be phase-separating, defines three classes of alloys where CE and HT complement each other to uncover new ordered structures.
Favorite, J.A.
1999-09-01
In previous work, exponential convergence of Monte Carlo solutions using the reduced source method with Legendre expansion has been achieved only in one-dimensional rod and slab geometries. In this paper, the method is applied to three-dimensional (right parallelepiped) problems, with resulting evidence suggesting success. As implemented in this paper, the method approximates an angular integral of the flux with a discrete-ordinates numerical quadrature. It is possible that this approximation introduces an inconsistency that must be addressed.
NASA Astrophysics Data System (ADS)
Pandir, Yusuf; Duzgun, Hasan Huseyin
2016-06-01
In this study, we investigate some new analytical solutions to the fractional Sine-Gordon equation by using the new version of generalized F-expansion method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, new analytical solutions were obtained in terms Jacobi elliptic functions.
Apparatus and method for measuring the expansion properties of a cement composition
Spangle, Lloyd B.
1983-01-01
An apparatus is disclosed which is useful for measuring the expansion properties of semi-solid materials which expand to a solid phase, upon curing, such as cement compositions. The apparatus includes a sleeve, preferably cylindrical, which has a vertical slit on one side, to allow the sleeve to expand. Mounted on the outside of the sleeve are several sets of pins, consisting of two pins each. The two pins in each set are located on opposite sides of the slit. In the test procedure, the sleeve is filled with wet cement, which is then cured to a solid. As the cement cures it causes the sleeve to expand. The actual expansion of the sleeve represents an expansion factor for the cement. This factor is calculated by measuring the distance across the pins of each set, when the sleeve is empty, and again after the cured cement expands the sleeve.
Jackson, T. S.; Read, N.
2010-02-15
Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d. The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dimension D{sub p} of paths on the latter MST; our previous results lead us to predict that D{sub p}=2 for d>d{sub c}=6. Using a renormalization-group approach, we confirm the result for d>6 and calculate D{sub p} to first order in epsilon=6-d for d<6 using the connection with critical percolation, with the result D{sub p}=2-epsilon/7+O(epsilon{sup 2}).
Nishimura, Shin
2015-12-15
The spherical coordinates expressions of the Rosenbluth potentials are applied to the field particle portion in the linearized Coulomb collision operator. The Sonine (generalized Laguerre) polynomial expansion formulas for this operator allowing general field particles' velocity distributions are derived. An important application area of these formulas is the study of flows of thermalized particles in NBI-heated or burning plasmas since the energy space structure of the fast ions' slowing down velocity distribution cannot be expressed by usual orthogonal polynomial expansions, and since the Galilean invariant property and the momentum conservation of the collision must be distinguished there.
Homentcovschi, Dorel; Miles, Ronald N.
2010-01-01
The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct. PMID:20707432
Homentcovschi, Dorel; Miles, Ronald N
2010-08-01
The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct.
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation
Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah
2014-01-01
F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327
F-expansion method and new exact solutions of the Schrödinger-KdV equation.
Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah
2014-01-01
F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327
Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio
2014-01-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530
Lukić, Sergio; Hey, Jody
2012-01-01
We present an implementation of a recently introduced method for estimating the allele-frequency spectrum under the diffusion approximation. For single-nucleotide polymorphism (SNP) frequency data from multiple populations, the method computes numerical solutions to the allele-frequency spectrum (AFS) under a complex model that includes population splitting events, migration, population expansion, and admixture. The solution to the diffusion partial differential equation (PDE) that mimics the evolutionary process is found by means of truncated polynomial expansions. In the absence of gene flow, our computation of frequency spectra yields exact results. The results are compared to those that use a finite-difference method and to forward diffusion simulations. In general, all the methods yield comparable results, although the polynomial-based approach is the most accurate in the weak-migration limit. Also, the economical use of memory attained by the polynomial expansions makes the study of models with four populations possible for the first time. The method was applied to a four-population model of the human expansion out of Africa and the peopling of the Americas, using the Environmental Genome Project (EGP) SNP database. Although our confidence intervals largely overlapped previous analyses of these data, some were significantly different. In particular, estimates of migration among African, European, and Asian populations were considerably lower than those in a previous study and the estimated time of migration out of Africa was earlier. The estimated time of founding of a human population outside of Africa was 52,000 years (95% confidence interval: 36,000–80,800 years). PMID:22865734
Pessi, Jenni; Lassila, Ilkka; Meriläinen, Antti; Räikkönen, Heikki; Hæggström, Edward; Yliruusi, Jouko
2016-08-01
We introduce a robust, stable, and reproducible method to produce nanoparticles based on expansion of supercritical solutions using carbon dioxide as a solvent. The method, controlled expansion of supercritical solution (CESS), uses controlled mass transfer, flow, pressure reduction, and particle collection in dry ice. CESS offers control over the crystallization process as the pressure in the system is reduced according to a specific profile. Particle formation takes place before the exit nozzle, and condensation is the main mechanism for postnucleation particle growth. A 2-step gradient pressure reduction is used to prevent Mach disk formation and particle growth by coagulation. Controlled particle growth keeps the production process stable. With CESS, we produced piroxicam nanoparticles, 60 mg/h, featuring narrow size distribution (176 ± 53 nm). PMID:27368121
NASA Technical Reports Server (NTRS)
Savin, Raymond C
1955-01-01
The generalized shock-expansion method is applied to obtain solutions to the flow field about pointed bodies of revolution at high supersonic airspeeds and small angles of attack. Simple explicit expressions are obtained for the surface Mach numbers and surface pressures in the special case of slender bodies. In the case of inclined cones, algebraic solutions are obtained defining the entire flow field. Experimental pressure-distribution data for cones and ogives at Mach numbers from 3 to 5 are included. (author)
Spectral expansion method in problems of laser-beam propagation in the turbulent atmosphere.
Aksenov, V P; Mironov, V L
1978-11-01
A mixed spectral expansion over elementary spherical and plane waves is suggested for use as an approximate solution of the stochastic wave equation describing propagation of optical waves in a turbulent medium. In this case, the complex amplitude of an elementary plane wave is calculated as a solution of a shortened equation, considering only the phase fluctuations of this wave. It is shown that such an approximate solution uniformly approximates statistical moments of the field (up to the fourth order, inclusive) under arbitrary conditions of wave propagationin a turbulent medium and conditions of wave diffraction on the transmitting aperture.
Heim, J.R.
1993-02-23
The invention provides a high magnetic field coil. The invention provides a preloaded compressive force to the coil maintain the integrity of the coil. The compressive force is obtained by reinforcing the coil with two materials of different thermal expansion rates and then heating the coil to 700 C to obtain the desired compression. The embodiment of the invention uses Nb[sub 3]Sn as the conducting wire, since Nb[sub 3]Sn must be heated to 700 C to cause a reaction which makes Nb[sub 3]Sn superconducting.
Heim, Joseph R.
1993-01-01
The invention provides a high magnetic field coil. The invention provides a preloaded compressive force to the coil maintain the integrity of the coil. The compressive force is obtained by reinforcing the coil with two materials of different thermal expansion rates and then heating the coil to 700.degree. C. to obtain the desired compression. The embodiment of the invention uses Nb.sub.3 Sn as the conducting wire, since Nb.sub.3 Sn must be heated to 700.degree. C. to cause a reaction which makes Nb.sub.3 Sn superconducting.
NASA Astrophysics Data System (ADS)
Nishimura, S.; Sugama, H.; Maaßberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-01
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maaßberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Nishimura, S.; Sugama, H.; Maassberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-15
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Zhou, Q.; Birkholzer, J. T.; Tsang, C.-F.
2011-05-01
Veling (2010) pointed to 'a serious mistake' and 'mathematical inconsistency' in Zhou et al. (2009) because the dimensionless flow equations in Equation 4 (in terms of dimensionless hydraulic head rise in the aquifer and the aquitard) would give rise to additional terms when back converting to the groundwater flow equations, in the case that initial conditions for hydraulic head were spatially variable. He added, however, that the conclusions of the paper remain valid when uniform initial conditions are assumed. We accept this comment because we have indeed assumed uniform initial conditions in the system but failed to state this explicitly in the publication, partially because this assumption is very common in groundwater hydrology when deriving analytical and semi-analytical solutions. The same assumption was employed, for example, by Veling in Veling and Maas (2009), as stated 'For the ease of presentation we assume from here on that {phi}{sub i0} (r, z) ... are all equal to zero. An arbitrary initial function ... will complicate the solution, but not essentially'. We shall emphasize that with this assumption, our semi-analytical solutions and their derivations are correct.
Naher, Hasibun; Abdullah, Farah Aini; Akbar, M Ali
2013-01-01
The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple. PMID:23741355
NASA Astrophysics Data System (ADS)
Kumar, Hitender; Chand, Fakir
2013-03-01
The (2+1)-dimensional Maccari and nonlinear Schrödinger equations are reduced to a nonlinear ordinary differential equation (ODE) by using a simple transformation, various solutions of the nonlinear ODE are obtained by using extended F-expansion and projective Ricatti equation methods. With the aid of solutions of the nonlinear ODE more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Assemblies and methods for mitigating effects of reactor pressure vessel expansion
Challberg, Roy C.; Gou, Perng-Fei; Chu, Cherk Lam; Oliver, Robert P.
1999-01-01
Support assemblies for allowing RPV radial expansion while simultaneously limiting horizontal, vertical, and azimuthal movement of the RPV within a nuclear reactor are described. In one embodiment, the support assembly includes a support block and a guide block. The support block includes a first portion and a second portion, and the first portion is rigidly coupled to the RPV adjacent the first portion. The guide block is rigidly coupled to a reactor pressure vessel support structure and includes a channel sized to receive the second portion of the support block. The second portion of the support block is positioned in the guide block channel to movably couple the guide block to the support block.
Assemblies and methods for mitigating effects of reactor pressure vessel expansion
Challberg, R.C.; Gou, P.F.; Chu, C.L.; Oliver, R.P.
1999-07-27
Support assemblies for allowing RPV radial expansion while simultaneously limiting horizontal, vertical, and azimuthal movement of the RPV within a nuclear reactor are described. In one embodiment, the support assembly includes a support block and a guide block. The support block includes a first portion and a second portion, and the first portion is rigidly coupled to the RPV adjacent the first portion. The guide block is rigidly coupled to a reactor pressure vessel support structure and includes a channel sized to receive the second portion of the support block. The second portion of the support block is positioned in the guide block channel to movably couple the guide block to the support block. 6 figs.
An Expansion of the Trait-State-Occasion Model: Accounting for Shared Method Variance
ERIC Educational Resources Information Center
LaGrange, Beth; Cole, David A.
2008-01-01
This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…
Hayami, Masao; Seino, Junji; Nakai, Hiromi
2014-07-30
An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster. PMID:24889356
Assessing the Jeans Anisotropic Multi-Gaussian Expansion method with the Illustris simulation
NASA Astrophysics Data System (ADS)
Li, Hongyu; Li, Ran; Mao, Shude; Xu, Dandan; Long, R. J.; Emsellem, Eric
2016-02-01
We assess the effectiveness of the Jeans Anisotropic Multi-Gaussian Expansion (JAM) technique with a state-of-the-art cosmological hydrodynamic simulation, the Illustris project. We perform JAM modelling on 1413 simulated galaxies with stellar mass M* > 1010 M⊙, and construct an axisymmetric dynamical model for each galaxy. Combined with a Markov chain Monte Carlo simulation, we recover the projected root-mean-square velocity (Vrms) field of the stellar component, and investigate constraints on the stellar mass-to-light ratio, M*/L, and the fraction of dark matter fDM within 2.5 effective radii (Re). We find that the enclosed total mass within 2.5 Re is well constrained to within 10 per cent. However, there is a degeneracy between the dark matter and stellar components with correspondingly larger individual errors. The 1σ scatter in the recovered M*/L is 30-40 per cent of the true value. The accuracy of the recovery of M*/L depends on the triaxial shape of a galaxy. There is no significant bias for oblate galaxies, while for prolate galaxies the JAM-recovered stellar mass is on average 18 per cent higher than the input values. We also find that higher image resolutions alleviate the dark matter and stellar mass degeneracy and yield systematically better parameter recovery.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution. PMID:26366651
NASA Astrophysics Data System (ADS)
Roy, Ajit K.
An analytical method capable of predicting the in-plane (hoop) and interlaminar (radial) components of effective coefficients of thermal expansion (CTE) of laminated orthotropic rings is presented. This method is based on the linear theory of elasticity assuming the plane-stress condition in the (r, theta) plane of the ring and is applicable to any aspect ratio of the ring. A comparative study of the effective CTE for thin rings indicates that although 2D lamination theory can predict the in-plane CTE quite accurately, it overpredicts the values of the interlaminar CTE by a large amount. As an example, for a thin ring made with T300/5208 laminates, the 2D theory predicts an interlaminar CTE that is 29 percent higher than that predicted by the present method.
The study on the methods of ellipsoid expansion in high-speed railway in high elevation area
NASA Astrophysics Data System (ADS)
Yang, Zhi; Wen, HongYan; Nie, GuangYu; Gao, Hong
2015-12-01
With the development of high-speed railway in recent years, the previous precision of control surveying and the methods of data processing will not meet the requirement of high-speed railway any longer. In view of the characteristics of precision is much higher in large-scale precise construction and the superiority of precision in reform of large-scale engineering control networks, in this paper, using the algorithm of ellipsoid expansion to deal with overrun coordinate projection distortion in high-speed railway, then compares with common calculation method of surveying, we get a conclusion that this method can get minimum projection and it accord with the requirement of high-precision control surveying.
Antos, Roman; Veis, Martin
2010-12-20
We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal-tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides. PMID:21197026
Antos, Roman; Veis, Martin
2010-12-20
We demonstrate an enhancement of the plane wave expansion method treating two-dimensional photonic crystals by applying Fourier factorization with generally elliptic polarization bases. By studying three examples of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the permittivity function is simply expanded without changing coordinates, and to the normal vector method using a normal-tangential polarization transform. The compared calculations clearly show that our approach yields the best convergence properties owing to the complete continuity of our distribution of polarization bases. The presented methodology enables us to study more general systems such as periodic elements with an arbitrary cross-section or devices such as photonic crystal waveguides.
Energy Expansion for the Period of Anharmonic Oscillators by the Method of Lindstedt-Poincare
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2004-01-01
A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt-Poincare.
Yu, Huimin; Zhao, Xiuhua; Zu, Yuangang; Zhang, Xinjuan; Zu, Baishi; Zhang, Xiaonan
2012-01-01
The particle sizes of pharmaceutical substances are important for their bioavailability. Bioavailability can be improved by reducing the particle size of the drug. In this study, artemisinin was micronized by the rapid expansion of supercritical solutions (RESS). The particle size of the unprocessed white needle-like artemisinin particles was 30 to 1200 μm. The optimum micronization conditions are determined as follows: extraction temperature of 62 °C, extraction pressure of 25 MPa, precipitation temperature 45 °C and nozzle diameter of 1000 μm. Under the optimum conditions, micronized artemisinin with a (mean particle size) MPS of 550 nm is obtained. By analysis of variance (ANOVA), extraction temperature and pressure have significant effects on the MPS of the micronized artemisinin. The particle size of micronized artemisinin decreased with increasing extraction temperature and pressure. Moreover, the SEM, LC-MS, FTIR, DSC and XRD allowed the comparison between the crystalline initial state and the micronization particles obtained after the RESS process. The results showed that RESS process has not induced degradation of artemisinin and that processed artemisinin particles have lower crystallinity and melting point. The bulk density of artemisinin was determined before and after RESS process and the obtained results showed that it passes from an initial density of 0.554 to 0.128 g·cm−3 after the processing. The decrease in bulk density of the micronized powder can increase the liquidity of drug particles when they are applied for medicinal preparations. These results suggest micronized powder of artemisinin can be of great potential in drug delivery systems. PMID:22606030
Rodrigo, J.L.; Carrasco, P.; Alamo, J. )
1989-05-01
Previous disagreement about the thermal expansion of the rhombohedral compound, NZP-type, NaTi/sub 2/(PO/sub 4/)/sub 3/ is clarified. It is shown that thermal stresses affect the thermal expansion, but they relax after some time of storage. Its anisotropic thermal expansion, has been calculate from high temperature X-ray diffraction, and it is linear in the range from room temperature up to 800{sup 0}C. The predictability of thermal expansion and the tailoring of the composition of NZP ceramics require checking whether the thermal effect on the rotations and distortions of the atomic polyhedra in this structure is the responsible for the high anisotropy in the thermal expansion. This effect has been determined experimentally by solving the chemical structure at five different temperatures, applying the Rietveld method to deconvolute the powder X-ray diffraction profiles.
COMET-PE: an incident fluence response expansion transport method for radiotherapy calculations
NASA Astrophysics Data System (ADS)
Hayward, Robert M.; Rahnema, Farzad
2013-05-01
Accurate dose calculation is a central component of radiotherapy treatment planning. A new method of dose calculation has been developed based on transport theory and validated by comparison to Monte Carlo methods. The coarse mesh transport method has been extended to allow coupled photon-electron transport in 3D. The method combines stochastic pre-computation with a deterministic solver to achieve high accuracy and precision. To enhance the method for radiotherapy calculations, a new angular basis was derived, and an analytical source treatment was developed. Validation was performed by comparison to DOSXYZnrc using a heterogeneous interface phantom composed of water, aluminum, and lung. Calculations of both kinetic energy released per unit mass and dose were compared. Good agreement was found with a maximum error and root mean square relative error of less than 1.5% for all cases. The results show that the new method achieves an accuracy comparable to Monte Carlo.
Shi, Shouyuan; Chen, Caihua; Prather, Dennis W
2004-09-01
We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.
NASA Astrophysics Data System (ADS)
Chang, Zhe; Lin, Hai-Nan
2015-01-01
Type Ia supernovae (SNe Ia) are often used as the standard candles to probe the anisotropic expansion of the Universe. In this paper, we make a comprehensive comparison between the hemisphere comparison (HC) method and dipole-fitting (DF) method in searching for the cosmological preferred direction using the Union2 data set, a compilation of 557 well-calibrated SNe Ia. We find that the directions of the faintest SNe Ia derived from these two methods are approximately opposite. Monte Carlo simulations show that the results of the HC method strongly depend on the distribution of the data points in the sky. The coincidence that the HC method and DF method give two completely opposite directions may be due to the extremely non-uniform distribution of the Union2 data set.
