Peselnick, L.; Robie, R.A.
1962-01-01
The recent measurements of the elastic constants of calcite by Reddy and Subrahmanyam (1960) disagree with the values obtained independently by Voigt (1910) and Bhimasenachar (1945). The present authors, using an ultrasonic pulse technique at 3 Mc and 25??C, determined the elastic constants of calcite using the exact equations governing the wave velocities in the single crystal. The results are C11=13.7, C33=8.11, C44=3.50, C12=4.82, C13=5.68, and C14=-2.00, in units of 1011 dyncm2. Independent checks of several of the elastic constants were made employing other directions and polarizations of the wave velocities. With the exception of C13, these values substantially agree with the data of Voigt and Bhimasenachar. ?? 1962 The American Institute of Physics.
Renormalization of curvature elastic constants for elastic and fluid membranes
NASA Astrophysics Data System (ADS)
Ami, S.; Kleinert, H.
1987-02-01
We study the fluctuations of membranes with area and curvature elasticity and calculate the renormalization of the curvature elastic constants due to thermal fluctuations. For the mean curvature elastic constant the result is the same as obtained previously for “ideal membranes” which resist only to curvature deformations. The renormalization of the gaussian curvature, on the other hand, depends on the elastic contants. In an incompressible membrane, it is five times weaker than in an ideal membrane.
Elastic constants of layers in isotropic laminates.
Heyliger, Paul R; Ledbetter, Hassel; Kim, Sudook; Reimanis, Ivar
2003-11-01
The individual laminae elastic constants in multilayer laminates composed of dissimilar isotropic layers were determined using ultrasonic-resonance spectroscopy and the linear theory of elasticity. Ultrasonic resonance allows one to measure the free-vibration response spectrum of a traction-free solid under periodic vibration. These frequencies depend on pointwise density, laminate dimensions, layer thickness, and layer elastic constants. Given a material with known mass but unknown constitution, this method allows one to extract the elastic constants and density of the constituent layers. This is accomplished by measuring the frequencies and then minimizing the differences between these and those calculated using the theory of elasticity for layered media to select the constants that best replicate the frequency-response spectrum. This approach is applied to a three-layer, unsymmetric laminate of WpCu, and very good agreement is found with the elastic constants of the two constituent materials. PMID:14649998
Athermal nonlinear elastic constants of amorphous solids.
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar
2010-08-01
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elastoplasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of our calculations we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place. PMID:20866874
Athermal nonlinear elastic constants of amorphous solids
NASA Astrophysics Data System (ADS)
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar
2010-08-01
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elastoplasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of our calculations we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place.
Stresses and elastic constants of crystalline sodium, from molecular dynamics
Schiferl, S.K.
1985-02-01
The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340K. The total adiabatic potential of a system of sodium atoms is represented by pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the results to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. 45 refs., 10 figs., 4 tabs.
Elastic constants at low temperatures - Recent measurements on technological materials at NBS
NASA Technical Reports Server (NTRS)
Ledbetter, H. M.
1978-01-01
Solid-state low-temperature elastic properties have been experimentally studied at the NBS Cryogenic Division for four years. Most studies were between room temperature and liquid-helium temperature; some were only to liquid-nitrogen temperature. Two dynamic (high-frequency) experimental methods were used, pulse-echo and resonance, resulting in adiabatic elastic constants. The present paper reviews these studies for 47 technological materials - metals, alloys, and composites. The elastic constants primarily discussed are Young's modulus, the shear modulus, the bulk modulus (reciprocal compressibility), and Poisson's ratio. A summary table is presented to show which base metals tend to exhibit regular, irregular, or anomalous behavior in their elastic constant/temperature curves.
The elastic constants of the human lens
Fisher, R. F.
1971-01-01
1. When the lens is spun around its antero-posterior polar axis in an apparatus designed for the purpose, high speed photography can be used to record its changing profile. By this method a variable radial centrifugal force can be applied to the lens which mimics the pull of the zonule. 2. If the lens is not stressed at its centre beyond 100 Nm-2 it behaves as a truly elastic body. When stressed beyond this limit visco-elastic strain is produced at its poles. 3. The human lens has isotropic elastic properties at the extremes of life, but at the other times Young's Modulus of Elasticity varies with the direction in which it is measured. 4. Young's Modulus of Elasticity of the lens varies with age, polar elasticity and equatorial elasticity, at birth being 0·75 × 103 and 0·85 × 103 Nm-2 respectively, while at 63 years of age both are equal to 3 × 103 Nm-2. 5. A comparison of Young's Modulus of the young human lens with that of the rabbit and cat shows that the polar elasticity of the lenses of these animals was 5 times greater in the young rabbit, and 21 times greater in the adult cat. Equatorial elasticities of the rabbit and human lens were equal, while in the cat the equatorial elasticity was four times greater. 6. A mathematical model showing the lens substance possessing a nucleus of lower isotropic elasticity than that of the isotropic elastic cortex surrounding it, accounts for the difference between polar and equatorial elasticity of the intact adult lens. 7. The implications of these findings are discussed in relation to: (i) accommodation and the rheological properties of the lens; (ii) possible differences in the physical state of the lenticular proteins in the cortex and nucleus which may account for the senile variations in Young's Modulus of Elasticity in these regions of the lens; (iii) the loss of accommodation due solely to an increase in Young's Modulus of Elasticity of the lens between the ages of 15 and 60. This would amount to 44% of the
Measuring liquid crystal elastic constants with free energy perturbations.
Joshi, Abhijeet A; Whitmer, Jonathan K; Guzmán, Orlando; Abbott, Nicholas L; de Pablo, Juan J
2014-02-14
A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants. PMID:24837037
Elastic constant versus temperature behavior of three hardened maraging steels
NASA Technical Reports Server (NTRS)
Ledbetter, H. M.; Austin, M. W.
1985-01-01
Elastic constants of three maraging steels were determined by measuring ultrasonic velocities. Annealed steels show slightly lower bulk moduli and considerably lower shear moduli than hardened steels. All the elastic constants (Young's modulus, shear modulus, bulk modulus and Poisson's ratio) show regular temperature behavior between 76 and 400 K. Young's modulus and the shear modulus increase with increasing yield strength, but the bulk modulus and Poisson's ratio are relatively unchanged. Elastic anisotropy is quite small.
Extended temperature dependence of elastic constants in cubic crystals.
Telichko, A V; Sorokin, B P
2015-08-01
To extend the theory of the temperature dependence of the elastic constants in cubic crystals beyond the second- and third-order elastic constants, the fourth-order elastic constants, as well as the non-linearity in the thermal expansion temperature dependence, have been taken into account. Theoretical results were represented as temperature functions of the effective elastic constants and compared with experimental data for a number of cubic crystals, such as alkali metal halides, and elements gold and silver. The relations obtained give a more accurate description of the experimental temperature dependences of second-order elastic constants for a number of cubic crystals, including deviations from linear behavior. A good agreement between theoretical estimates and experimental data has been observed. PMID:25819879
The elastic constants of San Carlos olivine to 17 GPa
Abramson, E.H.; Brown, J.M.; Slutsky, L.J.; Zaug, J.
1997-06-01
All elastic constants, the average bulk and shear moduli, and the lattice parameters of San Carlos olivine (Fo{sub 90}) (initial density 3.355gm/cm{sup 3}) have been determined to a pressure of 12 GPa at room temperature. Measurements of c{sub 11}, c{sub 33}, c{sub 13}, and c{sub 55} have been extended to 17 GPa. The pressure dependence of the adiabatic, isotropic (Hashin-Shtrikman bounds) bulk modulus, and shear modulus may be expressed as K{sub HS}=129.4+4.29P and by G{sub HS}=78+1.71P{minus}0.027P{sup 2}, where both the pressure and the moduli are in gigapascals. The isothermal compression of olivine is described by a bulk modulus given as K{sub T}=126.3+4.28P. Elastic constants other than c{sub 55} can be adequately represented by a linear relationship in pressure. In the order (c{sub 11},c{sub 12},c{sub 13},c{sub 22},c{sub 23},c{sub 33},c{sub 44},c{sub 55},c{sub 66}) the 1 bar intercepts (gigapascal units) are (320.5, 68.1, 71.6, 196.5, 76.8, 233.5, 64.0, 77.0, 78.7). The first derivatives are (6.54, 3.86, 3.57, 5.38, 3.37, 5.51, 1.67, 1.81, 1.93). The second derivative for c{sub 55} is {minus}0.070GPa{sup {minus}1}. Incompressibilities for the three axes may also be expressed as linear relationships with pressure. In the order of {bold a, b}, and {bold c} axes the intercepts in gigapascals are (547.8, 285.8, 381.8) and the first derivatives are (20.1, 12.3, 14.0).{copyright} 1997 American Geophysical Union
Resonant ultrasound spectroscopy for elastic constant measurements
Dixon, R.D.; Migliori, A.; Roe, L.H.
1993-12-31
All objects exhibit vibrational resonances when mechanically excited. These resonant frequencies are determined by density, geometry, and elastic moduli. Resonant ultrasound spectroscopy (RUS) takes advantage of the known relationship between the parameters. In particular, for a freely suspended object, with three of the four parameters (vibrational spectra, density, geometry, or elastic moduli) known the remaining one can be calculated. From a materials characterization standpoint it is straight-forward to measure density and geometry but less so to measure all the elastic moduli. It has recently become possible to quickly and accurately measure vibrational spectra, and using code written at Los Alamos, calculate all the elastic moduli simultaneously. This is done to an accuracy of better than one percent for compression and 0.1 percent for shear. RUS provides rapid acquisition of materials information here-to-fore obtainable only with difficulty. It will greatly facilitate the use of real materials properties in models and thus make possible more realistic modeling results. The technique is sensitive to phase changes and microstructure. This offers a change to input real data into microstructure and phase change models. It will also enable measurement of moduli at locations in and about a weld thus providing information for a validating coupled thermomechanical calculations.
The calculation of elastic constants from displacement fluctuations
NASA Astrophysics Data System (ADS)
Meyers, M. T.; Rickman, J. M.; Delph, T. J.
2005-09-01
We present a methodology for the accurate and efficient extraction of elastic constants in homogeneous solids via the calculation of the atomic displacement correlation function. This approach is validated for cubic solids parametrized by both Lennard-Jones and embedded-atom method potentials. Finally, we also discuss the extension of this method to obtain the elastic properties of inhomogeneous solids.
Elastic Constants of the β1-AgCd Alloy
NASA Astrophysics Data System (ADS)
Matsuo, Yoshie; Makita, Tomoko; Suzuki, Toshiharu; Nagasawa, Akira
1981-04-01
The elastic constants of single crystal of β1-AgCd alloy with 47.9± 0.1 at.%Cd have been measured in a temperature range between 180 K and 360 K, using a ultrasonic pulse-cho overlapping method. It is found that with increasing temperature, the elastic constants CL{=}(C11+C12+2C44)/2 and C44 decrease linearly but C'{=}(C11-C12)/2 increases. In addition, this alloy shows a high elastic anisotropy in comparison with other Ag-based β1-phase alloys such as AgMg and AgZn.
Elastic constants of Ultrasonic Additive Manufactured Al 3003-H18.
Foster, D R; Dapino, M J; Babu, S S
2013-01-01
Ultrasonic Additive Manufacturing (UAM), also known as Ultrasonic Consolidation (UC), is a layered manufacturing process in which thin metal foils are ultrasonically bonded to a previously bonded foil substrate to create a net part. Optimization of process variables (amplitude, normal load and velocity) is done to minimize voids along the bonded interfaces. This work pertains to the evaluation of bonds in UAM builds through ultrasonic testing of a build's elastic constants. Results from ultrasonic testing on UAM parts indicate orthotropic material symmetry and a reduction of up to 48% in elastic constant values compared to a control sample. The reduction in elastic constant values is attributed to interfacial voids. In addition, the elastic constants in the plane of the Al foils have nearly the same value, while the constants normal to the foil direction have much different values. In contrast, measurements from builds made with Very High Power Ultrasonic Additive Manufacturing (VHP UAM) show a drastic improvement in elastic properties, approaching values similar to that of bulk aluminum. PMID:22939821
Effect of molecular orientation on the elastic constants of polypropylene.
Kumar, S. R.; Renusch, D. P.; Grimsditch, M.; Materials Science Division; Amoco Polymers Research & Development
2000-03-07
The Brillouin spectroscopic measurements of elastic properties of polypropylene films fabricated by different processing techniques are described. We find that the elastic symmetry and the associated elastic constants are dependent on the molecular orientation brought about by the processing conditions used to produce the films. We have shown that Brillouin scattering techniques can successfully be used to track the molecular orientation induced by uniaxial stretching. We find a direct correspondence between the Brillouin measurements and optical birefringence measurements, illustrating that molecular orientation plays a dominant role in determining the mechanical anisotropy in these materials.
Distribution of local elastic constants in nanofilms of metals
NASA Astrophysics Data System (ADS)
Meng, Dong-Yuan; Lin, Ping; Yan, Xue-Song; Qi, Xin; Yang, Lei
2012-07-01
The distribution of local elastic constants of nanofilms was studied by the stress-fluctuation approach. The Lennard-Jones (L-J) and the second-moment approximation of tight-binding (TB-SMA) potential are used as models to investigate the differences between the pair-wise and many-body atomic interaction. Firstly the configurations of the nanofilm are obtained by the simulations, and then with the configurations, elastic constants are calculated. The behaviors of C11(n) and C12(n) are different for L-J films. Inner layers have larger C11(n) and smaller C12(n). For TB-SMA films, the distributions are different from L-J films'. The outmost layers have the smallest value, while the secondary outer layers have the largest and the behaviors of C11(n) and C12(n) are similar. This distribution can be explained by the competition between electron redistribution and lower coordination near the free surfaces. Compared to L-J model TB-SMA is better to describe the system. Furthermore, as the temperature increases, the elastic constants get larger while the distributions of the local elastic constants almost remain the same.
The estimated elastic constants for a single bone osteonal lamella.
Yoon, Young June; Cowin, Stephen C
2008-02-01
Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the collagen fibril whose diameter is the order of 20 nm. The next structural level is the collagen fiber with a diameter of the order of 80 nm. A lamella is a laminate structure, composed of multiple collagen fibers with embedded minerals and consists of several laminates. The thickness of one laminate in the lamella is approximately 130 nm. All collagen fibers in a laminate in the lamella are oriented in one direction. However, the laminates rotate relative to the adjacent laminates. In this work, all collagen fibers in a lamella are assumed to be aligned in the longitudinal direction. This kind of bone with all collagen fibers aligned in one direction is called a parallel fibered bone. The effective elastic constants for a parallel fibered bone are estimated by assuming periodic substructures. These results provide a database for estimating the anisotropic poroelastic constants of an osteon and also provide a database for building mathematical or computational models in bone micromechanics, such as bone damage mechanics and bone poroelasticity. PMID:17297631
Elastic constants of cubic and wurtzite boron nitrides
NASA Astrophysics Data System (ADS)
Nagakubo, A.; Ogi, H.; Sumiya, H.; Kusakabe, K.; Hirao, M.
2013-06-01
We synthesized pure polycrystalline cubic boron nitride (cBN) and wurtzite boron nitride (wBN) by the direct conversion method from hexagonal boron nitride, and measured their longitudinal-wave elastic constants CL between 20 and 300 K using picosecond ultrasound spectroscopy. Their room-temperature values are 945 ± 3 GPa and 930 ± 18 GPa for cBN and wBN, respectively. The shear modulus G of cBN was also determined by combining resonance ultrasound spectroscopy and micromechanics calculation as G = 410 GPa. We performed ab-initio calculations and confirmed that the generalized gradient approximation potential fails to yield correct elastic constants, which indicated the necessity of a hybrid-functional method.
Elastic constants of beryllium: a first-principles investigation.
Dal Corso, Andrea
2016-02-24
We apply several recently introduced projector-augmented wave, ultrasoft, and norm-conserving pseudopotentials (PPs) to the calculation of the elastic constants of beryllium and compare the results with previous theory and experiments. We discuss how the elastic constants depend on the Brillouin zone integration, the PP type, and the exchange and correlation functional. We find that although in percentage terms the elastic constants of beryllium depend on the PPs more than the crystal parameters or the bulk moduli, the differences between the local density approximation (LDA) and the Perdew, Burke, and Ernzerhof (PBE) generalized-gradient approximation are larger than the PP differences. The LDA overestimates compared to experiments, while the PBE values are higher than those of experiments but show a much better agreement. The PBEsol functional gives values that are slightly higher than those from PBE, with differences comparable to the PP uncertainty. We propose a simple formula to rationalize the internal relaxations in hexagonal close-packed crystals and show that Be relaxations are in reasonable agreement with this formula. The effects of internal relaxations on the values of C11 and C12 amount to a few per cent of C11, but up to 50% of C12. PMID:26809146
Elastic constants of beryllium: a first-principles investigation
NASA Astrophysics Data System (ADS)
Dal Corso, Andrea
2016-02-01
We apply several recently introduced projector-augmented wave, ultrasoft, and norm-conserving pseudopotentials (PPs) to the calculation of the elastic constants of beryllium and compare the results with previous theory and experiments. We discuss how the elastic constants depend on the Brillouin zone integration, the PP type, and the exchange and correlation functional. We find that although in percentage terms the elastic constants of beryllium depend on the PPs more than the crystal parameters or the bulk moduli, the differences between the local density approximation (LDA) and the Perdew, Burke, and Ernzerhof (PBE) generalized-gradient approximation are larger than the PP differences. The LDA overestimates compared to experiments, while the PBE values are higher than those of experiments but show a much better agreement. The PBEsol functional gives values that are slightly higher than those from PBE, with differences comparable to the PP uncertainty. We propose a simple formula to rationalize the internal relaxations in hexagonal close-packed crystals and show that Be relaxations are in reasonable agreement with this formula. The effects of internal relaxations on the values of C 11 and C 12 amount to a few per cent of C 11, but up to 50% of C 12.
