Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid

NASA Astrophysics Data System (ADS)

Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

2017-04-01

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

The effect of trench width on the behavior of buried rigid pipes

NASA Astrophysics Data System (ADS)

Balkaya, Müge; Saǧlamer, Ahmet

2014-12-01

In this study, in order to determine the effect of trench width (Bd) on the behavior of buried rigid pipes, a concrete pipe having an outside diameter of 150 cm and wall thickness (t) of 15 cm was analyzed using 2D PLAXIS finite element program. In the analyses, three different trench widths (Bd = 2.20 m, 3.40 m, and 4.40 m) were modeled. The results of the analyses indicated that, as the width of the trench increases, the axial force, shear force, bending moment, effective normal stress, and the earth load acting on the pipe increased. The variations of the loads acting on the pipe due to the increasing trench widths were also evaluated using the Marston load theory. When the loads calculated by the Marston Load Theory and the finite element analysis were compared with each other, it was seen that the Marston Load Theory resulted in slightly higher load values than the finite element analysis. On the other hand, for the two methods, the loads acting on the pipe increased with increasing trench width.

Analytical Study of Gravity Effects on Laminar Diffusion Flames

NASA Technical Reports Server (NTRS)

Edelman, R. B.; Fortune, O.; Weilerstein, G.

1972-01-01

A mathematical model is presented for the description of axisymmetric laminar-jet diffusion flames. The analysis includes the effects of inertia, viscosity, diffusion, gravity and combustion. These mechanisms are coupled in a boundary layer type formulation and solutions are obtained by an explicit finite difference technique. A dimensional analysis shows that the maximum flame width radius, velocity and thermodynamic state characterize the flame structure. Comparisons with experimental data showed excellent agreement for normal gravity flames and fair agreement for steady state low Reynolds number zero gravity flames. Kinetics effects and radiation are shown to be the primary mechanisms responsible for this discrepancy. Additional factors are discussed including elipticity and transient effects.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Modeling of laser transmission contour welding process using FEA and DoE

NASA Astrophysics Data System (ADS)

Acherjee, Bappa; Kuar, Arunanshu S.; Mitra, Souren; Misra, Dipten

2012-07-01

In this research, a systematic investigation on laser transmission contour welding process is carried out using finite element analysis (FEA) and design of experiments (DoE) techniques. First of all, a three-dimensional thermal model is developed to simulate the laser transmission contour welding process with a moving heat source. The commercial finite element code ANSYS® multi-physics is used to obtain the numerical results by implementing a volumetric Gaussian heat source, and combined convection-radiation boundary conditions. Design of experiments together with regression analysis is then employed to plan the experiments and to develop mathematical models based on simulation results. Four key process parameters, namely power, welding speed, beam diameter, and carbon black content in absorbing polymer, are considered as independent variables, while maximum temperature at weld interface, weld width, and weld depths in transparent and absorbing polymers are considered as dependent variables. Sensitivity analysis is performed to determine how different values of an independent variable affect a particular dependent variable.

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas

NASA Astrophysics Data System (ADS)

Vincenti, Henri; Vay, Jean-Luc

2018-07-01

The advent of massively parallel supercomputers, with their distributed-memory technology using many processing units, has favored the development of highly-scalable local low-order solvers at the expense of harder-to-scale global very high-order spectral methods. Indeed, FFT-based methods, which were very popular on shared memory computers, have been largely replaced by finite-difference (FD) methods for the solution of many problems, including plasmas simulations with electromagnetic Particle-In-Cell methods. For some problems, such as the modeling of so-called "plasma mirrors" for the generation of high-energy particles and ultra-short radiations, we have shown that the inaccuracies of standard FD-based PIC methods prevent the modeling on present supercomputers at sufficient accuracy. We demonstrate here that a new method, based on the use of local FFTs, enables ultrahigh-order accuracy with unprecedented scalability, and thus for the first time the accurate modeling of plasma mirrors in 3D.

The finite-dimensional Freeman thesis.

PubMed

Rudolph, Lee

2008-06-01

I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.

Forest fuel treatment detection using multi-temporal airborne Lidar data and high resolution aerial imagery ---- A case study at Sierra Nevada, California

NASA Astrophysics Data System (ADS)

Su, Y.; Guo, Q.; Collins, B.; Fry, D.; Kelly, M.

2014-12-01

Forest fuel treatments (FFT) are often employed in Sierra Nevada forest (located in California, US) to enhance forest health, regulate stand density, and reduce wildfire risk. However, there have been concerns that FFTs may have negative impacts on certain protected wildlife species. Due to the constraints and protection of resources (e.g., perennial streams, cultural resources, wildlife habitat, etc.), the actual FFT extents are usually different from planned extents. Identifying the actual extent of treated areas is of primary importance to understand the environmental influence of FFTs. Light detection and ranging (Lidar) is a powerful remote sensing technique that can provide accurate forest structure measurements, which provides great potential to monitor forest changes. This study used canopy height model (CHM) and canopy cover (CC) products derived from multi-temporal airborne Lidar data to detect FFTs by an approach combining a pixel-wise thresholding method and a object-of-interest segmentation method. We also investigated forest change following the implementation of landscape-scale FFT projects through the use of normalized difference vegetation index (NDVI) and standardized principle component analysis (PCA) from multi-temporal high resolution aerial imagery. The same FFT detection routine was applied on the Lidar data and aerial imagery for the purpose of comparing the capability of Lidar data and aerial imagery on FFT detection. Our results demonstrated that the FFT detection using Lidar derived CC products produced both the highest total accuracy and kappa coefficient, and was more robust at identifying areas with light FFTs. The accuracy using Lidar derived CHM products was significantly lower than that of the result using Lidar derived CC, but was still slightly higher than using aerial imagery. FFT detection results using NDVI and standardized PCA using multi-temporal aerial imagery produced almost identical total accuracy and kappa coefficient. Both methods showed relatively limited capacity to detect light FFT areas, and had higher false detection rate (recognized untreated areas as treated areas) compared to the methods using Lidar derived parameters.

Proceedings of the second SISAL users` conference

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

Feo, J T; Frerking, C; Miller, P J

1992-12-01

This report contains papers on the following topics: A sisal code for computing the fourier transform on S{sub N}; five ways to fill your knapsack; simulating material dislocation motion in sisal; candis as an interface for sisal; parallelisation and performance of the burg algorithm on a shared-memory multiprocessor; use of genetic algorithm in sisal to solve the file design problem; implementing FFT`s in sisal; programming and evaluating the performance of signal processing applications in the sisal programming environment; sisal and Von Neumann-based languages: translation and intercommunication; an IF2 code generator for ADAM architecture; program partitioning for NUMA multiprocessor computer systems;more » mapping functional parallelism on distributed memory machines; implicit array copying: prevention is better than cure ; mathematical syntax for sisal; an approach for optimizing recursive functions; implementing arrays in sisal 2.0; Fol: an object oriented extension to the sisal language; twine: a portable, extensible sisal execution kernel; and investigating the memory performance of the optimizing sisal compiler.« less

[Finite element stress analysis of all-ceramic continuous crowns of the lower anterior teeth in differential shoulder thickness].

PubMed

Ouyang, Shao-bo; Wang, Jun; Zhang, Hong-bin; Liao, Lan; Zhu, Hong-shui

2014-04-01

To investigate the stress distributions under load in 3 types of all-ceramic continuous crowns of the lower anterior teeth with differential shoulder thickness. Cone-beam CT (CBCT) was used to scan the in vitro mandibular central incisors, and achieve three-dimensional finite element model of all-ceramic continuous crowns with different shoulder width by using Mimics, Abaqus software. Different load conditions were simulated based on this model to study the effect of shoulder width variation on finite element analysis of 3 kinds of different all-ceramic materials of incisors fixed continuous crowns of the mandibular. Using CBCT, Mimics10.01 software and Abaqus 6.11 software, three-dimensional finite element model of all-ceramic continuous crowns of the mandibular incisor, abutment, periodontal ligament and alveolar bone was established. Different ceramic materials and various shoulder width had minor no impact on the equivalent stress peak of periodontal membrane, as well as alveolar bone. With the same shoulder width and large area of vertical loading of 120 N, the tensile stress was the largest in In-Ceram Alumina, followed by In-Ceram Zirconia and the minimum was IPS.Empress II. Under large area loading of 120 N 45° labially, when the material was IPS.Empress II, with the shoulder width increased, the porcelain plate edge of the maximum tensile stress value increased, while the other 2 materials had no obvious change. Finite element model has good geometric similarity. In the setting range of this study, when the elastic modulus of ceramic materials is bigger, the tensile stress of the continuous crown is larger. Supported by Research Project of Department of Education, Jiangxi Province (GJJ09130).

Optimal Alignment of Structures for Finite and Periodic Systems.

PubMed

Griffiths, Matthew; Niblett, Samuel P; Wales, David J

2017-10-10

Finding the optimal alignment between two structures is important for identifying the minimum root-mean-square distance (RMSD) between them and as a starting point for calculating pathways. Most current algorithms for aligning structures are stochastic, scale exponentially with the size of structure, and the performance can be unreliable. We present two complementary methods for aligning structures corresponding to isolated clusters of atoms and to condensed matter described by a periodic cubic supercell. The first method (Go-PERMDIST), a branch and bound algorithm, locates the global minimum RMSD deterministically in polynomial time. The run time increases for larger RMSDs. The second method (FASTOVERLAP) is a heuristic algorithm that aligns structures by finding the global maximum kernel correlation between them using fast Fourier transforms (FFTs) and fast SO(3) transforms (SOFTs). For periodic systems, FASTOVERLAP scales with the square of the number of identical atoms in the system, reliably finds the best alignment between structures that are not too distant, and shows significantly better performance than existing algorithms. The expected run time for Go-PERMDIST is longer than FASTOVERLAP for periodic systems. For finite clusters, the FASTOVERLAP algorithm is competitive with existing algorithms. The expected run time for Go-PERMDIST to find the global RMSD between two structures deterministically is generally longer than for existing stochastic algorithms. However, with an earlier exit condition, Go-PERMDIST exhibits similar or better performance.

Elastic guided waves in a layered plate with rectangular cross section.

PubMed

Mukdadi, O M; Desai, Y M; Datta, S K; Shah, A H; Niklasson, A J

2002-11-01

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Stabilization of a finite slice in miscible displacement in homogeneous porous media

NASA Astrophysics Data System (ADS)

Pramanik, Satyajit; Mishra, Manoranjan

2016-11-01

We numerically studied the miscible displacement of a finite slice of variable viscosity and density. The stability of the finite slice depends on different flow parameters, such as displacement velocity U, mobility ratio R , and the density contrast. Series of numerical simulations corresponding to different ordered pair (R, U) in the parameter space, and a given density contrast reveal six different instability regions. We have shown that independent of the width of the slice, there always exists a region of stable displacement, and below a critical value of the slice width, this stable region increases with decreasing slice width. Further we observe that the viscous fingering (buoyancy-induced instability) at the upper interface induces buoyancy-induced instability (viscous fingering) at the lower interface. Besides the fundamental fluid dynamics understanding, our results can be helpful to model CO2 sequestration and chromatographic separation.

On the performance of piezoelectric harvesters loaded by finite width impulses

NASA Astrophysics Data System (ADS)

Doria, A.; Medè, C.; Desideri, D.; Maschio, A.; Codecasa, L.; Moro, F.

2018-02-01

The response of cantilevered piezoelectric harvesters loaded by finite width impulses of base acceleration is studied analytically in the frequency domain in order to identify the parameters that influence the generated voltage. Experimental tests are then performed on harvesters loaded by hammer impacts. The latter are used to confirm analytical results and to validate a linear finite element (FE) model of a unimorph harvester. The FE model is, in turn, used to extend analytical results to more general harvesters (tapered, inverse tapered, triangular) and to more general impulses (heel strike in human gait). From analytical and numerical results design criteria for improving harvester performance are obtained.

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

DOE PAGES

Li, Fei; Yu, Peicheng; Xu, Xinlu; ...

2017-01-12

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k 1|, while keepsmore » additional main NCI modes well outside the range of physical interest with higher |k 1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.« less

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

NASA Astrophysics Data System (ADS)

Li, Fei; Yu, Peicheng; Xu, Xinlu; Fiuza, Frederico; Decyk, Viktor K.; Dalichaouch, Thamine; Davidson, Asher; Tableman, Adam; An, Weiming; Tsung, Frank S.; Fonseca, Ricardo A.; Lu, Wei; Mori, Warren B.

2017-05-01

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1 ˆ direction). We show that this eliminates the main NCI modes with moderate |k1 | , while keeps additional main NCI modes well outside the range of physical interest with higher |k1 | . These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1 ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

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

Li, Fei; Yu, Peicheng; Xu, Xinlu

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k 1|, while keepsmore » additional main NCI modes well outside the range of physical interest with higher |k 1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.« less

AutoCAD-To-NASTRAN Translator Program

NASA Technical Reports Server (NTRS)

Jones, A.

1989-01-01

Program facilitates creation of finite-element mathematical models from geometric entities. AutoCAD to NASTRAN translator (ACTON) computer program developed to facilitate quick generation of small finite-element mathematical models for use with NASTRAN finite-element modeling program. Reads geometric data of drawing from Data Exchange File (DXF) used in AutoCAD and other PC-based drafting programs. Written in Microsoft Quick-Basic (Version 2.0).

Morphodynamics structures induced by variations of the channel width

NASA Astrophysics Data System (ADS)

Duro, Gonzalo; Crosato, Alessandra; Tassi, Pablo

2014-05-01

In alluvial channels, forcing effects, such as a longitudinally varying width, can induce the formation of steady bars (Olesen, 1984). The type of bars that form, such as alternate, central or multiple, will mainly depend on the local flow width-to-depth ratio and on upstream conditions (Struiksma et al., 1985). The effects on bar formation of varying the channel width received attention only recently and investigations, based on flume experiments and mathematical modelling, are mostly restricted to small longitudinal sinusoidal variations of the channel width (e.g. Repetto et al., 2002; Wu and Yeh, 2005, Zolezzi et al., 2012; Frascati and Lanzoni, 2013). In this work, we analyze the variations in equilibrium bed topography in a longitudinal width-varying channel with characteristic scales of the Waal River (The Netherlands) using two different 2D depth-averaged morphodynamic models, one based on the Delft3D code and one on Telemac-Mascaret system. In particular, we explore the effects of changing the wavelength of sinusoidal width variations in a straight channel, focusing on the effects of the spatial lag between bar formation and forcing that is observed in numerical models and laboratory experiments (e.g. Crosato et al, 2011). We extend the investigations to finite width variations in which longitudinal changes of the width-to-depth ratio are such that they may affect the type of bars that become unstable (alternate, central or multiple bars). Numerical results are qualitatively validated with field observations and the resulting morphodynamic pattern is compared with the physics-based predictor of river bar modes by Crosato and Mosselman (2009). The numerical models are finally used to analyse the experimental conditions of Wu and Yeh (2005). The study should be seen as merely exploratory. The aim is to investigate possible approaches for future research aiming at assessing the effects of artificial river widening and narrowing to control bar formation in alluvial rivers. References Crosato A. and Mosselman E., 2009. Simple physics-based predictor for the number of river bars and the transition between meandering and braiding. Water Resources Research, 45, W03424, doi: 10.1029/2008WR007242. Crosato A., Mosselman E., Desta F.B. and Uijttewaal W.S.J., 2011. Experimental and numerical evidence for intrinsic nonmigrating bars in alluvial channels. Water Resources Research, AGU, 47(3), W03511, doi 10.1029/2010WR009714. Frascati A. and Lanzoni S., 2013. A mathematical model for meandering rivers with varying width. J. Geophys. Res.Earth Surf., 118, doi:10.1002/jgrf.20084. Olesen K.W., 1984. Alternate bars in and meandering of alluvial rivers. In: River Meandering, Proc. of the Conf. Rivers '83, 24-26 Oct. 1983, New Orleans, Louisiana, U.S.A., ed. Elliott C.M., pp. 873-884, ASCE, New York. ISBN 0-87262-393-9. Repetto R., Tubino, M. and Paola C., 2002. Planimetric instability of channels with variable width. J. Fluid Mech., 457, 79-109. Struiksma N., Olesen K.W., Flokstra C. and De Vriend H.J., 1985. Bed deformation in curved alluvial channels. J. Hydraul. Res., 23(1), 57- 79. Wu F.-C. and Yeh T.-H., 2005. Forced bars induced by variations of channel width: Implications for incipient bifurcation. J. Geophys. Res., 110, F02009, doi:10.1029/2004JF000160. Zolezzi, G., R. Luchi, and M. Tubino (2012), Modeling morphodynamic processes in meandering rivers with spatial width variations, Rev. Geophys., 50, RG4005, doi:10.1029/2012RG000392.

Resonance and decay phenomena lead to quantum mechanical time asymmetry

NASA Astrophysics Data System (ADS)

Bohm, A.; Bui, H. V.

2013-04-01

The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over -∞ < t < +∞. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 <= t < +∞, which predicts a finite "beginning of time" t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ = hslash/Γ.

Characterization of the Coupling Between Adjacent Finite Ground Coplanar (FGC) Waveguides

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Katehi, Linda P. B.; Tentzeris, Emmanouil M.

1997-01-01

Coupling between adjacent Finite Ground Coplanar (FGC) waveguides as a function of the line geometry is presented for the first time. A two Dimension-Finite Difference Time Domain (2D-FDTD) analysis and measurements are used to show that the coupling decreases as the line to line separation and the grOUnd plane width increases. Furthermore, it is shown that for a given spacing between the center lines of two FGC lines, the coupling is lower if the ground plane width is smaller Lastly, electric field plots generated from the 2D-FDTD technique are presented which demonstrate a strong slotline mode is established in the coupled FGC line.

Subject-Specific Finite Element Analysis of the Carpal Tunnel Cross-Sectional to Examine Tunnel Area Changes in Response to Carpal Arch Loading

PubMed Central

Walia, Piyush; Erdemir, Ahmet; Li, Zong-Ming

2017-01-01

Background Manipulating the carpal arch width (i.e. distance between hamate and trapezium bones) has been suggested as a means to increase carpal tunnel cross-sectional area and alleviate median nerve compression. The purpose of this study was to develop a finite element model of the carpal tunnel and to determine an optimal force direction to maximize area. Methods A planar geometric model of carpal bones at hamate level was reconstructed from MRI with inter-carpal joint spaces filled with a linear elastic surrogate tissue. Experimental data with discrete carpal tunnel pressures (50, 100, 150, and 200 mmHg) and corresponding carpal bone movements were used to obtain material property of surrogate tissue by inverse finite element analysis. The resulting model was used to simulate changes of carpal arch widths and areas with directional variations of a unit force applied at the hook of hamate. Findings Inverse finite element model predicted the experimental area data within 1.5% error. Simulation of force applications showed that carpal arch width and area were dependent on the direction of force application, and minimal arch width and maximal area occurred at 138° (i.e. volar-radial direction) with respect to the hamate-to-trapezium axis. At this force direction, the width changed to 24.4 mm from its initial 25.1 mm (3% decrease), and the area changed to 301.6 mm2 from 290.3 mm2 (4% increase). Interpretation The findings of the current study guide biomechanical manipulation to gain tunnel area increase, potentially helping reduce carpal tunnel pressure and relieve symptoms of compression median neuropathy. PMID:28073093

A Finite-Orbit-Width Fokker-Planck solver for modeling of RF Current Drive in ITER

NASA Astrophysics Data System (ADS)

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

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of constants-of-motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. A recent development is the capability to obtain solution simultaneously for FOW ions and Zero-Orbit-Width (ZOW) electrons. As a practical application, the code is used for simulation of alpha-particle heating by high-harmonic waves in ITER scenarios. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions such as alphas or NBI-produced deuterons, through finite Larmor-radius effects. Based on simulations, we formulate conditions where the fast ions absorb less than 10% of RF power. Supported by USDOE Grants ER54649, ER54744, and SC0006614.

Finite-width Laplace sum rules for 0-+ pseudoscalar glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Wang, Feng; Chen, Junlong; Liu, Jueping

2015-10-01

The correlation function of the 0-+ pseudoscalar glueball current is calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the pure classical contribution from instantons and the perturbative one into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free and more important than the pure perturbative one. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width resonance is adopted. The properties of the 0-+ pseudoscalar glueball are investigated via a family of the QCD Laplacian sum rules. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the 0-+ resonance in which the glueball fraction is dominant are obtained.

Properties of Fructan:Fructan 1-Fructosyltransferases from Chicory and Globe Thistle, Two Asteracean Plants Storing Greatly Different Types of Inulin1

PubMed Central

Vergauwen, Rudy; Van Laere, André; Van den Ende, Wim

2003-01-01

Remarkably, within the Asteraceae, a species-specific fructan pattern can be observed. Some species such as artichoke (Cynara scolymus) and globe thistle (Echinops ritro) store fructans with a considerably higher degree of polymerization than the one observed in chicory (Cichorium intybus) and Jerusalem artichoke (Helianthus tuberosus). Fructan:fructan 1-fructosyltransferase (1-FFT) is the enzyme responsible for chain elongation of inulin-type fructans. 1-FFTs were purified from chicory and globe thistle. A comparison revealed that chicory 1-FFT has a high affinity for sucrose (Suc), fructose (Fru), and 1-kestose as acceptor substrate. This makes redistribution of Fru moieties from large to small fructans very likely during the period of active fructan synthesis in the root when import and concentration of Suc can be expected to be high. In globe thistle, this problem is avoided by the very low affinity of 1-FFT for Suc, Fru, and 1-kestose and the higher affinity for inulin as acceptor substrate. Therefore, the 1-kestose formed by Suc:Suc 1-fructosyltransferase is preferentially used for elongation of inulin molecules, explaining why inulins with a much higher degree of polymerization accumulate in roots of globe thistle. Inulin patterns obtained in vitro from 1-kestose and the purified 1-FFTs from both species closely resemble the in vivo inulin patterns. Therefore, we conclude that the species-specific fructan pattern within the Asteraceae can be explained by the different characteristics of their respective 1-FFTs. Although 1-FFT and bacterial levansucrases clearly differ in their ability to use Suc as a donor substrate, a kinetic analysis suggests that 1-FFT also works via a ping-pong mechanism. PMID:12970504

Mathematical modeling of influence of ion size effects in an electrolyte in a nanoslit with overlapped EDL

NASA Astrophysics Data System (ADS)

Rajni, Kumar, Prashant

2017-10-01

Many nanofluidic systems are being used in a wide range of applications due to advances in nanotechnology. Due to nanoscale size of the system, the physics involved in the electric double layer and consequently the different phenomena related to it are different than those at microscale. The Poisson-Boltzmann equation governing the electric double layer in the system has many shortcomings such as point sized ions. The inclusion of finite size of ions give rise to various electrokinetic phenomena. Electrocapillarity is one such phenomena where the size effect plays an important role. Theeffect of asymmetric finite ion sizes in nano-confinement in the view of osmotic pressure and electrocapillarity is analyzed. As the confinement width of the system becomes comparable with the Debye length, the overlapped electric double layer (EDL) is influenced and significantly deformed by the steric effects. The osmotic pressure from the modified Poisson-Boltzmann equation in nanoslit is obtained. Due to nonlinear nature of the modified PB equation, the solution is obtained through numerical method. Afterwards, the electrocapillarity due to the steric effect is analyzed under constant surface potential condition at the walls of the nanoslit along with the flat interface assumption.

Flipping Undergraduate Finite Mathematics: Findings and Implications

ERIC Educational Resources Information Center

Guerrero, Shannon; Beal, Melissa; Lamb, Chris; Sonderegger, Derek; Baumgartel, Drew

2015-01-01

This paper reports on a research project that investigated the effects of a flipped instructional approach on student attitudes and achievement in a lower division university-level Finite Mathematics course. The project employed a mixed-methods design that included content exams, an attitude survey, open-ended student responses, observations, and…

A Feminist Family Therapy Scale.

ERIC Educational Resources Information Center

Black, Leora; Piercy, Fred P.

1991-01-01

Reports on development and psychometric properties of Feminist Family Therapy Scale (FFTS), a 17-item instrument intended to reflect degree to which family therapists conceptualize process of family therapy from feminist-informed perspective. Found that the instrument discriminated between self-identified feminists and nonfeminists, women and men,…

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Nonlinear temperature dependent failure analysis of finite width composite laminates

NASA Technical Reports Server (NTRS)

Nagarkar, A. P.; Herakovich, C. T.

1979-01-01

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.

ERIC Educational Resources Information Center

Hart, Eric W.; And Others

1990-01-01

Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)

A Note on Powers in Finite Fields

ERIC Educational Resources Information Center

Aabrandt, Andreas; Hansen, Vagn Lundsgaard

2016-01-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

PubMed

Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

2005-12-01

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

Discrete Mathematics and Curriculum Reform.

ERIC Educational Resources Information Center

Kenney, Margaret J.

1996-01-01

Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

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

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

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

Three-dimensional finite-element analysis of chevron-notched fracture specimens

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Stress-intensity factors and load-line displacements were calculated for chevron-notched bar and rod fracture specimens using a three-dimensional finite-element analysis. Both specimens were subjected to simulated wedge loading (either uniform applied displacement or uniform applied load). The chevron-notch sides and crack front were assumed to be straight. Crack-length-to-specimen width ratios (a/w) ranged from 0.4 to 0.7. The width-to-thickness ratio (w/B) was 1.45 or 2. The bar specimens had a height-to-width ratio of 0.435 or 0.5. Finite-element models were composed of singularity elements around the crack front and 8-noded isoparametric elements elsewhere. The models had about 11,000 degrees of freedom. Stress-intensity factors were calculated by using a nodal-force method for distribution along the crack front and by using a compliance method for average values. The stress intensity factors and load-line displacements are presented and compared with experimental solutions from the literature. The stress intensity factors and load-line displacements were about 2.5 and 5 percent lower than the reported experimental values, respectively.

A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code

DOE PAGES

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

2016-09-08

The time-dependent bounce-averaged CQL3D flux-conservative finite-difference Fokker–Planck equation (FPE) solver has been upgraded to include finite-orbit-width (FOW) capabilities which are necessary for an accurate description of neoclassical transport, losses to the walls, and transfer of particles, momentum, and heat to the scrape-off layer. The FOW modifications are implemented in the formulation of the neutral beam source, collision operator, RF quasilinear diffusion operator, and in synthetic particle diagnostics. The collisional neoclassical radial transport appears naturally in the FOW version due to the orbit-averaging of local collision coefficients coupled with transformation coefficients from local (R, Z) coordinates along each guiding-center orbit tomore » the corresponding midplane computational coordinates, where the FPE is solved. In a similar way, the local quasilinear RF diffusion terms give rise to additional radial transport of orbits. We note that the neoclassical results are obtained for ‘full’ orbits, not dependent on a common small orbit-width approximation. Results of validation tests for the FOW version are also presented.« less

Global kinetic simulations of neoclassical toroidal viscosity in low-collisional perturbed tokamak plasmas

NASA Astrophysics Data System (ADS)

Matsuoka, Seikichi; Idomura, Yasuhiro; Satake, Shinsuke

2017-10-01

The neoclassical toroidal viscosity (NTV) caused by a non-axisymmetric magnetic field perturbation is numerically studied using two global kinetic simulations with different numerical approaches. Both simulations reproduce similar collisionality ( νb*) dependencies over wide νb * ranges. It is demonstrated that resonant structures in the velocity space predicted by the conventional superbanana-plateau theory exist in the small banana width limit, while the resonances diminish when the banana width becomes large. It is also found that fine scale structures are generated in the velocity space as νb* decreases in the large banana width simulations, leading to the νb* -dependency of the NTV. From the analyses of the particle orbit, it is found that the finite k∥ mode structure along the bounce motion appears owing to the finite orbit width, and it suffers from bounce phase mixing, suggesting the generation of the fine scale structures by the similar mechanism as the parallel phase mixing of passing particles.

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Chen, Junlong; Liu, Jueping

2017-01-01

The more carefully defined and more appropriate 2++ tensor glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.

Unexpected finite size effects in interfacial systems: Why bigger is not always better—Increase in uncertainty of surface tension with bulk phase width

NASA Astrophysics Data System (ADS)

Longford, Francis G. J.; Essex, Jonathan W.; Skylaris, Chris-Kriton; Frey, Jeremy G.

2018-06-01

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase Ll/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

Appendix F : finite element analysis of end region.

DOT National Transportation Integrated Search

2013-03-01

FE (finite element) modeling was conducted to 1) provide a better understanding of the : elastic behavior of the end region prior to cracking and 2) to evaluate the effects of bearing pad : stiffness and width on end region elastic stresses. The FEA ...

Modeling wildland fire containment with uncertain flame length and fireline width

Treesearch

Romain Mees; David Strauss; Richard Chase

1993-01-01

We describe a mathematical model for the probability that a fireline succeeds in containing a fire. The probability increases as the fireline width increases, and also as the fire's flame length decreases. More interestingly, uncertainties in width and flame length affect the computed containment probabilities, and can thus indirectly affect the optimum allocation...

Formation of a vortex at the edge of a plate

NASA Technical Reports Server (NTRS)

Anton, Leo

1956-01-01

The flow about the plate of infinite width may be represented as a potential flow with discontinuity surfaces which extend from the plate edges. For prescribed form and vortex distribution of the discontinuity surfaces, the velocity field may be calculated by means of a conformal representation. One condition is that the velocity at the plate edges must be finite. However, it is not sufficient for determination of the form and vortex distribution of the surface. However, on the basis of a similitude requirement one succeeds in finding a solution of this problem for the plate of infinite width which is correct for the very beginning of the motion of the fluid. Starting from this solution, the further development of the vortex distribution and shape of the surface are observed in the case of a plate of finite width.

ASIC For Complex Fixed-Point Arithmetic

NASA Technical Reports Server (NTRS)

Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.

1995-01-01

Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.

Cloud cover typing from environmental satellite imagery. Discriminating cloud structure with Fast Fourier Transforms (FFT)

NASA Technical Reports Server (NTRS)

Logan, T. L.; Huning, J. R.; Glackin, D. L.

1983-01-01

The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs.

Discrete Mathematics and the Secondary Mathematics Curriculum.

ERIC Educational Resources Information Center

Dossey, John

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

Comparison of Numerical Approaches to a Steady-State Landscape Equation

NASA Astrophysics Data System (ADS)

Bachman, S.; Peckham, S.

2008-12-01

A mathematical model of an idealized fluvial landscape has been developed, in which a land surface will evolve to preserve dendritic channel networks as the surface is lowered. The physical basis for this model stems from the equations for conservation of mass for water and sediment. These equations relate the divergence of the 2D vector fields showing the unit-width discharge of water and sediment to the excess rainrate and tectonic uplift on the land surface. The 2D flow direction is taken to be opposite to the water- surface gradient vector. These notions are combined with a generalized Manning-type flow resistance formula and a generalized sediment transport law to give a closed mathematical system that can, in principle, be solved for all variables of interest: discharge of water and sediment, land surface height, vertically- averaged flow velocity, water depth, and shear stress. The hydraulic geometry equations (Leopold et. al, 1964, 1995) are used to incorporate width, depth, velocity, and slope of river channels as powers of the mean-annual river discharge. Combined, they give the unit- width discharge of the stream as a power, γ, of the water surface slope. The simplified steady-state model takes into account three components among those listed above: conservation of mass for water, flow opposite the gradient, and a slope-discharge exponent γ = -1 to reflect mature drainage networks. The mathematical representation of this model appears as a second-order hyperbolic partial differential equation (PDE) where the diffusivity is inversely proportional to the square of the local surface slope. The highly nonlinear nature of this PDE has made it very difficult to solve both analytically and numerically. We present simplistic analytic solutions to this equation which are used to test the validity of the numerical algorithms. We also present three such numerical approaches which have been used in solving the differential equation. The first is based on a nonlinear diffusion filtering technique (Welk et. al, 2007) that has been applied successfully in the context of image processing. The second uses a Ritz finite element approach to the Euler-Lagrange formulation of the PDE in which an eighth degree polynomial is solved whose coefficients are locally dependent on slope and elevation. Lastly, we show a variant to the diffusion filtering approach in which a single-stage Runge-Kutta method is used to iterate a time-derivative to steady- state. The relative merits and drawbacks of these approaches are discussed, as well as stability and consistency requirements.

Integrating First-Year Technology and Finite Mathematics Courses

ERIC Educational Resources Information Center

Shafii-Mousavi, Morteza; Kochanowski, Paul

2006-01-01

This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

A note on powers in finite fields

NASA Astrophysics Data System (ADS)

Aabrandt, Andreas; Lundsgaard Hansen, Vagn

2016-08-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.

Fracture and crack growth in orthotropic laminates. Part 1: Analysis of a hybrid, unidirectional laminate with damage

NASA Technical Reports Server (NTRS)

Goree, J. G.

1982-01-01

The fracture behavior of unifirectional hybrid (buffer strip) composite laminates is studied. Three particular solutions are discussed: (1) broken fibers in a unidirectional half plane; (2) adjoined half planes of different fiber and matrix properties and (3) the solution of two half planes bounding a third distinct region of finite width. This finite width region represents a buffer strip and the potential of this strip to arrest a crack that originates in one of the half planes is investigated. The analysis is based on a materials modeling approach using the classical shear lag assumption to described the stress transfer between fibers. Explicit fiber and matrix properties of the three regions are retained and changes in the laminate behavior as a function of the relative material properties, buffer strip width and initial crack length are discussed.

Numerical simulation on behaviour of timber-concrete composite beams in fire

NASA Astrophysics Data System (ADS)

Du, Hao; Hu, Xiamin; Zhang, Bing; Minli, Yao

2017-08-01

This paper established sequentially coupled thermal-mechanical models of timber--concrete composite (TCC) beams by finite element software ANSYS to investigate the fire resistance of TCC beam. Existing experimental results were used to verify the coupled thermal-mechanical model. The influencing parameters consisted of the width of timber beam, the thickness of the concrete slab and the timber board. Based on the numerical results, the effects of these parameters on fire resistance of TCC beams were investigated in detail. The results showed that modeling results agreed well with test results, and verified the reliability of the finite element model. The width of the timber beam had a significant influence on the fire resistance of TCC beams. The fire resistance of TCC beams would be enhanced by increasing the width of timber beam, the thickness of concrete slab and the timber board.

Mathematical modelling of convective processes in a weld pool under electric arc surfacing

NASA Astrophysics Data System (ADS)

Sarychev, V. D.; Granovskii, A. Yu; Nevskii, S. A.; Konovalov, S. V.

2017-01-01

The authors develop the mathematical model of convective processes in a molten pool under electric arc surfacing with flux-cored wire. The model is based on the ideas of how convective flows appear due to temperature gradient and action of electromagnetic forces. Influence of alloying elements in the molten metal was modeled as a non-linear dependence of surface tension upon temperature. Surface tension and its temperature coefficient were calculated according to the electron density functional method with consideration to asymmetric electron distribution at the interface “molten metal / shielding gas”. Simultaneous solution of Navier-Stokes and Maxwell equations according to finite elements method with consideration to the moving heat source at the interface showed that there is a multi-vortex structure in the molten metal. This structure gives rise to a downward heat flux which, at the stage of heating, moves from the centre of the pool and stirs it full width. At the cooling stage this flux moves towards the centre of the pool and a single vortex is formed near the symmetry centre. This flux penetration is ∼ 10 mm. Formation of the downward heat flux is determined by sign reversal of the temperature coefficient of surface tension due to the presence of alloying elements.

Investigation of flood routing by a dynamic wave model in trapezoidal channels

NASA Astrophysics Data System (ADS)

Sulistyono, B. A.; Wiryanto, L. H.