He, Yue-Jing; Hung, Wei-Chih; Lai, Zhe-Ping
2016-01-01
In this study, a numerical simulation method was employed to investigate and analyze superstructure fiber Bragg gratings (SFBGs) with five duty cycles (50%, 33.33%, 14.28%, 12.5%, and 10%). This study focuses on demonstrating the relevance between design period and spectral characteristics of SFBGs (in the form of graphics) for SFBGs of all duty cycles. Compared with complicated and hard-to-learn conventional coupled-mode theory, the result of the present study may assist beginner and expert designers in understanding the basic application aspects, optical characteristics, and design techniques of SFBGs, thereby indirectly lowering the physical concepts and mathematical skills required for entering the design field. To effectively improve the accuracy of overall computational performance and numerical calculations and to shorten the gap between simulation results and actual production, this study integrated a perfectly matched layer (PML), perfectly reflecting boundary (PRB), object meshing method (OMM), and boundary meshing method (BMM) into the finite element method (FEM) and eigenmode expansion method (EEM). The integrated method enables designers to easily and flexibly design optical fiber communication systems that conform to the specific spectral characteristic by using the simulation data in this paper, which includes bandwidth, number of channels, and band gap size. PMID:26861322
He, Yue-Jing; Hung, Wei-Chih; Lai, Zhe-Ping
2016-01-01
In this study, a numerical simulation method was employed to investigate and analyze superstructure fiber Bragg gratings (SFBGs) with five duty cycles (50%, 33.33%, 14.28%, 12.5%, and 10%). This study focuses on demonstrating the relevance between design period and spectral characteristics of SFBGs (in the form of graphics) for SFBGs of all duty cycles. Compared with complicated and hard-to-learn conventional coupled-mode theory, the result of the present study may assist beginner and expert designers in understanding the basic application aspects, optical characteristics, and design techniques of SFBGs, thereby indirectly lowering the physical concepts and mathematical skills required for entering the design field. To effectively improve the accuracy of overall computational performance and numerical calculations and to shorten the gap between simulation results and actual production, this study integrated a perfectly matched layer (PML), perfectly reflecting boundary (PRB), object meshing method (OMM), and boundary meshing method (BMM) into the finite element method (FEM) and eigenmode expansion method (EEM). The integrated method enables designers to easily and flexibly design optical fiber communication systems that conform to the specific spectral characteristic by using the simulation data in this paper, which includes bandwidth, number of channels, and band gap size. PMID:26861322
A ghost cell expansion method for reducing communications in solving PDE problems
Ding, Chris H.Q.; He, Yun
2001-05-01
In solving Partial Differential Equations, such as the Barotropic equations in ocean models, on Distributed Memory Computers, finite difference methods are commonly used. Most often, processor subdomain boundaries must be updated at each time step. This boundary update process involves many messages of small sizes, therefore large communication overhead. Here we propose a new approach which expands the ghost cell layers and thus updates boundaries much less frequently ---reducing total message volume and grouping small messages into bigger ones. Together with a technique for eliminating diagonal communications, the method speedup communication substantially, up to 170%. We explain the method and implementation in details, provide systematic timing results and performance analysis on Cray T3E and IBM SP.
Action First--Understanding Follows: An Expansion of Skills-Based Training Using Action Method.
ERIC Educational Resources Information Center
Martin, Colin
1988-01-01
This paper discusses the concept of training trainers in the skills they need to perform competently as trainers and how they follow their skills mastery with discussion on their new theoretical insight. Moreno's action method (psychodrama, sociodrama, sociometry, and role training) is the model used. (JOW)
Method of Producing Controlled Thermal Expansion Coat for Thermal Barrier Coatings
NASA Technical Reports Server (NTRS)
Brindley, William J. (Inventor); Miller, Robert A. (Inventor); Aikin, Beverly J. M. (Inventor)
2000-01-01
An improved thermal barrier coating and method for producing and applying such is disclosed herein. The thermal barrier coatings includes a high temperature substrate, a first bond coat layer applied to the substrate of MCrAlX and a second bond coat layer of MCrAlX with particles of a particulate dispersed throughout the MCrAlX and the preferred particulate is Al2O3. The particles of the particulate dispersed throughout the second bond coat layer preferably have a diameter of less then the height of the peaks of the second bond coat layer or a diameter of less than 5 micron. The method of producing the second bond coat layer may either include the steps of mechanical alloying of particles throughout the second bond coat layer, attrition milling the particles of the particulate throughout the second bond coat layer, or using electrophoresis to disperse the particles throughout the second bond coat layer. In the preferred embodiment of the invention the first bond coat layer is applied to the substrate. and then the second bond coat layer is thermally sprayed onto the first bond coat layer. Further, in a preferred embodiment of the invention a ceramic insulating layer covers the second bond coat layer.
Vagov, A; Schomerus, H; Zalipaev, V V
2009-11-01
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field. PMID:20365055
A maximal chromatic expansion method of mapping multichannel imagery into color space. [North Dakota
NASA Technical Reports Server (NTRS)
Juday, R. D.; Abotteen, R. A. (Principal Investigator)
1978-01-01
The author has identified the following significant results. A color film generation method that maximally expands the chromaticity and aligns Kauth brightness with the gray axis was presented. In comparison with the current LACIE film product, the new color film product has more contrast and more colors and appears to be brighter. The field boundaries in the new product were more pronounced than in the current LACIE product. The speckle effect was one problem in the new product. The yellowness speckle can be treated using an equation. This equation can be used to eliminate any speckle introduced by the greenness. This product leads logically toward another that will employ quantitative colorimetry which will account for some of the eye's perception of color stimuli.
Numerical modeling of the expansion phase of steam explosions. Part 1, Method and validation
Hyder, M.L.; Farawila, Y.M.; Abdel-Khalik, S.I.; Halvorson, P.J.
1992-05-01
In the development of the Severe Accident Analysis Program for the Savannah River production reactors, it was recognized that certain accidents have -the potential for causing damaging steam explosions. Steam explosions can occur when metals, such as the aluminum-based fuel used at Savannah River, are melted and come into contact with water. This condition is unstable, and local turbulence can lead to the generation of great quantities of steam within a few milliseconds. This phenomenon has been observed in several reactor incidents and experiments (BORAX, SPERT-1, SL-1, probably Chernobyl) where it caused damage to the reactor and associated structures. The massive SRS reactor buildings are likely to withstand any imaginable steam explosion. However, reactor components and building structures including hatches, ventilation ducts, etc., could be at risk if such an explosion occurred. The goal for this study was to develop a computer code that could be used parametrically to predict the effects of various steam explosions on their surroundings. This would be able to predict whether a steam explosion of a given magnitude would be likely to fail a particular structure. This would require, of course, that the magnitude of the explosion be specified through some combination of judgment and calculation. The requested code, identified as the K-FIX(GT) code, was developed and delivered by the contractor, along with extensive documentation. The several individual reports that constitute the documentation are each being issued as a separate WSRC report. Documentation includes several model calculations, and. representation of these in graphic form. This report incorporates Report GTRSR-006, which gives an overview of the methods used in the development of K-FIX(GT), and the results of a comparison with experiments in the literature. The authors conclude that the results of the comparison calculation are in reasonable agreement with observations.
ERIC Educational Resources Information Center
McArdle, Heather K.
1997-01-01
Describes a week-long activity for general to honors-level students that addresses Hubble's law and the universal expansion theory. Uses a discrepant event-type activity to lead up to the abstract principles of the universal expansion theory. (JRH)
Hayami, Masao; Seino, Junji; Nakai, Hiromi
2015-05-28
An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.
NASA Astrophysics Data System (ADS)
Huang, Y. G.; Wang, L. G.; Lu, Y. L.; Chen, J. R.; Zhang, J. H.
2015-09-01
Based on the two-dimensional elasticity theory, this study established a mechanical model under chordally opposing distributed compressive loads, in order to perfect the theoretical foundation of the flattened Brazilian splitting test used for measuring the indirect tensile strength of rocks. The stress superposition method was used to obtain the approximate analytic solutions of stress components inside the flattened Brazilian disk. These analytic solutions were then verified through a comparison with the numerical results of the finite element method (FEM). Based on the theoretical derivation, this research carried out a contrastive study on the effect of the flattened loading angles on the stress value and stress concentration degree inside the disk. The results showed that the stress concentration degree near the loading point and the ratio of compressive/tensile stress inside the disk dramatically decreased as the flattened loading angle increased, avoiding the crushing failure near-loading point of Brazilian disk specimens. However, only the tensile stress value and the tensile region were slightly reduced with the increase of the flattened loading angle. Furthermore, this study found that the optimal flattened loading angle was 20°-30°; flattened load angles that were too large or too small made it difficult to guarantee the central tensile splitting failure principle of the Brazilian splitting test. According to the Griffith strength failure criterion, the calculative formula of the indirect tensile strength of rocks was derived theoretically. This study obtained a theoretical indirect tensile strength that closely coincided with existing and experimental results. Finally, this paper simulated the fracture evolution process of rocks under different loading angles through the use of the finite element numerical software ANSYS. The modeling results showed that the Flattened Brazilian Splitting Test using the optimal loading angle could guarantee the tensile
NASA Astrophysics Data System (ADS)
Chen, Zaigao; Wang, Jianguo; Wang, Yue
2016-09-01
The cathode plasma expansion has been widely investigated and is recognized as impedance collapse in a relativistic backward wave oscillator (RBWO). However, the process of formation and expansion of cathode plasma is very complicated, and the thickness of plasma is only several millimeters, so the simulation of cathode plasma requires high temporal and spatial resolutions. Only the scaled-down diode model and the thin gas layer model are considered in the previous hybrid simulation, and there are few numerical studies on the effect of cathode plasma expansion on the RBWO. In this paper, the moving-boundary conformal particle-in-cell method is proposed; the cathode plasma front is treated in this novel method as the actual cathode surface, and the explosive electron emission boundary moves as the expansion of cathode plasma. Moreover, in order to accurately simulate the electromagnetic field near the cathode surface, the conformal finite-difference time-domain method based on the enlarged cell technique is adopted. The numerical simulation indicates that the diode voltage decreases and the beam current increases as cathode plasma expands; when the cathode plasma velocity is 10 cm/μs, the pulse duration of the generated microwave decreases from 30 ns to 10 ns, the working frequency decreases from 9.83 GHz to 9.64 GHz, and the output power decreases 30% in the course of cathode plasma expansion.
Dimitrov, I. K.; Zhang, X.; Solovyov, V. F.; Chubar, O.; Li, Qiang
2015-07-07
Recent advances in second-generation (YBCO) high-temperature superconducting wire could potentially enable the design of super high performance energy storage devices that combine the high energy density of chemical storage with the high power of superconducting magnetic storage. However, the high aspect ratio and the considerable filament size of these wires require the concomitant development of dedicated optimization methods that account for the critical current density in type-II superconductors. In this study, we report on the novel application and results of a CPU-efficient semianalytical computer code based on the Radia 3-D magnetostatics software package. Our algorithm is used to simulate andmore » optimize the energy density of a superconducting magnetic energy storage device model, based on design constraints, such as overall size and number of coils. The rapid performance of the code is pivoted on analytical calculations of the magnetic field based on an efficient implementation of the Biot-Savart law for a large variety of 3-D “base” geometries in the Radia package. The significantly reduced CPU time and simple data input in conjunction with the consideration of realistic input variables, such as material-specific, temperature, and magnetic-field-dependent critical current densities, have enabled the Radia-based algorithm to outperform finite-element approaches in CPU time at the same accuracy levels. Comparative simulations of MgB2 and YBCO-based devices are performed at 4.2 K, in order to ascertain the realistic efficiency of the design configurations.« less
Dimitrov, I. K.; Zhang, X.; Solovyov, V. F.; Chubar, O.; Li, Qiang
2015-07-07
Recent advances in second-generation (YBCO) high-temperature superconducting wire could potentially enable the design of super high performance energy storage devices that combine the high energy density of chemical storage with the high power of superconducting magnetic storage. However, the high aspect ratio and the considerable filament size of these wires require the concomitant development of dedicated optimization methods that account for the critical current density in type-II superconductors. In this study, we report on the novel application and results of a CPU-efficient semianalytical computer code based on the Radia 3-D magnetostatics software package. Our algorithm is used to simulate and optimize the energy density of a superconducting magnetic energy storage device model, based on design constraints, such as overall size and number of coils. The rapid performance of the code is pivoted on analytical calculations of the magnetic field based on an efficient implementation of the Biot-Savart law for a large variety of 3-D “base” geometries in the Radia package. The significantly reduced CPU time and simple data input in conjunction with the consideration of realistic input variables, such as material-specific, temperature, and magnetic-field-dependent critical current densities, have enabled the Radia-based algorithm to outperform finite-element approaches in CPU time at the same accuracy levels. Comparative simulations of MgB_{2} and YBCO-based devices are performed at 4.2 K, in order to ascertain the realistic efficiency of the design configurations.
ATAT@WIEN2k: An interface for cluster expansion based on the linearized augmented planewave method
NASA Astrophysics Data System (ADS)
Chakraborty, Monodeep; Spitaler, Jürgen; Puschnig, Peter; Ambrosch-Draxl, Claudia
2010-05-01
We have developed an interface between the all-electron density functional theory code WIEN2k, and the MIT Ab-initio Phase Stability (MAPS) code of the Alloy-Theoretic Automated Toolkit (ATAT). WIEN2k is an implementation of the full-potential linearized augmented planewave method which yields highly accurate total energies and optimized geometries for any given structure. The ATAT package consists of two parts. The first one is the MAPS code, which constructs a cluster expansion (CE) in conjunction with a first-principles code. These results form the basis for the second part, which computes the thermodynamic properties of the alloy. The main task of the CE is to calculate the many-body potentials or effective cluster interactions (ECIs) from the first-principles total energies of different structures or supercells using the structure-inversion technique. By linking MAPS seamlessly with WIEN2k we have created a tool to obtain the ECIs for any lattice type of an alloy. We have chosen fcc Al-Ti and bcc W-Re to evaluate our implementation. Our calculated ECIs exhibit all features of a converged CE and compare well with literature results.
Giese, Timothy J.; York, Darrin M.
2010-01-01
We extend the Kohn–Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a “Jacob’s ladder” comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn–Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements. PMID:21197976
Giese, Timothy J; York, Darrin M
2010-12-28
We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.
NASA Astrophysics Data System (ADS)
Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali
2016-07-01
In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
Expansion: A Plan for Success.
ERIC Educational Resources Information Center
Callahan, A.P.
This report provides selling brokers' guidelines for the successful expansion of their operations outlining a basic method of preparing an expansion plan. Topic headings are: The Pitfalls of Expansion (The Language of Business, Timely Financial Reporting, Regulatory Agencies of Government, Preoccupation with the Facade of Business, A Business Is a…
Sullivan, P.; Eurek, K.; Margolis, R.
2014-07-01
Because solar power is a rapidly growing component of the electricity system, robust representations of solar technologies should be included in capacity-expansion models. This is a challenge because modeling the electricity system--and, in particular, modeling solar integration within that system--is a complex endeavor. This report highlights the major challenges of incorporating solar technologies into capacity-expansion models and shows examples of how specific models address those challenges. These challenges include modeling non-dispatchable technologies, determining which solar technologies to model, choosing a spatial resolution, incorporating a solar resource assessment, and accounting for solar generation variability and uncertainty.
Anderson, Robert C.; Jones, Jack M.; Kollie, Thomas G.
1982-01-01
The present invention is directed to the fabrication of an article of uranium-2.4 wt. % niobium alloy in which the linear thermal expansion in the direction transverse to the extrusion direction is less than about 0.98% between 22.degree. C. and 600.degree. C. which corresponds to a value greater than the 1.04% provided by previous extrusion operations over the same temperature range. The article with the improved thermal expansion possesses a yield strength at 0.2% offset of at least 400 MPa, an ultimate tensile strength of 1050 MPa, a compressive yield strength of at least 0.2% offset of at least 675 MPa, and an elongation of at least 25% over 25.4 mm/sec. To provide this article with the improved thermal expansion, the uranium alloy billet is heated to 630.degree. C. and extruded in the alpha phase through a die with a reduction ratio of at least 8.4:1 at a ram speed no greater than 6.8 mm/sec. These critical extrusion parameters provide the article with the desired decrease in the linear thermal expansion while maintaining the selected mechanical properties without encountering crystal disruption in the article.
NASA Astrophysics Data System (ADS)
Sakaguchi, Toshimasa; Fujigaki, Motoharu; Murata, Yorinobu
2015-03-01
Accurate and wide-range shape measurement method is required in industrial field. The same technique is possible to be used for a shape measurement of a human body for the garment industry. Compact 3D shape measurement equipment is also required for embedding in the inspection system. A shape measurement by a phase shifting method can measure the shape with high spatial resolution because the coordinates can be obtained pixel by pixel. A key-device to develop compact equipment is a grating projector. Authors developed a linear LED projector and proposed a light source stepping method (LSSM) using the linear LED projector. The shape measurement euipment can be produced with low-cost and compact without any phase-shifting mechanical systems by using this method. Also it enables us to measure 3D shape in very short time by switching the light sources quickly. A phase unwrapping method is necessary to widen the measurement range with constant accuracy for phase shifting method. A general phase unwrapping method with difference grating pitches is often used. It is one of a simple phase unwrapping method. It is, however, difficult to apply the conventional phase unwrapping algorithm to the LSSM. Authors, therefore, developed an expansion unwrapping algorithm for the LSSM. In this paper, an expansion algorithm of measurement range suited for 3D shape measurement using two pitches of projected grating with the LSSM was evaluated.
Kovalchuk, V. I.; Kozlovsky, I. V.; Tartakovsky, V. K.
2011-05-15
A method for solving Faddeev equations in configuration space for a bound state and a continuous spectrum of the system of three nucleons was developed on the basis of expansions in K harmonics. Coulomb interaction and particle spins were not taken into account in this study. The method in question was used to describe the triton bound state and differential cross sections for neutron-deuteron scattering at subthreshold incident-neutron energies. The Volkov, Malfliet-Tjon, and Eikemeier-Hackenbroich local nucleon-nucleon potentials were employed in the present calculations.
NASA Technical Reports Server (NTRS)
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Gao, Jiali; Wang, Yingjie
2012-02-21
A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.
Accelerating the loop expansion
Ingermanson, R.
1986-07-29
This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi/sup 4/ theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs.
Novel Foraminal Expansion Technique
Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-01-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Novel Foraminal Expansion Technique.