NASA Astrophysics Data System (ADS)
Andronesi, Ovidiu C.; Ramadan, Saadallah; Ratai, Eva-Maria; Jennings, Dominique; Mountford, Carolyn E.; Sorensen, A. Gregory
2010-04-01
The purpose of this work was to design and implement constant adiabaticity gradient modulated pulses that have improved slice profiles and reduced artifacts for spectroscopic imaging on 3 T clinical scanners equipped with standard hardware. The newly proposed pulses were designed using the gradient offset independent adiabaticity (GOIA, Tannus and Garwood [13]) method using WURST modulation for RF and gradient waveforms. The GOIA-WURST pulses were compared with GOIA-HS n (GOIA based on nth-order hyperbolic secant) and FOCI (frequency offset corrected inversion) pulses of the same bandwidth and duration. Numerical simulations and experimental measurements in phantoms and healthy volunteers are presented. GOIA-WURST pulses provide improved slice profile that have less slice smearing for off-resonance frequencies compared to GOIA-HS n pulses. The peak RF amplitude of GOIA-WURST is much lower (40% less) than FOCI but slightly higher (14.9% more) to GOIA-HS n. The quality of spectra as shown by the analysis of lineshapes, eddy currents artifacts, subcutaneous lipid contamination and SNR is improved for GOIA-WURST. GOIA-WURST pulse tested in this work shows that reliable spectroscopic imaging could be obtained in routine clinical setup and might facilitate the use of clinical spectroscopy.
Elastic constants and dynamics in nematic liquid crystals
NASA Astrophysics Data System (ADS)
Humpert, Anja; Allen, Michael P.
2015-09-01
In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay-Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay-Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.
Unified dark fluid with constant adiabatic sound speed and cosmic constraints
NASA Astrophysics Data System (ADS)
Xu, Lixin; Wang, Yuting; Noh, Hyerim
2012-02-01
As is known, more than 90% of the energy content in the Universe is made of unknown dark component. Usually this dark fluid is separated into two parts: dark matter and dark energy. However, it may be a mixture of these two energy components, or just one exotic unknown fluid. This property is dubbed as dark degeneracy. With this motivation, in this paper, a unified dark fluid having constant adiabatic sound speed cs2=α, which is in the range [0,1], is studied. At first, via the energy conservation equation, its energy density, ρd/ρd0=(1-Bs)+Bsa-3(1+α) where Bs is related to integration constant from energy conservation equation as another model parameter, is presented. Then by using the Markov Chain Monte Carlo method with currently available cosmic observational data sets which include type Ia supernova Union 2, baryon acoustic oscillation, and WMAP 7-year data of cosmic background radiation, we show that small values of α are favored in this unified dark fluid model. Furthermore, we show that smaller values of α<10-5 are required to match matter (baryon) power spectrum from SDSS DR7.
Unstable slippage across a fault that separates elastic media of different elastic constants
Weertman, J.
1980-03-10
In this study it is demonstrated that relatively slow, quasi-static slippage on a fault that separates 2 half-spaces of different elastic constants can become unstable if the slippage is governed by the Amontons-Coulomb friction law.(The shear stress across a fault required for slipping motion is proportional to the normal compressive stress across the fault.) If the 2 half-spaces have identical properties, unstable slippage is not possible under this friction law. The unstable slippage that is investigated in this work is a consequences of the existence of a short-range normal traction stress that gliding edge dislocations produce across an interface between 2 half-spaces of different elastic constants. This normal traction stress does not exist if the 2 half-spaces have identical properties. (Recent work of Dundurs, Comninous et al. has revealed the importance of the short-range traction stress components to crack problems.) 30 references.
NASA Astrophysics Data System (ADS)
Vaidya, B.; Mignone, A.; Bodo, G.; Massaglia, S.
2015-08-01
Context. An equation of state (EoS) is a relation between thermodynamic state variables and it is essential for closing the set of equations describing a fluid system. Although an ideal EoS with a constant adiabatic index Γ is the preferred choice owing to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Aims: In the present work we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation, and temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation-equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes. Methods: We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS. The first employs root-finder methods and it is best suited for EoS in analytical form. The second is based on lookup tables and interpolation and results in a more computationally efficient approach, although care must be taken to ensure thermodynamic consistency. Results: A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is 500-104 K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although the employment of lookup table methods (when possible) can
Elastic constants and velocity surfaces of indurated anisotropic shales
Johnston, J.E.; Christensen, N.I.
1994-09-01
The velocities of two Devonian-Mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation. Both samples were found to be transversely isotropic at elevated pressures with the main symmetry axis perpendicular to bedding. The elastic constants of the shales were used to calculate phase and group velocity surfaces as a function of angle to the bedding normal. Multiple velocity measurements in non-symmetry directions, not undertaken in previously published studies of shales, have been used to confirm features observed on calculated velocity surfaces. It is demonstrated that velocities measured in non-symmetry directions are phase velocities. Group velocities were found to be significantly lower than the corresponding phase velocities of the shales due to their high anisotropies. Shear wave splitting was found to be negligible for propagation directions within approximately 30{degrees} of the bedding normals.
Ab Initio Simulation Beryllium in Solid Molecular Hydrogen: Elastic Constant
NASA Astrophysics Data System (ADS)
Guerrero, Carlo L.; Perlado, Jose M.
2016-03-01
In systems of inertial confinement fusion targets Deuterium-Tritium are manufactured with a solid layer, it must have specific properties to increase the efficiency of ignition. Currently there have been some proposals to model the phases of hydrogen isotopes and hence their high pressure, but these works do not allow explaining some of the structures present at the solid phase change effect of increased pressure. By means of simulation with first principles methods and Quantum Molecular Dynamics, we compare the structural difference of solid molecular hydrogen pure and solid molecular hydrogen with beryllium, watching beryllium inclusion in solid hydrogen matrix, we obtain several differences in mechanical properties, in particular elastic constants. For C11 the difference between hydrogen and hydrogen with beryllium is 37.56%. This may produce a non-uniform initial compression and decreased efficiency of ignition.
Mangia, Silvia; Liimatainen, Timo; Garwood, Michael; Tkac, Ivan; Henry, Pierre-Gilles; Deelchand, Dinesh; Michaeli, Shalom
2011-08-01
In this work, we investigated the frequency-offset dependence of the rotating frame longitudinal (R(1ρ)) and transverse (R(2ρ)) relaxation rate constants when using hyperbolic-secant adiabatic full passage pulses or continuous-wave spin-lock irradiation. Phantom and in vivo measurements were performed to validate theoretical predictions of the dominant relaxation mechanisms existing during adiabatic full passage pulses when using different settings of the frequency offset relative to the carrier. In addition, adiabatic R(1ρ) and R(2ρ) values of total creatine and N-acetylaspartate were measured in vivo from the human brain at 4 T. When the continuous-wave pulse power was limited to safe specific absorption rates for humans, simulations revealed a strong dependence of R(1ρ) and R(2ρ) values on the frequency offset for both dipolar interactions and anisochronous exchange mechanisms. By contrast, theoretical and experimental results showed adiabatic R(1ρ) and R(2ρ) values to be practically invariant within the large subregion of the bandwidth of the hyperbolic-secant pulse where complete inversion was achieved. However, adiabatic R(1ρ) and R(2ρ) values of the methyl protons of total creatine (at 3.03 ppm) were almost doubled when compared with those of the methyl protons of N-acetylaspartate (at 2.01 ppm) in spite of the fact that these resonances were in the flat region of the inversion band of the adiabatic full passage pulses. We conclude that differences in adiabatic R(1ρ) and R(2ρ) values of human brain metabolites are not a result of their chemical shifts, but instead reflect differences in dynamics. PMID:21264976
Mangia, Silvia; Liimatainen, Timo; Garwood, Michael; Tkac, Ivan; Henry, Pierre-Gilles; Deelchand, Dinesh; Michaeli, Shalom
2011-01-01
In this work, we investigated the frequency-offset dependence of the rotating frame longitudinal (R1ρ) and transverse (R2ρ) relaxation rate constants when using hyperbolic-secant adiabatic full passage pulses or continuous-wave spin-lock irradiation. Phantom and in vivo measurements were performed to validate theoretical predictions of the dominant relaxation mechanisms existing during adiabatic full passage pulses when using different settings of the frequency offset relative to the carrier. In addition, adiabatic R1ρ and R2ρ values of total creatine and N-acetylaspartate were measured in vivo from the human brain at 4 T. When the continuous-wave pulse power was limited to safe specific absorption rates for humans, simulations revealed a strong dependence of R1ρ and R2ρ values on the frequency offset for both dipolar interactions and anisochronous exchange mechanisms. By contrast, theoretical and experimental results showed adiabatic R1ρ and R2ρ values to be practically invariant within the large subregion of the bandwidth of the hyperbolic-secant pulse where complete inversion was achieved. However, adiabatic R1ρ and R2ρ values of the methyl protons of total creatine (at 3.03 ppm) were almost doubled when compared with those of the methyl protons of N-acetylaspartate (at 2.01 ppm) in spite of the fact that these resonances were in the flat region of the inversion band of the adiabatic full passage pulses. We conclude that differences in adiabatic R1ρ and R2ρ values of human brain metabolites are not a result of their chemical shifts, but instead reflect differences in dynamics. PMID:21264976
Nondestructive characterization of the elastic constants of fiber reinforced composites
NASA Technical Reports Server (NTRS)
Mal, Ajit K.; Lih, Shyh-Shiuh; Bar-Cohen, Yoseph
1993-01-01
Composite structural components may be subjected to a variety of defects resulting in a sharp reduction in their load carrying capacity or even catastrophic failure. Thus, it is extremely important to have the means to monitor the degradation suffered by critical components of a structure for safe operation during its service life. A nondestructive method based on ultrasonics has recently been developed for the quantitative evaluation of composite structural components during service. The experimental part of the technique uses a two-transducer, pitch-catch type arrangement to generate a variety of elastic waves within the specimen immersed in water. The recorded reflection data are then analyzed by means of a theoretical model to back out the relevant properties. In this paper the method is applied to determine the stiffness constants of unidirectional graphite/epoxy materials. The measurements are shown to be efficient and sufficiently accurate so that it can be used for early detection of material degradation in composite structural elements during service.
Measuring elastic constants using non-contact ultrasonic techniques
NASA Astrophysics Data System (ADS)
Edwards, R. S.; Perry, R.; Cleanthous, D.; Backhouse, D. J.; Moore, I. J.; Clough, A. R.; Stone, D. I.
2012-05-01
The use of ultrasound for measuring elastic constants and phase transitions is well established. Standard measurements use piezoelectric transducers requiring couplant and contact with the sample. Recently, non-destructive testing (NDT) has seen an increase in the use of non-contact ultrasonic techniques, for example electromagnetic acoustic transducers (EMATs) and laser ultrasound, due to their many benefits. For measurements of single crystals over a range of temperatures non-contact techniques could also bring many benefits. These techniques do not require couplant, and hence do not suffer from breaking of the bond between transducer and sample during thermal cycling, and will potentially lead to a simpler and more adaptable measurement system with lower risk of sample damage. We present recent work adapting EMAT advances from NDT to measurements of single crystals at cryogenic temperatures and illustrate this with measurements of magnetic phase transitions in Gd64Sc36 using both contact and non-contact transducers. We discuss the measurement techniques implemented to overcome noise problems, and a digital pulse-echo-overlap technique, using data analysis in the frequency domain to measure the velocity.
Theoretical prediction of Debye temperature & elastic constants of geophysical mineral
NASA Astrophysics Data System (ADS)
Singh, Chandra K.; Pandey, Anjani K.; Pandey, Brijesh K.
2016-05-01
Technological applications of the materials can be explored upto the desired limit of accuracy with the better knowledge of its mechanical and thermal properties such as ductility brittleness and Debye temperature. For the resistance to fracture (K) and plastic deformation (G) the ratio K/G is treated as an indication of ductile or brittle character of solids. In the present work we have tested the condition of ductility and brittleness with the calculated values of K/G for the geophysical minerals MgO and CaO, which are in good agreement with the corresponding experimental values. We have also computed the Debye temperature (θD) for the selected samples using average sound velocity obtained by using the values of resistance to fracture (K) and plastic deformation (G). It is observed that both the minerals are Brittle in nature and the calculated values of Debye temperature is in good agreement with the corresponding experimental values. Thus it is concluded that the nature and Debye temperature of geophysical minerals can be predicted upto high temperature simply with the knowledge of its elastic stiffness constant only.
Venkata Sai, D; Mirri, G; Kouwer, P H J; Sahoo, R; Musevic, I; Dhara, Surajit
2016-03-01
We report the first experimental studies on the temperature dependence of viscoelastic properties of a room temperature discotic nematic liquid crystal. The splay elastic constant is greater than the bend elastic constant and both show unusual temperature and order parameter dependence. The rotational viscosity is remarkably larger than conventional calamitic liquid crystals. We provide a simple physical explanation based on the columnar short-range order to account for the the unusual temperature dependence of the elastic constants. PMID:26883494
On the reduction of elastic constants for multiphase composites
Markenscoff, X.; Jasiuk, I.
1995-12-31
The reduction in the number of elastic parameters in a multiphase multiply connected composite with body forces is examined on the basis of the invariance of stress under a change in elastic compliances. The conditions obtained are the generalization of the Michell conditions for domains containing inclusions of a different material. Several cases and examples are presented. The conditions allowing for linear (in space) transformation of the elastic compliances are also examined.
Third-order elastic constants of the alloy Fe 72Pt 28
NASA Astrophysics Data System (ADS)
Vinu, T. P.; Menon, C. S.
2004-09-01
The complete sets of second- and third-order elastic constants of the cubic Fe72Pt28 have been obtained using the strain energy density derived from interactions up to three nearest neighbours of each atom in the unit cell. The finite strain elasticity theory has been used to get the strain energy density of Fe72Pt28. The strain energy density is compared with the strain-dependent lattice energy density obtained from the continuum model approximation and the expressions for the second- and third-order elastic constants of Fe72Pt28 are given. The second-order potential parameter is deduced from the measured second-order elastic constants of Fe72Pt28 and the third-order potential parameter is estimated from the Lennard-Jones inter-atomic potential for Fe72Pt28. The inter-lattice displacements; the three independent second-order elastic constants and the six independent third-order elastic constants of Fe72Pt28 are also determined. The second-order elastic constants are compared with the experimental elastic constants of Fe72Pt28. We also study the effect of pressure on the second-order elastic constants of Fe72Pt28.
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Kalluri, Sreeramesh
1991-01-01
The temperature-dependent engineering elastic constants of a directionally solidified nickel-base superalloy were estimated from the single-crystal elastic constants of nickel and MAR-MOO2 superalloy by using Wells' method. In this method, the directionally solidified (columnar-grained) nickel-base superalloy was modeled as a transversely isotropic material, and the five independent elastic constants of the transversely isotropic material were determined from the three independent elastic constants of a cubic single crystal. Solidification for both the single crystals and the directionally solidified superalloy was assumed to be along the (001) direction. Temperature-dependent Young's moduli in longitudinal and transverse directions, shear moduli, and Poisson's ratios were tabulated for the directionally solidified nickel-base superalloy. These engineering elastic constants could be used as input for performing finite element structural analysis of directionally solidified turbine engine components.
Elastic constants of α Ti-7Al measured using resonant ultrasound spectroscopy
NASA Astrophysics Data System (ADS)
Adebisi, R. A.; Sathish, S.; Pilchak, A. L.; Shade, P. A.
2016-02-01
The five independent elastic constants of a single-phase (α, HCP crystal structure) titanium alloy, Ti-7Al, have been measured for the first time using resonant ultrasound spectroscopy (RUS). RUS is a nondestructive evaluation method that mea-sures the mechanical resonance of solids and uses the resonance frequencies to extract a complete set of elastic constants of the solid material. The elastic constants of titanium alloys vary substantially depending on manufacturing history and composition. In addition, available data on the elastic constants of titanium alloys is limited. The elastic constants data for Ti-7Al are presented in this paper and the results are compared to the available data for other titanium alloys that are similar in composition.
Quick and accurate estimation of the elastic constants using the minimum image method
NASA Astrophysics Data System (ADS)
Tretiakov, Konstantin V.; Wojciechowski, Krzysztof W.
2015-04-01
A method for determining the elastic properties using the minimum image method (MIM) is proposed and tested on a model system of particles interacting by the Lennard-Jones (LJ) potential. The elastic constants of the LJ system are determined in the thermodynamic limit, N → ∞, using the Monte Carlo (MC) method in the NVT and NPT ensembles. The simulation results show that when determining the elastic constants, the contribution of long-range interactions cannot be ignored, because that would lead to erroneous results. In addition, the simulations have revealed that the inclusion of further interactions of each particle with all its minimum image neighbors even in case of small systems leads to results which are very close to the values of elastic constants in the thermodynamic limit. This enables one for a quick and accurate estimation of the elastic constants using very small samples.
NASA Astrophysics Data System (ADS)
Mirzaev, Sirojiddin Z.; Kaatze, Udo
2016-09-01
Ultrasonic spectra of mixtures of nitrobenzene with n-alkanes, from n-hexane to n-nonane, are analyzed. They feature up to two Debye-type relaxation terms with discrete relaxation times and, near the critical point, an additional relaxation term due to the fluctuations in the local concentration. The latter can be well represented by the dynamic scaling theory. Its amplitude parameter reveals the adiabatic coupling constant of the mixtures of critical composition. The dependence of this thermodynamic parameter upon the length of the n-alkanes corresponds to that of the slope in the pressure dependence of the critical temperature and is thus taken another confirmation of the dynamic scaling model. The change in the variation of the coupling constant and of several other mixture parameters with alkane length probably reflects a structural change in the nitrobenzene- n-alkane mixtures when the number of carbon atoms per alkane exceeds eight.