2017-08-01

The problems of flood wave propagation, in bodies of waters, cause by intense rains or breaking of control structures, represent a great challenge in the mathematical modeling processes. This research concerns about the development and application of a mathematical model based on the Saint Venant's equations, to study the behavior of the propagation of a flood wave in trapezoidal channels. In these equations, the momentum equation transforms to partial differential equation which has two parameters related to cross-sectional area and discharge of the channel. These new formulas have been solved by using an explicit finite difference scheme. In computation procedure, after computing the discharge from the momentum equation, the cross-sectional area will be obtained from the continuity equation for a given point of channel. To evaluate the behavior of the control variables, several scenarios for the main channel as well as for flood waves are considered and different simulations are performed. The simulations demonstrate that for the same bed width, the peak discharge in trapezoidal channel smaller than in rectangular one at a specific distance along the channel length and so, that roughness coefficient and bed slope of the channel play a strong game on the behavior of the flood wave propagation.

Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons

NASA Astrophysics Data System (ADS)

Scammell, H. D.; Sushkov, O. P.

2017-01-01

Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.

Optimal Assignment Problem Applications of Finite Mathematics to Business and Economics. [and] Difference Equations with Applications. Applications of Difference Equations to Economics and Social Sciences. [and] Selected Applications of Mathematics to Finance and Investment. Applications of Elementary Algebra to Finance. [and] Force of Interest. Applications of Calculus to Finance. UMAP Units 317, 322, 381, 382.

ERIC Educational Resources Information Center

Gale, David; And Others

Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…

Design of multiplier-less sharp transition width non-uniform filter banks using gravitational search algorithm

NASA Astrophysics Data System (ADS)

Bindiya T., S.; Elias, Elizabeth

2015-01-01

In this paper, multiplier-less near-perfect reconstruction tree-structured filter banks are proposed. Filters with sharp transition width are preferred in filter banks in order to reduce the aliasing between adjacent channels. When sharp transition width filters are designed as conventional finite impulse response filters, the order of the filters will become very high leading to increased complexity. The frequency response masking (FRM) method is known to result in linear-phase sharp transition width filters with low complexity. It is found that the proposed design method, which is based on FRM, gives better results compared to the earlier reported results, in terms of the number of multipliers when sharp transition width filter banks are needed. To further reduce the complexity and power consumption, the tree-structured filter bank is made totally multiplier-less by converting the continuous filter bank coefficients to finite precision coefficients in the signed power of two space. This may lead to performance degradation and calls for the use of a suitable optimisation technique. In this paper, gravitational search algorithm is proposed to be used in the design of the multiplier-less tree-structured uniform as well as non-uniform filter banks. This design method results in uniform and non-uniform filter banks which are simple, alias-free, linear phase and multiplier-less and have sharp transition width.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

Coupling Between Microstrip Lines With Finite Width Ground Plane Embedded in Thin Film Circuits

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Dalton, Edan; Tentzeris, Manos M.; Papapolymerou, John

2003-01-01

Three-dimensional (3D) interconnects built upon multiple layers of polyimide are required for constructing 3D circuits on CMOS (low resistivity) Si wafers, GaAs, and ceramic substrates. Thin film microstrip lines (TFMS) with finite width ground planes embedded in the polyimide are often used. However, the closely spaced TFMS lines a r e susceptible to high levels of coupling, which degrades circuit performance. In this paper, Finite Difference Time Domain (FDTD) analysis and experimental measurements a r e used to show that the ground planes must be connected by via holes to reduce coupling in both the forward and backward directions. Furthermore, it is shown that coupled microstrip lines establish a slotline type mode between the two ground planes and a dielectric waveguide type mode, and that the via holes recommended here eliminate these two modes.

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

Elements of Mathematics, Book 11: Finite Probability Spaces.

ERIC Educational Resources Information Center

Exner, Robert; And Others

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

PIC simulations of the trapped electron filamentation instability in finite-width electron plasma waves

NASA Astrophysics Data System (ADS)

Winjum, B. J.; Banks, J. W.; Berger, R. L.; Cohen, B. I.; Chapman, T.; Hittinger, J. A. F.; Rozmus, W.; Strozzi, D. J.; Brunner, S.

2012-10-01

We present results on the kinetic filamentation of finite-width nonlinear electron plasma waves (EPW). Using 2D simulations with the PIC code BEPS, we excite a traveling EPW with a Gaussian transverse profile and a wavenumber k0λDe= 1/3. The transverse wavenumber spectrum broadens during transverse EPW localization for small width (but sufficiently large amplitude) waves, while the spectrum narrows to a dominant k as the initial EPW width increases to the plane-wave limit. For large EPW widths, filaments can grow and destroy the wave coherence before transverse localization destroys the wave; the filaments in turn evolve individually as self-focusing EPWs. Additionally, a transverse electric field develops that affects trapped electrons, and a beam-like distribution of untrapped electrons develops between filaments and on the sides of a localizing EPW. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Research and Development Program at LLNL under project tracking code 12-ERD-061. Supported also under Grants DE-FG52-09NA29552 and NSF-Phy-0904039. Simulations were performed on UCLA's Hoffman2 and NERSC's Hopper.

A Finite Element Analysis of a Carbon Fiber Composite Micro Air Vehicle Wing

DTIC Science & Technology

2012-03-22

3. Errors in the manufacturing of the laminate resulting in errors in ply orientation. Each of these was examined in order to determine a root ...material properties. 4.2.4. Vein Width The widths of the individual veins of the manufactured wing were varied linearly from root to tip of the...wing. In the sizing of the engineered wing, the width of the veins were varied linearly from the root of the vein to the tip. For manufacturing

Reconstruction of spherically symmetric objects from slit-imaged emission: limitations due to finite slit width

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

Mueller, M.M.

1979-11-01

A simple method for reconstructing spherically symmetric objects from slit-imaged emission was recently described by Vest and Steel. Although this method is valid for infinitesimal slit widths and practically noise-free irradiance data, it is shown here that its validity does not extend to slits of practical width in the laser-fusion program. However, a method is given for reducing the Vest--Steel plots with practical apertures to obtain information on core diameter, shell diameter, and shell thickness.

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

NASA Technical Reports Server (NTRS)

Gyekenyesi, G. S.; Mendelson, A.

1972-01-01

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Parsimonious mathematical characterization of channel shape and size

USDA-ARS?s Scientific Manuscript database

This work has two purposes: 1) using a Leopold and Maddock (1953) hydraulic geometry approach, present a mathematically parsimonious, two parameter, characterization of channel shape and size; and 2) analytically quantify cross-sectional area, top width, average depth, critical energy, and bankfull ...

Large-Eddy Simulation of Internal Flow through Human Vocal Folds

NASA Astrophysics Data System (ADS)

Lasota, Martin; Šidlof, Petr

2018-06-01

The phonatory process occurs when air is expelled from the lungs through the glottis and the pressure drop causes flow-induced oscillations of the vocal folds. The flow fields created in phonation are highly unsteady and the coherent vortex structures are also generated. For accuracy it is essential to compute on humanlike computational domain and appropriate mathematical model. The work deals with numerical simulation of air flow within the space between plicae vocales and plicae vestibulares. In addition to the dynamic width of the rima glottidis, where the sound is generated, there are lateral ventriculus laryngis and sacculus laryngis included in the computational domain as well. The paper presents the results from OpenFOAM which are obtained with a large-eddy simulation using second-order finite volume discretization of incompressible Navier-Stokes equations. Large-eddy simulations with different subgrid scale models are executed on structured mesh. In these cases are used only the subgrid scale models which model turbulence via turbulent viscosity and Boussinesq approximation in subglottal and supraglottal area in larynx.

Real-Time, Polyphase-FFT, 640-MHz Spectrum Analyzer

NASA Technical Reports Server (NTRS)

Zimmerman, George A.; Garyantes, Michael F.; Grimm, Michael J.; Charny, Bentsian; Brown, Randy D.; Wilck, Helmut C.

1994-01-01

Real-time polyphase-fast-Fourier-transform, polyphase-FFT, spectrum analyzer designed to aid in detection of multigigahertz radio signals in two 320-MHz-wide polarization channels. Spectrum analyzer divides total spectrum of 640 MHz into 33,554,432 frequency channels of about 20 Hz each. Size and cost of polyphase-coefficient memory substantially reduced and much of processing loss of windowed FFTs eliminated.

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

The mechanism of the formation of the hemiaminal and Schiff base from the benzaldehyde and triazole studied by means of the topological analysis of electron localisation function and catastrophe theory

NASA Astrophysics Data System (ADS)

Berski, Slawomir; Zbigniew Ciunik, Leszek

2015-04-01

The mechanisms of reaction of benzaldehyde (ald) with 4-amine-4H-1,2,4-triazole (4at), leading to Schiff base (Sch) and water, were investigated using topological analysis of the electron localisation function and catastrophe theory. Two reactions (synthesis of hemiaminal and synthesis of Schiff base) are represented by one catastrophe sequence: ald+4at: 1-14-[FF†F†FFTS1FF†F†FF†F†CF†]-2-9-[C†FFTS3F†F†FFF]-0:Sch+H2O with only fold (F) and cusp (C) catastrophes. The first reaction, in which a molecule of the hemiaminal is formed, consists of 14 steps separated by 13 catastrophes. The mechanism is non-concerted. The covalent bond C-N is formed after the formation of the O-H bond is terminated. The Schiff base formation through the water molecule elimination in the second reaction requires nine steps with eight catastrophes. The mechanism is non-concerted because first the C-O bond is broken and then the proton transfer occurs that results in the O-H bond creation.

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Voigt equivalent widths and spectral-bin single-line transmittances: Exact expansions and the MODTRAN®5 implementation

NASA Astrophysics Data System (ADS)

Berk, Alexander

2013-03-01

Exact expansions for Voigt line-shape total, line-tail and spectral bin equivalent widths and for Voigt finite spectral bin single-line transmittances have been derived in terms of optical depth dependent exponentially-scaled modified Bessel functions of integer order and optical depth independent Fourier integral coefficients. The series are convergent for the full range of Voigt line-shapes, from pure Doppler to pure Lorentzian. In the Lorentz limit, the expansion reduces to the Ladenburg and Reiche function for the total equivalent width. Analytic expressions are derived for the first 8 Fourier coefficients for pure Lorentzian lines, for pure Doppler lines and for Voigt lines with at most moderate Doppler dependence. A strong-line limit sum rule on the Fourier coefficients is enforced to define an additional Fourier coefficient and to optimize convergence of the truncated expansion. The moderate Doppler dependence scenario is applicable to and has been implemented in the MODTRAN5 atmospheric band model radiative transfer software. Finite-bin transmittances computed with the truncated expansions reduce transmittance residuals compared to the former Rodgers-Williams equivalent width based approach by ∼2 orders of magnitude.

A finite element-boundary integral method for cavities in a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

Electric and magnetic superlattices in trilayer graphene

NASA Astrophysics Data System (ADS)

Uddin, Salah; Chan, K. S.

2016-01-01

The properties of one dimensional Kronig-Penney type of periodic electric and vector potential on ABC-trilayer graphene superlattices are investigated. The energy spectra obtained with periodic vector potentials shows the emergence of extra Dirac points in the energy spectrum with finite energies. For identical barrier and well widths, the original as well as the extra Dirac points are located in the ky = 0 plane. An asymmetry between the barrier and well widths causes a shift in the extra Dirac points away from the ky = 0 plane. Extra Dirac points having same electron hole crossing energy as that of the original Dirac point as well as finite energy Dirac points are generated in the energy spectrum when periodic electric potential is applied to the system. By applying electric and vector potential together, the symmetry of the energy spectrum about the Fermi level is broken. A tunable band gap is induced in the energy spectrum by applying both electric and vector potential simultaneously with different barrier and well widths.

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

Aquifer response to stream-stage and recharge variations. I. Analytical step-response functions

USGS Publications Warehouse

Moench, A.F.; Barlow, P.M.

2000-01-01

Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.Laplace transform step-response functions are presented for various homogeneous confined and leaky aquifer types and for anisotropic, homogeneous unconfined aquifers interacting with perennial streams. Flow is one-dimensional, perpendicular to the stream in the confined and leaky aquifers, and two-dimensional in a plane perpendicular to the stream in the water-table aquifers. The stream is assumed to penetrate the full thickness of the aquifer. The aquifers may be semi-infinite or finite in width and may or may not be bounded at the stream by a semipervious streambank. The solutions are presented in a unified manner so that mathematical relations among the various aquifer configurations are clearly demonstrated. The Laplace transform solutions are inverted numerically to obtain the real-time step-response functions for use in the convolution (or superposition) integral. To maintain linearity in the case of unconfined aquifers, fluctuations in the elevation of the water table are assumed to be small relative to the saturated thickness, and vertical flow into or out of the zone above the water table is assumed to occur instantaneously. Effects of hysteresis in the moisture distribution above the water table are therefore neglected. Graphical comparisons of the new solutions are made with known closed-form solutions.

Notch Sensitivity of Woven Ceramic Matrix Composites Under Tensile Loading: An Experimental, Analytical, and Finite Element Study

NASA Technical Reports Server (NTRS)

Haque, A.; Ahmed, L.; Ware, T.; Jeelani, S.; Verrilli, Michael J. (Technical Monitor)

2001-01-01

The stress concentrations associated with circular notches and subjected to uniform tensile loading in woven ceramic matrix composites (CMCs) have been investigated for high-efficient turbine engine applications. The CMC's were composed of Nicalon silicon carbide woven fabric in SiNC matrix manufactured through polymer impregnation process (PIP). Several combinations of hole diameter/plate width ratios and ply orientations were considered in this study. In the first part, the stress concentrations were calculated measuring strain distributions surrounding the hole using strain gages at different locations of the specimens during the initial portion of the stress-strain curve before any microdamage developed. The stress concentration was also calculated analytically using Lekhnitskii's solution for orthotropic plates. A finite-width correction factor for anisotropic and orthotropic composite plate was considered. The stress distributions surrounding the circular hole of a CMC's plate were further studied using finite element analysis. Both solid and shell elements were considered. The experimental results were compared with both the analytical and finite element solutions. Extensive optical and scanning electron microscopic examinations were carried out for identifying the fracture behavior and failure mechanisms of both the notched and notched specimens. The stress concentration factors (SCF) determined by analytical method overpredicted the experimental results. But the numerical solution underpredicted the experimental SCF. Stress concentration factors are shown to increase with enlarged hole size and the effects of ply orientations on stress concentration factors are observed to be negligible. In all the cases, the crack initiated at the notch edge and propagated along the width towards the edge of the specimens.

An experimental study of arch perimeter and arch width increase with mandibular expansion: a finite element method.

PubMed

Baswaraj; Hemanth, M; Jayasudha; Patil, Chandrashekhargouda; Sunilkumar, P; Raghuveer, H P; Chandralekha, B

2013-01-01

The objective of this study was to estimate the increase in arch perimeter associated with mandibular lateral expansion, To estimate the increase in intermolar width with mandibular lateral expansion and to find out the changes of tooth inclination with mandibular expansion. The mandibular bone with dentition of indian skeletal specimen was obtained. The computer tomogram (CT) slices of the mandible were taken. Finite element model (FEM): Numerical representation of the geometry was created by dividing the geometry into finite number of elements and the elements were connected together with nodes at the junction. The result of the study showed when 10° of lateral expansion was applied to the lower buccal segment at the center of rotation found at 4.3 mm below the root apex of first molar, a space of 1.3 mm between the canine and first premolar, and thus an increase in arch perimeter of 2.6 mm. The tip of the mesiolingual cusp of the first molar moved 4.2 mm laterally, resulting in a change in intermolar width by 8.4 mm. Three-dimensional simulation showed that 1 mm of intermolar expansion increased the arch perimeter by 0.30 mm. As the finite element method evolves and scientists are able to more clearly define physical properties of biological tissues, more accurate information can be generated at the level that other analytical methods cannot fully provide data.This result would be of value clinically for prediction of the effects of mandibular expansion.

Experience of validation and tuning of turbulence models as applied to the problem of boundary layer separation on a finite-width wedge

NASA Astrophysics Data System (ADS)

Babulin, A. A.; Bosnyakov, S. M.; Vlasenko, V. V.; Engulatova, M. F.; Matyash, S. V.; Mikhailov, S. V.

2016-06-01

Modern differential turbulence models are validated by computing a separation zone generated in the supersonic flow past a compression wedge lying on a plate of finite width. The results of three- and two-dimensional computations based on the ( q-ω), SST, and Spalart-Allmaras turbulence models are compared with experimental data obtained for 8°, 25°, and 45° wedges by A.A. Zheltovodov at the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences. An original law-of-the-wall boundary condition and modifications of the SST model intended for improving the quality of the computed separation zone are described.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

NASA Astrophysics Data System (ADS)

Koochi, Ali; Hosseini-Toudeshky, Hossein; Abadyan, Mohamadreza

2018-03-01

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin-Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

Reconfigurable optofluidic switch for generation of optical pulse width modulation based on tunable reflective interface.

PubMed

Mansuori, M; Zareei, G H; Hashemi, H

2015-10-01

We present a numerical method for generation of optical pulse width modulation (PWM) based on tunable reflective interface by using a microfluidic droplet. We demonstrate a single layer, planar, optofluidic PWM switch that is driven by excited alternating microbubbles. The main parameters of generation of this PWM such as frequency and speed of switching can be controlled by the mass flow rates of input fluids, and the shape of plug or droplet. Advantages of this design are the reconfigurability in design and the easy control of the switching parameters. The validation of the proposed design is carried out by employing the finite element method (FEM) for the mechanical simulation and the finite-difference time-domain (FDTD) for the optical simulation.

Analysis of surface cracks in finite plates under tension or bending loads

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1979-01-01

Stress-intensity factors calculated with a three-dimensional, finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads are presented. A wide range of configuration parameters was investigated. The ratio of crack depth to plate thickness ranged from 0.2 to 0.8 and the ratio of crack depth to crack length ranged from 0.2 to 2.0. The effects of plate width on stress-intensity variations along the crack front was also investigated. A wide-range equation for stress-intensity factors along the crack front as a function of crack depth, crack length, plate thickness, and plate width was developed for tension and bending loads. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. A modified form of the equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.

Coupling Between CPW and Slotline Modes in Finite Ground CPW with Unequal Ground Plane Widths

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Papapolymerou, John; Williams, W. D. (Technical Monitor); Tentzeris, Emmanouil M.

2002-01-01

The coupling between the desired CPW mode and the unwanted, slotline, mode is presented for finite ground coplanar waveguides with unequal ground plane widths. Measurements, quasi-static conformal mapping, and Method of Moment analysis are performed to determine the dependence of the slotline mode excitation on the physical dimensions of the FGC line and on the frequency range of operation. Introduction: Finite ground coplanar waveguide (FGC) is often used in low cost Monolithic Microwave Integrated Circuits (MMICs) because of its many advantages over microstrip and conventional CoPlanar Waveguide (CPW). It is uniplanar, which facilitates easy connection of series and shunt elements without via holes, supports a low loss, quasi-TEM mode over a wide frequency band, and since the ground planes are electrically and physically narrow, typically less than lambda/5 wide where lambda is the guided wavelength, they reduce the circuit size and the influence of higher order modes. However, they still support the parasitic slotline mode that plagues all CPW transmission lines.

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

DTIC Science & Technology

2017-08-01

filtering, correlation and radio- astronomy . In this report approximate transforms that closely follow the DFT have been studied and found. The approximate...communications, data networks, sensor networks, cognitive radio, radar and beamforming, imaging, filtering, correlation and radio- astronomy . FFTs efficiently...public release; distribution is unlimited. 4.3 Digital Hardware and Design Architectures Collaboration for Astronomy Signal Processing and Electronics

Robust High Data Rate MIMO Underwater Acoustic Communications

DTIC Science & Technology

2011-09-30

We solved it via exploiting FFTs. The extended CAN algorithm is referred to as periodic CAN ( PeCAN ). Unlike most existing sequence construction...methods which are algebraic and deterministic in nature, we start the iteration of PeCAN from random phase initializations and then proceed to...covert UAC applications. We will use PeCAN sequences for more in-water experimentations to demonstrate their effectiveness. Temporal Resampling: In

Ras Signaling Inhibitors Attenuate Disease in Adjuvant-Induced Arthritis via Targeting Pathogenic Antigen-Specific Th17-Type Cells.

PubMed

Zayoud, Morad; Marcu-Malina, Victoria; Vax, Einav; Jacob-Hirsch, Jasmine; Elad-Sfadia, Galit; Barshack, Iris; Kloog, Yoel; Goldstein, Itamar

2017-01-01

The Ras family of GTPases plays an important role in signaling nodes downstream to T cell receptor and CD28 activation, potentially lowering the threshold for T-cell receptor activation by autoantigens. Somatic mutation in NRAS or KRAS may cause a rare autoimmune disorder coupled with abnormal expansion of lymphocytes. T cells from rheumatoid arthritis (RA) patients show excessive activation of Ras/MEK/ERK pathway. The small molecule farnesylthiosalicylic acid (FTS) interferes with the interaction between Ras GTPases and their prenyl-binding chaperones to inhibit proper plasma membrane localization. In the present study, we tested the therapeutic and immunomodulatory effects of FTS and its derivative 5-fluoro-FTS (F-FTS) in the rat adjuvant-induced arthritis model (AIA). We show that AIA severity was significantly reduced by oral FTS and F-FTS treatment compared to vehicle control treatment. FTS was as effective as the mainstay anti-rheumatic drug methotrexate, and combining the two drugs significantly increased efficacy compared to each drug alone. We also discovered that FTS therapy inhibited both the CFA-driven in vivo induction of Th17 and IL-17/IFN-γ producing "double positive" as well as the upregulation of serum levels of the Th17-associated cytokines IL-17A and IL-22. By gene microarray analysis of effector CD4 + T cells from CFA-immunized rats, re-stimulated in vitro with the mycobacterium tuberculosis heat-shock protein 65 (Bhsp65), we determined that FTS abrogated the Bhsp65-induced transcription of a large list of genes (e.g., Il17a/f, Il22, Ifng, Csf2, Lta, and Il1a). The functional enrichment bioinformatics analysis showed significant overlap with predefined gene sets related to inflammation, immune system processes and autoimmunity. In conclusion, FTS and F-FTS display broad immunomodulatory effects in AIA with inhibition of the Th17-type response to a dominant arthritogenic antigen. Hence, targeting Ras signal-transduction cascade is a potential novel therapeutic approach for RA.

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Quark gluon bags as reggeons

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

Bugaev, K. A.; Petrov, V. K.; Zinovjev, G. M.

2009-05-15

The influence of the medium-dependent finite width of quark gluon plasma (QGP) bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags being heavier than 2 GeV from a variety of the lattice QCD data and get thatmore » the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown, these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that in addition to the {sigma}T{sup 4} term the lattice QCD pressure contains T-linear and T{sup 4}lnT terms in the range of temperatures between 240 and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at high temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.« less

Effects of Prosthetic Material and Framework Design on Stress Distribution in Dental Implants and Peripheral Bone: A Three-Dimensional Finite Element Analysis.

PubMed

Arinc, Hakan

2018-06-22

BACKGROUND The purpose of this study was to evaluate the effects of prosthetic material and framework design on the stress within dental implants and peripheral bone using finite element analysis (FEA). MATERIAL AND METHODS A mandibular implant-supported fixed dental prosthesis with different prosthetic materials [cobalt-chromium-supported ceramic (C), zirconia-supported ceramic (Z), and zirconia-reinforced polymethyl methacrylate (ZRPMMA)-supported resin (ZP)] and different connector widths (2, 3, and 4 mm) within the framework were used to evaluate stress via FEA under oblique loading conditions. Maximum principal (smax), minimum principal (smin), and von Mises (svM) stress values were obtained. RESULTS Minimum stress values were observed in the model with a 2-mm connector width for C and ZP. The models with 3-mm and 4-mm connector widths showed higher stress values than the model with a 2-mm connector width for C (48-50%) and ZP (50-52%). Similar stress values were observed in the 3- and 4-mm models. There was no significant difference in the amount of stress with Z regardless of connector width. The Z and ZP models showed similar stress values in the 3- and 4-mm models and higher stress values than in the C model. Z, ZP, and C showed the highest stress values for the model with a 2-mm connector width. CONCLUSIONS Changes in the material and width of connectors may influence stress on cortical bone, cancellous bone, and implants. C was associated with the lowest stress values. Higher maximum and minimum principal stress values were seen in cortical bone compared to cancellous bone.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Quantal Time Asymmetry: Mathematical Foundation and Physical Interpretation

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

Bohm, A.

2010-07-29

Time in standard quantum mechanics extends from -{infinity}t{sub 0}(Feynman (1948)). In experiments on single Ba{sup +} ions, Dehmelt and others observed this finite preparation timemore » as the ensemble of onset-times t{sub 0}{sup 1}, t{sub 0}{sup 2},...,t{sub 0}{sup n} of dark periods. How the semigroup time evolution, t{sub 0{identical_to}}0

On some methods of discrete systems behaviour simulation

NASA Astrophysics Data System (ADS)

Sytnik, Alexander A.; Posohina, Natalia I.

1998-07-01

The project is solving one of the fundamental problems of mathematical cybernetics and discrete mathematics, the one connected with synthesis and analysis of managing systems, depending on the research of their functional opportunities and reliable behaviour. This work deals with the case of finite-state machine behaviour restoration when the structural redundancy is not available and the direct updating of current behaviour is impossible. The described below method, uses number theory to build a special model of finite-state machine, it is simulating the transition between the states of the finite-state machine using specially defined functions of exponential type with the help of several methods of number theory and algebra it is easy to determine, whether there is an opportunity to restore the behaviour (with the help of this method) in the given case or not and also derive the class of finite-state machines, admitting such restoration.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Production of extra quarks decaying to dark matter beyond the narrow width approximation at the LHC

NASA Astrophysics Data System (ADS)

Moretti, Stefano; O'Brien, Dermot; Panizzi, Luca; Prager, Hugo

2017-08-01

This paper explores the effects of finite width in processes of pair production of an extra heavy quark with charge 2 /3 (top partner) and its subsequent decay into a bosonic dark matter (DM) candidate—either scalar or vector—and SM up-type quarks at the Large Hadron Collider (LHC). This dynamics has been ignored so far in standard experimental searches of heavy quarks decaying to DM and we assess herein the regions of validity of current approaches, based on the assumption that the extra quarks have a narrow width. Further, we discuss the configurations of masses, widths and couplings where the latter breaks down.

The finite element method in low speed aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1975-01-01

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Curvature estimation for multilayer hinged structures with initial strains

NASA Astrophysics Data System (ADS)

Nikishkov, G. P.

2003-10-01

Closed-form estimate of curvature for hinged multilayer structures with initial strains is developed. The finite element method is used for modeling of self-positioning microstructures. The geometrically nonlinear problem with large rotations and large displacements is solved using step procedure with node coordinate update. Finite element results for curvature of the hinged micromirror with variable width is compared to closed-form estimates.

The gamma decay of the giant dipole resonance: from zero to finite temperature

NASA Astrophysics Data System (ADS)

Bracco, Angela; Camera, Franco

2016-08-01

This paper is intended to give a selected and rather brief overview of the work made in the last thirty years to study the properties of the giant dipole resonance focusing in particular on nuclei formed at finite temperatures using heavy ion reactions. The physical problems that are discussed (using examples of particular results) in this paper can be grouped into 3 major topics: (i) the temperature dependence of the GDR width; (ii) the dipole oscillation in reaction dynamics; (iii) the isospin mixing at finite temperature.

Finite element validation of stress intensity factor calculation models for thru-thickness and thumb-nail cracks in double edge notch specimens

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

Beres, W.; Koul, A.K.

1994-09-01

Stress intensity factors for thru-thickness and thumb-nail cracks in the double edge notch specimens, containing two different notch radius (R) to specimen width (W) ratios (R/W = 1/8 and 1/16), are calculated through finite element analysis. The finite element results are compared with predictions based on existing empirical models for SIF calculations. The effects of a change in R/W ratio on SIF of thru-thickness and thumb-nail cracks are also discussed. 34 refs.

Coupling of Peridynamics and Finite Element Formulation for Multiscale Simulations

DTIC Science & Technology

2012-10-16

unidirectional fiber - reinforced composites, Computer Methods in Applied Mechanics and Engineering 217 (2012) 247-261. [44] S. A. Silling, M. Epton...numerical testing for different grid widths to horizon ratios , (4) development of an approach to add another material variable in the given approach...partition of unity principle, (3) numerical testing for different grid widths to horizon ratios , (4) development of an approach to add another

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

SDU: A Semidefinite Programming-Based Underestimation Method for Stochastic Global Optimization in Protein Docking

DTIC Science & Technology

2007-04-01

optimization methodology we introduce. State-of-the-art protein - protein docking approaches start by identifying conformations with good surface /chemical com...side-chains on the interface ). The protein - protein docking literature (e.g., [8] and the references therein) is predominantly treating the docking...mations by various measures of surface complementarity which can be efficiently computed using fast Fourier correlation tech- niques (FFTs). However, when

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

PubMed Central

Landry, Nicholas W.; Knezevic, Marko

2015-01-01

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. PMID:28793566

Shear Heating-Induced Thermal Pressurization During the Nucleation of Earthquakes

NASA Astrophysics Data System (ADS)

Schmitt, S. V.; Segall, P.

2008-12-01

Shear heating-induced thermal pressurization has long been posited as a weakening mechanism during earthquakes. It is often assumed that thermal pressurization does not become important until earthquakes become moderate to large in magnitude. Schmitt et al. [AGU, 2007] confirmed the estimate of Segall and Rice [JGR, 2006] that thermal pressurization becomes dominant during the quasi-static nucleation phase by conducting 2D numerical simulations that account for full thermomechanical coupling, with rate and state dependent friction. In that work, thermal pressurization becomes the dominant weakening mechanism at slip rates of 10-5 to 10-3 m/s, depending on the fault zone hydraulic diffusivity. Interestingly, the thermal pressurization process leads to a contraction of the nucleation zone, rather than the growing crack (aging law) or unidirectional slip pulse (slip law) associated with drained rate- and state-dependent frictional nucleation. The results of Schmitt et al. [AGU, 2007] had a shortcoming in that the principal slip surface was treated as a zero-width feature, while in reality it should be a finite-width shear zone. We address that shortcoming with a new set of numerical simulations. We assume a finite-width fault governed by rate and state friction with the radiation damping approximation to simulate inertial effects. Both thermal and hydraulic diffusion are computed via finite differences on separate, coupled grids that adaptively remesh to minimize computational expense while maintaining accuracy. New results suggest that the thermal pressurization effect is modestly reduced by including the finite thickness of the shear zone. Despite the reduction in the effect, the new results still indicate that (1) thermal pressurization is important before seismic slip and (2) thermal pressurization restricts growth of the nucleation zone.

Exploring the Effectiveness of Different Approaches to Teaching Finite Mathematics

ERIC Educational Resources Information Center

Smeal, Mary; Walker, Sandra; Carter, Jamye; Simmons-Johnson, Carolyn; Balam, Esenc

2013-01-01

Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

NASA Astrophysics Data System (ADS)

Srokowski, Tomasz

2017-03-01

The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.

Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons.

PubMed

Ratas, Irmantas; Pyragas, Kestutis

2016-09-01

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.

An experimental study of miscible viscous fingering of annular ring

NASA Astrophysics Data System (ADS)

Nagatsu, Yuichiro; Othman, Hamirul Bin; Mishra, Manoranjan

2017-11-01

Understanding the viscous fingering (VF) dynamics of finite width sample is important in the fields especially such as liquid chromatography and groundwater contamination and mixing in microfluidics. In this paper, we experimentally investigate such hydrodynamical morphology of VF using a Hele-Shaw flow system in which a miscible annular ring of fluid is displaced radially. Experiments are performed to investigate the effects of the sample volume, the effects of dispersion and log mobility ratio R on the dynamics of VF pattern and onset of such instability. Depending whether the finite width ring is more or less viscous than the carrier fluid, the log mobility ratio R becomes positive or negative respectively. The experiments are successfully conducted to obtain the VF patterns for R>0 and R<0, of the finite annular ring at the inner and outer radial interfaces, respectively. It is found that in the radial displacement, the inward finger moves slower than the outward finger. The experimental results are found to be qualitatively in good agreement with the corresponding linear stability analysis and non-linear simulations results available in the literature.

Studying the Immunomodulatory Effects of Small Molecule Ras Inhibitors in Animal Models of Rheumatoid Arthritis

DTIC Science & Technology

2017-10-01

methotrexate (MTX) provides a superior protective effect compared to monotherapy. (iii) In the AIA model the FTS derivative, F-FTS, showed higher...therapeutic efficacy compared to FTS. (iv) The functional genomics studies showed that FTS therapy inhibits the in vivo TH17 immune response. (v) FTS semi... Description shall include pertinent data and graphs in sufficient detail to explain any significant results achieved. A succinct description of the

Two dimensional Fourier transform methods for fringe pattern analysis

NASA Astrophysics Data System (ADS)

Sciammarella, C. A.; Bhat, G.

An overview of the use of FFTs for fringe pattern analysis is presented, with emphasis on fringe patterns containing displacement information. The techniques are illustrated via analysis of the displacement and strain distributions in the direction perpendicular to the loading, in a disk under diametral compression. The experimental strain distribution is compared to the theoretical, and the agreement is found to be excellent in regions where the elasticity solution models well the actual problem.

Simulation of RF-fields in a fusion device

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

De Witte, Dieter; Bogaert, Ignace; De Zutter, Daniel

2009-11-26

In this paper the problem of scattering off a fusion plasma is approached from the point of view of integral equations. Using the volume equivalence principle an integral equation is derived which describes the electromagnetic fields in a plasma. The equation is discretized with MoM using conforming basis functions. This reduces the problem to solving a dense matrix equation. This can be done iteratively. Each iteration can be sped up using FFTs.

Width effects in transonic flow over a rectangular cavity

DOE PAGES

Beresh, Steven J.; Wagner, Justin L.; Henfling, John F.; ...

2015-07-24

A previous experiment by the present authors studied the flow over a finite-width rectangular cavity at freestream Mach numbers 1.5–2.5. In addition, this investigation considered the influence of three-dimensional geometry that is not replicated by simplified cavities that extend across the entire wind-tunnel test section. The latter configurations have the attraction of easy optical access into the depths of the cavity, but they do not reproduce effects upon the turbulent structures and acoustic modes due to the length-to-width ratio, which is becoming recognized as an important parameter describing the nature of the flow within narrower cavities.

Influence of electrode width of interdigital transducer on third-order nonlinearity of surface acoustic wave devices on 42°YX-LiTaO3 substrate

NASA Astrophysics Data System (ADS)

Nakagawa, Ryo; Hashimoto, Ken-ya

2018-07-01

In this paper, we discuss the influence of the electrode width of an interdigital transducer on the third-order nonlinearity of surface acoustic wave (SAW) devices. First, an estimation technique of third-order nonlinear signals based on the linear finite element method is proposed, and the variation of nonlinear signal level with electrode width is estimated. Then, several one-port SAW resonators with different electrode widths are fabricated, and measured nonlinear signal levels are compared with simulation. As predicted by the numerical simulation, nonlinear signal levels became large with electrode width. However, harmonics takes a minimum at a certain electrode width. This tendency disagrees with the simulation. The variation of nonlinear coefficients is evaluated by numerical fitting for the measured data using the nonlinear signal simulator proposed by the authors. As the result, it is concluded that the generation mechanism is not limited to the acoustic strain in electrodes.

Effective Widths of Compression-Loaded Plates With a Cutout

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.

2000-01-01

A study of the effects of cutouts and laminate construction on the prebuckling and initial postbuckling stiffnesses, and the effective widths of compression-loaded, laminated-composite and aluminum square plates is presented. The effective-width concept is extended to plates with cutouts, and experimental and nonlinear finite-element analysis results are presented. Behavioral trends are compared for seven plate families and for cutout-diameter-to-plate-width ratios up to 0.66. A general compact design curve that can be used to present and compare the effective widths for a wide range of laminate constructions is also presented. A discussion of how the results can be used and extended to include certain types of damage, cracks, and other structural discontinuities or details is given. Several behavioral trends are described that initially appear to be nonintuitive. The results demonstrate a complex interaction between cutout size and plate orthotropy that affects the axial stiffness and effective width of a plate subjected to compression loads.

