Nonlinear interaction of strong S-waves with the rupture front in the shallow subsurface

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2017-12-01

Shallow deformation in moderate to large earthquakes is sometimes distributed rather than being concentrated on a single fault plane. Strong high-frequency S-waves interact with the rupture front to produce this effect. For strike-slip faults, the rupture propagation velocity is a fraction of the S-wave velocity. The rupture propagation vector refracts essentially vertically in the low (S-wave) velocity shallow subsurface. So does the propagation direction of S-waves. The shallow rupture front is essentially mode 3 near the surface. Strong S-waves arrive before the rupture front. They continue to arrive for several seconds in a large event. There are simple scaling relationships. The dynamic Coulomb stress ratio of horizontal stress on horizontal planes from S-waves is the normalized acceleration in g's. For fractured rock and gravel, frictional failure occurs when the normalized acceleration exceeds the effective coefficient of friction. Acceleration tends to saturate at that level as the anelastic strain rate increases rapidly with stress. For muddy materials, failure begins at a low normalized acceleration but increases slowly with dynamic stress. Dynamic accelerations sometimes exceed 1 g. In both cases, the rupture tip finds the shallow subsurface already in nonlinear failure down to a few to tens of meters depth. The material does not distinguish between S-wave and rupture tip stresses. Both stresses add to the stress invariant and hence to the anelastic strain rate tensor. Surface anelastic strain from fault slip is thus distributed laterally over a distance scaling to the depth of nonlinearity from S-waves. The environs of the fault anelastically accommodate the fault slip at depth. This process differs from blind faults where the shallow coseismic strain is mostly elastic and interseismic anelastic processes accommodate the long-term shallow deformation.

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

NASA Astrophysics Data System (ADS)

Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen

2016-09-01

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Comparing stochastic point-source and finite-source ground-motion simulations: SMSIM and EXSIM

USGS Publications Warehouse

Boore, D.M.

2009-01-01

Comparisons of ground motions from two widely used point-source and finite-source ground-motion simulation programs (SMSIM and EXSIM) show that the following simple modifications in EXSIM will produce agreement in the motions from a small earthquake at a large distance for the two programs: (1) base the scaling of high frequencies on the integral of the squared Fourier acceleration spectrum; (2) do not truncate the time series from each subfault; (3) use the inverse of the subfault corner frequency for the duration of motions from each subfault; and (4) use a filter function to boost spectral amplitudes at frequencies near and less than the subfault corner frequencies. In addition, for SMSIM an effective distance is defined that accounts for geometrical spreading and anelastic attenuation from various parts of a finite fault. With these modifications, the Fourier and response spectra from SMSIM and EXSIM are similar to one another, even close to a large earthquake (M 7), when the motions are averaged over a random distribution of hypocenters. The modifications to EXSIM remove most of the differences in the Fourier spectra from simulations using pulsing and static subfaults; they also essentially eliminate any dependence of the EXSIM simulations on the number of subfaults. Simulations with the revised programs suggest that the results of Atkinson and Boore (2006), computed using an average stress parameter of 140 bars and the original version of EXSIM, are consistent with the revised EXSIM with a stress parameter near 250 bars.

Mechanical relaxations and 1/f noise in Bi, Nb, and Fe films

NASA Astrophysics Data System (ADS)

Alers, G. B.; Weissman, M. B.

1991-10-01

Anelastic piezoresistance and 1/f noise were measured in the same samples to compare mechanical relaxations with 1/f noise. In bismuth below 200 K, both effects could be fitted to a model invoking one class of mobile defects. In niobium, both the anelastic piezoresistance and the noise scaled with the concentration of dissolved hydrogen. A well-defined peak in noise versus temperature was observed without any peak in the anelastic response. In iron, noise apparently from a carbon Snoek relaxation was observed at 220 K in a sample with high impurity concentration and at 300 K with low impurity concentration. No anelastic feature was found at 220 K in the high-impurity-concentration sample. The broad nature of 1/f noise appears to arise not from a fundamental source but from the generally poor quality of thin films.

Optimal vibration control of a rotating plate with self-sensing active constrained layer damping

NASA Astrophysics Data System (ADS)

Xie, Zhengchao; Wong, Pak Kin; Lo, Kin Heng

2012-04-01

This paper proposes a finite element model for optimally controlled constrained layer damped (CLD) rotating plate with self-sensing technique and frequency-dependent material property in both the time and frequency domain. Constrained layer damping with viscoelastic material can effectively reduce the vibration in rotating structures. However, most existing research models use complex modulus approach to model viscoelastic material, and an additional iterative approach which is only available in frequency domain has to be used to include the material's frequency dependency. It is meaningful to model the viscoelastic damping layer in rotating part by using the anelastic displacement fields (ADF) in order to include the frequency dependency in both the time and frequency domain. Also, unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate in which the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator under an linear quadratic regulation (LQR) controller. After being compared with verified data, this newly proposed finite element model is validated and could be used for future research.

Anelastic characterization of soft poroelastic materials by anelastography

NASA Astrophysics Data System (ADS)

Flores B, Carolina; Ammann, Jean Jacques; Rivera, Ricardo

2008-11-01

This paper presents the ID characterization of the local anelastic strain determined in soft poroelastic materials through acoustic scattering in a creep test configuration. Backscattering signals are obtained at successive times in a specimen submitted to a constant stress, applied coaxially to the acoustic beam of a 5 MHz ultrasonic transducer operated in pulse-echo mode. The local displacement is measured by determining the local shift between the RF traces by performing a running cross-correlation operation between equivalent segments extracted from two pairs of RF traces. The local strain the in the specimen is obtained as the displacement gradient. The method has been implemented on biphasic porous materials that present poroelastic behaviors such as synthetic latex sponges impregnated with viscous liquids. The strain/time curves have been interpreted through a continuous bimodal anelastic model (CBA), composed of an infinite set of Kelvin-Voigt cells connected in series with an elastic spring. The fit of an experimental strain/time curve selected at a specific depth through the CBA model allow characterizing the local anelastic behavior through a set of 7 characteristics parameters for the specimen at this location: three short-term and three long-term anelastic parameters and one elastic constant.

The thin hot plume beneath Iceland

USGS Publications Warehouse

Allen, R.M.; Nolet, G.; Morgan, W.J.; Vogfjord, K.; Bergsson, B.H.; Erlendsson, P.; Foulger, G.R.; Jakobsdottir, S.; Julian, B.R.; Pritchard, M.; Ragnarsson, S.; Stefansson, R.

1999-01-01

We present the results of a seismological investigation of the frequency-dependent amplitude variations across Iceland using data from the HOTSPOT array currently deployed there. The array is composed of 30 broad-band PASSCAL instruments. We use the parameter t(*), defined in the usual manner from spectral ratios (Halderman and Davis 1991), to compare observed S-wave amplitude variations with those predicted due to both anelastic attenuation and diffraction effects. Four teleseismic events at a range of azimuths are used to measure t(*). A 2-D vertical cylindrical plume model with a Gaussian-shaped velocity anomaly is used to model the variations. That part of t(*) caused by attenuation was estimated by tracing a ray through IASP91, then superimposing our plume model velocity anomaly and calculating the path integral of 1/vQ. That part of t(*) caused by diffraction was estimated using a 2-D finite difference code to generate synthetic seismograms. The same spectral ratio technique used for the data was then used to extract a predicted t(*). The t(*) variations caused by anelastic attenuation are unable to account for the variations we observe, but those caused by diffraction do. We calculate the t(*) variations caused by diffraction for different plume models and obtain our best-fit plume, which exhibits good agreement between the observed and measured t(*). The best-fit plume model has a maximum S-velocity anomaly of - 12 per cent and falls to 1/e of its maximum at 100 km from the plume centre. This is narrower than previous estimates from seismic tomography, which are broadened and damped by the methods of tomography. This velocity model would suggest greater ray theoretical traveltime delays than observed. However, we find that for such a plume, wave-front healing effects at frequencies of 0.03-0.175 Hz (the frequency range used to pick S-wave arrivals) causes a 40 per cent reduction in traveltime delay, reducing the ray theoretical delay to that observed.

Progress and challenges in global mantle attenuation tomography (Invited)

NASA Astrophysics Data System (ADS)

Romanowicz, B. A.

2009-12-01

Global anelastic tomography has lagged behind elastic tomography, because of the difficulty to separate elastic and anelastic effects accumulated in the amplitudes of seismic waves as they propagate long distances through the heterogeneous mantle. Specifically, amplitudes are very sensitive to scattering and lateral gradients in elastic structure. Until now, these gradients - or the short wavelength features of elastic models - have not been tightly enough constrained due to a combination of (1) use of approximate wave propagation theories; (2) necessary damping due to incomplete coverage and bandwidth. Different schemes have been designed to circumvent these shortcomings in attenuation tomography, which limit resolution to long wavelengths and introduce large uncertainties in the estimation of the strength of lateral variations in attenuation. We review the robust information on anelastic structure available so far from first and second generation global upper mantle models. We discuss improvements that can be expected with, in particular, the availability of accurate numerical schemes for wave propagation in a 3D elastic earth, as well as the associated challenges, and prospects for unraveling the 3D attenuation structure of the lower mantle.

Fortnightly Earth Rotation, Ocean Tides, and Mantle Anelasticity

NASA Technical Reports Server (NTRS)

Ray, Richard D.; Egbert, Gary D.

2011-01-01

Sustained accurate measurements of earth rotation are one of the prime goals of Global Geodetic Observing System (GGOS). We here concentrate on the fortnightly (Mf) tidal component of earth-rotation data to obtain new results concerning anelasticity of the mantle at this period. The study comprises three parts: (1) a new determination of the Mf component of polar motion and length-of-day from a multi-decade time series of space-geodetic data; (2) the use of the polar-motion determination as one constraint in the development of a hydrodynamic ocean model of the Mf tide; and (3) the use of these results to place new constraints on mantle anelasticity. Our model of the Mf ocean tide assimilates more than fourteen years of altimeter data from the Topex/Poseidon and Jason-1 satellites. The polar motion data, plus tide-gauge data and independent altimeter data, give useful additional information, with only the polar motion putting constraints on tidal current velocities. The resulting ocean-tide model, plus the dominant elastic body tide, leaves a small residual in observed length-of-day caused by mantle anelasticity. The inferred effective tidal 0 of the anelastic body tide is 90 and is in line with a omega-alpha frequency dependence with alpha in the range 0.2--0.3.

A Global Upper-Mantle Tomographic Model of Shear Attenuation

NASA Astrophysics Data System (ADS)

Karaoglu, H.; Romanowicz, B. A.

2016-12-01

Mapping anelastic 3D structure within the earth's mantle is key to understanding present day mantle dynamics, as it provides complementary constraints to those obtained from elastic structure, with the potential to distinguish between thermal and compositional heterogeneity. For this, we need to measure seismic wave amplitudes, which are sensitive to both elastic (through focusing and scattering) and anelastic structure. The elastic effects are less pronounced at long periods, so previous global upper-mantle attenuation models are based on teleseismic surface wave data, sometimes including overtones. In these studies, elastic effects are considered either indirectly, by eliminating data strongly contaminated by them (e.g. Romanowicz, 1995; Gung and Romanowicz, 2004), or by correcting for elastic focusing effects using an approximate linear approach (Dalton et al., 2008). Additionally, in these studies, the elastic structure is held fixed when inverting for intrinsic attenuation . The importance of (1) having a good starting elastic model, (2) accurate modeling of the seismic wavefield and (3) joint inversion for elastic and anelastic structure, becomes more evident as the targeted resolution level increases. Also, velocity dispersion effects due to anelasticity need to be taken into account. Here, we employ a hybrid full waveform inversion method, inverting jointly for global elastic and anelastic upper mantle structure, starting from the latest global 3D shear velocity model built by our group (French and Romanowicz, 2014), using the spectral element method for the forward waveform modeling (Capdeville et al., 2003), and normal-mode perturbation theory (NACT - Li and Romanowicz, 1995) for kernel computations. We present a 3D upper-mantle anelastic model built by using three component fundamental and overtone surface waveforms down to 60 s as well as long period body waveforms down to 30 s. We also include source and site effects to first order as frequency independent scalar factors. The robustness of the inversion method is assessed through synthetic and resolution tests. We discuss salient features of the resulting anelastic model and in particular the well-resolved strong correlation with tectonics observed in the first 200 km of the mantle.

Effects of dislocations on polycrystal anelasticity

NASA Astrophysics Data System (ADS)

Sasaki, Y.; Takei, Y.; McCarthy, C.; Suzuki, A.

2017-12-01

Effects of dislocations on the seismic velocity and attenuation have been poorly understood, because only a few experimental studies have been performed [Guéguen et al., 1989; Farla et al., 2012]. By using organic borneol as a rock analogue, we measured dislocation-induced anelasticity accurately over a broad frequency range. We first measured the flow law of borneol aggregates by uniaxial compression tests under a confining pressure of 0.8 MPa. A transition from diffusion creep (n = 1) to dislocation creep (n = 5) was captured at about σ = 1 MPa (40°C-50°C). After deforming in the dislocation creep regime, sample microstructure showed irregular grain shape consistent with grain boundary migration. Next, we conducted three creep tests at σ = 0.27 MPa (diffusion creep regime), σ = 1.3 MPa and σ = 1.9 MPa (dislocation creep regime) on the same sample in increasing order, and measured Young's modulus E and attenuation Q-1 after each creep test by forced oscillation tests. The results show that as σ increased, E decreased and Q-1 increased. These changes induced by dislocations, however, almost fully recovered during the forced oscillation tests performed for about two weeks under a small stress (σ = 0.27 MPa) due to the dislocation recovery (annihilation). In order to constrain the time scale of the dislocation-induced anelastic relaxation, we further measured Young's modulus E at ultrasonic frequency before and after the dislocation creep and found that E at 106 Hz is not influenced by dislocations. Because E at 100 Hz is reduced by dislocations by 10%, the dislocation-induced anelastic relaxation occurs mostly between 102-106 Hz which is at a higher frequency than grain-boundary-induced anelasticity. To avoid dislocation recovery during the anelasticity measurement, we are now trying to perform an in-situ measurement of anelasticity while simultaneously deforming under a high stress associated with dislocation creep. The combination of persistent creep stress with small amplitude perturbations is similar to a seismic wave traveling through a region of active tectonic deformation.

Influence of composition and heat treatment on damping and magnetostrictive properties of Fe–18%(Ga + Al) alloys

DOE PAGES

Golovin, I. S.; Palacheva, V. V.; Zadorozhnyy, V. Yu.; ...

2014-07-16

The structure, magnetostriction and damping properties of Fe 82Ga (18–x)Al x (x = 0, 5, 8, 12) alloys were analyzed. The anelastic response of Fe–18(Ga + Al) alloys was studied as a function of temperature (from 0 to 600 °C), frequency (from 0.01 to 200 Hz) and amplitude (from 0.0004% to 0.2%) of forced vibrations. The origin of the relatively high damping capacity of Fe–Ga–Al alloy at room temperature was determined by applying a magnetic field and different heat treatment regimes. The substitution of Ga by Al in Fe–18% Ga alloys was found to decrease magnetostriction and damping. The heatmore » treatment of alloys influences the damping capacity of alloys more than variations of their chemical compositions. Thermally activated frequency and temperature-dependent anelastic effects in Fe–Ga–Al alloys were analyzed and the corresponding activation parameters for relaxation processes were evaluated. Internal friction effects caused by structural transformations were recorded and were found to be consistent with the A2 → D0 3 → L1 2 reaction. Thus, the physical mechanisms for all anelastic effects are discussed.« less

Source phase shift - A new phenomenon in wave propagation due to anelasticity. [in free oscillations of earth model

NASA Technical Reports Server (NTRS)

Buland, R.; Yuen, D. A.; Konstanty, K.; Widmer, R.

1985-01-01

The free oscillations of an anelastic earth model due to earthquakes were calculated directly by means of the correspondence principle from wave propagation theory. The formulation made it possible to find the source phase which is not predictable using first order perturbation theory. The predicted source phase was largest for toroidal modes with source components proportional to the radial strain scalar instead of the radial displacement scalar. The source phase increased in relation to the overtone number. In addition, large relative differences were found in the excitation modulus and the phase when the elastic excitation was small. The effect was sufficient to bias estimates of source properties and elastic structure.

Determination of intrinsic attenuation in the oceanic lithosphere-asthenosphere system

NASA Astrophysics Data System (ADS)

Takeuchi, Nozomu; Kawakatsu, Hitoshi; Shiobara, Hajime; Isse, Takehi; Sugioka, Hiroko; Ito, Aki; Utada, Hisashi

2017-12-01

We recorded P and S waves traveling through the oceanic lithosphere-asthenosphere system (LAS) using broadband ocean-bottom seismometers in the northwest Pacific, and we quantitatively separated the intrinsic (anelastic) and extrinsic (scattering) attenuation effects on seismic wave propagation to directly infer the thermomechanical properties of the oceanic LAS. The strong intrinsic attenuation in the asthenosphere obtained at higher frequency (~3 hertz) is comparable to that constrained at lower frequency (~100 seconds) by surface waves and suggests frequency-independent anelasticity, whereas the intrinsic attenuation in the lithosphere is frequency dependent. This difference in frequency dependence indicates that the strong and broad peak dissipation recently observed in the laboratory exists only in the asthenosphere and provides new insight into what distinguishes the asthenosphere from the lithosphere.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

Saturn Dynamo Model (Invited)

NASA Astrophysics Data System (ADS)

Glatzmaier, G. A.

2010-12-01

There has been considerable interest during the past few years about the banded zonal winds and global magnetic field on Saturn (and Jupiter). Questions regarding the depth to which the intense winds extend below the surface and the role they play in maintaining the dynamo continue to be debated. The types of computer models employed to address these questions fall into two main classes: general circulation models (GCMs) based on hydrostatic shallow-water assumptions from the atmospheric and ocean modeling communities and global non-hydrostatic deep convection models from the geodynamo and solar dynamo communities. The latter class can be further divided into Boussinesq models, which do not account for density stratification, and anelastic models, which do. Recent efforts to convert GCMs to deep circulation anelastic models have succeeded in producing fluid flows similar to those obtained from the original deep convection anelastic models. We describe results from one of the original anelastic convective dynamo simulations and compare them to a recent anelastic dynamo benchmark for giant gas planets. This benchmark is based on a polytropic reference state that spans five density scale heights with a radius and rotation rate similar to those of our solar system gas giants. The resulting magnetic Reynolds number is about 3000. Better spatial resolution will be required to produce more realistic predictions that capture the effects of both the density and electrical conductivity stratifications and include enough of the turbulent kinetic energy spectrum. Important additional physics may also be needed in the models. However, the basic models used in all simulation studies of the global dynamics of giant planets will hopefully first be validated by doing these simpler benchmarks.

Solid pole tide in global GPS and superconducting gravimeter observations: Signal retrieval and inference for mantle anelasticity

NASA Astrophysics Data System (ADS)

Ding, Hao; Chao, Benjamin F.

2017-02-01

The mantle anelasticity plays an important role in Earth's interior dynamics. Here we seek to determine the lower-mantle anelasticity through the solution of the complex Love numbers at the Chandler wobble period. The Love numbers h21, l21, δ21 and k21 are obtained in the frequency domain by dividing off the observed polar motion, or more specifically the pole tide potential, from the observed GPS 3-D displacement field and SG gravity variation. The latter signals are obtained through the array processing method of OSE (optimal sequence estimation) that results in greatly enhanced signals to be extracted from global array data. The resultant Love number estimates h21 = 0.6248 (± 5 e - 4) - 0.013 (± 5 e - 3) i, l21 = 0.0904 (± 8 e - 4) - 0.0008 (± 2 e - 3) i, δ21 = 1.156 (± 2 e - 3) - 0.003 (± 1 e - 3) i and k21 = 0.3125 (± 2 e - 3) - 0.0069 (± 3 e - 3) i are thus well-constrained in comparison to past estimates that vary considerably. They further lead to estimates of the corresponding mantle anelastic parameters fr and fi, which in turn determines, under the single-absorption band assumption, the dispersion exponent of α = 0.21 ± 0.02 with respect to the reference frequency of 5 mHz. We believe our estimate is robust and hence can better constrain the mantle anelasticity and attenuation models of the Earth interior.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Brouwer Award Lecture: Anelastic tides of close-in satellites and exoplanets

NASA Astrophysics Data System (ADS)

Ferraz-Mello, Sylvio

2016-05-01

This lecture reviews a new theory of the anelastic tides of celestial bodies in which the deformation of the body is the result of a Newtonian creep inversely proportional to the viscosity of the body and, along each radius, directly proportional to the distance from the actual surface of the body to the equilibrium. The first version of the theory (AAS/DDA 2012; CeMDA 2013), was restricted to homogeneous bodies. It was applied to many different bodies as the Moon, Mercury, super-Earths and hot Jupiters. An improved version (AAS/DDA 2014) included also the loss of angular momentum due to stellar winds and was applied to the study of the rotational evolution of active stars hosting massive companions. One more recent version (Folonier et al. AAS/DDA 2013; DPS 2015) allowed for the consideration of layered structures and was applied to Titan and Mercury. The resulting anelastic tides depend on the nature of the considered body. In the case of low-viscosity bodies (high relaxation factor), as gaseous planets and stars, the results are nearly the same of Darwin's theory. For instance, in these cases the dissipation grows proportionally to the tidal frequency. In the case of high-viscosity rocky satellites and planets (low relaxation factor), the results are structurally different: the dissipation varies with the tidal frequency following an inverse power law and the rotation may be driven to several attractors whose frequencies are 1/2, 1, 3/2, 2, 5/2,… times the orbital mean-motion, even when no permanent triaxiality exists.

Fault friction, regional stress, and crust-mantle coupling in southern California from finite element models

NASA Technical Reports Server (NTRS)

Bird, P.; Baumgardner, J.

1984-01-01

To determine the correct fault rheology of the Transverse Ranges area of California, a new finite element to represent faults and a mangle drag element are introduced into a set of 63 simulation models of anelastic crustal strain. It is shown that a slip rate weakening rheology for faults is not valid in California. Assuming that mantle drag effects on the crust's base are minimal, the optimal coefficient of friction in the seismogenic portion of the fault zones is 0.4-0.6 (less than Byerly's law assumed to apply elsewhere). Depending on how the southern California upper mantle seismic velocity anomaly is interpreted, model results are improved or degraded. It is found that the location of the mantle plate boundary is the most important secondary parameter, and that the best model is either a low-stress model (fault friction = 0.3) or a high-stress model (fault friction = 0.85), each of which has strong mantel drag. It is concluded that at least the fastest moving faults in southern California have a low friction coefficient (approximtely 0.3) because they contain low strength hydrated clay gouges throughout the low-temperature seismogenic zone.

Experimental study on anelasticty of polycrystalline material for seismological application

NASA Astrophysics Data System (ADS)

Takei, Y.; Karasawa, F.

2012-12-01

Due to the recent progress in seismology, we can obtain highly-resolved seismic velocity structures in the upper mantle. In order to interpret the velocity structures in terms of temperature heterogeneity, chemical heterogeneity, and fluid/melt distribution, it is important to assess the quantitative effects of temperature, chemical composition, and fluid/melt on Vp and Vs. Although these effects at the ultrasonic frequencies (anharmonic effect, poroelastic effect) have been measured and assessed quantitatively, these effects at the seismic frequencies are subject to large uncertainty due to the uncertainty in rock anelasticity, which additionally causes modulus relaxation at lower frequencies (anelastic effect). Previous studies have shown that anelasticity of polycrystalline materials follows the similarity rule in which frequency normalized to the Maxwell frequency, f/fM, can be used as a master variable (Morris & Jackson, 2009a; McCarthy et al, 2012). The general applicability of this Maxwell frequency scaling shows that the anelastic relaxation in those experiments is caused by diffusionally accommodated grain boundary sliding (GBS) (Gribb & Cooper, 1998; McCarthy et al, 2012). However, normalized frequency of the existing experimental data is usually considerably lower than the seismic frequencies normalized to the Maxwell frequency of the upper mantle (f/fM=106-1010). Therefore, in order to clarify the mechanism and scaling law applicable to the seismic waves, we have to measure anelasticity at higher normalized frequencies. Theoretical models (e.g., Raj, 1975; Morris & Jackson, 2009b) predict that at higher normalized frequencies, dominant GBS mechanism changes from diffusionally accommodated GBS to elastically accommodated GBS. However, the transition frequency and total relaxation strength associated with the elastically accommodated GBS, which are important in the application to seismology, have so far been difficult to constrain theoretically. Experimental data for these quantities are few (Jackson & Faul, 2010) and more data are needed. In this study, anelasticity of polycrystalline material at higher normalized frequencies (f/fM) was measured by using a rock analogue (organic polycrystal). Compared to the previous study by using the same analogue material (McCarthy et al 2012, homorogous temperature T/Tm = 0.67 - 0.61, f = 0.0001 - 2 Hz, f/fM = 0.1 - 5×104), anelasticity data were obtained at lower temperatures (T/Tm = 0.61 - 0.57), higher frequencies (f = 0.0001 - 50 Hz), and hence at higher normalized frequencies (f/fM = 0.1 - 5×107). We improved the accuracy of the modulus (Young's modulus) and Q-1 measurements by improving the stiffness of the apparatus and by correcting the data for a small time delay caused by measuring instruments. Based on the obtained data, we would like to discuss the mechanism and scaling law active in the seismic waves.

Elastic and anelastic structure of the lowermost mantle beneath the Western Pacific using waveform inversion

NASA Astrophysics Data System (ADS)

Konishi, K.; Deschamps, F.; Fuji, N.

2015-12-01

We investigate quasi-2D elastic and anelastic structure of the lowermost mantle beneath the Western Pacific by inverting S and ScS waveforms. The transverse component data were obtained from F-net for 32 deep sources beneath Tonga and Fiji, filtered between 12.5 and 200 s. We observe a regional variation of S and ScS arrival times and amplitude ratio, according to which we divide our region of interest into four sub-regions and perform 1D waveform inversion for S-wave velocity and Qμ value simultaneously. We find S-shaped structure of S-wave velocity beneath the whole region with sub-regional variation of S-wave velocity peak depths, which can explain regional difference in travel times. Qμ structure varies with sub-regions as well, but the physical interpretation has not yet done.

ASR4. Anelastic Strain Recovery Analysis Code

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

Warpinski, N.R.

ASR4 is a nonlinear least-squares regression of Anelastic Strain Recovery (ASR) data for the purpose of determining in situ stress orientations and magnitudes. ASR4 fits the viscoelastic model of Warpinski and Teufel to measure ASR data, calculates the stress orientations directly, and stress magnitudes if sufficient input data are available. The code also calculates the stress orientation using strain-rosette equations, and it calculates stress magnitudes using Blanton`s approach, assuming sufficient input data are available.

Anelastic Strain Recovery Analysis Code

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

ASR4 is a nonlinear least-squares regression of Anelastic Strain Recovery (ASR) data for the purpose of determining in situ stress orientations and magnitudes. ASR4 fits the viscoelastic model of Warpinski and Teufel to measure ASR data, calculates the stress orientations directly, and stress magnitudes if sufficient input data are available. The code also calculates the stress orientation using strain-rosette equations, and it calculates stress magnitudes using Blanton''s approach, assuming sufficient input data are available.

A general methodology for inverse estimation of the elastic and anelastic properties of anisotropic open-cell porous materials—with application to a melamine foam

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

Cuenca, Jacques, E-mail: jcuenca@kth.se; Van der Kelen, Christophe; Göransson, Peter

2014-02-28

This paper proposes an inverse estimation method for the characterisation of the elastic and anelastic properties of the frame of anisotropic open-cell foams used for sound absorption. A model of viscoelasticity based on a fractional differential constitutive equation is used, leading to an augmented Hooke's law in the frequency domain, where the elastic and anelastic phenomena appear as distinctive terms in the stiffness matrix. The parameters of the model are nine orthotropic elastic moduli, three angles of orientation of the material principal directions and three parameters governing the anelastic frequency dependence. The inverse estimation consists in numerically fitting the modelmore » on a set of transfer functions extracted from a sample of material. The setup uses a seismic-mass measurement repeated in the three directions of space and is placed in a vacuum chamber in order to remove the air from the pores of the sample. The method allows to reconstruct the full frequency-dependent complex stiffness matrix of the frame of an anisotropic open-cell foam and in particular it provides the frequency of maximum energy dissipation by viscoelastic effects. The characterisation of a melamine foam sample is performed and the relation between the fractional-derivative model and other types of parameterisations of the augmented Hooke's law is discussed.« less

A general methodology for inverse estimation of the elastic and anelastic properties of anisotropic open-cell porous materials—with application to a melamine foam

NASA Astrophysics Data System (ADS)

Cuenca, Jacques; Van der Kelen, Christophe; Göransson, Peter

2014-02-01

This paper proposes an inverse estimation method for the characterisation of the elastic and anelastic properties of the frame of anisotropic open-cell foams used for sound absorption. A model of viscoelasticity based on a fractional differential constitutive equation is used, leading to an augmented Hooke's law in the frequency domain, where the elastic and anelastic phenomena appear as distinctive terms in the stiffness matrix. The parameters of the model are nine orthotropic elastic moduli, three angles of orientation of the material principal directions and three parameters governing the anelastic frequency dependence. The inverse estimation consists in numerically fitting the model on a set of transfer functions extracted from a sample of material. The setup uses a seismic-mass measurement repeated in the three directions of space and is placed in a vacuum chamber in order to remove the air from the pores of the sample. The method allows to reconstruct the full frequency-dependent complex stiffness matrix of the frame of an anisotropic open-cell foam and in particular it provides the frequency of maximum energy dissipation by viscoelastic effects. The characterisation of a melamine foam sample is performed and the relation between the fractional-derivative model and other types of parameterisations of the augmented Hooke's law is discussed.

Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography

NASA Astrophysics Data System (ADS)

Jousset, Philippe; Neuberg, Jürgen; Jolly, Arthur

2004-11-01

Magma properties are fundamental to explain the volcanic eruption style as well as the generation and propagation of seismic waves. This study focusses on magma properties and rheology and their impact on low-frequency volcanic earthquakes. We investigate the effects of anelasticity and topography on the amplitudes and spectra of synthetic low-frequency earthquakes. Using a 2-D finite-difference scheme, we model the propagation of seismic energy initiated in a fluid-filled conduit embedded in a homogeneous viscoelastic medium with topography. We model intrinsic attenuation by linear viscoelastic theory and we show that volcanic media can be approximated by a standard linear solid (SLS) for seismic frequencies above 2 Hz. Results demonstrate that attenuation modifies both amplitudes and dispersive characteristics of low-frequency earthquakes. Low frequency volcanic earthquakes are dispersive by nature; however, if attenuation is introduced, their dispersion characteristics will be altered. The topography modifies the amplitudes, depending on the position of the seismographs at the surface. This study shows that we need to take into account attenuation and topography to interpret correctly observed low-frequency volcanic earthquakes. It also suggests that the rheological properties of magmas may be constrained by the analysis of low-frequency seismograms.

Seismic structure of the European crust and upper mantle based on adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, H.; Bozdag, E.; Peter, D.; Tromp, J.

2013-12-01

We present a new crustal and upper mantle model for the European continent and the North Atlantic Ocean, named EU60. It is constructed based on adjoint tomography and involves 3D variations in elastic wavespeeds, anelastic attenuation, and radial/azimuthal anisotropy. Long-wavelength elastic wavespeed structure of EU60 agree with previous body- and surface-wave tomographic models. Some hitherto unidentified features, such as the Adria microplate, naturally emerge from smoothed starting model. Subducting slabs, slab detachment, ancient suture zones, continental rifts and back-arc basins are well resolved in EU60. For anelastic structure, we find an anti-correlation between shear wavespeeds and anelastic attenuation at shallow depths. At greater depths, this anti-correlation becomes relatively weak, in agreement with previous attenuation studies at global scales. Consistent with radial anisotropy in 1D reference models, the European continent is dominated by features with radially anisotropic parameter xi>1, indicating the presence of horizontal flow within the upper mantle. In addition, subduction zones, such as the Apennines and Hellenic arcs, are characterized as vertical flow with xi<1 at depths greater than 150~km. For azimuthal anisotropy, we find that the direction of fast anisotropic axis is well correlated with complicated tectonic evolution in this region, such as extension along the North Atlantic Ridge, trench retreat in the Mediterranean and counter-clockwise rotation of the Anatolian Plate. The ``point spread function'' is used to assess image quality and analyze tradeoff between different model parameters.

Anelasticity of olivine single crystals investigated by stress-reduction tests and high-angular resolution electron backscatter diffraction

NASA Astrophysics Data System (ADS)

Wallis, D.; Hansen, L. N.; Kempton, I.; Wilkinson, A. J.

2017-12-01

Geodynamic phenomena, including glacial isostatic adjustment and postseismic deformation, can involve transient deformation in response to changes in differential stress acting on mantle rocks. As such, rheological models of transient deformation are incorporated in predictions of associated processes, including sea-level rise and stress redistribution after earthquakes. However, experimental constraints on rheological models for transient deformation of mantle materials are sparse. In particular, experiments involving stress reductions have been lacking. Moreover, a material's response to a reduction in stress can provide clues to the microphysical processes controlling deformation. To constrain models of transient deformation of mantle rocks we performed stress-reduction tests on single crystals of olivine at 1250-1300°C. Mechanical and piezoelectric actuators controlled constant initial stress during creep. At various strain intervals stress was reduced near-instantaneously using the piezoelectric actuator, inducing both elastic and anelastic (time-dependent) lengthening of the samples. A range of magnitudes of stress reduction were applied, typically unloading 10-90% of the initial stress. High-angular resolution electron backscatter diffraction (HR-EBSD), based on cross-correlation of diffraction patterns, was used to map dislocation density and elastic strain distributions in the recovered samples. Magnitudes of anelastic back-strain increase with increasing magnitudes of stress reduction and show a marked increase when stress reductions exceed 50% of the initial stress, consistent with previous observations in metals and alloys. This observation is inconsistent with the Burgers rheological model commonly used to describe transient behaviour and suggests that the style of rheological behaviour depends on the magnitude of stress change. HR-EBSD maps reveal that the crystal lattices are smoothly curved and generally lack subgrain boundaries and elastic strain heterogeneities. The dependence of the anelastic behaviour on the initial stress, combined with the lack of subgrain boundaries, suggest that the anelastic behaviour is controlled by local interactions between dislocations, rather than resistance imposed by the lattice or subgrain boundaries.

Mechanical rejuvenation in bulk metallic glass induced by thermo-mechanical creep

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

Tong, Yang; Dmowski, W.; Bei, Hongbin

Using high energy X-ray diffraction we studied the temperature, stress, and time effect on structural changes in a Zr-based bulk metallic glass induced by thermo-mechanical creep. Pair distribution functions obtained from two-dimensional diffraction patterns show that thermo-mechanical creep induces structural disordering, but only when the stress beyond a threshold is applied. A similar threshold behavior was observed for anelastic strain. We conclude that anelastic creep strain induces rejuvenation, whereas plastic strain does not.

Mechanical rejuvenation in bulk metallic glass induced by thermo-mechanical creep

DOE PAGES

Tong, Yang; Dmowski, W.; Bei, Hongbin; ...

2018-02-16

Using high energy X-ray diffraction we studied the temperature, stress, and time effect on structural changes in a Zr-based bulk metallic glass induced by thermo-mechanical creep. Pair distribution functions obtained from two-dimensional diffraction patterns show that thermo-mechanical creep induces structural disordering, but only when the stress beyond a threshold is applied. A similar threshold behavior was observed for anelastic strain. We conclude that anelastic creep strain induces rejuvenation, whereas plastic strain does not.

Inverse estimation of the elastic and anelastic properties of the porous frame of anisotropic open-cell foams.

PubMed

Cuenca, Jacques; Göransson, Peter

2012-08-01

This paper presents a method for simultaneously identifying both the elastic and anelastic properties of the porous frame of anisotropic open-cell foams. The approach is based on an inverse estimation procedure of the complex stiffness matrix of the frame by performing a model fit of a set of transfer functions of a sample of material subjected to compression excitation in vacuo. The material elastic properties are assumed to have orthotropic symmetry and the anelastic properties are described using a fractional-derivative model within the framework of an augmented Hooke's law. The inverse estimation problem is formulated as a numerical optimization procedure and solved using the globally convergent method of moving asymptotes. To show the feasibility of the approach a numerically generated target material is used here as a benchmark. It is shown that the method provides the full frequency-dependent orthotropic complex stiffness matrix within a reasonable degree of accuracy.

Inelastic deformation and phenomenological modeling of aluminum including transient effect

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

Cho, C.W.

A review was made of several phenomenological theories which have recently been proposed to describe the inelastic deformation of crystalline solids. Hart's deformation theory has many advantages, but there are disagreements with experimental deformation at stress levels below yield. A new inelastic deformation theory was proposed, introducing the concept of microplasticity. The new model consists of five deformation elements: a friction element representing a deformation element controlled by dislocation glide, a nonrecoverable plastic element representing the dislocation leakage rate over the strong dislocation barriers, a microplastic element representing the dislocation leakage rate over the weak barriers, a short range anelasticmore » spring element representing the recoverable anelastic strain stored by piled-up dislocations against the weak barriers, and a long range anelastic spring element representing the recoverable strain stored by piled-up dislocations against the strong barriers. Load relaxation and tensile testing in the plastic range were used to determine the material parameters for the plastic friction elements. The short range and long range anelastic moduli and the material parameters for the kinetics of microplasticity were determined by the measurement of anelastic loops and by performing load relaxation tests in the microplastic region. Experimental results were compared with a computer simulation of the transient deformation behavior of commercial purity aluminum. An attempt was made to correlate the material parameters and the microstructure from TEM. Stability of material parameters during inelastic deformation was discussed and effect of metallurgical variables was examined experimentally. 71 figures, 5 tables.« less

Modelling atmospheric flows with adaptive moving meshes

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas

2012-04-01

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) - employed in the integration of the underlying anelastic PDEs - that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.