Ozer, Ali Fahir; Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-08-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Novel Foraminal Expansion Technique.
Ozer, Ali Fahir; Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-08-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis.
NASA Astrophysics Data System (ADS)
Wang, Jintao; Liu, Ziyong; Xu, Changhong; Li, Zhanhong
2014-07-01
The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3 (DSL-2329) plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5×10-4 K-1 and 5.4×1010 Pa-1, respectively.
Shelley, Brandon C.; Gowing, Geneviève; Svendsen, Clive N.
2014-01-01
A cell expansion technique to amass large numbers of cells from a single specimen for research experiments and clinical trials would greatly benefit the stem cell community. Many current expansion methods are laborious and costly, and those involving complete dissociation may cause several stem and progenitor cell types to undergo differentiation or early senescence. To overcome these problems, we have developed an automated mechanical passaging method referred to as “chopping” that is simple and inexpensive. This technique avoids chemical or enzymatic dissociation into single cells and instead allows for the large-scale expansion of suspended, spheroid cultures that maintain constant cell/cell contact. The chopping method has primarily been used for fetal brain-derived neural progenitor cells or neurospheres, and has recently been published for use with neural stem cells derived from embryonic and induced pluripotent stem cells. The procedure involves seeding neurospheres onto a tissue culture Petri dish and subsequently passing a sharp, sterile blade through the cells effectively automating the tedious process of manually mechanically dissociating each sphere. Suspending cells in culture provides a favorable surface area-to-volume ratio; as over 500,000 cells can be grown within a single neurosphere of less than 0.5 mm in diameter. In one T175 flask, over 50 million cells can grow in suspension cultures compared to only 15 million in adherent cultures. Importantly, the chopping procedure has been used under current good manufacturing practice (cGMP), permitting mass quantity production of clinical-grade cell products. PMID:24962813
Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo; Nishida, Yusuke
2015-05-15
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.
Mareschi, Katia; Rustichelli, Deborah; Calabrese, Roberto; Gunetti, Monica; Sanavio, Fiorella; Castiglia, Sara; Risso, Alessandra; Ferrero, Ivana; Tarella, Corrado; Fagioli, Franca
2012-01-01
Mesenchymal stem cells (MSCs) are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of “optimal” conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm2. After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm2. Statistical analyses were performed. Cumulative Population Doublings (PD) did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm2 did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use. PMID:23715383
Mareschi, Katia; Rustichelli, Deborah; Calabrese, Roberto; Gunetti, Monica; Sanavio, Fiorella; Castiglia, Sara; Risso, Alessandra; Ferrero, Ivana; Tarella, Corrado; Fagioli, Franca
2012-01-01
Mesenchymal stem cells (MSCs) are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of "optimal" conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm(2). After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm(2). Statistical analyses were performed. Cumulative Population Doublings (PD) did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm(2) did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use.
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
NASA Astrophysics Data System (ADS)
Kumar, Rajinder; Nivarthi, Sriram S.; Davis, H. Ted; Kroll, D. M.; Maier, Robert S.
1999-11-01
The lattice-Boltzmann (LB) method, derived from lattice gas automata, is a relatively new technique for studying transport problems. The LB method is investigated for its accuracy to study fluid dynamics and dispersion problems. Two problems of relevance to flow and dispersion in porous media are addressed: (i) Poiseuille flow between parallel plates (which is analogous to flow in pore throats in two-dimensional porous networks), and (ii) flow through an expansion-contraction geometry (which is analogous to flow in pore bodies in two-dimensional porous networks). The results obtained from the LB simulations are compared with analytical solutions when available, and with solutions obtained from a finite element code (FIDAP) when analytical results are not available. Excellent agreement is found between the LB results and the analytical/FIDAP solutions in most cases, indicating the utility of the lattice-Boltzmann method for solving fluid dynamics and dispersion problems. Copyright
NASA Astrophysics Data System (ADS)
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
NASA Technical Reports Server (NTRS)
Yos, William T. (Inventor); Cantrell, John H., Jr. (Inventor)
2004-01-01
A method and apparatus for measuring changes in intracranial pressure (ICP) utilizing the variation of the surface wave propagation parameters of the patient's skull to determine the change in ICP. In one embodiment, the method comprises the steps of transmitting an ultrasonic bulk compressional wave onto the surface of the skull at a predetermined angle with respect to the skull so as to produce a surface wave, receiving the surface wave at an angle with respect tn the skull which is substantially the same as the predetermined angle and at a location that is a predetermined distance from where the ultrasonic bulk compressional wave was transmitted upon the skull, determining the retardation or advancement in phase of the received surface wave with respect to a reference phase, and processing the determined retardation or advancement in phase to determine circumferential expansion or contraction of the skull and utilizing the determined circumferential change to determine the change in intracranial pressure.
Hsue, Young-Chung; Yang, Tzong-Jer
2004-01-01
We propose a modified plane-wave expansion method to calculate transmittivity and reflectivity of a semi-infinite photonic crystal (PC) with interface. This method is based on an expanded completeness basis, including both the propagation and evanescence modes. We use this approach to deal with two kinds of problems: one is to determine the normal direction of the largest attenuation strength for a semi-infinite PC in the gap frequencies; the other is to calculate the transmittivity and reflectivity of a PC slab. To demonstrate the extensive utilization of our approach, we revisit the same system as studied by Phys. Rev. B 52, 8992 (1995)] and find that our results are in good agreement with ones obtained by Sakoda's paper.
Samin, Adib; Lahti, Erik; Zhang, Jinsuo
2015-08-15
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
Tissue expansion in perspective.
Sharpe, D. T.; Burd, R. M.
1989-01-01
Tissue expansion is a recent advance in skin cover technique. Its empirical use has enabled many previously difficult reconstructions to be completed without recourse to distant flaps. Its high complication rate and lack of basic scientific understanding at present restrict its use to selected cases, but the quality of repairs possible by this method encourage further serious scientific study. Images fig. 1 fig. 2 fig. 3 fig. 4 fig. 5 PMID:2589784
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale. PMID:27333052
NASA Astrophysics Data System (ADS)
Lee, Keonhee; Oh, Jumi
2016-01-01
A notion of measure expansivity for flows was introduced by Carrasco-Olivera and Morales in [3] as a generalization of expansivity, and they proved that there were no measure expansive flows on closed surfaces. In this paper we introduce a concept of weak measure expansivity for flows which is really weaker than that of measure expansivity, and show that there is a weak measure expansive flow on a closed surface. Moreover we show that any C1 stably weak measure expansive flow on a C∞ closed manifold M is Ω-stable, and any C1 stably measure expansive flow on M satisfies both Axiom A and the quasi-transversality condition.
NASA Astrophysics Data System (ADS)
Human, Hendrik G. C.
1997-01-01
Selective dissociation of UF6 using three wavelength IR irradiation did not yield the desired results initially. Various spectroscopic methods such as UV and IR absorption of UF6, fluorescence of UF6 and Time-of-Flight Mass Spectrometry of the products of irradiation, were implemented to investigate the nature of the interaction. These techniques identified the source of the problem as the presence of condensates in the flow-cooled gas, and were used to select conditions to minimise this effect.
NASA Technical Reports Server (NTRS)
Wagner, Richard D., Jr.
1959-01-01
In a recent article on hypersonic flow, Lees and Kubota suggested a modification of the local-expansion method to predict the surface pressures in the region of a nose-cylinder junction where Newtonian theory fails. The modification consists of matching the Newtonian pressure distribution and the Prandtl-Meyer relation at the point on the nose surface where both the pressure and the pressure gradient, predicted by these two solution, are equal. With this approximation, the pressure distribution can be predicted quite accurately up to the nose-cylinder junction for blunt-nosed bodies of continuous curvature, provided centrifugal-force effects are negligible. The purpose of this note is to facilitate the application of Lees' suggestion and to draw attention to some of its consequences.
Dalir, Nemat
2014-01-01
An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed. PMID:27433511
Expansion techniques for collisionless stellar dynamical simulations
NASA Astrophysics Data System (ADS)
Meiron, Yohai
2016-02-01
We present ETICS, a collisionless N-body code based on two kinds of series expansions of the Poisson equation, implemented for graphics processing units (GPUs). The code is publicly available and can be used as a standalone program or as a library (an AMUSE plugin is included). One of the two expansion methods available is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a ``pure'' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms.
Nishimoto, Yoshio
2015-09-01
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well. PMID:26342360
Nishimoto, Yoshio
2015-09-07
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
Shortt, Alex J; Secker, Genevieve A; Lomas, Richard J; Wilshaw, Stacy P; Kearney, John N; Tuft, Stephen J; Daniels, Julie T
2009-02-01
Human amniotic membrane (HAM) is employed as a substrate for the ex-vivo expansion of limbal epithelial cells (LECs) used to treat corneal epithelial stem cell deficiency in humans. The optimal method of HAM preparation for this purpose is unknown. This study evaluated the ability of different preparations of stored HAM to serve as substrates for LEC expansion ex-vivo. The effect of removing the amniotic epithelial cells (decellularisation) from HAM prior to seeding of LECs, the effect of glycerol cryopreservation and the effect of peracetic acid (PAA) sterilization and antibiotic disinfection were evaluated using different HAM test groups. Human LECs were cultured on each preparation and the following outcomes were assessed: confluence of growth, cell density, cell morphology and expression of the putative LESC markers deltaN-p63alpha and ABCG2. Removing amniotic epithelial cells prior to seeding of LECs resulted in a higher percentage of confluence but a lower cell density than intact HAM suggesting that decellularisation does not increase proliferation, but rather that it facilitates migration of LECs resulting in larger cells. Decellularisation did not affect the percentage of cells expressing the putative LESC markers deltaN-p63alpha (< or =4% in both intact and acellular groups) and ABCG2 (< or =3% in both intact and acellular groups). Glycerol cryopreservation of HAM resulted in poor morphology and a low proportion of cells expressing deltaN-p63alpha (< or =6%) and ABCG2 (< or =8%). HAM frozen at -80 degrees C in Hank's Balanced Salt Solution (HBSS) was superior, demonstrating excellent morphology of cultured LECs and high levels of deltaN-p63alpha (< or =68%) and ABCG2 (< or =62%) expression (p<0.001). The use of PAA or antibiotics to decontaminate HAM does not appear to affect this function. The variables affecting the ability of HAM to serve as a substrate for LEC expansion ex-vivo are poorly understood. The use of glycerol as a cryoprotectant impairs
Imani, S Misagh; Goudarzi, A M; Ghasemi, S E; Kalani, A; Mahdinejad, J
2014-10-01
In this article, finite element method is used to investigate the mechanical behavior of a stent and to determine the biomechanical interaction between the stent and the artery in a stenting procedure. The main objective of this study is to reach to a model close to a real condition of coronary stent placement. Unlike most of the models proposed in the literature, all the steps of the deployment of a stent in the stenotic vessel (i.e. pressure increasing, constant load pressure and pressure decreasing) are simulated in this article to show the behavior of the stent in different stages of implantation. The results indicate that the first step of deployment, that is, pressure increasing, plays a main role in the success of stent implantation. So that, in order to compare the behavior of different types of stents, it is sufficient to compare their behavior at the end of pressure increasing step. In order to show the application of the findings in stent versus stent studies, three commercially available stents (the Palmaz-Schatz, Multi-Link and NIR stents) are modeled and their behavior is compared at the end of pressure increasing step. The effect of stent design on the restenosis rate is investigated. According to the findings, the possibility of restenosis is lower for Multi-Link and NIR stents in comparison with Palmaz-Schatz stent which is in good agreement with clinical results. Therefore, the testing methodology outlined here is proposed as a simple and economical alternative for "stent versus stent" complicated clinical trials.
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation.
NASA Astrophysics Data System (ADS)
Third, J. R.; Chen, Y.; Müller, C. R.
2016-07-01
Lattice-Boltzmann method (LBM) simulations of a gas-fluidised bed have been performed. In contrast to the current state-of-the-art coupled computational fluid dynamics-discrete element method (CFD-DEM) simulations, the LBM does not require a closure relationship for the particle-fluid interaction force. Instead, the particle-fluid interaction can be calculated directly from the detailed flow profile around the particles. Here a comparison is performed between CFD-DEM and LBM simulations of a small fluidised bed. Simulations are performed for two different values of the superficial gas velocity and it is found that the LBM predicts a larger bed expansion for both flowrates. Furthermore the particle-fluid interaction force obtained for LBM simulations is compared to the force which would be predicted by a CFD-DEM model under the same conditions. On average the force predicted by the CFD-DEM closure relationship is found to be significantly smaller than the force obtained from the LBM.
Hsu, Jin-Chen; Wu, Tsung-Tsong
2008-02-01
Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.
A numerical method for determining the strain rate intensity factor under plane strain conditions
NASA Astrophysics Data System (ADS)
Alexandrov, S.; Kuo, C.-Y.; Jeng, Y.-R.
2016-07-01
Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.
Thermal Expansion of Polyurethane Foam
NASA Technical Reports Server (NTRS)
Lerch, Bradley A.; Sullivan, Roy M.
2006-01-01
expansion tests and the response of the microstructure. A novel optical method is described which is appropriate for measuring thermal expansion at high temperatures without influencing the thermal expansion measurement. Detailed microstructural investigations will also be described which show cell expansion as a function of temperature. Finally, a phenomenological model on thermal expansion will be described.
Micromechanics of expansive mechanisms in expansive cement concretes
NASA Astrophysics Data System (ADS)
Cohen, M. D.
The kinetics of hydration were studied by monitoring the presence of various compounds by X-ray diffractometer, a chemical extraction method, and scanning electron microscope. These studies indicated that the rates of depletion of the expanding particles and sulfates are higher in the finer blends, which is why expansion stops earlier in these blends. It is shown that the double curvature phenomenon (strength-drop and sudden increase in the rate of expansion) is caused by mechanical failure (e.g., microcracking) of the matrix surrounding the expanding particles that are producing ettringite crystals. The theory of protective and partial protective coating is reviewed. A hypothesis is introduced which assumes that monosulfate is not formed immediately when ettringite stops forming but is preceded by an intermediate phase. Shrinkage studies show that expansive cements shrink more than portland cements. The results of these studies were used to develop a modified model of the expansive process. It was shown theoretically that the time of expansion is inversely proportional to the surface area of the expansive clinker and directly proportional to the amount of sulfate used.
Operator product expansion algebra
Holland, Jan; Hollands, Stefan
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Expansion techniques for collisionless stellar dynamical simulations
Meiron, Yohai; Li, Baile; Holley-Bockelmann, Kelly; Spurzem, Rainer
2014-09-10
We present graphics processing unit (GPU) implementations of two fast force calculation methods based on series expansions of the Poisson equation. One method is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other method is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a 'pure' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took ∼0.1 s (depending on expansion cutoff), making simulations with as many as 10{sup 8} particles fast for a comparatively small number of nodes.
Expansion of the planetary disturbing function.
NASA Technical Reports Server (NTRS)
Broucke, R.; Smith, G.
1971-01-01
Some methods are described for the expansion of the disturbing function in planetary theory. One method uses the classical binomial expansion theorem or a successive approximation process derived from it. Another method is a direct application of the Laplace series expansions. For both methods it is proposed to first prepare the series to be manipulated by a scaling operation. These methods can be applied either in a literal or in a numerical form, or any combination of both, but they are especially designed for use on a large scale digital computer with standard Poisson series programs. No usage is made of Newcomb operators or derivatives of Laplace coefficients.
Anderson, R.C.; Jones, J.M.; Kollie, T.G.
1982-05-24
The present invention is directed to the fabrication of an article of uranium-2.4 wt % niobium alloy in which the linear thermal expansion in the direction transverse to the extrusion direction is less than about 0.98% between 22 and 600/sup 0/C which corresponds to a value greater than the 1.04% provided by previous extrusion operations over the same temperature range. The article with the improved thermal expansion possesses a yield strength at 0.2% offset of at least 400 MPa, an ultimate tensile strength of 1050 MPa, a compressive yield strength of at least 0.2% offset of at least 675 MPa, and an elongation of at least 25% over 25.4 mm/s. To provide this article with the improved thermal expansion, the uranium alloy billet is heated to 630/sup 0/C and extruded in the alpha phase through a die with a reduction ratio of at least 8.4:1 at a ram speed no greater than 6.8 mm/s. These critical extrusion parameters provide the article with a desired decrease in the linear thermal expansion while maintaining the selected mechanical properties without encountering crystal disruption in the article.
A first collision source method for ATTILA, an unstructured tetrahedral mesh discrete ordinates code
Wareing, T.A.; Morel, J.E.; Parsons, D.K.
1998-12-01
A semi-analytic first collision source method is developed for the transport code, ATTILA, a three-dimensional, unstructured tetrahedral mesh, discrete-ordinates code. This first collision source method is intended to mitigate ray effects due to point sources. The method is third-order accurate, which is the same order of accuracy as the linear-discontinuous spatial differencing scheme used in ATTILA. Numerical results are provided to demonstrate the accuracy and efficiency of the first collision source method.
Adapted polynomial chaos expansion for failure detection
Paffrath, M. Wever, U.
2007-09-10
In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.
Pressurized electrolysis stack with thermal expansion capability
Bourgeois, Richard Scott
2015-07-14
The present techniques provide systems and methods for mounting an electrolyzer stack in an outer shell so as to allow for differential thermal expansion of the electrolyzer stack and shell. Generally, an electrolyzer stack may be formed from a material with a high coefficient of thermal expansion, while the shell may be formed from a material having a lower coefficient of thermal expansion. The differences between the coefficients of thermal expansion may lead to damage to the electrolyzer stack as the shell may restrain the thermal expansion of the electrolyzer stack. To allow for the differences in thermal expansion, the electrolyzer stack may be mounted within the shell leaving a space between the electrolyzer stack and shell. The space between the electrolyzer stack and the shell may be filled with a non-conductive fluid to further equalize pressure inside and outside of the electrolyzer stack.
Expansion-based passive ranging
NASA Technical Reports Server (NTRS)
Barniv, Yair
1993-01-01
This paper describes a new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they have been used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts--as well as the other parameters--can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline resulting in a proportionately higher depth accuracy.
Expansion-based passive ranging
NASA Technical Reports Server (NTRS)
Barniv, Yair
1993-01-01
A new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases is described. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they were used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts - as well as the other parameters - can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline - resulting in a proportionately higher depth accuracy.