The principle of finiteness - a guideline for physical laws

NASA Astrophysics Data System (ADS)

Sternlieb, Abraham

2013-04-01

I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Flipping Freshman Mathematics

ERIC Educational Resources Information Center

Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

2015-01-01

Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

Hybrid VLSI/QCA Architecture for Computing FFTs

NASA Technical Reports Server (NTRS)

Fijany, Amir; Toomarian, Nikzad; Modarres, Katayoon; Spotnitz, Matthew

2003-01-01

A data-processor architecture that would incorporate elements of both conventional very-large-scale integrated (VLSI) circuitry and quantum-dot cellular automata (QCA) has been proposed to enable the highly parallel and systolic computation of fast Fourier transforms (FFTs). The proposed circuit would complement the QCA-based circuits described in several prior NASA Tech Briefs articles, namely Implementing Permutation Matrices by Use of Quantum Dots (NPO-20801), Vol. 25, No. 10 (October 2001), page 42; Compact Interconnection Networks Based on Quantum Dots (NPO-20855) Vol. 27, No. 1 (January 2003), page 32; and Bit-Serial Adder Based on Quantum Dots (NPO-20869), Vol. 27, No. 1 (January 2003), page 35. The cited prior articles described the limitations of very-large-scale integrated (VLSI) circuitry and the major potential advantage afforded by QCA. To recapitulate: In a VLSI circuit, signal paths that are required not to interact with each other must not cross in the same plane. In contrast, for reasons too complex to describe in the limited space available for this article, suitably designed and operated QCAbased signal paths that are required not to interact with each other can nevertheless be allowed to cross each other in the same plane without adverse effect. In principle, this characteristic could be exploited to design compact, coplanar, simple (relative to VLSI) QCA-based networks to implement complex, advanced interconnection schemes.

Books and monographs on finite element technology

NASA Technical Reports Server (NTRS)

Noor, A. K.

1985-01-01

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Validation of High Displacement Piezoelectric Actuator Finite Element Models

NASA Technical Reports Server (NTRS)

Taleghani, B. K.

2000-01-01

The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.

A mathematical model for describing the mechanical behaviour of root canal instruments.

PubMed

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

Exact solution of finite parabolic potential disc-like quantum dot with and without electric field R. Djelti, S. Bentata and Z. Aziz: Trimer barrier hight effect oh the nature of the electronic state of the superlatice GaAs/AlxGa1-xAs Bibhas K. Dutta and Prasanta K. Mahapatra: Study of velocity-dependent collision effects on Lamb dip and crossover resonances in three-level system

NASA Astrophysics Data System (ADS)

Hassanien, H. H.; Abdelmoly, S. S.; Elmeshad, N.

The exact series solutions of finite parabolic potential disc-like quantum dot are given in the absence and presence of uniform applied electric field. We define some normalized parameters. From the complex eigenenergy E=E0 - i G/2, due to the electric field, we calculate the resonance width G of a bounded state. The ground and the first excited state of the electron and the hole are obtained with and without the electric field. The corresponding envelope functions are presented as a function of the disc dimensionality, radius R and half-width L.

Estimation of Stress Concentration Factor of Plate with Hole using Piezoelectric Actuator and Finite Element Method

NASA Astrophysics Data System (ADS)

Abuzaid, A.; Hrairi, M.; Shaik Dawood, M. S. I.

2017-03-01

In this paper, the effect of piezoelectric actuators placed above a circular hole of a rectangular plate subjected to uniform uniaxial tension is studied. The core idea is to investigate the stress (compression/tension) produced by the piezoelectric actuators on the stress distribution around the hole and along the width of the host plate. For this purpose, Finite Element Analysis (FEA) was carried out through parametric study in ANSYS software. The results demonstrated that the positive electric field would decrease and change the state of the stress distribution along the width of the host plate in contrast to the negative applied electric filed which increases the stress distribution smoothly without affecting its behaviour. The results also indicated that the reduction of the stress concentration factor increases with the decrease of the ratio (D/W) for the same applied positive electric field.

Finite element analysis of a composite crash box subjected to low velocity impact

NASA Astrophysics Data System (ADS)

Shaik Dawood, M. S. I.; Ghazilan, A. L. Ahmad; Shah, Q. H.

2017-03-01

In this work, finite element analyses using LS-DYNA had been carried out to investigate the energy absorption capability of a composite crash box. The analysed design incorporates grooves to the cross sectional shape and E-Glass/Epoxy as design material. The effects of groove depth, ridge lines, plane width, material properties, wall thickness and fibre orientation had been quantitatively analysed and found to significantly enhance the energy absorption capability of the crash box.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

NASA Astrophysics Data System (ADS)

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

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance

NASA Astrophysics Data System (ADS)

Rosestolato, M.; Święch, A.

2017-02-01

We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Revisiting NMR composite pulses for broadband 2H excitation

PubMed Central

Shen, Ming; Roopchand, Rabia; Mananga, Eugene S.; Amoureux, Jean-Paul; Chen, Qun; Boutis, Gregory S.; Hu, Bingwen

2014-01-01

Quadrupolar echo NMR spectroscopy of static solids often requires RF excitation that covers spectral widths exceeding 100 kHz, which is difficult to obtain due to instrumental limitations. In this work we revisit four well-known composite pulses (COM-I, II, III and IV) for broadband excitation in deuterium quadrupolar echo spectroscopy. These composite pulses are combined with several phase cycling schemes that were previously shown to decrease finite pulse width distortions in deuterium solid-echo experiments performed with two single pulses. The simulations and experiments show that COM-II and IV composite pulses combined with an 8-step phase cycling aid in achieving broadband excitation with limited pulse width distortions. PMID:25583576

Understanding quantum phenomena without solving the Schrödinger equation: the case of the finite square well

NASA Astrophysics Data System (ADS)

Barsan, Victor

2015-11-01

An approximate formula for the energy levels of the bound states of a particle in a finite square well are obtained, without using the Schrödinger equation. The physics and mathematics involved in this approach are accessible to a gifted high school student.

Addressable-Matrix Integrated-Circuit Test Structure

NASA Technical Reports Server (NTRS)

Sayah, Hoshyar R.; Buehler, Martin G.

1991-01-01

Method of quality control based on use of row- and column-addressable test structure speeds collection of data on widths of resistor lines and coverage of steps in integrated circuits. By use of straightforward mathematical model, line widths and step coverages deduced from measurements of electrical resistances in each of various combinations of lines, steps, and bridges addressable in test structure. Intended for use in evaluating processes and equipment used in manufacture of application-specific integrated circuits.

Cracking and debonding of a thin fiber reinforced concrete overlay.

DOT National Transportation Integrated Search

2017-04-01

Previous field studies suggested that macro-fibers incorporated in thin overlay pavements will result in reduced crack opening widths, vertical deflections, and debonding rates compared to that of unreinforced overlays. A simple finite element (FE) m...

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Liou, Meng-Sing; Van Leer, Bram

1989-01-01

The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.

R A Fisher, design theory, and the Indian connection.

PubMed

Rau, A R P

2009-09-01

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.

Three-Dimensional Nonlinear Finite Element Analysis and Microcomputed Tomography Evaluation of Microgap Formation in a Dental Implant Under Oblique Loading.

PubMed

Jörn, Daniela; Kohorst, Philipp; Besdo, Silke; Borchers, Lothar; Stiesch, Meike

2016-01-01

Since bacterial leakage along the implant-abutment interface may be responsible for peri-implant infections, a realistic estimation of the interface gap width during function is important for risk assessment. The purpose of this study was to compare two methods for investigating microgap formation in a loaded dental implant, namely, microcomputed tomography (micro-CT) and three-dimensional (3D) nonlinear finite element analysis (FEA); additionally, stresses to be expected during loading were also evaluated by FEA. An implant-abutment complex was inspected for microgaps between the abutment and implant in a micro-CT scanner under an oblique load of 200 N. A numerical model of the situation was constructed; boundary conditions and external load were defined according to the experiment. The model was refined stepwise until its load-displacement behavior corresponded sufficiently to data from previous load experiments. FEA of the final, validated model was used to determine microgap widths. These were compared with the widths as measured in micro-CT inspection. Finally, stress distributions were evaluated in selected regions. No microgaps wider than 13 μm could be detected by micro-CT for the loaded implant. FEA revealed gap widths up to 10 μm between the implant and abutment at the side of load application. Furthermore, FEA predicted plastic deformation in a limited area at the implant collar. FEA proved to be an adequate method for studying microgap formation in dental implant-abutment complexes. FEA is not limited in gap width resolution as are radiologic techniques and can also provide insight into stress distributions within the loaded complex.

The effect of anisotropic heat transport on magnetic islands in 3-D configurations

NASA Astrophysics Data System (ADS)

Schlutt, M. G.; Hegna, C. C.

2012-08-01

An analytic theory of nonlinear pressure-induced magnetic island formation using a boundary layer analysis is presented. This theory extends previous work by including the effects of finite parallel heat transport and is applicable to general three dimensional magnetic configurations. In this work, particular attention is paid to the role of finite parallel heat conduction in the context of pressure-induced island physics. It is found that localized currents that require self-consistent deformation of the pressure profile, such as resistive interchange and bootstrap currents, are attenuated by finite parallel heat conduction when the magnetic islands are sufficiently small. However, these anisotropic effects do not change saturated island widths caused by Pfirsch-Schlüter current effects. Implications for finite pressure-induced island healing are discussed.

Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles

ERIC Educational Resources Information Center

Cigas, John; Hsin, Wen-Jung

2005-01-01

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…

Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming

ERIC Educational Resources Information Center

Gurski, Katharine F.

2009-01-01

We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…

Variational and WKB Descriptions of Laterally Localized Eigenmodes in Non-Collinear Optical Parametric Amplifiers

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

Afeyan, Bedros; Charbonneau-Lefort, Mathieu; Fejer, Martin

With a finite lateral width pump, non-collinear interactions result in metastable or stable laterally localized bound states. The physical processes involved are group velocity walk-off, diffraction, chirped QPM gratings and different pump shapes.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

DOT National Transportation Integrated Search

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Stimulus-Response Theory of Finite Automata, Technical Report No. 133.

ERIC Educational Resources Information Center

Suppes, Patrick

The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device…

The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers.

ERIC Educational Resources Information Center

Tsamir, Pessia

1999-01-01

Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…

The p-Version of the Finite Element Method for Domains with Corners and for Infinite Domains

DTIC Science & Technology

1988-11-01

Finite Element Method, Prenticw-Hall, 1973. [24] Szabo, B. A. :PROBE : The Theoretical Manual(Release 1.0), Noetic Tech. Cor. St Louis, MO., 1985...National Bureau of Standards. " To be an international center of study and research for foreign students in numerical mathematics who are supported by

What Diagrams Argue in Late Imperial Chinese Combinatorial Texts.

PubMed

Bréard, Andrea

2015-01-01

Attitudes towards diagrammatic reasoning and visualization in mathematics were seldom spelled out in texts from pre-modern China, although illustrations figure prominently in mathematical literature since the eleventh century. Taking the sums of finite series and their combinatorial interpretation as a case study, this article investigates the epistemological function of illustrations from the eleventh to the nineteenth century that encode either the mathematical objects themselves or represent their related algorithms. It particularly focuses on the two illustrations given in Wang Lai's (1768-1813) Mathematical Principles of Sequential Combinations, arguing that they reflect a specific mode of nineteenth-century mathematical argumentative practice and served as a heuristic model for later authors.

Model Of Bearing With Hydrostatic Damper

NASA Technical Reports Server (NTRS)

Goggin, David G.

1991-01-01

Improved mathematical model of rotational and vibrational dynamics of bearing package in turbopump incorporates effects of hydrostatic damper. Part of larger finite-element model representing rotational and vibrational dynamics of rotor and housing of pump. Includes representations of deadband and nonlinear stiffness and damping of ball bearings, nonlinear stiffness and damping of hydrostatic film, and stiffness of bearing support. Enables incorporation of effects of hydrostatic damper into overall rotor-dynamic mathematical model without addition of mathematical submodel of major substructure.

Towards a unified solution of localization failure with mixed finite elements

NASA Astrophysics Data System (ADS)

Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas

2015-04-01

Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. As a fundamental enhancement of the displacement-pressure formulation above mentioned, this kind of formulation benefits of the following advantages: it provides enhanced rate of convergence for the strain (and stress) and it is able to deal with incompressible situations. The method is completed with constitutive laws from Von Mises and Drucker-Prager local plasticity models with nonlinear strain softening. Moreover, global and local error norms are discussed to support the advantages of the proposed method. Then, numerical examples of stability analysis of slopes are presented to demonstrate the capability of the method. It will be shown that not only soil slopes can be modeled but also snow avalanche release and their weak layer fracture can be similarly treated. Consequently, this formulation appears to be a general and accurate tool for the solution of mechanical problem involving failure with localization bands [3,4]. References [1] Y.R. Rashid, 'Ultimate strength analysis of prestressed concrete pressure vessels', Nuclear Engineering and Design, Volume 7, Issue 4, April, Pages 334-344, 1968. [2] M. Cervera, M. Chiumenti, D. Di Capua. 'Benchmarking on bifurcation and localization in J 2 plasticity for plane stress and plane strain conditions.' Computer Methods in Applied Mechanics and Engineering, Vol. 241-244, Pages 206-224, 2012. [3] L. Benedetti, M. Cervera, M. Chiumenti. 'Stress-accurate mixed FEM for soil failure under shallow foundations involving strain localization in plasticity' Computers and Geotechnics, Vol. 64, pp. 32-47, 2015. [4] Cervera, M., Chiumenti, M., Benedetti, L., Codina, R. 'Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity' Computer Methods in Applied Mechanics and Engineering, to appear, 2015.

On size and geometry effects on the brittle fracture of ferritic and tempered martensitic steels

NASA Astrophysics Data System (ADS)

Odette, G. R.; Chao, B. L.; Lucas, G. E.

1992-09-01

A finite element computation of nonsingular crack tip fields was combined with a weakest link statistics model of cleavage fracture. Model predictions for three point bend specimens with various widths and crack depth to width ratios are qualitatively consistent with a number of trends observed in a 12 Cr martensitic stainless steel. The toughness “benefits” of small sizes and shallow cracks are primarily reflected in strain limits rather than net section stress capacities, which is significant to fusion structures subject to large secondary stresses.

Calibration approach for fluorescence lifetime determination for applications using time-gated detection and finite pulse width excitation.

PubMed

Keller, Scott B; Dudley, Jonathan A; Binzel, Katherine; Jasensky, Joshua; de Pedro, Hector Michael; Frey, Eric W; Urayama, Paul

2008-10-15

Time-gated techniques are useful for the rapid sampling of excited-state (fluorescence) emission decays in the time domain. Gated detectors coupled with bright, economical, nanosecond-pulsed light sources like flashlamps and nitrogen lasers are an attractive combination for bioanalytical and biomedical applications. Here we present a calibration approach for lifetime determination that is noniterative and that does not assume a negligible instrument response function (i.e., a negligible excitation pulse width) as does most current rapid lifetime determination approaches. Analogous to a transducer-based sensor, signals from fluorophores of known lifetime (0.5-12 ns) serve as calibration references. A fast avalanche photodiode and a GHz-bandwidth digital oscilloscope is used to detect transient emission from reference samples excited using a nitrogen laser. We find that the normalized time-integrated emission signal is proportional to the lifetime, which can be determined with good reproducibility (typically <100 ps) even for data with poor signal-to-noise ratios ( approximately 20). Results are in good agreement with simulations. Additionally, a new time-gating scheme for fluorescence lifetime imaging applications is proposed. In conclusion, a calibration-based approach is a valuable analysis tool for the rapid determination of lifetime in applications using time-gated detection and finite pulse width excitation.

Validation of the Two-Parameter-Fracture Criterion for Various Crack Configurations Made of 2014-T6 (TL) Aluminum Alloy Using Finite Element Fracture Simulations

NASA Astrophysics Data System (ADS)

McQuilkin, Martin

The Two-Parameter- Fracture-Criterion (TPFC) was validated using an elastic-plastic two-dimensional (2D) finite-element code, ZIP2D, with the plane-strain- core concept. Fracture simulations were performed on three crack configurations: (1) middle-crack-tension, M(T), (2) single-edge- crack-tension, SE(T), and (3) single-edge crack-bend, SE(B), specimens. They were made of 2014-T6 (TL) aluminum alloy. Fracture test data from Thomas Orange work (NASA) were only available on M(T) specimens (one-half width, w = 1.5 to 6 in.) and they were all tested at cryogenic (-320 o F) temperature. All crack configurations were analysed over a very wide range of widths (w = 0.75 to 24 in.) and crack-length- to-width ratios ranged from 0.2 to 0.8. The TPFC was shown to fit the simulated fracture data fairly well (within 6.5%) for all crack configurations for net-section stresses less than the material proportional limit. For M(T) specimens, a simple approximation was shown to work well for net-section stresses greater than the proportional limit. Further study is needed for net-section stresses greater than the proportional limit for the SE(T) and SE(B) specimens.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

[Mathematical models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

Analysis of dual-frequency MEMS antenna using H-MRTD method

NASA Astrophysics Data System (ADS)

Yu, Wenge; Zhong, Xianxin; Chen, Yu; Wu, Zhengzhong

2004-10-01

For applying micro/nano technologies and Micro-Electro-Mechanical System (MEMS) technologies in the Radio Frequency (RF) field to manufacture miniature microstrip antennas. A novel MEMS dual-band patch antenna designed using slot-loaded and short-circuited size-reduction techniques is presented in this paper. By controlling the short-plane width, the two resonant frequencies, f10 and f30, can be significantly reduced and the frequency ratio (f30/f10) is tunable in the range 1.7~2.3. The Haar-Wavelet-Based multiresolution time domain (H-MRTD) with compactly supported scaling function for a full three-dimensional (3-D) wave to Yee's staggered cell is used for modeling and analyzing the antenna for the first time. Associated with practical model, an uniaxial perfectly matched layer (UPML) absorbing boundary conditions was developed, In addition , extending the mathematical formulae to an inhomogenous media. Numerical simulation results are compared with those using the conventional 3-D finite-difference time-domain (FDTD) method and measured. It has been demonstrated that, with this technique, space discretization with only a few cells per wavelength gives accurate results, leading to a reduction of both memory requirement and computation time.

FINITE-STATE APPROXIMATIONS TO DENUMERABLE-STATE DYNAMIC PROGRAMS,

DTIC Science & Technology

AIR FORCE OPERATIONS, LOGISTICS), (*INVENTORY CONTROL, DYNAMIC PROGRAMMING), (*DYNAMIC PROGRAMMING, APPROXIMATION(MATHEMATICS)), INVENTORY CONTROL, DECISION MAKING, STOCHASTIC PROCESSES, GAME THEORY, ALGORITHMS, CONVERGENCE

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Comments on "Drill-string horizontal dynamics with uncertainty on the frictional force" by T.G. Ritto, M.R. Escalante, Rubens Sampaio, M.B. Rosales [J. Sound Vib. 332 (2013) 145-153

NASA Astrophysics Data System (ADS)

Li, Zifeng

2016-12-01

This paper analyzes the mechanical and mathematical models in "Ritto et al. (2013) [1]". The results are that: (1) the mechanical model is obviously incorrect; (2) the mathematical model is not complete; (3) the differential equation is obviously incorrect; (4) the finite element equation is obviously not discretized from the corresponding mathematical model above, and is obviously incorrect. A mathematical model of dynamics should include the differential equations, the boundary conditions and the initial conditions.

An Application of Mathematical Groups to Structures of Human Groups. Applications of Finite Mathematics to Anthropology and Sociology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 476.

ERIC Educational Resources Information Center

Carlson, Roger

This module is designed for students with a high school algebra background. The goal is to present the elements of the group idea, primarily by way of a geometric model, and to see its application to the study of kinship relations within certain human groups. The material opens with a presentation of clans in a hypothetical society in an early…

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

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

Oler, Kiri J.; Miller, Carl H.

In this paper, we present a methodology for reverse engineering integrated circuits, including a mathematical verification of a scalable algorithm used to generate minimal finite state machine representations of integrated circuits.

Solving cross-disciplinary problems by mathematical modelling

NASA Astrophysics Data System (ADS)

Panfilov, D. A.; Romanchikov, V. V.; Krupin, K. N.

2018-03-01

The article deals with the creation of a human tibia 3D model by means of “Autodesk Revit-2016” PC based on tomogram data. The model was imported into “Lira- SAPR2013 R4” software system. To assess the possibility of education and the nature of bone fracture (and their visualization), the Finite Element Analysis (FEA) method was used. The geometric parameters of the BBK model corresponded to the physical parameters of the individual. The compact plate different thickness is modeled by rigidity properties of the finite elements in accordance with the parameters on the roentgenogram. The BBK model included parameters of the outer compact plate and the spongy substance having a more developed structure of the epiphysic region. In the “Lira-SAPR2013 R4” software system, mathematical modeling of the traumatic effect was carried out and the analysis of the stress-strain state of the finite element model of the tibia was made to assess fracture conditions.

Finite-element modeling and micromagnetic modeling of perpendicular writers

NASA Astrophysics Data System (ADS)

Heinonen, Olle; Bozeman, Steven P.

2006-04-01

We compare finite-element modeling (FEM) and fully micromagnetic modeling results of four prototypical writers for perpendicular recording. In general, the agreement between the two models is quite good in the vicinity of saturated or near-saturated magnetic material, such as the pole tip, for quantities such as the magnetic field, the gradient of the magnetic field and the write width. However, in the vicinity of magnetic material far from saturation, e.g., return pole or trailing edge write shield, there can be large qualitative and quantitative differences.

Structural properties and magic structures in hydrogenated finite and infinite silicon nanowires

NASA Astrophysics Data System (ADS)

Zdetsis, A. D.; Koukaras, E. N.; Garoufalis, C. S.

2007-11-01

Unusual effects such as bending and "canting," related with the stability, have been identified by ab initio real-space calculations for hydrogenated silicon nanowires. We have examined in detail the electronic and structural properties of finite and infinite nanowires as a function of length (and width) and have developed stability and bending rules, demonstrating that "magic" wires do not bend. Reconstructed 2×1 nanowires are practically as stable as the magic ones. Our calculations are in good agreement with the experimental data of Ma et al. [Science 299, 1874 (2003).].

Modeling and design optimization of adhesion between surfaces at the microscale.

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

Sylves, Kevin T.

2008-08-01

This research applies design optimization techniques to structures in adhesive contact where the dominant adhesive mechanism is the van der Waals force. Interface finite elements are developed for domains discretized by beam elements, quadrilateral elements or triangular shell elements. Example analysis problems comparing finite element results to analytical solutions are presented. These examples are then optimized, where the objective is matching a force-displacement relationship and the optimization variables are the interface element energy of adhesion or the width of beam elements in the structure. Several parameter studies are conducted and discussed.

Hybrid transfer-matrix FDTD method for layered periodic structures.

PubMed

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

2009-03-15

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

Mathematical simulation of convective-radiative heat transfer in a ventilated rectangular cavity with consideration of internal mass transfer

NASA Astrophysics Data System (ADS)

Sheremet, M. A.; Shishkin, N. I.

2012-07-01

Mathematical simulation of the nonstationary regimes of heat-and-mass transfer in a ventilated rectangular cavity with heat-conducting walls of finite thickness in the presence of a heat-generating element of constant temperature has been carried out with account for the radiative heat transfer in the Rosseland approximation. As mechanisms of energy transfer in this cavity, the combined convection and the thermal radiation in the gas space of the cavity and the heat conduction in the elements of its fencing solid shell were considered. The mathematical model formulated in the dimensionless stream function-vorticity vector-temperature-concentration variables was realized numerically with the use of the finite-difference method. The streamline, temperature-field, and concentration distributions reflecting the influence of the Rayleigh number (Ra = 104, 105, 106), the nonstationarity (0 < τ ≤ 1000), and the optical thickness of the medium (τλ = 50, 100, 200) on the regimes of the gas flow and the heat-and-mass transfer in the cavity have been obtained.

The study of heat penetration of kimchi soup on stationary and rotary retorts.

PubMed

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-03-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F 0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F 0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R(2)=0.975). The changes in nodal temperature and F 0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%.

The Study of Heat Penetration of Kimchi Soup on Stationary and Rotary Retorts

PubMed Central

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-01-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R2=0.975). The changes in nodal temperature and F0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%. PMID:25866751

Modelling of subarachnoid space width changes in apnoea resulting as a function of blood flow parameters.

PubMed

Kalicka, Renata; Mazur, Kamila; Wolf, Jacek; Frydrychowski, Andrzej F; Narkiewicz, Krzysztof; Winklewski, Pawel J

2017-09-01

During apnoea, the pial artery is subjected to two opposite physiological processes: vasoconstriction due to elevated blood pressure and vasorelaxation driven by rising pH in the brain parenchyma. We hypothesized that the pial artery response to apnoea may vary, depending on which process dominate. Apnoea experiments were performed in a group of 19 healthy, non-smoking volunteers (9 men and 10 women). The following parameters were obtained for further analysis: blood pressure, the cardiac (from 0.5 to 5.0Hz) and slow (<0.5Hz) components of subarachnoid space width, heart rate, mean cerebral blood flow velocity in the internal carotid artery, pulsatility and resistivity index, internal carotid artery diameter, blood oxygen saturation and end-tidal carbon dioxide. The experiment consisted of three apnoeas, sequentially: 30s, 60s and maximal apnoea. The breath-hold was separated for 5minute rest. The control process is sophisticated, involving internal cross-couplings and cross-dependences. The aim of work was to find a mathematical dependence between data. Unexpectedly, the modelling revealed two different reactions, on the same experimental procedure. As a consequence, there are two subsets of cardiac subarachnoid space width responses to breath-hold in humans. A positive cardiac subarachnoid space width change to apnoea depends on changes in heart rate and cerebral blood flow velocity. A negative cardiac subarachnoid space width change to apnoea is driven by heart rate, mean arterial pressure and pulsatility index changes. The described above two different reactions to experimental breath-hold provides new insights into our understanding of the complex mechanisms governing the adaptation to apnoea in humans. We proposed a mathematical methodology that can be used in further clinical research. Copyright © 2017 Elsevier Inc. All rights reserved.

Laser Cutting of Multilayered Kevlar Plates

NASA Astrophysics Data System (ADS)

Yilbas, B. S.; Al-Sulaiman, F.; Karakas, C.; Ahsan, M.

2007-12-01

Laser cutting of Kevlar plates, consisting of multilayered laminates, with different thicknesses are carried out. A mathematical model is developed to predict the kerf width, thermal efficiency, and specific energy requirements during cutting. Optical microscopy and Scanning Electron Microscopy (SEM) are employed to obtain the micrographs of the cutting sections. The kerf width size is measured and compared with the predictions. A factorial analysis is carried out to assess the affecting parameters on the mean kerf width and dimensionless damage sizes. It is found that the kerf width and damage sizes changes sharply when increasing cutting speed from 0.03 to 0.08 m/s. Thermal efficiency of the cutting process increases with increasing thickness and cutting speed while specific energy reduces with increasing thickness. The main effects of cutting parameters are found to be significant on the mean kerf width and dimensionless damage sizes, which is more pronounced for the workpiece bottom surface, where locally distributed char formation and sideways burning are observed.

Slow light effect analysis excited by plasmon-induced transparency in metal-dielectric-metal waveguide

NASA Astrophysics Data System (ADS)

Jin, Gui; Huang, Xiaoyi

2018-02-01

We propose and demonstrate a metal-dielectric-metal(MDM) waveguide side coupled with two stubs to realize plasmon induced transparency (PIT) effect. The dispersion relation of the structure has been plotted by solving the dispersion equation of MDM three layer structure, the transmission spectrum is investigated by coupled mode theory (CMT) and Finite Element Method (FEM) simulation, the CMT results can. The surface plasmon device can also be used as a EIT-like filter with a variable full width of half-maximum (FWHM) and highest transmission over 88%. The maximum group index ng is 42 with a group velocity of 0.023ܿ and transmission of 48%, The normalized delay-bandwidth product (NDBP) can be modulated through changing the gap width of resonators and waveguide bus, the highest is 0.641 at gap width 10 nm, and lowest is 0.246 at 30 nm. The dispersion of group velocity (GVD) changes drastically at narrow gap width and becomes more and more flat at broader gap width, this opens up an avenue for designing optical buffers, switches and modulators.

Well-behaved dynamics in a dissipative nonideal periodically kicked rotator.

PubMed

Chacón, R; Martínez García-Hoz, A

2003-12-01

Well-behaved dynamical properties are found in a dissipative kicked rotator subjected to a periodic string of asymmetric pulses of finite amplitude and width. The stability boundaries of the equilibrium are determined to arbitrary approximation for trigonometric pulses by means of circular harmonic balance, and to first approximation for general elliptic pulses by means of an elliptic harmonic balance method. The bifurcation behavior at the stability boundaries is determined numerically. We show how the extension of the instability region of the equilibrium in pulse parameter space reaches a maximum as the pulse width is varied. We also characterize the dependence of the mean duration of the transients to the equilibrium on the pulse width. The evolution of the basins of attraction of chaotic attractors when solely the pulse width is varied is characterized numerically. Finally, we show that the order-chaos route when solely the width of the pulses is altered appears to be especially rich, including different types of crises. The mechanism underlying these reshaping-induced crises is discussed with the aid of a two-dimensional map.

Pulsatile Hormonal Signaling to Extracellular Signal-regulated Kinase

PubMed Central

Perrett, Rebecca M.; Voliotis, Margaritis; Armstrong, Stephen P.; Fowkes, Robert C.; Pope, George R.; Tsaneva-Atanasova, Krasimira; McArdle, Craig A.

2014-01-01

Gonadotropin-releasing hormone (GnRH) is secreted in brief pulses that stimulate synthesis and secretion of pituitary gonadotropin hormones and thereby mediate control of reproduction. It acts via G-protein-coupled receptors to stimulate effectors, including ERK. Information could be encoded in GnRH pulse frequency, width, amplitude, or other features of pulse shape, but the relative importance of these features is unknown. Here we examine this using automated fluorescence microscopy and mathematical modeling, focusing on ERK signaling. The simplest scenario is one in which the system is linear, and response dynamics are relatively fast (compared with the signal dynamics). In this case integrated system output (ERK activation or ERK-driven transcription) will be roughly proportional to integrated input, but we find that this is not the case. Notably, we find that relatively slow response kinetics lead to ERK activity beyond the GnRH pulse, and this reduces sensitivity to pulse width. More generally, we show that the slowing of response kinetics through the signaling cascade creates a system that is robust to pulse width. We, therefore, show how various levels of response kinetics synergize to dictate system sensitivity to different features of pulsatile hormone input. We reveal the mathematical and biochemical basis of a dynamic GnRH signaling system that is robust to changes in pulse amplitude and width but is sensitive to changes in receptor occupancy and frequency, precisely the features that are tightly regulated and exploited to exert physiological control in vivo. PMID:24482225

Analysis of Age-Related Changes in Asian Facial Skeletons Using 3D Vector Mathematics on Picture Archiving and Communication System Computed Tomography.

PubMed

Kim, Soo Jin; Kim, So Jung; Park, Jee Soo; Byun, Sung Wan; Bae, Jung Ho

2015-09-01

There are marked differences in facial skeletal characteristics between Asian and Caucasian. However, ethnic differences in age-related facial skeletal changes have not yet been fully established. The aims of this study were to evaluate age-related changes in Asian midfacial skeletons and to explore ethnic differences in facial skeletal structures with aging between Caucasian and Asian. The study included 108 men (aged 20-79 years) and 115 women (aged 20-81 years). Axial CT images with a gantry tilt angle of 0 were analyzed. We measured three-dimensional (3D) coordinates at each point with a pixel lens cursor in a picture archiving and communication system (PACS), and angles and widths between the points were calculated using 3D vector mathematics. We analyzed angular changes in 4 bony regions, including the glabellar, orbital, maxillary, and pyriform aperture regions, and changes in the orbital aperture width (distance from the posterior lacrimal crest to the frontozygomatic suture) and the pyriform width (between both upper margins of the pyriform aperture). All 4 midfacial angles in females and glabellar and maxillary angles in males showed statistically significant decreases with aging. On the other hand, the orbital and pyriform widths did not show statistically significant changes with aging. The results of this study suggest that Asian midfacial skeletons may change continuously throughout life, and that there may be significant differences in the midfacial skeleton between both sexes and between ethnic groups.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

Electronic thermometry in tunable tunnel junction

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

Maksymovych, Petro

A tunable tunnel junction thermometry circuit includes a variable width tunnel junction between a test object and a probe. The junction width is varied and a change in thermovoltage across the junction with respect to the change in distance across the junction is determined. Also, a change in biased current with respect to a change in distance across the junction is determined. A temperature gradient across the junction is determined based on a mathematical relationship between the temperature gradient, the change in thermovoltage with respect to distance and the change in biased current with respect to distance. Thermovoltage may bemore » measured by nullifying a thermoelectric tunneling current with an applied voltage supply level. A piezoelectric actuator may modulate the probe, and thus the junction width, to vary thermovoltage and biased current across the junction. Lock-in amplifiers measure the derivatives of the thermovoltage and biased current modulated by varying junction width.« less

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Mathematical analysis on the cosets of subgroup in the group of E-convex sets

NASA Astrophysics Data System (ADS)

Abbas, Nada Mohammed; Ajeena, Ruma Kareem K.

2018-05-01

In this work, analyzing the cosets of the subgroup in the group of L – convex sets is presented as a new and powerful tool in the topics of the convex analysis and abstract algebra. On L – convex sets, the properties of these cosets are proved mathematically. Most important theorem on a finite group of L – convex sets theory which is the Lagrange’s Theorem has been proved. As well as, the mathematical proof of the quotient group of L – convex sets is presented.

Specialized Silicon Compilers for Language Recognition.

DTIC Science & Technology

1984-07-01

realizations of non-deterministic automata have been reported that solve these problems in diffierent ways. Floyd and Ullman [ 281 have presented a...in Applied Mathematics, pages 19-31. American Mathematical Society, 1967. [ 281 Floyd, R. W. and J. D. Ullman. The Compilation of Regular Expressions...Shannon (editor). Automata Studies, chapter 1, pages 3-41. Princeton University Press, Princeton. N. J., 1956. [44] Kohavi, Zwi . Switching and Finite

Quantum mechanics on periodic and non-periodic lattices and almost unitary Schwinger operators

NASA Astrophysics Data System (ADS)

Arik, Metin; Ildes, Medine

2018-05-01

In this work, we uncover the mathematical structure of the Schwinger algebra and introduce almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations between these algebras and show that the almost unitary Schwinger operators are equivalent to the Schwinger algebra. We introduce new representations for MN(C) in terms of these algebras.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Stretch-dependent changes in surface profiles of the human crystalline lens during accommodation: a finite element study.

PubMed

Pour, Hooman Mohammad; Kanapathipillai, Sangarapillai; Zarrabi, Khosrow; Manns, Fabrice; Ho, Arthur

2015-03-01

A non-linear isotropic finite element (FE) model of a 29-year-old human crystalline lens was constructed to study the effects of various geometrical parameters on lens accommodation. The model simulates dis-accommodation by stretching of the lens and predicts the change in surface profiles of the lens capsule, cortex and nucleus at select states of stretching/accommodation. Multiple regression analysis (MRA) is used to develop a stretch-dependent mathematical model relating the lens sagittal height to the radial position of the lens surface as a function of dis-accommodative stretch. A load analysis is performed to compare the finite element results to empirical results from lens stretcher studies. Using the predicted geometrical changes, the optical response of the whole eye during accommodation was analysed by ray-tracing. Aspects of lens shape change relative to stretch were evaluated, including change in diameter, central thickness and accommodation. Maximum accommodation achieved was 10.29 D. From the multiple regression analysis, the stretch-dependent mathematical model of the lens shape related lens curvatures as a function of lens ciliary stretch well (maximum mean-square residual error 2.5 × 10(-3 ) μm, p < 0.001). The results are compared with those from in vitro studies. The finite element and ray-tracing predictions are consistent with Ex Vivo Accommodation Simulator (EVAS) studies in terms of load and power change versus change in thickness. The mathematical stretch-dependent model of accommodation presented may have utility in investigating lens behaviour at states other than the relaxed or fully accommodated states. © 2015 The Authors. Clinical and Experimental Optometry © 2015 Optometry Australia.