Local models of astrophysical discs

NASA Astrophysics Data System (ADS)

Latter, Henrik N.; Papaloizou, John

2017-12-01

Local models of gaseous accretion discs have been successfully employed for decades to describe an assortment of small-scale phenomena, from instabilities and turbulence, to dust dynamics and planet formation. For the most part, they have been derived in a physically motivated but essentially ad hoc fashion, with some of the mathematical assumptions never made explicit nor checked for consistency. This approach is susceptible to error, and it is easy to derive local models that support spurious instabilities or fail to conserve key quantities. In this paper we present rigorous derivations, based on an asympototic ordering, and formulate a hierarchy of local models (incompressible, Boussinesq and compressible), making clear which is best suited for a particular flow or phenomenon, while spelling out explicitly the assumptions and approximations of each. We also discuss the merits of the anelastic approximation, emphasizing that anelastic systems struggle to conserve energy unless strong restrictions are imposed on the flow. The problems encountered by the anelastic approximation are exacerbated by the disc's differential rotation, but also attend non-rotating systems such as stellar interiors. We conclude with a defence of local models and their continued utility in astrophysical research.

Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography

NASA Astrophysics Data System (ADS)

Jousset, P.; Neuberg, J.

2003-04-01

Magma properties are fundamental to explain the volcanic eruption style as well as the generation and propagation of seismic waves. This study focusses on rheological magma properties and their impact on low-frequency volcanic earthquakes. We investigate the effects of anelasticity and topography on the amplitudes and spectra of synthetic low-frequency earthquakes. Using a 2D finite difference scheme, we model the propagation of seismic energy initiated in a fluid-filled conduit embedded in a 2D homogeneous viscoelastic medium with topography. Topography is introduced by using a mapping procedure that stretches the computational rectangular grid into a grid which follows the topography. We model intrinsic attenuation by linear viscoelastic theory and we show that volcanic media can be approximated by a standard linear solid for seismic frequencies (i.e., above 2 Hz). Results demonstrate that attenuation modifies both amplitude and dispersive characteristics of low-frequency earthquakes. Low-frequency events are dispersive by nature; however, if attenuation is introduced, their dispersion characteristics will be altered. The topography modifies the amplitudes, depending on the position of seismographs at the surface. This study shows that we need to take into account attenuation and topography to interpret correctly observed low-frequency volcanic earthquakes. It also suggests that the rheological properties of magmas may be constrained by the analysis of low-frequency seismograms.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

Implementation of a Message Passing Interface into a Cloud-Resolving Model for Massively Parallel Computing

NASA Technical Reports Server (NTRS)

Juang, Hann-Ming Henry; Tao, Wei-Kuo; Zeng, Xi-Ping; Shie, Chung-Lin; Simpson, Joanne; Lang, Steve

2004-01-01

The capability for massively parallel programming (MPP) using a message passing interface (MPI) has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The design for the MPP with MPI uses the concept of maintaining similar code structure between the whole domain as well as the portions after decomposition. Hence the model follows the same integration for single and multiple tasks (CPUs). Also, it provides for minimal changes to the original code, so it is easily modified and/or managed by the model developers and users who have little knowledge of MPP. The entire model domain could be sliced into one- or two-dimensional decomposition with a halo regime, which is overlaid on partial domains. The halo regime requires that no data be fetched across tasks during the computational stage, but it must be updated before the next computational stage through data exchange via MPI. For reproducible purposes, transposing data among tasks is required for spectral transform (Fast Fourier Transform, FFT), which is used in the anelastic version of the model for solving the pressure equation. The performance of the MPI-implemented codes (i.e., the compressible and anelastic versions) was tested on three different computing platforms. The major results are: 1) both versions have speedups of about 99% up to 256 tasks but not for 512 tasks; 2) the anelastic version has better speedup and efficiency because it requires more computations than that of the compressible version; 3) equal or approximately-equal numbers of slices between the x- and y- directions provide the fastest integration due to fewer data exchanges; and 4) one-dimensional slices in the x-direction result in the slowest integration due to the need for more memory relocation for computation.

Anelastic Mantle Structure beneath the Northern Philippine Sea from Phase Pair Method

NASA Astrophysics Data System (ADS)

Shito, A.; Shibutani, T.

2001-12-01

Anelasticity of the mantle provides important constraints on its dynamics, in complement to elasticity, however, studies of lateral variation in attenuation are few, especially at short periods. In this study, we determine the body wave attenuation structure of the mantle beneath the northern part of the Philippine Sea. Elastic tomography studies [e.g. van der Hilst et al., 1991; Fukao et al., 1992] show a stagnant Pacific lithosphere just above the 660 km discontinuity in this region. This stagnation was caused by the trench retreat due to the back arc spreading during the past 17 - 30 Ma [Seno et al., 1993; van der Hilst, 1995; Shito and Shibutani, 2001]. Anelastic properties of the mantle and lithosphere may play important roles in the interaction of the slab and mantle of this area. To study the attenuation structure, we examine the difference of the observed attenuation between P and S waves. The S-P phase pair method measures δ t* using the differential spectral decay between S and P waves arriving at the same station, assuming a constant Qα }/Q{β over the frequency band of 0.5 to 1.25 Hz. We use 20 earthquakes in the Izu-Bonin slab which were recorded at 43 broad-band stations of the J-array and FREESIA networks in Japan. About 700 phase pairs are used to invert for the 2-D attenuation structure. The resultant preliminary Q model shows the local variations of attenuation in the subduction zone. The slab is imaged as a low attenuation area (Qα > 1000), while Qα values in the range of 100 - 350 are found in the mantle wedge.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

A high-order strong stability preserving Runge-Kutta method for three-dimensional full waveform modeling and inversion of anelastic models

NASA Astrophysics Data System (ADS)

Wang, N.; Shen, Y.; Yang, D.; Bao, X.; Li, J.; Zhang, W.

2017-12-01

Accurate and efficient forward modeling methods are important for high resolution full waveform inversion. Compared with the elastic case, solving anelastic wave equation requires more computational time, because of the need to compute additional material-independent anelastic functions. A numerical scheme with a large Courant-Friedrichs-Lewy (CFL) condition number enables us to use a large time step to simulate wave propagation, which improves computational efficiency. In this work, we apply the fourth-order strong stability preserving Runge-Kutta method with an optimal CFL coeffiecient to solve the anelastic wave equation. We use a fourth order DRP/opt MacCormack scheme for the spatial discretization, and we approximate the rheological behaviors of the Earth by using the generalized Maxwell body model. With a larger CFL condition number, we find that the computational efficient is significantly improved compared with the traditional fourth-order Runge-Kutta method. Then, we apply the scattering-integral method for calculating travel time and amplitude sensitivity kernels with respect to velocity and attenuation structures. For each source, we carry out one forward simulation and save the time-dependent strain tensor. For each station, we carry out three `backward' simulations for the three components and save the corresponding strain tensors. The sensitivity kernels at each point in the medium are the convolution of the two sets of the strain tensors. Finally, we show several synthetic tests to verify the effectiveness of the strong stability preserving Runge-Kutta method in generating accurate synthetics in full waveform modeling, and in generating accurate strain tensors for calculating sensitivity kernels at regional and global scales.

LaAlO3: A substrate material with unusual ferroelastic properties

NASA Astrophysics Data System (ADS)

Kustov, S.; Liubimova, Iu.; Salje, E. K. H.

2018-01-01

Twin boundary dynamics in LaAlO3 is associated with non-linear anelasticity. Ultrasonic studies of non-linear twin boundary dynamics between 80 and 520 K show that cooling substrates from temperatures near the ferroelastic transition at 813 K generate three characteristic thermal regimes with different non-linear dynamics. Twin boundaries are initially highly mobile. Anelastic strain amplitudes versus stress are power law distributed with an exponent of 2.5. No de-pinning was found down to elastic strain amplitudes of ɛ0 ˜ 10-7. The power law is gradually replaced between 370 K and 280 K by few large singularities (jerks) due to massive rearrangements of the domain structure for ɛ0 larger than ca. 5 × 10-5. At lower temperatures, the domain structure is pinned with well-defined thresholds for de-pinning. The de-pinning is not accompanied by global rearrangements of twin patterns below room temperature. Unexpectedly, the low-temperature critical de-pinning strain amplitude decreases with decreasing temperature, which may indicate an additional, so far unknown phase transition near 40 K.

CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS

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

Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.

2013-09-01

Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and stellar dynamos. This qualitative agreement fuels the idea that both numerical models and astrophysical objects may operate in the same asymptotic regime of dynamics. This can be tested by exploring the scaling behavior of the models. For convection-driven incompressible spherical shell dynamos with constant material properties, scaling laws had been established previously that relate flow velocity and magnetic field strength to the available power. Here we analyzemore » 273 direct numerical simulations using the anelastic approximation, involving also cases with radius-dependent magnetic, thermal, and viscous diffusivities. These better represent conditions in gas giant planets and low-mass stars compared to Boussinesq models. Our study provides strong support for the hypothesis that both mean velocity and mean magnetic field strength scale as a function of the power generated by buoyancy forces in the same way for a wide range of conditions.« less

Elasticity and dislocation anelasticity of crystals

NASA Astrophysics Data System (ADS)

Nikanorov, S. P.; Kardashev, B. K.

The book is concerned with the application of the results of physical acoustic studies of elasticity and dislocation anelasticity to the investigation of interatomic interactions and interactions between lattice defects. The analysis of the potential functions determining the energy of interatomic interactions is based on a study of the elastic properties of crystals over a wide temperature range; data on the dislocation structure and on the interaction between dislocations and point defects are based mainly on a study of inelastic effects. Particular attention is given to the relationship between microplastic effects and the initial stage of plastic deformation under conditions of elastic oscillations, when the multiplication of dislocations is negligible.

A nonreflecting upper boundary condition for anelastic nonhydrostatic mesoscale gravity-wave models

NASA Technical Reports Server (NTRS)

Kim, Young-Joon; Kar, Sajal K.; Arakawa, Akio

1993-01-01

A sponge layer is formulated to prevent spurious reflection of vertically propagating quasi-stationary gravity waves at the upper boundary of a two-dimensional numerical anelastic nonhydrostatic model. The sponge layer includes damping of both Newtonian-cooling type and Rayleigh-friction type, whose coefficients are determined in such a way that the reflectivity of wave energy at the bottom of the layer is zero. Unlike the formulations in earlier studies, our formulation includes the effects of vertical discretization, vertical mean density variation, and nonhydrostaticity. This sponge formulation is found effective in suppressing false downward reflection of waves for various types of quasi-stationary forcing.

Volumetric strain in relation to particle displacements for body and surface waves in a general viscoelastic half-space

USGS Publications Warehouse

Borcherdt, R.D.

1988-01-01

Dilatational earth strain, associated with the radiation fields for several hundred local, regional, and teleseismic earthquakes, has been recorded over an extended bandwidth and dynamic range at four borehole sites near the San Andreas fault, CA. The general theory of linear viscoelasticity is applied to account for anelasticity of the near-surface materials and to provide a mathematical basis for interpretation of seismic radiation fields as detected simultaneously by co-located volumetric strain meters and seismometers. The general theory is applied to describe volumetric strain and displacement for general (homogeneous or inhomogeneous) P and S waves in an anelastic whole space. Solutions to the free-surface reflection problems for incident general P and S-I waves are used to evaluate the effect of the free surface on observations from co-located sensors. Corresponding expressions are derived for a Rayleigh-type surface wave on a linear viscoelastic half-space. The theory predicts a number of anelastic wave field characteristics that can be inferred from observation of volumetric strains and displacement fields as detected by co-located sensors that cannot be inferred from either sensor alone. -from Author

Elastic Heterogeneity in Metallic Glasses

NASA Astrophysics Data System (ADS)

Dmowski, W.; Iwashita, T.; Chuang, C.-P.; Almer, J.; Egami, T.

2010-11-01

When a stress is applied on a metallic glass it deforms following Hook’s law. Therefore it may appear obvious that a metallic glass deforms elastically. Using x-ray diffraction and anisotropic pair-density function analysis we show that only about (3)/(4) in volume fraction of metallic glasses deforms elastically, whereas the rest of the volume is anelastic and in the experimental time scale deform without resistance. We suggest that this anelastic portion represents residual liquidity in the glassy state. Many theories, such as the free-volume theory, assume the density of defects in the glassy state to be of the order of 1%, but this result shows that it is as much as a quarter.

Composition-dependent damping and relaxation dynamics in miscible polymer blends above glass transition temperature by anelastic spectroscopy

NASA Astrophysics Data System (ADS)

Wu, Xuebang; Shang, Shuying; Xu, Qiaoling; Liu, Changsong; Zhu, Zhengang; Zhang, Guangzhao

2008-07-01

Anelastic spectroscopy is used to study the composition dependence of the damping and molecular relaxation dynamics in miscible poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) blends above the glass transition temperature. The ultrahigh damping peak of the relaxation type is shown to be associated with the liquid-liquid transition of PMMA. A higher PEO concentration leads to a higher damping performance and a lower transition temperature. The decreasing activation energy with increasing PEO concentration indicates a drastic increase in molecular mobility. Moreover, the relaxation time reveals a transition from the Vogel-Fulcher-Tamman behavior to the Arrhenius behavior due to the intermolecular guest-host interactions.

Analytical computation of three-dimensional synthetic seismograms by Modal Summation: method, validation and applications

NASA Astrophysics Data System (ADS)

La Mura, Cristina; Gholami, Vahid; Panza, Giuliano F.

2013-04-01

In order to enable realistic and reliable earthquake hazard assessment and reliable estimation of the ground motion response to an earthquake, three-dimensional velocity models have to be considered. The propagation of seismic waves in complex laterally varying 3D layered structures is a complicated process. Analytical solutions of the elastodynamic equations for such types of media are not known. The most common approaches to the formal description of seismic wavefields in such complex structures are methods based on direct numerical solutions of the elastodynamic equations, e.g. finite-difference, finite-element method, and approximate asymptotic methods. In this work, we present an innovative methodology for computing synthetic seismograms, complete of the main direct, refracted, converted phases and surface waves in three-dimensional anelastic models based on the combination of the Modal Summation technique with the Asymptotic Ray Theory in the framework of the WKBJ - approximation. The three - dimensional models are constructed using a set of vertically heterogeneous sections (1D structures) that are juxtaposed on a regular grid. The distribution of these sections in the grid is done in such a way to fulfill the requirement of weak lateral inhomogeneity in order to satisfy the condition of applicability of the WKBJ - approximation, i.e. the lateral gradient of the parameters characterizing the 1D structure has to be small with respect to the prevailing wavelength. The new method has been validated comparing synthetic seismograms with the records available of three different earthquakes in three different regions: Kanto basin (Japan) triggered by the 1990 Odawara earthquake Mw= 5.1, Romanian territory triggered by the 30 May 1990 Vrancea intermediate-depth earthquake Mw= 6.9 and Iranian territory affected by the 26 December 2003 Bam earthquake Mw= 6.6. Besides the advantage of being a useful tool for assessment of seismic hazard and seismic risk reduction, it is characterized by high efficiency, in fact, once the study region is identified and the 3D model is constructed, the computation, at each station, of the three components of the synthetic signal (displacement, velocity, and acceleration) takes less than 3 hours on a 2 GHz CPU.

Nonlinear anelastic modal theory for solar convection

NASA Technical Reports Server (NTRS)

Latour, J.; Toomre, J.; Zahn, J.-P.

1983-01-01

Solar envelope models are developed using single-mode anelastic equations as a description of turbulent convection which provide estimates for the variation with depth of the largest convective cellular flows, with horizontal sizes comparable to the total depth of the convection zone. These models can be used to describe compressible motions occurring over many density scale heights. Single-mode anelastic solutions are obtained for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy flux explicitly carried by the big cell, while a subgrid scale representation of turbulent heat transport is incorporated into the treatment near the surface. It is shown that the single-mode equations allow two solutions for the same horizontal wavelength which are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is found that the upward directed flow experiences large pressure effects which can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. It is suggested that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so weak in the solar atmosphere.

Compressible Convection Experiment using Xenon Gas in a Centrifuge

NASA Astrophysics Data System (ADS)

Menaut, R.; Alboussiere, T.; Corre, Y.; Huguet, L.; Labrosse, S.; Deguen, R.; Moulin, M.

2017-12-01

We present here an experiment especially designed to study compressible convection in the lab. For significant compressible convection effects, the parameters of the experiment have to be optimized: we use xenon gaz in a cubic cell. This cell is placed in a centrifuge to artificially increase the apparent gravity and heated from below. With these choices, we are able to reach a dissipation number close to Earth's outer core value. We will present our results for different heating fluxes and rotation rates. We success to observe an adiabatic gradient of 3K/cm in the cell. Studies of pressure and temperature fluctuations lead us to think that the convection takes place under the form of a single roll in the cell for high heating flux. Moreover, these fluctuations show that the flow is geostrophic due to the high rotation speed. This important role of rotation, via Coriolis force effects, in our experimental setup leads us to develop a 2D quasigeostrophic compressible model in the anelastic liquid approximation. We test numerically this model with the finite element solver FreeFem++ and compare its results with our experimental data. In conclusion, we will present our project for the next experiment in which the cubic cell will be replace by a annulus cell. We will discuss the new expected effects due to this geometry as Rossby waves and zonal flows.

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

Majda, Andrew J.; Xing, Yulong; Mohammadian, Majid

Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamics and the microscale balanced hot tower (BHT) dynamics involve simplified balanced equations without gravity waves for vertical vorticity amplification due to moist heatmore » sources and incorporate nonlinear advective fluxes across scales. The BMV model is the central one for tropical cyclogenesis in the embryo. The moist mesoscale wave (MMW) dynamics involves simplified equations for mesoscale moisture fluctuations, as well as linear hydrostatic waves driven by heat sources from moisture and eddy flux divergences. A simplified cloud physics model for deep convection is introduced here and used to study moist axisymmetric plumes in the BHT model. A simple application in periodic geometry involving the effects of mesoscale vertical shear and moist microscale hot towers on vortex amplification is developed here to illustrate features of the coupled multi-scale models. These results illustrate the use of these models in isolating key mechanisms in the embryo in a simplified content.« less

Strain coupling mechanisms and elastic relaxation associated with spin state transitions in LaCoO3

NASA Astrophysics Data System (ADS)

Zhang, Zhiying; Koppensteiner, Johannes; Schranz, Wilfried; Prabhakaran, Dharmalingam; Carpenter, Michael A.

2011-04-01

Advantage is taken of the wealth of experimental data relating to the evolution with temperature of spin states of Co3 + in LaCoO3 in order to undertake a detailed investigation of the mechanisms by which changes in electronic structure can influence strain, and elastic and anelastic relaxations in perovskites. The macroscopic strain accompanying changes in the spin state in LaCoO3 is predominantly a volume strain arising simply from the change in effective ionic radius of the Co3 + ions. This acts to renormalize the octahedral tilting transition temperature in a manner that is easily understood in terms of coupling between the tilt and spin order parameters. Results from resonant ultrasound spectroscopy at high frequencies (0.1-1.5 MHz) reveal stiffening of the shear modulus which scales qualitatively with a spin order parameter defined in terms of changing Co-O bond lengths. From this finding, in combination with results from dynamic mechanical analysis at low frequencies (0.1-50 Hz) and data from the literature, four distinctive anelastic relaxation mechanisms are identified. The relaxation times of these are displayed on an anelasticity map and are tentatively related to spin-spin relaxation, spin-lattice relaxation, migration of twin walls and migration of magnetic polarons. The effective activation energy for the freezing of twin wall motion below ~ 590 K at low frequencies was found to be 182 ± 21 kJ mol - 1 (1.9 ± 0.2 eV) which is attributed to pinning by pairs of oxygen vacancies, though the local mechanisms appear to have a spread of relaxation times. It seems inevitable that twin walls due to octahedral tilting must have quite different characteristics from the matrix in terms of local spin configurations of Co3 + . A hysteresis in the elastic properties at high temperatures further emphasizes the importance of oxygen content in controlling the properties of LaCoO3.

Simulation of all-scale atmospheric dynamics on unstructured meshes

NASA Astrophysics Data System (ADS)

Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng

2016-10-01

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

Numerical modeling and model updating for smart laminated structures with viscoelastic damping

NASA Astrophysics Data System (ADS)

Lu, Jun; Zhan, Zhenfei; Liu, Xu; Wang, Pan

2018-07-01

This paper presents a numerical modeling method combined with model updating techniques for the analysis of smart laminated structures with viscoelastic damping. Starting with finite element formulation, the dynamics model with piezoelectric actuators is derived based on the constitutive law of the multilayer plate structure. The frequency-dependent characteristics of the viscoelastic core are represented utilizing the anelastic displacement fields (ADF) parametric model in the time domain. The analytical model is validated experimentally and used to analyze the influencing factors of kinetic parameters under parametric variations. Emphasis is placed upon model updating for smart laminated structures to improve the accuracy of the numerical model. Key design variables are selected through the smoothing spline ANOVA statistical technique to mitigate the computational cost. This updating strategy not only corrects the natural frequencies but also improves the accuracy of damping prediction. The effectiveness of the approach is examined through an application problem of a smart laminated plate. It is shown that a good consistency can be achieved between updated results and measurements. The proposed method is computationally efficient.

Forearc deformation and great subduction earthquakes: implications for cascadia offshore earthquake potential.

PubMed

McCaffrey, R; Goldfinger, C

1995-02-10

The maximum size of thrust earthquakes at the world's subduction zones appears to be limited by anelastic deformation of the overriding plate. Anelastic strain in weak forearcs and roughness of the plate interface produced by faults cutting the forearc may limit the size of thrust earthquakes by inhibiting the buildup of elastic strain energy or slip propagation or both. Recently discovered active strike-slip faults in the submarine forearc of the Cascadia subduction zone show that the upper plate there deforms rapidly in response to arc-parallel shear. Thus, Cascadia, as a result of its weak, deforming upper plate, may be the type of subduction zone at which great (moment magnitude approximately 9) thrust earthquakes do not occur.

Universal mechanism of thermo-mechanical deformation in metallic glasses

DOE PAGES

Dmowski, W.; Tong, Y.; Iwashita, T.; ...

2015-02-11

Here we investigated the atomistic structure of metallic glasses subjected to thermo-mechanical creep deformation using high energy x-ray diffraction and molecular dynamics simulation. The experiments were performed in-situ, at high temperatures as a time dependent deformation in the elastic regime, and ex-situ on samples quenched under stress. We show that all the anisotropic structure functions of the samples undergone thermo-mechanical creep can be scaled into a single curve, regardless of the magnitude of anelastic strain, stress level and the sign of the stress, demonstrating universal behavior and pointing to unique atomistic unit of anelastic deformation. The structural changes due tomore » creep are strongly localized within the second nearest neighbors, involving only a small group of atoms.« less

Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

USGS Publications Warehouse

Hsi-Ping, Liu

1990-01-01

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment. -Author

Origins of anisotropic seismic attenuation of the inner core - intrinsic anelasticity of hcp iron alloy

NASA Astrophysics Data System (ADS)

Redfern, Simon

2015-04-01

Earth's inner core is elastically anisotropic, with seismology showing faster wave propagation along the polar axis compared to the equatorial plane. Some inner core studies report anisotropic seismic attenuation. Attenuation of body-waves has, previously, been postulated to be due to scattering by anisotropic microstructure, but recent normal mode studies also show strong anisotropic attenuation (Mäkinen et al. 2014). This suggests that the anisotropic attenuation is a result of the intrinsic (and anisotropic) anelastic properties of the solid iron alloy forming Earth's inner core. Here, I consider the origins of inner core anisotropic attenuation. Possibilities include grain boundary relaxation, dislocation bowing/glide, or point defect (alloying element) relaxations. The inner core is an almost perfect environment for near-equilibrium crystallisation, with very low temperature gradients across the inner core, low gravity, and slow crystallisation rates. It is assumed that grain sizes may be of the order of hundreds of metres. This implies vanishingly small volumes of grain boundary, and insignificant grain boundary relaxation. The very high homologous temperature and the absence of obvious deviatoric stress, also leads one to conclude that dislocation densities are low. On the other hand, estimates for light element concentrations are of the order of a few % with O, S, Si, C and H at various times being suggested as candidate elements. Light element solutes in hcp metals contribute to intrinsic anelastic attenuation if they occur in sufficient concentrations to pair and form elastic dipoles. Switching of dipoles under the stress of a passing seismic wave will result in anelastic mechanical loss. Such attenuation has been measured in hcp metals in the lab, and is anisotropic due to the intrinsic elastic anisotropy of the host lattice. Such solute pair relaxations result in a "Zener effect", which is suggested here to be responsible for observed anisotropic seismic attenuation. Zener relaxation magnitude scales with solute concentration and is consistent with around 5% light element. Variations in attenuation are expected in a core with spatially varying concentrations of light element, and attenuation tomography of the inner core could, therefore, be employed to map chemical heterogeneity.

Intrinsic Aniostropic Anelasticity of Hcp Iron Due to Light Element Solute Atoms

NASA Astrophysics Data System (ADS)

Redfern, S. A. T.

2014-12-01

Earth's inner core is elastically anisotropic, with seismology showing faster wave propagation along the polar axis compared to the equatorial plane. Some inner core studies report anisotropic seismic attenuation. Attenuation of body-waves has, previously, been postulated to be due to scattering by anisotropic microstructure, but recent normal mode studies also show strong anisotropic attenuation (Mäkinen et al. 2014). This suggests that the anisotropic attenuation is a result of the intrinsic (and anisotropic) anelastic properties of the solid iron alloy forming Earth's inner core. Here, I consider the origins of inner core anisotropic attenuation. Possibilities include grain boundary relaxation, dislocation bowing/glide, or point defect (alloying element) relaxations. The inner core is an almost perfect environment for near-equilibrium crystallisation, with very low temperature gradients across the inner core, low gravity, and slow crystallisation rates. It is assumed that grain sizes may be of the order of hundreds of metres. This implies vanishingly small volumes of grain boundary, and insignificant grain boundary relaxation. The very high homologous temperature and the absence of obvious deviatoric stress, also leads one to conclude that dislocation densities are low. On the other hand, estimates for light element concentrations are of the order of a few % with O, S, Si, C and H at various times being suggested as candidate elements. Light element solutes in hcp metals contribute to intrinsic anelastic attenuation if they occur in sufficient concentrations to pair and form elastic dipoles. Switching of dipoles under the stress of a passing seismic wave will result in anelastic mechanical loss. Such attenuation has been measured in hcp metals in the lab, and is anisotropic due to the intrinsic elastic anisotropy of the host lattice. Such solute pair relaxations result in a "Zener effect", which is suggested here to be responsible for observed anisotropic seismic attenuation. Zener relaxation magnitude scales with solute concentrationand is consistent with around 5% loght element. Variations in attenuation are expected in a core with spatially varying concentrations of light element, and attenuation tomography of the inner core could, therefore, be employed to map chemical heterogeneity.

Determination of three-dimensional stress orientations in the Wenchuan earthquake Fault Scientific Drilling (WFSD) hole-1: A preliminary result by anelastic strain recovery measurements of core samples

NASA Astrophysics Data System (ADS)

Cui, J.; Lin, W.; Wang, L.; Tang, Z.; Sun, D.; Gao, L.; Wang, W.

2010-12-01

A great and destructive earthquake (Ms 8.0; Mw 7.9), Wunchuan earthquake struck on the Longmen Shan foreland trust zone in Sichuan province, China on 12 May 2008 (Xu et al., 2008; Episodes, Vol.31, pp.291-301). As a rapid response scientific drilling project, Wenchuan earthquake Fault Scientific Drilling (WFSD) started on 6 November 2008 shorter than a half of year from the date of earthquake main shock. The first pilot borehole (hole-1) has been drilled to the target depth (measured depth 1201 m MD, vertical depth 1179 m) at Hongkou, Dujianyan, Sichuan and passed through the main fault of the earthquake around 589 m MD. We are trying to determine three dimensional in-situ stress states in the WFSD boreholes by a core-based method, anelastic strain recovery (ASR) method (Lin et al., 2006; Tectonophysics, Vol4.26, pp.221-238). This method has been applied in several scientific drilling projects (TCDP: Lin et al., 2007; TAO, Vol.18, pp.379-393; NanTtoSEIZE: Byrne et al., 2009; GRL, Vol.36, L23310). These applications confirm the validity of using the ASR technique in determining in situ stresses by using drilled cores. We collected total 15 core samples in a depth range from 340 m MD to 1180 m MD, approximately for ASR measurements. Anelastic normal strains, measured every ten minutes in nine directions, including six independent directions, were used to calculate the anelastic strain tensors. The data of the ASR tests conducted at hole-1 is still undergoing analysis. As a tentative perspective, more than 10 core samples showed coherent strain recovery over one - two weeks. However, 2 or 3 core samples cannot be re-orientated to the global system. It means that we cannot rink the stress orientation determined by the core samples to geological structure. Unfortunately, a few core samples showed irregular strain recovery and were not analyzed further. The preliminary results of ASR tests at hole-1 show the stress orientations and stress regime changes a lot with the depth.

Anelasticity maps for acoustic dissipation associated with phase transitions in minerals

NASA Astrophysics Data System (ADS)

Carpenter, Michael A.; Zhang, Zhiying

2011-07-01

Acoustic dissipation due to structural phase transitions in minerals could give rise to large seismic attenuation effects superimposed on the high temperature background contribution from dislocations and grain boundaries in the Earth. In addition to the possibility of a sharp peak actually at a transition point for both compressional and shear waves, significant attenuation might arise over wider temperature intervals due to the mobility of transformation twins or other defects associated with the transition. Attenuation due to structural phase transitions in quartz, pyroxenes, perovskites, stishovite and hollandite, or to spin state transitions of Fe2+ in magnesiowüstite and perovskite and the hcp/bcc transition in iron-nickel (Fe-Ni) alloy, are reviewed from this perspective. To these can be added possible loss behaviour associated with reconstructive transitions which might occur by a ledge mechanism on topotactic interfaces (orthopyroxene/clinopyroxene, olivine/spinel and perovskite/postperovskite), with impurities (Snoek effect) or with mobility of protons. There are experimental difficulties associated with measuring dissipation effects in situ at simultaneous high pressures and temperatures, so reliance is currently placed on investigation of analogue phases such as LaCoO3 for spin-state behaviour and LaAlO3 for the dynamics of ferroelastic twin walls. Similarly, it is not possible to measure loss dynamics simultaneously at the low stresses and low frequencies that pertain in seismic waves, so reliance must be placed on combining different techniques, such as dynamic mechanical analysis (low frequency, relatively high stress) and resonant ultrasound spectroscopy (high frequency, low stress), to extrapolate acoustic loss behaviour over wide frequency, temperature and stress intervals. In this context 'anelasticity maps' provide a convenient means of representing different loss mechanisms. Contouring of the inverse mechanical quality factor, Q-1, can be achieved if the appropriate constitutive laws are known. The overall approach is illustrated using the examples of spin-state transitions of Co3+ in LaCoO3 and twin mobility in single crystals of the rhombohedral phase of LaAlO3. Anelasticity maps of this type should give seismologists a clearer view of the characteristic patterns of seismic velocity and attenuation that could be used to detect (or rule out) the presence of particular phase transitions or loss behaviour in the core and mantle.

Magnetoconvection dynamics in a stratified layer. 1: Two-dimensional simulations and visualization

NASA Astrophysics Data System (ADS)

Lantz, Steven R.; Sudan, R. N.

1995-03-01

To gain insight in the problem of fluid convection below solar photosphere, time-dependent magnetohydrodynamic convection is studied by numerical simulation to the magneto-anelastic equations, a model appropiate for low Mach numbers. Numerical solutions to the equations are generated on a two-dimensional Cartesian mesh by a finite-difference, predictor-corrector algorithm. The thermodynamic properties of the fluid are held constant at the rigid, stress-free top and bottom boundaries of the computational box, while lateral boundaries are treated as periodic. In most runs the background polytropic fluid configuration is held fixed at Rayleigh number R = 5.44 times the critical value, Prandtl number P = 1.8, and aspect ratio a = 1, while the magnetic parameters are allowed to vary. The resulting dynamical behavior is shown to be strongly influenced by a horizontal magnetic field which is imposed at the bottom boundary. As the field strength increases from zero, an initially unsteady 'single-roll' state, featuring complex time dependence is replaced by a steady 'traveling-wave tilted state; then, an oscillatory or 'sloshing' state; then, a steady two-poll state with no tilting; and finally, a stationary state. Because the magnetic field is matched onto a potential field at the top boundary, it can penetrate into the nonconducting region above. By varying a magnetic diffusivity, the concentrations of weak magnetic fields at the top of these flows can be shown to be explainable in terms of an advection-diffusion balance.

Anisotropic constitutive modeling for nickel-base single crystal superalloys. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Sheh, Michael Y.

1988-01-01

An anisotropic constitutive model was developed based on crystallographic slip theory for nickel base single crystal superalloys. The constitutive equations developed utilizes drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments were conducted to evaluate the existence of back stress in single crystal superalloy Rene N4 at 982 C. The results suggest that: (1) the back stress is orientation dependent; and (2) the back stress state variable is required for the current model to predict material anelastic recovery behavior. The model was evaluated for its predictive capability on single crystal material behavior including orientation dependent stress-strain response, tension/compression asymmetry, strain rate sensitivity, anelastic recovery behavior, cyclic hardening and softening, stress relaxation, creep and associated crystal lattice rotation. Limitation and future development needs are discussed.

A Self-Consistent Fault Slip Model for the 2011 Tohoku Earthquake and Tsunami

NASA Astrophysics Data System (ADS)

Yamazaki, Yoshiki; Cheung, Kwok Fai; Lay, Thorne

2018-02-01

The unprecedented geophysical and hydrographic data sets from the 2011 Tohoku earthquake and tsunami have facilitated numerous modeling and inversion analyses for a wide range of dislocation models. Significant uncertainties remain in the slip distribution as well as the possible contribution of tsunami excitation from submarine slumping or anelastic wedge deformation. We seek a self-consistent model for the primary teleseismic and tsunami observations through an iterative approach that begins with downsampling of a finite fault model inverted from global seismic records. Direct adjustment of the fault displacement guided by high-resolution forward modeling of near-field tsunami waveform and runup measurements improves the features that are not satisfactorily accounted for by the seismic wave inversion. The results show acute sensitivity of the runup to impulsive tsunami waves generated by near-trench slip. The adjusted finite fault model is able to reproduce the DART records across the Pacific Ocean in forward modeling of the far-field tsunami as well as the global seismic records through a finer-scale subfault moment- and rake-constrained inversion, thereby validating its ability to account for the tsunami and teleseismic observations without requiring an exotic source. The upsampled final model gives reasonably good fits to onshore and offshore geodetic observations albeit early after-slip effects and wedge faulting that cannot be reliably accounted for. The large predicted slip of over 20 m at shallow depth extending northward to 39.7°N indicates extensive rerupture and reduced seismic hazard of the 1896 tsunami earthquake zone, as inferred to varying extents by several recent joint and tsunami-only inversions.

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

NASA Astrophysics Data System (ADS)

Liu, Qinya; Tromp, Jeroen

2008-07-01

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δlnm = δm/m denotes relative model perturbations in the volume V, δlnd denotes relative topographic variations on solid-solid or fluid-solid boundaries Σ, and ∇Σδlnd denotes surface gradients in relative topographic variations on fluid-solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δlnm, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δlnd. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.

Seismic Attenuation of Teleseismic Body Waves in Cascadia, Measured on the Amphibious Array

NASA Astrophysics Data System (ADS)

Eilon, Z.; Abers, G. A.

2015-12-01

Fundamental questions remain about the nature of the asthenosphere, including its dynamical relationship to overlying lithosphere, melt content, and entrainment in subduction zones. We examine the evolution of this low-velocity, highly attenuating layer using data from the Cascadia Initiative's Amphibious Array, which provides unprecedented coverage of an oceanic plate from ridge crest to trench to sub-arc. Our study extends the suite of measurements achievable with OBS data, augmenting traditional travel time analysis with integrated attenuation data that are a powerful tool for imaging melt/fluids and the variation of asthenospheric character with age. Cooling models, coupled with experimentally-derived anelastic scaling relationships, indicate that thermal gradients should cause appreciable decrease in attenuation of teleseismic body waves with increasing age. This long-wavelength cooling trend may be perturbed by highly attenuating melt or volatiles concentrated at the ridge axis or beneath the Cascades arc, depending on melt fraction and pore geometry. Attenuation beyond the trench should be a strong function of the fate of asthenospheric entrainment beneath subducted plates, with implications for mass transfer to the deep mantle as well as recent models of sub-slab anisotropy. The Amphibious Array, with <70 km spacing of OBS and on-land broadband seismometers deployed between 2011 and 2015, provides a dataset of ~1 x 105 arrivals from ~700 Mw>6.0 teleseismic earthquakes. We use a spectral ratio method to compute differential attenuation (Δt*) from body wave teleseisms recorded at OBS and land stations, allowing us to estimate path-integrated quality factor in the upper mantle. Preliminary results reveal variations of ~3 s in differential travel time and >0.5 s in ΔtS* across the 0-10 Ma oceanic plate, demonstrating the strong thermal control on anelasticity. Large values of Δt* observed east of the trench may indicate entrainment of highly attenuating asthenosphere during subduction, although more work is required to categorize and remove the signal of the overriding plate. This work complements previous studies using surface waves and contributes to our developing understanding of anelastic controls on seismic parameters by probing the Earth in a different frequency range.