Bullough, B
1976-09-01
Several factors are influencing role expansion for registered nurses, among them the shortage of primary care physicians, the federal government, the physician's assistant movement, the growing complexity of acute hospital care, educational reform, and the women's liberation movement. As state licensure statutes are revised to allow for role expansion, the changing laws themselves become a factor supporting the movement.
New Hamiltonian expansions adapted to the Trojan problem
NASA Astrophysics Data System (ADS)
Páez, Rocío Isabel; Locatelli, Ugo; Efthymiopoulos, Christos
2016-07-01
) in order to find an `averaged over the fast angle' model derived from H_b , circumventing the problem of the series' limited convergence due to the collision singularity at the 1:1 MMR. Finally, using this averaged model, we compute semi-analytically the position of the most important secondary resonances and compare the results with those found by numerical stability maps in specific examples. We find a very good agreement between semi-analytical and numerical results in a domain whose border coincides with the transition to large-scale chaotic Trojan motions.
Semi-analytical modeling of the NIO1 source
Cazzador, M.; Cavenago, M.; Serianni, G.; Veltri, P.
2015-04-08
NIO1 is a compact and versatile negative ion source, with a total current of 130 mA accelerated to 60 keV. Negative ions are created inside the plasma, which is inductively coupled to an external rf cylindrical coil operating in the range of 2 ± 0.2 MHz. The plasma is confined in the source chamber (a 50 mm radius cylinder) by a multipole magnetic field and the ions are extracted through a 3x3 matrix of apertures. The use of cesium, to enhance the negative ion production by H{sub 0} bombardment of the surfaces, is foreseen in a second stage of the operation, so that at present time the source is operating in pure volume configuration. This paper presents a model aimed to describe the main physical phenomena occurring in the source, focusing on the rf coupling with the plasma and the evolution of plasma parameters in the source. With respect to more sophisticated models of negative ion sources here we aimed to develop a fast tool capable of qualitatively describing the response of the system to variations in the basic operating parameters. The findings of this models is finally compared with the first experimental results of NIO1.
Semi-analytical modelling of positive corona discharge in air
NASA Astrophysics Data System (ADS)
Pontiga, Francisco; Yanallah, Khelifa; Chen, Junhong
2013-09-01
Semianalytical approximate solutions of the spatial distribution of electric field and electron and ion densities have been obtained by solving Poisson's equations and the continuity equations for the charged species along the Laplacian field lines. The need to iterate for the correct value of space charge on the corona electrode has been eliminated by using the corona current distribution over the grounded plane derived by Deutsch, which predicts a cos m θ law similar to Warburg's law. Based on the results of the approximated model, a parametric study of the influence of gas pressure, the corona wire radius, and the inter-electrode wire-plate separation has been carried out. Also, the approximate solutions of the electron number density has been combined with a simplified plasma chemistry model in order to compute the ozone density generated by the corona discharge in the presence of a gas flow. This work was supported by the Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) and by the Ministerio de Ciencia e Innovacion, Spain, within the European Regional Development Fund contracts FQM-4983 and FIS2011-25161.
Danovitch, G M; Bricker, N S
1976-09-01
Whether volume expansion influences NaC1 reabsorption by the diluting segment of the nephron remains a matter of controversy. In the present studies this question has been examined in normal unanesthetized dogs, undergoing maximal water diuresis. Free water clearance (CH2O/GFR) has been used as the index of NaC1 reabsorption in the diluting segment. Three expressions have been employed for "distal delivery" of NaC1: a) V/GFR, designated as the "volume term"; b) (CNa/GFR + CH2O/GFR), the "sodium term;" and c) (CC1/GFR + CH2O/GFR), the "chloride term". The validity of these terms is discussed. Three techniques were used to increase distal delivery: 1) the administration of acetazolamide to dogs in which extracellular fluid (ECF) volume was not expanded (grop 1); 2) "moderate" volume expansion (group 2); and 3) "marked" volume expansion (group 3). CH2O/GFR increased progressively with rising values for "distal delivery" regardless of which term was used to calculate the latter. With all three delivery terms, differences in distal NaC1 reabsorption emerged between the two volume-expanded groups, though only with the "chloride" term did substantial differences also emerge between the nonexpanded group 1 dogs and both volume-expanded groups. In group 1, values for CH2O/GFR increased in close to a linear fashion up to distal delivery values equal to 24% of the volume of glomerular filtrate. However, at high rates of distal delivery the rate of rise of CH2O/GFR was less in group 2 than in group 1 and the depression of values was even greater in group 3. Within the limits of the techniques used, the data suggest that volume expansion inhibits fractional NaC1 reabsorption in the diluting segment of the nephron in a dose-related fashion. The "chloride" term was found to be superior to the "volume" and "sodium" terms in revealing these changes.
ERIC Educational Resources Information Center
Fakhruddin, Hasan
1993-01-01
Describes a paradox in the equation for thermal expansion. If the calculations for heating a rod and subsequently cooling a rod are determined, the new length of the cool rod is shorter than expected. (PR)
Nelson, E.A.; Christensen, E.J.; Mackey, H.E.; Sharitz, R.R.; Jensen, J.R.; Hodgson, M.E.
1984-02-01
Since 1954, cooling water discharges from K Reactor ({anti X} = 370 cfs {at} 59 C) to Pen Branch have altered vegetation and deposited sediment in the Savannah River Swamp forming the Pen Branch delta. Currently, the delta covers over 300 acres and continues to expand at a rate of about 16 acres/yr. Examination of delta expansion can provide important information on environmental impacts to wetlands exposed to elevated temperature and flow conditions. To assess the current status and predict future expansion of the Pen Branch delta, historic aerial photographs were analyzed using both basic photo interpretation and computer techniques to provide the following information: (1) past and current expansion rates; (2) location and changes of impacted areas; (3) total acreage presently affected. Delta acreage changes were then compared to historic reactor discharge temperature and flow data to see if expansion rate variations could be related to reactor operations.
Weakly relativistic plasma expansion
Fermous, Rachid Djebli, Mourad
2015-04-15
Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.
Thermal expansion properties of composite materials
NASA Technical Reports Server (NTRS)
Johnson, R. R.; Kural, M. H.; Mackey, G. B.
1981-01-01
Thermal expansion data for several composite materials, including generic epoxy resins, various graphite, boron, and glass fibers, and unidirectional and woven fabric composites in an epoxy matrix, were compiled. A discussion of the design, material, environmental, and fabrication properties affecting thermal expansion behavior is presented. Test methods and their accuracy are discussed. Analytical approaches to predict laminate coefficients of thermal expansion (CTE) based on lamination theory and micromechanics are also included. A discussion is included of methods of tuning a laminate to obtain a near-zero CTE for space applications.
Effective Expansion: Balance between Shrinkage and Hygroscopic Expansion.
Suiter, E A; Watson, L E; Tantbirojn, D; Lou, J S B; Versluis, A
2016-05-01
The purpose of this study was to investigate the relationship between hygroscopic expansion and polymerization shrinkage for compensation of polymerization shrinkage stresses in a restored tooth. One resin-modified glass-ionomer (RMGI) (Ketac Nano, 3M ESPE), 2 compomers (Dyract, Dentsply; Compoglass, Ivoclar), and a universal resin-based composite (Esthet•X HD, Dentsply) were tested. Volumetric change after polymerization ("total shrinkage") and during 4 wk of water storage at 37°C was measured using an optical method (n= 10). Post-gel shrinkage was measured during polymerization using a strain gauge method (n= 10). Extracted human molars with large mesio-occluso-distal slot preparations were restored with the tested restorative materials. Tooth surfaces at baseline (preparation), after restoration, and during 4 wk of 37°C water storage were scanned with an optical scanner to determine cuspal flexure (n= 8). Occlusal interface integrity was measured using dye penetration. Data were analyzed using analysis of variance and post hoc tests (significance level 0.05). All tested materials shrunk after polymerization. RMGI had the highest total shrinkage (4.65%) but lowest post-gel shrinkage (0.35%). Shrinkage values dropped significantly during storage in water but had not completely compensated polymerization shrinkage after 4 wk. All restored teeth initially exhibited inward (negative) cuspal flexure due to polymerization shrinkage. Cuspal flexure with the RMGI restoration was significantly less (-6.4 µm) than with the other materials (-12.1 to -14.1 µm). After 1 d, cuspal flexure reversed to +5.0 µm cuspal expansion with the RMGI and increased to +9.3 µm at 4 wk. After 4 wk, hygroscopic expansion compensated cuspal flexure in a compomer (Compoglass) and reduced flexure with Dyract and resin-based composite. Marginal integrity (93.7% intact restoration wall) was best for the Compoglass restorations and lowest (73.1%) for the RMGI restorations. Hygroscopic
Effective Expansion: Balance between Shrinkage and Hygroscopic Expansion.
Suiter, E A; Watson, L E; Tantbirojn, D; Lou, J S B; Versluis, A
2016-05-01
The purpose of this study was to investigate the relationship between hygroscopic expansion and polymerization shrinkage for compensation of polymerization shrinkage stresses in a restored tooth. One resin-modified glass-ionomer (RMGI) (Ketac Nano, 3M ESPE), 2 compomers (Dyract, Dentsply; Compoglass, Ivoclar), and a universal resin-based composite (Esthet•X HD, Dentsply) were tested. Volumetric change after polymerization ("total shrinkage") and during 4 wk of water storage at 37°C was measured using an optical method (n= 10). Post-gel shrinkage was measured during polymerization using a strain gauge method (n= 10). Extracted human molars with large mesio-occluso-distal slot preparations were restored with the tested restorative materials. Tooth surfaces at baseline (preparation), after restoration, and during 4 wk of 37°C water storage were scanned with an optical scanner to determine cuspal flexure (n= 8). Occlusal interface integrity was measured using dye penetration. Data were analyzed using analysis of variance and post hoc tests (significance level 0.05). All tested materials shrunk after polymerization. RMGI had the highest total shrinkage (4.65%) but lowest post-gel shrinkage (0.35%). Shrinkage values dropped significantly during storage in water but had not completely compensated polymerization shrinkage after 4 wk. All restored teeth initially exhibited inward (negative) cuspal flexure due to polymerization shrinkage. Cuspal flexure with the RMGI restoration was significantly less (-6.4 µm) than with the other materials (-12.1 to -14.1 µm). After 1 d, cuspal flexure reversed to +5.0 µm cuspal expansion with the RMGI and increased to +9.3 µm at 4 wk. After 4 wk, hygroscopic expansion compensated cuspal flexure in a compomer (Compoglass) and reduced flexure with Dyract and resin-based composite. Marginal integrity (93.7% intact restoration wall) was best for the Compoglass restorations and lowest (73.1%) for the RMGI restorations. Hygroscopic
Detecting range expansions from genetic data
Peter, Benjamin M; Slatkin, Montgomery
2014-01-01
We propose a method that uses genetic data to test for the occurrence of a recent range expansion and to infer the location of the origin of the expansion. We introduce a statistic ψ (the directionality index) that detects asymmetries in the two-dimensional allele frequency spectrum of pairs of population. These asymmetries are caused by the series of founder events that happen during an expansion and they arise because low frequency alleles tend to be lost during founder events, thus creating clines in the frequencies of surviving low-frequency alleles. Using simulations, we show that ψ is more powerful for detecting range expansions than both FST and clines in heterozygosity. We also show how we can adapt our approach to more complicated scenarios such as expansions with multiple origins or barriers to migration and we illustrate the utility of ψ by applying it to a data set from modern humans. PMID:24152007
Business information query expansion through semantic network
NASA Astrophysics Data System (ADS)
Gong, Zhiguo; Muyeba, Maybin; Guo, Jingzhi
2010-02-01
In this article, we propose a method for business information query expansions. In our approach, hypernym/hyponymy and synonym relations in WordNet are used as the basic expansion rules. Then we use WordNet Lexical Chains and WordNet semantic similarity to assign terms in the same query into different groups with respect to their semantic similarities. For each group, we expand the highest terms in the WordNet hierarchies with hypernym and synonym, the lowest terms with hyponym and synonym and all other terms with only synonym. In this way, the contradictory caused by full expansion can be well controlled. Furthermore, we use collection-related term semantic network to further improve the expansion performance. And our experiment reveals that our solution for query expansion can improve the query performance dramatically.
Clinical grade expansion of MSCs.
Capelli, C; Pedrini, O; Valgardsdottir, R; Da Roit, F; Golay, J; Introna, M
2015-12-01
Producing advanced therapy medicinal products (ATMP) according to Good Manufacturing Practice (GMP) guidelines represents a global challenge for the expansion of cells intended for human use. Mesenchymal stromal cells (MSCs) from different sources are one of the most actively developed cell type for a variety of clinical applications in cellular therapy. Complying with GMP means defining accurately both the production process and the release criteria required for a final safe product. We have here reported our manufacturing experience on 103 consecutive clinical-grade in vitro expansions of both bone marrow-derived and umbilical cord-derived mesenchymal stromal cells together with description of methods and reagents utilized in our Cell Factory. The same animal- and serum-free medium, additioned with human platelet lysate, has been used for all the expansions performed. This is the largest experience published so far with this alternative and clinical-grade reagent (compared to the traditional fetal bovine serum) and shows the feasibility and the reproducibility of the method. Indeed, we have been able to produce a sufficient number of MSCs to treat 57 patients so far, enrolled in 7 different experimental phase I/II protocols. PMID:26092523
Optimal Electric Utility Expansion
1989-10-10
SAGE-WASP is designed to find the optimal generation expansion policy for an electrical utility system. New units can be automatically selected from a user-supplied list of expansion candidates which can include hydroelectric and pumped storage projects. The existing system is modeled. The calculational procedure takes into account user restrictions to limit generation configurations to an area of economic interest. The optimization program reports whether the restrictions acted as a constraint on the solution. All expansionmore » configurations considered are required to pass a user supplied reliability criterion. The discount rate and escalation rate are treated separately for each expansion candidate and for each fuel type. All expenditures are separated into local and foreign accounts, and a weighting factor can be applied to foreign expenditures.« less
Thermal expansion in nanoresonators
NASA Astrophysics Data System (ADS)
Mancardo Viotti, Agustín; Monastra, Alejandro G.; Moreno, Mariano F.; Florencia Carusela, M.
2016-08-01
Inspired by some recent experiments and numerical works related to nanoresonators, we perform classical molecular dynamics simulations to investigate the thermal expansion and the ability of the device to act as a strain sensor assisted by thermally-induced vibrations. The proposed model consists in a chain of atoms interacting anharmonically with both ends clamped to thermal reservoirs. We analyze the thermal expansion and resonant frequency shifts as a function of temperature and the applied strain. For the transversal modes the shift is approximately linear with strain. We also present analytical results from canonical calculations in the harmonic approximation showing that thermal expansion is uniform along the device. This prediction also works when the system operates in a nonlinear oscillation regime at moderate and high temperatures.
NASA Astrophysics Data System (ADS)
Gefken, Paul; Curran, Donald; Nesterenko, Vitali F.; Cai, Jing
2006-07-01
Two spherical cavity expansion experiments were performed with SiC-N to provide high-strain rate data for developing ceramic armor penetration models. Here, an explosive charge is detonated within a cavity machined in the ceramic, generating a pulse that moves radially outward. The particle velocity at multiple radial locations from the charge, including at the charge radii, was measured and the fractured ceramic was recovered for posttest evaluation. From the particle velocity histories we derived displacement, radial strain and circumferential strain histories. In the recovered samples we observed the regions where comminution, radial cracking and circumferential cracking occurred. The elastic properties of initial undamaged SiC-N and shocked damaged material were measured using a resonant ultrasound spectroscopy (RUS). Comparison of these measurements illustrated the posttest condition of the SiC-N material. Hot isostatic pressing of "as is" SiC-N material demonstrated a significant increase in the quality factor. The same procedure applied to SiC-N damaged in spherical cavity experiments resulted in a significant recovery of the elastic properties.
Siciliano, Camilla; Ibrahim, Mohsen; Scafetta, Gaia; Napoletano, Chiara; Mangino, Giorgio; Pierelli, Luca; Frati, Giacomo; De Falco, Elena
2015-01-01
Mesenchymal stem cells (MSCs) are adult multipotent cells currently employed in several clinical trials due to their immunomodulating, angiogenic and repairing features. The adipose tissue is certainly considered an eligible source of MSCs. Recently, putative adipose tissue derived MSCs (ADMSCs) have been isolated from the mediastinal depots. However, very little is known about the properties, the function and the potential of human mediastinal ADMSCs (hmADMSCs). However, the lack of standardized methodologies to culture ADMSCs prevents comparison across. Herein for the first time, we report a detailed step by step description to optimize the isolation and the expansion methodology of hmADMSCs using a virally inactivated good manufacturing practice (GMP)-grade platelet lysate, highlighting the critical aspects of the procedure and providing useful troubleshooting suggestions. Our approach offers a reproducible system which could provide standardization across laboratories. Moreover, our system is time and cost effective, and it can provide a reproducible source of adipose stem cells to enable future studies to unravel new insights regard this promising stem cell population. PMID:24306273
Gefken, Paul; Curran, Donald; Nesterenko, Vitali F.; Cai, Jing
2006-07-28
Two spherical cavity expansion experiments were performed with SiC-N to provide high-strain rate data for developing ceramic armor penetration models. Here, an explosive charge is detonated within a cavity machined in the ceramic, generating a pulse that moves radially outward. The particle velocity at multiple radial locations from the charge, including at the charge radii, was measured and the fractured ceramic was recovered for posttest evaluation. From the particle velocity histories we derived displacement, radial strain and circumferential strain histories. In the recovered samples we observed the regions where comminution, radial cracking and circumferential cracking occurred. The elastic properties of initial undamaged SiC-N and shocked damaged material were measured using a resonant ultrasound spectroscopy (RUS). Comparison of these measurements illustrated the posttest condition of the SiC-N material. Hot isostatic pressing of ''as is'' SiC-N material demonstrated a significant increase in the quality factor. The same procedure applied to SiC-N damaged in spherical cavity experiments resulted in a significant recovery of the elastic properties.
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2006-01-01
In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)
NASA Technical Reports Server (NTRS)
1985-01-01
Under an Egyptian government contract, PADCO studies urban growth in the Nile Area. They were assisted by LANDSAT survey maps and measurements provided by TAC. TAC had classified the raw LANDSAT data and processed it into various categories to detail urban expansion. PADCO crews spot checked the results, and correlations were established.