Free energy perturbation method for measuring elastic constants of liquid crystals
NASA Astrophysics Data System (ADS)
Joshi, Abhijeet
There is considerable interest in designing liquid crystals capable of yielding specific morphological responses in confined environments, including capillaries and droplets. The morphology of a liquid crystal is largely dictated by the elastic constants, which are difficult to measure and are only available for a handful of substances. In this work, a first-principles based method is proposed to calculate the Frank elastic constants of nematic liquid crystals directly from atomistic models. These include the standard splay, twist and bend deformations, and the often-ignored but important saddle-splay constant. The proposed method is validated using a well-studied Gay-Berne(3,5,2,1) model; we examine the effects of temperature and system size on the elastic constants in the nematic and smectic phases. We find that our measurements of splay, twist, and bend elastic constants are consistent with previous estimates for the nematic phase. We further outline the implementation of our approach for the saddle-splay elastic constant, and find it to have a value at the limits of the Ericksen inequalities. We then proceed to report results for the elastic constants commonly known liquid crystals namely 4-pentyl-4'-cynobiphenyl (5CB) using atomistic model, and show that the values predicted by our approach are consistent with a subset of the available but limited experimental literature.
Elastic constants of GaN between 10 and 305 K
NASA Astrophysics Data System (ADS)
Adachi, K.; Ogi, H.; Nagakubo, A.; Nakamura, N.; Hirao, M.; Imade, M.; Yoshimura, M.; Mori, Y.
2016-06-01
Using the antenna-transmission resonant ultrasound spectroscopy, we measured the elastic constants of GaN between 10 and 305 K using 72 resonance frequencies. The mode Grüneisen parameter is determined from temperature dependence of each elastic constant, which is larger along the c axis than along the a axis, showing anisotropy in lattice anharmonicity. The zero-temperature elastic constants, determined using the Einstein-oscillator model, yield the Debye characteristic temperature of 636 K. The ab-initio calculation is carried out for deducing the elastic constants, and comparison between calculations and measurements at 0 K reveals that the local-density-approximation potential is preferable for theoretically evaluating characteristics of GaN. The theoretical calculation also supports the anisotropy in lattice anharmonicity.
Phonon frequencies and elastic constants of cubic Pu from electronic structure theory
Straub, G.K.
1996-11-01
The phonon frequencies and elastic constants of plutonium are calculated using a model for the electronic structure that treats the valance electrons as a pseudopotential and the f-electrons in tight-binding theory. An effective interaction between ions is presented with electron screening treated in the Thomas-Fermi approximation and the f-electrons contributing bonding and repulsive terms to the potential. The phonon frequencies and elastic constants are calculated using the face-centered cubic lattice structure for both the {alpha}-, and {delta}-phases of Pu. The electronic structure predicts the qualitative behavior of the elastic constants and the transverse branches of the phonon dispersion curves in agreement with experimental values of the elastic constants for B-phase Pu.
NASA Astrophysics Data System (ADS)
Yang, Jing; Cheng, Jianchun; Berthelot, Yves H.
2002-03-01
An inverse method based on a combination of the wavelet transform and artificial neural networks is presented. The method is used to recover the elastic constants of a fiber-reinforced composite plate from experimental measurements of ultrasonic Lamb waves generated and detected with lasers. In this method, the elastic constants are not recovered from the dispersion curves but rather directly from the measured waveforms. Transient waveforms obtained by numerical simulations for different elastic constants are used as input to train the neural network. The wavelet transform is used to extract the eigenvectors from the Lamb wave signals to simplify the structure of the neutral network. The eigenvectors are then introduced into a multilayer internally recurrent neural network with a back-propagation algorithm. Finally, experimental waveforms recoded on a titanium-graphite composite plate are used as input to recover the elastic constants of the material.
NASA Technical Reports Server (NTRS)
Marques, E. R. C.; Williams, J. H., Jr.
1986-01-01
The elastic constants of a fiberglass epoxy unidirectional composite are determined by measuring the phase velocities of longitudinal and shear stress waves via the through transmission ultrasonic technique. The waves introduced into the composite specimens were generated by piezoceramic transducers. Geometric lengths and the times required to travel those lengths were used to calculate the phase velocities. The model of the transversely isotropic medium was adopted to relate the velocities and elastic constants.
Bounds on Elastic Constants for Random Polycrystals of Laminates
Berryman, J G
2004-04-30
A well-known result due to Hill provides an exact expression for the bulk modulus of any multicomponent elastic composite whenever the constituents are isotropic and the shear modulus is uniform throughout. Although no precise analog of Hill's result is available for the opposite case of uniform bulk modulus and varying shear modulus, it is shown here that some similar statements can be made for shear behavior of random polycrystals composed of laminates of isotropic materials. In particular, the Hashin-Shtrikman-type bounds of Peselnick, Meister, and Watt for random polycrystals composed of hexagonal (transversely isotropic) grains are applied to the problem of polycrystals of laminates. An exact product formula relating the Reuss estimate of bulk modulus and an effective shear modulus (of laminated grains composing the system) to products of the eigenvalues for quasi-compressional and quasi-uniaxial shear eigenvectors also plays an important role in the analysis of the overall shear behavior of the random polycrystal. When the bulk modulus is uniform in such a system, the equations are shown to reduce to a simple form that depends prominently on the uniaxial shear eigenvalue - as expected from physical arguments concerning the importance of uniaxial shear in these systems. One application of the analytical results presented here is for benchmarking numerical procedures used for estimating elastic behavior of complex composites.
Determination of the dynamic elastic constants of recycled aggregate concrete
NASA Astrophysics Data System (ADS)
Tsoumani, A. A.; Barkoula, N.-M.; Matikas, T. E.
2015-03-01
Nowadays, construction and demolition waste constitutes a major portion of the total solid waste production in the world. Due to both environmental and economical reasons, an increasing interest concerning the use of recycled aggregate to replace aggregate from natural sources is generated. This paper presents an investigation on the properties of recycled aggregate concrete. Concrete mixes are prepared using recycled aggregates at a substitution level between 0 and 100% of the total coarse aggregate. The influence of this replacement on strengthened concrete's properties is being investigated. The properties estimated are: density and dynamic modulus of elasticity at the age of both 7 and 28 days. Also, flexural strength of 28 days specimens is estimated. The determination of the dynamic elastic modulus was made using the ultrasonic pulse velocity method. The results reveal that the existence of recycled aggregates affects the properties of concrete negatively; however, in low levels of substitution the influence of using recycled aggregates is almost negligible. Concluding, the controlled use of recycled aggregates in concrete production may help solve a vital environmental issue apart from being a solution to the problem of inadequate concrete aggregates.
Adlem, K; Čopič, M; Luckhurst, G R; Mertelj, A; Parri, O; Richardson, R M; Snow, B D; Timimi, B A; Tuffin, R P; Wilkes, D
2013-08-01
Here we report the chemical induction of the twist-bend nematic phase in a nematic mixture of ether-linked liquid crystal dimers by the addition of a dimer with methylene links; all dimers have an odd number of groups in the spacer connecting the two mesogenic groups. The twist-bend phase has been identified from its optical texture and x-ray scattering pattern as well as NMR spectroscopy, which demonstrates the phase chirality. Theory predicts that the key macroscopic property required for the stability of this chiral phase formed from achiral molecules is for the bend elastic constant to tend to be negative; in addition the twist elastic constant should be smaller than half the splay elastic constant. To test these important aspects of the prediction we have measured the bend and splay elastic constants in the nematic phase preceding the twist-bend nematic using the classic Frederiks methodology and all three elastic constants employing the dynamic light scattering approach. Our results show that, unlike the splay, the bend elastic constant is small and decreases significantly as the transition to the induced twist-bend nematic phase is approached, but then exhibits unexpected behavior prior to the phase transition. PMID:24032852
Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone
Deuerling, Justin M.; Yue, Weimin; Espinoza Orías, Alejandro A.; Roeder, Ryan K.
2009-01-01
The anisotropic elastic constants of human cortical bone were predicted using a specimen-specific micromechanical model that accounted for structural parameters across multiple length scales. At the nano-scale, the elastic constants of the mineralized collagen fibril were estimated from measured volume fractions of the constituent phases, namely apatite crystals and Type I collagen. The elastic constants of the extracellular matrix (ECM) were predicted using the measured orientation distribution function (ODF) for the apatite crystals to average the contribution of misoriented mineralized collagen fibrils. Finally, the elastic constants of cortical bone tissue were determined by accounting for the measured volume fraction of Haversian porosity within the ECM. Model predictions using the measured apatite crystal ODF were not statistically different from experimental measurements for both the magnitude and anisotropy of elastic constants. In contrast, model predictions using common idealized assumptions of perfectly aligned or randomly oriented apatite crystals were significantly different from the experimental measurements. A sensitivity analysis indicated that the apatite crystal volume fraction and ODF were the most influential structural parameters affecting model predictions of the magnitude and anisotropy, respectively, of elastic constants. PMID:19664772
Bowing effect in elastic constants of dilute Ga(As,N) alloys
NASA Astrophysics Data System (ADS)
Berggren, Jonas; Hanke, Michael; Trampert, Achim
2016-05-01
We study the elastic properties of dilute Ga(As,N) thin films grown on GaAs(001) by means of nano-indentation and complementary dynamic finite element calculations. The experimental results of indentation modulus are compared with simulations in order to extract the cubic elastic constants cij as a function of nitrogen content of the Ga(As,N) alloys. Both, indentation modulus and elastic constants decrease with increasing nitrogen content, which proves a strong negative bowing effect in this system in contrast to Vegard's law.
Third-order elastic constants of diamond determined from experimental data
NASA Astrophysics Data System (ADS)
Winey, J. M.; Hmiel, A.; Gupta, Y. M.
2016-06-01
The pressure derivatives of the second-order elastic constants (SOECs) of diamond were determined by analyzing previous sound velocity measurements under hydrostatic stress [McSkimin and Andreatch, J. Appl. Phys., vol. 43, 1972, pp. 2944] [4]. Our analysis corrects an error in the previously reported results. Using the corrected pressure derivatives, together with published data for the nonlinear elastic response of shock-compressed diamond [Lang and Gupta, Phys. Rev. Lett., vol. 106, 2011, pp. 125502] [3], a complete and corrected set of third-order elastic constants (TOECs) is presented that differs significantly from TOECs published previously.
Elastic constants of a Laves phase compound: C15 NbCr{sub 2}
Ormeci, A. |; Chu, F.; Wills, J.M.; Chen, S.P.; Albers, R.C.; Thoma, D.J.; Mitchell, T.E.
1997-04-01
The single-crystal elastic constants of C15 NbCr{sub 2} have been computed by using a first-principles, self-consistent, full-potential total energy method. From these single-crystal elastic constants the isotropic elastic moduli are calculated using the Voigt and Reuss averages. The calculated values are in fair agreement with the experimental values. The implications of the results are discussed with regards to Poisson`s ratio and the direction dependence of Young`s modulus.
Experimental Determination of High-Order Bending Elastic Constants of Lipid Bilayers.
Toscano-Flores, Liliana G; Jacinto-Méndez, Damián; Carbajal-Tinoco, Mauricio D
2016-06-30
We present a method to describe the formation of small lipid vesicles in terms of three bending elastic constants that can be experimentally measured. Our method combines a general expression of the elastic free energy of the bilayer and the thermodynamic description of molecular aggregation. The resulting model requires the size distribution of liposomes, which is determined from the X-ray scattered intensity spectra of vesicular dispersions. By using two different preparation methods, we studied a series of vesicular solutions made of distinct lipids and we obtained their corresponding bending elastic constants that are consistent with known bending rigidities. PMID:27267752
The modified Black-Scholes model via constant elasticity of variance for stock options valuation
NASA Astrophysics Data System (ADS)
Edeki, S. O.; Owoloko, E. A.; Ugbebor, O. O.
2016-02-01
In this paper, the classical Black-Scholes option pricing model is visited. We present a modified version of the Black-Scholes model via the application of the constant elasticity of variance model (CEVM); in this case, the volatility of the stock price is shown to be a non-constant function unlike the assumption of the classical Black-Scholes model.
Formulas for the elastic constants of plates with integral waffle-like stiffening
NASA Technical Reports Server (NTRS)
Dow, Norris R; Libove, Charles; Hubka, Ralph E
1954-01-01
Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)
High Temperature Elastic Constants of Langatate from RUS Measurements up to 1100?C
Shyam, Amit; Lara-Curzio, Edgar
2008-01-01
This paper reports on the langatate (LGT) elastic constants and their temperature coefficients measured from room temperature (25degC) to 1100degC using resonant ultrasound spectroscopy (RUS). The constants were extracted by iteratively fitting the resonant peaks with those calculated by Lagrangian mechanics at each temperature where the RUS measurements were taken. In addition, the RUS technique was used to extract the elastic and piezoelectric constants in the 25degC to 120degC temperature range. The extraction of LGT elastic constants up to 1100degC presented in this paper represents a critical step towards the design and fabrication of LGT acoustic wave devices for high temperature and harsh environment applications.
NASA Astrophysics Data System (ADS)
Hmiel, A.; Winey, J. M.; Gupta, Y. M.; Desjarlais, M. P.
2016-05-01
Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.
Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index
NASA Astrophysics Data System (ADS)
Mignone, A.; McKinney, Jonathan C.
2007-07-01
The role of the equation of state (EoS) for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant Γ-law EoS, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic EoS that better approximates the single-specie relativistic gas. The paper focuses on three different topics. First, the influence of a more realistic EoS on the propagation of fast magnetosonic shocks is investigated. This calls into question the validity of the constant Γ-law EoS in problems where the temperature of the gas substantially changes across hydromagnetic waves. Secondly, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general EoS and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic EoS can considerably bear upon the solution when transitions from cold to hot gas (or vice versa) are present. Under these circumstances, a polytropic EoS can significantly endanger the solution.
Every, A G; Sumanya, C; Mathe, B A; Zhang, X; Comins, J D
2016-07-01
Surface Brillouin scattering of light allows the angular-dependent velocities of Rayleigh surface acoustic waves (SAW), pseudo-SAW and longitudinal lateral waves (L) on the surface of an opaque crystal to be measured, and the elastic constants thereby determined. Closed form expressions exist for the surface wave velocities in high symmetry directions on crystallographic symmetry planes, and these have been exploited in the past for obtaining the values of the elastic constants. This paper describes a procedure for obtaining an optimized set of elastic constants from SAW, pseudo-SAW and L velocities measured in arbitrary directions in the (001) and (110) surfaces of cubic crystals. It does so by affecting a linearization of the numerically determined angular-dependent SAW and pseudo-SAW velocities near the best fit, and using analytic expressions for the L velocity. The method also generates covariance ellipsoids, from which the uncertainties in the determined values of the elastic constants can be read off. The method is illustrated using surface Brillouin scattering data to obtain the room-temperature elastic constants C11, C12 and C44 of the cubic crystals VC0.75 and Rh3Nb. PMID:26899728
Accurate calculations of the high-pressure elastic constants based on the first-principles
NASA Astrophysics Data System (ADS)
Wang, Chen-Ju; Gu, Jian-Bing; Kuang, Xiao-Yu; Yang, Xiang-Dong
2015-08-01
The energy term corresponding to the first order of the strain in Taylor series expansion of the energy with respect to strain is always ignored when high-pressure elastic constants are calculated. Whether the modus operandi would affect the results of the high-pressure elastic constants is still unsolved. To clarify this query, we calculate the high-pressure elastic constants of tantalum and rhenium when the energy term mentioned above is considered and neglected, respectively. Results show that the neglect of the energy term corresponding to the first order of the strain indeed would influence the veracity of the high-pressure elastic constants, and this influence becomes larger with pressure increasing. Therefore, the energy term corresponding to the first-order of the strain should be considered when the high-pressure elastic constants are calculated. Project supported by the National Natural Science Foundation of China (Grant No. 11274235), the Young Scientist Fund of the National Natural Science Foundation of China (Grant No. 11104190), and the Doctoral Education Fund of Education Ministry of China (Grant Nos. 20100181110086 and 20110181120112).
Apparatus for measuring elastic constants of single crystals by a resonance technique up to 1825 K
Goto, T.; Anderson, O.L.
1988-08-01
By holding the rectangular parallelepiped specimen between long, thinalumina buffer rods, we can detect the resonance vibration of a specimen even attemperatures above 1800 K. This new technique, in combination with the theoryfor the calculation of the resonance frequency spectrum of a rectangularparallelepiped specimen, enables us to determine the high-temperature elastic properties of single-crystal materials. The first application of this new device was to determine the elastic stiffness constants of single-crystal corundum up to 1825 K.