Elastic and anelastic relaxation behaviour of perovskite multiferroics II: PbZr0.53Ti0.47O3 (PZT)-PbFe0.5Ta0.5O3 (PFT).

PubMed

Schiemer, J A; Lascu, I; Harrison, R J; Kumar, A; Katiyar, R S; Sanchez, D A; Ortega, N; Mejia, C Salazar; Schnelle, W; Shinohara, H; Heap, A J F; Nagaratnam, R; Dutton, S E; Scott, J F; Nair, B; Mathur, N D; Carpenter, M A

2017-01-01

Elastic and anelastic properties of ceramic samples of multiferroic perovskites with nominal compositions across the binary join PbZr 0.53 Ti 0.47 O 3 -PbFe 0.5 Ta 0.5 O 3 (PZT-PFT) have been assembled to create a binary phase diagram and to address the role of strain relaxation associated with their phase transitions. Structural relationships are similar to those observed previously for PbZr 0.53 Ti 0.47 O 3 -PbFe 0.5 Nb 0.5 O 3 (PZT-PFN), but the magnitude of the tetragonal shear strain associated with the ferroelectric order parameter appears to be much smaller. This leads to relaxor character for the development of ferroelectric properties in the end member PbFe 0.5 Ta 0.5 O 3 . As for PZT-PFN, there appear to be two discrete instabilities rather than simply a reorientation of the electric dipole in the transition sequence cubic-tetragonal-monoclinic, and the second transition has characteristics typical of an improper ferroelastic. At intermediate compositions, the ferroelastic microstructure has strain heterogeneities on a mesoscopic length scale and, probably, also on a microscopic scale. This results in a wide anelastic freezing interval for strain-related defects rather than the freezing of discrete twin walls that would occur in a conventional ferroelastic material. In PFT, however, the acoustic loss behaviour more nearly resembles that due to freezing of conventional ferroelastic twin walls. Precursor softening of the shear modulus in both PFT and PFN does not fit with a Vogel-Fulcher description, but in PFT there is a temperature interval where the softening conforms to a power law suggestive of the role of fluctuations of the order parameter with dispersion along one branch of the Brillouin zone. Magnetic ordering appears to be coupled only weakly with a volume strain and not with shear strain but, as with multiferroic PZT-PFN perovskites, takes place within crystals which have significant strain heterogeneities on different length scales.

Results of the SDCS (Special Data Collection System) Attenuation Experiment

DTIC Science & Technology

1981-10-30

stations one can infer the degree of anelastic attenuation under each station. The design of the experiment by DARPA is based on an implicit assumption of...complete listing of the events is shown in Appendix A. Since the SDCS experiment was designed to resolve problemR arising from a study of Ms-mb, it was... designated by different symbols as follows: Symbol A (At* - ) <-a B -0 < (At* -) < 0 C 0 < (At* P) < + D (At* -> + -52- 30 - N I 50 P 0,244 o" 0.231 cr

Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse Tube

NASA Technical Reports Server (NTRS)

Lee, Jeffrey M.

1999-01-01

This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.

Strength and Deformation Behaviour of Cap Rocks Above the CO2SINK-Reservoir

NASA Astrophysics Data System (ADS)

Mutschler, T.; Triantafyllidis, T.; Balthasar, K.; Norden, B.

2009-04-01

The cap-rock of the CO2SINK storage site close to Ketzin consists of clay rich rocks which are typical for cap rock formations above CO2 storage reservoirs. The strength and deformation behaviour of such claystone samples are therefore of fundamental importance for the characterization of secure geological storage of CO2. The elastic and anelastic deformation behaviour limits the maximum injection pressure during CO2-injection and is part of the security measures for the long term storage of CO2. The laboratory experiments where performed on samples gathered from the injection well of the Ketzin pilot test site in Germany and are compared with the elastic and anelastic behaviour of samples from the same Keuper formation in a near-surface outcrop in the Southwest of Germany showing a similar lithology. The samples from the outcrop allowed drilling of samples with a standard size of 100 mm diameter and 200 mm height as well as large samples with a diameter of 550 mm and a height of 1200 mm. The investigations have a special emphasis on the viscous behaviour of the clay stones and its scaling behaviour. A special triaxial testing procedure is applied both on standard and large size samples allowing the determination of the strength, stiffness and viscosity behaviour of the rock in one experimental run. Multi-stage technique (stepwise variation of the confining pressure) gives the strength behaviour of each single sample while applying a constant deformation rate. Stepwise varied deformation rates on the other hand lead to steps in the stress-strain-curve from which the viscosity index is determined. The viscosity index is directly used in the Norton's constitutive relations for viscoplastic simulations. The combination of tests allows for the determination of a broad range of elastic and anelastic properties. The comparison of results - both for elastic and anelastic behaviour - from standard and large samples shows that for the examined rocks a scale effect is negligible. Transition from cataclastic to non-cataclastic behaviour - the transition limit - occurs in a similar range of applied levels of pressure and deformation rates even at room temperature. The obtained transition limit is very important for the judgment of the sealing capacity and integrity of the cap rock. The deformation rates predicted for the pressure and temperature conditions of the caprock at Ketzin test site are far beneath the determined transition limit during the injection and after stop of injection. As a 0° friction angle is used for pressure and deformation limit at Ketzin, the measured elastic and anelastic behaviour of the real caprock act as additional safety margin during injection and in the post injection phase. As the examined rocks are typical for many possible storage sites, the discussed results are of importance beyond the Ketzin Pilot Experiment CO2SINK.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

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

Konor, Celal S.; Randall, David A.

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Prediction of Test Mass Thermal Noise by Measurement of the Anelastic Aftereffect

NASA Astrophysics Data System (ADS)

Beilby, Mark A.; Saulson, Peter R.; Abramovici, Alex

1997-04-01

The thermal noise from the internal modes of test masses of interferometric gravitational wave detectors depends on the dissipation at the frequencies of interest. To date, predictions have been based on the Qs of resonances, all at frequencies higher than the expected signals. We have developed a method to determine the dissipation of test masses in the signal band, using the anelastic aftereffect, the creep J(τ) of a test mass after a compressive stress has been released. The loss angle φ(ω) is approximately given by the logarithmic derivative of J(τ) evaluated at τ=1/ω. For a transparent material such as fused silica, a convenient way to measure J(τ) is via the photoelastic effect. We will describe the apparatus that we have constructed, present measurements of the losses in dummy test masses made from BK7 glass and fused silica, and discuss the application of this method to LIGO test masses.

Prediction of Test Mass Thermal Noise by Measurement of the Anelastic Aftereffect

NASA Astrophysics Data System (ADS)

Beilby, Mark A.; Saulson, Peter R.; Abramovici, Alex

1996-05-01

The thermal noise from the internal modes of the test masses of interferometric gravitational wave detectors depends on the dissipation at the frequencies of interest. To date, predictions have been based on the Q's of resonances, all at frequencies higher than the expected signals. We have developed a method to determine the dissipation of test masses in the signal band, using the anelastic aftereffect, the creep J(τ) of a test mass after a compressive stress has been released. The loss angle φ(ω) is approximately given by the logarithmic derivative of J(τ) evaluated at τ = 1/ω. For a transparent material such as fused silica, a convenient way to measure J(τ) is via the photoelastic effect. We will describe the apparatus that we have constructed, present measurements of the losses in a dummy test mass made from BK7 glass, and discuss the application of this method to LIGO test masses.

Evolution of Our Understanding of the Solar Dynamo During Solar Cycle 24

NASA Astrophysics Data System (ADS)

Munoz-Jaramillo, A.

2017-12-01

Solar cycle 24 has been an exciting cycle for our understanding of the solar dynamo: 1. It was the first cycle for which dynamo based predictions were ever used teaching us valuable lessons. 2. It has given us the opportunity to observe a deep minimum and a weak cycle with a high level of of observational detail . 3. It is full of breaktrhoughs in anelastic MHD dynamo simulations (regular cycles, buoyant flux-tubes, mounder-like events). 4. It has seen the creation of bridges between the kinematic flux-transport and anelastic MHD approaches. 5. It has ushered a new generation of realistic surface flux-transport simulations 6. We have achieved significant observational progress in our understanding of solar cycle propagation. The objective of this talk is to highlight some of the most important results, giving special emphasis on what they have taught us about solar cycle predictability.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 2: Quasi-geostrophic Rossby modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia-gravity modes on a midlatitude f plane.The results of our normal-mode analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.

ASR4: A computer code for fitting and processing 4-gage anelastic strain recovery data

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

Warpinski, N.R.

A computer code for analyzing four-gage Anelastic Strain Recovery (ASR) data has been modified for use on a personal computer. This code fits the viscoelastic model of Warpinski and Teufel to measured ASR data, calculates the stress orientation directly, and computes stress magnitudes if sufficient input data are available. The code also calculates the stress orientation using strain-rosette equations, and its calculates stress magnitudes using Blanton's approach, assuming sufficient input data are available. The program is written in FORTRAN, compiled with Ryan-McFarland Version 2.4. Graphics use PLOT88 software by Plotworks, Inc., but the graphics software must be obtained by themore » user because of licensing restrictions. A version without graphics can also be run. This code is available through the National Energy Software Center (NESC), operated by Argonne National Laboratory. 5 refs., 3 figs.« less

Rock anelasticity due to patchy saturation and fabric heterogeneity: A double double-porosity model of wave propagation

NASA Astrophysics Data System (ADS)

Ba, Jing; Xu, Wenhao; Fu, Li-Yun; Carcione, José M.; Zhang, Lin

2017-03-01

Heterogeneity of rock's fabric can induce heterogeneous distribution of immiscible fluids in natural reservoirs, since the lithological variations (mainly permeability) may affect fluid migration in geological time scales, resulting in patchy saturation of fluids. Therefore, fabric and saturation inhomogeneities both affect wave propagation. To model the wave effects (attenuation and velocity dispersion), we introduce a double double-porosity model, where pores saturated with two different fluids overlap with pores having dissimilar compressibilities. The governing equations are derived by using Hamilton's principle based on the potential energy, kinetic energy, and dissipation functions, and the stiffness coefficients are determined by gedanken experiments, yielding one fast P wave and four slow Biot waves. Three examples are given, namely, muddy siltstones, clean dolomites, and tight sandstones, where fabric heterogeneities at three different spatial scales are analyzed in comparison with experimental data. In muddy siltstones, where intrapore clay and intergranular pores constitute a submicroscopic double-porosity structure, wave anelasticity mainly occurs in the frequency range (104-107 Hz), while in pure dolomites with microscopic heterogeneity of grain contacts and tight sandstones with mesoscopic heterogeneity of less consolidated sands, it occurs at 103-107 Hz and 101-103 Hz (seismic band), respectively. The predicted maximum quality factor of the fast compressional wave for the sandstone is the lowest (approximately 8), and that of the dolomite is the highest. The results of the diffusive slow waves are affected by the strong friction effects between solids and fluids. The model describes wave propagation in patchy-saturated rocks with fabric heterogeneity at different scales, and the relevant theoretical predictions agree well with the experimental data in fully and partially saturated rocks.

Grain size-sensitive viscoelastic relaxation and seismic properties of polycrystalline MgO

NASA Astrophysics Data System (ADS)

Barnhoorn, A.; Jackson, I.; Fitz Gerald, J. D.; Kishimoto, A.; Itatani, K.

2016-07-01

Torsional forced-oscillation experiments on a suite of synthetic MgO polycrystals, of high-purity and average grain sizes of 1-100 µm, reveal strongly viscoelastic behavior at temperatures of 800-1300°C and periods between 1 and 1000 s. The measured shear modulus and associated strain energy dissipation both display monotonic variations with oscillation period, temperature, and grain size. The data for the specimens of intermediate grain size have been fitted to a generalized Burgers creep function model that is also broadly consistent with the results for the most coarse-grained specimen. The mild grain size sensitivity for the relaxation time τL, defining the lower end of the anelastic absorption band, is consistent with the onset of elastically accommodated grain boundary sliding. The upper end of the anelastic absorption band, evident in the highest-temperature data for one specimen only, is associated with the Maxwell relaxation time τM marking the transition toward viscous behavior, conventionally ascribed a stronger grain size sensitivity. Similarly pronounced viscoelastic behavior was observed in complementary torsional microcreep tests, which confirm that the nonelastic strains are mainly recoverable, i.e., anelastic. With an estimated activation volume for the viscoelastic relaxation, the experimentally constrained Burgers model has been extrapolated to the conditions of pressure and temperature prevailing in the Earth's uppermost lower mantle. For a plausible grain size of 10 mm, the predicted dissipation Q-1 ranges from 10-3 to 10-2 for periods of 3-3000 s. Broad consistency with seismological observations suggests that the lower mantle ferropericlase phase might account for much of its observed attenuation.

Refining the phase diagram of Pb{sub 1−x}La{sub x}(Zr{sub 0.9}Ti{sub 0.1}){sub 1−x/4}O{sub 3} ceramics by structural, dielectric, and anelastic spectroscopy investigations

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

Craciun, F., E-mail: Floriana.Craciun@isc.cnr.it; Cordero, F.; Ciuchi, I. V.

2015-05-14

We present the results of dielectric and anelastic spectroscopy measurements, together with X-ray diffraction investigations, which allow us to establish more precisely the phase diagram of Pb{sub 1−x}La{sub x}(Zr{sub 0.9}Ti{sub 0.1}){sub 1−x/4}O{sub 3} (PLZT x/90/10) in the compositional range around the AFE/FE phase boundary (0 < x < 0.04). From structural analysis and polarization-electric field measurements, we have found that the ground state of PLZT samples with x < 0.025 is rhombohedral R3c, while samples with x > 0.032 are antiferroelectric with orthorhombic Pbam structure. In-between, for compositions with 0.025 ≤ x ≤ 0.032, a coexistence of the AFE/FE phases is evidenced. The use of complementary dielectric and anelastic techniques allows tomore » follow the phase transitions shifts throughout all the interesting composition range and to construct the temperature-composition phase diagram. The tilt instability line, separating the R3c and R3m low and high temperature phases, has been evidenced. Moreover, the new transition, associated with the onset of disordered tilting preceding the long range order of the R3c phase, previously found in Zr-rich Pb(Zr,Ti)O{sub 3}, is confirmed in rhombohedral PLZT x/90/10 compositions.« less

Anelastic Models of Fully-Convective Stars: Differential Rotation, Meridional Circulation and Residual Entropy

NASA Astrophysics Data System (ADS)

Sainsbury-Martinez, Felix; Browning, Matthew; Miesch, Mark; Featherstone, Nicholas A.

2018-01-01

Low-Mass stars are typically fully convective, and as such their dynamics may differ significantly from sun-like stars. Here we present a series of 3D anelastic HD and MHD simulations of fully convective stars, designed to investigate how the meridional circulation, the differential rotation, and residual entropy are affected by both varying stellar parameters, such as the luminosity or the rotation rate, and by the presence of a magnetic field. We also investigate, more specifically, a theoretical model in which isorotation contours and residual entropy (σ‧ = σ ‑ σ(r)) are intrinsically linked via the thermal wind equation (as proposed in the Solar context by Balbus in 2009). We have selected our simulation parameters in such as way as to span the transition between Solar-like differential rotation (fast equator + slow poles) and ‘anti-Solar’ differential rotation (slow equator + fast poles), as characterised by the convective Rossby number and △Ω. We illustrate the transition from single-celled to multi-celled MC profiles, and from positive to negative latitudinal entropy gradients. We show that an extrapolation involving both TWB and the σ‧/Ω link provides a reasonable estimate for the interior profile of our fully convective stars. Finally, we also present a selection of MHD simulations which exhibit an almost unsuppressed differential rotation profile, with energy balances remaining dominated by kinetic components.

Underestimation of Microearthquake Size by the Magnitude Scale of the Japan Meteorological Agency: Influence on Earthquake Statistics

NASA Astrophysics Data System (ADS)

Uchide, Takahiko; Imanishi, Kazutoshi

2018-01-01

Magnitude scales based on the amplitude of seismic waves, including the Japan Meteorological Agency magnitude scale (Mj), are commonly used in routine processes. The moment magnitude scale (Mw), however, is more physics based and is able to evaluate any type and size of earthquake. This paper addresses the relation between Mj and Mw for microearthquakes. The relative moment magnitudes among earthquakes are well constrained by multiple spectral ratio analyses. The results for the events in the Fukushima Hamadori and northern Ibaraki prefecture areas of Japan imply that Mj is significantly and systematically smaller than Mw for microearthquakes. The Mj-Mw curve has slopes of 1/2 and 1 for small and large values of Mj, respectively; for example, Mj = 1.0 corresponds to Mw = 2.0. A simple numerical simulation implies that this is due to anelastic attenuation and the recording using a finite sampling interval. The underestimation affects earthquake statistics. The completeness magnitude, Mc, for magnitudes lower than which the magnitude-frequency distribution deviates from the Gutenberg-Richter law, is effectively lower for Mw than that for Mj, by taking into account the systematic difference between Mj and Mw. The b values of the Gutenberg-Richter law are larger for Mw than for Mj. As the b values for Mj and Mw are well correlated, qualitative argument using b values is not affected. While the estimated b values for Mj are below 1.5, those for Mw often exceed 1.5. This may affect the physical implication of the seismicity.

Spectral-element simulations of carbon dioxide (CO2) sequestration time-lapse monitoring

NASA Astrophysics Data System (ADS)

Morency, C.; Luo, Y.; Tromp, J.

2009-12-01

Geologic sequestration of CO2, a green house gas, represents an effort to reduce the large amount of CO2 generated as a by-product of fossil fuels combustion and emitted into the atmosphere. This process of sequestration involves CO2 storage deep underground. There are three main storage options: injection into hydrocarbon reservoirs, injection into methane-bearing coal beds, or injection into deep saline aquifers, that is, highly permeable porous media. The key issues involve accurate monitoring of the CO2, from the injection stage to the prediction & verification of CO2 movement over time for environmental considerations. A natural non-intrusive monitoring technique is referred to as ``4D seismics'', which involves 3D time-lapse seismic surveys. The success of monitoring the CO2 movement is subject to a proper description of the physics of the problem. We propose to realize time-lapse migrations comparing acoustic, elastic, and poroelastic simulations of 4D seismic imaging to characterize the storage zone. This approach highlights the influence of using different physical theories on interpreting seismic data, and, more importantly, on extracting the CO2 signature from the seismic wave field. Our simulations are performed using a spectral-element method, which allows for highly accurate results. Biot's equations are implemented to account for poroelastic effects. Attenuation associated with the anelasticity of the rock frame and frequency-dependent viscous resistance of the pore fluid are accommodated based upon a memory variable approach. The sensitivity of observables to the model parameters is quantified based upon finite-frequency sensitivity kernels calculated using an adjoint method.

Full Waveform Inversion for Seismic Velocity And Anelastic Losses in Heterogeneous Structures

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

Askan, A.; /Carnegie Mellon U.; Akcelik, V.

2009-04-30

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to amore » variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.« less

The Effect of Sedimentary Basins on Through-Passing Short-Period Surface Waves

NASA Astrophysics Data System (ADS)

Feng, L.; Ritzwoller, M. H.

2017-12-01

Surface waves propagating through sedimentary basins undergo elastic wave field complications that include multiple scattering, amplification, the formation of secondary wave fronts, and subsequent wave front healing. Unless these effects are accounted for accurately, they may introduce systematic bias to estimates of source characteristics, the inference of the anelastic structure of the Earth, and ground motion predictions for hazard assessment. Most studies of the effects of basins on surface waves have centered on waves inside the basins. In contrast, we investigate wave field effects downstream from sedimentary basins, with particular emphasis on continental basins and propagation paths, elastic structural heterogeneity, and Rayleigh waves at 10 s period. Based on wave field simulations through a recent 3D crustal and upper mantle model of East Asia, we demonstrate significant Rayleigh wave amplification downstream from sedimentary basins in eastern China such that Ms measurements obtained on the simulated wave field vary by more than a magnitude unit. We show that surface wave amplification caused by basins results predominantly from elastic focusing and that amplification effects produced through 3D basin models are reproduced using 2D membrane wave simulations through an appropriately defined phase velocity map. The principal characteristics of elastic focusing in both 2D and 3D simulations include (1) retardation of the wave front inside the basins; (2) deflection of the wave propagation direction; (3) formation of a high amplitude lineation directly downstream from the basin bracketed by two low amplitude zones; and (4) formation of a secondary wave front. Finally, by comparing the impact of elastic focusing with anelastic attenuation, we argue that on-continent sedimentary basins are expected to affect surface wave amplitudes more strongly through elastic focusing than through the anelastic attenuation.

Spatio-Temporal Modelling of the Pre-Eruptive Strain Localization in a Volcanic Edifice Using a Maxwell-Elasto-Brittle Rheology

NASA Astrophysics Data System (ADS)

Dansereau, V.; Got, J. L.

2017-12-01

Before a volcanic eruption, the pressurization of the volcanic edifice by a magma reservoir induces earthquakes and damage in the edifice; damage lowers the strength of the edifice and decreases its elastic properties. Anelastic deformations cumulate and lead to rupture and eruption. These deformations translate into surface displacements, measurable via GPS or InSAR (e.g., Kilauea, southern flank, or Piton de la Fournaise, eastern flank).Attempts to represent these processes are usually based on a linear-elastic rheology. More recently, linear elastic-perfectly plastic or elastic-brittle damage approaches were used to explain the time evolution of the surface displacements in basaltic volcanoes before an eruption. However these models are non-linear elastic, and can not account for the anelastic deformation that occurs during the pre-eruptive process. Therefore, they can not be used to represent the complete eruptive cycle, comprising loading and unloading phases. Here we present a new rheological approach for modelling the eruptive cycle called Maxwell-Elasto-Brittle, which incorporates a viscous-like relaxation of the stresses in an elastic-brittle damage framework. This mechanism allows accounting for the anelastic deformations that cumulate and lead to rupture and eruption. The inclusion of healing processes in this model is another step towards a complete spatio-temporal representation of the eruptive cycle. Plane-strain Maxwell-EB modelling of the deformation of a magma reservoir and volcanic edifice will be presented. The model represents the propagation of damage towards the surface and the progressive localization of the deformation along faults under the pressurization of the magma reservoir. This model allows a complete spatio-temporal representation of the rupture process. We will also discuss how available seismicity records and time series of surface displacements could be used jointly to constrain the model.

Elastic and anelastic structure of the lowermost mantle beneath the Western Pacific from waveform inversion

NASA Astrophysics Data System (ADS)

Konishi, Kensuke; Fuji, Nobuaki; Deschamps, Frédéric

2017-03-01

We investigate the elastic and anelastic structure of the lowermost mantle at the western edge of the Pacific large low shear velocity province (LLSVP) by inverting a collection of S and ScS waveforms. The transverse component data were obtained from F-net for 31 deep earthquakes beneath Tonga and Fiji, filtered between 12.5 and 200 s. We observe a regional variation of S and ScS arrival times and amplitude ratios, according to which we divide our region of interest into three subregions. For each of these subregions, we then perform 1-D (depth-dependent) waveform inversions simultaneously for radial profiles of shear wave velocity (VS) and seismic quality factor (Q). Models for all three subregions show low VS and low Q structures from 2000 km depth down to the core-mantle boundary. We further find that VS and Q in the central subregion, sampling the Caroline plume, are substantially lower than in the surrounding regions, whatever the depth. In the central subregion, VS-anomalies with respect to PREM (dVS) and Q are about -2.5 per cent and 216 at a depth of 2850 km, and -0.6 per cent and 263 at a depth of 2000 km. By contrast, in the two other regions, dVS and Q are -2.2 per cent and 261 at a depth of 2850 km, and -0.3 per cent and 291 at a depth of 2000 km. At depths greater than ∼2500 km, these differences may indicate lateral variations in temperature of ∼100 K within the Pacific LLSVP. At shallower depths, they may be due to the temperature difference between the Caroline plume and its surroundings, and possibly to a small fraction of iron-rich material entrained by the plume.

Resolving Discrepancies Between Observed and Predicted Dynamic Topography on Earth

NASA Astrophysics Data System (ADS)

Richards, F. D.; Hoggard, M.; White, N. J.

2017-12-01

Compilations of well-resolved oceanic residual depth measurements suggest that present-day dynamic topography differs from that predicted by geodynamic simulations in two significant respects. At short wavelengths (λ ≤ 5,000 km), much larger amplitude variations are observed, whereas at long wavelengths (λ > 5,000 km), observed dynamic topography is substantially smaller. Explaining the cause of this discrepancy with a view to reconciling these different approaches is central to constraining the structure and dynamics of the deep Earth. Here, we first convert shear wave velocity to temperature using an experimentally-derived anelasticity model. This relationship is calibrated using a pressure and temperature-dependent plate model that satisfies age-depth subsidence, heat flow measurements, and seismological constraints on the depth to the lithosphere-asthenosphere boundary. In this way, we show that, at short-wavelengths, observed dynamic topography is consistent with ±150 ºC asthenospheric temperature anomalies. These inferred thermal buoyancy variations are independently verified by temperature measurements derived from geochemical analyses of mid-ocean ridge basalts. Viscosity profiles derived from the anelasticity model suggest that the asthenosphere has an average viscosity that is two orders of magnitude lower than that of the underlying upper mantle. The base of this low-viscosity layer coincides with a peak in azimuthal anisotropy observed in recent seismic experiments. This agreement implies that lateral asthenospheric flow is rapid with respect to the underlying upper mantle. We conclude that improved density and viscosity models of the uppermost mantle, which combine a more comprehensive physical description of the lithosphere-asthenosphere system with recent seismic tomographic models, can help to resolve spectral discrepancies between observed and predicted dynamic topography. Finally, we explore possible solutions to the long-wavelength discrepancy that exploit the velocity to density conversion described above combined with radial variation of mantle viscosity.

State variable theories based on Hart's formulation

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

Korhonen, M.A.; Hannula, S.P.; Li, C.Y.

In this paper a review of the development of a state variable theory for nonelastic deformation is given. The physical and phenomenological basis of the theory and the constitutive equations describing macroplastic, microplastic, anelastic and grain boundary sliding enhanced deformation are presented. The experimental and analytical evaluation of different parameters in the constitutive equations are described in detail followed by a review of the extensive experimental work on different materials. The technological aspects of the state variable approach are highlighted by examples of the simulative and predictive capabilities of the theory. Finally, a discussion of general capabilities, limitations and futuremore » developments of the theory and particularly the possible extensions to cover an even wider range of deformation or deformation-related phenomena is presented.« less

Penetrative convection

NASA Technical Reports Server (NTRS)

Moore, D. R.

1981-01-01

The current state of understanding of the most directly observable solar convection, the granulation and supergranulation is summarized. The body of work in which the complete time dependent Navier-Stokes equations and entropy transport equation are solved for a fully compressible atmosphere is considered. Relevant anelastic and incompressible calculations in two dimensions are also discussed.

Searching for 3D Viscosity Models of Glacial Isostatic Adjustment in Support of the Global ICE-6G_C Ice History Model

NASA Astrophysics Data System (ADS)

LI, T., II; Wu, P.; Steffen, H.; Wang, H.

2017-12-01

The global ice history model ICE-6G_C was constructed based on the laterally homogeneous earth model VM5a. The combined model of glacial isostatic adjustment (GIA) called ICE-6G_C (VM5a) fits global observations of GIA simultaneously well. However, seismic and geological observations clearly show that the Earth's mantle is laterally heterogeneous. Our aim therefore is to search for the best laterally heterogeneous viscosity models with ICE-6G_C ice history that is able to fit the global relative sea-level (RSL) data, the peak uplift rates (from GNSS) and peak g-dot rates (from the GRACE satellite mission) in Laurentia and Fennoscandia simultaneously. The Coupled Laplace-Finite Element Method is used to compute gravitationally self-consistent sea levels with time dependent coastlines and rotational feedback in addition to changes in deformation, gravity and the state of stress. As a start, the VM5a Earth model is used as the radial background viscosity structure but other radial background viscosity models will also be investigated. Lateral mantle viscosity structure is obtained by the superposition of the radial background viscosity and the lateral viscosity perturbations logarithmically. The latter is inferred from a seismic tomography model using a scaling relationship that takes into account the effects of anharmonicity, anelasticity and non-thermal effects. We will show that several laterally heterogeneous mantle viscosity models can fit the global sea level, GPS and GRACE data better than laterally homogeneous models, provided that the scaling relationship for mantle heterogeneity under northern Europe is allowed to be different from that under Laurentia. In addition, the effects of laterally heterogeneous lithosphere, as inferred from seismic tomography, and the lateral changes in sub-lithospheric properties will also be presented.

Quasi-dynamic Earthquake Cycle Simulation in a Viscoelastic Medium with Memory Variables

NASA Astrophysics Data System (ADS)

Hirahara, K.; Ohtani, M.; Shikakura, Y.

2011-12-01

Earthquake cycle simulations based on rate and state friction laws have successfully reproduced the observed complex earthquake cycles at subduction zones. Most of simulations have assumed elastic media. The lower crust and the upper mantle have, however, viscoelastic properties, which cause postseismic stress relaxation. Hence the slip evolution on the plate interfaces or the faults in long earthquake cycles is different from that in elastic media. Especially, the viscoelasticity plays an important role in the interactive occurrence of inland and great interplate earthquakes. In viscoelastic media, the stress is usually calculated by the temporal convolution of the slip response function matrix and the slip deficit rate vector, which needs the past history of slip rates at all cells. Even if properly truncating the convolution, it requires huge computations. This is why few simulation studies have considered viscoelastic media so far. In this study, we examine the method using memory variables or anelastic functions, which has been developed for the time-domain finite-difference calculation of seismic waves in a dissipative medium (e.g., Emmerich and Korn,1987; Moczo and Kristek, 2005). The procedure for stress calculation with memory variables is as follows. First, we approximate the time-domain slip response function calculated in a viscoelastic medium with a series of relaxation functions with coefficients and relaxation times derived from a generalized Maxell body model. Then we can define the time-domain material-independent memory variable or anelastic function for each relaxation mechanism. Each time-domain memory variable satisfies the first-order differential equation. As a result, we can calculate the stress simply by the product of the unrelaxed modulus and the slip deficit subtracted from the sum of memory variables without temporal convolution. With respect to computational cost, we can summarize as in the followings. Dividing the plate interface into N cells, in elastic media, the stress at all cells is calculated by the product of the slip response function matrix and the slip deficit vector. The computational cost is O(N**2). With H-matrices method, we can reduce this to O(N)-O(NlogN) (Ohtani et al. 2011). The memory size is also reduced from O(N**2) to O(N). In viscoelastic media, the product of the unrelaxed modulus matrix and the vector of the slip deficit subtracted from the sum of memory variables costs O(N) with H-matrices method, which is the same as in elastic ones. If we use m relaxation functions, m x N differential equations are additionally solved at a time. The increase in memory size is (4m+1) x N**2. For approximation of slip response function, we need to estimate coefficients and relaxation times for m relaxation functions non-linearly with constraints. Because it is difficult to execute the non-linear least square estimation with constraints, we consider only m=2 with satisfying constraints. Test calculations in a layered or 3-D heterogeneous viscoelastic structure show this gives the satisfactory approximation. As an example, we report a 2-D earthquake cycle simulation for the 2011 giant Tohoku earthquake in a layered viscoelastic medium.

The geometry of discombinations and its applications to semi-inverse problems in anelasticity

PubMed Central

Yavari, Arash; Goriely, Alain

2014-01-01

The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid. PMID:25197257

Fortnightly Ocean Tides, Earth Rotation, and Mantle Anelasticity

NASA Technical Reports Server (NTRS)

Ray, Richard; Egbert, Gary

2012-01-01

The fortnightly Mf ocean tide is the largest of the long-period tides (periods between 1 week and 18.6 years), but Mf is still very small, generally 2 cm or less. All long-period tides are thought to be near equilibrium with the astronomical tidal potential, with an almost pure zonal structure. However, several lines of evidence point to Mf having a significant dynamic response to forcing. We use a combination of numerical modeling, satellite altimetry, and observations of polar motion to determine the Mf ocean tide and to place constraints on certain global properties, such as angular momentum. Polar motion provides the only constraints on Mf tidal currents. With a model of the Mf ocean tide in hand, we use it to remove the effects of the ocean from estimates of fortnightly variations in length-of-day. The latter is dominated by the earth's body tide, but a small residual allows us to place new constraints on the anelasticity of the earth's mantle. The result gives the first experimental confirmation of theoretical predictions made by Wahr and Bergen in 1986.

NGA-West2 equations for predicting vertical-component PGA, PGV, and 5%-damped PSA from shallow crustal earthquakes

USGS Publications Warehouse

Stewart, Jonathan P.; Boore, David M.; Seyhan, Emel; Atkinson, Gail M.

2016-01-01

We present ground motion prediction equations (GMPEs) for computing natural log means and standard deviations of vertical-component intensity measures (IMs) for shallow crustal earthquakes in active tectonic regions. The equations were derived from a global database with M 3.0–7.9 events. The functions are similar to those for our horizontal GMPEs. We derive equations for the primary M- and distance-dependence of peak acceleration, peak velocity, and 5%-damped pseudo-spectral accelerations at oscillator periods between 0.01–10 s. We observe pronounced M-dependent geometric spreading and region-dependent anelastic attenuation for high-frequency IMs. We do not observe significant region-dependence in site amplification. Aleatory uncertainty is found to decrease with increasing magnitude; within-event variability is independent of distance. Compared to our horizontal-component GMPEs, attenuation rates are broadly comparable (somewhat slower geometric spreading, faster apparent anelastic attenuation), VS30-scaling is reduced, nonlinear site response is much weaker, within-event variability is comparable, and between-event variability is greater.

Questions on the existence, persistence, and mechanical effects of a very small melt fraction in the asthenosphere

NASA Astrophysics Data System (ADS)

Holtzman, Benjamin K.

2016-02-01

This paper integrates current questions in rock physics on the effects and behavior of very small melt fractions (≪1%) in the asthenosphere. In experiment and theory, it has been shown that a very small melt fraction forming a connected network has a large effect on the diffusion creep shear viscosity, as well as in the anelastic behavior. Because small concentrations of volatiles, particularly H2O and CO2, significantly lower the peridotite solidus, a small melt fraction is expected in the asthenosphere. Even with connected networks, permeability will be low and surface tension will generate a strong force resisting complete draining of small melt fractions. The anelastic reduction of shear velocity due to melt could cause a ≥5% shear velocity contrast across the solidus, consistent with the contrast measured on features in the shallow suboceanic upper mantle that are often interpreted as the lithosphere-asthenosphere boundary. This article was corrected on 12 MAR 2016. See the end of the full text for details.

Subgrid Scale Modeling in Solar Convection Simulations using the ASH Code

NASA Technical Reports Server (NTRS)

Young, Y.-N.; Miesch, M.; Mansour, N. N.

2003-01-01

The turbulent solar convection zone has remained one of the most challenging and important subjects in physics. Understanding the complex dynamics in the solar con- vection zone is crucial for gaining insight into the solar dynamo problem. Many solar observatories have generated revealing data with great details of large scale motions in the solar convection zone. For example, a strong di erential rotation is observed: the angular rotation is observed to be faster at the equator than near the poles not only near the solar surface, but also deep in the convection zone. On the other hand, due to the wide range of dynamical scales of turbulence in the solar convection zone, both theory and simulation have limited success. Thus, cutting edge solar models and numerical simulations of the solar convection zone have focused more narrowly on a few key features of the solar convection zone, such as the time-averaged di erential rotation. For example, Brun & Toomre (2002) report computational finding of differential rotation in an anelastic model for solar convection. A critical shortcoming in this model is that the viscous dissipation is based on application of mixing length theory to stellar dynamics with some ad hoc parameter tuning. The goal of our work is to implement the subgrid scale model developed at CTR into the solar simulation code and examine how the differential rotation will be a affected as a result. Specifically, we implement a Smagorinsky-Lilly subgrid scale model into the ASH (anelastic spherical harmonic) code developed over the years by various authors. This paper is organized as follows. In x2 we briefly formulate the anelastic system that describes the solar convection. In x3 we formulate the Smagorinsky-Lilly subgrid scale model for unstably stratifed convection. We then present some preliminary results in x4, where we also provide some conclusions and future directions.

Tsunami-driven gravity waves in the presence of vertically varying background and tidal wind structures

NASA Astrophysics Data System (ADS)

Laughman, B.; Fritts, D. C.; Lund, T. S.

2017-05-01

Many characteristics of tsunami-driven gravity waves (TDGWs) enable them to easily propagate into the thermosphere and ionosphere with appreciable amplitudes capable of producing detectable perturbations in electron densities and total electron content. The impact of vertically varying background and tidal wind structures on TDGW propagation is investigated with a series of idealized background wind profiles to assess the relative importance of wave reflection, critical-level approach, and dissipation. These numerical simulations employ a 2-D nonlinear anelastic finite-volume neutral atmosphere model which accounts for effects accompanying vertical gravity wave (GW) propagation such as amplitude growth with altitude. The GWs are excited by an idealized tsunami forcing with a 50 cm sea surface displacement, a 400 km horizontal wavelength, and a phase speed of 200 ms-1 consistent with previous studies of the tsunami generated by the 26 December 2004 Sumatra earthquake. Results indicate that rather than partial reflection and trapping, the dominant process governing TDGW propagation to thermospheric altitudes is refraction to larger and smaller vertical scales, resulting in respectively larger and smaller vertical group velocities and respectively reduced and increased viscous dissipation. Under all considered background wind profiles, TDGWs were able to attain ionospheric altitudes with appreciable amplitudes. Finally, evidence of nonlinear effects is observed and the conditions leading to their formation is discussed.