Band gap engineering in finite elongated graphene nanoribbon heterojunctions: Tight-binding model

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

Tayo, Benjamin O.

2015-08-15

A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width W{sub L}, the middle part is a GNR of width W{sub M}, and the right part is a GNR of width W{sub R}. We assume that the left and right parts of the GNR heterojunction interactmore » with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which W{sub L} = W{sub R}, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely.« less

Intrinsic line shape of electromagnetic radiation from a stack of intrinsic Josephson junctions synchronized by an internal cavity resonance

NASA Astrophysics Data System (ADS)

Koshelev, Alexei

2013-03-01

Stacks of intrinsic Josephson-junctions are realized in mesas fabricated out of layered superconducting single crystals, such as Bi2Sr2CaCu2O8 (BSCCO). Synchronization of phase oscillations in different junctions can be facilitated by the coupling to the internal cavity mode leading to powerful and coherent electromagnetic radiation in the terahertz frequency range. An important characteristic of this radiation is the shape of the emission line. A finite line width appears due to different noise sources leading to phase diffusion. We investigated the intrinsic line shape caused by the thermal noise for a mesa fabricated on the top of a BSCCO single crystal. In the ideal case of fully synchronized stack the finite line width is coming from two main contributions, the quasiparticle-current noise inside the mesa and the fluctuating radiation in the base crystal. We compute both contributions and conclude that for realistic mesa's parameters the second mechanism typically dominates. The role of the cavity quality factor in the emission line spectrum is clarified. Analytical results were verified by numerical simulations. In real mesa structures part of the stack may not be synchronized and chaotic dynamics of unsynchronized junctions may determine the real line width. Work supported by UChicago Argonne, LLC, under contract No. DE-AC02-06CH11357.

Propagation of a finite bubble in a Hele-Shaw channel of variable depth

NASA Astrophysics Data System (ADS)

Juel, Anne; Franco-Gomez, Andres; Thompson, Alice; Hazel, Andrew

2017-11-01

We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred rail is introduced to provide a small axially-uniform depth constriction. We demonstrate experimentally that this channel geometry can be used as a passive sorting device. Single air bubbles carried within silicone oil are generally transported on one side of the rail. However, for flow rates marginally larger than a critical value, a narrow band of bubble sizes on the order of the rail width can propagate over the rail, while bubbles of other sizes segregate to the side of the rail. The width of this band of bubble sizes increases with flow rate and the size of the most stable bubble can be tuned by varying the rail width. We present a depth-averaged theory which reveals that the mechanism relies on a non-trivial interaction between capillary and viscous forces that is fully dynamic, rather than being a simple modification of capillary static solutions. In contrast, for larger bubbles and sufficiently large imposed flow rates, we find that initially centred bubbles do not converge onto a steady mode of propagation. Instead they transiently explore weakly unstable steady modes, an evolution which results in their break-up and eventual settling into a steady state of changed topology. The financial support of CONICYT and the Leverhulme Trust are gratefully acknowledged.

Synchrotron radiation-based quasi-elastic scattering using time-domain interferometry with multi-line gamma rays.

PubMed

Saito, Makina; Masuda, Ryo; Yoda, Yoshitaka; Seto, Makoto

2017-10-02

We developed a multi-line time-domain interferometry (TDI) system using 14.4 keV Mössbauer gamma rays with natural energy widths of 4.66 neV from 57 Fe nuclei excited using synchrotron radiation. Electron density fluctuations can be detected at unique lengths ranging from 0.1 nm to a few nm on time scales from several nanoseconds to the sub-microsecond order by quasi-elastic gamma-ray scattering (QGS) experiments using multi-line TDI. In this report, we generalize the established expression for a time spectrum measured using an identical single-line gamma-ray emitter pair to the case of a nonidentical pair of multi-line gamma-ray emitters by considering the finite energy width of the incident synchrotron radiation. The expression obtained illustrates the unique characteristics of multi-line TDI systems, where the finite incident energy width and use of a nonidentical emitter pair produces further information on faster sub-picosecond-scale dynamics in addition to the nanosecond dynamics; this was demonstrated experimentally. A normalized intermediate scattering function was extracted from the spectrum and its relaxation form was determined for a relaxation time of the order of 1 μs, even for relatively large momentum transfer of ~31 nm -1 . The multi-line TDI method produces a microscopic relaxation picture more rapidly and accurately than conventional single-line TDI.

A New Principle in Physiscs: the Principle "Finiteness", and Some Consequences

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

Abraham Sternlieb

2010-06-25

In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of "legitimate" laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory ormore » principle in physics. I propose "finiteness" as a postulate (like the constancy of the speed of light in vacuum, "c"), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.« less

A mathematical model of diffusion from a steady source of short duration in a finite mixing layer

NASA Astrophysics Data System (ADS)

Bianconi, Roberto; Tamponi, Matteo

This paper presents an analytical unsteady-state solution to the atmospheric dispersion equation for substances subject to chemical-physical decay in a finite mixing layer for releases of short duration. This solution is suitable for describing critical events relative to accidental release of toxic, flammable or explosive substances. To implement the solution, the Modello per Rilasci a Breve Termine (MRBT) code has been developed, for some characteristics parameters of which the results of the sensitivity analysis are presented. Moreover some examples of application to the calculation of exposure to toxic substances and to the determination of the ignition field of flammable substances are described. Finally, the mathematical model described can be used to interpret the phenomenon of pollutant accumulation.

A novel stock forecasting model based on High-order-fuzzy-fluctuation Trends and Back Propagation Neural Network

PubMed Central

Dai, Zongli; Zhao, Aiwu; He, Jie

2018-01-01

In this paper, we propose a hybrid method to forecast the stock prices called High-order-fuzzy-fluctuation-Trends-based Back Propagation(HTBP)Neural Network model. First, we compare each value of the historical training data with the previous day's value to obtain a fluctuation trend time series (FTTS). On this basis, the FTTS blur into fuzzy time series (FFTS) based on the fluctuation of the increasing, equality, decreasing amplitude and direction. Since the relationship between FFTS and future wave trends is nonlinear, the HTBP neural network algorithm is used to find the mapping rules in the form of self-learning. Finally, the results of the algorithm output are used to predict future fluctuations. The proposed model provides some innovative features:(1)It combines fuzzy set theory and neural network algorithm to avoid overfitting problems existed in traditional models. (2)BP neural network algorithm can intelligently explore the internal rules of the actual existence of sequential data, without the need to analyze the influence factors of specific rules and the path of action. (3)The hybrid modal can reasonably remove noises from the internal rules by proper fuzzy treatment. This paper takes the TAIEX data set of Taiwan stock exchange as an example, and compares and analyzes the prediction performance of the model. The experimental results show that this method can predict the stock market in a very simple way. At the same time, we use this method to predict the Shanghai stock exchange composite index, and further verify the effectiveness and universality of the method. PMID:29420584

A novel stock forecasting model based on High-order-fuzzy-fluctuation Trends and Back Propagation Neural Network.

PubMed

Guan, Hongjun; Dai, Zongli; Zhao, Aiwu; He, Jie

2018-01-01

In this paper, we propose a hybrid method to forecast the stock prices called High-order-fuzzy-fluctuation-Trends-based Back Propagation(HTBP)Neural Network model. First, we compare each value of the historical training data with the previous day's value to obtain a fluctuation trend time series (FTTS). On this basis, the FTTS blur into fuzzy time series (FFTS) based on the fluctuation of the increasing, equality, decreasing amplitude and direction. Since the relationship between FFTS and future wave trends is nonlinear, the HTBP neural network algorithm is used to find the mapping rules in the form of self-learning. Finally, the results of the algorithm output are used to predict future fluctuations. The proposed model provides some innovative features:(1)It combines fuzzy set theory and neural network algorithm to avoid overfitting problems existed in traditional models. (2)BP neural network algorithm can intelligently explore the internal rules of the actual existence of sequential data, without the need to analyze the influence factors of specific rules and the path of action. (3)The hybrid modal can reasonably remove noises from the internal rules by proper fuzzy treatment. This paper takes the TAIEX data set of Taiwan stock exchange as an example, and compares and analyzes the prediction performance of the model. The experimental results show that this method can predict the stock market in a very simple way. At the same time, we use this method to predict the Shanghai stock exchange composite index, and further verify the effectiveness and universality of the method.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Application of the Finite Element Method to Reveal the Causes of Loss of Planeness of Hot-Rolled Steel Sheets during Laser Cutting

NASA Astrophysics Data System (ADS)

Garber, E. A.; Bolobanova, N. L.; Trusov, K. A.

2018-01-01

A finite element technique is developed to simulate the stresses and the strains during strip flattening to reveal the causes of the cutting-assisted loss of planeness of hot-rolled steel sheets processed in roller levelers. The loss of planeness is found to be caused by a nonuniform distribution of the flattening-induced longitudinal tensile stresses over the strip thickness and width. The application of tensile forces to a strip in a roller leveler decreases this nonuniformity and prevents loss of planeness in cutting.

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

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

Liu, Yueqiang, E-mail: yueqiang.liu@ccfe.ac.uk; Chapman, I. T.; Graves, J. P.

2014-05-15

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does notmore » contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects.« less

Optimization of self-acting step thrust bearings for load capacity and stiffness.

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1972-01-01

Linearized analysis of a finite-width rectangular step thrust bearing. Dimensionless load capacity and stiffness are expressed in terms of a Fourier cosine series. The dimensionless load capacity and stiffness were found to be a function of the dimensionless bearing number, the pad length-to-width ratio, the film thickness ratio, the step location parameter, and the feed groove parameter. The equations obtained in the analysis were verified. The assumptions imposed were substantiated by comparing the results with an existing exact solution for the infinite width bearing. A digital computer program was developed which determines optimal bearing configuration for maximum load capacity or stiffness. Simple design curves are presented. Results are shown for both compressible and incompressible lubrication. Through a parameter transformation the results are directly usable in designing optimal step sector thrust bearings.

Reduced ion bootstrap current drive on NTM instability

NASA Astrophysics Data System (ADS)

Qu, Hongpeng; Wang, Feng; Wang, Aike; Peng, Xiaodong; Li, Jiquan

2018-05-01

The loss of bootstrap current inside magnetic island plays a dominant role in driving the neoclassical tearing mode (NTM) instability in tokamak plasmas. In this work, we investigate the finite-banana-width (FBW) effect on the profile of ion bootstrap current in the island vicinity via an analytical approach. The results show that even if the pressure gradient vanishes inside the island, the ion bootstrap current can partly survive due to the FBW effect. The efficiency of the FBW effect is higher when the island width becomes smaller. Nevertheless, even when the island width is comparable to the ion FBW, the unperturbed ion bootstrap current inside the island cannot be largely recovered by the FBW effect, and thus the current loss still exists. This suggests that FBW effect alone cannot dramatically reduce the ion bootstrap current drive on NTMs.

Initial design of 12S-10P outer-rotor field excitation flux switching motor with different rotor width

NASA Astrophysics Data System (ADS)

Othman, Syed Muhammad Naufal bin Syed; Sulaiman, Erwan bin; Husin, Zhafir Aizat; Khan, Faisal; Mazlan, Mohamed Mubin Aizat

2015-05-01

This paper proposes an initial design of 12 slot, 10 pole outer-rotor field-excitation flux switching motor (FEFSM) with two different rotor width based from 2 different formula to design the rotor width. Hence, initial design include the three coil test to determine the U, W, V-phase, the flux strengthening and weakening, flux at various armature coil and field-excitation coil current, and finally the torque at various JA and JE. As for the materials, the stator and rotor consists of steel sheets made of electromagnetic steels, copper for armature coils and field excitation coils as the only field for magnetic flux source. There will be some design specification and restriction on outer-rotor FEFSM based on 2D-Finite Element Analysis will be applied to design the proposed machine.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

The mathematics behind chimera states

NASA Astrophysics Data System (ADS)

Omel’chenko, O. E.

2018-05-01

Chimera states are self-organized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, Ott-Antonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed.

Recent literature on structural modeling, identification, and analysis

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1990-01-01

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Evanescent wave coupling in terahertz waveguide arrays.

PubMed

Reichel, K S; Sakoda, N; Mendis, R; Mittleman, D M

2013-07-15

We study energy transfer among an array of identical finite-width parallel-plate waveguides in close proximity, via evanescent wave coupling of broadband terahertz waves. We observe stronger coupling with larger plate separations and longer propagation paths. This work establishes a platform to investigate new opportunities for THz components and devices based on evanescent wave coupling.

Biological control via "ecological" damping: An approach that attenuates non-target effects.

PubMed

Parshad, Rana D; Quansah, Emmanuel; Black, Kelly; Beauregard, Matthew

2016-03-01

In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population, that functions as a top predator, in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous", and uncontrollable population levels, in a finite time. We next improve the mathematical model and incorporate controls that are shown to drive down the invasive population growth and, in certain cases, eliminate blow-up. Hence, the population does not reach an uncontrollable level. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in Parshad et al. (2014). Lastly, we confirm the existence of spatiotemporal chaos. Copyright © 2016 Elsevier Inc. All rights reserved.

Surface acoustic wave diffraction driven mechanisms in microfluidic systems.

PubMed

Fakhfouri, Armaghan; Devendran, Citsabehsan; Albrecht, Thomas; Collins, David J; Winkler, Andreas; Schmidt, Hagen; Neild, Adrian

2018-06-26

Acoustic forces arising from high-frequency surface acoustic waves (SAW) underpin an exciting range of promising techniques for non-contact manipulation of fluid and objects at micron scale. Despite increasing significance of SAW-driven technologies in microfluidics, the understanding of a broad range of phenomena occurring within an individual SAW system is limited. Acoustic effects including streaming and radiation force fields are often assumed to result from wave propagation in a simple planar fashion. The propagation patterns of a single SAW emanating from a finite-width source, however, cause a far richer range of physical effects. In this work, we seek a better understanding of the various effects arising from the incidence of a finite-width SAW beam propagating into a quiescent fluid. Through numerical and experimental verification, we present five distinct mechanisms within an individual system. These cause fluid swirling in two orthogonal planes, and particle trapping in two directions, as well as migration of particles in the direction of wave propagation. For a range of IDT aperture and channel dimensions, the relative importance of these mechanisms is evaluated.

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations.

PubMed

Hong, Hyunsuk; O'Keeffe, Kevin P; Strogatz, Steven H

2016-10-01

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction p of oscillators are positively coupled, attracting all others, while the remaining fraction 1-p are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a critical width γ c in the frequency distribution below which the system spontaneously synchronizes. Moreover, this γ c is independent of p. Hence, our model and the traditional Kuramoto model (recovered when p = 1) have the same critical width γ c . We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of p < 1.

Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons

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

Singh, S. V.; Devanandhan, S.; Lakhina, G. S.

2013-01-15

Obliquely propagating ion-acoustic soliatry waves are examined in a magnetized plasma composed of kappa distributed electrons and fluid ions with finite temperature. The Sagdeev potential approach is used to study the properties of finite amplitude solitary waves. Using a quasi-neutrality condition, it is possible to reduce the set of equations to a single equation (energy integral equation), which describes the evolution of ion-acoustic solitary waves in magnetized plasmas. The temperature of warm ions affects the speed, amplitude, width, and pulse duration of solitons. Both the critical and the upper Mach numbers are increased by an increase in the ion temperature.more » The ion-acoustic soliton amplitude increases with the increase in superthermality of electrons. For auroral plasma parameters, the model predicts the soliton speed, amplitude, width, and pulse duration, respectively, to be in the range of (28.7-31.8) km/s, (0.18-20.1) mV/m; (590-167) m, and (20.5-5.25) ms, which are in good agreement with Viking observations.« less

Radiative decay rate of excitons in square quantum wells: Microscopic modeling and experiment

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

Khramtsov, E. S.; Grigoryev, P. S.; Ignatiev, I. V.

The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schrödinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the high-order finite-difference scheme. The microscopic calculations are compared with the results obtained by the standard variational approach. The exciton binding energies found by two methods coincide within 0.1 meV for the wide range of QW widths. The radiative decay rate is calculated for QWs of various widths using the exciton wave functions obtained by direct andmore » variational methods. The radiative decay rates are confronted with the experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW heterostructures grown by molecular beam epitaxy. The calculated and measured values are in good agreement, though slight differences with earlier calculations of the radiative decay rate are observed.« less

A verification procedure for MSC/NASTRAN Finite Element Models

NASA Technical Reports Server (NTRS)

Stockwell, Alan E.

1995-01-01

Finite Element Models (FEM's) are used in the design and analysis of aircraft to mathematically describe the airframe structure for such diverse tasks as flutter analysis and actively controlled landing gear design. FEM's are used to model the entire airplane as well as airframe components. The purpose of this document is to describe recommended methods for verifying the quality of the FEM's and to specify a step-by-step procedure for implementing the methods.

Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows.

DTIC Science & Technology

1986-09-01

respectively. Here h is a parameter which is usually related to the size of the grid associated with the finite element partitioning of Q. Then one... grid and of not at least performing serious mesh refinement studies. It also points out the usefulness of rigorous results concerning the stability...overconstrained the .1% approximate velocity field. However, by employing different grids for the ’z pressure and velocity fields, the linear-constant

Radiation Diffusion:. AN Overview of Physical and Numerical Concepts

NASA Astrophysics Data System (ADS)

Graziani, Frank

2005-12-01

An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed

The Frame Game

ERIC Educational Resources Information Center

Edwards, Michael Todd; Cox, Dana C.

2011-01-01

In this article, the authors explore framing, a non-multiplicative technique commonly employed by students as they construct similar shapes. When students frame, they add (or subtract) a "border" of fixed width about a geometric object. Although the approach does not yield similar shapes in general, the mathematical underpinnings of…

A new mathematical formulation of the line-by-line method in case of weak line overlapping

NASA Technical Reports Server (NTRS)

Ishov, Alexander G.; Krymova, Natalie V.

1994-01-01

A rigorous mathematical proof is presented for multiline representation on the equivalent width of a molecular band which consists in the general case of n overlapping spectral lines. The multiline representation includes a principal term and terms of minor significance. The principal term is the equivalent width of the molecular band consisting of the same n nonoverlapping spectral lines. The terms of minor significance take into consideration the overlapping of two, three and more spectral lines. They are small in case of the weak overlapping of spectral lines in the molecular band. The multiline representation can be easily generalized for optically inhomogeneous gas media and holds true for combinations of molecular bands. If the band lines overlap weakly the standard formulation of line-by-line method becomes too labor-consuming. In this case the multiline representation permits line-by-line calculations to be performed more effectively. Other useful properties of the multiline representation are pointed out.

Three-dimensional analysis of chevron-notched specimens by boundary integral method

NASA Technical Reports Server (NTRS)

Mendelson, A.; Ghosn, L.

1983-01-01

The chevron-notched short bar and short rod specimens was analyzed by the boundary integral equations method. This method makes use of boundary surface elements in obtaining the solution. The boundary integral models were composed of linear triangular and rectangular surface segments. Results were obtained for two specimens with width to thickness ratios of 1.45 and 2.00 and for different crack length to width ratios ranging from 0.4 to 0.7. Crack opening displacement and stress intensity factors determined from displacement calculations along the crack front and compliance calculations were compared with experimental values and with finite element analysis.

Selective Laser Melting of Pure Copper

NASA Astrophysics Data System (ADS)

Ikeshoji, Toshi-Taka; Nakamura, Kazuya; Yonehara, Makiko; Imai, Ken; Kyogoku, Hideki

2017-12-01

Appropriate building parameters for selective laser melting of 99.9% pure copper powder were investigated at relatively high laser power of 800 W for hatch pitch in the range from 0.025 mm to 0.12 mm. The highest relative density of the built material was 99.6%, obtained at hatch pitch of 0.10 mm. Building conditions were also studied using transient heat analysis in finite element modeling of the liquidation and solidification of the powder layer. The estimated melt pool length and width were comparable to values obtained by observations using a thermoviewer. The trend for the melt pool width versus the hatch pitch agreed with experimental values.

Selective Laser Melting of Pure Copper

NASA Astrophysics Data System (ADS)

Ikeshoji, Toshi-Taka; Nakamura, Kazuya; Yonehara, Makiko; Imai, Ken; Kyogoku, Hideki

2018-03-01

Appropriate building parameters for selective laser melting of 99.9% pure copper powder were investigated at relatively high laser power of 800 W for hatch pitch in the range from 0.025 mm to 0.12 mm. The highest relative density of the built material was 99.6%, obtained at hatch pitch of 0.10 mm. Building conditions were also studied using transient heat analysis in finite element modeling of the liquidation and solidification of the powder layer. The estimated melt pool length and width were comparable to values obtained by observations using a thermoviewer. The trend for the melt pool width versus the hatch pitch agreed with experimental values.

Design considerations of electromagnetic force in a direct drive permanent magnet brushless motor

NASA Astrophysics Data System (ADS)

Chen, H. S.; Tsai, M. C.

2008-04-01

In this paper, a numerical study of electromagnetic force associated with the width of stator teeth, width of rotor back iron, and slot opening for a ten-pole nine-slot direct drive permanent magnet brushless motor is presented. The study calculates the amplitude of the electromagnetic force on the rotating rotor by using the finite-element method. The results show that the amplitude of electromagnetic force, which may cause the noise and vibration of motors, changes with the variation of these above mentioned three factors. The relationship between the considerations of output torque and the minimization of noise and vibration is also established in this paper.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Further Development of Ko Displacement Theory for Deformed Shape Predictions of Nonuniform Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2009-01-01

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

Contact behavior modelling and its size effect on proton exchange membrane fuel cell

NASA Astrophysics Data System (ADS)

Qiu, Diankai; Peng, Linfa; Yi, Peiyun; Lai, Xinmin; Janßen, Holger; Lehnert, Werner

2017-10-01

Contact behavior between the gas diffusion layer (GDL) and bipolar plate (BPP) is of significant importance for proton exchange membrane fuel cells. Most current studies on contact behavior utilize experiments and finite element modelling and focus on fuel cells with graphite BPPs, which lead to high costs and huge computational requirements. The objective of this work is to build a more effective analytical method for contact behavior in fuel cells and investigate the size effect resulting from configuration alteration of channel and rib (channel/rib). Firstly, a mathematical description of channel/rib geometry is outlined in accordance with the fabrication of metallic BPP. Based on the interface deformation characteristic and Winkler surface model, contact pressure between BPP and GDL is then calculated to predict contact resistance and GDL porosity as evaluative parameters of contact behavior. Then, experiments on BPP fabrication and contact resistance measurement are conducted to validate the model. The measured results demonstrate an obvious dependence on channel/rib size. Feasibility of the model used in graphite fuel cells is also discussed. Finally, size factor is proposed for evaluating the rule of size effect. Significant increase occurs in contact resistance and porosity for higher size factor, in which channel/rib width decrease.

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

Analytic expression and propagation properties of hollow Gaussian beams for the off-waist incident case in strongly nonlocal media

NASA Astrophysics Data System (ADS)

Dai, Zhiping; Ling, Xiaohui; Tang, Shiqing

2018-06-01

In this paper, the propagation properties of hollow Gaussian beams (HGBs) are discussed in detail when they are off-waist incident in strongly nonlocal media. A set of mathematic expressions are given to describe the evolutions of the beam intensity, the beam width, and the real beam radius. Numerical simulations are carried out to illustrate these propagation properties depended on the off-waist incidence. It is found that a HGB always periodically transforms its transverse patterns during propagation. Accordingly, the beam width and the real beam radius are also periodic during propagation.

Reactive nanolaminate pulsed-laser ignition mechanism: Modeling and experimental evidence of diffusion limited reactions

DOE PAGES

Yarrington, C. D.; Abere, M. J.; Adams, D. P.; ...

2017-04-03

We irradiated Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm 2 and 1189 W/cm 2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. While the shorter pulse shows uniform brightness, videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model themore » progress from reactants to products at both pulse widths. Finally, the model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.« less

Experimental Determination of Ultra-Sharp Stray Field Distribution from a Magnetic Vortex Core Structure

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

Huang, L.; Zhu, Y.; Zhong, H.

2009-08-01

The fine magnetic stray field from a vortex structure of micron-sized permalloy (Ni{sub 80}Fe{sub 20}) elements has been studied by high-resolution magnetic force microscopy. By systematically studying the width of the stray field gradient distribution at different tip-to-sample distances, we show that the half-width at half-maximum (HWHM) of the signal from vortex core can be as narrow as {approx}21 nm at a closest tip-to-sample distance of 23 nm, even including the convolution effect of the finite size of the magnetic tip. A weak circular reverse component is found around the center of the magnetic vortex in the measured magnetic forcemore » microscope (MFM) signals, which can be attributed to the reverse magnetization around the vortex core. Successive micromagnetic and MFM imaging simulations show good agreements with our experimental results on the width of the stray field distribution.« less

Opportunities for shear energy scaling in bulk acoustic wave resonators.

PubMed

Jose, Sumy; Hueting, Raymond J E

2014-10-01

An important energy loss contribution in bulk acoustic wave resonators is formed by so-called shear waves, which are transversal waves that propagate vertically through the devices with a horizontal motion. In this work, we report for the first time scaling of the shear-confined spots, i.e., spots containing a high concentration of shear wave displacement, controlled by the frame region width at the edge of the resonator. We also demonstrate a novel methodology to arrive at an optimum frame region width for spurious mode suppression and shear wave confinement. This methodology makes use of dispersion curves obtained from finite-element method (FEM) eigenfrequency simulations for arriving at an optimum frame region width. The frame region optimization is demonstrated for solidly mounted resonators employing several shear wave optimized reflector stacks. Finally, the FEM simulation results are compared with measurements for resonators with Ta2O5/ SiO2 stacks showing suppression of the spurious modes.

Substructure System Identification for Finite Element Model Updating

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Blades, Eric L.

1997-01-01

This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for Finite Element Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order finite element models.

Effect of electron cyclotron beam width to neoclassical tearing mode stabilization by minimum seeking control in ITER

NASA Astrophysics Data System (ADS)

Park, Minho; Na, Yong-Su; Seo, Jaemin; Kim, M.; Kim, Kyungjin

2018-01-01

We report the effect of the electron cyclotron (EC) beam width on the full suppression time of neoclassical tearing mode (NTM) using the finite difference method (FDM) based minimum seeking controller in ITER. An integrated numerical system is setup for time-dependent simulations of the NTM evolution in ITER by solving the modified Rutherford equation together with the plasma equilibrium, transport, and EC heating and current drive. The calculated magnetic island width and growth rate is converted to the Mirnov diagnostic signal as an input to the controller to mimic the real experiment. In addition, 10% of the noise is enforced to this diagnostic signal to evaluate the robustness of the controller. To test the dependency of the NTM stabilization time on the EC beam width, the EC beam width scan is performed for a perfectly aligned case first, then for cases with the feedback control using the minimum seeking controller. When the EC beam is perfectly aligned, the narrower the EC beam width, the smaller the NTM stabilization time is observed. As the beam width increases, the required EC power increases exponentially. On the other hand, when the minimum seeking controller is applied, NTM stabilization sometimes fails as the EC beam width decreases. This is consistently observed in the simulation with various representations of the noise as well as without the noise in the Mirnov signal. The higher relative misalignment, misalignment divided by the beam width, is found to be the reason for the failure with the narrower beam widths. The EC stabilization effect can be lower for the narrower beam widths than the broader ones even at the same misalignment due to the smaller ECCD at the island O-point. On the other hand, if the EC beam is too wide, the NTM stabilization time takes too long. Accordingly, the optimal EC beam width range is revealed to exist in the feedback stabilization of NTM.

Infinity Computer and Calculus

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.

2007-09-01

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this survey talk, a new computational methodology (that is not related to nonstandard analysis) is described. It is based on the principle `The part is less than the whole' applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology allows us to introduce the Infinity Computer working with all these numbers (its simulator is presented during the lecture). The new computational paradigm both gives possibilities to execute computations of a new type and simplifies fields of mathematics where infinity and/or infinitesimals are encountered. Numerous examples of the usage of the introduced computational tools are given during the lecture.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

[Application of Finite Element Method in Thoracolumbar Spine Traumatology].

PubMed

Zhang, Min; Qiu, Yong-gui; Shao, Yu; Gu, Xiao-feng; Zeng, Ming-wei

2015-04-01

The finite element method (FEM) is a mathematical technique using modern computer technology for stress analysis, and has been gradually used in simulating human body structures in the biomechanical field, especially more widely used in the research of thoracolumbar spine traumatology. This paper reviews the establishment of the thoracolumbar spine FEM, the verification of the FEM, and the thoracolumbar spine FEM research status in different fields, and discusses its prospects and values in forensic thoracolumbar traumatology.

Utilising flags to reduce drag around a short finite circular cylinder

NASA Astrophysics Data System (ADS)

Javadi, Kh.; Kiani, F.; Tahaye Abadi, M.

2018-03-01

This paper utilises flags to decrease the drag around a short finite circular cylinder. Wall-adapted large eddy simulation and two-way fluid-structure interaction methods were applied to resolve unsteady turbulent flow structure. The far-field Reynolds number of the current configuration based on the cylinder diameter was chosen to be 20,000. In addition, the length-to-diameter ratio of the cylinder was assumed to be L/D = 2 whereas the flexible flag had a width-to-diameter ratio of W/D = 1.5. The results were compared with the regular short finite circular cylinder and the rigid flagged cylinder in our previous work. The results indicate that utilising flags inside the near-wake region of the cylinder reduces the pressure drag. The physical mechanism of this drag reduction is presented.

Emergence of currents as a transient quantum effect in nonequilibrium systems

NASA Astrophysics Data System (ADS)

Granot, Er'El; Marchewka, Avi

2011-09-01

Most current calculations are based on equilibrium or semi-equilibrium models. However, except for very special scenarios (like ring configuration), the current cannot exist in equilibrium. Moreover, unlike with equilibrium scenarios, there is no generic approach to confront out-of-equilibrium currents. In this paper we used recent studies on transient quantum mechanics to solve the current, which appears in the presence of very high density gradients and fast transients. It shows that the emerging current appears instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value, and remain constant for a finite period. It is shown that this nonequilibrium effect can be measured in real experiments (such as cooled rubidium atoms), where the discontinuity is replaced with a finite width (hundreds of nanometers) gradient.

Cardiac tissue geometry as a determinant of unidirectional conduction block: assessment of microscopic excitation spread by optical mapping in patterned cell cultures and in a computer model.

PubMed

Fast, V G; Kléber, A G

1995-05-01

Unidirectional conduction block (UCB) and reentry may occur as a consequence of an abrupt tissue expansion and a related change in the electrical load. The aim of this study was to evaluate critical dimensions of the tissue necessary for establishing UCB in heart cell culture. Neonatal rat heart cell cultures with cell strands of variable width emerging into a large cell area were grown using a technique of patterned cell growth. Action potential upstrokes were measured using a voltage sensitive dye (RH-237) and a linear array of 10 photodiodes with a 15 microns resolution. A mathematical model was used to relate action potential wave shapes to underlying ionic currents. UCB (block of a single impulse in anterograde direction - from a strand to a large area - and conduction in the retrograde direction) occurred in narrow cell strands with a width of 15(SD 4) microns (1-2 cells in width, n = 7) and there was no conduction block in strands with a width of 31(8) microns (n = 9, P < 0.001) or larger. The analysis of action potential waveshapes indicated that conduction block was either due to geometrical expansion alone (n = 5) or to additional local depression of conduction (n = 2). In wide strands, action potential upstrokes during anterograde conduction were characterised by multiple rising phases. Mathematical modelling showed that two rising phases were caused by electronic current flow, whereas local ionic current did not coincide with the rising portions of the upstrokes. (1) High resolution optical mapping shows multiphasic action potential upstrokes at the region of abrupt expansion. At the site of the maximum decrement in conduction, these peaks were largely determined by the electrotonus and not by the local ionic current. (2) Unidirectional conduction block occurred in strands with a width of 15(4) microns (1-2 cells).

Wildland firefighter safety zones: A review of past science and summary of future needs

Treesearch

B. W. Butler

2014-01-01

Current wildland firefighter safety zone guidelines are based on studies that assume flat terrain, radiant heating, finite flame width, constant flame temperature and high flame emissivity. Firefighter entrapments and injuries occur across a broad range of vegetation, terrain and atmospheric conditions generally when they are within two flame heights of the fire....

Spinning Q-balls in the complex signum-Gordon model

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

Arodz, H.; Karkowski, J.; Swierczynski, Z.

2009-09-15

Rotational excitations of compact Q-balls in the complex signum-Gordon model in 2+1 dimensions are investigated. We find that almost all such spinning Q-balls have the form of a ring of strictly finite width. In the limit of large angular momentum M{sub z}, their energy is proportional to |M{sub z}|{sup 1/5}.

Boundary Layer Model for Air Pollutant Concentrations Due to Highway Traffic

ERIC Educational Resources Information Center

Ragland, Kenneth W.; Peirce, J. Jeffrey

1975-01-01

A numerical solution of the three-dimensional steady-state diffusion equation for a finite width line source is presented. The wind speed and eddy diffusivity as a function of height above the roadway are obtained. Normalized ground level and elevated concentrations near a highway are obtained for winds perpendicular, parallel, and at 45 degrees.…

Optical response of bowtie antennas

NASA Astrophysics Data System (ADS)

Guo, Ying-Nan; Pan, Shi; Li, Xu-Feng; Wang, Shuo; Wang, Qiao

2010-10-01

Optical properties of bowtie antennas are investigated using a numerical method of finite-difference time-domain (FDTD). The optical response in the antenna feed gap is simulated as functions of its geometry parameters (flare angle, arm length, apex width, thickness, gap dimension, as well as the index of substrate), which provide a clear guideline to exploit such antenna structures in practice.

Balance functions in coalescence model

NASA Astrophysics Data System (ADS)

Bialas, A.

2004-01-01

It is shown that the quark-antiquark coalescence mechanism for pion production allows to explain the small pseudorapidity width of the balance function observed for central collisions of heavy ions, provided effects of the finite acceptance region and of the transverse flow are taken into account. In contrast, the standard hadronic cluster model is not compatible with this data.

Backscattering enhancement for Marshall-Palmer distributed rains for a W-band nadir-pointing radar with a finite beam width

NASA Technical Reports Server (NTRS)

Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Oguchi, Tomohiro

2005-01-01

In this paper, we expand the previous theory to be applied to a generic drop size distribution with spheroidal raindrops including spherical raindrops. Results will be used to discuss the multiple scattering effects on the backscatter measurements acquired by a W-band nadir-pointing radar.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

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

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Failure modes for compression loaded angle-ply plates with holes

NASA Technical Reports Server (NTRS)

Burns, S. W.; Herakovich, C. T.; Williams, J. G.

1987-01-01

A combined theoretical-experimental investigation of failure in notched, graphite-epoxy, angle-ply laminates subjected to far-field compression loading indicates that failure generally initiates on the hole boundary and propagates along a line parallel to the fiber orientation of the laminate. The strength of notched laminates with specimen width-to-hole diameter ratios of 5 and 10 are compared to the strength of unnotched laminates. The experimental results are complemented by a three-dimensional finite element stress analysis that includes interlaminar stresses around holes in (+/- theta)s laminates. The finite element predictions indicate that failure is initiated by shear stresses at the hole boundary.