Roh, Yongrae; Varadan, Vasundara V; Varadan, Vijay K
2002-06-01
Polyvinylidene fluoride (PVDF), a piezoelectric material, has many useful applications, for example, as sensors, transducers, and surface acoustic wave (SAW) devices. Models of performance of these devices would be useful engineering tools. However, the benefit of the model is only as accurate as the material properties used in the model. The purpose of this investigation is to measure the elastic, dielectric and piezoelectric properties over a frequency range, including the imaginary part (loss) of these properties. Measurements are difficult because poled material is available as thin films, and not all quantities can be measured in that form. All components of the elastic stiffness, dielectric tensor, and electromechanical coupling tensor are needed in the models. The material studied here is uniaxially oriented poled PVDF that has orthorhombic mm2 symmetry. Presented are the frequency dependence of all nine complex elastic constants, three complex dielectric constants, and five complex piezoelectric constants. The PVDF was produced at Raytheon Research Division, Lexington, MA. Measurements were made on thin films and on stacked, cubical samples. The elastic constants c44D and C55D, the dielectric constants epsilon11T and epsilon22T, as well as the piezoelectric constants g15 and g24 reported here have not been published before. The values were determined by ultrasonic measurements using an impedance analyzer and a least square data-fitting technique. PMID:12075977
Room-temperature elastic constants of Sc and ScD[sub 0. 18
Leisure, R.G. ); Schwarz, R.B.; Migliori, A.; Lei, M. )
1993-07-01
The complete set of elastic constants for Sc and ScD[sub 0.18] has been measured at room temperature. The results show that the addition of hydrogen to this rare-earth metal has a qualitatively different effect than the addition of hydrogen to transition metals such as palladium, vanadium, niobium, and tantalum. In the case of Sc all five elastic constants increase with the addition of hydrogen. The bulk modulus for ScD[sub 0.18] is 9.5% higher than that for Sc. The Debye temperature computed from the room-temperature elastic constants is 355 K for Sc and 371 K for ScD[sub 0.18].
Colloidal interactions in a homeotropic nematic cell with different elastic constants.
Tovkach, O M; Chernyshuk, S B; Lev, B I
2015-10-01
We propose a theoretical description of the interaction mediated by a nematic-liquid-crystal host with different Frank elastic constants. A general expression for the energy of such an interaction between colloidal particles of arbitrary size and shape suspended in a homeotropic cell is obtained. In the cells of large thickness, the presented potential converges to that found previously for small particles in the nematic bulk. In general, our results confirm the validity of the one-constant approximation for weakly elastically anisotropic nematic liquid crystals. For nematics with a high splay-to-bend ratio we predict a larger range of the interaction. Using the dependence of this range on the elastic constants, we show that there exists a qualitative similarity between the interactions in a nematic and in a smectic-A phase. It manifests itself, in particular, in a decrease of the angle between a chain of quadrupole particles and the uniform far-field director across a nematic-smectic-A phase transition. We also demonstrate that the anisotropy of the elastic constants can lead to the formation of thermodynamically stable linear superstructures of asymmetric particles (elastic monopoles) with large, compared to usual dipole chains, interparticle distances. PMID:26565263
Non-contact ultrasonic spectroscopy measurement of elastic constants and ultrasonic attenuation
Schwarz, R.B.; Kuokkala, V.T.; Srinivasan, S.; Visscher, W.M.
1991-01-01
We have developed an ultrasonic spectroscopy method for measuring the elastic constants of solids in hostile environments and over a broad temperature regime. The sample is cut as a rectangular parallelepiped, approximately 1 mm{sup 3} in volume. One or two of the sample surfaces are coated with a thin film of a magnetostrictive material such as nickel. The sample is placed coaxially with two solenoids. One solenoid is used to generate an AC magnetic field of small amplitude which stretches the films. By sweeping the frequency of this field, the sample is excited successively into its various mechanical resonance modes. The second solenoid detects the mechanical resonances. The elastic constants are then deduced from the spectrum of mechanical resonances measured at constant temperature. The internal friction is deduced from the width of the resonance peaks. Because the technique is strictly non-contact (the sample may be encapsulated in a fused silica tube), it is deal for measuring elastic constants in hostile environments or under controlled atmospheres. In its present version the system allows us to measure the elastic constants and ultrasonic attenuation of a given sample between 80 and 100 K. The operation of the system is exemplified by measurements on amorphous Ni{sub 80}P{sub 20} and crystalline Ti{sub 60}Cr{sub 40}. 17 refs., 6 figs.
NASA Astrophysics Data System (ADS)
Derby, B.
2007-08-01
A correlation is presented for the single-crystal elastic constants (Cij) of elemental (and IV-IV), III-V, and II-VI semiconductors with the diamond cubic, sphalerite, and wurtzite crystal structures. Both experimental data and theoretical calculations based on density functional theory follow the correlation. The elastic constants can be represented by an empirical linear relation that is a simple function of melting temperature TM and mean atomic volume Ω with Cij=Aij+Bij(kBTM/Ω) , where kB is Boltzmann’s constant. The empirical constants Aij and Bij are different for each of the groupings of semiconductors considered, which are identified as isomechanical groups. This correlation is similar in form to other correlations in the literature for diffusion data of materials that indicate the significance of the melting temperature as a scaling for lattice dynamic properties of materials.
NASA Astrophysics Data System (ADS)
Pestka, K. A.; Maynard, J. D.; Soukiassian, A.; Xi, X. X.; Schlom, D. G.; Le Page, Y.; Bernhagen, M.; Reiche, P.; Uecker, R.
2008-03-01
The complete elastic tensor of single crystal GdScO3 was determined using resonant ultrasound spectroscopy (RUS) in combination with ab initio calculations. The experimental determination of all nine elastic constants also provides a method for probing the dynamic lattice properties for this recently developed orthorhombic material. The experimentally determined elastic constants differed from theoretical values on average by 10%, and all but three of the nine elastic constants varied by less than 10%. These results indicate that ab initio calculations are now sufficiently accurate for the precise determination of the elastic tensor using RUS as the sole experimental source.
Johnson, W L; Kim, S A; Geiss, R; Flannery, C M; Soles, C L; Wang, C; Stafford, C M; Wu, W-L; Torres, J M; Vogt, B D; Heyliger, P R
2010-02-19
Elastic constants and cross-sectional dimensions of imprinted nanolines of poly(methyl methacrylate) (PMMA) on silicon substrates are determined nondestructively from finite-element inversion analysis of dispersion curves of hypersonic acoustic modes of these nanolines measured with Brillouin light scattering. The results for the cross-sectional dimensions, under the simplifying assumption of vertical sides and a semicircular top, are found to be consistent with dimensions determined from critical-dimension small-angle x-ray scattering measurements. The elastic constants C(11) and C(44) are found to be, respectively, 11.6% and 3.1% lower than their corresponding values for bulk PMMA. This result is consistent with the dimensional dependence of the quasi-static Young's modulus determined from buckling measurements on PMMA films with lower molecular weights. This study provides the first evidence of size-dependent effects on hypersonic elastic properties of polymers. PMID:20081293
Stebner, A. P.; Brown, D. W.; Brinson, L. C.
2013-05-27
Polycrystalline, monoclinic nickel-titanium specimens were subjected to tensile and compressive deformations while neutron diffraction spectra were recorded in situ. Using these data, orientation-specific and macroscopic Young's moduli are determined from analysis of linear-elastic deformation exhibited by 13 unique orientations of monoclinic lattices and their relationships to each macroscopic stress and strain. Five of 13 elastic compliance constants are also identified: s{sub 11} = 1.15, s{sub 15} = -1.10, s{sub 22} = 1.34, s{sub 33} = 1.06, s{sub 35} = -1.54, all Multiplication-Sign 10{sup -2} GPa{sup -1}. Through these results, recent atomistic calculations of monoclinic nickel-titanium elastic constants are validated.
Ultrasonic Determination of the Elastic Constants of Epoxy-natural Fiber Composites
NASA Astrophysics Data System (ADS)
Valencia, C. A. Meza; Pazos-Ospina, J. F.; Franco, E. E.; Ealo, Joao L.; Collazos-Burbano, D. A.; Garcia, G. F. Casanova
This paper shows the applications ultrasonic through-transmission technique to determine the elastic constants of two polymer-natural fiber composite materials with potential industrial application and economic and environmental advantages. The transversely isotropic coconut-epoxy and fique-epoxy samples were analyzed using an experimental setup which allows the sample to be rotated with respect to transducers faces and measures the time-of-flight at different angles of incidence. Then, the elastic properties of the material were obtained by fitting the experimental data to the Christoffel equation. Results show a good agreement between the measured elastic constants and the values predicted by an analytical model. The velocities as a function of the incidence angle are reported and the effect of the natural fiber on the stiffness of the composite is discussed.
Crowhurst, J C; Zaug, J M; Abramson, E H; Brown, J M; Ahre, D W
2002-08-22
Impulsive stimulated light scattering has been used to measure interfacial wave propagation speeds and elastic constants under conditions of high pressure. Data obtained from single-crystal Ge and Fe, and from polycrystalline Ta is presented. The method is complementary to other techniques for obtaining this type of information. There appears no fundamental reason why it cannot be extended to the 1 Mbar regime.
Using the spring constant method to analyze arterial elasticity in type 2 diabetic patients
2012-01-01
Background This study tests the validity of a newly-proposed spring constant method to analyze arterial elasticity in type 2 diabetic patients. Methods The experimental group comprised 66 participants (36 men and 30 women) ranging between 46 and 86 years of age, all with diabetes mellitus. In the experimental group, 21 participants suffered from atherosclerosis. All were subjected to the measurements of both the carotid-femoral pulse wave velocity (cfPWV) and the spring constant method. The comparison (control) group comprised 66 normal participants (37 men and 29 women) with an age range of 40 to 80 years who did not have diabetes mellitus. All control group members were subjected to measurement by the spring constant method. Results Statistical analysis of the experimental and control groups indicated a significant negative correlation between the spring constant and the cfPWV (P < .001; r = - 0.824 and – 0.71). Multivariate analysis similarly indicated a close relationship. The Student’s t test was used to examine the difference in the spring constant parameter between the experimental and control groups. A P-value less than .05 confirmed that the difference between the 2 groups was statistically significant. In receiver operating characteristic curve (ROC), the Area Under Curve (AUC, = 0.85) indicates good discrimination. These findings imply that the spring constant method can effectively identify normal versus abnormal characteristics of elasticity in normal and diabetic participants. Conclusions This study verifies the use of the spring constant method to assess arterial elasticity, and found it to be efficient and simple to use. The spring constant method should prove useful not only for improving clinical diagnoses, but also for screening diabetic patients who display early evidence of vascular disease. PMID:22531211
Allred, Clark L.; Yuan Xianglong; Hobbs, Linn W.; Bazant, Martin Z.
2004-10-01
The elastic constants of a wide range of models of defected crystalline and amorphous silicon are calculated, using the environment-dependent interatomic potential (EDIP). The defected crystalline simulation cells contain randomly generated defect distributions. An extensive characterization of point defects is performed, including structure, energy and influence on elastic constants. Three important conclusions are drawn. (1) Defects have independent effects on the elastic constants of silicon up to (at least) a defect concentration of 0.3%. (2) The linear effect of Frenkel pairs on the <110> Young's modulus of silicon is -1653 GPa per defect fraction. (3) 17 different point defect types cause a very similar decrease in the <110> Young's modulus: -(0.28{+-}0.05)% when calculated in isolation using a 1728-atom cell. These principles will be very useful for predicting the effect of radiation damage on the elastic modulus of silicon in the typical case in which point-defect concentrations can be estimated, but the exact distribution and species of defects is unknown. We also study amorphous samples generated in quenching the liquid with EDIP, including an ideal structure of perfect fourfold coordination, samples with threefold and fivefold coordinated defects, one with a nanovoid, and one with an amorphous inclusion in a crystalline matrix. In the last case, a useful finding is that the change in the Young's modulus is simply related to the volume fraction of amorphous material, as has also been observed by experiment.
Laoulache, R.N.; Maeder, P.F.; DiPippo, R.
1987-05-01
A Scheme is developed to describe the upward flow of a two-phase mixture of a single substance in a vertical adiabatic constant area pipe. The scheme is based on dividing the mixture into a homogeneous core surrounded by a liquid film. This core may be a mixture of bubbles in a contiguous liquid phase, or a mixture of droplets in a contiguous vapor phase. Emphasis is placed upon the latter case since the range of experimental measurements of pressure, temperature, and void fraction collected in this study fall in the slug-churn''- annular'' flow regimes. The core is turbulent, whereas the liquid film may be laminar or turbulent. Turbulent stresses are modeled by using Prandtl's mixing-length theory. The working fluid is Dichlorotetrafluoroethane CCIF{sub 2}-CCIF{sub 2} known as refrigerant 114 (R-114); the two-phase mixture is generated from the single phase substance by the process of flashing. In this study, the effect of the Froude and Reynolds numbers on the liquid film characteristics is examined. The compressibility is accounted for through the acceleration pressure gradient of the core and not directly through the Mach number. An expression for an interfacial friction coefficient between the turbulent core and the liquid film is developed; it is similar to Darcy's friction coefficient for a single phase flow in a rough pipe. Finally, an actual steam-water geothermal well is simulated; it is based on actual field data from New Zealand. A similarity theory is used to predict the steam-water mixture pressure and temperature starting with laboratory measurements on the flow of R-114.
Laoulache, R.N.; Maeder, P.F.; DiPippo, R.
1987-05-01
A scheme is developed to describe the upward flow of a two-phase mixture of a single substance in a vertical adiabatic constant area pipe. The scheme is based on dividing the mixture into a homogeneous core surrounded by a liquid film. This core may be a mixture of bubbles in a contiguous liquid phase, or a mixture of droplets in a contiguous vapor phase. The core is turbulent, whereas the liquid film may be laminar or turbulent. The working fluid is Dichlorotetrafluoroethane CClF/sub 2/-CClF/sub 2/ known as refrigerant 114 (R-114); the two-phase mixture is generated from the single phase substance by the process of flashing. In this study, the effect of the Froude and Reynolds numbers on the liquid film characteristics is examined. An expression for an interfacial friction coefficient between the turbulent core and the liquid film is developed; it is similar to Darcy's friction coefficient for a single phase flow in a rough pipe. Results indicate that for the range of Reynolds and Froude numbers considered, the liquid film is likely to be turbulent rather than laminar. The study also shows that two-dimensional effects are important, and the flow is never fully developed either in the film or the core. In addition, the new approach for the turbulent film is capable of predicting a local net flow rate that may be upward, downward, stationary, or stalled. An actual steam-water geothermal well is simulated. A similarity theory is used to predict the steam-water mixture pressure and temperature starting with laboratory measurements on the flow of R-114. Results indicate that the theory can be used to predict the pressure gradient in the two-phase region based on laboratory measurements.
NASA Technical Reports Server (NTRS)
Lyons, L. R.; Williams, D. J.
1976-01-01
Explorer 45 observations of ring current protons mirroring near the equator, 1-800 keV, are presented at constant first adiabatic invariant mu throughout the period of the December 17, 1971, geomagnetic storm. The parameter mu is obtained from simultaneous magnetic field and particle observations. Particle deceleration in response to the storm time magnetic field decrease causes ring current measurements viewed at constant energy to underestimate the storm time increase in proton intensities at energies not exceeding 200 keV. This adiabatic deceleration also accounts for the large flux decreases observed at energies above 200 keV during the storm, in contradiction with previous results (Soraas and Davis, 1968) obtained using a model for the storm time magnetic field.
NASA Astrophysics Data System (ADS)
Tanigaki, Kenichi; Kusumoto, Tatsuya; Ogi, Hirotsugu; Nakamura, Nobutomo; Hirao, Masahiko
2010-07-01
In this paper, a picosecond ultrasound measurement is conducted to evaluate the low-temperature elastic and optical properties of thin films and semiconductors. Specimens are cooled with liquid He through a heat exchanger in a cryostat, and an ultrahigh-frequency acoustic pulse is generated using a femtosecond light pulse, which propagates in the film-thickness direction. Pulse echoes of the longitudinal wave and Brillouin oscillation are observed by the changes in reflectivity of the time-delayed probe light, which depend on the material, and give the longitudinal-wave out-of-plane elastic constant. When the stiffness is known, the Brillouin oscillation provides the refractive index. We determined the stiffness of a Pt thin film and the refractive index of Si at 5 K. The methodology developed in this paper is useful for studing the elastic and optical properties of metallic thin films and transparent materials at cryogenic temperatures.
Taylor, DeCarlos E.
2014-08-07
The elastic constants of the α and γ polymorphs of cyclotrimethylene trinitramine (RDX) have been computed using dispersion corrected density functional theory (DFT). The DFT results validate the values obtained in several experiments using ultrasonic and impulsive stimulated thermal scattering techniques and disagree with those obtained using Brillouin scattering which, in general, exceed the other experimental and theoretical results. Compressibility diagrams at zero pressure are presented for the ab, ac, and bc crystallographic planes, and the anisotropic linear compressibility within the ac plane of α-RDX at 0 GPa, observed using ultrasonic and impulsive stimulated thermal scattering measurements, is verified using DFT. The pressure dependence of the elastic constants of α-RDX (0–4 GPa) and γ-RDX (4–8 GPa) is also presented.
Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model
NASA Astrophysics Data System (ADS)
Guo, Yun-Dong; Chen, Xiang-Rong; Yang, Xiang-Dong; Gou, Qing-Quan
2005-11-01
The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD) with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy. The project supported by National Natural Science Foundation of China under Grant No. 60436010 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education of China under Grant No. 2004176-6-4
All-optical measurement of elastic constants in nematic liquid crystals.
Klus, Bartłomiej; Laudyn, Urszula A; Karpierz, Mirosław A; Sahraoui, Bouchta
2014-12-01
In this article we present a new all-optical method to measure elastic constants connected with twist and bend deformations. The method is based on the optical Freedericksz threshold effect induced by the linearly polarized electro-magnetic wave. In the experiment elastic constants are measured of commonly used liquid crystals 6CHBT and E7 and two new nematic mixtures with low birefringence. The proposed method is neither very sensitive on the variation of cell thickness, beam waist or the power of a light beam nor does it need any special design of a liquid crystal cell. The experimental results are in good agreement with the values obtain by other methods based on an electro-optical effect. PMID:25606956
The temperature dependence of second and higher order elastic constants of NH4Cl
NASA Astrophysics Data System (ADS)
Tiwari, Alpana; Gaur, N. K.