Stochastic finite-fault simulation of ground motion from the August 11, 2012, M w 6.4 Ahar earthquake, northwestern Iran

NASA Astrophysics Data System (ADS)

Heidari, Reza

2016-04-01

In this study, the 11 August 2012 M w 6.4 Ahar earthquake is investigated using the ground motion simulation based on the stochastic finite-fault model. The earthquake occurred in northwestern Iran and causing extensive damage in the city of Ahar and surrounding areas. A network consisting of 58 acceleration stations recorded the earthquake within 8-217 km of the epicenter. Strong ground motion records from six significant well-recorded stations close to the epicenter have been simulated. These stations are installed in areas which experienced significant structural damage and humanity loss during the earthquake. The simulation is carried out using the dynamic corner frequency model of rupture propagation by extended fault simulation program (EXSIM). For this purpose, the propagation features of shear-wave including {Q}_s value, kappa value {k}_0 , and soil amplification coefficients at each site are required. The kappa values are obtained from the slope of smoothed amplitude of Fourier spectra of acceleration at higher frequencies. The determined kappa values for vertical and horizontal components are 0.02 and 0.05 s, respectively. Furthermore, an anelastic attenuation parameter is derived from energy decay of a seismic wave by using continuous wavelet transform (CWT) for each station. The average frequency-dependent relation estimated for the region is Q=(122± 38){f}^{(1.40± 0.16)}. Moreover, the horizontal to vertical spectral ratio H/V is applied to estimate the site effects at stations. Spectral analysis of the data indicates that the best match between the observed and simulated spectra occurs for an average stress drop of 70 bars. Finally, the simulated and observed results are compared with pseudo acceleration spectra and peak ground motions. The comparison of time series spectra shows good agreement between the observed and the simulated waveforms at frequencies of engineering interest.

Strain amplitude-dependent anelasticity in Cu-Ni solid solution due to thermally activated and athermal dislocation-point obstacle interactions

NASA Astrophysics Data System (ADS)

Kustov, S.; Gremaud, G.; Benoit, W.; Golyandin, S.; Sapozhnikov, K.; Nishino, Y.; Asano, S.

1999-02-01

Experimental investigations of the internal friction and the Young's modulus defect in single crystals of Cu-(1.3-7.6) at. % Ni have been performed for 7-300 K over a wide range of oscillatory strain amplitudes. Extensive data have been obtained at a frequency of vibrations around 100 kHz and compared with the results obtained for the same crystals at a frequency of ˜1 kHz. The strain amplitude dependence of the anelastic strain amplitude and the average friction stress acting on a dislocation due to solute atoms are also analyzed. Several stages in the strain amplitude dependence of the internal friction and the Young's modulus defect are revealed for all of the alloy compositions, at different temperatures and in different frequency ranges. For the 100 kHz frequency, low temperatures and low strain amplitudes (˜10-7-10-5), the amplitude-dependent internal friction and the Young's modulus defect are essentially temperature independent, and are ascribed to a purely hysteretic internal friction component. At higher strain amplitudes, a transition stage and a steep strain amplitude dependence of the internal friction and the Young's modulus defect are observed, followed by saturation at the highest strain amplitudes employed. These stages are temperature and frequency dependent and are assumed to be due to thermally activated motion of dislocations. We suggest that the observed regularities in the entire strain amplitude, temperature and frequency ranges correspond to a motion of dislocations in a two-component system of obstacles: weak but long-range ones, due to the elastic interaction of dislocations with solute atoms distributed in the bulk of the crystal; and strong short-range ones, due to the interaction of dislocations with solute atoms distributed close to dislocation glide planes. Based on these assumptions, a qualitative explanation is given for the variety of experimental observations.

Using Tectonic Tremor to Constrain Seismic-wave Attenuation in Cascadia

NASA Astrophysics Data System (ADS)

Littel, G.; Thomas, A.; Baltay, A.

2017-12-01

In addition to fast, seismic slip, many subduction zones also host slow, largely aseismic slip, accompanied by a weak seismic signal known as tectonic tremor. Tremor is a small amplitude, low-frequency seismic signal that originates at the plate interface, down-dip of where large earthquakes typically occur. The Cascadia subduction zone has not seen a large megathrust earthquake since 1700, yet its recurrence interval of 350-500 years motivates heightened interest in understanding the seismic hazard of the region. Of great importance is to understand the degree to which waves are attenuated as they leave the plate interface and travel towards populated regions of interest. Ground motion prediction equations (GMPEs) relate ground motion to a number of parameters, including earthquake magnitude, depth, style of faulting, and anelastic attenuation, and are typically determined empirically from earthquake ground motion recordings. In Cascadia, however, earthquakes of the moderate size typically used to constrain GMPEs occur relatively infrequently compared to tectonic tremor events, which, in contrast, occur periodically approximately every 10-19 months. Studies have shown that the abundant tectonic tremor in Cascadia, despite its small amplitudes, can be used to constrain seismic wave attenuation in GMPEs. Here we quantify seismic wave attenuation and determine its spatial variations in Cascadia by performing an inversion using tremor ground motion amplitudes, taken as peak ground acceleration (PGA) and peak ground velocity (PGV) from 1 min window waveforms of each individual tremor event. We estimate the anelastic attenuation parameter for varying regional sections along the Cascadia margin. Changes in seismic-wave attenuation along the Cascadia Subduction Zone could result in significantly different ground motions in the event of a very large earthquake, hence quantifying attenuation may help to better estimate the severity of shaking in densely populated metropolitan areas such as Vancouver, Seattle and Portland.

Anelastic properties of (TaSe 4) 2I at low frequencies

NASA Astrophysics Data System (ADS)

Salva, H.; Ghilarducci, A.; Monceau, P.; Levy, F.; D'Anna, G.; Benoit, W.

1995-05-01

We have performed torsion measurements in (TaSe 4) 2I in the temperature range 110-290 K and 5.10 -3-10 Hz measuring frequency. We have always found a dip in modulus at the Peierls transition and that deformation of measurement gives additional response in modulus and internal friction spectra. These results are compared with existing models.

Short-Period, Anelastic and Anisotropic, Waveform-Based 3D Middle East Model to Improve Nuclear Explosion Monitoring

DTIC Science & Technology

2014-08-30

initial wave speed model, M00, was used while model iteration 13, M13 , was used within. This expansion of the model does not significantly alter the...total misfit between M13 and M14. The increase in events, stations, and ray-based path coverage is displayed in Figure 4. Expanding the model domain

Long-Period Tidal Variations in the Length of Day

NASA Technical Reports Server (NTRS)

Ray, Richard D.; Erofeeva, Svetlana Y.

2014-01-01

A new model of long-period tidal variations in length of day is developed. The model comprises 80 spectral lines with periods between 18.6 years and 4.7 days, and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines. The anelastic properties followWahr and Bergen; experimental confirmation for their results now exists at the fortnightly period, but there remains uncertainty when extrapolating to the longest periods. The ocean modeling builds on recent work with the fortnightly constituent, which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation. This is a critical property when modeling most long-period tides, for which little observational data exist. Dynamic ocean effects are quite pronounced at shortest periods as out-of-phase rotation components become nearly as large as in-phase components. The model is tested against a 20 year time series of space geodetic measurements of length of day. The current international standard model is shown to leave significant residual tidal energy, and the new model is found to mostly eliminate that energy, with especially large variance reduction for constituents Sa, Ssa, Mf, and Mt.

Short-period cyclic loading system for in situ X-ray observation of anelastic properties at high pressure.

PubMed

Yoshino, Takashi; Yamazaki, Daisuke; Tange, Yoshinori; Higo, Yuji

2016-10-01

To determine the anelastic properties of materials of the Earth's interior, a short-period cyclic loading system was installed for in situ X-ray radiographic observation under high pressure to the multi-anvil deformation DIA press at the bending magnet beam line BL04B1 at SPring-8. The hydraulic system equipped with a piston controlled by a solenoid was designed so as to enable producing smooth sinusoidal stress in a wide range of oscillation period from 0.2 to 100 s and generating variable amplitudes. Time resolved X-ray radiography imaging of the sample and reference material provides their strain as a function of time during cyclic loading. A synchrotron X-ray radiation source allows us to resolve their strain variation with time even at the short period (<1 s). The minimum resolved strain is as small as 10 -4 , and the shortest oscillation period to detect small strain is 0.5 s. Preliminary experimental results exhibited that the new system can resolve attenuation factor Q -1 at upper mantle conditions. These results are in quantitative agreement with previously reported data obtained at lower pressures.

Effects of stratospheric lapse rate on thunderstorm cloud-top structure in a three-dimensional numerical simulation. I - Some basic results of comparative experiments

NASA Technical Reports Server (NTRS)

Schlesinger, Robert E.

1988-01-01

The effects of stratospheric temperature lapse rate on cloud top height/temperature structure for strongly sheared, mature, isolated midlatitude thunderstorms are investigated by performing three different experiments with an anelastic, three-dimensional model: (1) with an assumed stratospheric lapse rate of 0 K/km (i.e., the isothermal case), (2) with 3 K/km, and (3) with -3 K/km (i.e., the case of inversion). Kinematic storm structure is very similar in all three cases, especially in the troposphere; a strong quasi-steady updraft evolves and splits into a dominant cyclonic overshooting right-mover and a weaker, anticyclonic left-mover that does not reach the tropopause.

Anelastic attenuation structure of the southern Aegean subduction area

NASA Astrophysics Data System (ADS)

Ventouzi, Chrisanthi; Papazachos, Constantinos; Papaioannou, Christos; Hatzidimitriou, Panagiotis

2014-05-01

The study of the anelastic attenuation structure plays a very important role for seismic wave propagation and provides not only valuable constraints for the Earth's interior (temperature, relative viscosity, slab dehydration and melt transport) but also significant information for the simulation of strong ground motions. In order to investigate the attenuation structure of the broader Southern Aegean subduction area, acceleration spectra of intermediate depth earthquakes produced from data provided by two local networks which operated in the area were used. More specifically, we employed data from approximately 400 intermediate-depth earthquakes, as these were recorded from the EGELADOS seismic monitoring project which consisted of 65 land stations and 24 OBS recorders and operated during 2005-2007, as well as data from the earlier installed CYCNET local network, which operated during 2002-2005. A frequency-independent path attenuation operator t* was computed for both P and S arrivals for each waveform, using amplitude spectra generated by the recorded data of the aforementioned networks. Initially, estimated P and S traveltimes were examined and modeled as a function of epicentral distance for different groups of focal depths, using data from the CYCNET network in order to obtain the expected arrival information when original arrival times were not available. Two approaches to assess the spectral-decay were adopted for t* determination. Initially, an automated approach was used, where t* was automatically calculated from the slope of the acceleration spectrum, assuming an ω2 source model for frequencies above the corner frequency, fc. Estimation of t* was performed in the frequency band of 0.2 to 25 Hz, using only spectra with a signal-to-noise ratio larger than 3 for a frequency range of at least 4Hz for P-waves and 1Hz for S-waves, respectively. In the second approach, the selection of the linearly-decaying part of the spectra where t* was calculated, was carried out manually, after a visual inspection by the user for optimal spectral fitting. The observed t* data from both approaches were examined against hypocentral distance. In general, no significant linear trend, revealing dependence of t* with distance, could be observed on the original data, clearly a result of the significant spatial and depth variations of the anelastic attenuation structure that superimposes the distance effect. In order to further investigate this issue, a spatial variation of t* values for different hypocentral-depth groups was performed. The obtained results show that along-arc stations exhibit very low values of t*, while back-arc stations present much larger values. The observed t* along-arc/back-arc differences becomes more significant as the depth of the earthquakes increases, indicating the effect of the high-attenuation (low-Q) mantle wedge beneath the volcanic arc. For a more detailed view of the spatial variations of the whole path attenuation operator, we performed preliminary spatial interpolation of t* values for different hypocentral depth ranges. For "shallower" hypocentral depths, low values of t*, appear to be sparsely observed mainly in the back-arc area, but as hypocentral depths increase, a much larger area with higher attenuation is identified along the volcanic arc. This work has been partly supported by the 3D-SEGMENTS project #1337 funded by EC European Social Fund and the Operational Programme "Education and Lifelong Learning" of the ARISTEIA-I call of the Greek Secretariat of Research and Technology.

Geophysical constraints on the mantle structure of the Canadian Cordillera and North America Craton

NASA Astrophysics Data System (ADS)

Yu, T. C.; Currie, C. A.; Unsworth, M. J.

2017-12-01

In western Canada, geophysical data indicate that there is a pronounced contrast in mantle structure between the Canadian Cordillera (CC) and North America craton (NAC). The CC is characterized by lower mantle seismic velocity, higher surface heat flow, lower mantle electrical resistivity and lower effective elastic thickness. These observations are consistent with two distinct thermal regimes: the CC has hot and thin lithosphere, while the NAC lithosphere is cool and thick. The boundary between the CC and NAC coincides with the south-north trending Rocky Mountain Trench - Tintina Fault system. Earlier studies have hypothesized that the thin CC lithosphere is maintained by small-scale convection of hydrated mantle, whereas the NAC lithosphere is dry and resistant to thinning. Here, we test this hypothesis through a detailed examination of two independent data sets: (1) seismic shear-wave (Vs) tomography models and (2) magnetotelluric (MT) measurements of mantle electrical resistivity. We analyze tomography model NA07 at 50-250 km depth and create a mapping of Vs to temperature based on mantle composition (via Perple_X) and a correction for anelasticity. For the CC, the calculated temperature is relatively insensitive to mantle composition but strongly depends on the water content and anelastic correction. With a laboratory-based correction, the estimated temperature is 1150 °C at 100 km depth for wet mantle, compared to 1310 °C for dry mantle; no melt is predicted in either case. An empirical anelastic correction predicts a 115 °C hotter mantle and likely some melt. In contrast, composition is the main control on the calculated temperature for the NAC, especially at depths < 125 km. At 100 km depth, estimated temperatures are 690 °C for a pyrolite mantle and 760 °C for a dunite mantle. In the seismic analysis, there is a trade-off between temperature and water content for the CC; the observed velocities are consistent with a warm wet mantle and a hot dry mantle. To resolve this uncertainty, future work will analyze MT data, as electrical resistivity is sensitive to mantle temperature and hydration.

Advances in Global Adjoint Tomography -- Massive Data Assimilation

NASA Astrophysics Data System (ADS)

Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.

2015-12-01

Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified the conventional multi-taper method to obtain better frequency-dependent measurements of surface-wave phase and amplitude anomalies, and therefore more accurate adjoint sources, which are particularly important for anelastic tomography. We present a summary of these data culling and processing procedures for global adjoint tomography.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Source and site response study of the 2008 Mount Carmel, Illinois, earthquake

USGS Publications Warehouse

Hartzell, S.; Mendoza, C.

2011-01-01

Two separate inversions are performed using the ground-motion data from the 2008 Mount Carmel, Illinois, earthquake. One uses aftershocks as empirical Green’s functions to determine a finite-fault slip distribution. The second uses mainshock ground-motion spectra to calculate source, path, and site response parameters. The slip inversion reveals a prominent asperity at the hypocenter with an area of approximately 6 km2, moment of 7.0 x 1023 dyn cm (Mw 5.20), and stress drop of about 100 bars. Considering all major and minor slip, the total moment is 1.7 x 1024 dyn cm (Mw=5.45). The rupture velocity is not resolvable due to the small source area. After fixing the geometric spreading, the source, path, and site parameter inversion yields a similar moment of 8.8 x 1023 dyn cm (Mw 5.26) and a corner frequency of 0.89 Hz, which also give a stress drop of approximately 100 bars. Our combined geometric and anelastic attenuation function, Q(f)r-b=1137f0.12r-0.94, fits the regional spectral amplitudes, where the data is more plentiful, as well as previously derived attenuation relationships. Site response spectra show prominent resonant frequencies that correlate with the thickness of Mississippi River sediments and Mississippi embayment deposits. In addition, higher frequency resonance peaks are observed that most likely represent higher mode resonances and resonances from shallower structure.

In-situ stresses in low-permeability, nonmarine rocks

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

Warpinski, N.R.; Teufel, L.W.

In-situ stress measurements have been performed over a 2,500-ft (760-m) interval in the nonmarine section of the Cretaceous Mesaverde in the Piceance basin in Colorado. These measurements included 52 hydraulic fracture measurements of the minimum in-situ stress and 22 anelastic strain recovery (ASR) measurements. Stress data obtained in sandstones, shales, mudstones, siltstones, and coals show the effect of lithology on the magnitudes of the stresses.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 1: Nonhydrostatic inertia-gravity modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia-gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.

Calibration of the local magnitude scale ( M L ) for Peru

NASA Astrophysics Data System (ADS)

Condori, Cristobal; Tavera, Hernando; Marotta, Giuliano Sant'Anna; Rocha, Marcelo Peres; França, George Sand

2017-07-01

We propose a local magnitude scale ( M L ) for Peru, based on the original Richter definition, using 210 seismic events between 2011 and 2014, recorded by 35 broadband stations of the National Seismic Network operated by the Geophysical Institute of Peru. In the solution model, we considered 1057 traces of maximum amplitude records on the vertical channel from simulated Wood-Anderson seismograms of shallow events (depths between 0 and 60 km) and hypocentral distances less than 600 km. The attenuation factor has been evaluated in terms of geometrical spreading and anelastic attenuation coefficients. The magnitude M L was defined as M L = L o g 10 A W A +1.5855 L o g 10( R/100)+0.0008( R-100)+3± S, where, A W A is the displacement amplitude in millimeters (Wood-Anderson), R is the hypocentral distance (km), and S is the station correction. The results obtained for M L have good correlation with the m b , M s and M w values reported the ISC and NEIC. The anelastic attenuation curve obtained has a similar behavior to that other highly seismic regions. Station corrections were determined for all stations during the regression analysis resulting in values ranging between -0.97 and +0.73, suggesting a strong influence of local site effects on amplitude.

Upper mantle anisotropic attenuation of the Sierra Nevada and surroundings

NASA Astrophysics Data System (ADS)

Bernardino, M. J.; Jones, C. H.; Monsalve, G.

2016-12-01

We investigate the contribution of anelasticity in the generation of seismic velocity variations within the upper mantle of the Sierra Nevada and surrounding regions through teleseismic shear-wave attenuation. Given that anelastic effects are most sensitive to temperature and hydration and less to composition and small degrees of partial melt, we aim constrain the thermal structure beneath this region and identify locations where elevated upper mantle temperatures dominate. We also investigate the dependence of shear-wave attenuation on direction by accounting for seismic anisotropy in our measurements. S-wave t* values are determined from teleseismic S- and SKS- phases recorded on permanent and temporary deployments within the California region with particular focus on the Sierra Nevada Earthscope Project (SNEP) and the Sierran Paradox Experiment (SPE) stations. S-waveforms are rotated into the Sierran SFast, N75°E, and SSlow, N15°W, components. Following the method of Stachnik et al., (2004), S-wave spectra for each event are jointly inverted for a single seismic moment, M0k, and corner frequency, fck, for each event, and separate t* for each ray path. The resulting t*Fast and t*Slow measurements are then inverted for three-dimensional variations in (1/QFast) and (1/QSlow). Results are compared with previous magnetotelluric, surface heat flow, and body-wave velocity inversion studies.

Quantitative assessments of mantle flow models against seismic observations: Influence of uncertainties in mineralogical parameters

NASA Astrophysics Data System (ADS)

Schuberth, Bernhard S. A.

2017-04-01

One of the major challenges in studies of Earth's deep mantle is to bridge the gap between geophysical hypotheses and observations. The biggest dataset available to investigate the nature of mantle flow are recordings of seismic waveforms. On the other hand, numerical models of mantle convection can be simulated on a routine basis nowadays for earth-like parameters, and modern thermodynamic mineralogical models allow us to translate the predicted temperature field to seismic structures. The great benefit of the mineralogical models is that they provide the full non-linear relation between temperature and seismic velocities and thus ensure a consistent conversion in terms of magnitudes. This opens the possibility for quantitative assessments of the theoretical predictions. The often-adopted comparison between geodynamic and seismic models is unsuitable in this respect owing to the effects of damping, limited resolving power and non-uniqueness inherent to tomographic inversions. The most relevant issue, however, is related to wavefield effects that reduce the magnitude of seismic signals (e.g., traveltimes of waves), a phenomenon called wavefront healing. Over the past couple of years, we have developed an approach that takes the next step towards a quantitative assessment of geodynamic models and that enables us to test the underlying geophysical hypotheses directly against seismic observations. It is based solely on forward modelling and warrants a physically correct treatment of the seismic wave equation without theoretical approximations. Fully synthetic 3-D seismic wavefields are computed using a spectral element method for 3-D seismic structures derived from mantle flow models. This way, synthetic seismograms are generated independent of any seismic observations. Furthermore, through the wavefield simulations, it is possible to relate the magnitude of lateral temperature variations in the dynamic flow simulations directly to body-wave traveltime residuals. The synthetic traveltime data can then be compared - on statistical grounds - to the traveltime variations observed on Earth. Here, we now investigate the influence of uncertainties in the various input parameters that enter our modelling. This is especially important for the material properties at high pressure and high temperature entering the mineralogical models. In particular, this concerns uncertainties that arise from relating measurements in the laboratory to Earth properties on a global scale. As one example, we will address the question on the influence of anelasticity on the variance of global synthetic traveltime residuals. Owing to the differences in seismic frequency content between laboratory measurements (MHz to GHz) and the Earth (mHz to Hz), the seismic velocities given in the mineralogical models need to be adjusted; that is, corrected for dispersion due to anelastic effects. This correction will increase the sensitivity of the seismic velocities to temperature variations. The magnitude of this increase depends on absolute temperature, frequency, the frequency dependence of attenuation and the activation enthalpy of the dissipative process. Especially the latter two are poorly known for mantle minerals and our results indicate that variations in activation enthalpy potentially produce the largest differences in temperature sensitivity with respect to the purely elastic case. We will present new wave propagation simulations and corresponding statistical analyses of traveltime measurements for different synthetic seismic models spanning the possible range of anelastic velocity conversions (while being based on the same mantle circulation model).

Combined estimation of kappa and shear-wave velocity profile of the Japanese rock reference

NASA Astrophysics Data System (ADS)

Poggi, Valerio; Edwards, Benjamin; Fäh, Donat

2013-04-01

The definition of a common soil or rock reference is a key issue in probabilistic seismic hazard analysis (PSHA), microzonation studies, local site-response analysis and, more generally, when predicted or observed ground motion is compared for sites of different characteristics. A scaling procedure, which accounts for a common reference, is then necessary to avoid bias induced by the differences in the local geology. Nowadays methods requiring the definition of a reference condition generally prescribe the characteristic of a rock reference, calibrated using indirect estimation methods based on geology or on surface proxies. In most cases, a unique average shear-wave velocity value is prescribed (e.g. Vs30 = 800m/s as for class A of the EUROCODE8). Some attempts at defining the whole shape of a reference rock velocity profile have been described, often without a clear physical justification of how such a selection was performed. Moreover, in spite of its relevance in affecting the high-frequency part of the spectrum, the definition of the associated reference attenuation is in most cases missing or, when present, still remains quite uncertain. In this study we propose an approach that is based on the comparison between empirical anelastic amplification functions from spectral modeling of earthquakes and average S-wave velocities computed using the quarter-wavelength approach. The method is an extension of the approach originally proposed by Poggi et al. (2011) for Switzerland, and is here applied to Japan. For the analysis we make use of a selection of 36 stiff-soil and rock sites from the Japanese KiK-net network, for which a measured velocity profile is available. With respect to the previous study, however, we now analyze separately the elastic and anelastic contributions of the estimated empirical amplification. In a first step - which is consistent with the original work - only the elastic part of the amplification spectrum is considered. This procedure allows the retrieval of the shape of the velocity profile that is characterized by no relative amplification within the network. Subsequently, the contribution of intrinsic attenuation is analyzed, disaggregated from the anelastic function by using the frequency independent (and site-dependent) attenuation operator kappa (κ). By comparing the dependency of κ with the quarter-wavelength velocity at selected sites, a frequency-dependent predictive equation is established to model the attenuation characteristics of an arbitrary rock or stiff-soil velocity model, such as the reference model obtained in the first step. The result of this application can be used to model the site-dependent attenuation for any rock and stiff-soil site for which an estimation of the velocity profile or its corresponding quarter-wavelength velocity representation is available. As an additional output of the present study, we also propose a simplified method to estimate kappa from the average velocity estimates over the first 30m (Vs30). We provide an example of such predictions for a range of Vs30 velocities up to 2000m/s.

Using SW4 for 3D Simulations of Earthquake Strong Ground Motions: Application to Near-Field Strong Motion, Building Response, Basin Edge Generated Waves and Earthquakes in the San Francisco Bay Are

NASA Astrophysics Data System (ADS)

Rodgers, A. J.; Pitarka, A.; Petersson, N. A.; Sjogreen, B.; McCallen, D.; Miah, M.

2016-12-01

Simulation of earthquake ground motions is becoming more widely used due to improvements of numerical methods, development of ever more efficient computer programs (codes), and growth in and access to High-Performance Computing (HPC). We report on how SW4 can be used for accurate and efficient simulations of earthquake strong motions. SW4 is an anelastic finite difference code based on a fourth order summation-by-parts displacement formulation. It is parallelized and can run on one or many processors. SW4 has many desirable features for seismic strong motion simulation: incorporation of surface topography; automatic mesh generation; mesh refinement; attenuation and supergrid boundary conditions. It also has several ways to introduce 3D models and sources (including Standard Rupture Format for extended sources). We are using SW4 to simulate strong ground motions for several applications. We are performing parametric studies of near-fault motions from moderate earthquakes to investigate basin edge generated waves and large earthquakes to provide motions to engineers study building response. We show that 3D propagation near basin edges can generate significant amplifications relative to 1D analysis. SW4 is also being used to model earthquakes in the San Francisco Bay Area. This includes modeling moderate (M3.5-5) events to evaluate the United States Geologic Survey's 3D model of regional structure as well as strong motions from the 2014 South Napa earthquake and possible large scenario events. Recently SW4 was built on a Commodity Technology Systems-1 (CTS-1) at LLNL, new systems for capacity computing at the DOE National Labs. We find SW4 scales well and runs faster on these systems compared to the previous generation of LINUX clusters.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Numerical Modeling of S-Wave Generation by Fracture Damage in Underground Nuclear Explosions

DTIC Science & Technology

2009-09-30

Element Package, ABAQUS. A user -defined subroutine , VUMAT, was written that incorporates the micro-mechanics based damage constitutive law described...dynamic damage evolution on the elastic and anelastic response. 2) whereas the Ashby/Sammis model was only applicable to the case where the initial cracks ...are all parallel and the same size, we can now include a specified distribution of initial crack sizes with random azimuthal orientation about the

Path spectra derived from inversion of source and site spectra for earthquakes in Southern California

NASA Astrophysics Data System (ADS)

Klimasewski, A.; Sahakian, V. J.; Baltay, A.; Boatwright, J.; Fletcher, J. B.; Baker, L. M.

2017-12-01

A large source of epistemic uncertainty in Ground Motion Prediction Equations (GMPEs) is derived from the path term, currently represented as a simple geometric spreading and intrinsic attenuation term. Including additional physical relationships between the path properties and predicted ground motions would produce more accurate and precise, region-specific GMPEs by reclassifying some of the random, aleatory uncertainty as epistemic. This study focuses on regions of Southern California, using data from the Anza network and Southern California Seismic network to create a catalog of events magnitude 2.5 and larger from 1998 to 2016. The catalog encompasses regions of varying geology and therefore varying path and site attenuation. Within this catalog of events, we investigate several collections of event region-to-station pairs, each of which share similar origin locations and stations so that all events have similar paths. Compared with a simple regional GMPE, these paths consistently have high or low residuals. By working with events that have the same path, we can isolate source and site effects, and focus on the remaining residual as path effects. We decompose the recordings into source and site spectra for each unique event and site in our greater Southern California regional database using the inversion method of Andrews (1986). This model represents each natural log record spectra as the sum of its natural log event and site spectra, while constraining each record to a reference site or Brune source spectrum. We estimate a regional, path-specific anelastic attenuation (Q) and site attenuation (t*) from the inversion site spectra and corner frequency from the inversion event spectra. We then compute the residuals between the observed record data, and the inversion model prediction (event*site spectra). This residual is representative of path effects, likely anelastic attenuation along the path that varies from the regional median attenuation. We examine the residuals for our different sets independently to see how path terms differ between event-to-station collections. The path-specific information gained from this can inform development of terms for regional GMPEs, through understanding of these seismological phenomena.

Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 imperial valley, California, earthquake

USGS Publications Warehouse

Joyner, William B.; Boore, David M.

1981-01-01

We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. This new analysis uses a magnitude-independent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. An innovation in technique is introduced that decouples the determination of the distance dependence of the data from the magnitude dependence.

Deterministic Methods of Seismic Source Identification

DTIC Science & Technology

1983-09-30

activity is implied by Figure 7 , compared to that inferred from Fig- ure 6 . We expect that the residual scatter, about the one to one slope line...side of the boundary, and in this case the general forms of the conservation laws expressed by (3). (4) and ( 6 ), or ( 6 ) and ( 7 ). are the appropriate...such as given in (8) and ( 7 ). to obtain an integral equation for the unknown alastodynamic displacement field in an elastic (or anelastic) medium. Such

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes

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

Konor, Celal S.; Randall, David A.

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by runningmore » linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by runningmore » linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.« less

Numerical Mantle Convection Models With a Flexible Thermodynamic Interface

NASA Astrophysics Data System (ADS)

van den Berg, A. P.; Jacobs, M. H.; de Jong, B. H.

2001-12-01

Accurate material properties are needed for deep mantle (P,T) conditions in order to predict the longterm behavior of convection planetary mantles. Also the interpretation of seismological observations concerning the deep mantle in terms of mantle flow models calls for a consistent thermodynamical description of the basic physical parameters. We have interfaced a compressible convection code using the anelastic liquid approach based on finite element methods, to a database containing a full thermodynamic description of mantle silicates (Ita and King, J. Geophys. Res., 99, 15,939-15,940, 1994). The model is based on high resolution (P,T) tables of the relevant thermodynamic properties containing typically 50 million (P,T) table gridpoints to obtain resolution in (P,T) space of 1 K and an equivalent of 1 km. The resulting model is completely flexible such that numerical mantle convection experiments can be performed for any mantle composition for which the thermodynamic database is available. We present results of experiments for 2D cartesian models using a data base for magnesium-iron silicate in a pyrolitic composition (Stixrude and Bukowinski, Geoph.Monogr.Ser., 74, 131-142, 1993) and a recent thermodynamical model for magnesium silicate for the complete mantle (P,T) range, (Jacobs and Oonk, Phys. Chem. Mineral, 269, inpress 2001). Preliminary results of bulksound velocity distribution derived in a consistent way from the convection results and the thermodynamic database show a `realistic' mantle profile with bulkvelocity variations decreasing from several percent in the upper mantle to less than a percent in the deep lower mantle.

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

Schwarz, R.B.; Bach, H.T.; Harms, U.

We used a resonant-ultrasound-spectroscopy technique to measure the three independent elastic constants of PdH{sub x}, PdD{sub x}, and PdT{sub x} single crystals at 300 K. For 0.1x0.62 our PdH{sub x} crystals are two-phase mixtures of coherent {alpha} and {beta} hydride phases. For increasing x in this range, C{sub 44} decreases monotonically whereas C'=12(C11-C12) has a concave parabolic dependence. This difference is because C' is softened by an anelastic relaxation resulting from acoustic-stress-induced changes in the shape of the coherent lenticular-shape precipitates ({beta}-hydride precipitates in {alpha}-hydride matrix and {alpha}-hydride precipitates in {beta}-hydride matrix). In the {beta}-phase C' and C{sub 44} decreasemore » with increasing hydrogen (or deuterium or tritium) content. Furthermore, C' exhibits a strong isotope effect whereas C{sub 44} does not. This effect is attributed to differences in the excitation of optical phonons in Pd-H, Pd-D and Pd-T.« less

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

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.

Centroid — moment tensor solutions for July-September 2000

NASA Astrophysics Data System (ADS)

Dziewonski, A. M.; Ekström, G.; Maternovskaya, N. N.

2001-06-01

Centroid-moment tensor (CMT) solutions are presented for 308 earthquakes that occurred during the third quarter of 2000. The solutions are obtained using corrections for aspherical earth structure represented by a whole mantle shear velocity model SH8/U4L8 of Dziewonski and Woodward [Acoustical Imaging, Vol. 19, Plenum Press, New York, 1992, p. 785]. A model of anelastic attenuation of Durek and Ekström [Bull. Seism. Soc. Am. 86 (1996) 144] is used to predict the decay of the wave forms.

Observations on the deformation-induced beta internal friction peak in bcc metals

NASA Technical Reports Server (NTRS)

Dicarlo, J. A.

1974-01-01

During a study of the effects of electron irradiation on the tungsten alpha mechanism, internal friction data were obtained. The data indicate that the mechanism underlying the beta peak does not possess the relaxation parameters generally associated with a simple dislocation process. The significance of the experimental results in the light of beta observations in other metals is discussed. It is suggested that the beta peaks in deformed bcc metals are the anelastic result of the thermally-activated relaxation of deformation-induced imperfections.

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

Ground-motion prediction from tremor

USGS Publications Warehouse

Baltay, Annemarie S.; Beroza, Gregory C.

2013-01-01

The widespread occurrence of tremor, coupled with its frequency content and location, provides an exceptional opportunity to test and improve strong ground-motion attenuation relations for subduction zones. We characterize the amplitude of thousands of individual 5 min tremor events in Cascadia during three episodic tremor and slip events to constrain the distance decay of peak ground acceleration (PGA) and peak ground velocity (PGV). We determine the anelastic attenuation parameter for ground-motion prediction equations (GMPEs) to a distance of 150 km, which is sufficient to place important constraints on ground-motion decay. Tremor PGA and PGV show a distance decay that is similar to subduction-zone-specific GMPEs developed from both data and simulations; however, the massive amount of data present in the tremor observations should allow us to refine distance-amplitude attenuation relationships for use in hazard maps, and to search for regional variations and intrasubduction zone differences in ground-motion attenuation.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

A model for attenuation and scattering in the Earth's crust

NASA Astrophysics Data System (ADS)

Toksöz, M. Nafi; Dainty, Anton M.; Reiter, Edmund; Wu, Ru-Shan

1988-03-01

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda waves Rg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1 10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constant Q), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedo B 0=0.8 0.9 and a scattering extinction length of 17 32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. The Rg results indicate that Q increases with depth in the upper kilometer or two of the crust, at least in New England. Coda Q appears to be equivalent to intrinsic (anelastic) Q and indicates that this Q increases with frequency as Q=Q o f n , where n is in the range of 0.2 0.9. The intrinsic attenuation in the crust can be explained by a high constant Q (500≤ Q o≤2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence ( Q≃ Q o f 0.5) similar to those determined from the analysis of coda waves of regional seismograms. Q is low near the surface and high in the body of the crust.

Factors Affecting the Plasticity of Sodium Chloride, Lithium Fluoride, and Magnesium Oxide Single Crystals. 1

NASA Technical Reports Server (NTRS)

Stearns, Carl A.; Pack, Ann E.; Lad, Robert A.

1959-01-01

A study was made of the relative magnitude of the effects of various factors on the ductility of single crystals of sodium chloride (NaCl), lithium fluoride (LiF), and magnesium oxide (MgO). Specimen treatments included water-polishing, varying cleavage rate, annealing, quenching, X-irradiation, surface coating, aging, and combinations of some of these treatments. The mechanical behavior of the crystals was studied in flexure and in compression, the latter study being performed at both constant strain rate and constant load. Etch-pit studies were carried out to provide some pertinent information on the results of pretreatment on the dislocation concentration and distribution in the vicinity of the surface. The load deformation curves for these ionic single crystals show an initial region of very low slope which proved to be due to anelastic deformation. The extent of initial anelastic deformation is modified by specimen pretreatment in a way that suggests that this deformation is the result of expansion of cleaved-in dislocation loops, which can contract on the removal of the stress. The effects of the various pretreatments on the load and deflection at fracture are in accord with the prediction one might make with regard to their effect on the nucleation of fatal surface cracks. For NaCl, increases in ductility are always accompanied by increases in strength. The creep constants for NaCl are a function of treatments which affect the bulk structure but are not a function of treatments which only affect the surface.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

Turbulent Convection in an Anelastic Rotating Sphere: A Model for the Circulation on the Giant Planets

DTIC Science & Technology

2008-06-01

exterior weather layer, using a quasigeostrophic two layer channel model on a beta plane , where the colum- nar interior is therefore represented by a...116 5.4 The evolution of the ’it’ field in the weakly nonlinear run ........ .. 117 5.5 The zonal mean zonal velocity on the equatorial plane in...turbulence on a 8 plane . These two approaches have been in debate ever since. 1.3.1 Shallow Models The first to apply the "shallow" approach to

Global Attenuation Tomography and Implications for Upper-Mantle Thermal Structure

NASA Astrophysics Data System (ADS)

Dalton, C. A.; Ekström, G.; Dziewonski, A. M.