For the Long Island, New Jersey, and southern New England region, one facet of marsh drowning as a result of accelerated sea level rise is the expansion of salt marsh ponds and pannes. Over the past century, marsh ponds and pannes have formed and expanded in areas of poor drainag...
Physics suggests that the interplay of momentum, continuity, and geometry in outward radial flow must produce density and concomitant pressure reductions. In other words, this flow is intrinsically auto-expansive. It has been proposed that this process is the key to understanding...
Guzek, J.C.; Lujan, R.A.
1984-01-01
Disclosed is a cooler for television cameras and other temperature sensitive equipment. The cooler uses compressed gas ehich is accelerated to a high velocity by passing it through flow passageways having nozzle portions which expand the gas. This acceleration and expansion causes the gas to undergo a decrease in temperature thereby cooling the cooler body and adjacent temperature sensitive equipment.
ERIC Educational Resources Information Center
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
NASA Astrophysics Data System (ADS)
Koçak, H.; Dahong, Z.; Yildirim, A.
2011-05-01
In this study, a range-free method is proposed in order to determine the Antoine constants for a given material (salicylic acid). The advantage of this method is mainly yielding analytical expressions which fit different temperature ranges.
Orbital expansion of the congenitally anophthalmic socket.
Tucker, S M; Sapp, N; Collin, R
1995-01-01
BACKGROUND--Congenital anophthalmos is a rare condition in which intervention at an early age can stimulate orbital expansion and maximise facial symmetry. Much is still unknown, however, regarding the degree of soft tissue and bony orbital growth achieved using the orbital expanders presently available. METHODS--A retrospective review of 59 congenitally anophthalmic orbits in 42 patients was carried out. RESULTS--The soft tissue and bony orbital expansion achieved using serial solid shapes is reported, and experience with hydrophilic expanders and inflatable silicone expanders is reviewed. CONCLUSION--Although serially fitted solid shapes in the orbit lead to increased expansion of orbital soft tissue and bone compared with no orbital implant, further orbital tissue enlargement is required. The inflatable silicone expander may allow more rapid and extensive orbital tissue expansion, but design changes are needed to achieve this. PMID:7662633
Expansion tube test time predictions
NASA Technical Reports Server (NTRS)
Gourlay, Christopher M.
1988-01-01
The interaction of an interface between two gases and strong expansion is investigated and the effect on flow in an expansion tube is examined. Two mechanisms for the unsteady Pitot-pressure fluctuations found in the test section of an expansion tube are proposed. The first mechanism depends on the Rayleigh-Taylor instability of the driver-test gas interface in the presence of a strong expansion. The second mechanism depends on the reflection of the strong expansion from the interface. Predictions compare favorably with experimental results. The theory is expected to be independent of the absolute values of the initial expansion tube filling pressures.
Accelerated expansion through interaction
Zimdahl, Winfried
2009-05-01
Interactions between dark matter and dark energy with a given equation of state are known to modify the cosmic dynamics. On the other hand, the strength of these interactions is subject to strong observational constraints. Here we discuss a model in which the transition from decelerated to accelerated expansion of the Universe arises as a pure interaction phenomenon. Various cosmological scenarios that describe a present stage of accelerated expansion, like the {lambda}CDM model or a (generalized) Chaplygin gas, follow as special cases for different interaction rates. This unifying view on the homogeneous and isotropic background level is accompanied by a non-adiabatic perturbation dynamics which can be seen as a consequence of a fluctuating interaction rate.
China petrochemical expansion progressing
Not Available
1991-08-05
This paper reports on China's petrochemical expansion surge which is picking up speed. A worldscale petrochemical complex is emerging at Shanghai with an eye to expanding China's petrochemical exports, possibly through joint ventures with foreign companies, China Features reported. In other action, Beijing and Henan province have approved plans for a $1.2 billion chemical fibers complex at the proposed Luoyang refinery, China Daily reported.
Diffusion tensor image registration using polynomial expansion
NASA Astrophysics Data System (ADS)
Wang, Yuanjun; Chen, Zengai; Nie, Shengdong; Westin, Carl-Fredrik
2013-09-01
In this paper, we present a deformable registration framework for the diffusion tensor image (DTI) using polynomial expansion. The use of polynomial expansion in image registration has previously been shown to be beneficial due to fast convergence and high accuracy. However, earlier work was developed only for 3D scalar medical image registration. In this work, it is shown how polynomial expansion can be applied to DTI registration. A new measurement is proposed for DTI registration evaluation, which seems to be robust and sensitive in evaluating the result of DTI registration. We present the algorithms for DTI registration using polynomial expansion by the fractional anisotropy image, and an explicit tensor reorientation strategy is inherent to the registration process. Analytic transforms with high accuracy are derived from polynomial expansion and used for transforming the tensor's orientation. Three measurements for DTI registration evaluation are presented and compared in experimental results. The experiments for algorithm validation are designed from simple affine deformation to nonlinear deformation cases, and the algorithms using polynomial expansion give a good performance in both cases. Inter-subject DTI registration results are presented showing the utility of the proposed method.
Sun, Yang; Qi, Jinyi
2012-01-01
We report a novel method for estimating fluorescence impulse response function (fIRF) from noise-corrupted time-domain fluorescence measurements of biological tissue. This method is based on the use of higher-order Laguerre basis functions (LBFs) and a constrained least-square (CLS) approach that addresses the problem of overfitting due to increased model complexity. The method was extensively evaluated on fluorescence data from simulation, fluorescent standard dyes, ex vivo tissue samples of atherosclerotic plaques, and in vivo oral carcinoma. Current results demonstrate that this new method allows for rapid and accurate deconvolution of multiple channel fluorescence decays without adaptively adjusting the Laguerre scale parameter. The appropriate choice of the scale parameter is essential for accurate estimation of the fIRF. The method described here is anticipated to play an important role in the development of computational techniques for real-time analysis of time-resolved fluorescence data from biological tissues and to support the advancement of fluorescence lifetime instrumentation for biomedical diagnostics by providing a means for on-line robust analysis of fluorescence decay. PMID:22290334
Research progress on expansive soil cracks under changing environment.
Shi, Bei-xiao; Zheng, Cheng-feng; Wu, Jin-kun
2014-01-01
Engineering problems shunned previously rise to the surface gradually with the activities of reforming the natural world in depth, the problem of expansive soil crack under the changing environment becoming a control factor of expansive soil slope stability. The problem of expansive soil crack has gradually become a research hotspot, elaborates the occurrence and development of cracks from the basic properties of expansive soil, and points out the role of controlling the crack of expansive soil strength. We summarize the existing research methods and results of expansive soil crack characteristics. Improving crack measurement and calculation method and researching the crack depth measurement, statistical analysis method, crack depth and surface feature relationship will be the future direction. PMID:25013869
NASA Technical Reports Server (NTRS)
Ustinov, Y. A.
1978-01-01
The direct method for the solution of the spherical harmonics approximation to the equation of transfer of radiation is applied to the cases of (1) scattering of the solar radiation in the atmosphere with the Lambertian boundary and (2) thermal radiation transfer.
Bilinear Expansion For Redistribution Functions
NASA Astrophysics Data System (ADS)
Harutyunian, Haik; Alecian, Georges; Khachatryan, Knarik; Vardanyan, Ani
2016-11-01
We suggest here a method for construction of a bilinear expansion for an angle-averaged redistribution function. This function describes the elementary act of a photon scattering by a model two-level atom with the upper level broadened due to radiation damping. An eigenvalue and eigenvector determination problem is formulated and the relevant matrices are found analytically. Numerical procedures for their computations are elaborated as well. A simple method for the numerical calculations accuracy evaluation is suggested. It is shown that a family of redistribution functions describing the light scattering process within the spectral line frequencies can be constructed if the eigenvalue problem for the considered function is solved. It becomes possible if the eigenvalues and eigenvectors with the appropriate basic functions are used. The Voigt function and its derivatives used as basic functions are studied in detail as well.
Pole EXpansion and Selected Inversion (PEXSI)
2014-03-01
The Pole EXpansion and Selected Inversion method (PEXSI) is a fast method for evaluating certain selected elements of a matrix function. PEXSI is highly scalable on distributed memory parallel machines. For sparse matrices, the PEXSI method can be more efficient than the widely used diagonalization method for evaluating matrix functions, especially when a relatively large number of eigenpairs are needed to be computed in the diagonalization methond
Chakrabarti, J.; Sajjad Zahir, M.
1985-03-01
We show that the product of local current operators in quantum chromodynamics (QCD), when expanded in terms of condensates, such as psi-barpsi, G/sup a//sub munu/ G/sup a//sub munu/, psi-barGAMMA psipsi-barGAMMApsi, f/sub a/bcG/sup a//sub munu/G/sup b//sub nualpha/ x G/sup c//sub alphamu/, etc., yields a series in Planck's constant. This, however, provides no hint that the higher terms in such an expansion may be less significant.
Load regulating expansion fixture
Wagner, L.M.; Strum, M.J.
1998-12-15
A free standing self contained device for bonding ultra thin metallic films, such as 0.001 inch beryllium foils is disclosed. The device will regulate to a predetermined load for solid state bonding when heated to a bonding temperature. The device includes a load regulating feature, whereby the expansion stresses generated for bonding are regulated and self adjusting. The load regulator comprises a pair of friction isolators with a plurality of annealed copper members located therebetween. The device, with the load regulator, will adjust to and maintain a stress level needed to successfully and economically complete a leak tight bond without damaging thin foils or other delicate components. 1 fig.
Load regulating expansion fixture
Wagner, Lawrence M.; Strum, Michael J.
1998-01-01
A free standing self contained device for bonding ultra thin metallic films, such as 0.001 inch beryllium foils. The device will regulate to a predetermined load for solid state bonding when heated to a bonding temperature. The device includes a load regulating feature, whereby the expansion stresses generated for bonding are regulated and self adjusting. The load regulator comprises a pair of friction isolators with a plurality of annealed copper members located therebetween. The device, with the load regulator, will adjust to and maintain a stress level needed to successfully and economically complete a leak tight bond without damaging thin foils or other delicate components.
NASA Astrophysics Data System (ADS)
Mishakin, S. V.; Samsonov, S. V.
2011-08-01
We present a method for calculating the dispersion characteristics of eigenmodes of metal waveguides with helical corrugations on the inner surface, which is based on the transition to a new nonorthogonal system of coordinates. In the new coordinate system, the problem of finding helical-waveguide modes is rigorously equivalent to the problem of finding the modes of a circular unitradius waveguide which has an anisotropic filling and is homogenous in the longitudinal direction. To solve the equivalent problem, we expand the field of the desired eigenmode in the modes of an empty circular unit-radius waveguide. As a result, the problem is reduced to solving a generalized algebraic eigenvalue problem. The comparison with the results of earlier three-dimensional calculations shows that the developed method allows one to determine characteristics of helical-waveguides with sufficient accuracy for many important applications and requires much lower calculation costs.
Expansible quantum secret sharing network
NASA Astrophysics Data System (ADS)
Sun, Ying; Xu, Sheng-Wei; Chen, Xiu-Bo; Niu, Xin-Xin; Yang, Yi-Xian
2013-08-01
In the practical applications, member expansion is a usual demand during the development of a secret sharing network. However, there are few consideration and discussion on network expansibility in the existing quantum secret sharing schemes. We propose an expansible quantum secret sharing scheme with relatively simple and economical quantum resources and show how to split and reconstruct the quantum secret among an expansible user group in our scheme. Its trait, no requirement of any agent's assistant during the process of member expansion, can help to prevent potential menaces of insider cheating. We also give a discussion on the security of this scheme from three aspects.
Radial expansion for spinning conformal blocks
NASA Astrophysics Data System (ADS)
Costa, Miguel S.; Hansen, Tobias; Penedones, João; Trevisani, Emilio
2016-07-01
This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.
Hafeez, A; Mader, A; Ruhnke, I; Männer, K; Zentek, J
2016-01-01
The grinding of cereals by various milling methods as well as thermal treatment of feed may influence mineral digestibility and egg quality. The present study investigated the effect of feed produced by disc mill (D) and wedge-shaped disc mill (WSD), as mash (M) or expandate (E) on apparent ileal absorption (AIA) and apparent total digestibility (ATD) of calcium, phosphorus, magnesium, zinc, manganese, copper and iron, as well as on egg quality in laying hens. A total of 192 hens (Lohmann Brown) aged 19 wk, were assigned using a randomized design with a 2 × 2 factorial arrangement. Four experimental diets were offered ad libitum. Eggs were analyzed for weight, shape index, area, shell weight per unit surface area, yolk color, air cell, blood spot, Haugh unit, albumen and yolk measures (index, weight, height, width and length), shell measures (surface area, stability, density, thickness and membrane weight), as well as percent contents of albumen, yolk, shell, and shell membrane. The ATD for phosphorus, manganese, and copper was higher in WSD compared with D treatment (P = 0.028, P = 0.028 and P = 0.016, respectively). The interaction between milling methods and thermal treatment influenced ATD of copper (P = 0.033), which was higher in WSD+M group (41.0 ± 20.2) compared with D+E group (-3.21 ± 25.1), whereas no differences were observed for D+M (1.90 ± 37.8) and WSD+E (8.02 ± 36.2) groups. Egg stability tended to be higher in E compared with M treatment (P = 0.055). Albumen weight, percentage albumen weight, and albumen: yolk were higher and percentage yolk weight was lower in D compared with WSD treatment (P = 0.043, P = 0.027, P = 0.024, and P = 0.041, respectively). Number of blood spots was higher in E than M treatment (P = 0.053). In conclusion, use of a wedge-shaped disc mill resulted in higher ATD for phosphorus, manganese, and copper than use of a disc mill; however, digestibility for majority of minerals as well as egg quality parameters was
Hafeez, A; Mader, A; Ruhnke, I; Männer, K; Zentek, J
2016-01-01
The grinding of cereals by various milling methods as well as thermal treatment of feed may influence mineral digestibility and egg quality. The present study investigated the effect of feed produced by disc mill (D) and wedge-shaped disc mill (WSD), as mash (M) or expandate (E) on apparent ileal absorption (AIA) and apparent total digestibility (ATD) of calcium, phosphorus, magnesium, zinc, manganese, copper and iron, as well as on egg quality in laying hens. A total of 192 hens (Lohmann Brown) aged 19 wk, were assigned using a randomized design with a 2 × 2 factorial arrangement. Four experimental diets were offered ad libitum. Eggs were analyzed for weight, shape index, area, shell weight per unit surface area, yolk color, air cell, blood spot, Haugh unit, albumen and yolk measures (index, weight, height, width and length), shell measures (surface area, stability, density, thickness and membrane weight), as well as percent contents of albumen, yolk, shell, and shell membrane. The ATD for phosphorus, manganese, and copper was higher in WSD compared with D treatment (P = 0.028, P = 0.028 and P = 0.016, respectively). The interaction between milling methods and thermal treatment influenced ATD of copper (P = 0.033), which was higher in WSD+M group (41.0 ± 20.2) compared with D+E group (-3.21 ± 25.1), whereas no differences were observed for D+M (1.90 ± 37.8) and WSD+E (8.02 ± 36.2) groups. Egg stability tended to be higher in E compared with M treatment (P = 0.055). Albumen weight, percentage albumen weight, and albumen: yolk were higher and percentage yolk weight was lower in D compared with WSD treatment (P = 0.043, P = 0.027, P = 0.024, and P = 0.041, respectively). Number of blood spots was higher in E than M treatment (P = 0.053). In conclusion, use of a wedge-shaped disc mill resulted in higher ATD for phosphorus, manganese, and copper than use of a disc mill; however, digestibility for majority of minerals as well as egg quality parameters was
Adiabatic expansion of a strongly correlated pure electron plasma
Dubin, D.H.E.; O'Neil, T.M.
1986-02-17
Adiabatic expansion is proposed as a method of increasing the degree of correlation of a magnetically confined pure electron plasma. Quantum mechanical effects and correlation effects make the physics of the expansion quite different from that for a classical ideal gas. The proposed expansion may be useful in a current experimental effort to cool a pure electron plasma to the liquid and solid (crystalline) states.
Adiabatic expansion of a strongly correlated pure electron plasma
NASA Astrophysics Data System (ADS)
Dubin, D. H. E.; Oneil, T. M.
1986-02-01
Adiabatic expansion is proposed as a method of increasing the degree of correlation of a magnetically confined pure electron plasma. Quantum mechanical effects and correlation effects make the physics of the expansion quite different from that for a classical ideal gas. The proposed expansion may be useful in a current experimental effort to cool a pure electron plasma to the liquid and solid (crystalline) states.
Pallaver, Carl B.; Morgan, Michael W.
1978-01-01
A cryogenic expansion engine includes intake and exhaust poppet valves each controlled by a cam having adjustable dwell, the valve seats for the valves being threaded inserts in the valve block. Each cam includes a cam base and a ring-shaped cam insert disposed at an exterior corner of the cam base, the cam base and cam insert being generally circular but including an enlarged cam dwell, the circumferential configuration of the cam base and cam dwell being identical, the cam insert being rotatable with respect to the cam base. GI CONTRACTUAL ORIGIN OF THE INVENTION The invention described herein was made in the course of, or under, a contract with the UNITED STATES ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION.
Optical imaging. Expansion microscopy.
Chen, Fei; Tillberg, Paul W; Boyden, Edward S
2015-01-30
In optical microscopy, fine structural details are resolved by using refraction to magnify images of a specimen. We discovered that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification. By covalently anchoring specific labels located within the specimen directly to the polymer network, labels spaced closer than the optical diffraction limit can be isotropically separated and optically resolved, a process we call expansion microscopy (ExM). Thus, this process can be used to perform scalable superresolution microscopy with diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer lateral resolution in both cultured cells and brain tissue, performing three-color superresolution imaging of ~10(7) cubic micrometers of the mouse hippocampus with a conventional confocal microscope.
Expansive Visibilization to Stimulate EFL Teacher Reflection
ERIC Educational Resources Information Center
Ito, Ryu
2012-01-01
Despite the growing popularity of action research, bridging the gap between data collection and reflective data analysis still lacks a well-developed methodology. As a supplement to the traditional action research procedure for language teaching, I adopted a method called expansive visibilization (EV), which has the potential to be a reflective…
Karliner, M.
1985-09-01
The t-expansion is a nonperturbative calculational tool recently developed for Hamiltonian systems. A short review of the method is given. It is followed by a summary of applications to two dimensional spin systems and to four dimensional non-abelian lattice gauge theories. 5 refs., 3 figs.