Effect of strained Ge-based NMOSFETs with Ge0.93Si0.07 stressors on device layout

NASA Astrophysics Data System (ADS)

Hsu, Hung-Wen; Lee, Chang-Chun

2017-12-01

This research proposes a germanium (Ge)-based n-channel MOSFET with Ge0.93Si0.07 S/D stressor. A simulation technique is utilized to understand the layout effect of shallow trench isolation (STI) length, gate width, dummy active of diffusion (OD) length, and extended poly width on stress distribution in a channel region. Stress distribution in a channel region was simulated by ANSYS software based on finite element analysis. Furthermore, carrier mobility gain was evaluated by a second-order piezoresistance model. The piezoresistance coefficient of Ge nMOSFET varies from that of Si nMOSFET. The piezoresistance coefficient shows that longitudinal and transverse stresses are the dominant factors affecting the change in electron mobility in the channel region. For Ge-based nMOSFET, longitudinal stress tends to be tensile, whereas transverse stress tends to be compressive. Stress along channel length becomes more tensile when STI length decreases. By contrast, stress along the channel width becomes more compressive when gate width or extended poly width decreases. Electron mobility in Ge-based nMOSFET could be enhanced under the aforementioned conditions. The enhanced electron mobility becomes more significant as the device combines with a contact etching stop layer stressor. Moreover, the mobility can be improved by changing the STI length, gate width, dummy OD length, or extended poly width. This investigation systematically analyzed the relationship between layout factor and stress distribution.

Climate variability and the European agricultural production

NASA Astrophysics Data System (ADS)

Guimarães Nobre, Gabriela; Hunink, Johannes E.; Baruth, Bettina; Aerts, Jeroen C. J. H.; Ward, Philip J.

2017-04-01

By 2050, the global demand for maize, wheat and other major crops is expected to grow sharply. To meet this challenge, agricultural systems have to increase substantially their production. However, the expanding world population, coupled with a decline of arable land per person, and the variability in global climate, are obstacles to achieving the increasing demand. Creating a resilient agriculture system requires the incorporation of preparedness measures against weather-related events, which can trigger disruptive risks such as droughts. This study examines the influence of large-scale climate variability on agriculture production applying a robust decision-making tool named fast-and-frugal trees (FFT). We created FFTs using a dataset of crop production and indices of climate variability: the El Niño Southern Oscillation (SOI) and the North Atlantic Oscillation (NAO). Our main goal is to predict the occurrence of below-average crop production, using these two indices at different lead times. Initial results indicated that SOI and NAO have strong links with European low sugar beet production. For some areas, the FFTs were able to detect below-average productivity events six months before harvesting with hit rate and predictive positive value higher than 70%. We found that shorter lead times, such as three months before harvesting, have the highest predictive skill. Additionally, we observed that the responses of low production events to the phases of the NAO and SOI vary spatially and seasonally. Through the comprehension of the relationship between large scale climate variability and European drought related agricultural impact, this study reflects on how this information could potentially improve the management of the agricultural sector by coupling the findings with seasonal forecasting system of crop production.

Fast Fourier Transform Co-Processor (FFTC)- Towards Embedded GFLOPs

NASA Astrophysics Data System (ADS)

Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Wite, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland

2012-08-01

Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co- Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment.In frame of the ESA activity “Fast Fourier Transform DSP Co-processor (FFTC)” (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following:Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP.The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance.The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT- based processing tasks.A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses.The presentation will give and overview on the project, including the results of the validation of the FFTC ASIC prototypes.

Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs

NASA Astrophysics Data System (ADS)

Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas

2012-10-01

Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.

Ethnomathematics: The use of multiple linier regression Y = b 1 X 1 + b 2 X 2 + e in traditional house construction Saka Roras in Songan Village

NASA Astrophysics Data System (ADS)

Darmayasa, J. B.; Wahyudin; Mulyana, T.

2018-01-01

Ethnomathematics may be the connecting bridge between culture and technology and arts. Therefore, the exploration of mathematics values that intersects with cultural anthropology should be significantly conducted. One case containing such issue is the construction of Traditional House of Saka Roras in Bali. Thus, this research aimed to explore the mathematic concept adopted in the construction of such traditional Bale (house) located in Songan Village, Kintamani, Bali. Specifically, this research also aimed to investigate the selection of linear regression coefficient for the saka (pillar) in the Bale. This research applied Embedded Mix-Method Design. Meanwhile, the data collection was conducted by interview, observation and measurement of pillars of 32 Bale Saka Roras. The result of this research revealed that the connection between the width and height of pillars was stated in the formula Y = 26,3 + 18,2X, where X acted as stimulus variable. The coefficient value amounted to 18.2 showed that most preceding architects in Songan Village were more likely to use 19 as the coefficient towards the pillar width than the other coefficients such as 17, 20 and 21 as mentioned in book/palm-leaf manuscript entitled Kosala-Kosali. The last but not least, the researchers also figured out that the pillar width depended on the length of the house-owner candidate’s index finger.

Design study of piezoelectric energy-harvesting devices for generation of higher electrical power using a coupled piezoelectric-circuit finite element method.

PubMed

Zhu, Meiling; Worthington, Emma; Tiwari, Ashutosh

2010-01-01

This paper presents a design study on the geometric parameters of a cantilever-based piezoelectric energy-harvesting devices (EHD), which harvest energy from motion (vibration), for the purpose of scavenging more energy from ambient vibration energy sources. The design study is based on the coupled piezoelectric-circuit finite element method (CPCFEM), previously presented by Dr. Zhu. This model can calculate the power output of piezoelectric EHDS directly connected to a load resistor and is used in this paper to obtain the following simulation results for variations in geometric parameters such as the beam length, width and thickness, and the mass length, width, and height: 1) the current flowing through and the voltage developed across the load resistor, 2) the power dissipated by the resistor and the corresponding vibrational displacement amplitude, and 3) the resonant frequency. By studying these results, straightforward design strategies that enable the generation of more power are obtained for each geometric parameter, and a physical understanding of how each parameter affects the output power is given. It is suggested that, in designing with the aim of generating more power, the following strategies be used: 1) for the beam, a shorter length, larger width, and lower ratio of piezoelectric layer thickness to total beam thickness are preferred in the case of a fixed mass; 2) for the mass, a shortened mass length and a higher mass height are preferred in the case of variation in the mass length and the mass height with mass width and mass value remain fixed, and a wider width and small mass height are preferred in the case of variation in mass width and height (mass length and value remain fixed; and 3) for the case of a fixed total length, a shorter beam length and longer mass length are preferred. With the design strategies, output powers from the device can reach above 1 to 2 mW/cm(3), much higher than the 200 microW/cm(3) currently achieved in the published literature. This is an encouraging prospect for enabling a wider range of applications of the EHDs. In addition, physical insights into how each parameter influences output power are also discussed in detail.

Improved capacity to evaluate changes in intestinal mucosal surface area using mathematical modeling.

PubMed

Greig, Chasen J; Cowles, Robert A

2017-07-01

Quantification of intestinal mucosal growth typically relies on morphometric parameters, commonly villus height, as a surrogate for presumed changes in mucosal surface area (MSA). We hypothesized that using mathematical modeling based on multiple unique measurements would improve discrimination of the effects of interventions on MSA compared to standard measures. To determine the ability of mathematical modeling to resolve differences in MSA, a mouse model with enhanced serotonin (5HT) signaling known to stimulate mucosal growth was used. 5-HT signaling is potentiated by targeting the serotonin reuptake transporter (SERT) molecule. Selective serotonin reuptake inhibitor-treated wild-type (WT-SSRI), SERT-knockout (SERTKO), and wild-type C57Bl/6 (WT) mice were used. Distal ileal sections were H&E-stained. Villus height (VH), width (VW), crypt width (CW), and bowel diameter were used to calculate surface area enlargement factor (SEF) and MSA. VH alone for SERTKO and SSRI was significantly increased compared to WT, without a difference between SERTKO and WT-SSRI. VW and CW were significantly decreased for both SERTKO and WT-SSRI compared to WT, and VW for WT-SSRI was also decreased compared to SERTKO. These changes increased SEF and MSA for SERTKO and WT-SSRI compared to WT. Additionally, SEF and MSA were significantly increased for WT-SSRI compared to SERTKO. Mathematical modeling provides a valuable tool for differentiating changes in intestinal MSA. This more comprehensive assessment of surface area does not appear to correlate linearly with standard morphometric measures and represents a more comprehensive method for discriminating between therapies aimed at increasing functional intestinal mucosa. © 2017 Wiley Periodicals, Inc.

Finite element and analytical models for twisted and coiled actuator

NASA Astrophysics Data System (ADS)

Tang, Xintian; Liu, Yingxiang; Li, Kai; Chen, Weishan; Zhao, Jianguo

2018-01-01

Twisted and coiled actuator (TCA) is a class of recently discovered artificial muscle, which is usually made by twisting and coiling polymer fibers into spring-like structures. It has been widely studied since discovery due to its impressive output characteristics and bright prospects. However, its mathematical models describing the actuation in response to the temperature are still not fully developed. It is known that the large tensile stroke is resulted from the untwisting of the twisted fiber when heated. Thus, the recovered torque during untwisting is a key parameter in the mathematical model. This paper presents a simplified model for the recovered torque of TCA. Finite element method is used for evaluating the thermal stress of the twisted fiber. Based on the results of the finite element analyses, the constitutive equations of twisted fibers are simplified to develop an analytic model of the recovered torque. Finally, the model of the recovered torque is used to predict the deformation of TCA under varying temperatures and validated against experimental results. This work will enhance our understanding of the deformation mechanism of TCAs, which will pave the way for the closed-loop position control.

Mathematical simulation of bearing ring grinding process

NASA Astrophysics Data System (ADS)

Koltunov, I. I.; Gorbunova, T. N.; Tumanova, M. B.

2018-03-01

The paper suggests the method of forming a solid finite element model of the bearing ring. Implementation of the model allowed one to evaluate the influence of the inner cylindrical surface grinding scheme on the ring shape error.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Richard P. Feynman and the Feynman Diagrams

Science.gov Websites

available in full-text and on the Web. Documents: A Theorem and Its Application to Finite Tampers, DOE Fermi-Thomas Theory; DOE Technical Report, April 28, 1947 Mathematical Formulation of the Quantum Theory

The pressure distribution for biharmonic transmitting array: theoretical study

NASA Astrophysics Data System (ADS)

Baranowska, A.

2005-03-01

The aim of the paper is theoretical analysis of the finite amplitude waves interaction problem for the biharmonic transmitting array. We assume that the array consists of 16 circular pistons of the same dimensions that regrouped in two sections. Two different arrangements of radiating elements were considered. In this situation the radiating surface is non-continuous without axial symmetry. The mathematical model was built on the basis of the Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation. To solve the problem the finite-difference method was applied. On-axis pressure amplitude for different frequency waves as a function of distance from the source, transverse pressure distribution of these waves at fixed distances from the source and pressure amplitude distribution for them at fixed planes were examined. Especially changes of normalized pressure amplitude for difference frequency were studied. The paper presents mathematical model and some results of theoretical investigations obtained for different values of source parameters.

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

In analysis of normal traffic flow, it usually uses the static or dynamic model to numerical analyze based on fluid mechanics. However, in such handling process, the problem of massive modeling and data handling exist, and the accuracy is not high. Finite Element Method (FEM) is a production which is developed from the combination of a modern mathematics, mathematics and computer technology, and it has been widely applied in various domain such as engineering. Based on existing theory of traffic flow, ITS and the development of FEM, a simulation theory of the FEM that solves the problems existing in traffic flow is put forward. Based on this theory, using the existing Finite Element Analysis (FEA) software, the traffic flow is simulated analyzed with fluid mechanics and the dynamics. Massive data processing problem of manually modeling and numerical analysis is solved, and the authenticity of simulation is enhanced.

Thermal modeling of phase change solidification in thermal control devices including natural convection effects

NASA Technical Reports Server (NTRS)

Ukanwa, A. O.; Stermole, F. J.; Golden, J. O.

1972-01-01

Natural convection effects in phase change thermal control devices were studied. A mathematical model was developed to evaluate natural convection effects in a phase change test cell undergoing solidification. Although natural convection effects are minimized in flight spacecraft, all phase change devices are ground tested. The mathematical approach to the problem was to first develop a transient two-dimensional conduction heat transfer model for the solidification of a normal paraffin of finite geometry. Next, a transient two-dimensional model was developed for the solidification of the same paraffin by a combined conduction-natural-convection heat transfer model. Throughout the study, n-hexadecane (n-C16H34) was used as the phase-change material in both the theoretical and the experimental work. The models were based on the transient two-dimensional finite difference solutions of the energy, continuity, and momentum equations.

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

NASA Astrophysics Data System (ADS)

La Rocca, Michele; Adduce, Claudia; Sciortino, Giampiero; Pinzon, Allen Bateman

2008-10-01

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

Micromagnetic recording model of writer geometry effects at skew

NASA Astrophysics Data System (ADS)

Plumer, M. L.; Bozeman, S.; van Ek, J.; Michel, R. P.

2006-04-01

The effects of the pole-tip geometry at the air-bearing surface on perpendicular recording at a skew angle are examined through modeling and spin-stand test data. Head fields generated by the finite element method were used to record transitions within our previously described micromagnetic recording model. Write-field contours for a variety of square, rectangular, and trapezoidal pole shapes were evaluated to determine the impact of geometry on field contours. Comparing results for recorded track width, transition width, and media signal to noise ratio at 0° and 15° skew demonstrate the benefits of trapezoidal and reduced aspect-ratio pole shapes. Consistency between these modeled results and test data is demonstrated.

Superfocusing terahertz waves below lambda/250 using plasmonic parallel-plate waveguides.

PubMed

Zhan, Hui; Mendis, Rajind; Mittleman, Daniel M

2010-04-26

We experimentally demonstrate complete two-dimensional (2-D) confinement of terahertz (THz) energy in finite-width parallel-plate waveguides, defying conventional wisdom in the century-old field of microwave waveguide technology. We find that the degree of energy confinement increases exponentially with decreasing plate separation. We propose that this 2-D confinement is mediated by the mutual coupling of plasmonic edge modes, analogous to that observed in slot waveguides at optical wavelengths. By adiabatically tapering the width and the separation, we focus THz waves down to a size of 10 microm (approximately lambda/260) by 18 microm ( approximately lambda/145), which corresponds to a mode area of only 2.6 x 10(-5) lambda(2).

Extension of FRI for modeling of electrocardiogram signals.

PubMed

Quick, R Frank; Crochiere, Ronald E; Hong, John H; Hormati, Ali; Baechler, Gilles

2012-01-01

Recent work has developed a modeling method applicable to certain types of signals having a "finite rate of innovation" (FRI). Such signals contain a sparse collection of time- or frequency-limited pulses having a restricted set of allowable pulse shapes. A limitation of past work on FRI is that all of the pulses must have the same shape. Many real signals, including electrocardiograms, consist of pulses with varying widths and asymmetry, and therefore are not well fit by the past FRI methods. We present an extension of FRI allowing pulses having variable pulse width (VPW) and asymmetry. We show example results for electrocardiograms and discuss the possibility of application to signal compression and diagnostics.

Three-Dimensional Ignition and Flame Propagation Above Liquid Fuel Pools: Computational Analysis

NASA Technical Reports Server (NTRS)

Cai, Jinsheng; Sirignano, William A.

2001-01-01

A three-dimensional unsteady reactive Navier-Stokes code is developed to study the ignition and flame spread above liquid fuels initially below the flashpoint temperature. Opposed air flow to the flame spread due to forced and/or natural convection is considered. Pools of finite width and length are studied in air channels of prescribed height and width. Three-dimensional effects of the flame front near the edge of the pool are captured in the computation. The formation of a recirculation zone in the gas phase similar to that found in two-dimensional calculations is also present in the three-dimensional calculations. Both uniform spread and pulsating spread modes are found in the calculated results.

Thermal width of the upsilon at large 't Hooft coupling.

PubMed

Noronha, Jorge; Dumitru, Adrian

2009-10-09

We use the anti-de Sitter/conformal field theory correspondence to show that the heavy quark (static) potential in a strongly coupled plasma develops an imaginary part at finite temperature. Thus, deeply bound heavy quarkonia states acquire a small nonzero thermal width when the 't Hooft coupling lambda = g2N(c) > 1 and the number of colors N(c) --> infinity. In the dual gravity description, this imaginary contribution comes from thermal fluctuations around the bottom of the classical sagging string in the bulk that connects the heavy quarks located at the boundary. We predict a strong suppression of Upsilon's in heavy-ion collisions and discuss how this may be used to estimate the initial temperature.

Kinetic theory analysis of rarefied gas flow through finite length slots

NASA Technical Reports Server (NTRS)

Raghuraman, P.

1972-01-01

An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.

Iontophoretic transdermal drug delivery: a multi-layered approach.

PubMed

Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José A; Pena, Gonçalo

2017-12-11

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

The h-p Version of the Finite Element Method for Problems with Nonhomogeneous Essential Boundary Condition.

DTIC Science & Technology

1987-09-01

one commercial code based on the p and h-p version of the finite element, the program PROBE of NOETIC Technologies (St. Louis, MO). PROBE deals with two...Standards. o To be an international center of study and research for foreign students in numerical mathematics who are supported by foreign govern- ments or...ment agencies such as the National Bureau of Standards. o To be an international center of study and research for foreign students in numerical

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Applications of surface plasmon polaritons in terahertz spectral regime

NASA Astrophysics Data System (ADS)

Zhan, Hui

This thesis presents the experimental work on the applications of surface plasmon polariton (SPP) in terahertz (THz) spectral range. Apertureless near-field optical microscopy (ANSOM) has been widely used to study the localized SPP on various material surfaces. THz ANSOM technique was recently developed to combine the THz time-domain spectroscopy and the ANSOM technique to provide a near-field detection on the localized THz surface waves with improved spatial resolution and signal-noise ratio. We have studied the metal-insulator transition in vanadium dioxide (VO2) thin film using THz ANSOM. We observe a variation of the terahertz amplitude due to the phase transition induced by an applied voltage across the sample. The change of the terahertz signal is related to the abrupt change of the conductivity of the VO2 film at the metal-insulator transition. The subwavelength spatial resolution of this near-field microscopy makes it possible to detect signatures of metallic domains, which exist in the VO2 thin films in the vicinity of the phase transition. We experimentally investigate the propagation of guided waves in finite-width parallel-plate waveguides (PPWGs) in the terahertz spectral range. We observe the propagation of SPPs in this guiding structure, instead of the fundamental transverse electromagnetic (TEM) mode. We find that the two-dimensional (2-D) energy confinement within the finite-width PPWG increases exponentially as the plate separation is reduced. We speculate that edge plasmons play an important role in the energy confinement in this open-structure waveguide. For comparison, the infinite-width PPWGs, the plates of which are much wider than the THz beam size, are also studied with several plate separations. The free-space beam diffraction produces a Gaussian profile along the unconfined direction. The unusual electric field profiles along the vertical direction, perpendicular to the plate are observed. The field enhancement near the metal surfaces are also explained by the SPPs coupled to the metal surfaces. Based on the 2-D energy confinement in the finite-width PPWGs, we design the tapered slot waveguide by slowly tapering the plate width and slot gap. We first study the transverse component of the THz electric field, where a subwavelength 2-D energy confinement is observed. The output spot size strongly depends on the output facet size, where the slot gap and the tip width are in the same scale range. Subwavelength confinement is obtained, corresponding to lambda/4. Further confinement is limited by the spatial resolution of the detecting technique. To overcome this problem, we adapt the THz ASNOM setup to scattering-probe imaging technique, which has been proven to obtain deep subwavelength spatial resolution and great signal-noise ratio. Scattering-probe imaging setup measures the longitudinal component of the electric field of SPPs in the tapered slot waveguides. By slowly tapering the tip width and the slot gap, we squeeze a single-cycle THz pulse down to a size of 10 mum (lambda/260) by 18 mum (lambda/145), a mode area of only 2.6 x 10-5lambda2. We also observe a polarity reversal for the electric field between the guiding region near the upper and lower plates of the waveguide. This polarity flip is similar to that associated with the symmetric plasmon mode of slot waveguides.

Development library of finite elements for computer-aided design system of reed sensors

NASA Astrophysics Data System (ADS)

Kozlov, A. S.; Shmakov, N. A.; Tkalich, V. L.; Labkovskaia, R. I.; Kalinkina, M. E.; Pirozhnikova, O. I.

2018-05-01

The article is devoted to the development of a modern highly reliable element base of devices for security and fire alarm systems, in particular, to the improvement of the quality of contact cores (reed and membrane) of reed sensors. Modeling of elastic sensitive elements uses quadrangular elements of plates and shells, considered in the system of curvilinear orthogonal coordinates. The developed mathematical models and the formed finite element library are designed for systems of automated design of reed switch detectors to create competitive devices alarms. The finite element library is used for the automated system production of reed switch detectors both in series production and in the implementation of individual orders.

A parallelized binary search tree

USDA-ARS?s Scientific Manuscript database

PTTRNFNDR is an unsupervised statistical learning algorithm that detects patterns in DNA sequences, protein sequences, or any natural language texts that can be decomposed into letters of a finite alphabet. PTTRNFNDR performs complex mathematical computations and its processing time increases when i...

Proceedings of the 3rd Annual SCOLE Workshop

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr. (Compiler)

1987-01-01

Topics addressed include: modeling and controlling the Spacecraft Control Laboratory Experiment (SCOLE) configurations; slewing maneuvers; mathematical models; vibration damping; gravitational effects; structural dynamics; finite element method; distributed parameter system; on-line pulse control; stability augmentation; and stochastic processes.

Spectral interpolation - Zero fill or convolution. [image processing

NASA Technical Reports Server (NTRS)

Forman, M. L.

1977-01-01

Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.

Effects of transverse temperature field nonuniformity on stress in silicon sheet growth

NASA Technical Reports Server (NTRS)

Mataga, P. A.; Hutchinson, J. W.; Chalmers, B.; Bell, R. O.; Kalejs, J. P.

1987-01-01

Stress and strain rate distributions are calculated using finite element analysis for steady-state growth of thin silicon sheet temperature nonuniformities imposed in the transverse (sheet width) dimension. Significant reductions in residual stress are predicted to occur for the case where the sheet edge is cooled relative to its center provided plastic deformation with high creep rates is present.

The dynamics of domain walls and strings

NASA Technical Reports Server (NTRS)

Gregory, Ruth; Haws, David; Garfinkle, David

1989-01-01

The leading order finite-width corrections to the equation of motion describing the motion of a domain wall are derived. The regime in which this equation of motion is invalid is discussed. Spherically and cylindrically symmetric solutions to this equation of motion are found. A misconception that has arisen in recent years regarding the rigidity (or otherwise) of cosmic strings is also clarified.

Chiral interface at the finite temperature transition point of QCD

NASA Technical Reports Server (NTRS)

Frei, Z.; Patkos, A.

1990-01-01

The domain wall between coexisting chirally symmetric and broken symmetry regions is studied in a saddle point approximation to the effective three-flavor sigma model. In the chiral limit the surface tension varies in the range ((40 to -50)MeV)(exp 3). The width of the domain wall is estimated to be approximately or equal to 4.5 fm.

Energy Efficiency of Induction Motors Running Off Frequency Converters with Pulse-Width Voltage Modulation{sup 1}

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

Shvetsov, N. K., E-mail: elmash@em.ispu.ru

2016-11-15

The results of calculations of the increase in losses in an induction motor with frequency control and different forms of the supply voltage are presented. The calculations were performed by an analytic method based on harmonic analysis of the supply voltage as well as numerical calculation of the electromagnetic processes by the finite-element method.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Episodic growth of fold-thrust belts: Insights from Finite Element Modelling

NASA Astrophysics Data System (ADS)

Yang, Xiaodong; Peel, Frank J.; Sanderson, David J.; McNeill, Lisa C.

2017-09-01

The sequential development of a fold-thrust belt was investigated using 2D Finite Element Modelling (FEM). The new model results show that a thrust system is typically composed of three distinct regions: the thrust wedge, pre-wedge, and undeformed region. The thrust wedge involves growth that repeats episodically and cyclically. A cycle of wedge building starts as frontal accretion occurs, which is accompanied by a rapid increase in wedge width reducing the taper angle below critical. In response to this, the wedge interior (tracked here by the 50 m displacement position) rapidly propagates forwards into a region of incipient folding. The taper angle progressively increases until it obtains a constant apparent critical value (∼10°). During this period, the wedge experiences significant shortening after a new thrust initiates at the failure front, leading to a decrease in wedge width. Successive widening of the wedge and subsequent shortening and thrusting maintain a reasonably constant taper angle. The fold-thrust belt evolves cyclically, through a combination of rapid advancement of the wedge and subsequent gradual, slow wedge growth. The new model results also highlights that there is clear, although minor, deformation (0-10 m horizontal displacement) in front of the thrust wedge.

Buckling analysis of planar compression micro-springs

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

Zhang, Jing; Sui, Li; Shi, Gengchen

2015-04-15

Large compression deformation causes micro-springs buckling and loss of load capacity. We analyzed the impact of structural parameters and boundary conditions for planar micro-springs, and obtained the change rules for the two factors that affect buckling. A formula for critical buckling deformation of micro-springs under compressive load was derived based on elastic thin plate theory. Results from this formula were compared with finite element analysis results but these did not always correlate. Therefore, finite element analysis is necessary for micro-spring buckling analysis. We studied the variation of micro-spring critical buckling deformation caused by four structural parameters using ANSYS software undermore » two constraint conditions. The simulation results show that when an x-direction constraint is added, the critical buckling deformation increases by 32.3-297.9%. The critical buckling deformation decreases with increase in micro-spring arc radius or section width and increases with increase in micro-spring thickness or straight beam width. We conducted experiments to confirm the simulation results, and the experimental and simulation trends were found to agree. Buckling analysis of the micro-spring establishes a theoretical foundation for optimizing micro-spring structural parameters and constraint conditions to maximize the critical buckling load.« less

Two dimensional finite element thermal model of laser surface glazing for H13 tool steel

NASA Astrophysics Data System (ADS)

Kabir, I. R.; Yin, D.; Naher, S.

2016-10-01

A two dimensional (2D) transient thermal model with line-heat-source was developed by Finite Element Method (FEM) for laser surface glazing of H13 tool steel using commercial software-ANSYS 15. The geometry of the model was taken as a transverse circular cross-section of cylindrical specimen. Two different power levels (300W, 200W) were used with 0.2mm width of laser beam and 0.15ms exposure time. Temperature distribution, heating and cooling rates, and the dimensions of modified surface were analysed. The maximum temperatures achieved were 2532K (2259°C) and 1592K (1319°C) for laser power 300W and 200W respectively. The maximum cooling rates were 4.2×107 K/s for 300W and 2×107 K/s for 200W. Depths of modified zone increased with increasing laser power. From this analysis, it can be predicted that for 0.2mm beam width and 0.15ms time exposer melting temperature of H13 tool steel is achieved within 200-300W power range of laser beam in laser surface glazing.

Three Dimensional Parametric Analyses of Stress Concentration Factor and Its Mitigation in Isotropic and Orthotropic Plate with Central Circular Hole Under Axial In-Plane Loading

NASA Astrophysics Data System (ADS)

Nagpal, Shubhrata; Jain, Nitin Kumar; Sanyal, Shubhashis

2016-01-01

The problem of finding the stress concentration factor of a loaded rectangular plate has offered considerably analytical difficulty. The present work focused on understanding of behavior of isotropic and orthotropic plate subjected to static in-plane loading using finite element method. The complete plate model configuration has been analyzed using finite element method based software ANSYS. In the present work two parameters: thickness to width of plate (T/A) and diameter of hole to width of plate (D/A) have been varied for analysis of stress concentration factor (SCF) and its mitigation. Plates of five different materials have been considered for complete analysis to find out the sensitivity of stress concentration factor. The D/A ratio varied from 0.1 to 0.7 for analysis of SCF and varied from 0.1 to 0.5 for analyzing the mitigation of SCF. 0.01, 0.05 and 0.1 are considered as T/A ratio for all the cases. The results are presented in graphical form and discussed. The mitigation in SCF reported is very encouraging. The SCF is more sensitive to D/A ratio as compared to T/A.

Interval-Valued Rank in Finite Ordered Sets

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

Joslyn, Cliff; Pogel, Alex; Purvine, Emilie

We consider the concept of rank as a measure of the vertical levels and positions of elements of partially ordered sets (posets). We are motivated by the need for algorithmic measures on large, real-world hierarchically-structured data objects like the semantic hierarchies of ontolog- ical databases. These rarely satisfy the strong property of gradedness, which is required for traditional rank functions to exist. Representing such semantic hierarchies as finite, bounded posets, we recognize the duality of ordered structures to motivate rank functions which respect verticality both from the bottom and from the top. Our rank functions are thus interval-valued, and alwaysmore » exist, even for non-graded posets, providing order homomorphisms to an interval order on the interval-valued ranks. The concept of rank width arises naturally, allowing us to identify the poset region with point-valued width as its longest graded portion (which we call the “spindle”). A standard interval rank function is naturally motivated both in terms of its extremality and on pragmatic grounds. Its properties are examined, including the relation- ship to traditional grading and rank functions, and methods to assess comparisons of standard interval-valued ranks.« less

Finite element analysis on preferable I-bar clasp shape.

PubMed

Sato, Y; Tsuga, K; Abe, Y; Asahara, S; Akagawa, Y

2001-05-01

An I-bar clasp is one of the most popular direct retainers for distal-extension removable partial dentures. However, no adequate information is available on preferable shape as determined by biomechanics. This study aimed (1) to investigate, by finite element analysis (FEA), the dimensions and stress of I-bar clasps having the same stiffness, and (2) to estimate a mechanically preferable clasp design. Three-dimensional FEA models of I-bar clasps were created with vertical and horizontal straight sections connected by a curved section characterized by six parameters: thickness of the clasp tip, width of the clasp tip, radius of the curvature, horizontal distance between the base and the vertical axis, vertical dimension between the tip and the horizontal axis, and taper (change of width per unit length along the axis). Stress was calculated with a concentrated load of 5 N applied 2 mm from the tip of the clasp in the buccal direction. A thinner and wider clasp having an taper of 0.020-0.023 and radius of curvature of 2.75-3.00 showed less stress. The results suggest that such a shape might be the preferable I-bar clasp shape as biomechanical viewpoint.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Investigation of the effect of finite pulse errors on the BABA pulse sequence using the Floquet-Magnus expansion approach

NASA Astrophysics Data System (ADS)

Mananga, Eugene S.; Reid, Alicia E.

2013-01-01

This paper presents a study of finite pulse widths for the BABA pulse sequence using the Floquet-Magnus expansion (FME) approach. In the FME scheme, the first order ? is identical to its counterparts in average Hamiltonian theory (AHT) and Floquet theory (FT). However, the timing part in the FME approach is introduced via the ? function not present in other schemes. This function provides an easy way for evaluating the spin evolution during the time in between' through the Magnus expansion of the operator connected to the timing part of the evolution. The evaluation of ? is particularly useful for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provide a natural choice of ? , is ignored. This work uses the ? function to compare the efficiency of the BABA pulse sequence with ? and the BABA pulse sequence with finite pulses. Calculations of ? and ? are presented.

The GPRIME approach to finite element modeling

NASA Technical Reports Server (NTRS)

Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.

1983-01-01

GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

2018-04-01

Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory

DTIC Science & Technology

1990-12-07

Fundaqao Calouste Gulbenkian, Instituto Gulbenkian de Ci~ncia, Centro de C6lculo Cientifico , Coimbra, 1973. 28, Dirac, P. A. M., Spinors in Hilbert Space...Office of Scientific Research grants 1965 Mathematical Association of America Editorial Prize for the article entitled: "Linear Transformations on...matrices" 1966 L.R. Ford Memorial Prize awarded by the Mathematical Association of America for the article , "Permanents" 1989 Outstanding Computer

Nonconvex Model of Material Growth: Mathematical Theory

NASA Astrophysics Data System (ADS)

Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

2018-06-01

The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

Mathematical modeling of shell configurations made of homogeneous and composite materials experiencing intensive short actions and large displacements

NASA Astrophysics Data System (ADS)

Khairnasov, K. Z.

2018-04-01

The paper presents a mathematical model for solving the problem of behavior of shell configurations under the action of static and dynamic impacts. The problem is solved in geometrically nonlinear statement with regard to the finite element method. The composite structures with different material layers are considered. The obtained equations are used to study the behavior of shell configurations under the action of dynamic loads. The results agree well with the experimental data.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

Optimization of CO2 laser cutting parameters on Austenitic type Stainless steel sheet

NASA Astrophysics Data System (ADS)

Parthiban, A.; Sathish, S.; Chandrasekaran, M.; Ravikumar, R.

2017-03-01

Thin AISI 316L stainless steel sheet widely used in sheet metal processing industries for specific applications. CO2 laser cutting is one of the most popular sheet metal cutting processes for cutting of sheets in different profile. In present work various cutting parameters such as laser power (2000 watts-4000 watts), cutting speed (3500mm/min - 5500 mm/min) and assist gas pressure (0.7 Mpa-0.9Mpa) for cutting of AISI 316L 2mm thickness stainless sheet. This experimentation was conducted based on Box-Behenken design. The aim of this work is to develop a mathematical model kerf width for straight and curved profile through response surface methodology. The developed mathematical models for straight and curved profile have been compared. The Quadratic models have the best agreement with experimental data, and also the shape of the profile a substantial role in achieving to minimize the kerf width. Finally the numerical optimization technique has been used to find out best optimum laser cutting parameter for both straight and curved profile cut.

Finite-Element Methods for Real-Time Simulation of Surgery

NASA Technical Reports Server (NTRS)

Basdogan, Cagatay

2003-01-01

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Tomographic inversion of P-wave velocity and Q structures beneath the Kirishima volcanic complex, Southern Japan, based on finite difference calculations of complex traveltimes

USGS Publications Warehouse

Tomatsu, T.; Kumagai, H.; Dawson, P.B.

2001-01-01

We estimate the P-wave velocity and attenuation structures beneath the Kirishima volcanic complex, southern Japan, by inverting the complex traveltimes (arrival times and pulse widths) of waveform data obtained during an active seismic experiment conducted in 1994. In this experiment, six 200-250 kg shots were recorded at 163 temporary seismic stations deployed on the volcanic complex. We use first-arrival times for the shots, which were hand-measured interactively. The waveform data are Fourier transformed into the frequency domain and analysed using a new method based on autoregressive modelling of complex decaying oscillations in the frequency domain to determine pulse widths for the first-arrival phases. A non-linear inversion method is used to invert 893 first-arrival times and 325 pulse widths to estimate the velocity and attenuation structures of the volcanic complex. Wavefronts for the inversion are calculated with a finite difference method based on the Eikonal equation, which is well suited to estimating the complex traveltimes for the structures of the Kirishima volcano complex, where large structural heterogeneities are expected. The attenuation structure is derived using ray paths derived from the velocity structure. We obtain 3-D velocity and attenuation structures down to 1.5 and 0.5 km below sea level, respectively. High-velocity pipe-like structures with correspondingly low attenuation are found under the summit craters. These pipe-like structures are interpreted as remnant conduits of solidified magma. No evidence of a shallow magma chamber is visible in the tomographic images.

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

NASA Astrophysics Data System (ADS)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Efficient Controls for Finitely Convergent Sequential Algorithms

PubMed Central

Chen, Wei; Herman, Gabor T.

2010-01-01

Finding a feasible point that satisfies a set of constraints is a common task in scientific computing: examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems; an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice it usually converges faster than ART3 does. In this paper we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (i) finite convergence is retained and (ii) the speed of convergence is improved. The first of these two properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem. PMID:20953327

Mathematical equation for prediction of cat mandibular canal height dimension based on canine tooth width measurement.