2007-12-01

Observation of seismic-wave attenuation provides a direct measure of the Earth's anelasticity. The sensitivity of attenuation to temperature, composition, partial melt, and water content is different from that of seismic velocity, and joint interpretation of elastic and anelastic models may be used to improve constraints on these properties throughout the Earth. Historically, the development of attenuation models has lagged behind velocity models. However, the availability of large seismic datasets and improved techniques to treat these data have recently led to better and higher-resolution attenuation models. We have developed a new 3-D global model of shear attenuation in the upper mantle. This new model, QRFSI12, is derived from > 30,000 fundamental-mode Rayleigh wave amplitude measurements at each period (period range 50-250 s). The amplitudes are inverted simultaneously for the coefficients of the 3-D model as well as frequency-dependent amplitude correction factors for each source and receiver. We have found that focusing by elastic heterogeneity can significantly influence surface-wave amplitudes and that this effect can be modeled at long periods using ray-theoretical approximations. We therefore subtract focusing effects from the data prior to inversion by using phase-velocity maps determined from jointly inverting amplitude and phase-delay datasets. In the shallow mantle, QRFSI12 exhibits a strong correlation with tectonic features, and different tectonic provinces are characterized by distinct attenuative properties. At depths > 250 km, the model is dominated by high attenuation beneath the southeastern Pacific and eastern Africa and low attenuation associated with subduction zones in the western Pacific. Comparison of QRFSI12 with global shear-velocity models shows a strong anti-correlation throughout the upper mantle. At 100-km depth, a clear trend of increasing velocity and decreasing attenuation with increasing age of the seafloor is apparent, and tectonically active continental areas are associated with slower velocities and higher attenuation than stable continental interiors. At depths of 150 and 200 km, oceanic regions exhibit a larger decrease in attenuation per fractional increase in velocity than stable continental regions do, suggesting differences in the mechanisms that influence the seismic properties within these two regions. Comparison with recent laboratory measurements (Faul and Jackson, 2005) of attenuation and velocity for olivine helps to quantify the extent to which temperature alone can explain the observed variability. We find that the mineral-physics predictions agree well with the global seismic models for the oceanic regions between 150- and 250-km depth, but that the cratonic areas cannot be fit.

Using GIA observables to constrain the thermal contribution to lateral variations in mantle viscosity

NASA Astrophysics Data System (ADS)

Wu, P.; Wang, H.; van der Wal, W.; Shum, C.; Lee, H.; Braun, A.

2009-05-01

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, observations of the glacial isostatic adjustment (GIA) process are used to constrain the thermal contribution to lateral variations in upper and lower mantle viscosities. The Coupled Laplace-Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic earth with self-gravitating oceans, induced by either the ICE-5G or ICE-4G deglaciation models. GIA observations include global historic relative sea level data, GPS uplift rates in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide. The lateral viscosity perturbations are inferred from the high resolution seismic tomography model of Grand (2002) by using a conversion relation that takes into account both anelastic and anharmonic effects (Karato 2008). To determine the contribution of thermal effects in the upper and lower mantle, the scaling factor b is also inserted into the conversion relation: For b = 1, lateral velocity variations are caused by thermal effects alone; while b < 1 indicates a decreasing contribution of thermal effects; eventually when b = 0, there is no lateral viscosity variations exist and the Earth is laterally homogeneous. The value of b in the upper mantle is b1 while that in the lower mantle is b2. The lateral viscosity variations computed this way are superposed on a reference model that is able to give a reasonably good fit to the GIA observations. The parameter space for (b1, b2) is then searched to find the combination that yields the best improvement in fitting the GIA data in Laurentide, Fennoscandia or globally.

A total variation diminishing finite difference algorithm for sonic boom propagation models

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

The evolution of in-plane magnetic anisotropy in CoFeB/GaAs(001) films annealed at different temperatures

NASA Astrophysics Data System (ADS)

Tu, Hongqing; Wang, Ji; Wei, Lujun; Yuan, Yuan; Zhang, W.; You, Biao; Du, Jun

2018-05-01

A considerable in-plane uniaxial magnetic anisotropy (UMA) field (Hu ˜ 300 Oe) could be achieved when the amorphous CoFeB film was deposited on the GaAs(001) wafer by magnetron-sputtering after proper etch-annealed procedure. In order to get deep insights into the mechanism of the UMA, the film was annealed at different temperatures and the evolution of the in-plane magnetic anisotropy was investigated carefully. With increasing the annealing temperature (TA), the UMA could be maintained well when TA reached 250°C, but became very weak at 300°C. However, when TA was elevated to 400°C, another UMA (Hu ˜ 130 Oe) was built accompanied with a fourfold magnetic anisotropy with its strength of about 50 Oe. In terms of the magnetic anisotropy evolution along with TA, the anelastic strain, which is thought to be resulted from the interfacial interaction between CoFeB and GaAs, may play a dominant role in producing the enhanced UMA based on the `bond-orientational' anisotropy (BOA) model.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

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

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Waveform inversion of mantle Love waves: The born seismogram approach

NASA Technical Reports Server (NTRS)

Tanimoto, T.

1983-01-01

Normal mode theory, extended to the slightly laterally heterogeneous Earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the Earth's lateral heterogeneity at l=2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l=2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5% in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.

Waveform inversion of mantle Love waves - The Born seismogram approach

NASA Technical Reports Server (NTRS)

Tanimoto, T.

1984-01-01

Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the earth's lateral heterogeneity at l = 2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l = 2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 percent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Slip rates on San Francisco Bay area faults from anelastic deformation of the continental lithosphere

USGS Publications Warehouse

Geist, E.L.; Andrews, D.J.

2000-01-01

Long-term slip rates on major faults in the San Francisco Bay area are predicted by modeling the anelastic deformation of the continental lithosphere in response to regional relative plate motion. The model developed by Bird and Kong [1994] is used to simulate lithospheric deformation according to a Coulomb frictional rheology of the upper crust and a dislocation creep rheology at depth. The focus of this study is the long-term motion of faults in a region extending from the creeping section of the San Andreas fault to the south up to the latitude of Cape Mendocino to the north. Boundary conditions are specified by the relative motion between the Pacific plate and the Sierra Nevada - Great Valley microplate [Argus and Gordon, 2000]. Rheologic-frictional parameters are specified as independent variables, and prediction errors are calculated with respect to geologic estimates of slip rates and maximum compressive stress directions. The model that best explains the region-wide observations is one in which the coefficient of friction on all of the major faults is less than 0.15, with the coefficient of friction for the San Andreas fault being approximately 0.09, consistent with previous inferences of San Andreas fault friction. Prediction error increases with lower fault friction on the San Andreas, indicating a lower bound of ??SAF > 0.08. Discrepancies with respect to previous slip rate estimates include a higher than expected slip rate along the peninsula segment of the San Andreas fault and a slightly lower than expected slip rate along the San Gregorio fault.

Elasticity and Anelasticity of Materials from Time-Resolved X-ray Diffraction

NASA Astrophysics Data System (ADS)

Sinogeikin, S. V.; Smith, J.; Lin, C.; Bai, L.; Rod, E.; Shen, G.

2014-12-01

Recent advances in synchrotron sources, x-ray optics, area detectors, and sample environment control have enabled many time-resolved experimental techniques for studying materials at extreme pressure and temperature conditions. The High Pressure Collaborative Access Team (HPCAT) at the Advanced Photon Source has made a sustained effort to develop and assemble a powerful collection of high-pressure apparatus for time-resolved research, and considerable time has been invested in developing techniques for collecting high-quality time-resolved x-ray scattering data. In this talk we will outline recently developed capabilities at HPCAT for studying elasticity and anelasticity of minerals using fast compression and cyclic compression-decompression. A few recent studies will be highlighted. For example, with fast x-ray area detectors having millisecond time resolution, accurate thermal equations of state of materials at temperatures up to 1000K and megabar pressures can be collected in a matter of seconds using membrane-driven diamond anvil cells (DAC), yielding unprecedented time and pressure resolution of true isotherms. Short duration of the experiments eliminates temperature variation during the experiments and in general allows volume measurements at higher pressures and temperatures. Alternatively, high-frequency (kilohertz range) radial diffraction measurements in a panoramic DAC combined with fast, precise cyclic loading/unloading by piezo drive could provide the short time scale necessary for studying rheology of minerals from the elastic response and lattice relaxation as a function of pressure, temperature and strain rate. Finally, we consider some possible future applications for time-resolved high-pressure, high-temperature research of mantle minerals.

From micro to macro: the role of defects in the mechanical response of Earth and Planetary materials

NASA Astrophysics Data System (ADS)

McCarthy, Christine

2015-04-01

Microstructural features can greatly influence the bulk behavior of materials. Impurities, grain (and subgrain) size, dislocations, and partial melt can all affect the way that seismic waves are damped in the mantle, for instance, or how tidal energy is dissipated within an icy moon's outer shell. With proper scaling of the viscoelastic response, it is possible to use the attenuation signature -- for instance, the variation of Q with the micro/mesoscale evolution of deformation-induced strain (i.e. fabric) -- as a prospecting tool to determine active deformation structure within bodies of ice or rock at macroscopic (km) scale. In order to better interpret seismic data and provide better constraints for geophysical modeling, I design and perform laboratory experiments to directly measure the plastic and anelastic behaviours of various Earth and planetary materials, including polycrystalline ice. I will discuss findings from attenuation experiments, in particular results that suggest a coupling between deformation-induced microstructure effected by tectonics and attenuation behaviour. I will also discuss recent experiments that combine anelastic and frictional response using a custom-built biaxial friction apparatus. The experiments provide dynamic, frequency-dependent material properties of ice and ice on rock deformation at frequencies consistent with tidal forcing of Antarctic and Greenland glaciers. Such data can be used directly in models of glacier and ice stream flow and will inform our understanding of the complex glacier dynamics needed to improve predictions of sea level rise. Additionally, the experimental measurements can ultimately be compared with field observations to infer characteristics of the bed interface and the material composition of the bulk glacier.

Anelastic spherical dynamos with radially variable electrical conductivity

NASA Astrophysics Data System (ADS)

Dietrich, W.; Jones, C. A.

2018-05-01

A series of numerical simulations of the dynamo process operating inside gas giant planets has been performed. We use an anelastic, fully nonlinear, three-dimensional, benchmarked MHD code to evolve the flow, entropy and magnetic field. Our models take into account the varying electrical conductivity, high in the ionised metallic hydrogen region, low in the molecular outer region. Our suite of electrical conductivity profiles ranges from Jupiter-like, where the outer hydrodynamic region is quite thin, to Saturn-like, where there is a thick non-conducting shell. The rapid rotation leads to the formation of two distinct dynamical regimes which are separated by a magnetic tangent cylinder - mTC. Outside the mTC there are strong zonal flows, where Reynolds stress balances turbulent viscosity, but inside the mTC Lorentz force reduces the zonal flow. The dynamic interaction between both regions induces meridional circulation. We find a rich diversity of magnetic field morphologies. There are Jupiter-like steady dipolar fields, and a belt of quadrupolar dominated dynamos spanning the range of models between Jupiter-like and Saturn-like conductivity profiles. This diversity may be linked to the appearance of reversed sign helicity in the metallic regions of our dynamos. With Saturn-like conductivity profiles we find models with dipolar magnetic fields, whose axisymmetric components resemble those of Saturn, and which oscillate on a very long time-scale. However, the non-axisymmetric field components of our models are at least ten times larger than those of Saturn, possibly due to the absence of any stably stratified layer.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Subduction zone and crustal dynamics of western Washington; a tectonic model for earthquake hazards evaluation

USGS Publications Warehouse

Stanley, Dal; Villaseñor, Antonio; Benz, Harley

1999-01-01

The Cascadia subduction zone is extremely complex in the western Washington region, involving local deformation of the subducting Juan de Fuca plate and complicated block structures in the crust. It has been postulated that the Cascadia subduction zone could be the source for a large thrust earthquake, possibly as large as M9.0. Large intraplate earthquakes from within the subducting Juan de Fuca plate beneath the Puget Sound region have accounted for most of the energy release in this century and future such large earthquakes are expected. Added to these possible hazards is clear evidence for strong crustal deformation events in the Puget Sound region near faults such as the Seattle fault, which passes through the southern Seattle metropolitan area. In order to understand the nature of these individual earthquake sources and their possible interrelationship, we have conducted an extensive seismotectonic study of the region. We have employed P-wave velocity models developed using local earthquake tomography as a key tool in this research. Other information utilized includes geological, paleoseismic, gravity, magnetic, magnetotelluric, deformation, seismicity, focal mechanism and geodetic data. Neotectonic concepts were tested and augmented through use of anelastic (creep) deformation models based on thin-plate, finite-element techniques developed by Peter Bird, UCLA. These programs model anelastic strain rate, stress, and velocity fields for given rheological parameters, variable crust and lithosphere thicknesses, heat flow, and elevation. Known faults in western Washington and the main Cascadia subduction thrust were incorporated in the modeling process. Significant results from the velocity models include delineation of a previously studied arch in the subducting Juan de Fuca plate. The axis of the arch is oriented in the direction of current subduction and asymmetrically deformed due to the effects of a northern buttress mapped in the velocity models. This buttress occurs under the North Cascades region of Washington and under southern Vancouver Island. We find that regional faults zones such as the Devils Mt. and Darrington zones follow the margin of this buttress and the Olympic-Wallowa lineament forms its southern boundary east of the Puget Lowland. Thick, high-velocity, lower-crustal rocks are interpreted to be a mafic/ultramafic wedge occuring just above the subduction thrust. This mafic wedge appears to be jointly deformed with the arch, suggesting strong coupling between the subducting plate and upper plate crust in the Puget Sound region at depths >30 km. Such tectonic coupling is possible if brittle-ductile transition temperatures for mafic/ultramafic rocks on both sides of the thrust are assumed. The deformation models show that dominant north-south compression in the coast ranges of Washington and Oregon is controlled by a highly mafic crust and low heat flow, allowing efficient transmission of margin-parallel shear from Pacific plate interaction with North America. Complex stress patterns which curve around the Puget Sound region require a concentration of northwest-directed shear in the North Cascades of Washington. The preferred model shows that greatest horizontal shortening occurs across the Devils Mt. fault zone and the east end of the Seattle fault.

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

Finite Mathematics and Discrete Mathematics: Is There a Difference?

ERIC Educational Resources Information Center

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

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

Yadav, Rakesh K.; Poppenhaeger, Katja; Wolk, Scott J.

Despite the lack of a shear-rich tachocline region, low-mass fully convective (FC) stars are capable of generating strong magnetic fields, indicating that a dynamo mechanism fundamentally different from the solar dynamo is at work in these objects. We present a self-consistent three-dimensional model of magnetic field generation in low-mass FC stars. The model utilizes the anelastic magnetohydrodynamic equations to simulate compressible convection in a rotating sphere. A distributed dynamo working in the model spontaneously produces a dipole-dominated surface magnetic field of the observed strength. The interaction of this field with the turbulent convection in outer layers shreds it, producing small-scalemore » fields that carry most of the magnetic flux. The Zeeman–Doppler-Imaging technique applied to synthetic spectropolarimetric data based on our model recovers most of the large-scale field. Our model simultaneously reproduces the morphology and magnitude of the large-scale field as well as the magnitude of the small-scale field observed on low-mass FC stars.« less

GLASS TRANSITION AND DEGREE OF CONVERSION OF A LIGHT-CURED ORTHODONTIC COMPOSITE

PubMed Central

Sostena, Michela M. D. S.; Nogueira, Renata A.; Grandini, Carlos R.; Moraes, João Carlos Silos

2009-01-01

Objective: This study evaluated the glass transition temperature (Tg) and degree of conversion (DC) of a light-cured (Fill Magic) versus a chemically cured (Concise) orthodontic composite. Material and Methods: Anelastic relaxation spectroscopy was used for the first time to determine the Tg of a dental composite, while the DC was evaluated by infrared spectroscopy. The light-cured composite specimens were irradiated with a commercial LED light-curing unit using different exposure times (40, 90 and 120 s). Results: Fill Magic presented lower Tg than Concise (35-84°C versus 135°C), but reached a higher DC. Conclusions: The results of this study suggest that Fill Magic has lower Tg than Concise due to its higher organic phase content, and that when this light-cured composite is used to bond orthodontic brackets, a minimum energy density of 7.8 J/cm2 is necessary to reach adequate conversion level and obtain satisfactory adhesion. PMID:20027428

Calibration of an M L scale for South Africa using tectonic earthquake data recorded by the South African National Seismograph Network: 2006 to 2009

NASA Astrophysics Data System (ADS)

Saunders, Ian; Ottemöller, Lars; Brandt, Martin B. C.; Fourie, Christoffel J. S.

2013-04-01

A relation to determine local magnitude ( M L) based on the original Richter definition is empirically derived from synthetic Wood-Anderson seismograms recorded by the South African National Seismograph Network. In total, 263 earthquakes in the distance range 10 to 1,000 km, representing 1,681 trace amplitudes measured in nanometers from synthesized Wood-Anderson records on the vertical channel were considered to derive an attenuation relation appropriate for South Africa through multiple regression analysis. Additionally, station corrections were determined for 26 stations during the regression analysis resulting in values ranging between -0.31 and 0.50. The most appropriate M L scale for South Africa from this study satisfies the equation: {M_{{{L}}}} = {{lo}}{{{g}}_{{10}}}(A) + 1.149{{lo}}{{{g}}_{{10}}}(R) + 0.00063R + 2.04 - S The anelastic attenuation term derived from this study indicates that ground motion attenuation is significantly different from Southern California but comparable with stable continental regions.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Temperature-Dependent Electrical and Micromechanical Properties of Lanthanum Titanate with Additions of Yttria

NASA Technical Reports Server (NTRS)

Goldsby, Jon C.

2010-01-01

Temperature-dependent elastic properties were determined by establishing continuous flexural vibrations in the material at its lowest resonance frequency of 31tHz. The imaginary part of the complex impedance plotted as a function of frequency and temperature reveals a thermally activated peak, which decreases in magnitude as the temperature increases. Additions of yttria do not degrade the electromechanical in particularly the elastic and anelastic properties of lanthanum titanate. Y2O3/La2Ti2O7 exhibits extremely low internal friction and hence may be more mechanical fatigue-resistant at low strains.

Measurement of Newton's constant using a torsion balance with angular acceleration feedback.

PubMed

Gundlach, J H; Merkowitz, S M

2000-10-02

We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215+/-0.000092) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.

The self-consistent dynamic pole tide in non-global oceans

NASA Technical Reports Server (NTRS)

Dickman, S. R.

1988-01-01

The dynamic pole tide is determined by solving Laplace tide equations which take into account the presence of continents in oceans, oceanic self-gravitation and loading, and mantle elasticity. Dynamical effects are found to be only mild. It is shown that the dynamical pole tide contributes about one day more to the Chandler period than a static pole tide would, and dissipates wobble energy at a very weak rate. It is noted that, depending on the wobble period predicted for an oceanless elastic earth, mantle anelasticity at low frequencies may nevertheless contribute negligibly to the Chandler period.

Stratification and energy fluxes in the anelastic convection model

NASA Astrophysics Data System (ADS)

Hejda, Pavel; Reshetnyak, Maxim

2013-04-01

Convection in the planetary cores is usually connected with the geostrophic state. At the onset of convection, the ratio of horizontal scale to the scale along the axis of rotation is proportional to the cube root of the Ekman number, which characterises the ratio of the viscous forces to the Coriolis force. The Ekman number is extremely small in the liquid cores, which is a source of strong anisotropy. Even if further increase of the heat sources leads to decrease of anisotropy, the final state is still highly anisotropic. The influence of the rapid rotation on the structure of the flows in the physical space is also manifested by a substantial change of the spectral properties of the turbulence in the core (Reshetnyak and Hejda, 2008; Hejda and Reshetnyak, 2009). If for the non-rotating flow the kinetic energy in the wave space propagates from the large scales to the small dissipative scales (the so-called direct Richardson-Kolmogorov cascade), then in presence of rotation the turbulence degenerates to the quasi two-dimensional state and the inverse cascade of the kinetic energy is observed. Having in mind that Cartesian and spherical geometries exhibit similar results and reproduce the inverse cascades of the kinetic energy (Reshetnyak and Hejda, 2012), there is an open question how this cascade contributes to the more general energy balance, which includes the heat flux equation. As the heat energy definition in the Boussinesq model is quite questionable, we consider the anelastic model, where the heat fluxes can be compared with the kinetic energy fluxes in the adequate way. Here we consider the spherical geometry model in the shell that limits our study to the cascades in the azimuthal wave-number. As the self-consistent anelastic model includes new term, the adiabatic cooling, which produces "stratification" in the outer part of the core, we consider its influence on convection in the physical and wave spaces. We show that even small cooling can change the convection substantially, shifting maximum of convection to the inner part of the liquid core. Similar to the Boussinesq model the both direct and inverse cascades of the kinetic energy as well as the direct cascade of the specific entropy in the wave space occur. Reshetnyak, M. and Hejda, P., 2008. Direct and inverse cascades in the geodynamo. Nonlin. Proc. Geophys. 15, 873-880. Hejda, P. and Reshetnyak, M., 2009. Effect of anisotropy in the geostrophic turbulence. Phys. Earth Planet. Inter. 177, 152-160, doi: 10.1016/j.pepi.2009.08.006. Reshetnyak, M. and Hejda, P., 2012. Kinetic energy cascades in quasi-geostrophic convection in a spherical shell. Physica Scripta 86, article No. 018408, doi: 10.1088/0031-8949/86/01/018408.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Is Seismically Determined Q an Intrinsic Material Property?

NASA Astrophysics Data System (ADS)

Langston, C. A.

2003-12-01

The seismic quality factor, Q, has a well-defined physical meaning as an intrinsic material property associated with a visco-elastic or a non-linear stress-strain constitutive relation for a material. Measurement of Q from seismic waves, however, involves interpreting seismic wave amplitude and phase as deviations from some ideal elastic wave propagation model. Thus, assumptions in the elastic wave propagation model become the basis for attributing anelastic properties to the earth continuum. Scientifically, the resulting Q model derived from seismic data is no more than a hypothesis that needs to be verified by other independent experiments concerning the continuum constitutive law and through careful examination of the truth of the assumptions in the wave propagation model. A case in point concerns the anelasticity of Mississippi embayment sediments in the central U.S. that has important implications for evaluation of earthquake strong ground motions. Previous body wave analyses using converted Sp phases have suggested that Qs is ~30 in the sediments based on simple ray theory assumptions. However, detailed modeling of 1D heterogeneity in the sediments shows that Qs cannot be resolved by the Sp data. An independent experiment concerning the amplitude decay of surface waves propagating in the sediments shows that Qs must be generally greater than 80 but is also subject to scattering attenuation. Apparent Q effects seen in direct P and S waves can also be produced by wave tunneling mechanisms in relatively simple 1D heterogeneity. Heterogeneity is a general geophysical attribute of the earth as shown by many high-resolution data sets and should be used as the first litmus test on assumptions made in seismic Q studies before a Q model can be interpreted as an intrinsic material property.

Analysis of Ground Motion from An Underground Chemical Explosion

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

Pitarka, Arben; Mellors, Robert J.; Walter, William R.

Here in this paper we investigate the excitation and propagation of far-field seismic waves from the 905 kg trinitrotoluene equivalent underground chemical explosion SPE-3 recorded during the Source Physics Experiment (SPE) at the Nevada National Security Site. The recorded far-field ground motion at short and long distances is characterized by substantial shear-wave energy, and large azimuthal variations in P-and S-wave amplitudes. The shear waves observed on the transverse component of sensors at epicentral distances <50 m suggests they were generated at or very near the source. The relative amplitude of the shear waves grows as the waves propagate away frommore » the source. We analyze and model the shear-wave excitation during the explosion in the 0.01–10 Hz frequency range, at epicentral distances of up to 1 km. We used two simulation techniques. One is based on the empirical isotropic Mueller–Murphy (MM) (Mueller and Murphy, 1971) nuclear explosion source model, and 3D anelastic wave propagation modeling. The second uses a physics-based approach that couples hydrodynamic modeling of the chemical explosion source with anelastic wave propagation modeling. Comparisons with recorded data show the MM source model overestimates the SPE-3 far-field ground motion by an average factor of 4. The observations show that shear waves with substantial high-frequency energy were generated at the source. However, to match the observations additional shear waves from scattering, including surface topography, and heterogeneous shallow structure contributed to the amplification of far-field shear motion. Comparisons between empirically based isotropic and physics-based anisotropic source models suggest that both wave-scattering effects and near-field nonlinear effects are needed to explain the amplitude and irregular radiation pattern of shear motion observed during the SPE-3 explosion.« less

Analysis of Ground Motion from An Underground Chemical Explosion

DOE PAGES

Pitarka, Arben; Mellors, Robert J.; Walter, William R.; ...

2015-09-08

Here in this paper we investigate the excitation and propagation of far-field seismic waves from the 905 kg trinitrotoluene equivalent underground chemical explosion SPE-3 recorded during the Source Physics Experiment (SPE) at the Nevada National Security Site. The recorded far-field ground motion at short and long distances is characterized by substantial shear-wave energy, and large azimuthal variations in P-and S-wave amplitudes. The shear waves observed on the transverse component of sensors at epicentral distances <50 m suggests they were generated at or very near the source. The relative amplitude of the shear waves grows as the waves propagate away frommore » the source. We analyze and model the shear-wave excitation during the explosion in the 0.01–10 Hz frequency range, at epicentral distances of up to 1 km. We used two simulation techniques. One is based on the empirical isotropic Mueller–Murphy (MM) (Mueller and Murphy, 1971) nuclear explosion source model, and 3D anelastic wave propagation modeling. The second uses a physics-based approach that couples hydrodynamic modeling of the chemical explosion source with anelastic wave propagation modeling. Comparisons with recorded data show the MM source model overestimates the SPE-3 far-field ground motion by an average factor of 4. The observations show that shear waves with substantial high-frequency energy were generated at the source. However, to match the observations additional shear waves from scattering, including surface topography, and heterogeneous shallow structure contributed to the amplification of far-field shear motion. Comparisons between empirically based isotropic and physics-based anisotropic source models suggest that both wave-scattering effects and near-field nonlinear effects are needed to explain the amplitude and irregular radiation pattern of shear motion observed during the SPE-3 explosion.« less

A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium

NASA Astrophysics Data System (ADS)

Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean

2016-10-01

In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.

Elastic and anelastic relaxations associated with the incommensurate structure of Pr0.48Ca0.52MnO3

NASA Astrophysics Data System (ADS)

Carpenter, Michael A.; Howard, Christopher J.; McKnight, Ruth E. A.; Migliori, Albert; Betts, Jon B.; Fanelli, Victor R.

2010-10-01

The elastic and anelastic properties of a polycrystalline sample of Pr0.48Ca0.52MnO3 have been investigated by resonant ultrasound spectroscopy, as a function of temperature (10-1130 K) and magnetic field strength (0-15 T). Marked softening of the shear modulus as the Pnma↔incommensurate phase transition at ˜235K in zero field is approached from either side is consistent with pseudoproper ferroelastic character, driven by an order parameter with Γ3+ symmetry associated with Jahn-Teller ordering. This is accompanied by an increase in attenuation just below the transition point. The attenuation remains relatively high down to ˜80K , where there is a distinct Debye peak. It is attributed to coupling of shear strain with the Γ3+ order parameter which, in turn, controls the repeat distance of the incommensurate structure. Kinetic data extracted from the Debye peak suggest that the rate-controlling process could be related to migration of polarons. Elastic softening and stiffening as a function of magnetic field at constant temperatures between 177 and ˜225K closely resembles the behavior as a function of temperature at 0, 5, and 10 T and is consistent with thermodynamically continuous behavior for the phase transition in both cases. This overall pattern can be rationalized in terms of linear/quadratic coupling between the Γ3+ order parameter and an order parameter with Σ1 or Σ2 symmetry. It is also consistent with a dominant role for spontaneous strains in determining the strength of coupling, evolution of the incommensurate microstructure, and equilibrium evolution of the Jahn-Teller ordered structure through multicomponent order-parameter space.

Variable anelastic attenuation and site effect in estimating source parameters of various major earthquakes including M w 7.8 Nepal and M w 7.5 Hindu kush earthquake by using far-field strong-motion data

NASA Astrophysics Data System (ADS)

Kumar, Naresh; Kumar, Parveen; Chauhan, Vishal; Hazarika, Devajit

2017-10-01

Strong-motion records of recent Gorkha Nepal earthquake ( M w 7.8), its strong aftershocks and seismic events of Hindu kush region have been analysed for estimation of source parameters. The M w 7.8 Gorkha Nepal earthquake of 25 April 2015 and its six aftershocks of magnitude range 5.3-7.3 are recorded at Multi-Parametric Geophysical Observatory, Ghuttu, Garhwal Himalaya (India) >600 km west from the epicentre of main shock of Gorkha earthquake. The acceleration data of eight earthquakes occurred in the Hindu kush region also recorded at this observatory which is located >1000 km east from the epicentre of M w 7.5 Hindu kush earthquake on 26 October 2015. The shear wave spectra of acceleration record are corrected for the possible effects of anelastic attenuation at both source and recording site as well as for site amplification. The strong-motion data of six local earthquakes are used to estimate the site amplification and the shear wave quality factor ( Q β) at recording site. The frequency-dependent Q β( f) = 124 f 0.98 is computed at Ghuttu station by using inversion technique. The corrected spectrum is compared with theoretical spectrum obtained from Brune's circular model for the horizontal components using grid search algorithm. Computed seismic moment, stress drop and source radius of the earthquakes used in this work range 8.20 × 1016-5.72 × 1020 Nm, 7.1-50.6 bars and 3.55-36.70 km, respectively. The results match with the available values obtained by other agencies.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

PubMed

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-10-16

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Computing 3-D wavefields in mantle circulations models to test hypotheses on the origin of lower mantle heterogeneity under Africa directly against seismic observations

NASA Astrophysics Data System (ADS)

Schuberth, Bernhard; Zaroli, Christophe; Nolet, Guust

2015-04-01

Of particular interest for the tectonic evolution of the Atlantic region is the influence of lower mantle structure under Africa on flow in the upper mantle beneath the ocean basin. Along with its Pacific counterpart, the large African anomaly in the lowermost mantle with strongly reduced seismic velocities has received considerable attention in seismological and geodynamic studies. Several seismological observations are typically taken as an indication that these two anomalies are being caused by large-scale compositional variations and that they are piles of material with higher density than normal mantle rock. This would imply negative buoyancy in the lowermost mantle under Africa, which has important implications for the flow at shallower depth and inferences on the processes that led to the formation of the Atlantic Ocean basin. However, a large number of recent studies argue for a strong thermal gradient across the core-mantle boundary that might provide an alternative explanation for the lower mantle anomaly through the resulting large lateral temperature variations. Recently, we developed a new joint forward modeling approach to test such geodynamic hypotheses directly against the seismic observations: Seismic heterogeneity is predicted by converting the temperature field of a high-resolution 3-D mantle circulation model into seismic velocities using thermodynamic models of mantle mineralogy. 3-D global wave propagation in the synthetic elastic structures is then simulated using a spectral element method. Being based on forward modelling only, this approach allows us to generate synthetic wavefields and seismograms independently of seismic observations. The statistics of observed long-period body wave traveltime variations show a markedly different behaviour for P- and S-waves: the standard deviation of P-wave delay times stays almost constant with ray turning depth, while that of the S-wave delay times increases strongly throughout the mantle. In an earlier study, we showed that synthetic traveltime variations computed for an isochemical mantle circulation model with strong core heating can reproduce these different trends. This was taken as a strong indication that seismic heterogeneity in the lower mantle is likely dominated by thermal variations on large length-scales (i.e., relevant for long-period body waves). We will discuss the robustness of this earlier conclusion by exploring the uncertainties in the mineralogical models used to convert temperatures to seismic velocities. In particular, we investigate the influence of anelasticity on the standard deviation of our synthetic traveltime variations. Owing to the differences in seismic frequency content between laboratory measurements (MHz to GHz) and the Earth (mHz to Hz), the seismic velocities given in the mineralogical model need to be adjusted; that is, corrected for dispersion due to anelastic effects.

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

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.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

The SCEC Community Modeling Environment (SCEC/CME) - An Overview of its Architecture and Current Capabilities

NASA Astrophysics Data System (ADS)

Maechling, P. J.; Jordan, T. H.; Minster, B.; Moore, R.; Kesselman, C.; SCEC ITR Collaboration

2004-12-01

The Southern California Earthquake Center (SCEC), in collaboration with the San Diego Supercomputer Center, the USC Information Sciences Institute, the Incorporated Research Institutions for Seismology, and the U.S. Geological Survey, is developing the Southern California Earthquake Center Community Modeling Environment (CME) under a five-year grant from the National Science Foundation's Information Technology Research (ITR) Program jointly funded by the Geosciences and Computer and Information Science & Engineering Directorates. The CME system is an integrated geophysical simulation modeling framework that automates the process of selecting, configuring, and executing models of earthquake systems. During the Project's first three years, we have performed fundamental geophysical and information technology research and have also developed substantial system capabilities, software tools, and data collections that can help scientist perform systems-level earthquake science. The CME system provides collaborative tools to facilitate distributed research and development. These collaborative tools are primarily communication tools, providing researchers with access to information in ways that are convenient and useful. The CME system provides collaborators with access to significant computing and storage resources. The computing resources of the Project include in-house servers, Project allocations on USC High Performance Computing Linux Cluster, as well as allocations on NPACI Supercomputers and the TeraGrid. The CME system provides access to SCEC community geophysical models such as the Community Velocity Model, Community Fault Model, Community Crustal Motion Model, and the Community Block Model. The organizations that develop these models often provide access to them so it is not necessary to use the CME system to access these models. However, in some cases, the CME system supplements the SCEC community models with utility codes that make it easier to use or access these models. In some cases, the CME system also provides alternatives to the SCEC community models. The CME system hosts a collection of community geophysical software codes. These codes include seismic hazard analysis (SHA) programs developed by the SCEC/USGS OpenSHA group. Also, the CME system hosts anelastic wave propagation codes including Kim Olsen's Finite Difference code and Carnegie Mellon's Hercules Finite Element tool chain. The CME system can execute a workflow, that is, a series of geophysical computations using the output of one processing step as the input to a subsequent step. Our workflow capability utilizes grid-based computing software that can submit calculations to a pool of computing resources as well as data management tools that help us maintain an association between data files and metadata descriptions of those files. The CME system maintains, and provides access to, a collection of valuable geophysical data sets. The current CME Digital Library holdings include a collection of 60 ground motion simulation results calculated by a SCEC/PEER working group and a collection of Greens Functions calculated for 33 TriNet broadband receiver sites in the Los Angeles area.

The SCEC Community Modeling Environment(SCEC/CME): A Collaboratory for Seismic Hazard Analysis

NASA Astrophysics Data System (ADS)

Maechling, P. J.; Jordan, T. H.; Minster, J. B.; Moore, R.; Kesselman, C.

2005-12-01

The SCEC Community Modeling Environment (SCEC/CME) Project is an NSF-supported Geosciences/IT partnership that is actively developing an advanced information infrastructure for system-level earthquake science in Southern California. This partnership includes SCEC, USC's Information Sciences Institute (ISI), the San Diego Supercomputer Center (SDSC), the Incorporated Institutions for Research in Seismology (IRIS), and the U.S. Geological Survey. The goal of the SCEC/CME is to develop seismological applications and information technology (IT) infrastructure to support the development of Seismic Hazard Analysis (SHA) programs and other geophysical simulations. The SHA application programs developed on the Project include a Probabilistic Seismic Hazard Analysis system called OpenSHA. OpenSHA computational elements that are currently available include a collection of attenuation relationships, and several Earthquake Rupture Forecasts (ERFs). Geophysicists in the collaboration have also developed Anelastic Wave Models (AWMs) using both finite-difference and finite-element approaches. Earthquake simulations using these codes have been run for a variety of earthquake sources. Rupture Dynamic Model (RDM) codes have also been developed that simulate friction-based fault slip. The SCEC/CME collaboration has also developed IT software and hardware infrastructure to support the development, execution, and analysis of these SHA programs. To support computationally expensive simulations, we have constructed a grid-based scientific workflow system. Using the SCEC grid, project collaborators can submit computations from the SCEC/CME servers to High Performance Computers at USC and TeraGrid High Performance Computing Centers. Data generated and archived by the SCEC/CME is stored in a digital library system, the Storage Resource Broker (SRB). This system provides a robust and secure system for maintaining the association between the data seta and their metadata. To provide an easy-to-use system for constructing SHA computations, a browser-based workflow assembly web portal has been developed. Users can compose complex SHA calculations, specifying SCEC/CME data sets as inputs to calculations, and calling SCEC/CME computational programs to process the data and the output. Knowledge-based software tools have been implemented that utilize ontological descriptions of SHA software and data can validate workflows created with this pathway assembly tool. Data visualization software developed by the collaboration supports analysis and validation of data sets. Several programs have been developed to visualize SCEC/CME data including GMT-based map making software for PSHA codes, 4D wavefield propagation visualization software based on OpenGL, and 3D Geowall-based visualization of earthquakes, faults, and seismic wave propagation. The SCEC/CME Project also helps to sponsor the SCEC UseIT Intern program. The UseIT Intern Program provides research opportunities in both Geosciences and Information Technology to undergraduate students in a variety of fields. The UseIT group has developed a 3D data visualization tool, called SCEC-VDO, as a part of this undergraduate research program.

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

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

Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk; Tcheverda, Vladimir

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. Inmore » this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.« less

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources

PubMed Central

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-01-01

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947

Apparatus for dynamic and static measurements of mechanical properties of solids and of flux-lattice in type-II superconductors at low frequency (10 - 5-10 Hz) and temperature (4.7-500 K)

NASA Astrophysics Data System (ADS)

D'Anna, G.; Benoit, W.