Virial expansion coefficients in the harmonic approximation.
Armstrong, J R; Zinner, N T; Fedorov, D V; Jensen, A S
2012-08-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground-state properties at low temperature and the noninteracting high-temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as functions of dimension, temperature, interaction, and transition temperature between low- and high-energy limits. PMID:23005730
Burial Ground Expansion Hydrogeologic Characterization
Gaughan , T.F.
1999-02-26
Sirrine Environmental Consultants provided technical oversight of the installation of eighteen groundwater monitoring wells and six exploratory borings around the location of the Burial Ground Expansion.
Prediction of Service Lives of Bridge Expansion Joints
NASA Astrophysics Data System (ADS)
Huang, Ying-Hua; Lin, Jing-Jhan
2010-05-01
This paper presents a service-life prediction model of expansion joints. Significant factors influencing the service lives of expansion joints were identified by statistical methods. Artificial neural network was implemented to establish the service-life prediction model of expansion joints. Taken finger plate joints for illustration, eight statistically significant factors influencing the service lives of finger plate joints are identified among twenty one factors studied. Through these eight factors, the service lives of expansion joints can be predicted by the established model. The training and testing errors indicate that the established artificial neural network model can provide accurate predictions which are essential information for maintenance strategies.
Pentoney, Christopher; Harwell, Jeff; Leroy, Gondy
2014-01-01
Searching for medical information online is a common activity. While it has been shown that forming good queries is difficult, Google’s query suggestion tool, a type of query expansion, aims to facilitate query formation. However, it is unknown how this expansion, which is based on what others searched for, affects the information gathering of the online community. To measure the impact of social-based query expansion, this study compared it with content-based expansion, i.e., what is really in the text. We used 138,906 medical queries from the AOL User Session Collection and expanded them using Google’s Autocomplete method (social-based) and the content of the Google Web Corpus (content-based). We evaluated the specificity and ambiguity of the expansion terms for trigram queries. We also looked at the impact on the actual results using domain diversity and expansion edit distance. Results showed that the social-based method provided more precise expansion terms as well as terms that were less ambiguous. Expanded queries do not differ significantly in diversity when expanded using the social-based method (6.72 different domains returned in the first ten results, on average) vs. content-based method (6.73 different domains, on average). PMID:25954406
Pentoney, Christopher; Harwell, Jeff; Leroy, Gondy
2014-01-01
Searching for medical information online is a common activity. While it has been shown that forming good queries is difficult, Google's query suggestion tool, a type of query expansion, aims to facilitate query formation. However, it is unknown how this expansion, which is based on what others searched for, affects the information gathering of the online community. To measure the impact of social-based query expansion, this study compared it with content-based expansion, i.e., what is really in the text. We used 138,906 medical queries from the AOL User Session Collection and expanded them using Google's Autocomplete method (social-based) and the content of the Google Web Corpus (content-based). We evaluated the specificity and ambiguity of the expansion terms for trigram queries. We also looked at the impact on the actual results using domain diversity and expansion edit distance. Results showed that the social-based method provided more precise expansion terms as well as terms that were less ambiguous. Expanded queries do not differ significantly in diversity when expanded using the social-based method (6.72 different domains returned in the first ten results, on average) vs. content-based method (6.73 different domains, on average).
Asymptotic expansion of the lattice scalar propagator in coordinate space
NASA Astrophysics Data System (ADS)
Paladini, Beatrice; Sexton, James C.
1998-02-01
The asymptotic expansion of the massive scalar field propagator on a n- dimensional lattice is derived. The method used is based on the evaluation of the asymptotic expansion of the modified Bessel function Iν(ν2β) as the order ν grows to infinity.
Rowold, Daine J; Perez-Benedico, David; Stojkovic, Oliver; Garcia-Bertrand, Ralph; Herrera, Rene J
2016-11-15
Here we report the results of fine resolution Y chromosomal analyses (Y-SNP and Y-STR) of 267 Bantu-speaking males from three populations located in the southeast region of Africa. In an effort to determine the relative Y chromosomal affinities of these three genotyped populations, the findings are interpreted in the context of 74 geographically and ethnically targeted African reference populations representing four major ethno-linguistic groups (Afro-Asiatic, Niger Kordofanin, Khoisan and Pygmoid). In this investigation, we detected a general similarity in the Y chromosome lineages among the geographically dispersed Bantu-speaking populations suggesting a shared heritage and the shallow time depth of the Bantu Expansion. Also, micro-variations in the Bantu Y chromosomal composition across the continent highlight location-specific gene flow patterns with non-Bantu-speaking populations (Khoisan, Pygmy, Afro-Asiatic). Our Y chromosomal results also indicate that the three Bantu-speaking Southeast populations genotyped exhibit unique gene flow patterns involving Eurasian populations but fail to reveal a prevailing genetic affinity to East or Central African Bantu-speaking groups. In addition, the Y-SNP data underscores a longitudinal partitioning in sub-Sahara Africa of two R1b1 subgroups, R1b1-P25* (west) and R1b1a2-M269 (east). No evidence was observed linking the B2a haplogroup detected in the genotyped Southeast African Bantu-speaking populations to gene flow from contemporary Khoisan groups. PMID:27451076
Rowold, Daine J; Perez-Benedico, David; Stojkovic, Oliver; Garcia-Bertrand, Ralph; Herrera, Rene J
2016-11-15
Here we report the results of fine resolution Y chromosomal analyses (Y-SNP and Y-STR) of 267 Bantu-speaking males from three populations located in the southeast region of Africa. In an effort to determine the relative Y chromosomal affinities of these three genotyped populations, the findings are interpreted in the context of 74 geographically and ethnically targeted African reference populations representing four major ethno-linguistic groups (Afro-Asiatic, Niger Kordofanin, Khoisan and Pygmoid). In this investigation, we detected a general similarity in the Y chromosome lineages among the geographically dispersed Bantu-speaking populations suggesting a shared heritage and the shallow time depth of the Bantu Expansion. Also, micro-variations in the Bantu Y chromosomal composition across the continent highlight location-specific gene flow patterns with non-Bantu-speaking populations (Khoisan, Pygmy, Afro-Asiatic). Our Y chromosomal results also indicate that the three Bantu-speaking Southeast populations genotyped exhibit unique gene flow patterns involving Eurasian populations but fail to reveal a prevailing genetic affinity to East or Central African Bantu-speaking groups. In addition, the Y-SNP data underscores a longitudinal partitioning in sub-Sahara Africa of two R1b1 subgroups, R1b1-P25* (west) and R1b1a2-M269 (east). No evidence was observed linking the B2a haplogroup detected in the genotyped Southeast African Bantu-speaking populations to gene flow from contemporary Khoisan groups.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate. PMID:20866495
Genus expansion of HOMFLY polynomials
NASA Astrophysics Data System (ADS)
Mironov, A. D.; Morozov, A. Yu.; Sleptsov, A. V.
2013-11-01
In the planar limit of the' t Hooft expansion, the Wilson-loop vacuum average in the three-dimensional Chern-Simons theory (in other words, the HOMFLY polynomial) depends very simply on the representation (Young diagram), HR(A|q)|q=1 = (σ1(A)|R|. As a result, the (knot-dependent) Ooguri-Vafa partition function becomes a trivial τ -function of the Kadomtsev-Petviashvili hierarchy. We study higher-genus corrections to this formula for HR in the form of an expansion in powers of z = q - q-1. The expansion coefficients are expressed in terms of the eigenvalues of cut-and-join operators, i.e., symmetric group characters. Moreover, the z-expansion is naturally written in a product form. The representation in terms of cut-and-join operators relates to the Hurwitz theory and its sophisticated integrability. The obtained relations describe the form of the genus expansion for the HOMFLY polynomials, which for the corresponding matrix model is usually given using Virasoro-like constraints and the topological recursion. The genus expansion differs from the better-studied weak-coupling expansion at a finite number N of colors, which is described in terms of Vassiliev invariants and the Kontsevich integral.
Atom cooling by nonadiabatic expansion
Chen Xi; Muga, J. G.; Campo, A. del; Ruschhaupt, A.
2009-12-15
Motivated by the recent discovery that a reflecting wall moving with a square-root-in-time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear-in-time and square-root-in-time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wave functions studied the square-root-in-time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear-in-time (constant box-wall velocity) expansion leaves a nonzero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root-in-time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root-in-time expansion.
Ex vivo expansion of hematopoietic stem cells.
Xie, JingJing; Zhang, ChengCheng
2015-09-01
Ex vivo expansion of hematopoietic stem cells (HSCs) would benefit clinical applications in several aspects, to improve patient survival, utilize cord blood stem cells for adult applications, and selectively propagate stem cell populations after genetic manipulation. In this review we summarize and discuss recent advances in the culture systems of mouse and human HSCs, which include stroma/HSC co-culture, continuous perfusion and fed-batch cultures, and those supplemented with extrinsic ligands, membrane transportable transcription factors, complement components, protein modification enzymes, metabolites, or small molecule chemicals. Some of the expansion systems have been tested in clinical trials. The optimal condition for ex vivo expansion of the primitive and functional human HSCs is still under development. An improved understanding of the mechanisms for HSC cell fate determination and the HSC culture characteristics will guide development of new strategies to overcome difficulties. In the future, development of a combination treatment regimen with agents that enhance self-renewal, block differentiation, and improve homing will be critical. Methods to enhance yields and lower cost during collection and processing should be employed. The employment of an efficient system for ex vivo expansion of HSCs will facilitate the further development of novel strategies for cell and gene therapies including genome editing.
NASA Astrophysics Data System (ADS)
Tang, Guanglin; Yang, Ping; Sun, Bingqiang; Panetta, R. Lee; Kattawar, George W.
2016-06-01
The finite-difference time-domain (FDTD) and ray-by-ray (RBR) methods are techniques used to calculate the optical properties of nonspherical particles for small-to-moderate and large size parameters, respectively. The former is a rigorous method, and the latter is an approximate geometric-physical optics-hybrid method that takes advantage of both high efficiency of the geometric optics approach and high accuracy of the physical optics approach. In these two methods, the far field is calculated by mapping the near field to the far field with consideration of the phase interference. The mapping computation is more time-consuming than the near-field simulation when multiple scattering directions are involved, particularly in the case of the RBR implementation. To overcome the difficulty, in this study the fast multi-pole method is applied to both FDTD and RBR towards accelerating the far-field calculation, without degrading the accuracy of the simulation results.
Evaluating range-expansion models for calculating nonnative species' expansion rate.
Preuss, Sonja; Low, Matthew; Cassel-Lundhagen, Anna; Berggren, Asa
2014-07-01
Species range shifts associated with environmental change or biological invasions are increasingly important study areas. However, quantifying range expansion rates may be heavily influenced by methodology and/or sampling bias. We compared expansion rate estimates of Roesel's bush-cricket (Metrioptera roeselii, Hagenbach 1822), a nonnative species currently expanding its range in south-central Sweden, from range statistic models based on distance measures (mean, median, 95(th) gamma quantile, marginal mean, maximum, and conditional maximum) and an area-based method (grid occupancy). We used sampling simulations to determine the sensitivity of the different methods to incomplete sampling across the species' range. For periods when we had comprehensive survey data, range expansion estimates clustered into two groups: (1) those calculated from range margin statistics (gamma, marginal mean, maximum, and conditional maximum: ˜3 km/year), and (2) those calculated from the central tendency (mean and median) and the area-based method of grid occupancy (˜1.5 km/year). Range statistic measures differed greatly in their sensitivity to sampling effort; the proportion of sampling required to achieve an estimate within 10% of the true value ranged from 0.17 to 0.9. Grid occupancy and median were most sensitive to sampling effort, and the maximum and gamma quantile the least. If periods with incomplete sampling were included in the range expansion calculations, this generally lowered the estimates (range 16-72%), with exception of the gamma quantile that was slightly higher (6%). Care should be taken when interpreting rate expansion estimates from data sampled from only a fraction of the full distribution. Methods based on the central tendency will give rates approximately half that of methods based on the range margin. The gamma quantile method appears to be the most robust to incomplete sampling bias and should be considered as the method of choice when sampling the entire
Evaluating range-expansion models for calculating nonnative species' expansion rate
Preuss, Sonja; Low, Matthew; Cassel-Lundhagen, Anna; Berggren, Åsa
2014-01-01
Species range shifts associated with environmental change or biological invasions are increasingly important study areas. However, quantifying range expansion rates may be heavily influenced by methodology and/or sampling bias. We compared expansion rate estimates of Roesel's bush-cricket (Metrioptera roeselii, Hagenbach 1822), a nonnative species currently expanding its range in south-central Sweden, from range statistic models based on distance measures (mean, median, 95th gamma quantile, marginal mean, maximum, and conditional maximum) and an area-based method (grid occupancy). We used sampling simulations to determine the sensitivity of the different methods to incomplete sampling across the species' range. For periods when we had comprehensive survey data, range expansion estimates clustered into two groups: (1) those calculated from range margin statistics (gamma, marginal mean, maximum, and conditional maximum: ˜3 km/year), and (2) those calculated from the central tendency (mean and median) and the area-based method of grid occupancy (˜1.5 km/year). Range statistic measures differed greatly in their sensitivity to sampling effort; the proportion of sampling required to achieve an estimate within 10% of the true value ranged from 0.17 to 0.9. Grid occupancy and median were most sensitive to sampling effort, and the maximum and gamma quantile the least. If periods with incomplete sampling were included in the range expansion calculations, this generally lowered the estimates (range 16–72%), with exception of the gamma quantile that was slightly higher (6%). Care should be taken when interpreting rate expansion estimates from data sampled from only a fraction of the full distribution. Methods based on the central tendency will give rates approximately half that of methods based on the range margin. The gamma quantile method appears to be the most robust to incomplete sampling bias and should be considered as the method of choice when sampling the entire
Expansion/De-expansion Tool to Quantify the Accuracy of Prostate Contours
Chung, Eugene; Stenmark, Matthew H.; Evans, Cheryl; Narayana, Vrinda; McLaughlin, Patrick W.
2012-05-01
Purpose: Accurate delineation of the prostate gland on computed tomography (CT) remains a persistent challenge and continues to introduce geometric uncertainty into the planning and delivery of external beam radiotherapy. We, therefore, developed an expansion/de-expansion tool to quantify the contour errors and determine the location of the deviations. Methods and Materials: A planning CT scan and magnetic resonance imaging scan were prospectively acquired for 10 patients with prostate cancer. The prostate glands were contoured by 3 independent observers using the CT data sets with instructions to contour the prostate without underestimation but to minimize overestimation. The standard prostate for each patient was defined using magnetic resonance imaging and CT on multiple planes. After registration of the CT and magnetic resonance imaging data sets, the CT-defined prostates were scored for accuracy. The contours were defined as ideal if they were within a 2.5-mm expansion of the standard without underestimation, acceptable if they were within a 5.0-mm expansion and a 2.5-mm de-expansion, and unacceptable if they extended >5.0 mm or underestimated the prostate by >2.5 mm. Results: A total of 636 CT slices were individually analyzed, with the vast majority scored as ideal or acceptable. However, none of the 30 prostate contour sets had all the contours scored as ideal or acceptable. For all 3 observers, the unacceptable contours were more likely from underestimation than overestimation of the prostate. The errors were more common at the base and apex than the mid-gland. Conclusions: The expansion/de-expansion tool allows for directed feedback on the location of contour deviations, as well as the determination of over- or underestimation of the prostate. This metric might help improve the accuracy of prostate contours.
Moire interferometry for thermal expansion of composites
NASA Technical Reports Server (NTRS)
Bowles, D. E.; Tenney, D. R.; Post, D.; Herakovich, C. T.
1981-01-01
Moire interferometry by reflection has been demonstrated using a real reference grating of 1200 lines/mm. The method is shown to be well adapted to thermal environments. Thermal expansion coefficients of graphite-epoxy composites have been measured with high precision over a wide range from nearly zero to 3300 microstrains in the temperature range 297-422 K. Random errors characterized by one standard deviation can be as small as one microstrain.
Range expansion of heterogeneous populations.
Reiter, Matthias; Rulands, Steffen; Frey, Erwin
2014-04-11
Risk spreading in bacterial populations is generally regarded as a strategy to maximize survival. Here, we study its role during range expansion of a genetically diverse population where growth and motility are two alternative traits. We find that during the initial expansion phase fast-growing cells do have a selective advantage. By contrast, asymptotically, generalists balancing motility and reproduction are evolutionarily most successful. These findings are rationalized by a set of coupled Fisher equations complemented by stochastic simulations. PMID:24766021
Warp drive with zero expansion
NASA Astrophysics Data System (ADS)
Natário, José
2002-03-01
It is commonly believed that Alcubierre's warp drive works by contracting space in front of the warp bubble and expanding the space behind it. We show that this contraction/expansion is but a marginal consequence of the choice made by Alcubierre and explicitly construct a similar spacetime where no contraction/expansion occurs. Global and optical properties of warp-drive spacetimes are also discussed.
Range Expansion of Heterogeneous Populations
NASA Astrophysics Data System (ADS)
Reiter, Matthias; Rulands, Steffen; Frey, Erwin
2014-04-01
Risk spreading in bacterial populations is generally regarded as a strategy to maximize survival. Here, we study its role during range expansion of a genetically diverse population where growth and motility are two alternative traits. We find that during the initial expansion phase fast-growing cells do have a selective advantage. By contrast, asymptotically, generalists balancing motility and reproduction are evolutionarily most successful. These findings are rationalized by a set of coupled Fisher equations complemented by stochastic simulations.
Thermal Expansion of Vacuum Plasma Sprayed Coatings
NASA Technical Reports Server (NTRS)
Raj, S V.; Palczer, A. R.
2010-01-01
Metallic Cu-8%Cr, Cu-26%Cr, Cu-8%Cr-1%Al, NiAl and NiCrAlY monolithic coatings were fabricated by vacuum plasma spray deposition processes for thermal expansion property measurements between 293 and 1223 K. The corrected thermal expansion, (DL/L(sub 0) varies with the absolute temperature, T, as (DL/L(sub 0) = A(T - 293)(sup 3) + BIT - 293)(sup 2) + C(T - 293) + D, where, A, B, C and D are thermal, regression constants. Excellent reproducibility was observed for all of the coatings except for data obtained on the Cu-8%Cr and Cu-26%Cr coatings in the first heat-up cycle, which deviated from those determined in the subsequent cycles. This deviation is attributed to the presence of residual stresses developed during the spraying of the coatings, which are relieved after the first heat-up cycle. In the cases of Cu-8%Cr and NiAl, the thermal expansion data were observed to be reproducible for three specimens. The linear expansion data for Cu-8% Cr and Cu-26%Cr agree extremely well with rule of mixture (ROM) predictions. Comparison of the data for the Cu-8%Cr coating with literature data for Cr and Cu revealed that the thermal expansion behavior of this alloy is determined by the Cu-rich matrix. The data for NiAl and NiCrAlY are in excellent agreement with published results irrespective of composition and the methods used for processing the materials. The implications of these results on coating GRCop-84 copper alloy combustor liners for reusable launch vehicles are discussed.