PubMed

Santos, Miguel; Carreira, L Miguel

2016-06-01

The present study was performed in a sample of 33 cats and aimed (1) to characterise the mandible height (Mh), mandibular canal height (MCh) and the distance between the interdental alveolar margin and the mandibular canal (dIAM-MC); and (2) to develop a mathematical model for dimension prediction of MCh using the patient's age, weight (Wg) and canine tooth width at the free gingival margin level (wCGM) that was easily accessible during the oral examination. Age, sex, breed, weight, skull type and the wCGM were the recorded variables for each patient. Right and left lateral view skull radiographs were made followed by measurements of the mandible anatomical structures, taken between the third premolar distal root and the fourth premolar proximal root. Results were considered statistically significant for P values <0.05, and statistical analysis was performed using SPSS software. We observed a strong correlation only between wCGM and MCh, and a prediction mathematical model was developed to calculate the MCh, with a standard error of only 0.4 mm. Our study allows a surgeon to establish relationships between a physical parameter, such as wCGM, evaluated in an oral examination, and the mandibular canal, which is a very important anatomical structure to consider in surgical procedures. Ideally, surgeons should always plan their mandible work only after obtaining a final diagnosis achieved through the use of complementary imaging exams, such as intra- and extra-oral radiographs. Thus, this mathematical equation offers an additional tool, providing more information on the relationships between oral anatomical structures, reducing the risk of iatrogenic lesions and promoting patient safety. © ISFM and AAFP 2015.

Finite slice analysis (FINA) of sliced and velocity mapped images on a Cartesian grid

NASA Astrophysics Data System (ADS)

Thompson, J. O. F.; Amarasinghe, C.; Foley, C. D.; Rombes, N.; Gao, Z.; Vogels, S. N.; van de Meerakker, S. Y. T.; Suits, A. G.

2017-08-01

Although time-sliced imaging yields improved signal-to-noise and resolution compared with unsliced velocity mapped ion images, for finite slice widths as encountered in real experiments there is a loss of resolution and recovered intensities for the slow fragments. Recently, we reported a new approach that permits correction of these effects for an arbitrarily sliced distribution of a 3D charged particle cloud. This finite slice analysis (FinA) method utilizes basis functions that model the out-of-plane contribution of a given velocity component to the image for sequential subtraction in a spherical polar coordinate system. However, the original approach suffers from a slow processing time due to the weighting procedure needed to accurately model the out-of-plane projection of an anisotropic angular distribution. To overcome this issue we present a variant of the method in which the FinA approach is performed in a cylindrical coordinate system (Cartesian in the image plane) rather than a spherical polar coordinate system. Dubbed C-FinA, we show how this method is applied in much the same manner. We compare this variant to the polar FinA method and find that the processing time (of a 510 × 510 pixel image) in its most extreme case improves by a factor of 100. We also show that although the resulting velocity resolution is not quite as high as the polar version, this new approach shows superior resolution for fine structure in the differential cross sections. We demonstrate the method on a range of experimental and synthetic data at different effective slice widths.

Numerical analysis of the output waveguide design for 1.55 μm square microcavity lasers directly grown on GaAs substrates

NASA Astrophysics Data System (ADS)

Ma, Xing; Wang, Jun; Cheng, Zhuo; Yang, Zeyuan; Hu, Haiyang; Wang, Wei; Yin, Haiying; Huang, Yongqing; Ren, Xiaomin

2018-07-01

We report a structure design of 1.55 μm square microcavity lasers monolithically integrated on GaAs substrates. The mode characteristics of the microcavity lasers are numerically investigated by three-dimensional finite-difference time-domain method. The dependences of the high-quality factor modes on the side length of the microcavity, the width of the output waveguide and the etching depth are investigated in detail. The results demonstrate, for the microcavity structure with the side length of 12 μm, the output waveguide width of 1.0 μm and the etching depth of 3.55 μm, it is optimal to excite high-quality factor modes around wavelength of 1.55 μm. The mode wavelength and the mode quality factor are 1547.46 nm and 2416.28, respectively. The quality factor degrades rapidly with the waveguide width increasing, and increases with increasing etching depth.

Bragg reflection band width and optical rotatory dispersion of cubic blue-phase liquid crystals

NASA Astrophysics Data System (ADS)

Yoshida, Hiroyuki; Anucha, Konkanok; Ogawa, Yasuhiro; Kawata, Yuto; Ozaki, Masanori; Fukuda, Jun-ichi; Kikuchi, Hirotsugu

2016-10-01

The Bragg reflection band width and optical rotatory dispersion of liquid crystalline cholesteric blue phases (BPs) I and II are compared by numerical simulations. Attention is paid to the wavelength regions for which the reflection bands with lowest photon energies appear, i.e., the [110 ] direction for BP I and the [100 ] direction for BP II. Finite difference time domain and 4 ×4 matrix calculations performed on the theoretical director tensor distribution of BPs with the same material parameters show that BP II, which has simple cubic symmetry, has a wider photonic band gap than BP I, which has body centered cubic symmetry, possibly due to the fact that the density of the double-twist cylinders in BP II are twice that in BP I. The theoretical results on the Bragg reflection band width are supported by reflectance measurements performed on BPs I and II for light incident along the [110 ] and [100 ] directions, respectively.

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

Phillips, Benjamin R.; Baldridge, W. Scott; Gable, Carl W.

Finite volume calculations of the flow of rhyolite are presented to investigate the fate of viscous magmas flowing in planar fractures with realistic length to width ratios of up to 2500:1. Heat and mass transfer for a melt with a temperature dependent viscosity and the potential to undergo phase change are considered. Magma driving pressures and dike widths are chosen to satisfy simple elastic considerations. These models are applied within a parameter space relevant to the Banco Bonito rhyolite flow, Valles caldera, New Mexico. We estimate a maximum eruption duration for the event of ~200 days, realized at a minimummore » possible dike width of 5-6 m and driving pressure of 7-8 MPa. Simplifications in the current model may warrant scaling of these results. However, we demonstrate the applicability of our model to magma dynamics issues and suggest that such models may be used to infer information about both the timing of an eruption and the evolution of the associated magma source.« less

Effects of cloud size and cloud particles on satellite-observed reflected brightness

NASA Technical Reports Server (NTRS)

Reynolds, D. W.; Mckee, T. B.; Danielson, K. S.

1978-01-01

Satellite observations allowed obtaining data on the visible brightness of cumulus clouds over South Park, Colorado, while aircraft observations were made in cloud to obtain the drop size distributions and liquid water content of the cloud. Attention is focused on evaluating the relationship between cloud brightness, horizontal dimension, and internal microphysical structure. A Monte Carlo cloud model for finite clouds was run using different distributions of drop sizes and numbers, while varying the cloud depth and width to determine how theory would predict what the satellite would view from its given location in space. Comparison of these results to the satellite observed reflectances is presented. Theoretical results are found to be in good agreement with observations. For clouds of optical thickness between 20 and 60, monitoring cloud brightness changes in clouds of uniform depth and variable width gives adequate information about a cloud's liquid water content. A cloud having a 10:1 width to depth ratio is almost reaching its maximum brightness for a specified optical thickness.

Cyclotron resonance in InAs/AlSb quantum wells in magnetic fields up to 45 T

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

Spirin, K. E., E-mail: spirink@ipmras.ru; Krishtopenko, S. S.; Sadofyev, Yu. G.

Electron cyclotron resonance in InAs/AlSb heterostructures with quantum wells of various widths in pulsed magnetic fields up to 45 T are investigated. Our experimental cyclotron energies are in satisfactory agreement with the results of theoretical calculations performed using the eight-band kp Hamiltonian. The shift of the cyclotron resonance (CR) line, which corresponds to the transition from the lowest Landau level to the low magnetic-field region, is found upon varying the electron concentration due to the negative persistent photoconductivity effect. It is shown that the observed shift of the CR lines is associated with the finite width of the density ofmore » states at the Landau levels.« less

Top-quark decay at next-to-next-to-leading order in QCD.

PubMed

Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing

2013-01-25

We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and W boson width effects. In particular, we also show the first results of the fully differential decay rates for the top-quark semileptonic decay t → W(+)(l(+)ν)b at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

Fast readout algorithm for cylindrical beam position monitors providing good accuracy for particle bunches with large offsets

NASA Astrophysics Data System (ADS)

Thieberger, P.; Gassner, D.; Hulsart, R.; Michnoff, R.; Miller, T.; Minty, M.; Sorrell, Z.; Bartnik, A.

2018-04-01

A simple, analytically correct algorithm is developed for calculating "pencil" relativistic beam coordinates using the signals from an ideal cylindrical particle beam position monitor (BPM) with four pickup electrodes (PUEs) of infinitesimal widths. The algorithm is then applied to simulations of realistic BPMs with finite width PUEs. Surprisingly small deviations are found. Simple empirically determined correction terms reduce the deviations even further. The algorithm is then tested with simulations for non-relativistic beams. As an example of the data acquisition speed advantage, a Field Programmable Gate Array-based BPM readout implementation of the new algorithm has been developed and characterized. Finally, the algorithm is tested with BPM data from the Cornell Preinjector.

Flat tensile specimen design for advanced composites

NASA Technical Reports Server (NTRS)

Worthem, Dennis W.

1990-01-01

Finite element analyses of flat, reduced gage section tensile specimens with various transition region contours were performed. Within dimensional constraints, such as maximum length, tab region width, gage width, gage length, and minimum tab length, a transition contour radius of 41.9 cm produced the lowest stress values in the specimen transition region. The stresses in the transition region were not sensitive to specimen material properties. The stresses in the tab region were sensitive to specimen composite and/or tab material properties. An evaluation of stresses with different specimen composite and tab material combinations must account for material nonlinearity of both the tab and the specimen composite. Material nonlinearity can either relieve stresses in the composite under the tab or elevate them to cause failure under the tab.

Fast readout algorithm for cylindrical beam position monitors providing good accuracy for particle bunches with large offsets

DOE PAGES

Thieberger, Peter; Gassner, D.; Hulsart, R.; ...

2018-04-25

Here, a simple, analytically correct algorithm is developed for calculating “pencil” relativistic beam coordinates using the signals from an ideal cylindrical particle beam position monitor (BPM) with four pickup electrodes (PUEs) of infinitesimal widths. The algorithm is then applied to simulations of realistic BPMs with finite width PUEs. Surprisingly small deviations are found. Simple empirically determined correction terms reduce the deviations even further. The algorithm is then tested with simulations for non-relativistic beams. As an example of the data acquisition speed advantage, a FPGA-based BPM readout implementation of the new algorithm has been developed and characterized. Lastly, the algorithm ismore » tested with BPM data from the Cornell Preinjector.« less

Influence of the Strength Mismatch of a Narrow Gap Welded Joint of SA508 on the Plastic η Factor

NASA Astrophysics Data System (ADS)

Koo, J. M.; Huh, Y.; Seok, C. S.

2012-11-01

In this article, the influence of the strength mismatch of a narrow gap welded joint of SA508 on the η factor was evaluated. The η factor is the principal parameter that determines the plastic portion of the J-integral. The specimens for tensile and hardness tests were collected from piping with narrow gap welding and the stress-strain curve and hardness were obtained from those. From these results, the Ramberg-Osgood (R-O) constant was obtained. Also, the finite element analysis was performed with variations in the strength mismatch and the weld width. The η factor equation considering the strength mismatch and the weld width of a narrow gap welded joint was suggested.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

NASA Astrophysics Data System (ADS)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Fast readout algorithm for cylindrical beam position monitors providing good accuracy for particle bunches with large offsets

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

Thieberger, Peter; Gassner, D.; Hulsart, R.

Here, a simple, analytically correct algorithm is developed for calculating “pencil” relativistic beam coordinates using the signals from an ideal cylindrical particle beam position monitor (BPM) with four pickup electrodes (PUEs) of infinitesimal widths. The algorithm is then applied to simulations of realistic BPMs with finite width PUEs. Surprisingly small deviations are found. Simple empirically determined correction terms reduce the deviations even further. The algorithm is then tested with simulations for non-relativistic beams. As an example of the data acquisition speed advantage, a FPGA-based BPM readout implementation of the new algorithm has been developed and characterized. Lastly, the algorithm ismore » tested with BPM data from the Cornell Preinjector.« less

Restoration of isospin symmetry in highly excited nuclei

NASA Astrophysics Data System (ADS)

Sagawa, H.; Bortignon, P. F.; Colò, G.

1998-12-01

Explicit relations between the isospin mixing probability, the spreading width ΓIAS↓ of the Isobaric Analog State (IAS) and the statistical decay width Γc of the compound nucleus at finite excitation energy, are derived by using the Feshbach projection formalism. The temperature dependence of the isospin mixing probability is discussed quantitatively for the first time by using the values of ΓIAS↓ and of Γc calculated by means of microscopic models. It is shown that the mixing probability remains essentially constant up to a temperature of the order of 1 MeV and then decreases to about 1/4 of its zero temperature value, at higher temperature than ~3 MeV, due to the short decay time of the compound system.

Fast readout algorithm for cylindrical beam position monitors providing good accuracy for particle bunches with large offsets.

PubMed

Thieberger, P; Gassner, D; Hulsart, R; Michnoff, R; Miller, T; Minty, M; Sorrell, Z; Bartnik, A

2018-04-01

A simple, analytically correct algorithm is developed for calculating "pencil" relativistic beam coordinates using the signals from an ideal cylindrical particle beam position monitor (BPM) with four pickup electrodes (PUEs) of infinitesimal widths. The algorithm is then applied to simulations of realistic BPMs with finite width PUEs. Surprisingly small deviations are found. Simple empirically determined correction terms reduce the deviations even further. The algorithm is then tested with simulations for non-relativistic beams. As an example of the data acquisition speed advantage, a Field Programmable Gate Array-based BPM readout implementation of the new algorithm has been developed and characterized. Finally, the algorithm is tested with BPM data from the Cornell Preinjector.

A total life prediction model for stress concentration sites

NASA Technical Reports Server (NTRS)

Hartman, G. A.; Dawicke, D. S.

1983-01-01

Fatigue crack growth tests were performed on center crack panels and radial crack hole samples. The data were reduced and correlated with the elastic parameter K taking into account finite width and corner crack corrections. The anomalous behavior normally associated with short cracks was not observed. Total life estimates for notches were made by coupling an initiation life estimate with a propagation life estimate.

A total life prediction model for stress concentration sites

NASA Technical Reports Server (NTRS)

Hartman, G. A.; Dawicke, D. S.

1983-01-01

Fatigue crack growth tests were performed on center crack panels and radial crack hole samples. The data were reduced and correlated with the elastic parameter-K taking into account finite width and corner crack corrections. The anomalous behavior normally associated with short cracks was not observed. Total life estimates for notches were made by coupling an initiation life estimate with a propagation life estimate.

Neuroperformance Imaging

DTIC Science & Technology

2012-10-01

EMBC10.1722. 10. Mitra, P.P., Halperin, B.I.: Effects of finite gradient-pulse widths in pulsed- field - gradient diffusion measurements . Journal of Magnetic ...December 2011 ABSTRACT: The addition of a pair of magnetic field gradient pulses had initially enabled the measurement of spin motion to nuclear mag- netic...introduced a pair of (homogenous) magnetic field gradients into the spin echo experi- ment with the purpose of accurately measuring the scalar diffusion

Integrating Security into the Curriculum

DTIC Science & Technology

1998-12-01

predicate calculus, discrete math , and finite-state machine the- ory. In addition to applying standard mathematical foundations to constructing hardware and...models, specifi- cations, and the use of formal methods for verification and covert channel analysis. The means for analysis is based on discrete math , information

Finite Element Solution to the Helmholtz Equation with High Wave Number. Part 1. The h-Version of the FEM

DTIC Science & Technology

1993-11-01

4) between the exact solution and it’s best approximnation on the one and the FE-solution on the other hand. The determining equation for ti. & ielt ...Acknowledgement: The work of the first atitlhor wvas supported by Grant No 517 402 524 3 of the Gerinan Academic Exchange Service (l)AA[)). The work of thle second...methou, mn: A.K. Aziz (ed.), The mathematical foundations of tile finite element, method with applicai.4ons to partial differential equations, Academic

Solving the transport equation with quadratic finite elements: Theory and applications

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

Ferguson, J.M.

1997-12-31

At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

Computing Reliabilities Of Ceramic Components Subject To Fracture

NASA Technical Reports Server (NTRS)

Nemeth, N. N.; Gyekenyesi, J. P.; Manderscheid, J. M.

1992-01-01

CARES calculates fast-fracture reliability or failure probability of macroscopically isotropic ceramic components. Program uses results from commercial structural-analysis program (MSC/NASTRAN or ANSYS) to evaluate reliability of component in presence of inherent surface- and/or volume-type flaws. Computes measure of reliability by use of finite-element mathematical model applicable to multiple materials in sense model made function of statistical characterizations of many ceramic materials. Reliability analysis uses element stress, temperature, area, and volume outputs, obtained from two-dimensional shell and three-dimensional solid isoparametric or axisymmetric finite elements. Written in FORTRAN 77.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Transactions of the Army Conference on Applied Mathematics and Computing (10th) Held at West Point, New York on 16-19 Jun 92

DTIC Science & Technology

1993-03-01

1600 Break 1600 - 1700 General Session IV - Thayer Hall, Room 342 Chairperson: David W. Hislop , U.S. Army Research Office, Research Triangle Park...dynamics studies conducted in the 1950’s and 1960’% using finite difference and finite element methods, and in the 1970’s and 1980 ’s using Green’s...1966. [13] L. C. Young. Lectures on the Calculus of Variations and Optimal Control. Chelsa, 1980 . 68 Kinetically Driven Elastic Phase Boundary Motion

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

Remote sensing applied to numerical modelling. [water resources pollution

NASA Technical Reports Server (NTRS)

Sengupta, S.; Lee, S. S.; Veziroglu, T. N.; Bland, R.

1975-01-01

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

[Stress distribution in press-fit orthodontic microimplant bone interface].

PubMed

Wu, Jian-chao; Huang, Ji-na; Zhao, Shi-fang; Xu, Xue-jun

2006-12-01

The goal of this study is to analyse the stress distribution in the press-fit microimplant-bone interface and its indications for immediate loading of orthodontic microimplant. Three-dimensional finite element models were created of a 20 mm section of posterior mandible simplified in isosceles trapezoid shape, 30 mm in height, 10mm in upper side width, 14 mm in lower side width,with a single microimplant, 1.2 mm in diameter, 6 mm in length embedded in the bone. The cortical bone thickness was assumed as 1.6 mm. Cortical and cancellous bone were modeled as transversely isotropic and linearly elastic materials. Titanium was modeled as isotropic and linearly elastic material. Perfect bonding was assumed at microimplant- bone interfaces. ANSYS 9.0 finite element analysis software was used to generate the simplified finite element models of the local mandible-implant complex. 0 mm, 0.05 mm and 0.1 mm press-fit were arbitrarily set to the implant-bone interface to mimic the situation of immediate placement of microimplant. Stresses in the microimplant-bone interface were calculated under these "press-fit". Stresses distributed mainly in the cortical bone interface. At Omm press-fit, the stress was 0 MPa. For 0.05mm press-fit, the stress was 1648 MPa in mesio-distal direction, 1782MPa in occluso-gingival direction;and for 0.1 mm, it reached 2012MPa in mesio-distal direction, 2110MPa in occluso-gingival direction. As the "press-fit" increased, the stresses increased accordingly. Values of initial stress in the microimplant-bone interface due to press-fit generated by immediately placed microimplant were very high in these limited and simplified three dimensional finite element models. It reminded us that the initial stress be taken into consideration when immediate loading of the microimplant is planned. Supported by Research Fund of Health Bureau of Zhejiang Province (2005B104).

Mathematical theory of a relaxed design problem in structural optimization

NASA Technical Reports Server (NTRS)

Kikuchi, Noboru; Suzuki, Katsuyuki

1990-01-01

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Influence of Finite Element Software on Energy Release Rates Computed Using the Virtual Crack Closure Technique

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Goetze, Dirk; Ransom, Jonathon (Technical Monitor)

2006-01-01

Strain energy release rates were computed along straight delamination fronts of Double Cantilever Beam, End-Notched Flexure and Single Leg Bending specimens using the Virtual Crack Closure Technique (VCCT). Th e results were based on finite element analyses using ABAQUS# and ANSYS# and were calculated from the finite element results using the same post-processing routine to assure a consistent procedure. Mixed-mode strain energy release rates obtained from post-processing finite elem ent results were in good agreement for all element types used and all specimens modeled. Compared to previous studies, the models made of s olid twenty-node hexahedral elements and solid eight-node incompatible mode elements yielded excellent results. For both codes, models made of standard brick elements and elements with reduced integration did not correctly capture the distribution of the energy release rate acr oss the width of the specimens for the models chosen. The results suggested that element types with similar formulation yield matching results independent of the finite element software used. For comparison, m ixed-mode strain energy release rates were also calculated within ABAQUS#/Standard using the VCCT for ABAQUS# add on. For all specimens mod eled, mixed-mode strain energy release rates obtained from ABAQUS# finite element results using post-processing were almost identical to re sults calculated using the VCCT for ABAQUS# add on.

Efficient biosensing through 1D silver nanostructured devices using plasmonic effect.

PubMed

Afsheen, Sumera; Munir, Musarat; Isa Khan, Muhammad; Iqbal, Tahir; Abrar, M; Tahir, Muhammad Bilal; Rehman, Jalil Ur; Nadeem, Khalid; Ijaz, Mohsin; Nabi, Ghulam

2018-06-22

The current work explores the excitation of surface plasmon polarities on one dimensional (1D) silver nano grating device simulated on glass substrate, which can sense a very small change in refractive index of an analyte adjacent to it. The most recent modeling technique finite element analysis (FEA) is applied in this work by using COMSOL RF module. The models of 1D grating device of different slit widths with fixed periodicity and film thickness are simulated. The data is collected and then used to study higher refractive index unit per nanometer (RIU/nm) as well as effect of slits width on RIU. Numbers of investigations are done by the simulated data, like a dip in the transmission spectra of p-polarized light. This dip is due to SPP resonance with the variation of slit width. Furthermore, the most fascinating part of the research is COMSOL modeling that provides an opportunity to look into factors affecting higher RIU/nm while visualizing the cross-sectional view of the grating device and strong electric field enhancement at the surface of the metallic device. When the slit width is almost equal to half of the periodicity of the grating device, SPP resonance increases and it is maximum for the slit width equal to 2/3rd of the periodicity because the coupling efficiency is maximum. © 2018 IOP Publishing Ltd.

Representations of the Extended Poincare Superalgebras in Four Dimensions

NASA Astrophysics Data System (ADS)

Griffis, John D.

Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner's students spent considerable amount of time translating passages of this paper into more detailed and accessible papers and books. In 1975, R. Haag et al. investigated the possible extensions of the symmetries of relativistic quantum particles. They showed that the only consistent (super)symmetric extensions to the standard model of physics are obtained by using super charges to generate the odd part of a Lie superalgebra whose even part is generated by the Poincare group; this theory has become known as supersymmetry. In this paper, R. Haag et al. used a notation called supermultiplets to give the dimension of a representation and its multiplicity; this notation is described mathematically in chapter 5 of this thesis. By 1980 S. Ferrara et al. began classifying the representations of these algebras for dimensions greater than four, and in 1986 Strathdee published considerable work listing some representations for the Poincare superalgebra in any finite dimension. This work has been continued to date. We found the work of S. Ferrara et al. to be essential to our understanding extended supersymmetries. However, this paper was written using imprecise language meant for physicists, so it was far from trivial to understand the mathematical interpretation of this work. In this thesis, we provide a "translation" of the previous results (along with some other literature on the Extended Poincare Superalgebras) into a rigorous mathematical setting, which makes the subject more accessible to a larger audience. Having a mathematical model allows us to give explicit results and detailed proofs. Further, this model allows us to see beyond just the physical interpretation and it allows investigation by a purely mathematically adept audience. Our work was motivated by a paper written in 2012 by M. Chaichian et al, which classified all of the unitary, irreducible representations of the extended Poincare superalgebra in three dimensions. We consider only the four dimensional case, which is of interest to physicists working on quantum supergravity models without cosmological constant, and we provide explicit branching rules for the invariant subgroups corresponding to the most physically relevant symmetries of the irreducible representations of the Extended Poincare Superalgebra in four dimensions. However, it is possible to further generalize this work into any finite dimension. Such work would classify all possible finitely extended supersymmetric models.

Mathematical Models of the Common-Source and Common-Gate Amplifiers using a Metal-Ferroelectric-Semiconductor Field effect Transistor

NASA Technical Reports Server (NTRS)

Hunt, Mitchell; Sayyah, Rana; Mitchell, Cody; Laws, Crystal; MacLeod, Todd C.; Ho, Fat D.

2013-01-01

Mathematical models of the common-source and common-gate amplifiers using metal-ferroelectric- semiconductor field effect transistors (MOSFETs) are developed in this paper. The models are compared against data collected with MOSFETs of varying channel lengths and widths, and circuit parameters such as biasing conditions are varied as well. Considerations are made for the capacitance formed by the ferroelectric layer present between the gate and substrate of the transistors. Comparisons between the modeled and measured data are presented in depth as well as differences and advantages as compared to the performance of each circuit using a MOSFET.

Computing Surface Coordinates Of Face-Milled Spiral-Bevel Gear Teeth

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.; Litvin, Faydor L.

1995-01-01

Surface coordinates of face-milled spiral-bevel gear teeth computed by method involving numerical solution of governing equations. Needed to generate mathematical models of tooth surfaces for use in finite-element analyses of stresses, strains, and vibrations in meshing spiral-bevel gears.

Finite fringe hologram

NASA Technical Reports Server (NTRS)

Heflinger, L. O.

1970-01-01

In holographic interferometry a small movement of apparatus between exposures causes the background of the reconstructed scene to be covered with interference fringes approximately parallel to each other. The three-dimensional quality of the holographic image is allowable since a mathematical model will give the location of the fringes.

Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Thermomechanical Stresses Analysis of a Single Event Burnout Process

NASA Astrophysics Data System (ADS)

Tais, Carlos E.; Romero, Eduardo; Demarco, Gustavo L.

2009-06-01

This work analyzes the thermal and mechanical effects arising in a power Diffusion Metal Oxide Semiconductor (DMOS) during a Single Event Burnout (SEB) process. For studying these effects we propose a more detailed simulation structure than the previously used by other authors, solving the mathematical models by means of the Finite Element Method. We use a cylindrical heat generation region, with 5 W, 10 W, 50 W and 100 W for emulating the thermal phenomena occurring during SEB processes, avoiding the complexity of the mathematical treatment of the ion-semiconductor interaction.

Numerical modeling of heat transfer in the fuel oil storage tank at thermal power plant

NASA Astrophysics Data System (ADS)

Kuznetsova, Svetlana A.

2015-01-01

Presents results of mathematical modeling of convection of a viscous incompressible fluid in a rectangular cavity with conducting walls of finite thickness in the presence of a local source of heat in the bottom of the field in terms of convective heat exchange with the environment. A mathematical model is formulated in terms of dimensionless variables "stream function - vorticity vector speed - temperature" in the Cartesian coordinate system. As the results show the distributions of hydrodynamic parameters and temperatures using different boundary conditions on the local heat source.

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

Mathematical Simulation of Drying Process of Fibrous Material

NASA Astrophysics Data System (ADS)

Blejchař, Tomáš; Raška, Jiří; Jablonská, Jana

2018-06-01

The article describes mathematical simulation of flowing air through porous zone and water vaporisation from mentioned porous area which actually represents dried fibrous material - cotton towel. Simulation is based on finite volume method. Wet towel is placed in pipe and hot air flow through the towel. Water from towel is evaporated. Simulation of airflow through porous element is described first. Eulerian multiphase model is then used for simulation of water vaporisation from porous medium. Results of simulation are compared with experiment. Ansys Fluent 13.0 was used for calculation.

Finite Ground Coplanar (FGC) Waveguide: Characteristics and Advantages Evaluated for Radiofrequency and Wireless Communication Circuits

NASA Technical Reports Server (NTRS)

Ponchak, George E.

1999-01-01

Researchers in NASA Lewis Research Center s Electron Device Technology Branch are developing transmission lines for radiofrequency and wireless circuits that are more efficient, smaller, and make lower cost circuits possible. Traditionally, radiofrequency and wireless circuits have employed a microstrip or coplanar waveguide to interconnect the various electrical elements that comprise a circuit. Although a coplanar waveguide (CPW) is widely viewed as better than a microstrip for most applications, it too has problems. To solve these problems, NASA Lewis and the University of Michigan developed a new version of a coplanar waveguide with electrically narrow ground planes. Through extensive numerical modeling and experimental measurements, we have characterized the propagation constant of the FGC waveguide, the lumped and distributed circuit elements integrated in the FGC waveguide, and the coupling between parallel transmission lines. Although the attenuation per unit length is higher for the FGC waveguide because of higher conductor loss, the attenuation is comparable when the ground plane width is twice the center conductor width as shown in the following graph. An upper limit to the line width is derived from observations that when the total line width is greater than ld/2, spurious resonances due to the parallel plate waveguide mode are established. Thus, the ground plane width must be less than ld/4 where ld is the wavelength in the dielectric. Since the center conductor width S is typically less than l/10 to maintain good transverse electromagnetic mode characteristics, it follows that a ground plane width of B = 2S would also be electrically narrow. Thus, we can now treat the ground strips of the FGC waveguide the same way that the center conductor is treated.

The Role of Self-Assessment in Foundation of Mathematics Learning

NASA Astrophysics Data System (ADS)

Masriyah

2018-01-01

This research is motivated by the low performance of students who took Foundations of Mathematics course. This study was aimed to describe (1) the learning outcomes of students who learned Mathematics Foundation after learning axiomatic applying self-assessment; (2) the difficulty of students and the alternative solutions; and (3) the response of students toward Foundation of Mathematics learning taught by applying self-assessment. This research was a descriptive research. The subjects were 25 mathematics students who studied Foundation of Mathematics in odd semester of the 2015/2016 academic year. Data collection was done using questionnaires, and testing methods. Based on the results of data analysis, it can be concluded that the learning outcomes of students were categorized as “good.” Student responses were positive; the difficulties lied in the sub material: Classification of Axiom Systems and the requirements, Theorem and how the formation, and finite geometry. The alternatives deal with these difficulties are to give emphasis and explanation as needed on these materials, as well as provide some more exercises to reinforce their understanding.

Determination of the thermodynamic correction factor of fluids confined in nano-metric slit pores from molecular simulation

NASA Astrophysics Data System (ADS)

Collell, Julien; Galliero, Guillaume

2014-05-01

The multi-component diffusive mass transport is generally quantified by means of the Maxwell-Stefan diffusion coefficients when using molecular simulations. These coefficients can be related to the Fick diffusion coefficients using the thermodynamic correction factor matrix, which requires to run several simulations to estimate all the elements of the matrix. In a recent work, Schnell et al. ["Thermodynamics of small systems embedded in a reservoir: A detailed analysis of finite size effects," Mol. Phys. 110, 1069-1079 (2012)] developed an approach to determine the full matrix of thermodynamic factors from a single simulation in bulk. This approach relies on finite size effects of small systems on the density fluctuations. We present here an extension of their work for inhomogeneous Lennard Jones fluids confined in slit pores. We first verified this extension by cross validating the results obtained from this approach with the results obtained from the simulated adsorption isotherms, which allows to determine the thermodynamic factor in porous medium. We then studied the effects of the pore width (from 1 to 15 molecular sizes), of the solid-fluid interaction potential (Lennard Jones 9-3, hard wall potential) and of the reduced fluid density (from 0.1 to 0.7 at a reduced temperature T* = 2) on the thermodynamic factor. The deviation of the thermodynamic factor compared to its equivalent bulk value decreases when increasing the pore width and becomes insignificant for reduced pore width above 15. We also found that the thermodynamic factor is sensitive to the magnitude of the fluid-fluid and solid-fluid interactions, which softens or exacerbates the density fluctuations.

Determination of the thermodynamic correction factor of fluids confined in nano-metric slit pores from molecular simulation

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

Collell, Julien; Galliero, Guillaume, E-mail: guillaume.galliero@univ-pau.fr

2014-05-21

The multi-component diffusive mass transport is generally quantified by means of the Maxwell-Stefan diffusion coefficients when using molecular simulations. These coefficients can be related to the Fick diffusion coefficients using the thermodynamic correction factor matrix, which requires to run several simulations to estimate all the elements of the matrix. In a recent work, Schnell et al. [“Thermodynamics of small systems embedded in a reservoir: A detailed analysis of finite size effects,” Mol. Phys. 110, 1069–1079 (2012)] developed an approach to determine the full matrix of thermodynamic factors from a single simulation in bulk. This approach relies on finite size effectsmore » of small systems on the density fluctuations. We present here an extension of their work for inhomogeneous Lennard Jones fluids confined in slit pores. We first verified this extension by cross validating the results obtained from this approach with the results obtained from the simulated adsorption isotherms, which allows to determine the thermodynamic factor in porous medium. We then studied the effects of the pore width (from 1 to 15 molecular sizes), of the solid-fluid interaction potential (Lennard Jones 9-3, hard wall potential) and of the reduced fluid density (from 0.1 to 0.7 at a reduced temperature T* = 2) on the thermodynamic factor. The deviation of the thermodynamic factor compared to its equivalent bulk value decreases when increasing the pore width and becomes insignificant for reduced pore width above 15. We also found that the thermodynamic factor is sensitive to the magnitude of the fluid-fluid and solid-fluid interactions, which softens or exacerbates the density fluctuations.« less

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

PubMed

Decker, Gifford Z; Thomson, Scott L

2007-05-01

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

The effect of beamwidth on the analysis of electron-beam-induced current line scans

NASA Astrophysics Data System (ADS)

Luke, Keung L.

1995-04-01

A real electron beam has finite width, which has been almost universally ignored in electron-beam-induced current (EBIC) theories. Obvious examples are point-source-based EBIC analyses, which neglect both the finite volume of electron-hole carriers generated by an energetic electron beam of negligible width and the beamwidth when it is no longer negligible. Gaussian source-based analyses are more realistic but the beamwidth has not been included, partly because the generation volume is much larger than the beamwidth, but this is not always the case. In this article Donolato's Gaussian source-based EBIC equation is generalized to include the beamwidth of a Gaussian beam. This generalized equation is then used to study three problems: (1) the effect of beamwidth on EBIC line scans and on effective diffusion lengths and the results are applied to the analysis of the EBIC data of Dixon, Williams, Das, and Webb; (2) unresolved questions raised by others concerning the applicability of the Watanabe-Actor-Gatos method to real EBIC data to evaluate surface recombination velocity; (3) the effect of beamwidth on the methods proposed recently by the author to determine the surface recombination velocity and to discriminate between the Everhart-Hoff and Kanaya-Okayama ranges which is the correct one to use for analyzing EBIC line scans.

Electroosmotic flow and ionic conductance in a pH-regulated rectangular nanochannel

NASA Astrophysics Data System (ADS)

Sadeghi, Morteza; Saidi, Mohammad Hassan; Sadeghi, Arman

2017-06-01

Infinite series solutions are obtained for electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties of long pH-regulated rectangular nanochannels of low surface potential utilizing the double finite Fourier transform method. Closed form expressions are also obtained for channels of large height to width ratio for which the depthwise variations vanish. Neglecting the Stern layer impact, the effects of EDL (Electric Double Layer) overlap, multiple ionic species, and association/dissociation reactions on the surface are all taken into account. Moreover, finite-element-based numerical simulations are conducted to account for the end effects as well as to validate the analytical solutions. We show that, with the exception of the migratory ionic conductivity, all the physicochemical parameters are strong functions of the channel aspect ratio. Accordingly, a slit geometry is not a good representative of a rectangular channel when the width is comparable to the height. It is also observed that the distribution of the electrical potential is not uniform over the surface of a charge-regulated channel. In addition, unlike ordinary channels for which an increase in the background salt concentration is always accompanied by higher flow rates, quite the opposite may be true for a pH-regulated duct at higher salt concentrations.

Mathematical model of an indirect action fuel flow controller for aircraft jet engines

NASA Astrophysics Data System (ADS)

Tudosie, Alexandru-Nicolae

2017-06-01

The paper deals with a fuel mass flow rate controller with indirect action for aircraft jet engines. The author has identified fuel controller's main parts and its operation mode, then, based on these observations, one has determined motion equations of each main part, which have built system's non-linear mathematical model. In order to realize a better study this model was linearised (using the finite differences method) and then adimensionalized. Based on this new form of the mathematical model, after applying Laplace transformation, the embedded system (controller+engine) was described by the block diagram with transfer functions. Some Simulink-Matlab simulations were performed, concerning system's time behavior for step input, which lead to some useful conclusions and extension possibilities.