1990-12-01

A forced torsional pendulum which permits us to examine anelastic mechanical properties of solids as well as for flux-lattice in type-II superconductors, has been built to explore the low frequency and low temperature range. It works on the principle of dynamic frequency response function measurement and appears to be a powerful instrument for studying structural defect motions as well as flux line dynamics. As an additional quantity, the magnetization or the plastic strain can be statically measured by the same apparatus.

Quantification of Explosion Source Characteristics from Near Source, Regional and Teleseismic Distances

DTIC Science & Technology

1989-07-31

may be expressed as a combination of geometrical spreading and anelastic attenuation as, A = e -a I rn where: A = attenuation as a function of...of the source parameter estimates. Similar consistent results are obtained for the vertical component records. 26 . E .- .0 ~ Ub C>2 a) o 0~ M- PC oa -0...U - V9suu) apl)dr F.p LO. ______ ___2 - a. 4) 440 44~ 0 A* 0 4-4 0 uu 14 E 0. 0 w a- .6aa w ad 0 IV E E 28 UCZ 40 F.) o .*L 101 V- z Z. Ica 29 0 Long

The Mechanical Properties of Nanowires

PubMed Central

Wang, Shiliang; Shan, Zhiwei

2017-01-01

Applications of nanowires into future generation nanodevices require a complete understanding of the mechanical properties of the nanowires. A great research effort has been made in the past two decades to understand the deformation physics and mechanical behaviors of nanowires, and to interpret the discrepancies between experimental measurements and theoretical predictions. This review focused on the characterization and understanding of the mechanical properties of nanowires, including elasticity, plasticity, anelasticity and strength. As the results from the previous literature in this area appear inconsistent, a critical evaluation of the characterization techniques and methodologies were presented. In particular, the size effects of nanowires on the mechanical properties and their deformation mechanisms were discussed. PMID:28435775

Temperature Dependent Electrical and Micromechanical Properties of Lanthanum Titanate with Additions of Yttria

NASA Technical Reports Server (NTRS)

Goldsby, Jon C.

2003-01-01

Lanthanum titanate (La2Ti2O7) a layered distorted perovskite (1) with space group Pna2(sub 1) has been shown to have potential as a high temperature piezoelectric (2). However this highly refractory oxide compound must be consolidated at relatively high temperatures approximately 1400 C. Commercial La2Ti207 powders were mechanically alloyed with additions of Y2O3 to lower the consolidation temperature by 300 C and to provide post processing mechanical stability. Temperature dependent electrical, elastic and anelastic behavior were selected as nondestructive means of evaluating the effects of yttria on the properties of this ferroceramic material.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.

Global adjoint tomography: First-generation model

DOE PAGES

Bozdag, Ebru; Peter, Daniel; Lefebvre, Matthieu; ...

2016-09-22

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematicallymore » reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M w ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example, underneath Yellowstone. Here, this is a consequence of our multiscale smoothing strategy in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.« less

Global adjoint tomography: First-generation model

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

Bozdag, Ebru; Peter, Daniel; Lefebvre, Matthieu

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematicallymore » reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M w ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example, underneath Yellowstone. Here, this is a consequence of our multiscale smoothing strategy in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.« less

Preliminary ground motion prediction equations for the Central and Eastern United States

NASA Astrophysics Data System (ADS)

Graizer, V.

2014-12-01

At the current stage I used the database created under the Next Generation Attenuations (NGA-East) project by Cramer et al. (2013). In contrast to the active tectonic environment in the Western US (WUS) the strong motion record database for the stable continental environment in the Central and Eastern US (CEUS) is not sufficient to create purely empirical ground motion prediction equations (GMPE) covering required for the PSHA magnitude (4.5

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

A Finite Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces

DTIC Science & Technology

1991-09-01

Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces by Victor W. Sparrow...The nonlinear acoustic propagation effects require a numerical solution in the time domain. To model a porous ground surface, which in the frequency...incident on the hard and porous surfaces were produced. The model predicted that near grazing finite amplitude acoustic blast waves decay with distance

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Seismic Wave Propagation from Underground Chemical Explosions: Sensitivity to Velocity and Thickness of a Weathered Layer

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.

2017-12-01

Recorded motions from underground chemical explosions are complicated by long duration seismic coda as well as motion in the tangential direction. The inability to distinguish the origins of these complexities as either source or path effects comprises a limitation to effective monitoring of underground chemical explosions. With numerical models, it is possible to conduct rigorous sensitivity analyses for chemical explosive sources and their resulting ground motions under the influence of many attributes, including but not limited to complex velocity structure, topography, and non-linear source characteristics. Previously we found that topography can cause significant scattering in the direct wave but leads to relatively little motion in the coda. Here, we aim to investigate the contribution from the low-velocity weathered layer that exists in the shallow subsurface apart from and in combination with surface topography. We use SW4, an anelastic anisotropic fourth order finite difference code to simulate chemical explosive source in a 1D velocity structure consisting of a single weathered layer over a half space. A range of velocity magnitudes are used for the upper weathered layer with the velocities always being lower than that of the granitic underlaying layer. We find that for lower weathered layer velocities, the wave train is highly dispersed and causes a large percentage of energy to be contained in the coda in relation to the entire time series. The percentage of energy contained in the coda grows with distance from the source but saturates at a certain distance that depends on weathered layer velocity and thickness. The saturation onset distance increases with decreasing layer thickness and increasing velocity of the upper layer. Measurements of relative coda energy and coda saturation onset distance from real recordings can provide an additional constraint on the properties of the weathered layer in remote sites as well as test sites like the Nevada National Security Site (NNSS). The results of this modeling study will aid in distinguishing source effects from path effects to the recorded motions in experiments such as the Source Physics Experiment (SPE). This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Extension of the energy-to-moment parameter Θ to intermediate and deep earthquakes

NASA Astrophysics Data System (ADS)

Saloor, Nooshin; Okal, Emile A.

2018-01-01

We extend to intermediate and deep earthquakes the slowness parameter Θ originally introduced by Newman and Okal (1998). Because of the increasing time lag with depth between the phases P, pP and sP, and of variations in anelastic attenuation parameters t∗ , we define four depth bins featuring slightly different algorithms for the computation of Θ . We apply this methodology to a global dataset of 598 intermediate and deep earthquakes with moments greater than 1025 dyn∗cm. We find a slight increase with depth in average values of Θ (from -4.81 between 80 and 135 km to -4.48 between 450 and 700 km), which however all have intersecting one- σ bands. With widths ranging from 0.26 to 0.31 logarithmic units, these are narrower than their counterpart for a reference dataset of 146 shallow earthquakes (σ = 0.55). Similarly, we find no correlation between values of Θ and focal geometry. These results point to stress conditions within the seismogenic zones inside the Wadati-Benioff slabs more homogeneous than those prevailing at the shallow contacts between tectonic plates.

Metallic coatings of microelectromechanical structures at low temperatures: Stress, elasticity, and nonlinear dissipation

NASA Astrophysics Data System (ADS)

Collin, E.; Kofler, J.; Lakhloufi, S.; Pairis, S.; Bunkov, Yu. M.; Godfrin, H.

2010-06-01

We present mechanical measurements performed at low temperatures on cantilever-based microelectromechanical structures coated with a metallic layer. Two very different coatings are presented in order to illustrate the capabilities of the present approach, namely (soft) aluminum and (hard) niobium oxide. The temperature is used as a control parameter to access materials properties. We benefit from low temperature techniques to extract a phase-resolved measurement of the first mechanical resonance mode in cryogenic vacuum. By repeating the experiment on the same samples, after multiple metallic depositions, we can determine accurately the contribution of the coating layers to the mechanical properties in terms of surface stress, additional mass, additional elasticity, and damping. Analytic theoretical expressions are derived and used to fit the data. Taking advantage of the extremely broad dynamic range provided by the technique, we can measure the anelasticity of the thin metallic film. The key parameters describing the metals' dynamics are analyzed in an original way in order to provide new experimental grounds for future theoretical modelings of the underlying mechanisms.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

A study of ground motion attenuation in the Southern Great Basin, Nevada-California, using several techniques for estimates of Qs , log A 0, and coda Q

NASA Astrophysics Data System (ADS)

Rogers, A. M.; Harmsen, S. C.; Herrmann, R. B.; Meremonte, M. E.

1987-04-01

As a first step in the assessment of the earthquake hazard in the southern Great Basin of Nevada-California, this study evaluates the attenuation of peak vertical ground motions using a number of different regression models applied to unfiltered and band-pass-filtered ground motion data. These data are concentrated in the distance range 10-250 km. The regression models include parameters to account for geometric spreading, anelastic attenuation with a power law frequency dependence, source size, and station site effects. We find that the data are most consistent with an essentially frequency-independent Q and a geometric spreading coefficient less than 1.0. Regressions are also performed on vertical component peak amplitudes reexpressed as pseudo-Wood-Anderson peak amplitude estimates (PWA), permitting comparison with earlier work that used Wood-Anderson (WA) data from California. Both of these results show that Q values in this region are high relative to California, having values in the range 700-900 over the frequency band 1-10 Hz. Comparison of ML magnitudes from stations BRK and PAS for earthquakes in the southern Great Basin shows that these two stations report magnitudes with differences that are distance dependent. This bias suggests that the Richter log A0 curve appropriate to California is too steep for earthquakes occurring in southern Nevada, a result implicitly supporting our finding that Q values are higher than those in California. The PWA attenuation functions derived from our data also indicate that local magnitudes reported by California observatories for earthquakes in this region may be overestimated by as much as 0.8 magnitude units in some cases. Both of these results will have an effect on the assessment of the earthquake hazard in this region. The robustness of our regression technique to extract the correct geometric spreading coefficient n and anelastic attenuation Q is tested by applying the technique to simulated data computed with given n and Q values. Using a stochastic modeling technique, we generate suites of seismograms for the distance range 10-200 km and for both WA and short-period vertical component seismometers. Regressions on the peak amplitudes from these records show that our regression model extracts values of n and Q approximately equal to the input values for either low-Q California attenuation or high-Q southern Nevada attenuation. Regressions on stochastically modeled WA and PWA amplitudes also provides a method of evaluating differences in magnitudes from WA and PWA amplitudes due to recording instrument response characteristics alone. These results indicate a difference between MLWA and MLPWA equal to 0.15 magnitude units, which we term the residual instrument correction. In contrast to the peak amplitude results, coda Q determinations using the single scatterer theory indicate that Qc values are dependent on source type and are proportional to ƒp, where p = 0.8 to 1.0. This result suggests that a difference exists between attenuation mechanisms for direct waves and backscattered waves in this region.

A comparison of the finite difference and finite element methods for heat transfer calculations

NASA Technical Reports Server (NTRS)

Emery, A. F.; Mortazavi, H. R.

1982-01-01

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

Electron-phonon coupling from finite differences

NASA Astrophysics Data System (ADS)

Monserrat, Bartomeu

2018-02-01

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

NASA Astrophysics Data System (ADS)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

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

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

Internal friction and dislocation collective pinning in disordered quenched solid solutions

NASA Astrophysics Data System (ADS)

D'Anna, G.; Benoit, W.; Vinokur, V. M.

1997-12-01

We introduce the collective pinning of dislocations in disordered quenched solid solutions and calculate the macroscopic mechanical response to a small dc or ac applied stress. This work is a generalization of the Granato-Lücke string model, able to describe self-consistently short and long range dislocation motion. Under dc applied stress the long distance dislocation creep has at the microscopic level avalanche features, which result in a macroscopic nonlinear "glassy" velocity-stress characteristic. Under ac conditions the model predicts, in addition to the anelastic internal friction relaxation in the high frequency regime, a linear internal friction background which remains amplitude-independent down to a crossover frequency to a strongly nonlinear internal friction regime.

Small subsidence of the 660-km discontinuity beneath Japan probed by ScS reverberations

NASA Astrophysics Data System (ADS)

Kato, Mamoru; Misawa, Mika; Kawakatsu, Hitoshi

We investigate layering structure in the mantle beneath Japan using ScS reverberation waveforms of two recent large deep events in the northwest Pacific. We estimate regional variation of the elastic and anelastic structure of the mantle as well as properties of the major velocity discontinuities by modeling broadband seismograms recorded at two dense networks, J-Array and FREESIA. The 660-km discontinuity is the deepest in the region where the stagnant subducting slab in the transition zone is tomographically imaged, but the subsidence is of ∼10 km, much smaller than previous estimates with SS precursors. No significant elevation is detected for the 410-km discontinuity.

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

NASA Technical Reports Server (NTRS)

Stouffer, D. C.; Sheh, M. Y.

1988-01-01

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

A Numerical Model for Predicting Shoreline Changes.

DTIC Science & Technology

1980-07-01

minimal shorelines for finite - difference scheme of time lAt (B) . . . 27 11 Transport function Q(ao) = cos ao sin za o for selected values of z . 28 12...generate the preceding examples was based on the use of implicit finite differences . Such schemes, whether implicit or ex- plicit (or both), are...10(A) shows an initially straight shoreline. In any finite - difference scheme, after one time increment At, the shoreline is bounded below by the solid

Experimental Investigation of Hydrodynamic Self-Acting Gas Bearings at High Knudsen Numbers.

DTIC Science & Technology

1980-07-01

Reynolds equation. Two finite - difference algorithms were used to solve the equation. Numerical results - the predicted load and pitch angle - from the two...that should be used. The majority of the numerical solution are still based on the finite difference approximation of the governing equation. But in... finite difference method. Reddi and Chu [26) also noted that it is very difficult to compare the two techniques on the same level since the solution

Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids

DTIC Science & Technology

2006-12-01

theory for charged vacancy diffusion in elastic dielectric materials is formulated and implemented numerically in a finite difference code. The...one of the co-authors on neutral vacancy kinetics (Grinfeld and Hazzledine, 1997). The theory is implemented numerically in a finite difference code...accuracy of order ( )2x∆ , using a finite difference approximation (Hoffman, 1992) for the second spatial derivative of φ : ( )21 1 0ˆ2 /i i i i Rxφ

Impacts of Ocean Waves on the Atmospheric Surface Layer: Simulations and Observations

DTIC Science & Technology

2008-06-06

energy and pressure described in § 4 are solved using a mixed finite - difference pseudospectral scheme with a third-order Runge-Kutta time stepping with a...to that in our DNS code (Sullivan and McWilliams 2002; Sullivan et al. 2000). For our mixed finite - difference pseudospec- tral differencing scheme a...Poisson equation. The spatial discretization is pseu- dospectral along lines of constant or and second- order finite difference in the vertical

A Calculation Method for Convective Heat and Mass Transfer in Multiply-Slotted Film-Cooling Applications.

DTIC Science & Technology

1980-01-01

Transport of Heat ..... .......... 8 3. THE SOLUTION PROCEDURE ..... .. ................. 8 3.1 The Finite-Difference Grid Network ... .......... 8 3.2...The Finite-Difference Grid Network. Figure 4: The Iterative Solution Procedure used at each Streamwise Station. Figure 5: Velocity Profiles in the...the finite-difference grid in the y-direction. I is the mixing length. L is the distance in the x-direction from the injection slot entrance to the

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

NASA Astrophysics Data System (ADS)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI <0 and μI >0 in the phase diagram, and different values for the charged pion mass (or decay constant) and neutral pion mass (or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses. Supported by National Natural Science Foundation of China (11175088, 11475085, 11535005, 11690030) and the Fundamental Research Funds for the Central Universities (020414380074)

Seismic structure of the European upper mantle based on adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, Hejun; Bozdağ, Ebru; Tromp, Jeroen

2015-04-01

We use adjoint tomography to iteratively determine seismic models of the crust and upper mantle beneath the European continent and the North Atlantic Ocean. Three-component seismograms from 190 earthquakes recorded by 745 seismographic stations are employed in the inversion. Crustal model EPcrust combined with mantle model S362ANI comprise the 3-D starting model, EU00. Before the structural inversion, earthquake source parameters, for example, centroid moment tensors and locations, are reinverted based on global 3-D Green's functions and Fréchet derivatives. This study consists of three stages. In stage one, frequency-dependent phase differences between observed and simulated seismograms are used to constrain radially anisotropic wave speed variations. In stage two, frequency-dependent phase and amplitude measurements are combined to simultaneously constrain elastic wave speeds and anelastic attenuation. In these two stages, long-period surface waves and short-period body waves are combined to simultaneously constrain shallow and deep structures. In stage three, frequency-dependent phase and amplitude anomalies of three-component surface waves are used to simultaneously constrain radial and azimuthal anisotropy. After this three-stage inversion, we obtain a new seismic model of the European curst and upper mantle, named EU60. Improvements in misfits and histograms in both phase and amplitude help us to validate this three-stage inversion strategy. Long-wavelength elastic wave speed variations in model EU60 compare favourably with previous body- and surface wave tomographic models. Some hitherto unidentified features, such as the Adria microplate, naturally emerge from the smooth starting model. Subducting slabs, slab detachments, ancient suture zones, continental rifts and backarc basins are well resolved in model EU60. We find an anticorrelation between shear wave speed and anelastic attenuation at depths < 100 km. At greater depths, this anticorrelation becomes relatively weak, in agreement with previous global attenuation studies. Furthermore, enhanced attenuation is observed within the mantle transition zone beneath the North Atlantic Ocean. Consistent with typical radial anisotropy in 1-D reference models, the European continent is dominated by features with a radially anisotropic parameter ξ > 1, indicating predominantly horizontal flow within the upper mantle. In addition, subduction zones, such as the Apennines and Hellenic arcs, are characterized by vertical flow with ξ < 1 at depths greater than 150 km. We find that the direction of the fast anisotropic axis is closely tied to the tectonic evolution of the region. Averaged radial peak-to-peak anisotropic strength profiles identify distinct brittle-ductile deformation in lithospheric strength beneath oceans and continents. Finally, we use the `point-spread function' to assess image quality and analyse trade-offs between different model parameters.

Convergence of finite difference transient response computations for thin shells.

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Geers, T. L.

1973-01-01

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Analysis of transient, linear wave propagation in shells by the finite difference method

NASA Technical Reports Server (NTRS)

Geers, T. L.; Sobel, L. H.

1971-01-01

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

Coordinated Research Program in Pulsed Power Physics.

DTIC Science & Technology

1981-12-01

Ref. C11, this problem may be elimi- nated by factoring the tridiagonal , 2nd order, finite difference equation, Eq. (1), into two ist order finite ...13)Ti,o where 1h 2 /2 h2 = 2 - g + / -h g (1- - g) (14) 1+ h This solution to the finite difference equations consists of expo- nentially growing...December 1, 1981fl j,/,,- //,CJ’ .* ., .) - 13. NUMBEROF PAGES - A.)6 2 /’ij250 14. MONITORING AGENCY NAME & ADDRESS(iI different from Controlling

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

Preston, Leiph

Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

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.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Order of accuracy of QUICK and related convection-diffusion schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

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.

Mars’ Low Dissipation Factor at 11-h - Interpretation from Anelasticity-Based Dissipation Model

NASA Astrophysics Data System (ADS)

Castillo-Rogez, Julie; Choukroun, M.

2010-10-01

We explore the information contained in the ratio of the tidal Love number k2 to the dissipation factor Q characterizing the response of Mars to the tides exerted by its satellite Phobos (11-h period). Assuming that Mars can be approximated as a Maxwell body, Bills et al. [1] have inferred an average viscosity of the Martian mantle 8.7x1014 Pa s. Such a low viscosity appears inconsistent with Mars’ thermal evolution and current heat budget models. Alternative explanations include the presence of partial melt in the mantle [2], or the presence of an aquifer in the crust [3]. We revisit the interpretation of Mars’ k2/Q using a laboratory-based attenuation model that accounts for material viscoelasticity and anelasticity. As a first step, we have computed Mars’ k2/Q for an interior model that includes a solid inner core, a liquid core layer, a mantle, and crust (consistent with the observed moment of inertia, and k2 measured at the orbital period), and searched for the range of mantle viscosities that can explain the observed k2/Q. Successful models are characterized by an average mantle viscosity between 1018 and 1022 Pa s, which rules out the presence of partial melt in the mantle. We can narrow down that range by performing a more detailed calculation of the mineralogy and temperature profiles. Preliminary results will be presented at the meeting. References: [1] Bills et al. (2005) JGR 110, E00704; [2] Ruedas et al. (2009 White paper to the NRC Planetary Science decadal survey; [3] Bills et al. (2009) LPS 40, 1712. MC is supported by a NASA Postdoctoral Program Fellowship, administered by Oak Ridge Associated Universities. This work has been conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract to NASA. Government sponsorship acknowledged.

Contributions of phase and structural transformations in multicomponent Al-Mg alloys to the linear and nonlinear mechanisms of anelasticity

NASA Astrophysics Data System (ADS)

Golovin, I. S.; Bychkov, A. S.; Mikhailovskaya, A. V.; Dobatkin, S. V.

2014-02-01

The effects of the processes of severe plastic deformation (SPD), recrystallization, and precipitation of the β phase in multicomponent alloys of the Al-5Mg-Mn-Cr and Al-(4-5%)Mg-Mn-Zn-Sc systems on the mechanisms of grain-boundary relaxation and dislocation-induced microplasticity have been studied in some detail. To stabilize the ultrafine-grained structure and prevent grain growth, dispersed Al-transition-metal particles, such as Al3Zr, Al6Mn, Al7Cr, Al6(Mn,Cr), Al18Cr2Mg3 have been used. We have special interest in alloys with additions of scandium, which forms compounds of the Al3Sc type and favors the precipitation of finer particles compared to the aluminides of other transition metals. After SPD, Al-(4-5%)Mg-Mn-Zr-Sc alloys exhibit an enhanced recrystallization temperature. The general features of the dislocation and grain-boundary anelasticity that have been established for the binary Al-Mg alloys are retained; i.e., (1) the decrease in the dislocation density in the process of recrystallization of cold-worked alloys leads to the formation of a pseudo-peak in the curves of the temperature dependences of internal friction (TDIF) and to a decrease in the critical amplitude of deformation corresponding to the onset of dislocation motion in a stress field; (2) the precipitation of the β phase suppresses the grain-boundary relaxation; (3) the dissolution of the β phase, the passage of the magnesium atoms into the solid solution, and the precipitation of the β' phase upon heating hinder the motion of dislocations; (4) the coarsening of the highly dispersed particles containing Zr and Sc increases the dislocation mobility. The grain-boundary relaxation and dislocation-impurity interaction and their temperature dependences, as well as processes of the additional alloying of the binary alloys by Mn, Cr, Zr, and Sc, have been estimated quantitatively.

Research on Earth's rotation and the effect of atmospheric pressure on vertical deformation and sea level variability

NASA Technical Reports Server (NTRS)

Wahr, John

1993-01-01

The work done under NASA grant NAG5-485 included modelling the deformation of the earth caused by variations in atmospheric pressure. The amount of deformation near coasts is sensitive to the nature of the oceanic response to the pressure. The PSMSL (Permanent Service for Mean Sea Level) data suggest the response is inverted barometer at periods greater than a couple months. Green's functions were constructed to describe the perturbation of the geoid caused by atmospheric and oceanic loading and by the accompanying load-induced deformation. It was found that perturbation of up to 2 cm are possible. Ice mass balance data was used for continental glaciers to look at the glacial contributions to time-dependent changes in polar motion, the lod, the earth's gravitational field, the position of the earth's center-of-mass, and global sea level. It was found that there can be lateral, non-hydrostatic structure inside the fluid core caused by gravitational forcing from the mantle, from the inner core, or from topography at the core/mantle or inner core/outer core boundaries. The nutational and tidal response of a non-hydrostatic earth with a solid inner core was modeled. Monthly, global tide gauge data from PSMSL was used to look at the 18.6-year ocean tide, the 14-month pole tide, the oceanic response to pressure, the linear trend and inter-annual variability in the earth's gravity field, the global sea level rise, and the effects of post glacial rebound. The effects of mantle anelasticity on nutations, earth tides, and tidal variation in the lod was modeled. Results of this model can be used with Crustal Dynamics observations to look at the anelastic dissipation and dispersion at tidal periods. The effects of surface topography on various components of crustal deformation was also modeled, and numerical models were developed of post glacial rebound.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Time-domain finite-difference based analysis of induced crosstalk in multiwall carbon nanotube interconnects

NASA Astrophysics Data System (ADS)

Kumar, Amit; Nehra, Vikas; Kaushik, Brajesh Kumar

2017-08-01

Graphene rolled-up cylindrical sheets i.e. carbon nanotubes (CNTs) is one of the finest and emerging research area. This paper presents the investigation of induced crosstalk in coupled on-chip multiwalled carbon nanotube (MWCNT) interconnects using finite-difference analysis (FDA) in time-domain i.e. the finite-difference time-domain (FDTD) method. The exceptional properties of versatile MWCNTs profess their candidacy to replace conventional on-chip copper interconnects. Time delay and crosstalk noise have been evaluated for coupled on-chip MWCNT interconnects. With a decrease in CNT length, the obtained results for an MWCNT shows that transmission performance improves as the number of shells increases. It has been observed that the obtained results using the finite-difference time domain (FDTD) technique shows a very close match with the HSPICE simulated results.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Biomechanical Evaluation of Different Fixation Methods for Mandibular Anterior Segmental Osteotomy Using Finite Element Analysis, Part Two: Superior Repositioning Surgery With Bone Allograft.

PubMed

Kilinç, Yeliz; Erkmen, Erkan; Kurt, Ahmet

2016-01-01

In this study, the biomechanical behavior of different fixation methods used to fix the mandibular anterior segment following various amounts of superior repositioning was evaluated by using Finite Element Analysis (FEA). The three-dimensional finite element models representing 3 and 5 mm superior repositioning were generated. The gap in between segments was assumed to be filled by block bone allograft and resignated to be in perfect contact with the mandible and segmented bone. Six different finite element models with 2 distinct mobilization rate including 3 different fixation configurations, double right L (DRL), double left L (DLL), or double I (DI) miniplates with monocortical screws, correspondingly were created. A comparative evaluation has been made under vertical, horizontal and oblique loads. The von Mises and principal maximum stress (Pmax) values were calculated by finite element solver programme. The first part of our ongoing Finite Element Analysis research has been addressed to the mechanical behavior of the same fixation configurations in nongrafted models. In comparison with the findings of the first part of the study, it was concluded that bone graft offers superior mechanical stability without any limitation of mobilization and less stress on the fixative appliances as well as in the bone.

Effects of Verb Familiarity on Finiteness Marking in Children With Specific Language Impairment

PubMed Central

Rice, Mabel L.; Bontempo, Daniel E.

2015-01-01

Purpose Children with specific language impairment (SLI) have known deficits in the verb lexicon and finiteness marking. This study investigated a potential relationship between these 2 variables in children with SLI and 2 control groups considering predictions from 2 different theoretical perspectives, morphosyntactic versus morphophonological. Method Children with SLI, age-equivalent, and language-equivalent (LE) control children (n = 59) completed an experimental sentence imitation task that generated estimates of children's finiteness accuracy under 2 levels of verb familiarity—familiar real verbs versus unfamiliar real verbs—in clausal sites marked for finiteness. Imitations were coded and analyzed for overall accuracy as well as finiteness marking and verb root imitation accuracy. Results Statistical comparisons revealed that children with SLI did not differ from LE children and were less accurate than age-equivalent children on all dependent variables: overall imitation, finiteness marking imitation, and verb root imitation accuracy. A significant Group × Condition interaction for finiteness marking revealed lower levels of accuracy on unfamiliar verbs for the SLI and LE groups only. Conclusions Findings indicate a relationship between verb familiarity and finiteness marking in children with SLI and younger controls and help clarify the roles of morphosyntax, verb lexicon, and morphophonology. PMID:25611349

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.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach

PubMed Central

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-01-01

Using first principles calculations based on density functional theory and a coupled finite-fields/finite-differences approach, we study the dielectric properties, phonon dispersions and Raman spectra of ZnO, a material whose internal polarization fields require special treatment to correctly reproduce the ground state electronic structure and the coupling with external fields. Our results are in excellent agreement with existing experimental measurements and provide an essential reference for the characterization of crystallinity, composition, piezo- and thermo-electricity of the plethora of ZnO-derived nanostructured materials used in optoelectronics and sensor devices. PMID:24141391

A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2002-01-01

A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

NASA Technical Reports Server (NTRS)

Svard, Magnus; Gong, Jing; Nordstrom, Jan

2006-01-01

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Ground Motion Prediction Equations for the Central and Eastern United States

NASA Astrophysics Data System (ADS)

Seber, D.; Graizer, V.

2015-12-01

New ground motion prediction equations (GMPE) G15 model for the Central and Eastern United States (CEUS) is presented. It is based on the modular filter based approach developed by Graizer and Kalkan (2007, 2009) for active tectonic environment in the Western US (WUS). The G15 model is based on the NGA-East database for the horizontal peak ground acceleration and 5%-damped pseudo spectral acceleration RotD50 component (Goulet et al., 2014). In contrast to active tectonic environment the database for the CEUS is not sufficient for creating purely empirical GMPE covering the range of magnitudes and distances required for seismic hazard assessments. Recordings in NGA-East database are sparse and cover mostly range of M<6.0 with limited amount of near-fault recordings. The functional forms of the G15 GMPEs are derived from filters—each filter represents a particular physical phenomenon affecting the seismic wave radiation from the source. Main changes in the functional forms for the CEUS relative to the WUS model (Graizer and Kalkan, 2015) are a shift of maximum frequency of the acceleration response spectrum toward higher frequencies and an increase in the response spectrum amplitudes at high frequencies. Developed site correction is based on multiple runs of representative VS30 profiles through SHAKE-type equivalent-linear programs using time histories and random vibration theory approaches. Site amplification functions are calculated for different VS30 relative to hard rock definition used in nuclear industry (Vs=2800 m/s). The number of model predictors is limited to a few measurable parameters: moment magnitude M, closest distance to fault rupture plane R, average shear-wave velocity in the upper 30 m of the geological profile VS30, and anelastic attenuation factor Q0. Incorporating anelastic attenuation Q0 as an input parameter allows adjustments based on the regional crustal properties. The model covers the range of magnitudes 4.010 Hz) and is within the range of other models for frequencies lower than 2.5 Hz

New Model for Europa's Tidal Response Based after Laboratory Measurements

NASA Astrophysics Data System (ADS)

Castillo, J. C.; McCarthy, C.; Choukroun, M.; Rambaux, N.

2009-12-01

We explore the application of the Andrade model to the modeling of Europa’s tidal response at the orbital period and for different librations. Previous models have generally assumed that the satellite behaves as a Maxwell body. However, at the frequencies exciting Europa’s tides and librations, material anelasticity tends to dominate the satellite’s response for a wide range of temperatures, a feature that is not accounted for by the Maxwell model. Many experimental studies on the anelasticity of rocks, ice, and hydrates, suggest that the Andrade model usually provides a good fit to the dissipation spectra obtained for a wide range of frequencies, encompassing the tidal frequencies of most icy satellites. These data indicate that, at Europa’s orbital frequency, the Maxwell model overestimates water ice attenuation at temperature warmer than ~240 K, while it tends to significantly underestimate it at lower temperatures. Based on the available data we suggest an educated extrapolation of available data to Europa’s conditions. We compute the tidal response of a model of Europa differentiated in a rocky core and a water-rich shell. We assume various degrees of stratification of the core involving hydrated and anhydrous silicates, as well as an iron core. The water-rich shell of Europa is assumed to be fully frozen, or to have preserved a deep liquid layer. In both cases we consider a range of thermal structures, based on existing models. These structures take into account the presence of non-ice materials, especially hydrated salts. This new approach yields a greater tidal response (amplitude and phase lag) than previously expected. This is due to the fact that a greater volume of material dissipates tidal energy in comparison to models assuming a Maxwell body. Another feature of interest is that the tidal stress expected in Europa is at about the threshold between a linear and non-linear mechanical response of water ice as a function of stress. Increased stress at a time when Europa’s eccentricity was greater than its current value is likely to have resulted in significant dissipation increase. We will assess how this new approach affects our understanding of Europa, and we will quantify the tidal response of this satellite and the amount of tidal heating available to its evolution. Acknowledgements: Part of this work has been conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Government sponsorship acknowledged. Part of the experimental work was conducted at Brown University, funded by NASA. MC is supported by a NASA Postdoctoral Fellowship, administered by Oak Ridge Associated Universities.

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

The basic reproductive number, R0, is one of the most important epidemiological quantities. R0 provides a threshold for elimination and determines when a disease can spread or when a disease will die out. Classically, R0 is calculated assuming an infinite population of identical hosts. Previous work has shown that heterogeneity in the host mixing rate increases R0 in an infinite population. However, it has been suggested that in a finite population, heterogeneity in the mixing rate may actually decrease the finite-population reproductive numbers. Here, we outline a framework for discussing different types of heterogeneity in disease parameters, and how these affect disease spread and control. We calculate "finite-population reproductive numbers" with different types of heterogeneity, and show that in a finite population, heterogeneity has complicated effects on the reproductive number. We find that simple heterogeneity decreases the finite-population reproductive number, whereas heterogeneity in the intrinsic mixing rate (which affects both infectiousness and susceptibility) increases the finite-population reproductive number when R0 is small relative to the size of the population and decreases the finite-population reproductive number when R0 is large relative to the size of the population. Although heterogeneity has complicated effects on the finite-population reproductive numbers, its implications for control are straightforward: when R0 is large relative to the size of the population, heterogeneity decreases the finite-population reproductive numbers, making disease control or elimination easier than predicted by R0. Copyright © 2016 Elsevier Ltd. All rights reserved.

Viscoelastic love-type surface waves

USGS Publications Warehouse

Borcherdt, Roger D.

2008-01-01

The general theoretical solution for Love-Type surface waves in viscoelastic media provides theoreticalexpressions for the physical characteristics of the waves in elastic as well as anelastic media with arbitraryamounts of intrinsic damping. The general solution yields dispersion and absorption-coefficient curves for the waves as a function of frequency and theamount of intrinsic damping for any chosen viscoelastic model.Numerical results valid for a variety of viscoelastic models provide quantitative estimates of the physicalcharacteristics of the waves pertinent to models of Earth materials ranging from small amounts of damping in the Earth’s crust to moderate and large amounts of damping in soft soils and water-saturated sediments. Numerical results, presented herein, are valid for a wide range of solids and applications.

Tools for Modeling & Simulation of Molecular and Nanoelectronics Devices

DTIC Science & Technology

2012-06-14

implemented a prototype DFT simulation software using two different open source Finite Element (FE) libraries: DEALII and FENICS . These two libraries have been...ATK. In the first part of this Phase I project we investigated two different candidate finite element libraries, DEAL II and FENICS . Although both...element libraries, Deal.II and FEniCS /dolfin, for use as back-ends to a finite element DFT in ATK, Quantum Insight and QuantumWise A/S, October 2011.

Applications of discrete element method in modeling of grain postharvest operations

USDA-ARS?s Scientific Manuscript database

Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Finite Difference Schemes as Algebraic Correspondences between Layers

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1989-01-01

A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

NASA Technical Reports Server (NTRS)

Strong, Stuart L.; Meade, Andrew J., Jr.

1992-01-01

Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

NASA Astrophysics Data System (ADS)

Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, Vítor R.; Viyuela, Oscar

2018-03-01

We study finite-temperature dynamical quantum phase transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt echo (LE) induced metrics. We analyze the associated dynamical susceptibilities (Riemannian metrics), and derive analytic expressions for the case of two-band Hamiltonians. At zero temperature, the two quantities are identical, nevertheless, at finite temperatures they behave very differently. Using the fidelity LE, the zero-temperature DQPTs are gradually washed away with temperature, while the interferometric counterpart exhibits finite-temperature phase transitions. We analyze the physical differences between the two finite-temperature LE generalizations, and argue that, while the interferometric one is more sensitive and can therefore provide more information when applied to genuine quantum (microscopic) systems, when analyzing many-body macroscopic systems, the fidelity-based counterpart is a more suitable quantity to study. Finally, we apply the previous results to two representative models of topological insulators in one and two dimensions.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone.

PubMed

Vafaeian, B; El-Rich, M; El-Bialy, T; Adeeb, S

2014-08-01

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone. Copyright © 2014 Elsevier B.V. All rights reserved.

The State-of-the-Art Parabolic Equation Approximation as Applied to Underwater Acoustic Propagation with Discussions on Intensive Computations: An Invited Paper Presented at the Meeting of the Acoustical Society of America (108th) Held in Minneapolis, Minnesota on 8-12 October 1984

DTIC Science & Technology

1984-10-12

MCYwWWm M& de4 l 8.id iW d by N1wk "wt Finite Difference Reference Wavenumber Interface Split-Step Ordinary Difference Equation Wide Angle Parabolic...Problems D. Lee and S. Praiser J. Comp. & Math. with Appls., 7(2), pp. 195-202 (1981) Finite - Difference Solution to the Parabolic Wave Equation D. Lee, G...was incorporated into the ODE and finite difference models. At that time, we did not have a better implementation of the ODE solution, but we

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

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.

APPLICATION OF A FINITE-DIFFERENCE TECHNIQUE TO THE HUMAN RADIOFREQUENCY DOSIMETRY PROBLEM

EPA Science Inventory

A powerful finite difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method of moments approach in that its implementation requires much less computer memory. Consequently, it has the ca...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell. [for experimental atmospheric simulation

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

NASA Astrophysics Data System (ADS)

Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun

2008-07-01

Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Experimental validation of finite element modelling of a modular metal-on-polyethylene total hip replacement.