2016-05-01
We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). This ETSM has been applied to reveal the second order elastic constants (C11, C12 and C44) of NH4Cl as a function of temperature for temperature range 240K≤T≤440K. An abrupt decrease in C44 is observed due to disorder present in the crystal as a result of random orientations of tetrahedral ammonium molecule. Our calculated results show similar trend as revealed by experimental data. Besides third order elastic constants have also been studied and discussed as a function of temperature for 240K≤T≤440K.
NASA Astrophysics Data System (ADS)
Mohapatra, Himansu; Eckhardt, Craig J.
2007-03-01
Polymorphism is the property of a compound to crystallize in two or more crystalline phases containing different arrangements and/or conformations of the molecules in the crystal lattice. The Phenomenon of polymorphism is a major issue in the pharmaceutical industry especially in relation to drug uptake in the body, tablet processing and growth. This has led to considerable interest in predicting and understanding properties of drug polymorphs, and more recently the mechanical properties of the polymorphs. In this work, Brillouin scattering is used to probe the acoustic phonons of the monoclinic (P21/c) polymorph of the drug, carbamazepine (CBZ). By sampling a variety of acoustic phonons, the complete elastic constant tensor has been determined for this CBZ polymorph. The observed trend in the elastic constants: C11< C22˜C33 is qualitatively associated with the crystal growth pattern seen in CBZ. Investigation into the anisotropy of the intermolecular interactions has been investigated further by calculation of linear compressibilities.
Ultrasonic measurement of the elastic constants of potassium hydrogen phthalate single crystals
NASA Astrophysics Data System (ADS)
Alex, A. V.; Philip, J.
2000-09-01
Many organic crystals with orthorhombic symmetry exhibit electro-optic, ferroelectric, and triboluminescence properties. The potassium salt of phthalic acid (KAP), with the formula C8H5O4K, finds application in soft x-ray spectroscopy due to its large d spacing and has been reported to be piezoelectric as well. KAP crystallizes into orthorhombic structure with space group Pca21 All nine elastic constants of KAP have been determined by measuring the velocity of longitudinal and transverse ultrasonic waves propagating along different symmetry directions. Velocities have been measured by the ultrasonic pulse echo overlap technique by injecting waves generated by quartz transducers through a suitable bonding medium into the crystal. The McSkimin Δt correction has been applied to determine the velocities accurately. The temperature variation of selected elastic constants over the range 300-420 K has also been measured and reported.
Elastic constant C11 of 12C diamond between 10 and 613 K
NASA Astrophysics Data System (ADS)
Nagakubo, A.; Arita, M.; Ogi, H.; Sumiya, H.; Nakamura, N.; Hirao, M.
2016-05-01
We measured the temperature dependence of the elastic constant C11 of a 12C diamond monocrystal using picosecond ultrasonics between 10 and 613 K. We found that C11 is almost temperature independent below room temperature; the temperature coefficient around 300 K is -6.6 MPa/K. Our results show a significantly higher Einstein temperature than reported values by ˜30%, indicating that diamond has a larger zero-point energy, which remains dominant around ambient temperature. We also calculated the temperature dependence of the elastic constants using ab-initio methods, resulting in good agreement with measurements. Our study shows that below-ambient-temperature measurements are not sufficient to extract the Debye temperature and the Grüneisen parameter of high-Debye-temperature materials.
NASA Astrophysics Data System (ADS)
Kluge, M. D.; Wolf, D.; Lutsko, J. F.; Phillpot, S. R.
1990-03-01
A new formalism for use in atomistic simulations to calculate the full local elastic-constant tensor in terms of local stresses and strains is presented. Results of simulations on a high-angle (001) twist grain boundary are illustrated, using both a Lennard-Jones potential for Cu and an embedded-atom potential for Au. The two conceptionally rather different potentials show similar anomalies in all elastic constants, confined to within a few lattice planes of the grain boundary, with an especially dramatic reduction in the resistance to shear parallel to the grain-boundary plane. It is found that the primary cause of the anomalies is the atomic disorder near the grain boundary, as evidenced by the slice-by-slice radial distribution functions for the inhomogeneous interface system.
Elastic Constants of Indium Arsenide at Room Temperature by Resonant Ultrasound Spectroscopy
NASA Astrophysics Data System (ADS)
Arammash, Fouzi; Yin, Ming
2013-03-01
The three independent elastic constants, C11, C12, and C44 of indium arsenide (InAs) single crystal were determined at room temperature using resonant ultrasound spectroscopy (RUS) technique. We will present and compare our results with those obtained from more conventional measurement techniques. We also compare our results to those of other III-V compound semiconductors such as gallium arsenide (GaAs).
Surface acoustic wave velocity and elastic constants of cubic GaN
NASA Astrophysics Data System (ADS)
Jiménez Riobóo, Rafael J.; Cuscó, Ramon; Prieto, Carlos; Kopittke, Caroline; Novikov, Sergei V.; Artús, Luis
2016-06-01
We present high-resolution surface Brillouin scattering measurements on cubic GaN layers grown on GaAs substrate. By using a suitable scattering geometry, scattering by surface acoustic waves is recorded for different azimuthal angles, and the surface acoustic wave velocities are determined. A comparison of experimental results with numerical simulations of the azimuthal dependence of the surface wave velocity shows good agreement and allows a consistent set of elastic constants for c-GaN to be determined.
A fluctuation method to calculate the third order elastic constants in crystalline solids
Chen, Zimu; Qu, Jianmin
2015-05-28
This paper derives exact expressions of the isothermal third order elastic constants (TOE) in crystalline solids in terms of the kinetic and potential energies of the system. These expressions reveal that the TOE constants consist of a Born component and a relaxation component. The Born component is simply the third derivative of the system's potential energy with respect to the deformation, while the relaxation component is related to the non-uniform rearrangements of the atoms when the system is subject to a macroscopic deformation. Further, based on the general expressions derived here, a direct (fluctuation) method of computing the isothermal TOE constants is developed. Numerical examples of using this fluctuation method are given to compute the TOE constants of single crystal iron.
Mining for elastic constants of intermetallics from the charge density landscape
NASA Astrophysics Data System (ADS)
Kong, Chang Sun; Broderick, Scott R.; Jones, Travis E.; Loyola, Claudia; Eberhart, Mark E.; Rajan, Krishna
2015-02-01
There is a significant challenge in designing new materials for targeted properties based on their electronic structure. While in principle this goal can be met using knowledge of the electron charge density, the relationships between the density and properties are largely unknown. To help overcome this problem we develop a quantitative structure-property relationship (QSPR) between the charge density and the elastic constants for B2 intermetallics. Using a combination of informatics techniques for screening all the potentially relevant charge density descriptors, we find that C11 and C44 are determined solely from the magnitude of the charge density at its critical points, while C12 is determined by the shape of the charge density at its critical points. From this reduced charge density selection space, we develop models for predicting the elastic constants of an expanded number of intermetallic systems, which we then use to predict the mechanical stability of new systems. Having reduced the descriptors necessary for modeling elastic constants, statistical learning approaches may then be used to predict the reduced knowledge-based required as a function of the constituent characteristics.
NASA Astrophysics Data System (ADS)
Haldipur, P.; Margetan, F. J.; Thompson, R. B.
2004-02-01
In past work we reported on measurements of ultrasonic velocity, attenuation and backscattering in nickel-alloy materials used in the fabrication of rotating jet-engine components. Attenuation and backscattering were shown to be correlated to the average grain diameter, which varied with position in the billet specimens studied. The ultrasonic measurements and associated metallographic studies found the local microstructures to be approximately equiaxed and free of texture in these cubic-phase metals. In this paper we explore a method for deducing the single-crystal elastic constants of a metal using the combined ultrasonic and metallographic data for a polycrystalline specimen. We specifically consider the case seen in the jet-engine alloys: polycrystalline cubic microstructures having equiaxed, randomly oriented grains. We demonstrate how the three independent elastic constants {C11, C12, C44} can be deduced from the density, the mean grain diameter, the ultrasonic attenuation at one or more frequencies, and the longitudinal and shear wave speeds. The method makes use of the attenuation theory of Stanke and Kino, and the Hill averaging procedure for estimating the sonic velocity through a polycrystalline material. Elastic constant inputs to the velocity and attenuation models are adjusted to optimize the agreement with experiment. The method is demonstrated using several specimens of Inconel 718 and Waspaloy, and further tested using four specimens of pure Nickel.
Haldipur, P.; Margetan, F.J.; Thompson, R.B.
2004-02-26
In past work we reported on measurements of ultrasonic velocity, attenuation and backscattering in nickel-alloy materials used in the fabrication of rotating jet-engine components. Attenuation and backscattering were shown to be correlated to the average grain diameter, which varied with position in the billet specimens studied. The ultrasonic measurements and associated metallographic studies found the local microstructures to be approximately equiaxed and free of texture in these cubic-phase metals. In this paper we explore a method for deducing the single-crystal elastic constants of a metal using the combined ultrasonic and metallographic data for a polycrystalline specimen. We specifically consider the case seen in the jet-engine alloys: polycrystalline cubic microstructures having equiaxed, randomly oriented grains. We demonstrate how the three independent elastic constants {l_brace}C11, C12, C44{r_brace} can be deduced from the density, the mean grain diameter, the ultrasonic attenuation at one or more frequencies, and the longitudinal and shear wave speeds. The method makes use of the attenuation theory of Stanke and Kino, and the Hill averaging procedure for estimating the sonic velocity through a polycrystalline material. Elastic constant inputs to the velocity and attenuation models are adjusted to optimize the agreement with experiment. The method is demonstrated using several specimens of Inconel 718 and Waspaloy, and further tested using four specimens of pure Nickel.
Local Elastic Constants for Epoxy-Nanotube Composites from Molecular Dynamics Simulation
NASA Technical Reports Server (NTRS)
Frankland, S. J. V.; Gates, T. S.
2007-01-01
A method from molecular dynamics simulation is developed for determining local elastic constants of an epoxy/nanotube composite. The local values of C11, C33, K12, and K13 elastic constants are calculated for an epoxy/nanotube composite as a function of radial distance from the nanotube. While the results possess a significant amount of statistical uncertainty resulting from both the numerical analysis and the molecular fluctuations during the simulation, the following observations can be made. If the size of the region around the nanotube is increased from shells of 1 to 6 in thickness, then the scatter in the data reduces enough to observe trends. All the elastic constants determined are at a minimum 20 from the center of the nanotube. The C11, C33, and K12 follow similar trends as a function of radial distance from the nanotube. The K13 decreases greater distances from the nanotube and becomes negative which may be a symptom of the statistical averaging.
Temperature dependence of elastic constants of embedded-atom models of palladium
Wolf, R.J.; Mansour, K.A.; Lee, M.W. ); Ray, J.R. )
1992-10-01
The elastic constants of fcc palladium are calculated as a function of temperature for four different embedded-atom-method (EAM) models and compared to experimental values. Two of these EAM models have been derived by other workers whereas two of the models are new. Because of the elastic anomaly near 120 K, in the shear constant [ital C][sub 44] of Pd, the use of this zero-temperature elastic constant to determine the Pd EAM potential leads to errors in the calculated [ital C][sub 44] above the Debye temperature of 280 K where the potentials are to be used. To correct this behavior we determine the EAM potential in the two new EAM models so that [ital C][sub 44] is in much better agreement with the experimental value above the Debye temperature. Interestingly in both of these new models the melting temperature is significantly higher and in better agreement with the experimental value of 1825 K. One of our models uses a conventional EAM third-neighbor interaction model whereas our other model is a fifth-neighbor interaction model.
NASA Astrophysics Data System (ADS)
Ghosh, G.
2015-08-01
A comprehensive computational study of elastic properties of cementite (Fe3C) and its alloyed counterparts (M3C (M = Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, W, Zr, Cr2FeC and CrFe2C) having the crystal structure of Fe3C is carried out employing electronic density-functional theory (DFT), all-electron PAW pseudopotentials and the generalized gradient approximation for the exchange-correlation energy (GGA). Specifically, as a part of our systematic study of cohesive properties of solids and in the spirit of materials genome, following properties are calculated: (i) single-crystal elastic constants, Cij, of above M3Cs; (ii) anisotropies of bulk, Young's and shear moduli, and Poisson's ratio based on calculated Cijs, demonstrating their extreme anisotropies; (iii) isotropic (polycrystalline) elastic moduli (bulk, shear, Young's moduli and Poisson's ratio) of M3Cs by homogenization of calculated Cijs; and (iv) acoustic Debye temperature, θD, of M3Cs based on calculated Cijs. We provide a critical appraisal of available data of polycrystalline elastic properties of alloyed cementite. Calculated single crystal properties may be incorporated in anisotropic constitutive models to develop and test microstructure-processing-property-performance links in multi-phase materials where cementite is a constituent phase.
Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures
NASA Technical Reports Server (NTRS)
Sayir, Ali; Palko, James W.; Kriven, Waltraud M.; Sinogeikin, Sergey V.; Bass, Jay D.
2001-01-01
Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.
Elastic constants of bcc shape-memory binary alloys: Effect of the configurational ordering
NASA Astrophysics Data System (ADS)
Castán, T.; Planes, A.
1988-10-01
The relationship between the elastic shear modulus C'=1/2(C11-C12) and the atomic order state in a shape-memory binary alloy AxB1-x above its martensitic transition temperature is analyzed. We first present a simple method to evaluate the elastic constants in binary alloys, assuming the atoms interact via a two-body Morse potential. For CuZn and AgZn alloys, the potential parameters corresponding to the different A-A, B-B, and A-B pairs are determined from experimental data of the elastic constant C' for different alloy compositions. We next calculate C' at 0 K as a function of the ordering state. To do this, we use atomic configurations obtained with a Monte Carlo simulation of the Ising model for a bcc binary alloy, at each temperature Ti. We obtain a linear relationship between C' and the short-range-order parameter η. We also show that the deviations from the linear behavior observed when C' is represented against the square of the long-rang-order parameter come mainly from the critical behavior of the system near the order-disorder temperature Tc.
Strickland, Daniel J; Huang, Yun-Ru; Lee, Daeyeon; Gianola, Daniel S
2014-12-23
We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3- and 6-μm polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders of magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative humidity, implying a critical strain of ∼0.01 that is strikingly similar to that observed in metallic glasses (MGs) [Johnson WL, Samwer K (2005) Phys Rev Lett 95:195501] and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow. PMID:25489098
NASA Technical Reports Server (NTRS)
Vidal, C. R.; Stwalley, W. C.
1982-01-01
The molecular constants and their adiabatic corrections have been determined for the (A 1 Sigma +) - (X 1 Sigma +) system of the isotopic lithium hydrides: (Li-6)H, (Li-7)H, (Li-6)D, and (Li-7)D. Using a fully quantum mechanical variational method, the potential energy curves (IPA potentials) are determined. Extending the variational method, we have obtained for the first time adiabatic corrections of potential energy curves from isotopic spectroscopic data. A significant difference between the potential energy curves of the lithium hydrides and the lithium deuterides has been observed. When Li-6 was replaced by Li-7, a significant difference was only observed for the (A 1 Sigma +) state, but not for the (X 1 Sigma +) state.
NASA Astrophysics Data System (ADS)
Gascón, F.; Salazar, F.
1996-02-01
The displacement suffered by the points located on one face of a parallelepipedic specimen made of isotropic elastic material is studied, while subject to simple compression, which generates not only strain but also both a translational and a rotation effect. The displacement is measured by double-exposure speckle photography. The elastic constants of a material are computed by measuring the in-plane displacement of three points. The effect of the in-plane and out-of-plane displacements due to translation and rotation are analyzed. Extreme values for the tilt angle are estimated, as well as the maximum diameter of the read-out beam. The systematic uncertainty of the method is also studied. Both Young's modulus and Poisson's ratio are experimentally measured in aluminum.
Local elastic constants of LacI and implications for allostery.
Ribeiro, Andre A S T; Ortiz, Vanessa
2015-04-01
Allostery connects subtle changes in a protein's potential energy surface, induced by perturbations like ligand-binding, to significant changes in its function. Understanding this phenomenon and predicting its occurrence are major goals of current research in biophysics and molecular biology. In this paper we introduce a novel approach for studying complex structural transformations such as those typical for allostery. We show that the calculation and analysis of atomic elastic constants of a known allosterically regulated protein, lac repressor, highlights regions that are particularly prone to suffer structural deformation and are experimentally linked to allosteric function. The calculations are based on a high resolution, all-atom description of the protein. We also show that, for the present system, modifying the description of the system from an all-atom forcefield to an elastic network model yields qualitatively different results, indicating the importance of adequately describing the local environment surrounding the different parts of the protein. PMID:25700189
Berryman, J. G.
2012-03-01
While the well-known Voigt and Reuss (VR) bounds, and the Voigt-Reuss-Hill (VRH) elastic constant estimators for random polycrystals are all straightforwardly calculated once the elastic constants of anisotropic crystals are known, the Hashin-Shtrikman (HS) bounds and related self-consistent (SC) estimators for the same constants are, by comparison, more difficult to compute. Recent work has shown how to simplify (to some extent) these harder to compute HS bounds and SC estimators. An overview and analysis of a subsampling of these results is presented here with the main point being to show whether or not this extra work (i.e., in calculating both the HS bounds and the SC estimates) does provide added value since, in particular, the VRH estimators often do not fall within the HS bounds, while the SC estimators (for good reasons) have always been found to do so. The quantitative differences between the SC and the VRH estimators in the eight cases considered are often quite small however, being on the order of ±1%. These quantitative results hold true even though these polycrystal Voigt-Reuss-Hill estimators more typically (but not always) fall outside the Hashin-Shtrikman bounds, while the self-consistent estimators always fall inside (or on the boundaries of) these same bounds.
Ghosh, G.