Kinematics of Tape Recording.

ERIC Educational Resources Information Center

Coleman, J. J.

1982-01-01

Describes mathematics of the nonliner relationships between a constant-speed, capstan-driven magnetic tape transport mechanism and a constant-angular-velocity take-up reel. The relationship, derived from the sum of a partial, serves in recognition of a finite tape. Thickness can serve as an example of rotational kinematics. (Author/SK)

Application of NASTRAN/COSMIC in the analysis of ship structures to underwater explosion shock

NASA Technical Reports Server (NTRS)

Fallon, D. J.; Costanzo, F. A.; Handleton, R. T.; Camp, G. C.; Smith, D. C.

1987-01-01

The application of NASTRAN/COSMIC in predicting the transient motion of ship structures to underwater, non-contact explosions is discussed. Examples illustrate the finite element models, mathematical formulations of loading functions and, where available, comparisons between analytical and experimental results.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Solar Wind Suprathermal Electron Strahl Width from 1.3 to 5.4 AU

NASA Astrophysics Data System (ADS)

Goodrich, K. A.; Skoug, R. M.; Steinberg, J. T.; McComas, D. J.

2010-12-01

The solar wind suprathermal electron population typically includes an anisotropic anti-sunward field-aligned beam component, referred to as the strahl. As strahl electrons propagate anti-sunward in a decreasing interplanetary magnetic field, magnetic focusing acts to narrow the strahl beam width. At the same time, scattering processes work against the focusing and maintain strahl beams of finite width. The observed strahl width in the heliosphere is the result of the competition between focusing and scattering. The suprathermal electron strahl width and intensity observed by Ulysses from 1991 - 2008 have been newly examined. These observations cover radial distances between 1.3 and 5.4 AU, and span more than a solar cycle. The strahl width and intensity are characterized by fitting pitch angle distributions to a function consisting of a Gaussian, peaked parallel (or anti-parallel) to the interplanetary field, plus a constant term. Approximately 50 - 65% of the Ulysses pitch angle spectra yield reasonable fits in preliminary analysis, indicating distributions that are well-described by this simple function. For most of the Ulysses observations at energies below 429 eV, the strahl width lies between 20o and 90o. The Ulysses results contrast with previously reported ACE observations at 1 AU. In particular, the more distant Ulysses results appear shifted towards larger strahl widths, indicating that scattering becomes relatively more important than focusing beyond 1 AU. The Ulysses strahl widths are generally broader at heliospheric distances just beyond 2.5 AU than inside 2.5 AU. Between about 2.5 AU and 4.5 AU, the strahl width distribution varies little. Beyond 4.5 AU the strahl width again narrows, indicating that focusing begins to overcome scattering at these large distances. The distribution of strahl widths during the 1st (1992-1998) and 2nd (1998 - 2004) Ulysses polar orbits were compared, with little difference found. However a comparison of strahl widths during 1994, a year dominated by coronal hole high-speed solar wind, to 2000, a year dominated by slow solar wind, revealed a notable difference, with widths generally narrower during 1994 than in 2000. Here we present a comprehensive analysis regarding the variability of the strahl width and intensity with heliocentric distance, as well as with the estimated electron field line path length. In addition, we examine the occurrence of unidirectional and counterstreaming strahl electrons, as indicated by the fitting algorithm.

Finite Element Modeling of Micromachined MEMS Photon Devices

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

Datskos, P.G.; Evans, B.M.; Schonberger, D.

1999-09-20

The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We havemore » used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness.« less

Finite element modeling of micromachined MEMS photon devices

NASA Astrophysics Data System (ADS)

Evans, Boyd M., III; Schonberger, D. W.; Datskos, Panos G.

1999-09-01

The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We have used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness.

Ten Deg Off-Axis Test for Shear Properties in Fiber Composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1977-01-01

A combined theoretical and experimental investigation was conducted to assess the suitability of the 10 deg off-axis tensile test specimen for the intralaminar shear characterization of unidirectional composites. Composite mechanics, a combined-stress failure criterion, and a finite variation across the specimen width and the relative stress and strain magnitudes at the 10 deg plane. Strain gages were used to measure the strain variation across the specimen width at specimen midlength and near the end tabs. Specimens from Mod-I/epoxy, T-300/epoxy, and S-glass/epoxy were used in the experimental program. It was found that the 10 deg off-axis tensile test specimen is suitable for intralaminar shear characterization, and it is recommended that it should be considered as a possible standard test specimen for such a characterization.

Quantum confinement of exciton-polaritons in a structured (Al,Ga)As microcavity

NASA Astrophysics Data System (ADS)

Kuznetsov, Alexander S.; Helgers, Paul L. J.; Biermann, Klaus; Santos, Paulo V.

2018-05-01

The realization of quantum functionalities with polaritons in an all-semiconductor platform requires the control of the energy and spatial overlap of the wave functions of single polaritons trapped in potentials with precisely controlled shape and size. In this study we reach the confinement of microcavity polaritons in traps with an effective potential width down to 1 µm, produced by patterning the active region of the (Al,Ga)As microcavity between two molecular beam epitaxy growth runs. We correlate spectroscopic and structural data to show that the smooth surface relief of the patterned traps translates into a graded confinement potential characterized by lateral interfaces with a finite lateral width. We show that the structuring method is suitable for the fabrication of arrays of proximal traps, supporting hybridization between adjacent lattice sites.

A novel single-phase flux-switching permanent magnet linear generator used for free-piston Stirling engine

NASA Astrophysics Data System (ADS)

Zheng, Ping; Sui, Yi; Tong, Chengde; Bai, Jingang; Yu, Bin; Lin, Fei

2014-05-01

This paper investigates a novel single-phase flux-switching permanent-magnet (PM) linear machine used for free-piston Stirling engines. The machine topology and operating principle are studied. A flux-switching PM linear machine is designed based on the quasi-sinusoidal speed characteristic of the resonant piston. Considering the performance of back electromotive force and thrust capability, some leading structural parameters, including the air gap length, the PM thickness, the ratio of the outer radius of mover to that of stator, the mover tooth width, the stator tooth width, etc., are optimized by finite element analysis. Compared with conventional three-phase moving-magnet linear machine, the proposed single-phase flux-switching topology shows advantages in less PM use, lighter mover, and higher volume power density.

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

DOE PAGES

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

2018-04-27

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

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

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Analyses of radiation impedances of finite cylindrical ducts

NASA Astrophysics Data System (ADS)

Shao, W.; Mechefske, C. K.

2005-08-01

To aid in understanding the characteristics of acoustic radiation from finite cylindrical ducts with infinite flanges, mathematical expressions of generalized radiation impedances at the open ends have been developed. Newton's method is used to find the complex wavenumbers of radial modes for the absorption boundary condition. The self-radiation impedances and mutual impedances for some acoustic modes are calculated for the ducts with rigid and absorption walls. The results show that the acoustical conditions of the duct walls have a significant influence on the radiation impedance. The acoustical interaction between the two open ends of the ducts cannot be neglected, especially for plane waves. To increase the wall admittance will reduce this interference effect. This study creates the possibility for simulating the sound field inside finite ducts in future work.

Planning, creating and documenting a NASTRAN finite element model of a modern helicopter

NASA Technical Reports Server (NTRS)

Gabal, R.; Reed, D.; Ricks, R.; Kesack, W.

1985-01-01

Mathematical models based on the finite element method of structural analysis as embodied in the NASTRAN computer code are widely used by the helicopter industry to calculate static internal loads and vibration of airframe structure. The internal loads are routinely used for sizing structural members. The vibration predictions are not yet relied on during design. NASA's Langley Research Center sponsored a program to conduct an application of the finite element method with emphasis on predicting structural vibration. The Army/Boeing CH-47D helicopter was used as the modeling subject. The objective was to engender the needed trust in vibration predictions using these models and establish a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process.

Radon transport model into a porous ground layer of finite capacity

NASA Astrophysics Data System (ADS)

Parovik, Roman

2017-10-01

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

Quantum interval-valued probability: Contextuality and the Born rule

NASA Astrophysics Data System (ADS)

Tai, Yu-Tsung; Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr

2018-05-01

We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. While foundational results such as the Kochen-Specker and Gleason theorems are valid in the context of infinite precision, they fail to hold in general in a world with limited resources. Here we employ an interval-valued framework to establish bounds on the validity of those theorems in realistic experimental environments. In this way, not only can we quantify the idea of finite-precision measurement within our theory, but we can also suggest a possible resolution of the Meyer-Mermin debate on the impact of finite-precision measurement on the Kochen-Specker theorem.

Survey of meshless and generalized finite element methods: A unified approach

NASA Astrophysics Data System (ADS)

Babuška, Ivo; Banerjee, Uday; Osborn, John E.

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

Full quaternion based finite-time cascade attitude control approach via pulse modulation synthesis for a spacecraft.

PubMed

Mazinan, A H; Pasand, M; Soltani, B

2015-09-01

In the aspect of further development of investigations in the area of spacecraft modeling and analysis of the control scheme, a new hybrid finite-time robust three-axis cascade attitude control approach is proposed via pulse modulation synthesis. The full quaternion based control approach proposed here is organized in association with both the inner and the outer closed loops. It is shown that the inner closed loop, which consists of the sliding mode finite-time control approach, the pulse width pulse frequency modulator, the control allocation and finally the dynamics of the spacecraft is realized to track the three-axis referenced commands of the angular velocities. The pulse width pulse frequency modulators are in fact employed in the inner closed loop to accommodate the control signals to a number of on-off thrusters, while the control allocation algorithm provides the commanded firing times for the reaction control thrusters in the overactuated spacecraft. Hereinafter, the outer closed loop, which consists of the proportional linear control approach and the kinematics of the spacecraft is correspondingly designed to deal with the attitude angles that are presented by quaternion vector. It should be noted that the main motivation of the present research is to realize a hybrid control method by using linear and nonlinear terms and to provide a reliable and robust control structure, which is able to track time varying three-axis referenced commands. Subsequently, a stability analysis is presented to verify the performance of the overall proposed cascade attitude control approach. To prove the effectiveness of the presented approach, a thorough investigation is presented compared to a number of recent corresponding benchmarks. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A History of the Description of the Three-Dimensional Finite Rotation

NASA Astrophysics Data System (ADS)

Fraiture, Luc

2009-01-01

A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Multisource passive acoustic tracking: an application of random finite set data fusion

NASA Astrophysics Data System (ADS)

Ali, Andreas M.; Hudson, Ralph E.; Lorenzelli, Flavio; Yao, Kung

2010-04-01

Multisource passive acoustic tracking is useful in animal bio-behavioral study by replacing or enhancing human involvement during and after field data collection. Multiple simultaneous vocalizations are a common occurrence in a forest or a jungle, where many species are encountered. Given a set of nodes that are capable of producing multiple direction-of-arrivals (DOAs), such data needs to be combined into meaningful estimates. Random Finite Set provides the mathematical probabilistic model, which is suitable for analysis and optimal estimation algorithm synthesis. Then the proposed algorithm has been verified using a simulation and a controlled test experiment.

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

NASA Technical Reports Server (NTRS)

Lebiedzik, Catherine

1995-01-01

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Distributed Algorithms for Probabilistic Solution of Computational Vision Problems.

DTIC Science & Technology

1988-03-01

34 targets. Legters and Young (1982) developed an operator-based approach r% using foreground and background models and solved a least-squares minimiza...1960), "Finite Markov Chains", Van Nostrand, , - New York. Legters , G.R., and Young, T.Y. (1982), "A Mathematical Model for Computer Image Tracking

Remote sensing of earth terrain

NASA Technical Reports Server (NTRS)

Kong, Jin AU; Yueh, Herng-Aung; Shin, Robert T.

1991-01-01

Abstracts from 46 refereed journal and conference papers are presented for research on remote sensing of earth terrain. The topics covered related to remote sensing include the following: mathematical models, vegetation cover, sea ice, finite difference theory, electromagnetic waves, polarimetry, neural networks, random media, synthetic aperture radar, electromagnetic bias, and others.

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Analysis of the Efficiency of an A-Posteriori Error Estimator for Linear Triangular Finite Elements

DTIC Science & Technology

1991-06-01

Release 1.0, NOETIC Tech. Corp., St. Louis, Missouri, 1985. [28] R. VERFURTH, FEMFLOW-user guide. Version 1, Report, Universitiit Zirich, 1989. [29] R... study and research for foreign students in numerical mathematics who are supported by foreign governments or exchange agencies (Fulbright, etc

Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.

DTIC Science & Technology

1987-01-01

Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept

Control Systems with Pulse Width Modulation in Matrix Converters

NASA Astrophysics Data System (ADS)

Bondarev, A. V.; Fedorov, S. V.; Muravyova, E. A.

2018-03-01

In this article, the matrix frequency converter for the system of the frequency control of the electric drive is considered. Algorithms of formation of an output signal on the basis of pulse width modulation were developed for the quantitative analysis of quality of an output signal on the basis of mathematical models. On the basis of simulation models of an output signal, assessment of quality of this signal was carried out. The analysis of harmonic composition of the voltage output received on the basis of pulse width modulation was made for the purpose of determination of opportunities of the control system for improving harmonic composition. The result of such analysis led to the fact that the device formation of switching functions of the control system on the basis of PWM does not lead to a distortion reduction of a harmonic of the control signal, and leads to offset of harmonic in the field of frequencies, the multiple relatively carrier frequency.

Breakup Behavior of a Capillary Bridge on a Hydrophobic Stripe Separating Two Hydrophilic Stripes

NASA Astrophysics Data System (ADS)

Hartmann, Maximilian; Hardt, Steffen

2017-11-01

The breakup dynamics of a capillary bridge on a hydrophobic area between two liquid filaments occupying two parallel hydrophilic stripes is studied experimentally. In addition calculations with the finite-element software Surface Evolver are performed to obtain the corresponding stable minimal surfaces. Droplets of de-ionized water are placed on substrates with alternating hydrophilic and hydrophobic stripes of different width. Their volume decreases by evaporation. This results in a droplet shaped as the letter ``H'' covering two hydrophilic stripes separated by one hydrophobic stripe. The width of the capillary bridge d(t) on the hydrophobic stripe during the breakup process is observed using a high-speed camera mounted on a bright-field microscope. The results of the experiments and the numerical studies show that the critical width dcrit, indicating the point where the capillary bridge becomes unstable, mainly depends on the width ratio of the hydrophilic and hydrophobic stripes. It is found that the time derivative of d(t) first decreases after dcrit has been reached. The final breakup dynamics then follows a t 2 / 3 scaling. We kindly acknowledge the financial support by the German Research Foundation (DFG) within the Collaborative Research Centre 1194 ``Interaction of Transport and Wetting Processes'', Project A02a.

Fano resonances of a ring-shaped "hexamer" cluster at near-infrared wavelength

NASA Astrophysics Data System (ADS)

Liu, Tong-Tong; Xia, Feng; Sun, Peng; Liu, Li-Li; Du, Wei; Li, Meng-Xue; Kong, Wei-Jin; Wan, Yong; Dong, Li-Feng; Yun, Mao-Jin

2018-03-01

Fano resonances have been studied intensely in the last decade, since it is an important way to decrease the resonance line width and enhance local electric field. However, achieving a Fano line-shape with both narrow line width and high spectral contrast ratio is still a challenge. In this paper, we theoretically predict the Fano resonance induced by the extinction of normal plane wave in a ring-shaped hexamer cluster at near-infrared wavelength. In order to obtain the narrow Fano line width and high spectral contrast ratio, the relationships between the Fano line-shape and the parameters of the nanostructure are analyzed in detail. The nanostructure is simulated by using commercial software based on finite element method. The simulation results show that when the structural parameters are optimized, the Fano line width can be narrowed down 0.028 eV with a contrast ratio of 86%, and the local electric field enhancement factor at the Fano resonance wavelength can reach to 36. Furthermore, the effective mode volume of the structure is 3.9 ×10-23m3 which is lower than the available literature. These results indicate many potential applications of the Fano resonance in multiwavelength surface-enhanced Raman scattering and biosensing.

The electronic and optical properties of quantum nano-structures

NASA Astrophysics Data System (ADS)

Ham, Heon

In semiconducting quantum nano-structures, the excitonic effects play an important role when we fabricate opto-electronic devices, such as lasers, diodes, detectors, etc. To gain a better understanding of the excitonic effects in quantum nano-structures, we investigated the exciton binding energy, oscillator strength, and linewidth in quantum nano-structures using both the infinite and finite well models. We investigated also the hydrogenic impurity binding energy and the photoionization cross section of the hydrogenic impurity in a spherical quantum dot. In our work, the variational approach is used in all calculations, because the Hamiltonian of the system is not separable, due to the different symmetries of the Coulomb and confining potentials. In the infinite well model of the semiconducting quantum nanostructures, the binding energy of the exciton increases with decreasing width of the potential barriers due to the increase in the effective strength of the Coulomb interaction between the electron and hole. In the finite well model, the exciton binding energy reaches a peak value, and the binding energy decreases with further decrease in the width of the potential barriers. The exciton linewidth in the infinite well model increases with decreasing wire radius, because the scattering rate of the exciton increases with decreasing wire radius. In the finite well model, the exciton linewidth in a cylindrical quantum wire reaches a peak value and the exciton linewidth decreases with further decrease in the wire radius, because the exciton is not well confined at very smaller wire radii. The binding energy of the hydrogenic impurity in a spherical quantum dot has also calculated using both the infinite and the finite well models. The binding energy of the hydrogenic impurity was calculated for on center and off center impurities in the spherical quantum dots. With decreasing radii of the dots, the binding energy of the hydrogenic impurity increases in the infinite well model. The binding energy of the hydrogenic impurity in the finite well model reaches a peak value and decreases with further decrease in the dot radii for both on center and off center impurities. We have calculated the photoionization cross section as a function of the radius and the frequency using both the infinite and finite well models. The photoionizaton cross section has a peak value at a frequency where the photon energy equals the difference between the final and initial state energies of the impurity. The behavior of the cross section with dot radius depends upon the location of the impurity and the polarization of the electromagnetic field.

The characteristic of gap FBG and its application

NASA Astrophysics Data System (ADS)

Yang, Yuanhong; Hu, Jun; Liu, Xuejing; Jin, Wei

2015-07-01

A gap fiber Bragg grating (g-FBG) is fabricated by cutting a uniform FBG in the middle to introduce a small air gap between the two sections. Numerical and experimental investigations show that the g-FBG has the characteristics of both a phase shifted FBG and a Fizeau interferometer. The influence of the air-gap shift longitudinally or transversely with respect to the fiber central axis and temperature to g-FBG's spectrums are investigated with numerical simulation and experiments, and the mathematic models are made. Based on g-FBG's different sensitivity to gap width and temperature, a micro-gap and temperature simultaneous measurement sensor was demonstrated. And a g-FBG based tunable fiber ring laser with a narrow line-width is demonstrated.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Study of field shifts of Ramsey resonances on ultracold atoms and ions

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

Tabatchikova, K. S., E-mail: k.tabatchikova@gmail.com; Taichenachev, A. V.; Dmitriev, A. K.

2015-02-15

The effect of the finite laser radiation line width and spontaneous relaxation of levels on the efficiency of the suppression of the field shift of the central resonance for the generalized Ramsey scheme with pulses of different lengths and with a phase jump in the second pulse has been considered. The optimal parameters of the scheme corresponding to the minimum frequency shift and maximum amplitude of the resonance have been determined.

Cochlear anatomy using micro computed tomography (μCT) imaging

NASA Astrophysics Data System (ADS)

Kim, Namkeun; Yoon, Yongjin; Steele, Charles; Puria, Sunil

2008-02-01

A novel micro computed tomography (μCT) image processing method was implemented to measure anatomical features of the gerbil and chinchilla cochleas, taking into account the bent modailosis axis. Measurements were made of the scala vestibule (SV) area, the scala tympani (SV) area, and the basilar membrane (BM) width using prepared cadaveric temporal bones. 3-D cochlear structures were obtained from the scanned images using a process described in this study. It was necessary to consider the sharp curvature of mododailosis axis near the basal region. The SV and ST areas were calculated from the μCT reconstructions and compared with existing data obtained by Magnetic Resonance Microscopy (MRM), showing both qualitative and quantitative agreement. In addition to this, the width of the BM, which is the distance between the primary and secondary osseous spiral laminae, is calculated for the two animals and compared with previous data from the MRM method. For the gerbil cochlea, which does not have much cartilage in the osseous spiral lamina, the μCT-based BM width measurements show good agreement with previous data. The chinchilla BM, which contains more cartilage in the osseous spiral lamina than the gerbil, shows a large difference in the BM widths between the μCT and MRM methods. The SV area, ST area, and BM width measurements from this study can be used in building an anatomically based mathematical cochlear model.

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

PubMed

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Compact cantilever couplers for low-loss fiber coupling to silicon photonic integrated circuits.

PubMed

Wood, Michael; Sun, Peng; Reano, Ronald M

2012-01-02

We demonstrate coupling from tapered optical fibers to 450 nm by 250 nm silicon strip waveguides using compact cantilever couplers. The couplers consist of silicon inverse width tapers embedded within silicon dioxide cantilevers. Finite difference time domain simulations are used to design the length of the silicon inverse width taper to as short as 6.5 μm for a cantilever width of 2 μm. Modeling of various strip waveguide taper profiles shows reduced coupling losses for a quadratic taper profile. Infrared measurements of fabricated devices demonstrate average coupling losses of 0.62 dB per connection for the quasi-TE mode and 0.50 dB per connection for the quasi-TM mode across the optical telecommunications C band. In the wavelength range from 1477 nm to 1580 nm, coupling losses for both polarizations are less than 1 dB per connection. The compact, broadband, and low-loss coupling scheme enables direct access to photonic integrated circuits on an entire chip surface without the need for dicing or cleaving the chip.

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

NASA Astrophysics Data System (ADS)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

Mathematical Theories of Interaction with Oracles

DTIC Science & Technology

2013-10-01

have made a lasting impact on my mathematical perspective. I am grateful for the wonderful and stimulating discussion I had with Alan Frieze on...Otherwise, by Theorem 7.1, with probability at least 1−ε/2, we have ‖πθ⋆ −πθ̂(t−1)θ⋆‖ ≤ R(t−1, ε/2). On this event, ifR (t−1, ε/2) ≤ ε/8, then by a triangle... impact on how much benefit we gain from transfer learning when we are faced with only a finite sequence of learning problems. As such, it is certainly

Continuum mathematical modelling of pathological growth of blood vessels

NASA Astrophysics Data System (ADS)

Stadnik, N. E.; Dats, E. P.

2018-04-01

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Higgs decays to Z Z and Z γ in the standard model effective field theory: An NLO analysis

NASA Astrophysics Data System (ADS)

Dawson, S.; Giardino, P. P.

2018-05-01

We calculate the complete one-loop electroweak corrections to the inclusive H →Z Z and H →Z γ decays in the dimension-6 extension of the Standard Model Effective Field Theory (SMEFT). The corrections to H →Z Z are computed for on-shell Z bosons and are a precursor to the physical H →Z f f ¯ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite next-to-leading-order contributions to the decay widths. As a byproduct of our calculation, we obtain the first complete result for the finite corrections to Gμ in the SMEFT.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2018-04-01

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Surface-plasmon polariton scattering from a finite array of nanogrooves/ridges: Efficient mirrors

NASA Astrophysics Data System (ADS)

Sánchez-Gil, José A.; Maradudin, Alexei A.

2005-06-01

The scattering of surface-plasmon polaritons (SPP) by finite arrays of one-dimensional nanodefects on metal surfaces is theoretically investigated on the basis of the reduced Rayleigh equation. Numerical calculations are carried out that rigorously account for all the scattering channels: SPP reflection and transmission, and radiative leakage. We analyze the range of parameters (defect size and number) for which high SPP reflection efficiency (low radiative losses) is achieved within a SPP band gap (negligible SPP transmission), neglecting ohmic losses (justified for array lengths significantly shorter than the SPP inelastic length): Smaller defects play better as SPP mirrors (e.g., efficiency >90% at λ ˜650nm for Gaussian ridges/grooves with sub-30nm height and half-width) than larger defects, since the latter yield significant radiative losses.

[Stress analysis of femoral stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer].

PubMed

Oomori, H; Imura, S; Gesso, H

1992-04-01

To develop stem design achieving primary fixation of stems and effective load transfer to the femur, we studied stress analysis of stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer in stem-bone interface. The results of analyses of stem-bone interface stresses and von Mises stresses at the cortical bones indicated that ideal stem design features would be as follows: 1) Sufficient length, with the distal end extending beyond the isthmus region. 2) Maximum possible width, to contact the cortical bones in the isthmus region. 3) No collars but a lateral shoulder at the proximal portion. 4) A distal tip, to contact the cortical bones at the distal portion.

Three-dimension finite-element analyses of multiple electrodes bipolar RF global endometrial ablation

NASA Astrophysics Data System (ADS)

Hu, Tao; Panhao, Tang; Xiao, Jiahua

2015-03-01

Radio-frequency ablation (RFA) is a minimally invasive surgical procedure to thermally ablate the targeted diseased tissue. There have been many finite-element method (FEM) studies of cardiac and hepatic RFA, but hardly find any FEM study on endometrial ablation for abnormal uterine bleeding. In this paper, a FEM model was generated to analyze the temperature distribution of bipolar RF global endometrial ablation with three pairs of bipolar electrodes placed at the perimeter of the uterine cavity. COMSOL was utilized to calculate the RF electric fields and temperature fields by numerically solving the bioheat equation in the triangle uterine cavity range. The 55°C isothermal surfaces show the shape of the ablation dimensions (depth and width), which reasonably matched the experimental results.

Compression failure mechanisms of uni-ply composite plates with a circular cutout

NASA Technical Reports Server (NTRS)

Khamseh, A. R.; Waas, A. M.

1992-01-01

The effect of circular-hole size on the failure mode of uniply graphite-epoxy composite plates is investigated experimentally and analytically for uniaxial compressive loading. The test specimens are sandwiched between polyetherimide plastic for nondestructive evaluations of the uniply failure mechanisms associated with a range of hole sizes. Finite-element modeling based on classical lamination theory is conducted for the corresponding materials and geometries to reproduce the experimental results analytically. The type of compressive failure is found to be a function of hole size, with fiber buckling/kinking at the hole being the dominant failure mechanism for hole diam/plate width ratios exceeding 0.062. The results of the finite-element analysis supported the experimental data for these failure mechanisms and for those corresponding to smaller hole sizes.

A Mathematical Model for the Exhaust Gas Temperature Profile of a Diesel Engine

NASA Astrophysics Data System (ADS)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2015-09-01

This work presents a heat transfer model for the exhaust gas of a diesel power generator to determine the gas temperature profile in the exhaust pipe. The numerical methodology to solve the mathematical model was developed using a finite difference method approach for energy equation resolution and determination of temperature profiles considering turbulent fluid flow and variable fluid properties. The simulation was carried out for engine operation under loads from 0 kW to 40 kW. The model was compared with results obtained using the multidimensional Ansys CFX software, which was applied to solve the governor equations of turbulent fluid flow. The results for the temperature profiles in the exhaust pipe show a good proximity between the mathematical model developed and the multidimensional software.

Measurement of bow tie profiles in CT scanners using a real-time dosimeter

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

Whiting, Bruce R., E-mail: whitingbrucer@gmail.com; Evans, Joshua D.; Williamson, Jeffrey F.

2014-10-15

Purpose: Several areas of computed tomography (CT) research require knowledge about the intensity profile of the x-ray fan beam that is introduced by a bow tie filter. This information is considered proprietary by CT manufacturers, so noninvasive measurement methods are required. One method using real-time dosimeters has been proposed in the literature. A commercially available dosimeter was used to apply that method, and analysis techniques were developed to extract fan beam profiles from measurements. Methods: A real-time ion chamber was placed near the periphery of an empty CT gantry and the dose rate versus time waveform was recorded as themore » x-ray source rotated about the isocenter. In contrast to previously proposed analysis methods that assumed a pointlike detector, the finite-size ion chamber received varying amounts of coverage by the collimated x-ray beam during rotation, precluding a simple relationship between the source intensity as a function of fan beam angle and measured intensity. A two-parameter model for measurement intensity was developed that included both effective collimation width and source-to-detector distance, which then was iteratively solved to minimize the error between duplicate measurements at corresponding fan beam angles, allowing determination of the fan beam profile from measured dose-rate waveforms. Measurements were performed on five different scanner systems while varying parameters such as collimation, kVp, and bow tie filters. On one system, direct measurements of the bow tie profile were collected for comparison with the real-time dosimeter technique. Results: The data analysis method for a finite-size detector was found to produce a fan beam profile estimate with a relative error between duplicate measurement intensities of <5%. It was robust over a wide range of collimation widths (e.g., 1–40 mm), producing fan beam profiles that agreed with a relative error of 1%–5%. Comparison with a direct measurement technique on one system produced agreement with a relative error of 2%–6%. Fan beam profiles were found to differ for different filter types on a given system and between different vendors. Conclusions: A commercially available real-time dosimeter probe was found to be a convenient and accurate instrument for measuring fan beam profiles. An analysis method was developed that could handle a wide range of collimation widths by explicitly considering the finite width of the ion chamber. Relative errors in the profiles were found to be less than 5%. Measurements of five different clinical scanners demonstrate the variation in bow tie designs, indicating that generic bow tie models will not be adequate for CT system research.« less

Definition of the Mathematical Model Coefficients on the Weld Size of Butt Joint Without Edge Preparation

NASA Astrophysics Data System (ADS)

Sidorov, Vladimir P.; Melzitdinova, Anna V.

2017-10-01

This paper represents the definition methods for thermal constants according to the data of the weld width under the normal-circular heat source. The method is based on isoline contouring of “effective power - temperature conductivity coefficient”. The definition of coefficients provides setting requirements to the precision of welding parameters support with the enough accuracy for an engineering practice.

A study of the fundamental characteristics of 2175A extinction

NASA Technical Reports Server (NTRS)

Cardelli, Jason A.; Savage, Blair D.

1987-01-01

The characteristics of interstellar extinction were studied in the region of the 2175 A feature for lines of sight which appear to exhibit unusually weak ultraviolet extinction. The analysis was based upon a parameterization of the observed extinction via fitting specific mathematical functions in order to determine the position and width of the 2175 A feature. The data are currently being analyzed.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Numerical results on the transcendence of constants involving pi, e, and Euler's constant

NASA Technical Reports Server (NTRS)

Bailey, David H.

1988-01-01

The existence of simple polynomial equations (integer relations) for the constants e/pi, e + pi, log pi, gamma (Euler's constant), e exp gamma, gamma/e, gamma/pi, and log gamma is investigated by means of numerical computations. The recursive form of the Ferguson-Fourcade algorithm (Ferguson and Fourcade, 1979; Ferguson, 1986 and 1987) is implemented on the Cray-2 supercomputer at NASA Ames, applying multiprecision techniques similar to those described by Bailey (1988) except that FFTs are used instead of dual-prime-modulus transforms for multiplication. It is shown that none of the constants has an integer relation of degree eight or less with coefficients of Euclidean norm 10 to the 9th or less.

Sagittal focusing of synchrotron radiation X-rays using a winged crystal

PubMed Central

Nisawa, A.; Yoneda, Y.; Ueno, G.; Murakami, H.; Okajima, Y.; Yamamoto, K.; Senba, Y.; Uesugi, K.; Tanaka, Y.; Yamamoto, M.; Goto, S.; Ishikawa, T.

2013-01-01

A Si(111) winged crystal has been designed to minimize anticlastic bending and improve sagittal focusing efficiency. The crystal was thin with wide stiffening wings. The length-to-width ratio of the crystal was optimized by finite element analysis, and the optimal value was larger than the ‘golden value’. The analysis showed that the slope error owing to anticlastic bending is less than the Darwin width. The X-rays were focused two-dimensionally using the crystal and a tangentially bent mirror. The observed profiles of the focal spot agreed well with the results of a ray-tracing calculation in the energy range from 8 to 17.5 keV. X-ray diffraction measurements with a high signal-to-noise ratio using this focusing system were demonstrated for a small protein crystal. PMID:23412477

An Analytical Model of Joule Heating in Piezoresistive Microcantilevers

PubMed Central

Ansari, Mohd Zahid; Cho, Chongdu

2010-01-01

The present study investigates Joule heating in piezoresistive microcantilever sensors. Joule heating and thermal deflections are a major source of noise in such sensors. This work uses analytical and numerical techniques to characterise the Joule heating in 4-layer piezoresistive microcantilevers made of silicon and silicon dioxide substrates but with the same U-shaped silicon piezoresistor. A theoretical model for predicting the temperature generated due to Joule heating is developed. The commercial finite element software ANSYS Multiphysics was used to study the effect of electrical potential on temperature and deflection produced in the cantilevers. The effect of piezoresistor width on Joule heating is also studied. Results show that Joule heating strongly depends on the applied potential and width of piezoresistor and that a silicon substrate cantilever has better thermal characteristics than a silicon dioxide cantilever. PMID:22163433

An analytical model of joule heating in piezoresistive microcantilevers.

PubMed

Ansari, Mohd Zahid; Cho, Chongdu

2010-01-01

The present study investigates Joule heating in piezoresistive microcantilever sensors. Joule heating and thermal deflections are a major source of noise in such sensors. This work uses analytical and numerical techniques to characterise the Joule heating in 4-layer piezoresistive microcantilevers made of silicon and silicon dioxide substrates but with the same U-shaped silicon piezoresistor. A theoretical model for predicting the temperature generated due to Joule heating is developed. The commercial finite element software ANSYS Multiphysics was used to study the effect of electrical potential on temperature and deflection produced in the cantilevers. The effect of piezoresistor width on Joule heating is also studied. Results show that Joule heating strongly depends on the applied potential and width of piezoresistor and that a silicon substrate cantilever has better thermal characteristics than a silicon dioxide cantilever.

Investigation of a tubular dual-stator flux-switching permanent-magnet linear generator for free-piston energy converter

NASA Astrophysics Data System (ADS)

Sui, Yi; Zheng, Ping; Tong, Chengde; Yu, Bin; Zhu, Shaohong; Zhu, Jianguo

2015-05-01

This paper describes a tubular dual-stator flux-switching permanent-magnet (PM) linear generator for free-piston energy converter. The operating principle, topology, and design considerations of the machine are investigated. Combining the motion characteristic of free-piston Stirling engine, a tubular dual-stator PM linear generator is designed by finite element method. Some major structural parameters, such as the outer and inner radii of the mover, PM thickness, mover tooth width, tooth width of the outer and inner stators, etc., are optimized to improve the machine performances like thrust capability and power density. In comparison with conventional single-stator PM machines like moving-magnet linear machine and flux-switching linear machine, the proposed dual-stator flux-switching PM machine shows advantages in higher mass power density, higher volume power density, and lighter mover.

Early Onset of Kinetic Roughening due to a Finite Step Width in Hematin Crystallization

NASA Astrophysics Data System (ADS)

Olafson, Katy N.; Rimer, Jeffrey D.; Vekilov, Peter G.

2017-11-01

The structure of the interface of a growing crystal with its nutrient phase largely determines the growth dynamics. We demonstrate that hematin crystals, crucial for the survival of malaria parasites, transition from faceted to rough growth interfaces at increasing thermodynamic supersaturation Δ μ . Contrary to theoretical predictions and previous observations, this transition occurs at moderate values of Δ μ . Moreover, surface roughness varies nonmonotonically with Δ μ , and the rate constant for rough growth is slower than that resulting from nucleation and spreading of layers. We attribute these unexpected behaviors to the dynamics of step growth dominated by surface diffusion and the loss of identity of nuclei separated by less than the step width w . We put forth a general criterion for the onset of kinetic roughening using w as a critical length scale.