PubMed

Hua, Xijin; Wang, Ling; Al-Hajjar, Mazen; Jin, Zhongmin; Wilcox, Ruth K; Fisher, John

2014-07-01

Finite element models are becoming increasingly useful tools to conduct parametric analysis, design optimisation and pre-clinical testing for hip joint replacements. However, the verification of the finite element model is critically important. The purposes of this study were to develop a three-dimensional anatomic finite element model for a modular metal-on-polyethylene total hip replacement for predicting its contact mechanics and to conduct experimental validation for a simple finite element model which was simplified from the anatomic finite element model. An anatomic modular metal-on-polyethylene total hip replacement model (anatomic model) was first developed and then simplified with reasonable accuracy to a simple modular total hip replacement model (simplified model) for validation. The contact areas on the articulating surface of three polyethylene liners of modular metal-on-polyethylene total hip replacement bearings with different clearances were measured experimentally in the Leeds ProSim hip joint simulator under a series of loading conditions and different cup inclination angles. The contact areas predicted from the simplified model were then compared with that measured experimentally under the same conditions. The results showed that the simplification made for the anatomic model did not change the predictions of contact mechanics of the modular metal-on-polyethylene total hip replacement substantially (less than 12% for contact stresses and contact areas). Good agreements of contact areas between the finite element predictions from the simplified model and experimental measurements were obtained, with maximum difference of 14% across all conditions considered. This indicated that the simplification and assumptions made in the anatomic model were reasonable and the finite element predictions from the simplified model were valid. © IMechE 2014.

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

ERIC Educational Resources Information Center

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Finite micro-tab system for load control on a wind turbine

NASA Astrophysics Data System (ADS)

Bach, A. B.; Lennie, M.; Pechlivanoglou, G.; Nayeri, C. N.; Paschereit, C. O.

2014-06-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio.

The effectiveness of element downsizing on a three-dimensional finite element model of bone trabeculae in implant biomechanics.

PubMed

Sato, Y; Wadamoto, M; Tsuga, K; Teixeira, E R

1999-04-01

More validity of finite element analysis in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To investigate the effectiveness of element downsizing on the construction of a three-dimensional finite element bone trabeculae model, with different element sizes (600, 300, 150 and 75 microm) models were constructed and stress induced by vertical 10 N loading was analysed. The difference in von Mises stress values between the models with 600 and 300 microm element sizes was larger than that between 300 and 150 microm. On the other hand, no clear difference of stress values was detected among the models with 300, 150 and 75 microm element sizes. Downsizing of elements from 600 to 300 microm is suggested to be effective in the construction of a three-dimensional finite element bone trabeculae model for possible saving of computer memory and calculation time in the laboratory.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Relaxation of bending stresses and the reversibility of residual stresses in amorphous soft magnetic alloys

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

Kekalo, I. B.; Mogil’nikov, P. S., E-mail: pavel-mog@mail.ru

2015-06-15

The reversibility of residual bending stresses is revealed in ribbon samples of cobalt- and iron-based amorphous alloys Co{sub 69}Fe{sub 3.7}Cr{sub 3.8}Si{sub 12.5}B{sub 11} and Fe{sub 57}Co{sub 31}Si{sub 2.9}B{sub 9.1}: the ribbons that are free of applied stresses and bent under the action of residual stresses become completely or incompletely straight upon annealing at the initial temperatures. The influence of annealing on the relaxation of bending stresses is studied. Preliminary annealing is found to sharply decrease the relaxation rate of bending stresses, and the initial stage of fast relaxation of these stresses is absent. Complete straightening of preliminarily annealed ribbons ismore » shown to occur at significantly higher temperatures than that of the initial ribbons. Incomplete straightening of the ribbons is explained by the fact that bending stresses relaxation at high annealing temperatures proceeds due to both reversible anelastic deformation and viscous flow, which is a fully irreversible process. Incomplete reversibility is also caused by irreversible processes, such as the release of excess free volume and clustering (detected by small-angle X-ray scattering). The revealed differences in the relaxation processes that occur in the cobalt- and iron-based amorphous alloys are discussed in terms of different atomic diffusion mobilities in these alloys.« less

A guide to differences between stochastic point-source and stochastic finite-fault simulations

USGS Publications Warehouse

Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.

2009-01-01

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control observed ground motions.

THE PSTD ALGORITHM: A TIME-DOMAIN METHOD REQUIRING ONLY TWO CELLS PER WAVELENGTH. (R825225)

EPA Science Inventory

A pseudospectral time-domain (PSTD) method is developed for solutions of Maxwell's equations. It uses the fast Fourier transform (FFT), instead of finite differences on conventional finite-difference-time-domain (FDTD) methods, to represent spatial derivatives. Because the Fourie...

FINITE-DIFFERENCE ELECTROMAGNETIC DEPOSITION/THERMOREGULATORY MODEL: COMPARISON BETWEEN THEORY AND MEASUREMENTS (JOURNAL VERSION)

EPA Science Inventory

The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1983-01-01

An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.

A fast finite-difference algorithm for topology optimization of permanent magnets

NASA Astrophysics Data System (ADS)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Benchmark model correction of monitoring system based on Dynamic Load Test of Bridge

NASA Astrophysics Data System (ADS)

Shi, Jing-xian; Fan, Jiang

2018-03-01

Structural health monitoring (SHM) is a field of research in the area, and it’s designed to achieve bridge safety and reliability assessment, which needs to be carried out on the basis of the accurate simulation of the finite element model. Bridge finite element model is simplified of the structural section form, support conditions, material properties and boundary condition, which is based on the design and construction drawings, and it gets the calculation models and the results.But according to the design and specification requirements established finite element model due to its cannot fully reflect the true state of the bridge, so need to modify the finite element model to obtain the more accurate finite element model. Based on Da-guan river crossing of Ma - Zhao highway in Yunnan province as the background to do the dynamic load test test, we find that the impact coefficient of the theoretical model of the bridge is very different from the coefficient of the actual test, and the change is different; according to the actual situation, the calculation model is adjusted to get the correct frequency of the bridge, the revised impact coefficient found that the modified finite element model is closer to the real state, and provides the basis for the correction of the finite model.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Dynamic Modulus and Damping of Boron, Silicon Carbide, and Alumina Fibers

NASA Technical Reports Server (NTRS)

Dicarlo, J. A.; Williams, W.

1980-01-01

The dynamic modulus and damping capacity for boron, silicon carbide, and silicon carbide coated boron fibers were measured from-190 to 800 C. The single fiber vibration test also allowed measurement of transverse thermal conductivity for the silicon carbide fibers. Temperature dependent damping capacity data for alumina fibers were calculated from axial damping results for alumina-aluminum composites. The dynamics fiber data indicate essentially elastic behavior for both the silicon carbide and alumina fibers. In contrast, the boron based fibers are strongly anelastic, displaying frequency dependent moduli and very high microstructural damping. Ths single fiber damping results were compared with composite damping data in order to investigate the practical and basic effects of employing the four fiber types as reinforcement for aluminum and titanium matrices.

A compact finite element method for elastic bodies

NASA Technical Reports Server (NTRS)

Rose, M. E.

1984-01-01

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

Ablative Thermal Response Analysis Using the Finite Element Method

NASA Technical Reports Server (NTRS)

Dec John A.; Braun, Robert D.

2009-01-01

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

Stress-intensity factors for small surface and corner cracks in plates

NASA Technical Reports Server (NTRS)

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

1988-01-01

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

A three-dimensional thermal finite element analysis of AISI 304 stainless steel and copper dissimilar weldment

NASA Astrophysics Data System (ADS)

Singh, Gurdeep; Saxena, Ravindra K.; Pandey, Sunil

2018-04-01

The aim of this study to developed a 3-D thermal finite element model for dissimilar material welding of AISI-304 stainless steel and copper. Welding of similar material is widely studied using experimental and numerical methods but the problem becomes trivial for the welding of dissimilar materials especially in ferrous and nonferrous materials. Finite element analysis of dissimilar material welding is a cost-effective method for the understanding and analysis of the process. The finite element analysis has been performed to predict the heat affected zone and temperature distribution in AISI-304 stainless steel and copper dissimilar weldment using MSC Marc 2017®. Due to the difference in physical properties of these materials the behavior of heat affected zone and temperature distribution are perceived to be different. To verify the accuracy of the thermal finite element model, the welding process was simulated with butt-welded joints having same dimensions and parameters from Attarha and Far [1]. It is found from the study that the heat affected zone is larger in copper weld pads than in AISI 304 stainless steel due to large difference in thermal conductivity of these two weld pads.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

A method for modeling finite-core vortices in wake-flow calculations

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.

OpenSeesPy: Python library for the OpenSees finite element framework

NASA Astrophysics Data System (ADS)

Zhu, Minjie; McKenna, Frank; Scott, Michael H.

2018-01-01

OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. The framework allows users to perform finite element analysis with a scripting language and for developers to create both serial and parallel finite element computer applications as interpreters. For the last 15 years, Tcl has been the primary scripting language to which the model building and analysis modules of OpenSees are linked. To provide users with different scripting language options, particularly Python, the OpenSees interpreter interface was refactored to provide multi-interpreter capabilities. This refactoring, resulting in the creation of OpenSeesPy as a Python module, is accomplished through an abstract interface for interpreter calls with concrete implementations for different scripting languages. Through this approach, users are able to develop applications that utilize the unique features of several scripting languages while taking advantage of advanced finite element analysis models and algorithms.

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

NASA Technical Reports Server (NTRS)

Butler, T. D.; Weatherill, W. H.; Sebastian, J. D.; Ehlers, F. E.

1977-01-01

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Geological and geodynamic investigations of Alaskan tectonics: Responses in the ancient and modern geologic records to oblique plate convergence

NASA Astrophysics Data System (ADS)

Kalbas, James L.

Stratigraphic, structural, and geophysical modeling studies focusing on both the Mesozoic and modern development of southern Alaska aid in understanding the nature of tectonic responses to oblique plate convergence. Analyses of the Lower to Upper (?) Cretaceous Kahiltna assemblage of the western Alaska Range and the Upper Cretaceous Kuskokwim Group of the northern Kuskokwim Mountains provide a stratigraphic record of orogenic growth in southwestern Alaska. The Kahiltna assemblage records dominantly west-directed gravity-flow transport of sediment to the axis of an obliquely closing basin that made up the suture zone between the allochthonous Wrangellia composite terrane and the North American pericratonic margin. Stratigraphic, compositional, and geochronologic analyses suggest that submarine-fan systems of the Kahiltna basin were fed from the subearial suture zone and contain detrital grains derived from both allochthonous and pericratonic sources, thereby implying a relatively close proximity of the island-arc terrane to the North American margin by late Early Cretaceous time. In contrast, Upper Cretaceous strata exposed immediately west of the Kahiltna assemblage record marine deposition during a period of transition from island arc accretion to strike-slip tectonics. The new stratigraphic model presented here recognizes diverse bathyal- to shelfal-marine depositional systems within the Kuskokwim Group that represent distinctive regional sediment entry points to the basin. Collectively, these strata suggest that the Kuskokwim Group represents the waning stages of marine deposition in a long-lived intra-oceanic and continental margin basin. Geodynamic studies focus on the mechanics of contemporary fault systems in southern Alaska inboard of the collisional Yakutat microplate. Finite-element analyses predict that a poorly understood Holocene strike-slip fault in the St. Elias Mountains transfers shear from the Queen Charlotte fault northward to the Denali fault, thereby forming a continuous transform system that accommodates right-lateral motion of the Pacific plate and Yakutat microplate relative to the stable North American craton. Although the best-fit model implies some component of anelastic deformation in the vicinity of the St. Elias Mountains and the western Alaska Range, results imply overall block-like behavior throughout the area of interest.

Finite Mixture Multilevel Multidimensional Ordinal IRT Models for Large Scale Cross-Cultural Research

ERIC Educational Resources Information Center

de Jong, Martijn G.; Steenkamp, Jan-Benedict E. M.

2010-01-01

We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while…

Computational procedure for finite difference solution of one-dimensional heat conduction problems reduces computer time

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

Computational procedure reduces the numerical effort whenever the method of finite differences is used to solve ablation problems for which the surface recession is large relative to the initial slab thickness. The number of numerical operations required for a given maximum space mesh size is reduced.

Some Finite Difference Solutions of the Laminar Compressible Boundary Layer Showing the Effects of Upstream Transpiration Cooling

NASA Technical Reports Server (NTRS)

Howe, John T.

1959-01-01

Three numerical solutions of the partial differential equations describing the compressible laminar boundary layer are obtained by the finite difference method described in reports by I. Flugge-Lotz, D.C. Baxter, and this author. The solutions apply to steady-state supersonic flow without pressure gradient, over a cold wall and over an adiabatic wall, both having transpiration cooling upstream, and over an adiabatic wall with upstream cooling but without upstream transpiration. It is shown that for a given upstream wall temperature, upstream transpiration cooling affords much better protection to the adiabatic solid wall than does upstream cooling without transpiration. The results of the numerical solutions are compared with those of approximate solutions. The thermal results of the finite difference solution lie between the results of Rubesin and Inouye, and those of Libby and Pallone. When the skin-friction results of one finite difference solution are used in the thermal analysis of Rubesin and Inouye, improved agreement between the thermal results of the two methods of solution is obtained.

A General Formulation for Robust and Efficient Integration of Finite Differences and Phase Unwrapping on Sparse Multidimensional Domains

NASA Astrophysics Data System (ADS)

Costantini, Mario; Malvarosa, Fabio; Minati, Federico

2010-03-01

Phase unwrapping and integration of finite differences are key problems in several technical fields. In SAR interferometry and differential and persistent scatterers interferometry digital elevation models and displacement measurements can be obtained after unambiguously determining the phase values and reconstructing the mean velocities and elevations of the observed targets, which can be performed by integrating differential estimates of these quantities (finite differences between neighboring points).In this paper we propose a general formulation for robust and efficient integration of finite differences and phase unwrapping, which includes standard techniques methods as sub-cases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multi-dimensional information (e.g. multi-temporal, multi-frequency, multi-baseline observations), or external data (e.g. GPS measurements). The proposed approach requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist.The validation tests obtained on real SAR data confirm the validity of the method, which was integrated in our production chain and successfully used also in massive productions.

Elastic critical moment for bisymmetric steel profiles and its sensitivity by the finite difference method

NASA Astrophysics Data System (ADS)

Kamiński, M.; Supeł, Ł.

2016-02-01

It is widely known that lateral-torsional buckling of a member under bending and warping restraints of its cross-sections in the steel structures are crucial for estimation of their safety and durability. Although engineering codes for steel and aluminum structures support the designer with the additional analytical expressions depending even on the boundary conditions and internal forces diagrams, one may apply alternatively the traditional Finite Element or Finite Difference Methods (FEM, FDM) to determine the so-called critical moment representing this phenomenon. The principal purpose of this work is to compare three different ways of determination of critical moment, also in the context of structural sensitivity analysis with respect to the structural element length. Sensitivity gradients are determined by the use of both analytical and the central finite difference scheme here and contrasted also for analytical, FEM as well as FDM approaches. Computational study is provided for the entire family of the steel I- and H - beams available for the practitioners in this area, and is a basis for further stochastic reliability analysis as well as durability prediction including possible corrosion progress.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

High resolution digital elevation modelling from TLS and UAV campaign reveals structural complexity at the 2014/15 Holuhraun eruption site, Iceland

NASA Astrophysics Data System (ADS)

Müller, Daniel; Walter, Thomas R.; Schöpa, Anne; Witt, Tanja; Steinke, Bastian; Gudmundsson, Magnús T.; Dürig, Tobias

2017-07-01

Fissure eruptions are commonly linked to magma dikes at depth, associated with elastic and anelastic surface deformation. Elastic deformation is well described by subsidence above, uplift and lateral widening perpendicular to the dike plane. The anelastic part is associated with the formation of a graben, bordered by graben parallel faults that might express as sets of fractures at the surface. Additionally secondary structures, like push ups, bends and step overs yield information about the deforming domain. The formation of such structures associated with fissure eruptions, however, is barely preserved in nature because of the rapid erosion or sediment coverage. Therefore, simple normal fault displacements are commonly assumed at dikes. At the 2014/2015 Holuhraun eruption sites (Iceland), evidence is increasing that the developing fractures are showing variations in their displacement modes. In an attempt to investigate these variations, a fieldwork mapping project combining Terrestrial Laser Scanning (TLS) and Unmanned Aerial Vehicle (UAV) based aerophoto analysis was realized. From this data, we generated locally high resolution Digital Elevation Models (DEMs) and a structural map that allows for identification of kinematic indicators and assessing particularities of the observed structures. We identified 315 fracture segments from satellite data. For single segments we measured strike directions including the amount of opening and opening angles, indicating that many of the measured fractures show transtensional dislocations. Out of these, 81 % are showing significant left-lateral slip, only 17% right-lateral slip and 2% pure tensile opening. We show that local complexities in the fracture traces and geometries are closely related to variations in the transtensional opening direction. Moreover, we identified local changes in fracture azimuths and offsets close to eruption sites, which we speculate to be associated with geometrical changes in the magma feeder itself. Results highlight that opening of fractures associated with an erupting fissure commonly show transtensional modes having both, left-lateral and right-lateral slip, with important implications for interpreting the expression of surface structures at rift zones elsewhere. Results further highlight the great value of UAV based high resolution data to contribute to the integrity of observations of structural complexities at local geologic events.

Multiscale Simulation of Moist Global Atmospheric Flows

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

Grabowski, Wojciech W.; Smolarkiewicz, P. K.

The overarching goal of this award was to include phase changes of the water substance and accompanying latent heating and precipitation processes into the all-scale nonhydrostatic atmospheric dynamics EUlerian/LAGrangian (EULAG) model. The model includes fluid flow solver that is based on either an unabbreviated set of the governing equations (i.e., compressible dynamics) or a simplified set of equations without sound waves (i.e., sound-proof, either anelastic or pseudo-incompressible). The latter set has been used in small-scale dynamics for decades, but its application to the all-scale dynamics (from small-scale to planetary) has never been studied in practical implementations. The highlight of themore » project is the development of the moist implicit compressible model that can be run by applying time steps, as long as the anelastic model is limited only by the computational stability of the fluid flow and not by the speed of sound waves that limit the stability of explicit compressible models. Applying various versions of the EULAG model within the same numerical framework allows for an unprecedented comparison of solutions obtained with various sets of the governing equations and straightforward evaluation of the impact of various physical parameterizations on the model solutions. The main outcomes of this study are reported in three papers, two published and one currently under review. These papers include comparisons between model solutions for idealized moist problems across the range of scales from small to planetary. These tests include: moist thermals rising in the stable-stratified environment (following Grabowski and Clark, J. Atmos. Sci. 1991) and in the moist-neutral environment (after Bryan and Fritsch, Mon. Wea. Rev. 2002), moist flows over a mesoscale topography (as in Grabowski and Smolarkiewicz, Mon. Wea. Rev. 2002), deep convection in a sheared environment (following Weisman and Klemp, Mon. Wea. Rev. 1982), moist extension of the baroclinic wave on the sphere of Jablonowski and Williamson (Q. J. R. Met. Soc. 2006), and moist extension of the Held-Suarez idealized climate benchmark (Held and Suarez, Bull. Amer. Met. Soc., 1994).« less

Geodynamic modelling of the rift-drift transition: Application to the Red Sea

NASA Astrophysics Data System (ADS)

Fierro, E.; Schettino, A.; Capitanio, F. A.; Ranalli, G.

2017-12-01

The onset of oceanic accretion after a rifting phase is generally accompanied by an initial fast pulse of spreading in the case of volcanic margins, such that the effective spreading rate exceeds the relative far-field velocity between the two plates for a short time interval. This pulse has been attributed to edge-driven convention (EDC), although our numerical modelling shows that the shear stress at the base of the lithosphere cannot exceed 1 MPa. In general, we have developed a 2D numerical model of the mantle instabilities during the rifting phase, in order to determine the geodynamic conditions at the rift-drift transition. The model was tested using Underworld II software, variable rheological parameters, and temperature and stress-dependent viscosity. Our results show an increase of strain rates at the top of the lithosphere with the lithosphere thickness as well as with the initial width of the margin up to 300 km. Beyond this value, the influence of the initial rift width can be neglected. An interesting outcome of the numerical model is the existence of an axial zone characterized by higher strain rates, which is flanked by two low-strain stripes. As a consequence, the model suggests the existence of an area of syn-rift compression within the rift valley. Regarding the post-rift phase, we propose that at the onset of a seafloor spreading, a phase of transient creep allows the release of the strain energy accumulated in the mantle lithosphere during the rifting phase, through anelastic relaxation. Then, the conjugated margins would be subject to post-rift contraction and eventually to tectonic inversion of the rift structures. To explore the tenability of this model, we introduce an anelastic component in the lithosphere rheology, assuming both the classical linear Kelvin-Voigt rheology and a non-linear Kelvin model. The non-linear model predicts viable relaxation times ( 1-2Myrs) to explain the post-rift tectonic inversion observed along the Arabian continental margin and the episodic initial fast seafloor spreading in the central Red Sea, where the role of EDC has been invoked.

The Sensitivity of Joint Inversions of Seismic and Geodynamic Data to Mantle Viscosity

NASA Astrophysics Data System (ADS)

Lu, C.; Grand, S. P.; Forte, A. M.; Simmons, N. A.

2017-12-01

Seismic tomography has mapped the existence of large scale mantle heterogeneities in recent years. However, the origin of these velocity anomalies in terms of chemical and thermal variations is still under debate due to the limitations of tomography. Joint inversion of seismic, geodynamic, and mineral physics observations has proven to be a powerful tool to decouple thermal and chemical effects in the deep mantle (Simmons et al. 2010). The approach initially attempts to find a model that can be explained assuming temperature controls lateral variations in mantle properties and then to consider more complicated lateral variations that account for the presence of chemical heterogeneity to further fit data. The geodynamic observations include Earth's free air gravity field, tectonic plate motions, dynamic topography and the excess ellipticity of the core. The sensitivity of the geodynamic observables to density anomalies, however, depends on an assumed radial mantle viscosity profile. Here we perform joint inversions of seismic and geodynamic data using a number of published viscosity profiles. The goal is to test the sensitivity of joint inversion results to mantle viscosity. For each viscosity model, geodynamic sensitivity kernels are calculated and used to jointly invert the geodynamic observations as well as a new shear wave data set for a model of density and seismic velocity. Also, compared with previous joint inversion studies, two major improvements have been made in our inversion. First, we use a nonlinear inversion to account for anelastic effects. Applying the very fast simulate annealing (VFSA) method, we let the elastic scaling factor and anelastic parameters from mineral physics measurements vary within their possible ranges and find the best fitting model assuming thermal variations are the cause of the heterogeneity. We also include an a priori subducting slab model into the starting model. Thus the geodynamic and seismic signatures of short wavelength subducting slabs are better accounted for in the inversions. Reference: Simmons, N. A., A. M. Forte, L. Boschi, and S. P. Grand (2010), GyPSuM: A joint tomographic model of mantle density and seismic wave speeds, Journal of Geophysical Research: Solid Earth, 115(B12), B12310

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

1976-01-01

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

A mimetic finite difference method for the Stokes problem with elected edge bubbles

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

Lipnikov, K; Berirao, L

2009-01-01

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this articlemore » is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.« less

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.

Broadband ground motion simulation using a paralleled hybrid approach of Frequency Wavenumber and Finite Difference method

NASA Astrophysics Data System (ADS)

Chen, M.; Wei, S.

2016-12-01

The serious damage of Mexico City caused by the 1985 Michoacan earthquake 400 km away indicates that urban areas may be affected by remote earthquakes. To asses earthquake risk of urban areas imposed by distant earthquakes, we developed a hybrid Frequency Wavenumber (FK) and Finite Difference (FD) code implemented with MPI, since the computation of seismic wave propagation from a distant earthquake using a single numerical method (e.g. Finite Difference, Finite Element or Spectral Element) is very expensive. In our approach, we compute the incident wave field (ud) at the boundaries of the excitation box, which surrounding the local structure, using a paralleled FK method (Zhu and Rivera, 2002), and compute the total wave field (u) within the excitation box using a parallelled 2D FD method. We apply perfectly matched layer (PML) absorbing condition to the diffracted wave field (u-ud). Compared to previous Generalized Ray Theory and Finite Difference (Wen and Helmberger, 1998), Frequency Wavenumber and Spectral Element (Tong et al., 2014), and Direct Solution Method and Spectral Element hybrid method (Monteiller et al., 2013), our absorbing boundary condition dramatically suppress the numerical noise. The MPI implementation of our method can greatly speed up the calculation. Besides, our hybrid method also has a potential use in high resolution array imaging similar to Tong et al. (2014).

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

Numerical models of diapiric structures: comparison of the 2D finite deformation field between Rayleigh-Taylor like and down-built like diapirs

NASA Astrophysics Data System (ADS)

Fuchs, Lukas; Schmeling, Harro; Koyi, Hemin

2013-04-01

Magmatic and salt diapirs are common structures in different tectonic regimes. Salt diapirs can act as possible hydrocarbon traps and, moreover, they could be used as repositories for nuclear waste disposal. Understanding the evolution and the dynamics of diapirs as well as their driving mechanisms has fundamental and applied significance. In general, salt diapirs seem to be driven by differential loading of sediments creating an uneven load that drives the salt from high to low pressure areas, e.g. a down-built diapir. Magmatic diapirs, instead, seem to be driven by buoyancy where lighter material rises vertically through a heavier overburden, i.e. a classical Rayleigh-Taylor instability [RTI]. These different driving mechanisms and dynamics strongly govern the internal deformation of the diapirs. In this study, we use a two-dimensional finite difference code (FDCON) in combination with a marker and cell method to calculate the finite deformation within diapiric structures. Thereby, we distinguish between the two different driving mechanisms, i.e. the differential loading and the buoyancy. We calculate the different finite deformation patterns during the evolution of RTI's and down-built diapirs for different viscosity ratios m = -?buoyant- ?overburden. The deformation pattern in the buoyant layer shows similarities for both diapiric structures, like high shear deformation at the bottom, a high finite deformation within the middle of the stem, and an increasing maximum finite deformation for a decreasing m. However, the strain partitioning between the overburden and the source layer is different within down-built diapirs compared to the RTI's, even for down-built diapirs with m = 1. Thus a higher amount of the total strain induced by down-building is concentrated within the buoyant layer. Moreover, in the case of viscosity ratios of m = 0.1 or 1 the sinking overburden units create an internal rotation within the diapiric bulb. This rotation depends indirectly on the sedimentation rate as it determines the width of the sediment basin; the higher the sedimentation rate, the wider the basins and the weaker the internal rotation. In addition, the viscous drag between the sinking overburden and the rising diapir creates a stronger and wider band of finite deformation along the edges of the down-built diapir in comparison to the RTI.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

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

Akhil Datta-Gupta

2006-12-31

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitudemore » more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.« less

The morphological state space revisited: what do phylogenetic patterns in homoplasy tell us about the number of possible character states?

PubMed Central

Hoyal Cuthill, Jennifer F.

2015-01-01

Biological variety and major evolutionary transitions suggest that the space of possible morphologies may have varied among lineages and through time. However, most models of phylogenetic character evolution assume that the potential state space is finite. Here, I explore what the morphological state space might be like, by analysing trends in homoplasy (repeated derivation of the same character state). Analyses of ten published character matrices are compared against computer simulations with different state space models: infinite states, finite states, ordered states and an ‘inertial' model, simulating phylogenetic constraints. Of these, only the infinite states model results in evolution without homoplasy, a prediction which is not generally met by real phylogenies. Many authors have interpreted the ubiquity of homoplasy as evidence that the number of evolutionary alternatives is finite. However, homoplasy is also predicted by phylogenetic constraints on the morphological distance that can be traversed between ancestor and descendent. Phylogenetic rarefaction (sub-sampling) shows that finite and inertial state spaces do produce contrasting trends in the distribution of homoplasy. Two clades show trends characteristic of phylogenetic inertia, with decreasing homoplasy (increasing consistency index) as we sub-sample more distantly related taxa. One clade shows increasing homoplasy, suggesting exhaustion of finite states. Different clades may, therefore, show different patterns of character evolution. However, when parsimony uninformative characters are excluded (which may occur without documentation in cladistic studies), it may no longer be possible to distinguish inertial and finite state spaces. Interestingly, inertial models predict that homoplasy should be clustered among comparatively close relatives (parallel evolution), whereas finite state models do not. If morphological evolution is often inertial in nature, then homoplasy (false homology) may primarily occur between close relatives, perhaps being replaced by functional analogy at higher taxonomic scales. PMID:26640650

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

A Discrete Approach to Computer-Oriented Calculus.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

1979-01-01

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

Effects of Crimped Fiber Paths on Mixed Mode Delamination Behaviors in Woven Fabric Composites

DTIC Science & Technology

2016-09-01

continuum finite - element models. Three variations of a plain-woven fabric architecture—each of which had different crimped fiber paths—were considered... Finite - Element Analysis Fracture Mechanics Fracture Toughness Mixed Modes Strain Energy Release Rate 16. SECURITY...polymer FB Fully balanced laminate FEA Finite - element analysis FTCM Fracture toughness conversion mechanism G Shear modulus GI, GII, GIII Mode

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Transport properties of bilayer graphene due to charged impurity scattering: Temperature-dependent screening and substrate effects

NASA Astrophysics Data System (ADS)

Linh, Dang Khanh; Khanh, Nguyen Quoc

2018-03-01

We calculate the zero-temperature conductivity of bilayer graphene (BLG) impacted by Coulomb impurity scattering using four different screening models: unscreened, Thomas-Fermi (TF), overscreened and random phase approximation (RPA). We also calculate the conductivity and thermal conductance of BLG using TF, zero- and finite-temperature RPA screening functions. We find large differences between the results of the models and show that TF and finite-temperature RPA give similar results for diffusion thermopower Sd. Using the finite-temperature RPA, we calculate temperature and density dependence of Sd in BLG on SiO2, HfO2 substrates and suspended BLG for different values of interlayer distance c and distance between the first layer and the substrate d.

Establishing the 3-D finite element solid model of femurs in partial by volume rendering.

PubMed

Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin

2013-01-01

It remains rare to report three-dimensional (3-D) finite element solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D finite element modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D finite element solid model of femurs in partial by volume rendering. A 3-D finite element model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the finite-element analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D finite element of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D finite element solid model created in partial is more real and fit for finite element analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

The effect of in situ/in vitro three-dimensional quantitative computed tomography image voxel size on the finite element model of human vertebral cancellous bone.

PubMed

Lu, Yongtao; Engelke, Klaus; Glueer, Claus-C; Morlock, Michael M; Huber, Gerd

2014-11-01

Quantitative computed tomography-based finite element modeling technique is a promising clinical tool for the prediction of bone strength. However, quantitative computed tomography-based finite element models were created from image datasets with different image voxel sizes. The aim of this study was to investigate whether there is an influence of image voxel size on the finite element models. In all 12 thoracolumbar vertebrae were scanned prior to autopsy (in situ) using two different quantitative computed tomography scan protocols, which resulted in image datasets with two different voxel sizes (0.29 × 0.29 × 1.3 mm(3) vs 0.18 × 0.18 × 0.6 mm(3)). Eight of them were scanned after autopsy (in vitro) and the datasets were reconstructed with two voxel sizes (0.32 × 0.32 × 0.6 mm(3) vs. 0.18 × 0.18 × 0.3 mm(3)). Finite element models with cuboid volume of interest extracted from the vertebral cancellous part were created and inhomogeneous bilinear bone properties were defined. Axial compression was simulated. No effect of voxel size was detected on the apparent bone mineral density for both the in situ and in vitro cases. However, the apparent modulus and yield strength showed significant differences in the two voxel size group pairs (in situ and in vitro). In conclusion, the image voxel size may have to be considered when the finite element voxel modeling technique is used in clinical applications. © IMechE 2014.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Energy stable and high-order-accurate finite difference methods on staggered grids

NASA Astrophysics Data System (ADS)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

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.

Experiments with explicit filtering for LES using a finite-difference method

NASA Technical Reports Server (NTRS)

Lund, T. S.; Kaltenbach, H. J.

1995-01-01

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Temperature and frequency dependence of anelasticity in a nickel oscillator

NASA Astrophysics Data System (ADS)

Berg, Robert F.

1995-09-01

The frequency dependence of the real and imaginary parts of a nickel oscillator's transfer function is described over 3 decades in frequency by the use of simple expressions. These expressions incorporate only the resonance frequency ω0, the quality factor Q, and a characteristic exponent β determined by a single measurement of creep. They are based on the ansatz φ(ω)=Q-1(ω/ω0)-β, where φ is the imaginary part of the spring constant. Over a 100 K range of temperature T, the exponent β≂0.18 was constant even though Q(T) changed by a factor of 8. These expressions are potentially useful for accurately describing a mechanical oscillator whose transfer function must be modeled at frequencies far below ω0. Examples include accelerometers based on a flexure element and suspensions for interferometric gravitational wave detectors.

Characterisation of an Al-BN nanocomposite prepared by ball milling and hot extrusion

NASA Astrophysics Data System (ADS)

Arlic, U.; Drozd, Z.; Trojanová, Z.; Molnárová, O.; Kasakewitsch, A.

2017-07-01

Aluminium-matrix-nanocomposites were manufactured by ball milling of microscale aluminium powder with BN nanoparticles in air, followed by subsequent consolidation by hot extrusion. The microstructure of the samples was studied using scanning electron microscopy. Vickers microhardness measurements were used to probe the mechanical properties of the samples. The amplitude dependent damping of the nanocomposites was measured at room temperature after thermal treatment of samples, and the linear thermal expansion was measured over a wide temperature range from room temperature up to 670K in the as-extruded state. The experimental results give a comprehensive picture of the behaviour of this nanocomposite system over the range of thermomechanical treatment conditions examined in this study. Based on these experimental data some possible influences of BN nanoparticles on the anelastic, plastic and thermal properties of microcrystalline aluminium are discussed.

Dynamical buoyancy of hydrodynamic eddies. [in solar atmosphere

NASA Technical Reports Server (NTRS)

Parker, E. N.

1991-01-01

The dynamical pressure reduction within a vortex tube produces both a tension along the tube and a general buoyancy, analogous to magnetic flux tubes. The dynamical buoyancy causes convective cells to rise at speeds comparable to the rms fluid velocity within the cell. Consequently, the convective cells in a stratified atmosphere are more active than indicated by the standard anelastic approximation. The coherent convective cells at each level actively crowd upward into the convective cells above, elbowing weaker cells out of the way and flattening themselves and others against the upper surface of the convective region. These effects can be seen in the recent SOUP observations of the solar granulation. Deeper in the convective zone the inhomogeneity of the buoyancy may explain the random character of the convective motions that turns up in recent numerical simulations.

Creep of chemically vapor deposited SiC fibers

NASA Technical Reports Server (NTRS)

Dicarlo, J. A.

1984-01-01

The creep, thermal expansion, and elastic modulus properties for chemically vapor deposited SiC fibers were measured between 1000 and 1500 C. Creep strain was observed to increase logarithmically with time, monotonically with temperature, and linearly with tensile stress up to 600 MPa. The controlling activation energy was 480 + or - 20 kJ/mole. Thermal pretreatments near 1200 and 1450 C were found to significantly reduce fiber creep. These results coupled with creep recovery observations indicate that below 1400 C fiber creep is anelastic with neglible plastic component. This allowed a simple predictive method to be developed for describing fiber total deformation as a function of time, temperature, and stress. Mechanistic analysis of the property data suggests that fiber creep is the result of beta-SiC grain boundary sliding controlled by a small percent of free silicon in the grain boundaries.

Computer Generated Pictorial Stores Management Displays for Fighter Aircraft.

DTIC Science & Technology

1983-05-01

questionnaire rating-scale data. KRISHNAIAH FINITE INTERSECTION TESTS (FITs) - A set of tests conducted after significant MANOVA results are found to...the Social Sciences (SPSS) (Reference 2). To further examine significant performance differences, the Krishnaiah Finite Intersection Test (FIT), a...New York: McGraw-Hill Book Company, 1975. 3. C. M. Cox, P. R. Krishnaiah , J. C. Lee, J. M. Reising, and F. J. Schuurman, A study on Finite Intersection

The finite ground plane effect on the microstrip antenna radiation patterns

NASA Technical Reports Server (NTRS)

Huang, J.

1983-01-01

The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system.

PubMed

Wang, Pei; Xianlong, Gao; Li, Haibin

2013-08-01

It is demonstrated in many thermodynamic textbooks that the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we discuss the inequivalence of microcanonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Application of numerical methods to heat transfer and thermal stress analysis of aerospace vehicles

NASA Technical Reports Server (NTRS)

Wieting, A. R.

1979-01-01

The paper describes a thermal-structural design analysis study of a fuel-injection strut for a hydrogen-cooled scramjet engine for a supersonic transport, utilizing finite-element methodology. Applications of finite-element and finite-difference codes to the thermal-structural design-analysis of space transports and structures are discussed. The interaction between the thermal and structural analyses has led to development of finite-element thermal methodology to improve the integration between these two disciplines. The integrated thermal-structural analysis capability developed within the framework of a computer code is outlined.

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Socio-economic applications of finite state mean field games.

PubMed

Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

2014-11-13

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

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

Extrinsic Versus Intrinsic Seismic Anisotropy and Attenuation

NASA Astrophysics Data System (ADS)

Montagner, J. P.; Ricard, Y. R.; Capdeville, Y.; Bodin, T.; Wang, N.