2015-08-15
A comprehensive computational study of elastic properties of cementite (Fe{sub 3}C) and its alloyed counterparts (M{sub 3}C (M = Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, W, Zr, Cr{sub 2}FeC and CrFe{sub 2}C) having the crystal structure of Fe{sub 3}C is carried out employing electronic density-functional theory (DFT), all-electron PAW pseudopotentials and the generalized gradient approximation for the exchange-correlation energy (GGA). Specifically, as a part of our systematic study of cohesive properties of solids and in the spirit of materials genome, following properties are calculated: (i) single-crystal elastic constants, C{sub ij}, of above M{sub 3}Cs; (ii) anisotropies of bulk, Young’s and shear moduli, and Poisson’s ratio based on calculated C{sub ij}s, demonstrating their extreme anisotropies; (iii) isotropic (polycrystalline) elastic moduli (bulk, shear, Young’s moduli and Poisson’s ratio) of M{sub 3}Cs by homogenization of calculated C{sub ij}s; and (iv) acoustic Debye temperature, θ{sub D}, of M{sub 3}Cs based on calculated C{sub ij}s. We provide a critical appraisal of available data of polycrystalline elastic properties of alloyed cementite. Calculated single crystal properties may be incorporated in anisotropic constitutive models to develop and test microstructure-processing-property-performance links in multi-phase materials where cementite is a constituent phase.
Determination of the plane specific elastic constants of Waspaloy using neutron diffraction
Stone, H.J.; Reed, R.C.; Holden, T.M.
1999-01-08
In the present paper, the plane specific elastic constants for Waspaloy, a high strength nickel-base superalloy, have been determined with a considerable degree of precision. For this purpose, in-situ tensile tests have been carried out in a neutron diffractometer. The data which are reported are of considerable significance, since they allow an accurate determination of the residual stress slate from an estimate of the local d-spacing from the hkl lattice reflection. Thus, the data should be of interest to those interested in the determination of the residual stress state in components which are fabricated from Waspaloy, and nickel-base superalloys in general.
Elastic constants for superplastically formed/diffusion-bonded corrugated sandwich core
NASA Technical Reports Server (NTRS)
Ko, W. L.
1980-01-01
Formulas and associated graphs for evaluating the effective elastic constants for a superplastically formed/diffusion bonded (SPF/DB) corrugated sandwich core, are presented. A comparison of structural stiffnesses of the sandwich core and a honeycomb core under conditions of equal sandwich core density was made. The stiffness in the thickness direction of the optimum SPF/DB corrugated core (that is, triangular truss core) is lower than that of the honeycomb core, and that the former has higher transverse shear stiffness than the latter.
NASA Astrophysics Data System (ADS)
Yoneda, A.; Cooray, T.; Shatskiy, A.; Sohag, H.
2010-12-01
Elastic properties of minerals plays an indispensable role in the studies of Earth's interior as it is essential for interpretation of seismic velocity structure of the Earth, due to its feasibility of comparison with the seismological observations. And it also provides information on structure, bonding, and the nature of phase transitions in minerals. Resonant Ultrasound Spectroscopy (RUS) has been one of the leading methods of determining elastic constants of materials by measuring number of natural vibration modes. Owing to developments of high frequency RUS up to 50 MHz (HRUS), it emerge as a powerful technique in study of high pressure phases of mantel minerals in which samples are restricted to be sub millimeter size. In this study stishovite was selected due to exceptional interest on it as a prototype phase of the lower mantle silicates, because it exhibits silicon in six-fold coordination. Large single crystals (up to 0.8x0.8x1.5mm) of stishovite were synthesized at 12 GPa from single crystal quartz and water (SiO2+15wt% H2O) by slow cooling method (from 1450 C to 800 C) in Kawai-type uniaxial split sphere apparatus (USSA5000). Quality of the crystals was confirmed by polarized microscope study, micro focus x-ray diffractometry and precision x-ray diffractometry. From FTIR measurements water content in synthesized crystals was confirmed to be less than 7 wt. ppm. Crystal was grind and polished into a rectangle, parallel to crystallographic axis having edges of 230x290x500 micron meter. Then it was measured with HRUS for ~20 resonance peaks between 6-20 MHz range. From these peaks, six independent elastic constants C11 = 449 GPa, C33 = 775 GPa, C12 = 200 GPa, C13 = 198 GPa, C44 = 254 GPa and C66 = 318 GPa were determined through a kind of inversion analysis . Although the present C11 value is slightly smaller than previous Brillouin scattering data, other five elastic constants are within the scatter among Brillouin scattering data.
Polynomial Expressions for Estimating Elastic Constants From the Resonance of Circular Plates
NASA Technical Reports Server (NTRS)
Salem, Jonathan A.; Singh, Abhishek
2005-01-01
Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.
NASA Astrophysics Data System (ADS)
Râsander, M.; Moram, M. A.
2015-10-01
We have performed density functional calculations using a range of local and semi-local as well as hybrid density functional approximations of the structure and elastic constants of 18 semiconductors and insulators. We find that most of the approximations have a very small error in the lattice constants, of the order of 1%, while the errors in the elastic constants and bulk modulus are much larger, at about 10% or better. When comparing experimental and theoretical lattice constants and bulk modulus we have included zero-point phonon effects. These effects make the experimental reference lattice constants 0.019 Å smaller on average while making the bulk modulus 4.3 GPa stiffer on average. According to our study, the overall best performing density functional approximations for determining the structure and elastic properties are the PBEsol functional, the two hybrid density functionals PBE0 and HSE (Heyd, Scuseria, and Ernzerhof), as well as the AM05 functional.
Haycraft, James J
2009-12-01
The acoustic phonons of the epsilon polymorph of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclo [5.5.0.0(5,9).0(3,11)] dodecane (epsilon-CL-20) have been studied using Brillouin scattering spectroscopy. Analysis of the acoustic phonon velocities allowed determination of the complete stiffness tensor for this energetic material. The results are compared to a theoretical determination of the epsilon-CL-20 elastic constants, bulk moduli, and shear moduli. The observed ordering of elastic constants, C(22)>C(33)>C(11), is noted to be different from other nitramine energetic materials. Finally, the elasticity of epsilon-CL-20 is compared to recently published reports on cyclotrimethylene trinitramine's (RDX) elasticity and the beta polymorph of cyclotetramethylene tetranitramine's (beta-HMX) elasticity. PMID:19968345
NASA Astrophysics Data System (ADS)
Mei, A. B.; Wilson, R. B.; Li, D.; Cahill, David G.; Rockett, A.; Birch, J.; Hultman, L.; Greene, J. E.; Petrov, I.
2014-06-01
Elastic constants are determined for single-crystal stoichiometric NaCl-structure VN(001), VN(011), and VN(111) epitaxial layers grown by magnetically unbalanced reactive magnetron sputter deposition on 001-, 011-, and 111-oriented MgO substrates at 430 °C. The relaxed lattice parameter ao = 0.4134 ± 0.0004 nm, obtained from high-resolution reciprocal space maps, and the mass density ρ = 6.1 g/cm3, determined from the combination of Rutherford backscattering spectroscopy and film thickness measurements, of the VN layers are both in good agreement with reported values for bulk crystals. Sub-picosecond ultrasonic optical pump/probe techniques are used to generate and detect VN longitudinal sound waves with measured velocities v001 = 9.8 ± 0.3, v011 = 9.1 ± 0.3, and v111 = 9.1 ± 0.3 km/s. The VN c11 elastic constant is determined from the sound wave velocity measurements as 585 ± 30 GPa; the c44 elastic constant, 126 ± 3 GPa, is obtained from surface acoustic wave measurements. From the combination of c11, c44, vhkl, and ρ we obtain the VN c12 elastic constant 178 ± 33 GPa, the VN elastic anisotropy A = 0.62, the isotropic Poisson ratio ν = 0.29, and the anisotropic Poisson ratios ν001 = 0.23, ν011 = 0.30, and ν111 = 0.29.
NASA Astrophysics Data System (ADS)
Lunt, A. J. G.; Xie, M. Y.; Baimpas, N.; Zhang, S. Y.; Kabra, S.; Kelleher, J.; Neo, T. K.; Korsunsky, A. M.
2014-08-01
Yttria Stabilised Zirconia (YSZ) is a tough, phase-transforming ceramic that finds use in a wide range of commercial applications from dental prostheses to thermal barrier coatings. Micromechanical modelling of phase transformation can deliver reliable predictions in terms of the influence of temperature and stress. However, models must rely on the accurate knowledge of single crystal elastic stiffness constants. Some techniques for elastic stiffness determination are well-established. The most popular of these involve exploiting frequency shifts and phase velocities of acoustic waves. However, the application of these techniques to YSZ can be problematic due to the micro-twinning observed in larger crystals. Here, we propose an alternative approach based on selective elastic strain sampling (e.g., by diffraction) of grain ensembles sharing certain orientation, and the prediction of the same quantities by polycrystalline modelling, for example, the Reuss or Voigt average. The inverse problem arises consisting of adjusting the single crystal stiffness matrix to match the polycrystal predictions to observations. In the present model-matching study, we sought to determine the single crystal stiffness matrix of tetragonal YSZ using the results of time-of-flight neutron diffraction obtained from an in situ compression experiment and Finite Element modelling of the deformation of polycrystalline tetragonal YSZ. The best match between the model predictions and observations was obtained for the optimized stiffness values of C11 = 451, C33 = 302, C44 = 39, C66 = 82, C12 = 240, and C13 = 50 (units: GPa). Considering the significant amount of scatter in the published literature data, our result appears reasonably consistent.
Lunt, A. J. G. Xie, M. Y.; Baimpas, N.; Korsunsky, A. M.; Zhang, S. Y.; Kabra, S.; Kelleher, J.; Neo, T. K.
2014-08-07
Yttria Stabilised Zirconia (YSZ) is a tough, phase-transforming ceramic that finds use in a wide range of commercial applications from dental prostheses to thermal barrier coatings. Micromechanical modelling of phase transformation can deliver reliable predictions in terms of the influence of temperature and stress. However, models must rely on the accurate knowledge of single crystal elastic stiffness constants. Some techniques for elastic stiffness determination are well-established. The most popular of these involve exploiting frequency shifts and phase velocities of acoustic waves. However, the application of these techniques to YSZ can be problematic due to the micro-twinning observed in larger crystals. Here, we propose an alternative approach based on selective elastic strain sampling (e.g., by diffraction) of grain ensembles sharing certain orientation, and the prediction of the same quantities by polycrystalline modelling, for example, the Reuss or Voigt average. The inverse problem arises consisting of adjusting the single crystal stiffness matrix to match the polycrystal predictions to observations. In the present model-matching study, we sought to determine the single crystal stiffness matrix of tetragonal YSZ using the results of time-of-flight neutron diffraction obtained from an in situ compression experiment and Finite Element modelling of the deformation of polycrystalline tetragonal YSZ. The best match between the model predictions and observations was obtained for the optimized stiffness values of C11 = 451, C33 = 302, C44 = 39, C66 = 82, C12 = 240, and C13 = 50 (units: GPa). Considering the significant amount of scatter in the published literature data, our result appears reasonably consistent.
NASA Astrophysics Data System (ADS)
Mozafari, E.; Shulumba, N.; Steneteg, P.; Alling, B.; Abrikosov, Igor A.
2016-08-01
We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ˜14 % from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.
First-principles elastic constants of α- and θ-Al2O3
NASA Astrophysics Data System (ADS)
Shang, Shunli; Wang, Yi; Liu, Zi-Kui
2007-03-01
Using an efficient strain-stress method, the first-principles elastic constants cij's of α-Al2O3 and θ-Al2O3 have been predicted within the local density approximation and the generalized gradient approximation. It is indicated that more accurate calculations of cij's can be accomplished by the local density approximation. The predicted cij's of θ-Al2O3 provide helpful guidance for future measurements, especially the predicted negative c15. The present results make the stress estimation in thermally grown oxides containing of α- and θ-Al2O3 possible, which in turn provide helpful insights for preventing the failure of thermal barrier coatings on components in gas-turbine engines.
Bounds and Estimates for Elastic Constants of Random Polycrystals of Laminates
Berryman, J G
2004-08-25
In order to obtain formulas providing estimates for elastic constants of random polycrystals of laminates, some known rigorous bounds of Peselnick, Meister, and Watt are first simplified. Then, some new self-consistent estimates are formulated based on the resulting analytical structure of these bounds. A numerical study is made, assuming first that the internal structure (i.e., the laminated grain structure) is not known, and then that it is known. The purpose of this aspect of the study is to attempt to quantify the differences in the predictions of properties of the same system being modeled when such internal structure of the composite medium and spatial correlation information is and is not available.
NASA Astrophysics Data System (ADS)
Madhuri, P. Lakshmi; Hiremath, Uma S.; Yelamaggad, C. V.; Madhuri, K. Priya; Prasad, S. Krishna
2016-04-01
Effect of a polymer network on the threshold voltage of the Fréedericksz transition, Frank elastic constants, switching speed, and the rotational viscosity are investigated in a polymer-stabilized bent-core nematic liquid crystal with different polymer concentrations. These polymer networks form virtual surfaces with a finite anchoring energy. The studies bring out several differences in comparison to similar studies with a calamitic liquid crystal as the nematic host. For example, on varying the polymer content the threshold voltage decreases initially, but exhibits a drastic increase above a critical concentration. A similar feature—reaching a minimum before rising—is seen for the bend elastic constant, which gets enhanced by an order of magnitude for a polymer content of 2.5 wt %. In contrast, the splay elastic constant has a monotonic variation although the overall enhancement is comparable to that of the bend elastic constant. The behavior changing at a critical concentration is also seen for the switching time and the associated rotational viscosity. The presence of the polymer also induces a shape change in the thermal dependence of the bend elastic constant. We explain the features observed here on the basis of images obtained from the optical and atomic force microscopy.
NASA Astrophysics Data System (ADS)
Hwang, Seho; Shin, Jehyun; Kim, Jongman; Won, Byeongho; Song, Wonkyoung; Kim, Changryol; Ki, Jungseok
2014-05-01
One of the most important physical properties is the measurement of the elastic constants of the formation in the evaluation of shale gas. Normally the elastic constants by geophysical well logging and the laboratory test are used in the design of hydraulic fracturing . The three inches diameter borehole of the depth of 505 m for the evaluation of shale gas drilled and was fully cored at the Haenan Basin, southwestern part of Korea Peninsula. We performed a various laboratory tests and geophysical well logging using slime hole logging system. Geophysical well logs include the radioactive logs such as natural gamma log, density log and neutron log, and monopole and dipole sonic log, and image logs. Laboratory tests are the axial compression test, elastic wave velocities and density, and static elastic constants measurements for 21 shale and sandstone cores. We analyzed the relationships between the physical properties by well logs and laboratory test as well as static elastic constants by laboratory tests. In the case of an sonic log using a monopole source of main frequency 23 kHz, measuring P-wave velocity was performed reliably. When using the dipole excitation of low frequency, the signal to noise ratio of the measured shear wave was very low. But when measuring using time mode in a predetermined depth, the signal to noise ratio of measured data relatively improved to discriminate the shear wave. P-wave velocities by laboratory test and sonic logging agreed well overall, but S-wave velocities didn't. The reason for the discrepancy between the laboratory test and sonic log is mainly the low signal to noise ratio of sonic log data by low frequency dipole source, and measuring S-wave in the small diameter borehole is still challenge. The relationship between the P-wave velocity and two dynamic elastic constants, Young's modulus and Poisson's ratio, shows a good correlation. And the relationship between the static elastic constants and dynamic elastic constants also
Elastic properties of solids at high pressure
NASA Astrophysics Data System (ADS)
Vekilov, Yu Kh; Krasilnikov, O. M.; Lugovskoy, A. V.
2015-11-01
This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of ( n≥2) for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0-600 GPa.
NASA Astrophysics Data System (ADS)
Navarrete, M.; Mejía-Uriarte, E. V.; Villagrán-Muniz, M.
2013-09-01
Mixtures of black rubber (natural rubber) vulcanizates containing various concentrations of sand particles, as hard fillers, were prepared to determine their elastic constants at low and high frequency using the photoacoustic technique. These parameters are related with the degree of sand filler dispersion which determines the changes in stiffness, as well as its potential as reinforcement material for treads in tires. The constants are recovered through measurements of the longitudinal wave and complemented with the predictions from the Kerner model to obtain the Poisson’s ratio. Some results are corroborated with tension and compression tests. The acoustic waves are acquired by two piezoelectric transducers, one centered at 3 kHz and the other at 240 kHz. The results show a slight increase in Young’s modulus at low frequencies; meanwhile at high frequencies, it increases by two orders of magnitude. In addition, we found that on adding small amounts of prepared sand, the stiffness increases and this is particularly convenient to reduce the energy losses by the rolling resistance in automotive vehicles.
Elastic Constants and Phonons of Tungsten-Nitride from First Principles
NASA Astrophysics Data System (ADS)
Dane, Christian; Finkenstadt, Daniel; Mehl, Michael; Curtarolo, Stefano
2013-03-01
Certain Tungsten Nitride (WN) crystal structures have been found to exhibit tendencies for exceptional hardness. Some researchers [S. Aydin et al., J. Mater. Res. 27, 1705 (2012)] have made the claim that these structures have hardness qualities that rival diamond. There are three specific structures with unique compositions that are of interest. By calculating the bulk and shear moduli as well as analyzing phonon dispersion plots, the properties of these structures can be compared to known structures like diamond. We used VASP density-functional methods implemented within the MedeA software package to strain each structure in a series of directions in increasing amounts. A simple linear fit of stress vs. strain found that the leading structure in terms of thermodynamic stability has elastic constants of C11 = 753 GPa, C12 = 126 GPa, and C44 = 172 GPa. These constants, while high, are significantly lower than diamond's. This indicates that previous calculations may have been mistaken in predicting the qualities of the WN system. Some of the difference between our results is due to the exchange-correlation functional chosen, namely, LDA vs. GGA.