Node-Expansion Operators for the UCT Algorithm
NASA Astrophysics Data System (ADS)
Yajima, Takayuki; Hashimoto, Tsuyoshi; Matsui, Toshiki; Hashimoto, Junichi; Spoerer, Kristian
Recent works on the MCTS and UCT framework in the domain of Go focused on introducing knowledge to the playout and on pruning variations from the tree, but so far node expansion has not been investigated. In this paper we show that delaying expansion according to the number of the siblings delivers a gain of more than 92% when compared to normal expansion. We propose three improvements; one that uses domain knowledge and two that are domain-independent methods. Experimental results show that all advanced operators significantly improve the UCT performance when compared to the basic delaying expansion. From the results we may conclude that the new expansion operators are an appropriate means to improve the UCT algorithm.
Expansion of Microbial Forensics.
Schmedes, Sarah E; Sajantila, Antti; Budowle, Bruce
2016-08-01
Microbial forensics has been defined as the discipline of applying scientific methods to the analysis of evidence related to bioterrorism, biocrimes, hoaxes, or the accidental release of a biological agent or toxin for attribution purposes. Over the past 15 years, technology, particularly massively parallel sequencing, and bioinformatics advances now allow the characterization of microorganisms for a variety of human forensic applications, such as human identification, body fluid characterization, postmortem interval estimation, and biocrimes involving tracking of infectious agents. Thus, microbial forensics should be more broadly described as the discipline of applying scientific methods to the analysis of microbial evidence in criminal and civil cases for investigative purposes.
Expansion and orthogonalization of measured modes for structure identification
NASA Technical Reports Server (NTRS)
Smith, Suzanne Weaver
1989-01-01
The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.
Expansion Microscopy with Conventional Antibodies and Fluorescent Proteins
Chozinski, Tyler J.; Halpern, Aaron R.; Okawa, Haruhisa; Kim, Hyeon-Jin; Tremel, Grant J.; Wong, Rachel O.L.; Vaughan, Joshua C.
2016-01-01
Expansion microscopy is a recently introduced technique in which fluorophores on fixed specimens are linked to a swellable polymer that is physically expanded to enable super-resolution microscopy with ordinary microscopes. We have developed and characterized new methods for linking fluorophores to the polymer that now enable expansion microscopy with conventional fluorescently-labeled antibodies and fluorescent proteins. Our methods simplify the procedure, expand the palette of compatible labels, and will aid in rapid dissemination of the technique. PMID:27064647
NASA Technical Reports Server (NTRS)
Zhang, Z.; Werner, F.; Cho, H.-M.; Wind, G.; Platnick, S.; Ackerman, A. S.; Di Girolamo, L.; Marshak, A.; Meyer, K.
2016-01-01
The bispectral method retrieves cloud optical thickness (t) and cloud droplet effective radius (re) simultaneously from a pair of cloud reflectance observations, one in a visible or near-infrared (VIS/NIR) band and the other in a shortwave infrared (SWIR) band. A cloudy pixel is usually assumed to be horizontally homogeneous in the retrieval. Ignoring subpixel variations of cloud reflectances can lead to a significant bias in the retrieved t and re. In the literature, the retrievals of t and re are often assumed to be independent and considered separately when investigating the impact of subpixel cloud reflectance variations on the bispectral method. As a result, the impact on t is contributed only by the subpixel variation of VIS/NIR band reflectance and the impact on re only by the subpixel variation of SWIR band reflectance. In our new framework, we use the Taylor expansion of a two-variable function to understand and quantify the impacts of subpixel variances of VIS/NIR and SWIR cloud reflectances and their covariance on the t and re retrievals. This framework takes into account the fact that the retrievals are determined by both VIS/NIR and SWIR band observations in a mutually dependent way. In comparison with previous studies, it provides a more comprehensive understanding of how subpixel cloud reflectance variations impact the t and re retrievals based on the bispectral method. In particular, our framework provides a mathematical explanation of how the subpixel variation in VIS/NIR band influences the re retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in re retrievals, leading to a potential contribution of positive bias to the re retrieval. We test our framework using synthetic cloud fields from a large-eddy simulation and real observations from Moderate Resolution Imaging Spectroradiometer. The predicted results based on our framework agree very well with the numerical simulations. Our
Phase cell cluster expansion for Euclidean field theories
Battle, G.A. III; Federbush, P.
1982-08-01
We adapt the cluster expansion first used to treat infrared problems for lattice models (a mass zero cluster expansion) to the usual field theory situation. The field is expanded in terms of spectral block spin functions and the cluster expansion given in terms of the expansion coefficients (phase cell variables); the other cluster expansion expresses correlation functions in terms of contributions from finite coupled subsets of these variables. Most of the present work is carried through in d space time dimensions (for phi/sup 4//sub 2/ the details of the cluster expansion are pursued and convergence is proven). Thus most of the results in this present work will apply to a treatment of phi/sup 4//sub 3/ to which we hope to return in a succeeding paper. Of particular interest in this paper is a substitute for the stability of the vaccum bound appropriate to this cluster expansion (for d = 2 and d = 3), and the new method for performing estimates with tree graphs. The phase cell cluster expansions have the renormalization group incorporated intimately into their structure. We hope they will be useful ultimately in treating four dimensional field theories.
Design of ultra-compact triplexer with function-expansion based topology optimization.
Zhang, Zejun; Tsuji, Yasuhide; Yasui, Takashi; Hirayama, Koichi
2015-02-23
In this paper, in order to optimize wavelength selective photonic devices using the function-expansion-based topology optimization method, several expansion functions are considered and the influence on the optimized structure based on each expansion function was investigated. Although the Fourier series is conventionally used in the function-expansion-based method, the optimized structure sometimes has a complicated refractive index distribution. Therefore, we employed a sampling function and a pyramid function to obtain a simpler structure through the optimal design. A triplexer was designed by using our method, and the comparison between the optimized structures based on the three expansion functions was also discussed in detail. PMID:25836433
Forecasting Urban Expansion Based on Night Lights
NASA Astrophysics Data System (ADS)
Stathakis, D.
2016-06-01
Forecasting urban expansion models are a very powerful tool in the hands of urban planners in order to anticipate and mitigate future urbanization pressures. In this paper, a linear regression forecasting urban expansion model is implemented based on the annual composite night lights time series available from National Oceanic and Atmospheric Administration (NOAA). The product known as 'stable lights' is used in particular, after it has been corrected with a standard intercalibration process to reduce artificial year-to-year fluctuations as much as possible. Forecasting is done for ten years after the end of the time series. Because the method is spatially explicit the predicted expansion trends are relatively accurately mapped. Two metrics are used to validate the process. The first one is the year-to-year Sum of Lights (SoL) variation. The second is the year-to-year image correlation coefficient. Overall it is evident that the method is able to provide an insight on future urbanization pressures in order to be taken into account in planning. The trends are quantified in a clear spatial manner.
Moire interferometry for thermal expansion of composites
NASA Technical Reports Server (NTRS)
Bowles, D. E.; Tenney, D. R.; Post, D.; Herakovich, C. T.
1982-01-01
Moire interferometry by reflection is described and demonstrated for the case of a real reference grating of 1200 lines/mm. Extraneous beams can be displaced and stopped by using a wedge-shaped air gap between reference and specimen gratings. Double-order dominance, the use of diffraction sequences for reflection, the isolation of preferred sequences, and the use of two-beam interference are discussed. Experimental accuracy is enhanced significantly by using several data points to establish displacements along a line, and random errors characterized by one standard deviation can be as small as one microstrain. The method is well adapted to thermal environments, coefficients of thermal expansion of selected graphite-epoxy laminates being determined in the temperature range of 297-422 K. Very good precision was achieved for a wide range of thermal expansion coefficients, from approximately zero to 27 microstrains/K.
On genus expansion of superpolynomials
NASA Astrophysics Data System (ADS)
Mironov, Andrei; Morozov, Alexei; Sleptsov, Alexei; Smirnov, Andrey
2014-12-01
Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β-deformed to Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots.
Energy recovery during expansion of compressed gas using power plant low-quality heat sources
Ochs, Thomas L.; O'Connor, William K.
2006-03-07
A method of recovering energy from a cool compressed gas, compressed liquid, vapor, or supercritical fluid is disclosed which includes incrementally expanding the compressed gas, compressed liquid, vapor, or supercritical fluid through a plurality of expansion engines and heating the gas, vapor, compressed liquid, or supercritical fluid entering at least one of the expansion engines with a low quality heat source. Expansion engines such as turbines and multiple expansions with heating are disclosed.
Anisotropic Expansion of a Thermal Dipolar Bose Gas
NASA Astrophysics Data System (ADS)
Tang, Y.; Sykes, A. G.; Burdick, N. Q.; DiSciacca, J. M.; Petrov, D. S.; Lev, B. L.
2016-10-01
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the postexpansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion.
Threshold expansion of Feynman diagrams within a configuration space technique
NASA Astrophysics Data System (ADS)
Groote, S.; Pivovarov, A. A.
2000-07-01
The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.
Free Expansion of a Weakly-Interacting Dipolar Fermi Gas
NASA Astrophysics Data System (ADS)
Takushi Nishimura,; Tomoyuki Maruyama,
2010-08-01
We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann and zero-temperature Thomas-Fermi gases in the Hartree-Fock and Landau-Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouville’s theorem in the long-time behaviors of the both gases.
Thermal Expansion of Hafnium Carbide
NASA Technical Reports Server (NTRS)
Grisaffe, Salvatore J.
1960-01-01
Since hafnium carbide (HfC) has a melting point of 7029 deg. F, it may have many high-temperature applications. A literature search uncovered very little information about the properties of HfC, and so a program was initiated at the Lewis Research Center to determine some of the physical properties of this material. This note presents the results of the thermal expansion investigation. The thermal-expansion measurements were made with a Gaertner dilatation interferometer calibrated to an accuracy of +/- 1 deg. F. This device indicates expansion by the movement of fringes produced by the cancellation and reinforcement of fixed wave-length light rays which are reflected from the surfaces of two parallel quartz glass disks. The test specimens which separate these disks are three small cones, each approximately 0.20 in. high.
Nonicosahedral pathways for capsid expansion
NASA Astrophysics Data System (ADS)
Cermelli, Paolo; Indelicato, Giuliana; Twarock, Reidun
2013-09-01
For a significant number of viruses a structural transition of the protein container that encapsulates the viral genome forms an important part of the life cycle and is a prerequisite for the particle becoming infectious. Despite many recent efforts the mechanism of this process is still not fully understood, and a complete characterization of the expansion pathways is still lacking. We present here a coarse-grained model that captures the essential features of the expansion process and allows us to investigate the conditions under which a viral capsid becomes unstable. Based on this model we demonstrate that the structural transitions in icosahedral viral capsids are likely to occur through a low-symmetry cascade of local expansion events spreading in a wavelike manner over the capsid surface.
Cosmological expansion and local physics
Faraoni, Valerio; Jacques, Audrey
2007-09-15
The interplay between cosmological expansion and local attraction in a gravitationally bound system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered, followed by various exact solutions describing a relativistic central object embedded in a Friedmann universe. It is shown that the 'all or nothing' behavior recently discovered (i.e., weakly coupled systems are comoving while strongly coupled ones resist the cosmic expansion) is limited to the de Sitter background. New exact solutions are presented which describe black holes perfectly comoving with a generic Friedmann universe. The possibility of violating cosmic censorship for a black hole approaching the big rip is also discussed.
Relativistic effects on plasma expansion
Benkhelifa, El-Amine; Djebli, Mourad
2014-07-15
The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.
18 CFR 154.309 - Incremental expansions.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 18 Conservation of Power and Water Resources 1 2012-04-01 2012-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... costs and revenues associated with the expansion, until the Commission authorizes the costs of...
48 CFR 570.403 - Expansion requests.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 48 Federal Acquisition Regulations System 4 2012-10-01 2012-10-01 false Expansion requests. 570... Continued Space Requirements 570.403 Expansion requests. (a) If the expansion space is in the general scope... justification under FAR 6.3. (b) If the expansion space needed is outside the general scope of the lease,...
18 CFR 154.309 - Incremental expansions.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 18 Conservation of Power and Water Resources 1 2011-04-01 2011-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... costs and revenues associated with the expansion, until the Commission authorizes the costs of...
48 CFR 570.403 - Expansion requests.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 48 Federal Acquisition Regulations System 4 2014-10-01 2014-10-01 false Expansion requests. 570... Continued Space Requirements 570.403 Expansion requests. (a) If the expansion space is in the general scope... justification under FAR 6.3. (b) If the expansion space needed is outside the general scope of the lease,...
18 CFR 154.309 - Incremental expansions.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... costs and revenues associated with the expansion, until the Commission authorizes the costs of...
18 CFR 154.309 - Incremental expansions.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 18 Conservation of Power and Water Resources 1 2014-04-01 2014-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... costs and revenues associated with the expansion, until the Commission authorizes the costs of...
48 CFR 570.403 - Expansion requests.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 48 Federal Acquisition Regulations System 4 2013-10-01 2013-10-01 false Expansion requests. 570... Continued Space Requirements 570.403 Expansion requests. (a) If the expansion space is in the general scope... justification under FAR 6.3. (b) If the expansion space needed is outside the general scope of the lease,...
18 CFR 154.309 - Incremental expansions.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... costs and revenues associated with the expansion, until the Commission authorizes the costs of...
48 CFR 570.403 - Expansion requests.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Expansion requests. 570... Continued Space Requirements 570.403 Expansion requests. (a) If the expansion space is in the general scope... FAR 6.3. (b) If the expansion space needed is outside the general scope of the lease,...
Frequency dependent thermal expansion in binary viscoelasticcomposites
Berryman, James G.
2007-12-01
The effective thermal expansion coefficient beta* of abinary viscoelastic composite is shown to be frequency dependent even ifthe thermal expansion coefficients beta A and beta B of both constituentsare themselves frequency independent. Exact calculations for binaryviscoelastic systems show that beta* is related to constituent valuesbeta A, beta B, volume fractions, and bulk moduli KA, KB, as well as tothe overall bulk modulus K* of the composite system. Then, beta* isdetermined for isotropic systems by first bounding (or measuring) K* andtherefore beta*. For anisotropic systems with hexagonal symmetry, theprincipal values of the thermal expansion beta*perp and beta*para can bedetermined exactly when the constituents form a layered system. In allthe examples studied, it is shown explicitly that the eigenvectors of thethermoviscoelastic system possess non-negative dissipation -- despite thecomplicated analytical behavior of the frequency dependent thermalexpansivities themselves. Methods presented have a variety ofapplications from fluid-fluid mixtures to fluid-solid suspensions, andfrom fluid-saturated porous media to viscoelastic solid-solidcomposites.
The Thermal Expansion Of Feldspars
NASA Astrophysics Data System (ADS)
Hovis, G. L.; Medford, A.; Conlon, M.
2009-12-01
Hovis and others (1) investigated the thermal expansion of natural and synthetic AlSi3 feldspars and demonstrated that the coefficient of thermal expansion (α) decreases significantly, and linearly, with increasing room-temperature volume (VRT). In all such feldspars, therefore, chemical expansion limits thermal expansion. The scope of this work now has been broadened to include plagioclase and Ba-K feldspar crystalline solutions. X-ray powder diffraction data have been collected between room temperature and 925 °C on six plagioclase specimens ranging in composition from anorthite to oligoclase. When combined with thermal expansion data for albite (2,3,4) a steep linear trend of α as a function of VRT emerges, reflecting how small changes in composition dramatically affect expansion behavior. The thermal expansion data for five synthetic Ba-K feldspars ranging in composition from 20 to 100 mole percent celsian, combined with data for pure K-feldspar (3,4), show α-VRT relationships similar in nature to the plagioclase series, but with a slope and intercept different from the latter. Taken as a group all Al2Si2 feldspars, including anorthite and celsian from the present study along with Sr- (5) and Pb-feldspar (6) from other workers, show very limited thermal expansion that, unlike AlSi3 feldspars, has little dependence on the divalent-ion (or M-) site occupant. This apparently is due to the necessitated alternation of Al and Si in the tetrahedral sites of these minerals (7), which in turn locks the tetrahedral framework and makes the M-site occupant nearly irrelevant to expansion behavior. Indeed, in feldspar series with coupled chemical substitution it is the change away from a 1:1 Al:Si ratio that gives feldspars greater freedom to expand. Overall, the relationships among α, chemical composition, and room-temperature volume provide useful predictive tools for estimating feldspar thermal expansion and give insight into the controls of expansion behavior in
Removable Type Expansion Bolt Innovative Design
NASA Astrophysics Data System (ADS)
Wang, Feng-Lan; Zhang, Bo; Gao, Bo; Liu, Yan-Xin; Gao, Bo
2016-05-01
Expansion bolt is a kind of the most common things in our daily life. Currently, there are many kinds of expansion bolts in the market. However, they have some shortcomings that mainly contain underuse and unremovement but our innovation of design makes up for these shortcomings very well. Principle of working follows this: expansion tube is fixed outside of bolt, steel balls and expansion covers are fixed inside. Meanwhile, the steel balls have 120° with each other. When using it ,expansion cover is moved in the direction of its internal part. So the front part of expansion bolt cover is increasingly becoming big and steel halls is moved outside. Only in this way can it be fixed that steel balls make expansion tube expand. When removing them, expansion bolt is moved outside. So the front part of expansion bolt cover is gradually becoming small and steel balls moves inside, after expansion tube shrinks, we can detach them.
Symmetry and combinatorics in the. delta. expansion for QED
Segev, B. )
1992-05-15
Combinatorics and symmetry are used to solve calculational problems in applying the {delta}-expansion method to QED. Adequate Feynman rules are used to simplify previous calculations and Ward identities are obtained. In the case with no external fermions an equivalence to the conventional loop expansion is established, both through the use of path integrals and through explicit calculations of the effective vertices. The Ward identities are reduced in this case to the conventional ones implied by gauge invariance.