2015-12-01

The apparent large scale anisotropy is the mixing of intrinsic anisotropic minerals (LPO) and extrinsic anisotropy due to materials with fine layering, fluid inclusions, cracks (SPO) . The same issue arises for attenuation (with many different anelastic processes). The proportion of extrinsic and intrinsic anisotropy and attenuation in the Earth mantle is still an open question. The interpretation of observations of seismic anisotropy and attenuation is the subject of controversies and often contradictory according to their intrinsic or extrinsic nature. Fine layering is a good candidate for explaining at the same time a large part of observed radial anisotropy (Wang et al., Geophys. Res. Lett., 2013) and attenuation (Ricard et al., Earth Planet. Sci. Lett., 2014). A plausible model of mixing of materials in a chaotic convecting fluid creates a spectrum of heterogeneity varying like 1/k (k wavenumber of the heterogeneity). A body wave propagating in a finely layered medium will be scattered and its distorted waveform can be interpreted as due to attenuation with a quality factor Q. We showed that, with the specific 1/k spectrum and only 6-9% RMS heterogeneity, the resulting apparent attenuation Q is frequency independent. Aggregates of randomly orientated anisotropic minerals are good candidates for giving rise to this extrinsic apparent attenuation. The relationship for a 1/k spectrum with apparent seismic anisotropy is also explored.

Fulde–Ferrell superfluids in spinless ultracold Fermi gases

NASA Astrophysics Data System (ADS)

Zheng, Zhen-Fei; Guo, Guang-Can; Zheng, Zhen; Zou, Xu-Bo

2018-06-01

The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

NASA Technical Reports Server (NTRS)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Microscopic and macroscopic instabilities in finitely strained porous elastomers

NASA Astrophysics Data System (ADS)

Michel, J. C.; Lopez-Pamies, O.; Ponte Castañeda, P.; Triantafyllidis, N.

2007-05-01

The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations—as captured through the effective properties—in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Backward Raman Amplification in the Long-wavelength Infrared

DTIC Science & Technology

2016-12-29

mechanism for generating intense, broad bandwidth, long-wavelength infrared radiation. An electromagnetic finite-difference time-domain simulation...couples a finite-difference time-domain electromagnetic solver with a collisional, relativistic cold fluid plasma model [30]. The simulation domain... electromagnetic simulations coupled to a relativistic cold fluid plasma model with electron- ion collisions. Using a pump pulse that could be generated by a CO

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

A full potential flow analysis with realistic wake influence for helicopter rotor airload prediction

NASA Technical Reports Server (NTRS)

Egolf, T. Alan; Sparks, S. Patrick

1987-01-01

A 3-D, quasi-steady, full potential flow solver was adapted to include realistic wake influence for the aerodynamic analysis of helicopter rotors. The method is based on a finite difference solution of the full potential equation, using an inner and outer domain procedure for the blade flowfield to accommodate wake effects. The nonlinear flow is computed in the inner domain region using a finite difference solution method. The wake is modeled by a vortex lattice using prescribed geometry techniques to allow for the inclusion of realistic rotor wakes. The key feature of the analysis is that vortices contained within the finite difference mesh (inner domain) were treated with a vortex embedding technique while the influence of the remaining portion of the wake (in the outer domain) is impressed as a boundary condition on the outer surface of the finite difference mesh. The solution procedure couples the wake influence with the inner domain solution in a consistent and efficient solution process. The method has been applied to both hover and forward flight conditions. Correlation with subsonic and transonic hover airload data is shown which demonstrates the merits of the approach.

Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

NASA Astrophysics Data System (ADS)

Gibbons, T. J.; Öztürk, E.; Sims, N. D.

2018-01-01

Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

NASA Astrophysics Data System (ADS)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Finite-difference modeling of the electroseismic logging in a fluid-saturated porous formation

NASA Astrophysics Data System (ADS)

Guan, Wei; Hu, Hengshan

2008-05-01

In a fluid-saturated porous medium, an electromagnetic (EM) wavefield induces an acoustic wavefield due to the electrokinetic effect. A potential geophysical application of this effect is electroseismic (ES) logging, in which the converted acoustic wavefield is received in a fluid-filled borehole to evaluate the parameters of the porous formation around the borehole. In this paper, a finite-difference scheme is proposed to model the ES logging responses to a vertical low frequency electric dipole along the borehole axis. The EM field excited by the electric dipole is calculated separately by finite-difference first, and is considered as a distributed exciting source term in a set of extended Biot's equations for the converted acoustic wavefield in the formation. This set of equations is solved by a modified finite-difference time-domain (FDTD) algorithm that allows for the calculation of dynamic permeability so that it is not restricted to low-frequency poroelastic wave problems. The perfectly matched layer (PML) technique without splitting the fields is applied to truncate the computational region. The simulated ES logging waveforms approximately agree with those obtained by the analytical method. The FDTD algorithm applies also to acoustic logging simulation in porous formations.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

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

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

Prediction of high-speed rotor noise with a Kirchhoff formula

NASA Technical Reports Server (NTRS)

Purcell, Timothy W.; Strawn, Roger C.; Yu, Yung H.

1987-01-01

A new methodology has been developed to predict the impulsive noise generated by a transonic rotor blade. The formulation uses a full-potential finite-difference method to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far-field. This Kirchhoff formula is written in a blade-fixed coordinate system. It requires initial data across a plane at the sonic radius. This data is provided by the finite-difference solution. Acoustic pressure predictions show excellent agreement with hover experimental data for two hover cases of 0.88 and 0.90 tip Mach number, the latter of which has delocalized transonic flow. These results represent the first successful prediction technique for peak pressure amplitudes using a computational code.

A comparative study on dynamic stiffness in typical finite element model and multi-body model of C6-C7 cervical spine segment.

PubMed

Wang, Yawei; Wang, Lizhen; Du, Chengfei; Mo, Zhongjun; Fan, Yubo

2016-06-01

In contrast to numerous researches on static or quasi-static stiffness of cervical spine segments, very few investigations on their dynamic stiffness were published. Currently, scale factors and estimated coefficients were usually used in multi-body models for including viscoelastic properties and damping effects, meanwhile viscoelastic properties of some tissues were unavailable for establishing finite element models. Because dynamic stiffness of cervical spine segments in these models were difficult to validate because of lacking in experimental data, we tried to gain some insights on current modeling methods through studying dynamic stiffness differences between these models. A finite element model and a multi-body model of C6-C7 segment were developed through using available material data and typical modeling technologies. These two models were validated with quasi-static response data of the C6-C7 cervical spine segment. Dynamic stiffness differences were investigated through controlling motions of C6 vertebrae at different rates and then comparing their reaction forces or moments. Validation results showed that both the finite element model and the multi-body model could generate reasonable responses under quasi-static loads, but the finite element segment model exhibited more nonlinear characters. Dynamic response investigations indicated that dynamic stiffness of this finite element model might be underestimated because of the absence of dynamic stiffen effect and damping effects of annulus fibrous, while representation of these effects also need to be improved in current multi-body model. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Flow adjustment inside large finite-size wind farms approaching the infinite wind farm regime

NASA Astrophysics Data System (ADS)

Wu, Ka Ling; Porté-Agel, Fernando

2017-04-01

Due to the increasing number and the growing size of wind farms, the distance among them continues to decrease. Thus, it is necessary to understand how these large finite-size wind farms and their wakes could interfere the atmospheric boundary layer (ABL) dynamics and adjacent wind farms. Fully-developed flow inside wind farms has been extensively studied through numerical simulations of infinite wind farms. The transportation of momentum and energy is only vertical and the advection of them is neglected in these infinite wind farms. However, less attention has been paid to examine the length of wind farms required to reach such asymptotic regime and the ABL dynamics in the leading and trailing edges of the large finite-size wind farms. Large eddy simulations are performed in this study to investigate the flow adjustment inside large finite-size wind farms in conventionally-neutral boundary layer with the effect of Coriolis force and free-atmosphere stratification from 1 to 5 K/km. For the large finite-size wind farms considered in the present work, when the potential temperature lapse rate is 5 K/km, the wind farms exceed the height of the ABL by two orders of magnitude for the incoming flow inside the farms to approach the fully-developed regime. An entrance fetch of approximately 40 times of the ABL height is also required for such flow adjustment. At the fully-developed flow regime of the large finite-size wind farms, the flow characteristics match those of infinite wind farms even though they have different adjustment length scales. The role of advection at the entrance and exit regions of the large finite-size wind farms is also examined. The interaction between the internal boundary layer developed above the large finite-size wind farms and the ABL under different potential temperature lapse rates are compared. It is shown that the potential temperature lapse rate plays a role in whether the flow inside the large finite-size wind farms adjusts to the fully-developed flow regime. The flow characteristics of the wake of these large finite-size wind farms are reported to forecast the effect of large finite-size wind farms on adjacent wind farms. A power deficit as large as 8% is found at a distance of 10 km downwind from the large finite-size wind farms.

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2015-08-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points). Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%. Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness. Copyright © 2015 Elsevier Ltd. All rights reserved.

A one-dimensional model to describe flow localization in viscoplastic slender bars subjected to super critical impact velocities

NASA Astrophysics Data System (ADS)

Vaz-Romero, A.; Rodríguez-Martínez, J. A.

2018-01-01

In this paper we investigate flow localization in viscoplastic slender bars subjected to dynamic tension. We explore loading rates above the critical impact velocity: the wave initiated in the impacted end by the applied velocity is the trigger for the localization of plastic deformation. The problem has been addressed using two kinds of numerical simulations: (1) one-dimensional finite difference calculations and (2) axisymmetric finite element computations. The latter calculations have been used to validate the capacity of the finite difference model to describe plastic flow localization at high impact velocities. The finite difference model, which highlights due to its simplicity, allows to obtain insights into the role played by the strain rate and temperature sensitivities of the material in the process of dynamic flow localization. Specifically, we have shown that viscosity can stabilize the material behavior to the point of preventing the appearance of the critical impact velocity. This is a key outcome of our investigation, which, to the best of the authors' knowledge, has not been previously reported in the literature.

A finite element analysis of a 3D auxetic textile structure for composite reinforcement

NASA Astrophysics Data System (ADS)

Ge, Zhaoyang; Hu, Hong; Liu, Yanping

2013-08-01

This paper reports the finite element analysis of an innovative 3D auxetic textile structure consisting of three yarn systems (weft, warp and stitch yarns). Different from conventional 3D textile structures, the proposed structure exhibits an auxetic behaviour under compression and can be used as a reinforcement to manufacture auxetic composites. The geometry of the structure is first described. Then a 3D finite element model is established using ANSYS software and validated by the experimental results. The deformation process of the structure at different compression strains is demonstrated, and the validated finite element model is finally used to simulate the auxetic behaviour of the structure with different structural parameters and yarn properties. The results show that the auxetic behaviour of the proposed structure increases with increasing compression strain, and all the structural parameters and yarn properties have significant effects on the auxetic behaviour of the structure. It is expected that the study could provide a better understanding of 3D auxetic textile structures and could promote their application in auxetic composites.

Optimum element density studies for finite-element thermal analysis of hypersonic aircraft structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Olona, Timothy; Muramoto, Kyle M.

1990-01-01

Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.

Glacial Isostatic Adjustment with ICE-6G{_}C (VM5a) and Laterally Heterogeneous Mantle Viscosity

NASA Astrophysics Data System (ADS)

Li, Tanghua; Wu, Patrick; Steffen, Holger

2017-04-01

Recently, Peltier et al. (2015) introduced the ICE-6GC (VM5a) ice-earth model pair, which has successfully explained many observations of Glacial Isostatic Adjustment (GIA) simultaneously. However, their earth model used (VM5a) to infer the ice history (ICE-6G_C) is laterally homogeneous with viscosity profile varying in the radial direction only. Since surface geology and seismic tomography clearly indicates that the Earth's material properties also vary in the lateral direction, laterally heterogeneity must be included in GIA models. This can be achieved by using the Coupled-Laplace-Finite-Element method (Wu 2004) to model GIA in a spherical, self-gravitating, compressible viscoelastic Earth with linear rheology and lateral heterogeneity. In fact, Wu et al (2013) have used such model with GIA observations (e.g. global relative sea level data, GRACE data with recent hydrology contributions removed and GPS crustal uplift rates) to study the thermal contribution to lateral heterogeneity in the mantle. Their lateral viscosity perturbations are inferred from the seismic shear wave tomography model S20A (Ekstrom & Dziewonski 1998) by applying a scaling law, which includes both the effect of anharmonicity and anelasticity. The thermal contribution to seismic tomography, which is represented by the beta factor in the scaling relationship, is searched in the upper and lower mantle, for the best combination that gives the best fit between GIA predictions and observations. However, their study is based on ICE-4G only, and the new ice-earth model pair may give other best beta value combinations in the upper and lower mantle. Here, we follow the work of Wu et al (2013) but use the new ICE-6GC ice model instead. The higher resolution seismic tomography model by Bunge & Grand (2000) substitutes S20A. Earth model VM5a is used as the reference background viscosity model. The full viscosity model is obtained by superposing the background model with the lateral viscosity perturbations inferred from the seismic tomography model (Bunge & Grand 2000) logarithmically. The preliminary results of these and other background viscosity profiles will be presented. References: Bunge, H.-P. & Grand, S. P. (2000). Mesozoic plate-motion history below the northeast Pacific Ocean from seismic images of the subducted Farallon slab. Nature, 405(6784):337-340. Peltier, W., Argus, D., and Drummond, R. (2015). Space geodesy constrains ice age terminal deglaciation: The global ICE-6GC (VM5a) model. Journal of Geophysical Research: Solid Earth, 120(1): 450-487. Wu, P. (2004). Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress. Geophysical Journal International, 158(2): 401-408. Wu, P., Wang, H.S. & Steffen, H. (2012). The role of thermal effect on mantle seismic anomalies under Laurentia and Fennoscandia from observations of Glacial Isostatic Adjustment. Geophysical Journal International, 192(1):7-17.

HYDROCARBON SPILL EXPOSURE ASSESSMENT MODELING

EPA Science Inventory

Hydrocarbon spills impact drinking water supplies at down gradient locations. onventional finite difference and finite element models of multiphase, multicomponent flow have extreme requirements for both computer time and site data. ite data and the intent of the modeling often d...

EXPOSURE ASSESSMENT MODELING FOR HYDROCARBON SPILLS INTO THE SUBSURFACE

EPA Science Inventory

Hydrocarbons which enter the subsurface through spills or leaks may create serious, long-lived ground-water contamination problems. onventional finite difference and finite element models of multiphase, multicomponent flow often have extreme requirements for both computer time an...

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

Projection methods for incompressible flow problems with WENO finite difference schemes

NASA Astrophysics Data System (ADS)

de Frutos, Javier; John, Volker; Novo, Julia

2016-03-01

Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.

Finite element analysis of TAVI: Impact of native aortic root computational modeling strategies on simulation outcomes.

PubMed

Finotello, Alice; Morganti, Simone; Auricchio, Ferdinando

2017-09-01

In the last few years, several studies, each with different aim and modeling detail, have been proposed to investigate transcatheter aortic valve implantation (TAVI) with finite elements. The present work focuses on the patient-specific finite element modeling of the aortic valve complex. In particular, we aim at investigating how different modeling strategies in terms of material models/properties and discretization procedures can impact analysis results. Four different choices both for the mesh size (from  20 k elements to  200 k elements) and for the material model (from rigid to hyperelastic anisotropic) are considered. Different approaches for modeling calcifications are also taken into account. Post-operative CT data of the real implant are used as reference solution with the aim of outlining a trade-off between computational model complexity and reliability of the results. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1991-01-01

A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Weak form implementation of the semi-analytical finite element (SAFE) method for a variety of elastodynamic waveguides

NASA Astrophysics Data System (ADS)

Hakoda, Christopher; Lissenden, Clifford; Rose, Joseph L.

2018-04-01

Dispersion curves are essential to any guided wave NDE project. The Semi-Analytical Finite Element (SAFE) method has significantly increased the ease by which these curves can be calculated. However, due to misconceptions regarding theory and fragmentation based on different finite-element software, the theory has stagnated, and adoption by researchers who are new to the field has been slow. This paper focuses on the relationship between the SAFE formulation and finite element theory, and the implementation of the SAFE method in a weak form for plates, pipes, layered waveguides/composites, curved waveguides, and arbitrary cross-sections is shown. The benefits of the weak form are briefly described, as is implementation in open-source and commercial finite element software.

Evidence for a Finite-Temperature Insulator.

PubMed

Ovadia, M; Kalok, D; Tamir, I; Mitra, S; Sacépé, B; Shahar, D

2015-08-27

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the "superinsulating" phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T < 0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator.

The role of finite-difference methods in design and analysis for supersonic cruise

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1976-01-01

Finite-difference methods for analysis of steady, inviscid supersonic flows are described, and their present state of development is assessed with particular attention to their applicability to vehicles designed for efficient cruise flight. Current work is described which will allow greater geometric latitude, improve treatment of embedded shock waves, and relax the requirement that the axial velocity must be supersonic.

A two-dimensional finite-difference solution for the temperature distribution in a radial gas turbine guide vane blade

NASA Technical Reports Server (NTRS)

Hosny, W. M.; Tabakoff, W.

1975-01-01

A two-dimensional finite difference numerical technique is presented to determine the temperature distribution in a solid blade of a radial guide vane. A computer program is written in Fortran IV for IBM 370/165 computer. The computer results obtained from these programs have a similar behavior and trend as those obtained by experimental results.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

Finite-element reentry heat-transfer analysis of space shuttle Orbiter

NASA Technical Reports Server (NTRS)

Ko, William L.; Quinn, Robert D.; Gong, Leslie

1986-01-01

A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

EPA Science Inventory

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

PubMed

Ding, Yi S; He, Yang

2017-08-21

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

NASA Astrophysics Data System (ADS)

Zhao, Yan; Belov, Pavel A.; Hao, Yang

2006-06-01

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

Evaluation of the 3D Finite Element Method Using a Tantalum Rod for Osteonecrosis of the Femoral Head

PubMed Central

Shi, Jingsheng; Chen, Jie; Wu, Jianguo; Chen, Feiyan; Huang, Gangyong; Wang, Zhan; Zhao, Guanglei; Wei, Yibing; Wang, Siqun

2014-01-01

Background The aim of this study was to contrast the collapse values of the postoperative weight-bearing areas of different tantalum rod implant positions, fibula implantation, and core decompression model and to investigate the advantages and disadvantages of tantalum rod implantation in different ranges of osteonecrosis in comparison with other methods. Material/Methods The 3D finite element method was used to establish the 3D finite element model of normal upper femur, 3D finite element model after tantalum rod implantation into different positions of the upper femur in different osteonecrosis ranges, and other 3D finite element models for simulating fibula implant and core decompression. Results The collapse values in the weight-bearing area of the femoral head of the tantalum rod implant model inside the osteonecrosis area, implant model in the middle of the osteonecrosis area, fibula implant model, and shortening implant model exhibited no statistically significant differences (p>0.05) when the osteonecrosis range was small (60°). The stress values on the artificial bone surface for the tantalum rod implant model inside the osteonecrosis area and the shortening implant model exhibited statistical significance (p<0.01). Conclusions Tantalum rod implantation into the osteonecrosis area can reduce the collapse values in the weight-bearing area when osteonecrosis of the femoral head (ONFH) was in a certain range, thereby obtaining better clinical effects. When ONFH was in a large range (120°), the tantalum rod implantation inside the osteonecrosis area, shortening implant or fibula implant can reduce the collapse values of the femoral head, as assessed by other methods. PMID:25479830

Optimized Finite-Difference Coefficients for Hydroacoustic Modeling

NASA Astrophysics Data System (ADS)

Preston, L. A.

2014-12-01

Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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.

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.

Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

DTIC Science & Technology

1989-10-01

paper, we study fast parallel preconditioners for systems of equations arising from the p-version finite element method. The p-version finite element...computations and the solution of a relatively small global auxiliary problem. We study two different methods. In the first (Section 3), the global...20], will be studied in the next section. Problem (3.12) is obviously much more easily solved than the original problem ,nd the procedure is highly

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

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.

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Study on Edge Thickening Flow Forming Using the Finite Elements Analysis

NASA Astrophysics Data System (ADS)

Kim, Young Jin; Park, Jin Sung; Cho, Chongdu

2011-08-01

This study is to examine the forming features of flow stress property and the incremental forming method with increasing the thickness of material. Recently, the optimized forming method is widely studied through the finite element analysis to optimize forming process conditions in many different forming fields. The optimal forming method should be adopted to meet geometric requirements as the reduction in volume per unit length of material such as forging, rolling, spinning etc. However conventional studies have not dealt with issue regarding volume per unit length. For the study we use the finite element method and model a gear part of an automotive engine flywheel as the study model, which is a weld assembly of a plate and a gear with respective different thickness. In simulation of the present study, a optimized forming condition for gear machining, considering the thickness of the outer edge of flywheel is studied using the finite elements analysis for the increasing thickness of the forming method. It is concluded from the study that forming method to increase the thickness per unit length for gear machining is reasonable using the finite elements analysis and forming test.

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

On One-Dimensional Stretching Functions for Finite-Difference Calculations

NASA Technical Reports Server (NTRS)

Vinokur, M.

1980-01-01

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

COMPARISON OF NUMERICAL SCHEMES FOR SOLVING A SPHERICAL PARTICLE DIFFUSION EQUATION

EPA Science Inventory

A new robust iterative numerical scheme was developed for a nonlinear diffusive model that described sorption dynamics in spherical particle suspensions. he numerical scheme had been applied to finite difference and finite element models that showed rapid convergence and stabilit...

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1985-01-01

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

HEMP 3D: A finite difference program for calculating elastic-plastic flow, appendix B

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations listed below are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time.

Finite-difference models of ordinary differential equations - Influence of denominator functions

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.; Smith, Arthur

1990-01-01

This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.

Finite element analysis of elasto-plastic soils. Report no. 4: Finite element analysis of elasto-plastic frictional materials for application to lunar earth sciences

NASA Technical Reports Server (NTRS)

Marr, W. A., Jr.

1972-01-01

The behavior of finite element models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These finite element models are used to analyze retaining walls and footings. Methods of improving the finite element solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of elements. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.

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.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1993-01-01

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

NASA Astrophysics Data System (ADS)

Yang, Zailin; Wang, Yao; Hei, Baoping

2013-12-01

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Design sensitivity analysis with Applicon IFAD using the adjoint variable method

NASA Technical Reports Server (NTRS)

Frederick, Marjorie C.; Choi, Kyung K.

1984-01-01

A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.

1980-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

A simple finite-difference scheme for handling topography with the first-order wave equation

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Huiskes, M. J.

2017-07-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

Synthesis of regional crust and upper-mantle structure from seismic and gravity data

NASA Technical Reports Server (NTRS)

Alexander, S. S.; Lavin, P. M.

1979-01-01

Available seismic and ground based gravity data are combined to infer the three dimensional crust and upper mantle structure in selected regions. This synthesis and interpretation proceeds from large-scale average models suitable for early comparison with high-altitude satellite potential field data to more detailed delineation of structural boundaries and other variations that may be significant in natural resource assessment. Seismic and ground based gravity data are the primary focal point, but other relevant information (e.g. magnetic field, heat flow, Landsat imagery, geodetic leveling, and natural resources maps) is used to constrain the structure inferred and to assist in defining structural domains and boundaries. The seismic data consists of regional refraction lines, limited reflection coverage, surface wave dispersion, teleseismic P and S wave delay times, anelastic absorption, and regional seismicity patterns. The gravity data base consists of available point gravity determinations for the areas considered.

Inferring the thermal structure of the Panama Basin by seismic attenuation

NASA Astrophysics Data System (ADS)

Vargas-Jimenez, C. A.; Pulido, J. E.; Hobbs, R. W.

2017-12-01

Using recordings of earthquakes on Oceanic Bottom Seismographs and onshore stations on the coastal margins of Colombia, Panama, and Ecuador, we discriminate intrinsic and scattering attenuation processes in the upper lithosphere of the Panama Basin. The tomographic images of the derived coda-Q values are correlated with estimates of Curie Point Depth and measured and theoretical heat flow. Our study reveals three tectonic domains where magmatic/hydrothermal activity or lateral variations of the lithologic composition in the upper lithosphere can account for the modelled thermal structure and the anelasticity. We find that the Costa Rica Ridge and the Panama Fracture Zone are significant tectonic features in the study area. We interpret a large and deep intrinsic attenuation anomaly as related to the heat source at this ocean spreading center and show how interactions with regional fault systems cause contrasting attenuation anomalies.

Thermal structure of the Panama Basin by analysis of seismic attenuation

NASA Astrophysics Data System (ADS)

Vargas, Carlos A.; Pulido, José E.; Hobbs, Richard W.

2018-04-01

Using recordings of earthquakes on Oceanic Bottom Seismographs and onshore stations on the coastal margins of Colombia, Panama, and Ecuador, we estimate attenuation parameters in the upper lithosphere of the Panama Basin. The tomographic images of the derived coda-Q values are correlated with estimates of Curie Point Depth and measured and theoretical heat flow. Our study reveals three tectonic domains where magmatic/hydrothermal activity or lateral variations of the lithologic composition in the upper lithosphere can account for the modeled thermal structure and the anelasticity. We find that the Costa Rica Ridge and the Panama Fracture Zone are significant tectonic features probably related to thermal anomalies detected in the study area. We interpret a large and deep intrinsic attenuation anomaly as related to the heat source at the Costa Rica Ridge and show how interactions with regional fault systems cause contrasting attenuation anomalies.

Experiments with a Regional Vector-Vorticity Model, and Comparison with Other Models

NASA Astrophysics Data System (ADS)

Konor, C. S.; Dazlich, D. A.; Jung, J.; Randall, D. A.

2017-12-01

The Vector-Vorticity Model (VVM) is an anelastic model with a unique dynamical core that predicts the three-dimensional vorticity instead of the three-dimensional momentum. The VVM is used in the CRMs of the Global Quasi-3D Multiscale Modeling Framework, which is discussed by Joon-Hee Jung and collaborators elsewhere in this session. We are updating the physics package of the VVM, replacing it with the physics package of the System for Atmosphere Modeling (SAM). The new physics package includes a double-moment microphysics, Mellor-Yamada turbulence, Monin-Obukov surface fluxes, and the RRTMG radiation parameterization. We briefly describe the VVM and show results from standard test cases, including TWP-ICE. We compare the results with those obtained using the earlier physics. We also show results from experiments on convection aggregation in radiative-convective equilibrium, and compare with those obtained using both SAM and the Regional Atmospheric Modeling System (RAMS).

The pole tide in deep oceans

NASA Technical Reports Server (NTRS)

Dickman, S. R.

1990-01-01

The fluid-dynamical theory of the pole tide is examined by describing the oceanic response to the Chandler wobble and assessing its implications for mantle anelasticity and low-frequency ocean dynamics. The Laplace tide equations accounting for bottom friction are given, and a spherical harmonic approach is delineated in which the time-independent portion of the tide height is expanded. Pole-tide height and related inertia products are linearly proportional to wobble amplitude, and the final equations are modified to account for mantle elasticity and oceanic loading. Results for pole tide effects are given for various earth models with attention to the role of boundary constraints. A dynamic effect is identified which lengthens the Chandler period by about 1 day more than static lengthening, a contribution that suggests a vigorous low-frequency response. The values derived are shown to agree with previous models that do not incorporate the effects of the pole tide.

The period and Q of the Chandler wobble

NASA Technical Reports Server (NTRS)

Smith, M. L.; Dahlen, F. A.

1981-01-01

The calculation of the theoretical period of the Chandler wobble is extended to account for the non-hydrostatic portion of the earth's equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide. The theoretical period of a realistic perfectly elastic earth with an equilibrium pole tide is found to be 426.7 sidereal days, which is 8.5 days shorter than the observed period of 435.2 days. Using Rayleigh's principle for a rotating earth, this discrepancy is exploited together with the observed Chandler Q to place constraints on the frequency dependence of mantle anelasticity. In all cases these limits arise from exceeding the 68 percent confidence limits of + or - 2.6 days in the observed period. Since slight departures from an equilibrium pole tide affect the Q much more strongly than the period, these limits are believed to be robust.

GIANT CORONAL LOOPS DOMINATE THE QUIESCENT X-RAY EMISSION IN RAPIDLY ROTATING M STARS

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

Cohen, O.; Yadav, R.; Garraffo, C.

2017-01-01

Observations indicate that magnetic fields in rapidly rotating stars are very strong, on both small and large scales. What is the nature of the resulting corona? Here we seek to shed some light on this question. We use the results of an anelastic dynamo simulation of a rapidly rotating fully convective M star to drive a physics-based model for the stellar corona. We find that due to the several kilo Gauss large-scale magnetic fields at high latitudes, the corona, and its X-ray emission are dominated by star-size large hot loops, while the smaller, underlying colder loops are not visible muchmore » in the X-ray. Based on this result, we propose that, in rapidly rotating stars, emission from such coronal structures dominates the quiescent, cooler but saturated X-ray emission.« less

Phenomenological model for transient deformation based on state variables

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

Jackson, M S; Cho, C W; Alexopoulos, P

The state variable theory of Hart, while providing a unified description of plasticity-dominated deformation, exhibits deficiencies when it is applied to transient deformation phenomena at stresses below yield. It appears that the description of stored anelastic strain is oversimplified. Consideration of a simple physical picture based on continuum dislocation pileups suggests that the neglect of weak barriers to dislocation motion is the source of these inadequacies. An appropriately modified description incorporating such barriers then allows the construction of a macroscopic model including transient effects. Although the flow relations for the microplastic element required in the new theory are not known,more » tentative assignments may be made for such functions. The model then exhibits qualitatively correct behavior when tensile, loading-unloading, reverse loading, and load relaxation tests are simulated. Experimental procedures are described for determining the unknown parameters and functions in the new model.« less

On the nature of low temperature internal friction peaks in metallic glasses

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

Khonik, V.A.; Spivak, L.V.

Low temperature (30 < T < 300 K) internal friction in a metallic glass Ni{sub 60}Nb{sub 40} subjected to preliminary inhomogeneous deformation by cold rolling, homogeneous tensile deformation or electrolytic charging with hydrogen is investigated. Cold rolling or hydrogenation result in appearance of similar internal friction peaks and hysteresis damping. Homogeneous deformation has no influence on low temperature internal friction. The phenomenon of microplastic deformation during hydrogenation of weakly stressed samples is revealed. It is argued that microplastic deformation of metallic glasses during hydrogenation without external stress takes place too. Plastic flow both on cold rolling and hydrogenation occurs viamore » formation and motion of dislocation-like defects which are the reason of the observed anelastic anomalies. It is concluded that low temperature internal friction peaks described in the literature for as-cast, cold deformed and hydrogenated samples have common dislocation-like origin.« less

Gravity Wave Interactions with Fine Structures in the Mesosphere and Lower Thermosphere

NASA Astrophysics Data System (ADS)

Mixa, Tyler; Fritts, David; Bossert, Katrina; Laughman, Brian; Wang, Ling; Lund, Thomas; Kantha, Lakshmi

2017-04-01

An anelastic numerical model is used to probe the influences of fine layering structures on gravity wave propagation in the Mesosphere and Lower Thermosphere (MLT). Recent lidar observations confirm the presence of persistent layered structures in the MLT that have sharp stratification and vertical scales below 1km. Gravity waves propagating through finely layered environments can excite and modulate the evolution of small scale instabilities that redefine the layering structure in these regions. Such layers in turn filter the outgoing wave spectra, promote ducting or reflection, hasten the onset of self-acceleration dynamics, and encourage wave/mean-flow interactions via energy and momentum transport. Using high resolution simulations of a localized gravity wave packet in a deep atmosphere, we identify the relative impacts of various wave and mean flow parameters to improve our understanding of these dynamics and complement recent state-of-the-art observations.

Computer program analyzes Buckling Of Shells Of Revolution with various wall construction, BOSOR

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1968-01-01

Computer program performs stability analyses for a wide class of shells without unduly restrictive approximations. The program uses numerical integration, finite difference of finite element techniques to solve with reasonable accuracy almost any buckling problem for shells exhibiting orthotropic behavior.

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

NASA Technical Reports Server (NTRS)

Gong, Jian; Volakis, John L.; Nurnberger, Michael W.

1995-01-01

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method

NASA Astrophysics Data System (ADS)

Lossa, Geoffrey; Deblecker, Olivier; Grève, Zacharie De

2018-05-01

In this work, we highlight the influence of the material uncertainties (magnetic permeability, electric conductivity of a Mn-Zn ferrite core, and electric permittivity of wire insulation) on the RLC parameters of a wound inductor extracted from the finite element method. To that end, the finite element method is embedded in a Monte Carlo simulation. We show that considering mentioned different material properties as real random variables, leads to significant variations in the distributions of the RLC parameters.

A finite-element simulation of galvanic coupling intra-body communication based on the whole human body.

PubMed

Song, Yong; Zhang, Kai; Hao, Qun; Hu, Lanxin; Wang, Jingwen; Shang, Fuzhou

2012-10-09

Simulation based on the finite-element (FE) method plays an important role in the investigation of intra-body communication (IBC). In this paper, a finite-element model of the whole body model used for the IBC simulation is proposed and verified, while the FE simulation of the galvanic coupling IBC with different signal transmission paths has been achieved. Firstly, a novel finite-element method for modeling the whole human body is proposed, and a FE model of the whole human body used for IBC simulation was developed. Secondly, the simulations of the galvanic coupling IBC with the different signal transmission paths were implemented. Finally, the feasibility of the proposed method was verified by using in vivo measurements within the frequency range of 10 kHz-5 MHz, whereby some important conclusions were deduced. Our results indicate that the proposed method will offer significant advantages in the investigation of the galvanic coupling intra-body communication.

A Finite-Element Simulation of Galvanic Coupling Intra-Body Communication Based on the Whole Human Body

PubMed Central

Song, Yong; Zhang, Kai; Hao, Qun; Hu, Lanxin; Wang, Jingwen; Shang, Fuzhou

2012-01-01

Simulation based on the finite-element (FE) method plays an important role in the investigation of intra-body communication (IBC). In this paper, a finite-element model of the whole body model used for the IBC simulation is proposed and verified, while the FE simulation of the galvanic coupling IBC with different signal transmission paths has been achieved. Firstly, a novel finite-element method for modeling the whole human body is proposed, and a FE model of the whole human body used for IBC simulation was developed. Secondly, the simulations of the galvanic coupling IBC with the different signal transmission paths were implemented. Finally, the feasibility of the proposed method was verified by using in vivo measurements within the frequency range of 10 kHz–5 MHz, whereby some important conclusions were deduced. Our results indicate that the proposed method will offer significant advantages in the investigation of the galvanic coupling intra-body communication. PMID:23202010

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

Coupled thermomechanical behavior of graphene using the spring-based finite element approach

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

Georgantzinos, S. K., E-mail: sgeor@mech.upatras.gr; Anifantis, N. K., E-mail: nanif@mech.upatras.gr; Giannopoulos, G. I., E-mail: ggiannopoulos@teiwest.gr

The prediction of the thermomechanical behavior of graphene using a new coupled thermomechanical spring-based finite element approach is the aim of this work. Graphene sheets are modeled in nanoscale according to their atomistic structure. Based on molecular theory, the potential energy is defined as a function of temperature, describing the interatomic interactions in different temperature environments. The force field is approached by suitable straight spring finite elements. Springs simulate the interatomic interactions and interconnect nodes located at the atomic positions. Their stiffness matrix is expressed as a function of temperature. By using appropriate boundary conditions, various different graphene configurations aremore » analyzed and their thermo-mechanical response is approached using conventional finite element procedures. A complete parametric study with respect to the geometric characteristics of graphene is performed, and the temperature dependency of the elastic material properties is finally predicted. Comparisons with available published works found in the literature demonstrate the accuracy of the proposed method.« less

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Polavarapu, Rinosh; Banerjee, Arindam

2017-11-01

The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.

Control of Finite-State, Finite Memory Stochastic Systems

NASA Technical Reports Server (NTRS)

Sandell, Nils R.

1974-01-01

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

NASA Astrophysics Data System (ADS)

Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong

2010-07-01

This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.

Biomechanical investigation of naso-orbitoethmoid trauma by finite element analysis.

PubMed

Huempfner-Hierl, Heike; Schaller, Andreas; Hemprich, Alexander; Hierl, Thomas

2014-11-01

Naso-orbitoethmoid fractures account for 5% of all facial fractures. We used data derived from a white 34-year-old man to make a transient dynamic finite element model, which consisted of about 740 000 elements, to simulate fist-like impacts to this anatomically complex area. Finite element analysis showed a pattern of von Mises stresses beyond the yield criterion of bone that corresponded with fractures commonly seen clinically. Finite element models can be used to simulate injuries to the human skull, and provide information about the pathogenesis of different types of fracture. Copyright © 2014 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Exploiting broad-area surface emitting lasers to manifest the path-length distributions of finite-potential quantum billiards.

PubMed

Yu, Y T; Tuan, P H; Chang, K C; Hsieh, Y H; Huang, K F; Chen, Y F

2016-01-11

Broad-area vertical-cavity surface-emitting lasers (VCSELs) with different cavity sizes are experimentally exploited to manifest the influence of the finite confinement strength on the path-length distribution of quantum billiards. The subthreshold emission spectra of VCSELs are measured to obtain the path-length distributions by using the Fourier transform. It is verified that the number of the resonant peaks in the path-length distribution decreases with decreasing the confinement strength. Theoretical analyses for finite-potential quantum billiards are numerically performed to confirm that the mesoscopic phenomena of quantum billiards with finite confinement strength can be analogously revealed by using broad-area VCSELs.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.