NASA Astrophysics Data System (ADS)
Gogu, C.; Yin, W.; Haftka, R.; Ifju, P.; Molimard, J.; Le Riche, R.; Vautrin, A.
2010-06-01
A major challenge in the identification of material properties is handling different sources of uncertainty in the experiment and the modelling of the experiment for estimating the resulting uncertainty in the identified properties. Numerous improvements in identification methods have provided increasingly accurate estimates of various material properties. However, characterizing the uncertainty in the identified properties is still relatively crude. Different material properties obtained from a single test are not obtained with the same confidence. Typically the highest uncertainty is associated with respect to properties to which the experiment is the most insensitive. In addition, the uncertainty in different properties can be strongly correlated, so that obtaining only variance estimates may be misleading. A possible approach for handling the different sources of uncertainty and estimating the uncertainty in the identified properties is the Bayesian method. This method was introduced in the late 1970s in the context of identification [1] and has been applied since to different problems, notably identification of elastic constants from plate vibration experiments [2]-[4]. The applications of the method to these classical pointwise tests involved only a small number of measurements (typically ten natural frequencies in the previously cited vibration test) which facilitated the application of the Bayesian approach. For identifying elastic constants, full field strain or displacement measurements provide a high number of measured quantities (one measurement per image pixel) and hence a promise of smaller uncertainties in the properties. However, the high number of measurements represents also a major computational challenge in applying the Bayesian approach to full field measurements. To address this challenge we propose an approach based on the proper orthogonal decomposition (POD) of the full fields in order to drastically reduce their dimensionality. POD is
Elastic constants of Si from HtN Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Yates, Henry; Karimi, M.; Matolyak, J.; Kaplan, T.; Mostoller, M.
1997-03-01
A simple and efficient way of calculating the elastic constants (C_ij) of silicon as a function of temperature is still lacking. A method that has proven to be useful in the calculation of C_ij is EhN molecular dynamics (MD). EhN MD was successfully applied by Ray et al.(J. Ray, Comput. Phys. Rep. 8, 109 (1988).) to the Stillinger-Weber (SW) Si potential at three temperatures. However, the calculation of C_ij using EhN MD requires a knowledge of the second derivatives of the potential, which can be difficult to evaluate for some potential models. Another technique is HtN MD, where H is the enthalpy, t is the tension, and N is the number of particles, which has been applied with less success to Si by Ray et al.. The appeal of the HtN ensemble is that the strain fluctuations are related to the C_ij through a very simple relationship and that the second derivatives are not needed. A recent study of C_ij for a Lennard-Jones potential using HtN MC and HtN MD indicated a much faster covergence rate for HtN MC over its MD counterpart. We calculate C_ij for the SW Si potential using HtN MC with the same conditions as those used by Ray et al. in doing EhN MD and compare the convergence of the two methods.
Gudelli, Vijay Kumar Kanchana, V.
2014-04-24
Structural, elastic, electronic and Fermi surface studies of AuTe{sub 2} have been carried out by means of first principles calculations based on density functional theory. The calculated ground state properties agree well with the experiment. Fermi surface and elastic constants are predicted for the first time and from the calculated elastic constants we find the compound to be mechanically stable satisfying the stability criteria of monoclinic structure. In addition, we also find the c-axis to be more compressible than the other two which is also speculated from the present work. The metallic behaviour of this compound is confirmed from the electronic band structure calculation as we find the bands to cross the Fermi level (E{sub F}). In addition, we also observe a FS topology change under pressure which is also explained in the present work.
Elastic constants determined by nanoindentation for p-type thermoelectric half-Heusler
Gahlawat, S.; Wheeler, L.; White, K. W. E-mail: kwwhite@uh.edu; He, R.; Chen, S.; Ren, Z. F. E-mail: kwwhite@uh.edu
2014-08-28
This paper presents a study of the elastic properties of the p-type thermoelectric half-Heusler material, Hf{sub 0.44}Zr{sub 0.44}Ti{sub 0.12}CoSb{sub 0.8}Sn{sub 0.2}, using nanoindentation. Large grain-sized polycrystalline specimens were fabricated for these measurements, providing sufficient indentation targets within single grains. Electron Backscatter Diffraction methods indexed the target grains for the correlation needed for our elastic analysis of individual single crystals for this cubic thermoelectric material. Elastic properties, including the Zener ratio and the Poisson ratio, obtained from the elasticity tensor are also reported.
Hajlaoui, C. Pedesseau, L.; Raouafi, F.; Ben Cheikh Larbi, F.; Even, J.; Jancu, J.-M.
2015-08-15
We report first-principle density functional calculations of the spontaneous polarization, piezoelectric stress constants, and elastic constants for the III–V wurtzite structure semiconductors InAs and InP. Using the density functional theory implemented in the VASP code, we obtain polarization values–0.011 and–0.013 C/m{sup 2}, and piezoelectric constants e{sub 33} (e{sub 31}) equal to 0.091 (–0.026) and 0.012 (–0.081) C/m{sup 2} for structurally relaxed InP and InAs respectively. These values are consistently smaller than those of nitrides. Therefore, we predict a smaller built-in electric field in such structures.
Cantrell, John H
2014-07-01
The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p1. For liquids the second-order elastic constants are C₁₁=A+p₁, C₁₂=A-p₁, and the third-order constants are C₁₁₁=-(B+5A+3p₁), C₁₁₂=-(B+A-p₁), and C₁₂₃=A-B-p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁=p₁γ+p₁, C₁₂=p₁γ-p₁, and the third-order constants are C₁₁₁=-p₁(γ(2)+4γ+3), C₁₁₂=-p₁(γ(2)-1), and C₁₂₃=-p₁ (γ(2)-2γ+1), where γ is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄=(1/2)(C₁₁-C₁₂)=p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3×10(-5). For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material 'nonlinearity parameters' associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids. PMID:24502870
NASA Technical Reports Server (NTRS)
Cantrell, John H.
2014-01-01
The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p(sub 1). For liquids the second-order elastic constants are C(sub 11) = A + p(sub 1), C(sub 12) = A -- p(sub 1), and the third-order constants are C(sub 111) = --(B + 5A + 3p(sub 1)), C(sub 112) = --(B + A -- p(sub 1)), and C(sub 123) = A -- B -- p1, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second order constants are C(sub 11) = p(sub 1)gamma + p9sub 1), C(sub 12) = p(sub 1)gamma -- p(sub 1), and the third-order constants are C(sub 111) = p(sub 1)(gamma(2) + 4gamma + 3), C(sub 112) = --p(sub 1)(gamma(2) -- 1), and C(sub 123) = --p(sub 1) (gamma(2) -- 2gamma + 1), where gamma is the ratio of specific heats. The inequality of C(sub 11) and C(sub 12) results in a nonzero shear constant C(sub 44) = (1/2)(C(sub 11) C(sub 12)) = p(sub 1) for both liquids and gases. For water at standard temperature and pressure the ratio of terms p1/A contributing to the second-order constants is approximately 4.3 x 10(-5). For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material 'nonlinearity parameters' associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.
Barkaoui, Abdelwahed; Chamekh, Abdessalem; Merzouki, Tarek; Hambli, Ridha; Mkaddem, Ali
2014-03-01
The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data. PMID:24123969
NASA Astrophysics Data System (ADS)
Shang, Shun-Li; Zhang, Hui; Wang, Yi; Liu, Zi-Kui
2010-09-01
Temperature-dependent elastic stiffness constants (cijs), including both the isothermal and isoentropic ones, have been predicted for rhombohedral α-Al2O3 and monoclinic θ-Al2O3 in terms of a quasistatic approach, i.e., a combination of volume-dependent cijs determined by a first-principles strain versus stress method and direction-dependent thermal expansions obtained by first-principles phonon calculations. A good agreement is observed between the predictions and the available experiments for α-Al2O3, especially for the off-diagonal elastic constants. In addition, the temperature-dependent cijs predicted herein, in particular the ones for metastable θ-Al2O3, enable the stress analysis at elevated temperatures in thermally grown oxides containing α- and θ-Al2O3, which are crucial to understand the failure of thermal barrier coatings in gas-turbine engines.
Yu, Meina; Zhou, Xiaochen; Jiang, Jinghua; Yang, Huai; Yang, Deng-Ke
2016-05-11
Chiral nematic liquid crystals possess a self-assembled helical structure and exhibit unique selective reflection in visible and infrared light regions. Their optical properties can be electrically tuned. The tuning involves the unwinding and restoring of the helical structure. We carried out an experimental study on the mechanism of the restoration of the helical structure. We constructed chiral nematic liquid crystals with variable elastic constants by doping bent-dimers and studied their impact on the restoration. With matched twist and bend elastic constants, the helical structure can be restored dramatically fast from the field-induced homeotropic state. Furthermore, defects can be eliminated to produce a perfect planar state which exhibits high selective reflection. PMID:27116620
Fumeron, Sébastien; Moraes, Fernando; Pereira, Erms
2016-09-01
The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K24. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a (2) H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K24. Considering an escaped-radial disclination inside a capillary tube with radius R0 of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle [Formula: see text] . Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius R0, the measurement of [Formula: see text] from the interference experiments involving two different radii allows us to algebraically retrieve K24. Our method allowed us to give the first reported estimation of K24 for the lyotropic chromonic liquid crystal Sunset Yellow FCF: K 24 = 2.1 pN. PMID:27589980
Aya, Satoshi; Ogino, Shohei; Hayashi, Yoshihiro; Okano, Kunihiko; Pociecha, Damian; Le, Khoa V; Araoka, Fumito; Kawauchi, Susumu; Gorecka, Ewa; Vaupotič, Nataša; Takezoe, Hideo; Ishikawa, Ken
2014-10-01
Elastic constants in liquid crystals are known to be in the range of pico- and several-tens piconewton (pN). We report herein that a bend elastic constant, K33, remarkably varies depending on a slight modification of the chemical structure in an analogous series of calamitic liquid crystals. In contrast to the record-high bend elastic constants (hundreds pN or sub-nN) reported previously in a compound with an azo linkage, analogous compounds with tolan and ester linkages show several-tens pN and pN, respectively. X-ray diffraction studies of these compounds reveal that smectic-like layer structures (cybotacticclusters) are formed in the nematic phase of only the homologous compounds with an azo linkage, certifying the idea that the existence of cybotactic clusters strongly enhances K33. Two theoretical considerations were made: (1) Based on molecular conformation calculation, flat molecules that have high torsional potential energy, such as the one with an azo linkage, easily pack to form cybotactic clusters. (2) Theoretical estimation was made of how much cluster volume ratio is necessary to give about 100-times-larger K33s. PMID:25375514
NASA Astrophysics Data System (ADS)
Sinogeikin, S. V.; Reichmann, H. J.; Bass, J. D.; Mackwell, S. J.; Jacobsen, S. D.
2001-12-01
Magnesiowustite is a major mineral in the lower mantle of the Earth. While the effect of temperature and pressure on the elasticity of MgO is well constrained, the effect of Fe on the elastic constants and their pressure derivatives is still uncertain, especially for compositions close to the Mg end-member. Here we present the Brillouin spectroscopy measurements of the single-crystal elastic constants of magnesiowustite at ambient conditions ( ~5.8 mol.% Fe) and to high pressures up to about 10 GPa ( ~1.3 mol.% Fe). The single-crystal samples were prepared by Mg:Fe interdiffusion between periclase single crystals and magnesiowustite powders with carefully controlled oxygen fugacity. The Brillouin scattering measurements were performed in platelet symmetric geometry, which significantly increases the accuracy, and is calibrated with respect to standard periclase sample. High-pressure measurements were performed in a large optical opening Merrill-Basset type diamond anvil cell with Methanol-Ethanol-Water mixture as a pressure-transmitting medium. The new results confirm earlier single-crystal ultrasonic measurements (gigahertz interferometry) which indicated that the behavior of the elastic moduli of magnesiowustite are highly nonlinear in Mg-rich end. A pronounced decrease in acoustic velocities with increasing Fe content is especially obvious in samples with Fe contents of <10 mol. %. The pressure derivatives of the elastic moduli of the sample with XFe = 1.3 mol % are equal to those of periclase within the experimental uncertainties, although the Fe content of the sample may be too small to allow compositional trends to be clearly identified.
A Simple Experiment for Determining the Elastic Constant of a Fine Wire
ERIC Educational Resources Information Center
Freeman, W. Larry; Freda, Ronald F.
2007-01-01
Many general physics laboratories involve the use of springs to demonstrate Hooke's law, and much ado is made about how this can be used as a model for describing the elastic characteristics of materials at the molecular or atomic level. In recent years, the proliferation of computers, and appropriate sensors, have made it possible to demonstrate…
NASA Astrophysics Data System (ADS)
Lee, Ji-Hoon; Yoon, Tae-Hoon; Choi, E.-Joon
2013-12-01
We report an unusual temperature dependence of the elastic constants of a rodlike nematic liquid crystal (RLC) mixed with a highly kinked bent-core liquid crystal (BLC). On cooling through the nematic phase, the splay elastic constant (K11) of the RLC-BLC mixture increased below the nematic-isotropic phase transition temperature, but started to decrease midway through the nematic phase. The decrease of K11 was more prominent with a greater concentration of BLC. On the other hand, the bend elastic constant (K33) of the RLC-BLC mixture monotonically increased through the nematic phase with decreasing temperature.
Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo
2016-07-01
The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. PMID:27079489
NASA Astrophysics Data System (ADS)
Nayek, Prasenjit; Karan, Santanu; Kundu, Sudarshan; Lee, Seung Hee; Das Gupta, Sudeshna; Roy, Soumen Kumar; Roy, Subir Kumar
2012-06-01
This report describes how doping liquid crystals (LC) with rod-like hexagonal semiconductor nanoprisms alters the dielectric and elastic properties of the composites as compared with a pristine nematic liquid crystal (NLC). Cadmium sulfide nanorods were synthesized via the solvothermal process and blended with a NLC. Nanorods were highly miscible with NLC and produced a topological defect-free texture up to a certain limit. A good dark state was achieved during the homeotropic configuration of the cell within that limit. Appreciable changes in splay and bend elastic constants of the LCs were observed after blending with nanorods. Long-range order was established in the hybrid system, and consequently the anisotropy was increased. The threshold voltage decreased dramatically by ˜31%. Dielectric study revealed a high-frequency mode, which might be due to anchoring of the LC with nanorods.
Two-vortex interactions and elastic constants in type II superconductors
Miesenboeck, H.M.
1984-07-01
The elastic energy of a distorted flux-line lattice is calculated on the basis of a two-vortex interaction. Such a description is completely sufficient throughout the whole induction range between the upper and lower critical fields H/sub c//sub 1/ and H/sub c//sub 2/. Therefore it is possible to calculate all elastic moduli from a common potential consisting of two parts, one of a combined ''electromagnetic London type,'' the other based on the core overlap of the flux lines. The results are highly nonlocal and are in agreement with previous calculations of Brandt, but are modified near H/sub c//sub 1/ for small k (the ratio between the penetration depth and the coherence length).
Determination of Constant Strain Gradients of Elastically Bent Crystal Using X-ray Mirage Fringes
NASA Astrophysics Data System (ADS)
Jongsukswat, Sukswat; Fukamachi, Tomoe; Hirano, Kenji; Ju, Dongying; Negishi, Riichirou; Shimojo, Masayuki; Hirano, Keiichi; Kawamura, Takaaki
2012-07-01
Two experimental approaches are studied to determine a parameter of the strain gradient in an elastically bent crystal. In one approach, the parameter is determined by measuring the third peak of the X-ray mirage interference fringes and in the other, by measuring the region where no mirage diffraction beam reaches on the lateral surface of the crystal. Using the X-rays from synchrotron radiation, the mirage fringes have been observed in the 220 reflection of the Si crystal whose strain is controlled in cantilever bending. These two approaches both give accurate values of the parameter of the strain gradient, showing good agreement with the values calculated using elastic theory. In addition, the residual strain due to gravity is observed by measuring mirage fringes when the bending force becomes zero.
NASA Astrophysics Data System (ADS)
Fivez, J.
2016-01-01
Starting from the coupled thermoelastic equations, an analytic formula is obtained for the surface deformation of a semi-infinite homogeneous and isotropic solid in an impulsive stimulated scattering (ISS) experiment. The surface ripple consists of a transient diffusive grating and a standing Rayleigh wave. The time evolution of the diffusive part directly reveals the thermal diffusivity. The oscillatory part then reveals the elastic properties, and explicit formulae are presented for retrieving the elastic moduli as a function of the frequency and amplitude of the standing Rayleigh wave. The analytic formulae not only allow to avoid time-consuming and delicate numerical integration but they also demonstrate the uniqueness of the inversion from signal to material parameters and offer direct insight into the error propagation. The formulae are applied to real experimental data, illustrating the strength and the limitations of the ISS technique.
NASA Astrophysics Data System (ADS)
Panov, V. P.; Nagaraj, M.; Vij, J. K.; Panarin, Yu. P.; Kohlmeier, A.; Tamba, M. G.; Lewis, R. A.; Mehl, G. H.
2010-10-01
Hydrocarbon linked mesogenic dimers are found to exhibit an additional nematic phase below the conventional uniaxial nematic phase as confirmed by x-ray diffraction. The phase produces unusual periodic stripe domains in planar cells. The stripes are found to be parallel to the rubbing direction (in rubbed cells) with a well-defined period equal to double the cell gap. The stripes appear without external electromagnetic field, temperature or thickness gradients, rubbing or hybrid alignment treatments. Simple modeling proposes a negative sign for at least one of the two elastic constants: splay and twist, as a necessary condition for the observed pattern.