Oshagh, Morteza; Aminsharifi, Ali Reza; Fallahzadeh, Mohammad Hossein; Ghodrati, Parisa
2014-01-01
Introduction Nocturnal enuresis has been found a common symptom among children with breathing problems and sleep apnea. The purpose of this study was to evaluate the therapeutic and placebo effects of slow maxillary expansion on nocturnal enuresis. Material and methods Four children with enuresis aged 7–12 years were selected. Rigid acrylic expansion appliances were fabricated and delivered to them. Frequency of enuresis was recorded by the parents during three stages: 1) before appliance delivery; 2) after appliance insertion without expansion; and 3) during expansion and retention. Results The frequency of wetting decreased significantly during the period of appliance use without expansion. During the expansion and retention phase, two patients became completely dry, and two patients improved significantly. Conclusions Maxillary expansion can have a positive effect on the treatment of nocturnal enuresis. Also, the placebo effect of the expansion appliance has significant effects on enuresis. PMID:24982782
Blood, blebs and lumen expansion.
Reichman-Fried, Michal; Raz, Erez
2016-04-01
A powerful combination of cell labelling, genetic tools and rapid imaging techniques in vivo has now led to a high-resolution description of lumen formation during angiogenesis in zebrafish. The study reveals a haemodynamic-force-driven and myosin-II-dependent cellular mechanism (termed inverse membrane blebbing) as the basis for lumen expansion in unicellular and multicellular angiogenic sprouts. PMID:27027487
French Expansion in North America.
ERIC Educational Resources Information Center
Jaenen, Cornelius J.
2001-01-01
Explores the French colonization in North America. Presents background information on New France, focusing on the French in Canada. Covers topics, such as how the French became interested in North American expansion, the French in Louisiana, colonial economics, and the reasons for the collapse of New France. Includes a bibliography. (CMK)
An automated gas expansion system
Abercrombie, K.
1993-01-01
The Metrology Laboratory at the Rocky Flats Plant has constructed a new Vacuum Gauge Calibration System based on gas expansion. The system is used to calibrate vacuum pressure gauges between 1 mTorr and 1000 mTorr. The paper discusses an overview of the system including layout, software, testing and performance.
An automated gas expansion system
Abercrombie, K.
1993-05-01
The Metrology Laboratory at the Rocky Flats Plant has constructed a new Vacuum Gauge Calibration System based on gas expansion. The system is used to calibrate vacuum pressure gauges between 1 mTorr and 1000 mTorr. The paper discusses an overview of the system including layout, software, testing and performance.
Mahler's Expansion and Boolean Functions
NASA Astrophysics Data System (ADS)
Michon, Jean-Francis; Valarcher, Pierre; YunÈs, Jean-Baptiste
2007-03-01
The substitution of X by X^2 in binomial polynomials generates sequences of integers by Mahler's expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) associated with boolean functions.
Educational Expansion and Economic Crisis.
ERIC Educational Resources Information Center
Klemm, Klaus
1987-01-01
Summarizes the expansion of education in the West Germany up to 1980. Examines the progress of the 1980s in view of unemployment and growing difficulties on entering a profession. Among the findings are a decline in enrollment of 20-24 year olds and a growth in opportunities for the children of immigrants. (Author/GEA)
Blood, blebs and lumen expansion.
Reichman-Fried, Michal; Raz, Erez
2016-04-01
A powerful combination of cell labelling, genetic tools and rapid imaging techniques in vivo has now led to a high-resolution description of lumen formation during angiogenesis in zebrafish. The study reveals a haemodynamic-force-driven and myosin-II-dependent cellular mechanism (termed inverse membrane blebbing) as the basis for lumen expansion in unicellular and multicellular angiogenic sprouts.
Moridis, G.
1992-03-01
The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.
Kim, Chang-Beom; Yang, Jin-Mo; Choi, Jong-Duk
2015-04-01
[Purpose] The aim of this study was to examine the effect of chest expansion resistance exercises (CERE) on chest expansion, maximal inspiratory pressure (MIP), and maximal expiratory pressure (MEP) in elderly people with inspiratory muscle weakness. [Subjects] Thirty elderly people with inspiratory muscle weakness (MIP < 80% of the predicted value) were randomly and equally assigned to a chest expansion resistance exercise (CERE) group, core conditioning exercise (CCE) group, and control group. [Methods] The intervention was applied to the CERE group and CCE group five times per week, 30 minutes each time, for six weeks. A tapeline was used to measure upper and lower chest expansion. MIP and MEP before and after the intervention were measured and compared. [Results] There was significant improvement in upper and lower chest expansion and MIP after the intervention in both the CERE group and the CCE group, whereas the control group did not show any significant difference. MEP did not significantly change in any of the three groups after the intervention. [Conclusion] The CERE group underwent greater changes than the CCE group, which proves that the CERE is more effective for improving elderly people's chest expansion capacity and MIP in elderly people. Therefore, application of the CERE by therapists is recommended if the environment and conditions are appropriate for enhancement of chest expansion capacity and MIP in elderly people.
A hybrid-perturbation-Galerkin technique which combines multiple expansions
NASA Technical Reports Server (NTRS)
Geer, James F.; Andersen, Carl M.
1989-01-01
A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.
Hole expansion of dual phase steels
Xu, Le; Barlat, Frederic; Lee, M.G.; Choi, Kyoo Sil; Sun, Xin
2012-06-01
In this work, the stretch-flangeability of dual phase (DP) steels was investigated through the hole expansion (HE) tests for three DP980 steel sheet samples. In order to understand the effect of hole surface quality on the HE results, the specimens were prepared with three hole machining methods, namely, electrical discharge machining (EDM), punching and laser cutting. The HE results were discussed in terms of the hole surface quality before and after testing. Moreover, the failure behaviour was analyzed based on the observations of the fracture surfaces using optical microscopy (OM) and scanning electron microscopy (SEM).
Kato expansion in quantum canonical perturbation theory
NASA Astrophysics Data System (ADS)
Nikolaev, Andrey
2016-06-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Edge singularities and structure of the 3-D Williams expansion
NASA Astrophysics Data System (ADS)
Apel, Thomas; Leguillon, Dominique; Pester, Cornelia; Yosibash, Zohar
2008-08-01
The elastic solution in a vicinity of a re-entrant wedge can be described by a Williams like expansion in terms of powers of the distance to a point on the edge. This expansion has a particular structure due to the invariance of the problem by translation parallel to the edge. We show here that some terms, so-called primary solutions, derive directly from solutions to the 2-D corner problem posed in the orthogonal cross section of the domain. The others, baptized shadow functions, derive of the primary solutions by integration along the axis parallel to the edge. This 3-D Williams expansion is shown to be equivalent to the edge expansion proposed by Costabel et al. [M. Costabel, M. Dauge, Z. Yosibash, A quasidual function method for extracting edge stress intensity functions, SIAM J. Math. Anal. 35 (5) (2004) 1177-1202]. To cite this article: T. Apel et al., C. R. Mecanique 336 (2008).
Multipole expansions and intense fields
NASA Astrophysics Data System (ADS)
Reiss, Howard R.
1984-02-01
In the context of two-body bound-state systems subjected to a plane-wave electromagnetic field, it is shown that high field intensity introduces a distinction between long-wavelength approximation and electric dipole approximation. This distinction is gauge dependent, since it is absent in Coulomb gauge, whereas in "completed" gauges of Göppert-Mayer type the presence of high field intensity makes electric quadrupole and magnetic dipole terms of importance equal to electric dipole at long wavelengths. Another consequence of high field intensity is that multipole expansions lose their utility in view of the equivalent importance of a number of low-order multipole terms and the appearance of large-magnitude terms which defy multipole categorization. This loss of the multipole expansion is gauge independent. Also gauge independent is another related consequence of high field intensity, which is the intimate coupling of center-of-mass and relative coordinate motions in a two-body system.
Hu, B.X.; He, C.
2008-01-01
An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases. ?? International Association for Mathematical Geology 2008.
Femtosecond dynamics of cluster expansion
NASA Astrophysics Data System (ADS)
Gao, Xiaohui; Wang, Xiaoming; Shim, Bonggu; Arefiev, Alexey; Tushentsov, Mikhail; Breizman, Boris; Downer, Mike
2010-03-01
Noble gas clusters irradiated by intense ultrafast laser expand quickly and become typical plasma in picosecond time scale. During the expansion, the clustered plasma demonstrates unique optical properties such as strong absorption and positive contribution to the refractive index. Here we studied cluster expansion dynamics by fs-time-resolved refractive index and absorption measurements in cluster gas jets after ionization and heating by an intense pump pulse. The refractive index measured by frequency domain interferometry (FDI) shows the transient positive peak of refractive index due to clustered plasma. By separating it from the negative contribution of the monomer plasma, we are able to determine the cluster fraction. The absorption measured by a delayed probe shows the contribution from clusters of various sizes. The plasma resonances in the cluster explain the enhancement of the absorption in our isothermal expanding cluster model. The cluster size distribution can be determined. A complete understanding of the femtosecond dynamics of cluster expansion is essential in the accurate interpretation and control of laser-cluster experiments such as phase-matched harmonic generation in cluster medium.
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Geographic Distribution and Expansion of Human Lyme Disease, United States.
Kugeler, Kiersten J; Farley, Grace M; Forrester, Joseph D; Mead, Paul S
2015-08-01
Lyme disease occurs in specific geographic regions of the United States. We present a method for defining high-risk counties based on observed versus expected number of reported human Lyme disease cases. Applying this method to successive periods shows substantial geographic expansion of counties at high risk for Lyme disease.
Generating expansion model incorporating compact DC power flow equations
Nderitu, D.G.; Sparrow, F.T.; Yu, Z.
1998-12-31
This paper presents a compact method of incorporating the spatial dimension into the generation expansion problem. Compact DC power flow equations are used to provide real-power flow coordination equations. Using these equations the marginal contribution of a generator to th total system loss is formulated as a function of that generator`s output. Incorporating these flow equations directly into the MIP formulation of the generator expansion problem results in a model that captures a generator`s true net marginal cost, one that includes both the cost of generation and the cost of transport. This method contrasts with other methods that iterate between a generator expansion model and an optimal power flow model. The proposed model is very compact and has very good convergence performance. A case study with data from Kenya is used to provide a practical application to the model.
Nonlinear effects on composite laminate thermal expansion
NASA Technical Reports Server (NTRS)
Hashin, Z.; Rosen, B. W.; Pipes, R. B.
1979-01-01
Analyses of Graphite/Polyimide laminates shown that the thermomechanical strains cannot be separated into mechanical strain and free thermal expansion strain. Elastic properties and thermal expansion coefficients of unidirectional Graphite/Polyimide specimens were measured as a function of temperature to provide inputs for the analysis. The + or - 45 degrees symmetric Graphite/Polyimide laminates were tested to obtain free thermal expansion coefficients and thermal expansion coefficients under various uniaxial loads. The experimental results demonstrated the effects predicted by the analysis, namely dependence of thermal expansion coefficients on load, and anisotropy of thermal expansion under load. The significance of time dependence on thermal expansion was demonstrated by comparison of measured laminate free expansion coefficients with and without 15 day delay at intermediate temperature.
Chemical recombination in an expansion tube
NASA Technical Reports Server (NTRS)
Bakos, Robert J.; Morgan, Richard G.
1994-01-01
The note describes the theoretical basis of chemical recombination in an expansion tube which simulates energy, Reynolds number, and stream chemistry at near-orbital velocities. Expansion tubes can satisfy ground-based hypersonic propulsion and aerothermal testing requirements.
A Power Series Expansion and Its Applications
ERIC Educational Resources Information Center
Chen, Hongwei
2006-01-01
Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.
Virial Expansion for a Strongly Correlated Fermi Gas
NASA Astrophysics Data System (ADS)
Hu, Hui
2011-03-01
Few-body physics can give considerable insight into the challenging many-body problem. A concrete example is the exact Tan relations linking the ``hard'' (few-body) physics at short distance, large-momentum and high frequency to the ``soft'' physics of the equation of state via a contact parameter. This has been demonstrated clearly using the operator product expansion (OPE) method which separates in a natural way few-body from many-body physics. In this talk, we present another example: the quantum virial expansion that bridges few-body and many-body physics. At large temperatures, the properties of a strongly correlated Fermi gas, either static or dynamic, can be expanded in terms of virial coefficients or expansion functions, calculable from the few-fermion solutions. For the equation of state in the resonant unitarity limit, we obtain for the first time an accurate third order virial coefficient. This has been experimentally verified in a measurement at ENS (Paris). For the single-particle spectral function, we demonstrate that an expansion up to second order is able to explain the main features of momentum-resolved RF spectroscopy in a resonantly interacting Fermi gas, as recently reported by JILA. We also obtain a virial expansion of the dynamic structure function, as measured at Swinburne University (Melbourne), and check that the second order expansion functions give the correct OPE coefficients in the limit of large momentum and frequency. The important feature of this expansion is the existence of a small parameter, the fugacity, even for strong interactions. In the future, we anticipate that higher-order virial expansions of dynamic properties such as the single-particle spectral function may provide useful insights into clarifying the debate on the pseudo-gap issue in resonantly interacting Fermi gases.
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2014-07-01
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2013-07-01
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(Rapid regulatory control of plant cell expansion and wall relaxation)
Cosgrove, D.J.
1990-01-01
This section presents a brief overview of accomplishments related to this project in the past 3-year period. Our work has focused on the basic mechanisms of plant cell expansion, particularly on the interrelations of water and solute transport with cell wall relaxation and expansion. To study these processes, we have developed new methods and used these methods to analyze the dynamic behavior of growth processes and to examine how various agents (GA, drought, light, genetic lesions) alter the growth machinery of the cell.
Mazzotti, M; Bartoli, I; Castellazzi, G; Marzani, A
2014-09-01
The paper aims at validating a recently proposed Semi Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (2.5D BEM) for the extraction of dispersion data in immersed waveguides of generic cross-section. To this end, three-dimensional vibroacoustic analyses are carried out on two waveguides of square and rectangular cross-section immersed in water using the commercial Finite Element software Abaqus/Explicit. Real wavenumber and attenuation dispersive data are extracted by means of a modified Matrix Pencil Method. It is demonstrated that the results obtained using the two techniques are in very good agreement. PMID:24890709
Image distortion analysis using polynomial series expansion.
Baggenstoss, Paul M
2004-11-01
In this paper, we derive a technique for analysis of local distortions which affect data in real-world applications. In the paper, we focus on image data, specifically handwritten characters. Given a reference image and a distorted copy of it, the method is able to efficiently determine the rotations, translations, scaling, and any other distortions that have been applied. Because the method is robust, it is also able to estimate distortions for two unrelated images, thus determining the distortions that would be required to cause the two images to resemble each other. The approach is based on a polynomial series expansion using matrix powers of linear transformation matrices. The technique has applications in pattern recognition in the presence of distortions. PMID:15521492
Prolate spheroidal harmonic expansion of gravitational field
Fukushima, Toshio
2014-06-01
As a modification of the oblate spheroidal case, a recursive method is developed to compute the point value and a few low-order derivatives of the prolate spheroidal harmonics of the second kind, Q{sub nm} (y), namely the unnormalized associated Legendre function (ALF) of the second kind with its argument in the domain, 1 < y < ∞. They are required in evaluating the prolate spheroidal harmonic expansion of the gravitational field in addition to the point value and the low-order derivatives of P-bar {sub nm}(t), the 4π fully normalized ALF of the first kind with its argument in the domain, |t| ≤ 1. The new method will be useful in the gravitational field computation of elongated celestial objects.
The path decomposition expansion and multidimensional tunneling
NASA Astrophysics Data System (ADS)
Auerbach, Assa; Kivelson, S.
This paper consists of two main topics. (i) The path decomposition expansion: a new path integral technique which allows us to break configuration space into disjoint regions and express the dynamics of the full system in terms of its parts. (ii) The application of the PDX and semiclassical methods for solving quantum-mechanical tunneling problems in multidimensions. The result is a conceptually simple, computationally straightforward method for calculating tunneling effects in complicated multidimensional potentials, even in cases where the nature of the states in the classically allowed regions is nontrivial. Algorithms for computing tunneling effects in general classes of problems are obtained.In addition, we present the detailed solutions to three model problems of a tunneling coordinate coupled to a phonon. This enables us to define various well-controlled approximation schemes, which help to reduce the dimensions of complicated tunneling calculations in real physical systems.
Space nuclear system expansion joints
NASA Technical Reports Server (NTRS)
Whitaker, W. D.; Shimazki, T. T.
1973-01-01
The engineering, design, and fabrication status of the expansion joint unit (EJU) to be employed in the NaK primary coolant piping loop of the 5-kwe Reactor thermoelectric system are described. Four EJU's are needed in the NaK primary coolant piping loop. The four EJU's which will be identical, utilize bellows as the flexing member, are hermetically sealed, and provide double containment. The bellows are of a nested-formed design, and are to be constructed of 1-ply thickness of 0.010-in. Inconel 718. The EJU's provide a minimum piping load margin of safety of +0.22.
Calculation of Turbulent Expansion Processes
NASA Technical Reports Server (NTRS)
Tollmien, Walter
1945-01-01
On the basis of certain formulas recently established by L. Prandtl for the turbulent interchange of momentum in stationary flows, various cases of "free turbulence" - that is, of flows without boundary walls - are treated in the present report. Prandtl puts the apparent shearing stress introduced by the turbulent momentum interchange. This present report deals first with the mixing of an air stream of uniform velocity with the adjacent still air, than with the expansion or diffusion of an air jet in the surrounding air space.
Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR
NASA Astrophysics Data System (ADS)
Takegoshi, K.; Miyazawa, Norihiro; Sharma, Kshama; Madhu, P. K.
2015-04-01
We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.
Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR
Takegoshi, K. Miyazawa, Norihiro; Sharma, Kshama; Madhu, P. K.
2015-04-07
We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.
Tensor integrand reduction via Laurent expansion
NASA Astrophysics Data System (ADS)
Hirschi, Valentin; Peraro, Tiziano
2016-06-01
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C ++ library N inja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface N inja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the N inja library and interfaced it to M adL oop, which is part of the public M adG raph5_ aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely C utT ools, S amurai, IREGI, PJF ry++ and G olem95. We find that N inja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than N inja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that N inja's performance scales well with both the rank and multiplicity of the considered process.