Computer design of porous active materials at different dimensional scales

NASA Astrophysics Data System (ADS)

Nasedkin, Andrey

2017-12-01

The paper presents a mathematical and computer modeling of effective properties of porous piezoelectric materials of three types: with ordinary porosity, with metallized pore surfaces, and with nanoscale porosity structure. The described integrated approach includes the effective moduli method of composite mechanics, simulation of representative volumes, and finite element method.

Gauge symmetries of the free supersymmetric string field theories

NASA Astrophysics Data System (ADS)

Neveu, A.; West, P. C.

1985-12-01

The gauge covariant local formulations of the free supersymmetric strings that contained a finite number of supplementary fields are extended so as to place all the generators of the Ramond-Neveu-Schwarz algebra on a more equal footing. Permanent address: King's College, Mathematics Department, London WC2R 2LS, UK.

A Formal Theory of Perception. Technical Report No. 161.

ERIC Educational Resources Information Center

Rottmayer, William Arthur

An attempt to build a mathematical model of a device that could learn geometry is discussed. The report discusses the background and motivation of the study, the coding problem, the derivation of Suppes "Stimulus-Response Theory of Finite Automata" used in the work in learning theory, and a summary of the technical work. (DB)

PATSTAGS: PATRAN-To-STAGSC-1 Translator

NASA Technical Reports Server (NTRS)

Otte, Neil

1993-01-01

PATSTAGS computer program translates data from PATRAN finite-element mathematical model into STAGS input records used for engineering analysis. Reads data from PATRAN neutral file and writes STAGS input records into STAGS input file and UPRESS data file. Supports translations of nodal constraints, and of nodal, element, force, and pressure data. Written in FORTRAN 77.

Modeling the Formation of Transverse Weld during Billet-on-Billet Extrusion

PubMed Central

Mahmoodkhani, Yahya; Wells, Mary; Parson, Nick; Jowett, Chris; Poole, Warren

2014-01-01

A comprehensive mathematical model of the hot extrusion process for aluminum alloys has been developed and validated. The plasticity module was developed using a commercial finite element package, DEFORM-2D, a transient Lagrangian model which couples the thermal and deformation phenomena. Validation of the model against industrial data indicated that it gave excellent predictions of the pressure during extrusion. The finite element predictions of the velocity fields were post-processed to calculate the thickness of the surface cladding as one billet is fed in after another through the die (i.e., the transverse weld). The mathematical model was then used to assess the effect a change in feeder dimensions would have on the shape, thickness and extent of the transverse weld during extrusion. Experimental measurements for different combinations of billet materials show that the model is able to accurately predict the transverse weld shape as well as the clad surface layer to thicknesses of 50 μm. The transverse weld is significantly affected by the feeder geometry shape, but the effects of ram speed, billet material and temperature on the transverse weld dimensions are negligible. PMID:28788629

The dynamics and control of large flexible space structures-V

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Diarra, C. M.; Kumar, V. K.

1982-01-01

A general survey of the progress made in the areas of mathematical modelling of the system dynamics, structural analysis, development of control algorithms, and simulation of environmental disturbances is presented. The use of graph theory techniques is employed to examine the effects of inherent damping associated with LSST systems on the number and locations of the required control actuators. A mathematical model of the forces and moments induced on a flexible orbiting beam due to solar radiation pressure is developed and typical steady state open loop responses obtained for the case when rotations and vibrations are limited to occur within the orbit plane. A preliminary controls analysis based on a truncated (13 mode) finite element model of the 122m. Hoop/Column antenna indicates that a minimum of six appropriately placed actuators is required for controllability. An algorithm to evaluate the coefficients which describe coupling between the rigid rotational and flexible modes and also intramodal coupling was developed and numerical evaluation based on the finite element model of Hoop/Column system is currently in progress.

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

Resistance of a plate in parallel flow at low Reynolds numbers

NASA Technical Reports Server (NTRS)

Janour, Zbynek

1951-01-01

The present paper gives the results of measurements of the resistance of a plate placed parallel to the flow in the range of Reynolds numbers from 10 to 2300; in this range the resistance deviates from the formula of Blasius. The lower limit of validity of the Blasius formula is determined and also the increase in resistance at the edges parallel to the flow in the case of a plate of finite width.

Internal and edge cracks in a plate of finite width under bending

NASA Technical Reports Server (NTRS)

Boduroglu, H.; Erdogan, F.

1983-01-01

Internal and edge cracks were studied by using Reissner's transverse shear theory. The effect of stress-free boundaries on the stress intensity factors in plates under bending were investigated. Among the results found, particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. The effect of Poisson's ratio on the stress intensity factors was studied.

Turbulent ship wakes: further evidence that the Earth is round.

PubMed

Lynch, David K

2005-09-20

When viewed from the stern, a ship's turbulent wake appears as a narrow strip of bubble-whitened water converging toward the horizon. The wake does not reach a sharp point on the horizon but has a finite angular width, indicating that the Earth is not flat, but rather round. A simple analysis of the geometry of the observations shows that the radius of the Earth can be estimated using only simple instruments and observations.

Mechanics of graben formation in crustal rocks - A finite element analysis

NASA Technical Reports Server (NTRS)

Melosh, H. J.; Williams, C. A., Jr.

1989-01-01

The mechanics of the initial stages of graben formation are examined, showing that the configuration of a graben (a pair of antithetically dipping normal faults) is the most energetically favorable fault configuration in elastic-brittle rocks subjected to pure extension. The stress field in the vicinity of a single initial normal fault is computed with a two-dimensional FEM. It is concluded that the major factor controlling graben width is the depth of the initial fault.

The Shock and Vibration Digest. Volume 12, Number 8,

DTIC Science & Technology

1980-08-01

half tme coefficient of 0.315 in the above lamina. Sequential delamination began when a strip equation because two surfaces are formed). of width D in...a striker plate. Each specimen study of the two-dimensional ( plane -strain) response was subjected to two separate impact loadings: an of an elastic...laminated plate; they used a finite ele- in- plane impact and a so-called shear-bending impact. ment/normal mode technique. The physical behavior The

Peri-implant stress correlates with bone and cement morphology: Micro-FE modeling of implanted cadaveric glenoids.

PubMed

Wee, Hwabok; Armstrong, April D; Flint, Wesley W; Kunselman, Allen R; Lewis, Gregory S

2015-11-01

Aseptic loosening of cemented joint replacements is a complex biological and mechanical process, and remains a clinical concern especially in patients with poor bone quality. Utilizing high resolution finite element analysis of a series of implanted cadaver glenoids, the objective of this study was to quantify relationships between construct morphology and resulting mechanical stresses in cement and trabeculae. Eight glenoid cadavers were implanted with a cemented central peg implant. Specimens were imaged by micro-CT, and subject-specific finite element models were developed. Bone volume fraction, glenoid width, implant-cortex distance, cement volume, cement-cortex contact, and cement-bone interface area were measured. Axial loading was applied to the implant of each model and stress distributions were characterized. Correlation analysis was completed across all specimens for pairs of morphological and mechanical variables. The amount of trabecular bone with high stress was strongly negatively correlated with both cement volume and contact between the cement and cortex (r = -0.85 and -0.84, p < 0.05). Bone with high stress was also correlated with both glenoid width and implant-cortex distance. Contact between the cement and underlying cortex may dramatically reduce trabecular bone stresses surrounding the cement, and this contact depends on bone shape, cement amount, and implant positioning. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Development of a Flexible Broadband Rayleigh Waves Comb Transducer with Nonequidistant Comb Interval for Defect Detection of Thick-Walled Pipelines

PubMed Central

He, Cunfu; Yan, Lyu; Zhang, Haijun

2018-01-01

It is necessary to develop a transducer that can quickly detect the inner and outer wall defects of thick-walled pipes, in order to ensure the safety of such pipes. In this paper, a flexible broadband Rayleigh-waves comb transducer based on PZT (lead zirconate titanate) for defect detection of thick-walled pipes is studied. The multiple resonant coupling theory is used to expand the transducer broadband and the FEA (Finite Element Analysis) method is used to optimize transducer array element parameters. Optimization results show that the best array element parameters of the transducer are when the transducer array element length is 30 mm, the thickness is 1.2 mm, the width of one end of is 1.5 mm, and the other end is 3 mm. Based on the optimization results, such a transducer was fabricated and its performance was tested. The test results were consistent with the finite-element simulation results, and the −3 dB bandwidth of the transducer reached 417 kHz. Transducer directivity test results show that the Θ−3dB beam width was equal to 10 °, to meet the defect detection requirements. Finally, defects of thick-walled pipes were detected using the transducer. The results showed that the transducer could detect the inner and outer wall defects of thick-walled pipes within the bandwidth. PMID:29498636

Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma

DOE PAGES

Kaganovich, I. D.; Sydorenko, D.

2016-11-18

Our paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite plasma or a finite size plasma with periodic boundary conditions. Even if the width of the plasma matches the resonance condition for a standing wave, a spatially growing wave is excited instead with the growth rate small compared to that of the standing wave in a periodic system. Furthermore, the approximate expression for this growth rate is γ≈(1/13)ω pe(nmore » b/n p)(Lω pe/v b)ln(Lω pe/v b)[1-0.18 cos (Lω pe/v b+π/2)], where ωpe is the electron plasma frequency, n b and n p are the beam and the plasma densities, respectively, v b is the beam velocity, and L is the plasma width. The frequency, wave number, and the spatial and temporal growth rates, as functions of the plasma size, exhibit band structure. Finally, the amplitude of saturation of the instability depends on the system length, not on the beam current. For short systems, the amplitude may exceed values predicted for infinite plasmas by more than an order of magnitude.« less

Development of a Flexible Broadband Rayleigh Waves Comb Transducer with Nonequidistant Comb Interval for Defect Detection of Thick-Walled Pipelines.

PubMed

Zhao, Huamin; He, Cunfu; Yan, Lyu; Zhang, Haijun

2018-03-02

It is necessary to develop a transducer that can quickly detect the inner and outer wall defects of thick-walled pipes, in order to ensure the safety of such pipes. In this paper, a flexible broadband Rayleigh-waves comb transducer based on PZT (lead zirconate titanate) for defect detection of thick-walled pipes is studied. The multiple resonant coupling theory is used to expand the transducer broadband and the FEA (Finite Element Analysis) method is used to optimize transducer array element parameters. Optimization results show that the best array element parameters of the transducer are when the transducer array element length is 30 mm, the thickness is 1.2 mm, the width of one end of is 1.5 mm, and the other end is 3 mm. Based on the optimization results, such a transducer was fabricated and its performance was tested. The test results were consistent with the finite-element simulation results, and the -3 dB bandwidth of the transducer reached 417 kHz. Transducer directivity test results show that the Θ -3dB beam width was equal to 10 °, to meet the defect detection requirements. Finally, defects of thick-walled pipes were detected using the transducer. The results showed that the transducer could detect the inner and outer wall defects of thick-walled pipes within the bandwidth.

Viscous-enstrophy scaling law for Navier-Stokes reconnection

NASA Astrophysics Data System (ADS)

Kerr, Robert M.

2017-11-01

Simulations of perturbed, helical trefoil vortex knots and anti-parallel vortices find ν-independent collapse of temporally scaled (√{ ν} Z) - 1 / 2, Z enstrophy, between when the loops first touch at tΓ, and when reconnection ends at tx for the viscosity ν varying by 256. Due to mathematical bounds upon higher-order norms, this collapse requires that the domain increase as ν decreases, possibly to allow large-scale negative helicity to grow as compensation for small-scale positive helicity and enstrophy growth. This mechanism could be a step towards explaining how smooth solutions of the Navier-Stokes can generate finite-energy dissipation in a finite time as ν -> 0 .

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

A new sensitivity analysis for structural optimization of composite rotor blades

NASA Technical Reports Server (NTRS)

Venkatesan, C.; Friedmann, P. P.; Yuan, Kuo-An

1993-01-01

This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semianalytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.

BOOK REVIEW: Symmetry and the Monster: One of the Greatest Quests of Mathematics

NASA Astrophysics Data System (ADS)

Szabo, R. J.

2007-04-01

The book Symmetry and the Monster: One of the Greatest Quests of Mathematics describes historical events leading up to the discovery of the Monster sporadic group, the largest simple sporadic group. It also expounds the significance and deep relationships between this group and other areas of mathematics and theoretical physics. It begins, in the prologue, with a nice overview of some of the mathematical drama surrounding the discovery of the Monster and its subsequent relationship to number theory (the so-called Moonshine conjectures). From a historical perspective, the book traces back to the roots of group theory, Galois theory, and steadily runs through time through the many famous mathematicians who contributed to group theory, including Lie, Killing and Cartan. Throughout, the author has provided a very nice and deep insight into the sociological and scientific problems at the time, and gives the reader a very prominent inside view of the real people behind the mathematics. The book should be an enjoyable read to anyone with an interest in the history of mathematics. For the non-mathematician the book makes a good, and mostly successful, attempt at being non-technical. Technical mathematical jargon is replaced with more heuristic, intuitive terminology, making the mathematical descriptions in the book fairly easy going. A glossary\\hspace{0.25pc} of\\hspace{0.25pc} terminology for noindent the more scientifically inclined is included in various footnotes throughout the book and in a comprehensive listing at the end of the book. Some more technical material is also included in the form of appendices at the end of the book. Some aspects of physics are also explained in a simple, intuitive way. The author further attempts at various places to give the non-specialist a glimpse into what mathematical proof is all about, and explains the difficulties and technicalities involved in this very nicely (for instance, he mentions the various 100+ page articles that appeared in the hey-day of finite group theory, indicating the enormous technical nature of the subject). The book nicely paints a dramatic landscape leading up to the discovery of the Monster group, and the problems that remain to this day in trying to understand its significance. One can really take from this book a feel of the mathematics leading up to its appearance, and the importance of the classification problem which was responsible for this. One also really gets an appreciation of the efforts and commitments of the mathematicians who contributed to the subject. All in all, this book achieves a nice balance between providing a beautiful historical account of group theory, and explaining the classification problem for finite groups in a way that is accessible to non-scientists. This should prove to be a good read for both the layperson interested in mathematics or mathematical physics, and also both mathematicians and physicists alike.

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

A study of direct moxibustion using mathematical methods.

PubMed

Liu, Miao; Kauh, Sang Ken; Lim, Sabina

2012-01-01

Direct moxibustion is an important and widely used treatment method in traditional medical science. The use of a mathematical method to analyse direct moxibustion treatment is necessary and helpful in exploring the new direct moxibustion instruments and their standardisation. Thus, this paper aims to use a mathematical method to study direct moxibustion in skin to demonstrate a direct relationship between direct moxibustion and skin stimuli. In this paper, the transient thermal response of skin layers is analysed to study direct moxibustion using the data got from standardised method to measure the temperature of a burning moxa cone. Numerical simulations based on an appropriate finite element model are developed to predict the heat transfer, thermal damage and thermal stress distribution of barley moxa cones and jujube moxa cones in the skin tissue. The results are verified by the ancient literatures of traditional Chinese medicine and clinical application, and showed that mathematical method can be a good interface between moxa cone and skin tissue providing the numerical value basis for moxibustion.

Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

Development of an Underactuated 2-DOF Wrist Joint using McKibben PAMs

NASA Astrophysics Data System (ADS)

Rajagopal, S. P.; Jain, S.; Ramasubramanian, S. N.; Johnson, B. V.; Dwivedy, S. K.

2014-10-01

In this work, model of an underactuated 2-DOF wrist joint with pneumatically actuated muscles is proposed. For the joint, McKibben-type artificial muscles are used in parallel configuration for the actuation. For each Degree of Freedom (DOF) one agonist-antagonist pair arrangement is usually used with a pulley mechanism. A mathematical model of wrist joint is derived using conventional forward kinematic analysis. The static model relating pressure in the muscle with the orientation of the wrist joint is obtained by combining the experimental data and mathematical model. Regulation of pressure can be achieved by pulse width modulation control of on/off solenoid valves. A set of free vibration experiments are done for the dynamic identification of the muscle characteristics.

Optimization of morphological parameters for mitigation pits on rear KDP surface: experiments and numerical modeling.

PubMed

Yang, Hao; Cheng, Jian; Chen, Mingjun; Wang, Jian; Liu, Zhichao; An, Chenhui; Zheng, Yi; Hu, Kehui; Liu, Qi

2017-07-24

In high power laser systems, precision micro-machining is an effective method to mitigate the laser-induced surface damage growth on potassium dihydrogen phosphate (KDP) crystal. Repaired surfaces with smooth spherical and Gaussian contours can alleviate the light field modulation caused by damage site. To obtain the optimal repairing structure parameters, finite element method (FEM) models for simulating the light intensification caused by the mitigation pits on rear KDP surface were established. The light intensity modulation of these repairing profiles was compared by changing the structure parameters. The results indicate the modulation is mainly caused by the mutual interference between the reflected and incident lights on the rear surface. Owing to the total reflection, the light intensity enhancement factors (LIEFs) of the spherical and Gaussian mitigation pits sharply increase when the width-depth ratios are near 5.28 and 3.88, respectively. To achieve the optimal mitigation effect, the width-depth ratios greater than 5.3 and 4.3 should be applied to the spherical and Gaussian repaired contours. Particularly, for the cases of width-depth ratios greater than 5.3, the spherical repaired contour is preferred to achieve lower light intensification. The laser damage test shows that when the width-depth ratios are larger than 5.3, the spherical repaired contour presents higher laser damage resistance than that of Gaussian repaired contour, which agrees well with the simulation results.

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Pruett, C. D.; Gatski, T. B.; Grosch, C. E.; Thacker, W. D.

2002-01-01

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Investigation of the Effect of Finite Pulse Errors on BABA Pulse Sequence Using Floquet-Magnus Expansion Approach.

PubMed

Mananga, Eugene S; Reid, Alicia E

This paper presents the study of finite pulse widths for the BABA pulse sequence using the Floquet-Magnus expansion (FME) approach. In the FME scheme, the first order F 1 is identical to its counterparts in average Hamiltonian theory (AHT) and Floquet theory (FT). However, the timing part in the FME approach is introduced via the Λ 1 ( t ) function not present in other schemes. This function provides an easy way for evaluating the spin evolution during "the time in between" through the Magnus expansion of the operator connected to the timing part of the evolution. The evaluation of Λ 1 ( t ) is useful especially for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provides a natural choice of Λ 1 (0) is ignored. This work uses the Λ 1 ( t ) function to compare the efficiency of the BABA pulse sequence with δ - pulses and the BABA pulse sequence with finite pulses. Calculations of Λ 1 ( t ) and F 1 are presented.

Investigation of the Effect of Finite Pulse Errors on BABA Pulse Sequence Using Floquet-Magnus Expansion Approach

PubMed Central

Mananga, Eugene S.; Reid, Alicia E.

2013-01-01

This paper presents the study of finite pulse widths for the BABA pulse sequence using the Floquet-Magnus expansion (FME) approach. In the FME scheme, the first order F1 is identical to its counterparts in average Hamiltonian theory (AHT) and Floquet theory (FT). However, the timing part in the FME approach is introduced via the Λ1 (t) function not present in other schemes. This function provides an easy way for evaluating the spin evolution during “the time in between” through the Magnus expansion of the operator connected to the timing part of the evolution. The evaluation of Λ1 (t) is useful especially for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provides a natural choice of Λ1 (0) is ignored. This work uses the Λ1 (t) function to compare the efficiency of the BABA pulse sequence with δ – pulses and the BABA pulse sequence with finite pulses. Calculations of Λ1 (t) and F1 are presented. PMID:25792763

An Approach for Assessing Delamination Propagation Capabilities in Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Krueger, Ronald

2007-01-01

An approach for assessing the delamination propagation capabilities in commercial finite element codes is presented and demonstrated for one code. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. Good agreement between the load-displacement relationship obtained from the propagation analysis results and the benchmark results could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as may be expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.

Dynamics of a localized spin excitation close to the spin-helix regime

NASA Astrophysics Data System (ADS)

Salis, Gian; Walser, Matthias; Altmann, Patrick; Reichl, Christian; Wegscheider, Werner

2014-03-01

The time evolution of a local spin excitation in a (001)-confined two-dimensional electron gas subjected to Rashba and Dresselhaus spin-orbit interactions of similar strength is investigated theoretically and compared with experimental data. Specifically, the consequences of a finite spatial extension of the initial spin polarization are studied for non-balanced Rashba and Dresselhaus terms and for finite cubic Dresselhaus spin-orbit interaction. We show that the initial out-of-plane spin polarization evolves into a helical spin pattern with a wave number that gradually approaches the value q0 of the persistent spin helix mode. In addition to an exponential decay of the spin polarization that is proportional to both the spin-orbit imbalance and the cubic Dresselhaus term, the finite width w of the spin excitation reduces the spin polarization by a factor that approaches exp(-q02w2 / 2) at longer times. This result bridges the gap between the formation of a long-lived helical spin mode and a spatially homogeneous spin decay described by the Dyakonov-Perel mechanism. This work is financially supported by NCCR QSIT.

An Approach to Assess Delamination Propagation Simulation Capabilities in Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Krueger, Ronald

2008-01-01

An approach for assessing the delamination propagation simulation capabilities in commercial finite element codes is presented and demonstrated. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. The load-displacement relationship and the total strain energy obtained from the propagation analysis results and the benchmark results were compared and good agreements could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as was expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.

Delamination and Stitched Failure in Stitched Composite Joints

NASA Technical Reports Server (NTRS)

Glaessgen, E. H.; Raju, I. S.; Poe, C. C., Jr.

1999-01-01

The effect of stitches on the failure of a single lap joint configuration was determined in a combined experimental and finite element study. The experimental program was conducted to determine debond growth under static monotonic loading. The stitches were shown to delay the initiation of the debond and provide load transfer beyond the load necessary to completely debond the stitched lap joint. The experimentally determined debond length vs. applied load was used as an input parameter in the finite element analysis of both configurations. The strain energy release rates at the debond from were calculated using plate finite elements. Nonlinear fastener elements were used to model the stitches and multipoint constraints were used to model the contact problem. Models of the unstitched configuration showed significant values of modes I and II across the width of the joint and showed that mode III is zero at the centerline but increases near the free edge. Models of the stitched configuration showed that the stitches were effective in reducing mode I to zero, but had less of an effect on modes II and III.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale m{sub IR}

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

Bornyakov, V. G.; Mitrjushkin, V. K.; Mueller-Preussker, M.

2010-03-01

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found themore » Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.« less

Phase field study of surface-induced melting and solidification from a nanovoid: Effect of dimensionless width of void surface and void size

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-05-01

The size effect and the effects of a finite-width surface on barrierless transformations between the solid (S), surface melt (SM), and melt (M) from a spherical nanovoid are studied using a phase field approach. Melting (SM → M and S → M) from the nanovoid occurs at temperatures which are significantly greater than the solid-melt equilibrium temperature θe but well below the critical temperature for solid instability. The relationships between the SM and M temperatures and the ratio of the void surface width and width of the solid-melt interface, Δ ¯ , are found for the nanovoids of different sizes. Below a critical ratio Δ¯ * , the melting occurs via SM and the melting temperature slightly reduces with an increase in Δ ¯ . Both S → SM and SM → M transformations have a jump-like character (excluding the case with the sharp void surface), causing small temperature hysteresis. However, the solid melts without SM for Δ ¯>Δ¯ * , and the melting temperature significantly increases with increasing Δ ¯ . The results for a nanovoid are compared with the melting/solidification of a nanoparticle, for which the melting temperatures, in contrast, are much lower than θe. A linear dependency of the melting temperatures with the inverse of the void radius is shown. The present study shows an unexplored way to control the melting from nanovoids by controlling the void size and the width and energy of the surface.

A Finite Element Procedure for Calculating Fluid-Structure Interaction Using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Chargin, Mladen; Gartmeier, Otto

1990-01-01

This report is intended to serve two purposes. The first is to present a survey of the theoretical background of the dynamic interaction between a non-viscid, compressible fluid and an elastic structure is presented. Section one presents a short survey of the application of the finite element method (FEM) to the area of fluid-structure-interaction (FSI). Section two describes the mathematical foundation of the structure and fluid with special emphasis on the fluid. The main steps in establishing the finite element (FE) equations for the fluid structure coupling are discussed in section three. The second purpose is to demonstrate the application of MSC/NASTRAN to the solution of FSI problems. Some specific topics, such as fluid structure analogy, acoustic absorption, and acoustic contribution analysis are described in section four. Section five deals with the organization of the acoustic procedure flowchart. Section six includes the most important information that a user needs for applying the acoustic procedure to practical FSI problems. Beginning with some rules concerning the FE modeling of the coupled system, the NASTRAN USER DECKs for the different steps are described. The goal of section seven is to demonstrate the use of the acoustic procedure with some examples. This demonstration includes an analytic verification of selected FE results. The analytical description considers only some aspects of FSI and is not intended to be mathematically complete. Finally, section 8 presents an application of the acoustic procedure to vehicle interior acoustic analysis with selected results.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

Investigation on the Crack Behaviour in Kevlar 49 Based Composite Materials using Extended Finite Element Method for Aerospace Applications

NASA Astrophysics Data System (ADS)

Handa, Danish; Sekhar Dondapati, Raja; Kumar, Abhinav

2017-08-01

Ductile to brittle transition (DTBT) is extensively observed in materials under cryogenic temperatures, thereby observing brittle failure due to the non-resistance of crack propagation. Owing to its outstanding mechanical and thermal properties, Kevlar 49 composites are widely used in aerospace applications under cryogenic temperatures. Therefore, in this paper, involving the assumption of linear elastic fracture mechanics (LEFM), mechanical characterization of Kevlar 49 composite is done using Extended Finite Element Method (X-FEM) technique in Abaqus/CAE software. Further, the failure of Kevlar 49 composites due to the propagation of crack at room temperature and the cryogenic temperature is investigated. Stress, strain and strain energy density as a function of the width of the Kevlar specimen is predicted, indicates that Kevlar 49 composites are suitable for use under cryogenic temperatures.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

Defect characterization by inductive heated thermography

NASA Astrophysics Data System (ADS)

Noethen, Matthias; Meyendorf, Norbert

2012-05-01

During inductive-thermographic inspection, an eddy current of high intensity is induced into the inspected material and the thermal response is detected by an infrared camera. Anomalies in the surface temperature during and after inductive heating correspond to inhomogeneities in the material. A finite element simulation of the surface crack detection process using active thermography with inductive heating has been developed. The simulation model is based on the finite element software ANSYS. The simulation tool was tested and used for investigations on steel components with different longitudinal orientated cracks, varying in shape, width and height. This paper focuses on surface connected longitudinal orientated cracks in austenitic steel. The results show that depending on the excitation frequency the temperature distribution of the material under test are different and a possible way to measure the depth of the crack will be discussed.

User's manual for two dimensional FDTD version TEA and TMA codes for scattering from frequency-independent dielectic materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Versions TEA and TMA are two dimensional numerical electromagnetic scattering codes based upon the Finite Difference Time Domain Technique (FDTD) first proposed by Yee in 1966. The supplied version of the codes are two versions of our current two dimensional FDTD code set. This manual provides a description of the codes and corresponding results for the default scattering problem. The manual is organized into eleven sections: introduction, Version TEA and TMA code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include files (TEACOM.FOR TMACOM.FOR), a section briefly discussing scattering width computations, a section discussing the scattering results, a sample problem set section, a new problem checklist, references and figure titles.

User's manual for two dimensional FDTD version TEA and TMA codes for scattering from frequency-independent dielectric materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Versions TEA and TMA are two dimensional electromagnetic scattering codes based on the Finite Difference Time Domain Technique (FDTD) first proposed by Yee in 1966. The supplied version of the codes are two versions of our current FDTD code set. This manual provides a description of the codes and corresponding results for the default scattering problem. The manual is organized into eleven sections: introduction, Version TEA and TMA code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include files (TEACOM.FOR TMACOM.FOR), a section briefly discussing scattering width computations, a section discussing the scattering results, a sample problem setup section, a new problem checklist, references, and figure titles.

Coupled Finite Element ? Potts Model Simulations of Grain Growth in Copper Interconnects

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

Radhakrishnan, Balasubramaniam; Gorti, Sarma B

The paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and themore » height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.« less

Fabrication, characterization, and modeling of piezoelectric fiber composites

NASA Astrophysics Data System (ADS)

Lin, Xiujuan; Zhou, Kechao; Button, Tim W.; Zhang, Dou

2013-07-01

Piezoelectric fiber composites (PFCs) with interdigitated electrodes have attracted increasing interest in a variety of industrial, commercial, and aerospace markets due to their unique flexibility, adaptability, and improved transverse actuation performance. Viscous plastic processing technique was utilized for the fabrication of PFCs with customized feature sizes. The assembly parameters showed great influence on the performance of PFCs, which was verified by the finite element analysis. The cracks were identified in the fibers underneath the electrode finger after several millions cycles due to the stress and electric field concentration. The electrode finger width was an important structural parameter and showed great influence on the actuation performance and the stress distribution in the PFCs. The finite element analysis revealed that wider electrode finger would be beneficial for reducing the risk of materials failure with slight influence on the actuation performance.

3D Finite Element Analysis of Some Structural Modified PC Sleeper with the Vibration Characteristics between Sleeper and Ballast

NASA Astrophysics Data System (ADS)

Sakai, Hirotaka; Urakawa, Fumihiro; Aikawa, Akira; Namura, Akira

The vibration of concrete sleepers is an important factor engendering track deterioration. In this paper, we created a three-dimensional finite element model to reproduce a prestressed concrete (PC) sleeper in detail, expressing influence of ballast layers with a 3D spring series and dampers to reproduce their vibration and dynamic characteristics. Determination of these parameters bases on the experimental modal analysis using an impact excitation technique for PC sleepers by adjusting the accelerance between the analytical results and experimental results. Furthermore, we compared the difference of these characteristics between normal sleepers and those with some structural modifications. Analytical results clarified that such means as sleeper width extension and increased sleeper thickness will influence the reduction of ballasted track vibration as improvements of PC sleepers.

A finite element program for postbuckling calculations (PSTBKL)

NASA Technical Reports Server (NTRS)

Simitses, G. T.; Carlson, R. L.; Riff, R.

1991-01-01

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermochemical loads. This report describes the computer program resulting from the research. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) have been anticipated and are considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strains is clearly demonstrated, through the chosen applications.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

On Multifunctional Collaborative Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2001-01-01

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

2D modeling of direct laser metal deposition process using a finite particle method

NASA Astrophysics Data System (ADS)

Anedaf, T.; Abbès, B.; Abbès, F.; Li, Y. M.

2018-05-01

Direct laser metal deposition is one of the material additive manufacturing processes used to produce complex metallic parts. A thorough understanding of the underlying physical phenomena is required to obtain a high-quality parts. In this work, a mathematical model is presented to simulate the coaxial laser direct deposition process tacking into account of mass addition, heat transfer, and fluid flow with free surface and melting. The fluid flow in the melt pool together with mass and energy balances are solved using the Computational Fluid Dynamics (CFD) software NOGRID-points, based on the meshless Finite Pointset Method (FPM). The basis of the computations is a point cloud, which represents the continuum fluid domain. Each finite point carries all fluid information (density, velocity, pressure and temperature). The dynamic shape of the molten zone is explicitly described by the point cloud. The proposed model is used to simulate a single layer cladding.

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1974-01-01

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Collective Surfing of Chemically Active Particles

NASA Astrophysics Data System (ADS)

Masoud, Hassan; Shelley, Michael J.

2014-03-01

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

Quantifying the effect of finite spectral bandwidth on extinction coefficient of species in laser absorption spectroscopy

NASA Astrophysics Data System (ADS)

Singh, Manjeet; Singh, Jaswant; Singh, Baljit; Ghanshyam, C.

2016-11-01

The aim of this study is to quantify the finite spectral bandwidth effect on laser absorption spectroscopy for a wide-band laser source. Experimental analysis reveals that the extinction coefficient of an analyte is affected by the bandwidth of the spectral source, which may result in the erroneous conclusions. An approximate mathematical model has been developed for optical intensities having Gaussian line shape, which includes the impact of source's spectral bandwidth in the equation for spectroscopic absorption. This is done by introducing a suitable first order and second order bandwidth approximation in the Beer-Lambert law equation for finite bandwidth case. The derived expressions were validated using spectroscopic analysis with higher SBW on a test sample, Rhodamine B. The concentrations calculated using proposed approximation, were in significant agreement with the true values when compared with those calculated with conventional approach.

On supersymmetry anomalies

NASA Astrophysics Data System (ADS)

Howe, P. S.; Parkes, A. J.; West, P. C.

1985-01-01

It is shown analytically that there are no one-loop supersymmetry anomalies in N = 2 and N = 4 supersymmetric Yang-Mills theories. This implies that the two-loop β functions in these theories are in accord with supersymmetry when the one-loop finite local counter terms required by supersymmetry are correctly taken into account. Permanent address: Department of Mathematics, King's College, London, UK.

On How "n" and "i" Turned out to Become Indices in Mathematical Sequences and Formulae

ERIC Educational Resources Information Center

Schubring, Gert

2011-01-01

The evolution of indexing sequences and series has been little studied so far, although this topic presents difficulties for students. This symbolisation signified, however, an important means for operating more generally with finite and infinite series. This paper investigates the first steps during the eighteenth century and then the different…

To Solve or Not to Solve, that Is the Problem

ERIC Educational Resources Information Center

Braiden, Doug

2011-01-01

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

An Analysis of Statements of the Multiplication Principle in Combinatorics, Discrete, and Finite Mathematics Textbooks

ERIC Educational Resources Information Center

Lockwood, Elise; Reed, Zackery; Caughman, John S.

2017-01-01

The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of…

KINETICS OF LOW SOURCE REACTOR STARTUPS. PART II

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

hurwitz, H. Jr.; MacMillan, D.B.; Smith, J.H.

1962-06-01

A computational technique is described for computation of the probability distribution of power level for a low source reactor startup. The technique uses a mathematical model, for the time-dependent probability distribution of neutron and precursor concentration, having finite neutron lifetime, one group of delayed neutron precursors, and no spatial dependence. Results obtained by the technique are given. (auth)

A Dynamic Process Model for Optimizing the Hospital Environment Cash-Flow

NASA Astrophysics Data System (ADS)

Pater, Flavius; Rosu, Serban

2011-09-01

In this article is presented a new approach to some fundamental techniques of solving dynamic programming problems with the use of functional equations. We will analyze the problem of minimizing the cost of treatment in a hospital environment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon.

Connecting Fair Division and Game Theory through the Optimization of Knaster's Procedure

ERIC Educational Resources Information Center

Jones, Michael A.

2003-01-01

In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's…

Earth and ocean modeling

NASA Technical Reports Server (NTRS)

Knezovich, F. M.

1976-01-01

A modular structured system of computer programs is presented utilizing earth and ocean dynamical data keyed to finitely defined parameters. The model is an assemblage of mathematical algorithms with an inherent capability of maturation with progressive improvements in observational data frequencies, accuracies and scopes. The Eom in its present state is a first-order approach to a geophysical model of the earth's dynamics.

Design and Simulation of Control Technique for Permanent Magnet Synchronous Motor Using Space Vector Pulse Width Modulation

NASA Astrophysics Data System (ADS)

Khan, Mansoor; Yong, Wang; Mustafa, Ehtasham

2017-07-01

After the rapid advancement in the field of power electronics devices and drives for last few decades, there are different kinds of Pulse Width Modulation techniques which have been brought to the market. The applications ranging from industrial appliances to military equipment including the home appliances. The vey common application for the PWM is three phase voltage source inverter, which is used to convert DC to AC in the homes to supply the power to the house in case electricity failure, usually named as Un-interrupted Power Supply. In this paper Space Vector Pulse Width Modulation techniques is discussed and analysed under the control technique named as Field Oriented Control. The working and implementation of this technique has been studied by implementing on the three phase bridge inverter. The technique is used to control the Permanente Magnet Synchronous Motor. The drive system is successfully implemented in MATLAB/Simulink using the mathematical equation and algorithm to achieve the satisfactory results. PI type of controller is used to tuned ers of the motothe parametr i.e. torque and current.

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