NASA Astrophysics Data System (ADS)
Eggert, Th.; Geilenkeuser, R.; Jäckel, M.
2000-07-01
We have measured the dielectric response ε( ω) and the thermal conductivity κ of polystyrene (PS) and of polycarbonate (PC) under high hydrostatic pressure (0.1 MPa
constant Ci can be determined. These results show that the product P¯γ l,t2 of the standard tunnelling model (STM) scales with the pressure-dependent elastic constants c11 and c44.
Wang, Xing; Zhang, Ligang; Guo, Ziyi; Jiang, Yun; Tao, Xiaoma; Liu, Libin
2016-09-01
CALPHAD-type modeling was used to describe the single-crystal elastic constants of the bcc solution phase in the ternary Ti-Nb-Zr system. The parameters in the model were evaluated based on the available experimental data and first-principle calculations. The composition-elastic properties of the full compositions were predicted and the results were in good agreement with the experimental data. It is found that the β phase can be divided into two regions which are separated by a critical dynamical stability composition line. The corresponding valence electron number per atom and the polycrystalline Young׳s modulus of the critical compositions are 4.04-4.17 and 30-40GPa respectively. Orientation dependencies of single-crystal Young׳s modulus show strong elastic anisotropy on the Ti-rich side. Alloys compositions with a Young׳s modulus along the <100> direction matching that of bone were found. The current results present an effective strategy for designing low modulus biomedical alloys using computational modeling. PMID:27235781
Shang, Shun-Li; Zhang, Hui; Wang, Yi; Liu, Zi-Kui
2010-09-22
Temperature-dependent elastic stiffness constants (c(ij)s), including both the isothermal and isoentropic ones, have been predicted for rhombohedral α-Al(2)O(3) and monoclinic θ-Al(2)O(3) in terms of a quasistatic approach, i.e., a combination of volume-dependent c(ij)s determined by a first-principles strain versus stress method and direction-dependent thermal expansions obtained by first-principles phonon calculations. A good agreement is observed between the predictions and the available experiments for α-Al(2)O(3), especially for the off-diagonal elastic constants. In addition, the temperature-dependent c(ij)s predicted herein, in particular the ones for metastable θ-Al(2)O(3), enable the stress analysis at elevated temperatures in thermally grown oxides containing α- and θ-Al(2)O(3), which are crucial to understand the failure of thermal barrier coatings in gas-turbine engines. PMID:21403195
Seung-Kyu Park; Sung-Hoon Baik; Hyung-Ki Cha; Stephen J. Reese; David H. Hurley
2010-08-01
Resonant ultrasound spectroscopy (RUS) is a useful technique for measuring the elastic properties of materials. In this study, two experimental approaches for performing RUS are experimentally analyzed and compared: 1) contact transduction using piezoelectric transducers (PZT) and 2) laser transduction using pulse laser excitation and laser interferometric detection. A single Zircaloy sample cut from a nuclear pressure tube was used for this study. By virtue of the non-contact nature, the quality factor, Q, for laser RUS is shown to be higher than the contact RUS. In addition, the probe beam for laser-RUS can be scanned to form a 2D image of each vibrational mode, which in turn enables unique mode identification. These defining characteristics of laser-RUS enable straightforward discrimination of closely spaced resonant modes and provide key advantages for improving the resolution of resonant ultrasound spectroscopy.
Osipov, M A; Pajak, G
2016-04-01
A molecular theory of both elastic constants and the flexoelectric coefficients of bent-core nematic liquid crystals has been developed taking into account dipole-dipole interactions as well as polar interactions determined by the bent molecular shape. It has been shown that if polar interactions are neglected, the elastic constants are increasing monotonically with the decreasing temperature. On the other hand, dipolar interactions between bent-core molecules may result in a dramatic increase of the bend flexocoefficient. As a result, the flexoelectric contribution to the bend elastic constant increases significantly, and the bend elastic constant appears to be very small throughout the nematic range and may vanish at a certain temperature. This temperature may then be identified as a temperature of the elastic instability of the bent-core nematic phase which induces a transition into the modulated phases with bend deformations like recently reported twist-bend phase. The temperature variation of the elastic constants is qualitatively similar to the typical experimental data for bent-core nematics. PMID:27118535
Core-Shell Microgels with Switchable Elasticity at Constant Interfacial Interaction.
Seuss, Maximilian; Schmolke, Willi; Drechsler, Astrid; Fery, Andreas; Seiffert, Sebastian
2016-06-29
Hydrogels based on poly(N-isopropylacrylamide) (pNIPAAm) exhibit a thermo-reversible volume phase transition from swollen to deswollen states. This change of the hydrogel volume is accompanied by changes of the hydrogel elastic and Young's moduli and of the hydrogel interfacial interactions. To decouple these parameters from one another, we present a class of submillimeter sized hydrogel particles that consist of a thermosensitive pNIPAAm core wrapped by a nonthermosensitive polyacrylamide (pAAm) shell, each templated by droplet-based microfluidics. When the microgel core deswells upon increase of the temperature to above 34 °C, the shell is stretched and dragged to follow this deswelling into the microgel interior, resulting in an increase of the microgel surficial Young's modulus. However, as the surface interactions of the pAAm shell are independent of temperature at around 34 °C, they do not considerably change during the pNIPAAm-core volume phase transition. This feature makes these core-shell microgels a promising platform to be used as building blocks to assemble soft materials with rationally and independently tunable mechanics. PMID:27276500
Dutta, Biswanath; Ghosh, Subhradip
2009-03-01
Understanding the role of the inter-atomic force constants in lattice dynamics of random binary alloys is a challenging problem. Addressing these inter-atomic interactions accurately is a necessity to obtain an accurate phonon spectrum and to calculate properties from them. Using a combination of ab initio density functional perturbation theory (DFPT) and the itinerant coherent potential approximation (ICPA), an analytic, self-consistent method for performing configuration averaging in random alloys, we model the inter-atomic force constants for Pd(0.96)Fe(0.04) and Pd(0.9)Fe(0.1) alloys based upon the ab initio results and intuitive arguments. The calculated phonon dispersion curves and elastic constants agree very well with the experimental results. Comparison of our results with those obtained in a model potential scheme is also done. The modeling of inter-atomic interactions in random alloys and their roles regarding the phonon-related properties are also discussed in light of these results. PMID:21817397
NASA Astrophysics Data System (ADS)
Palchik, V.
2013-03-01
The stress [crack damage stress ( σ cd) and uniaxial compressive strength ( σ c)] and strain characteristics [maximum total volumetric strain ( ɛ cd), axial failure strain ( ɛ af)], porosity ( n) and elastic constants [elastic modulus ( E) and Poisson's ratio ( ν)] and their ratios were coordinated with the existence of two different types (type 1 and type 2) of volumetric strain curve. Type 1 volumetric strain curve has a reversal point and, therefore, σ cd is less than the uniaxial compressive strength ( σ c). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., σ cd = σ c). It is confirmed that the ratio between the elastic modulus ( E) and the parameter λ = n/ ɛ cd strongly affects the crack damage stress ( σ cd) for both type 1 and type 2 volumetric strain curves. It is revealed that heterogeneous carbonate rock samples exhibit different types of the volumetric strain curve even within the same rock formation, and the range of σ cd/ σ c = 0.54-1 for carbonate rocks is wider than the range (0.71 < σ cd/ σ c < 0.84) obtained by other researchers for granites, sandstones and quartzite. It is established that there is no connection between the type of the volumetric strain curve and values of n, E, σ cd, ν, E/(1 - 2 ν), M R = E/ σ c and E/ λ. On the other hand, the type of volumetric strain curve is connected with the values of λ and the ratio between the axial failure strain ( ɛ af) and the maximum total volumetric strain ( ɛ cd). It is argued that in case of small ɛ af/ ɛ cd-small λ, volumetric strain curve follows the type 2.
Elastic constants and ultrasound attenuation in the spin-liquid phase of Cs2CuCl4
NASA Astrophysics Data System (ADS)
Streib, Simon; Kopietz, Peter; Cong, Pham Thanh; Wolf, Bernd; Lang, Michael; van Well, Natalija; Ritter, Franz; Assmus, Wolf
2015-03-01
The spin excitations in the spin-liquid phase of the anisotropic triangular lattice quantum antiferromagnet Cs2CuCl4 have been shown to propagate dominantly along the crystallographic b-axis. To test this dimensional reduction scenario, we have performed ultrasound experiments in the spin-liquid phase of Cs2CuCl4 probing the elastic constant c22 and the sound attenuation along the b-axis as a function of an external magnetic field along the a-axis. We show that our data can be quantitatively explained within the framework of a nearest neighbor spin- 1 / 2 Heisenberg chain, where fermions are introduced via the Jordan-Wigner transformation and the spin-phonon interaction arises from the usual exchange-striction mechanism. Financial support by the DFG via SFB/TRR49 is gratefully acknowledged.
Diffraction Profiles of Elasticity Bent Single Crystals with Constant Strain Gradients
Yan,H.; Kalenci, O.; Noyan, I.
2007-01-01
This work presents a set of equations that can be used to predict the dynamical diffraction profile from a non-transparent single crystal with a constant strain gradient examined in Bragg reflection geometry with a spherical incident X-ray beam. In agreement with previous work, the present analysis predicts two peaks: a primary diffraction peak, which would have still been observed in the absence of the strain gradient and which exits the specimen surface at the intersection point of the incident beam with the sample surface, and a secondary (mirage) peak, caused by the deflection of the wavefield within the material, which exits the specimen surface further from this intersection point. The integrated intensity of the mirage peak increases with increasing strain gradient, while its separation from the primary reflection peak decreases. The directions of the rays forming the mirage peak are parallel to those forming the primary diffraction peak. However, their spatial displacement might cause (fictitious) angular shifts in diffractometers equipped with area detectors or slit optics. The analysis results are compared with experimental data from an Si single-crystal strip bent in cantilever configuration, and the implications of the mirage peak for Laue analysis and high-precision diffraction measurements are discussed.
NASA Astrophysics Data System (ADS)
Yang, Jing; Cheng, Jian-Chun
2001-12-01
A new inverse method based on the wavelet transform and artificial neural networks (ANN) is presented to recover elastic constants of a fibre-reinforced composite plate from laser-based ultrasonic Lamb waves. The transient waveforms obtained by numerical simulations under different elastic constants are taken as the input of the ANN for training and learning. The wavelet transform is employed for extracting the eigenvectors from the raw Lamb wave signals so as to simplify the structure of the ANN. Then these eigenvectors are input to a multi-layer internally recurrent neural network with a back-propagation algorithm. Finally, the experimental waveforms are used as the input in the whole system to inverse elastic constants of the experimental material.
Mazel, Vincent; Busignies, Virginie; Diarra, Harona; Tchoreloff, Pierre
2013-11-01
The elastic properties of pharmaceutical powders and compacts are of great interest to understand the complex phenomena that occur during and after the tableting process. The elastic recovery after compression is known to be linked with adverse phenomena such as capping or delamination of tablets. Classically, the elastic behavior is modeled using linear elasticity and is characterized using only Young's modulus (E), often by using a value extrapolated at zero porosity. In this work, four pharmaceutical products were studied. The elastic behavior of compacts obtained using a large range of applied pressure was characterized. First, it was found more suitable to use apparent elastic moduli than extrapolations at zero porosity. Then, the results indicate that there was not always a good correlation between the values of Young's modulus and the actual elastic recovery of the compacts. Poisson's ratio (v), which differs from one product to another and is porosity-dependent, must be taken into account. Finally, the bulk modulus (K), which combines E and v, was shown to be well correlated with the elastic recovery of the compacts and can be considered as a relevant parameter to characterize the elastic behavior of pharmaceutical compacts. PMID:23963744
Preedy, Emily Callard; Perni, Stefano
2015-01-01
Periprosthetic osteolysis and implant loosening are the outcomes of wear debris generation in total joint replacements. Wear debris formed from the implanted materials consisting of metals, polymers, ceramic and bone cement initiate the immune system response. Often osteoblasts, the principal cell type in bone tissue adjacent to the prostheses, are directly impacted. In this study, the influence of cobalt, titanium and PMMA bone cement particles of different sizes, charges and compositions on mouse osteoblast adhesion, nanomechanics (elasticity and spring constant) and metabolic activity were investigated. These studies were accompanied by osteoblast mineralisation experiments and cell uptake after exposure to particles at defined time points. Our results demonstrate that alteration of the nanomechanical properties are mainly dependent on the metal type rather than nanoparticles size and concentration. Moreover, despite uptake increasing over exposure time, the cell characteristics exhibit changes predominately after the first 24 hours, highlighting that the cell responses to nanoparticle exposure are not cumulative. Understanding these processes is critical to expanding our knowledge of implant loosening and elucidating the nature of prosthetic joint failure. PMID:27019701
Stassis, C.
1993-10-01
The physical properties of the various phases of iron have been the subject of numerous of numerous theoretical and experimental investigations. Of particular interest is the appearance of the fcc {gamma}-phase between approximately 1,200 K and 1,670 K. The authors were able to growth in situ single crystals of fcc iron of sufficient size to perform an inelastic neutron scattering study of the lattice dynamics of this phase of iron. The phonon dispersion curves along the [00{xi}],[{xi}{xi}0] and [{xi}{xi}{xi}] symmetry directions were measured at 1,428 K. A limited number of phonons were also measured at 1,227 K and 1,640 K to assess the temperature dependence of the phonon frequencies. The data collected at 1,428 K were used to evaluate the elastic constants, the phonon density of states and the lattice contribution to the specific heat. The measured dispersion curves of {gamma}-Fe are qualitatively similar to those of Ni (measured at 296 K) and Ni{sub 0.3}Fe{sub 0.7} (measured at 296 and 573 K).
Adiabatic topological quantum computing
NASA Astrophysics Data System (ADS)
Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; Flammia, Steven T.; Neels, Alice
2015-07-01
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.
NASA Astrophysics Data System (ADS)
Pfeiffer, Jonathan B.; Kaufman, Yaniv; Wagner, Kelvin H.; Ledbetter, Hassel
2014-05-01
We utilized both resonant ultrasound spectroscopy (RUS) and Schaefer-Bergmann diffraction patterns (SBDP) to measure the elastic stiffness coefficients of the trigonal, non-piezo-electric crystal α-BaB2O4. RUS determines the elastic coefficients of a sample by matching measured resonant frequencies to a model of resonances. SBDP deduces the elastic coefficients by fitting the measured shape of the acousto-optic diffraction pattern to an acoustic slowness surface cross-section. We present our measured elastic coefficients of α-BaB2O4 from both RUS and SBDP experiments.
Andrushchak, A. S.; Laba, H. P.; Yurkevych, O. V.; Mytsyk, B. G.; Solskii, I. M.; Kityk, A. V.; Sahraoui, B.
2009-10-01
This paper presents the results of ultrasonic measurements of LiNbO{sub 3} and LiNbO{sub 3}:MgO crystals. The tensors of piezoelectric coefficients, elastic stiffness constants, and elastic compliances are determined for both crystals at room temperature. Combining these data with the results of piezo-optical measurements, a complete set of photoelastic tensor coefficients is also calculated. Doping of LiNbO{sub 3} crystals by MgO does not lead to a considerable modification of their elastic and photoelastic properties. However, LiNbO{sub 3}:MgO is characterized by a considerably higher resistance with respect to powerful light radiation, making it promising for future application in acousto-optic devices that deal with superpowerful laser radiation. Presented here are the complete tensor sets of elastic constants and photoelastic coefficients of LiNbO{sub 3} and LiNbO{sub 3}:MgO crystals that may be used for a geometry optimization of acousto-optical interaction providing the best diffraction efficiency of acousto-optical cells made of these materials.
Elastic constants and the structural phase transition in La sub 2-x Sr sub x CuO sub 4
Sarrao, J.L.; Lei, Ming; Stekel, A.; Bell, T.M.; Leisure, R.G.; Sham, L.J.; Visscher, W.M.; Migliori, A. ); Bussmann-Holder, A. Bayreuth Univ. ); Tanaka, I.; Kojima, H. . Faculty of Engineering)
1991-01-01
Resonant ultrasound spectroscopy is used to measure the temperature dependence of all six elastic moduli of La{sub 2-x}Sr{sub x}CuO{sub 4}. A giant softening (> 50% reduction) in the in-plane shear modulus, c{sub 66}, is observed and is attributed to the tetragonal-orthorhombic structural phase transition in this material. This phase transition and the corresponding softening is examined with a simple anharmonic mechanical model and a macroscopic Ginsburg-Landau formalism exploiting the full symmetry of the crystal. 16 refs., 5 figs.
The elastic constants of MgSiO3 perovskite at pressures and temperatures of the Earth's mantle.
Oganov, A R; Brodholt, J P; Price, G D
2001-06-21
The temperature anomalies in the Earth's mantle associated with thermal convection can be inferred from seismic tomography, provided that the elastic properties of mantle minerals are known as a function of temperature at mantle pressures. At present, however, such information is difficult to obtain directly through laboratory experiments. We have therefore taken advantage of recent advances in computer technology, and have performed finite-temperature ab initio molecular dynamics simulations of the elastic properties of MgSiO3 perovskite, the major mineral of the lower mantle, at relevant thermodynamic conditions. When combined with the results from tomographic images of the mantle, our results indicate that the lower mantle is either significantly anelastic or compositionally heterogeneous on large scales. We found the temperature contrast between the coldest and hottest regions of the mantle, at a given depth, to be about 800 K at 1,000 km, 1,500 K at 2,000 km, and possibly over 2,000 K at the core-mantle boundary. PMID:11418854
Zaug, J M
1998-08-21
Ultrasonic sound speed measurements via Impulsive Stimulated Light Scattering (ISLS) were made in single crystals of b-HMX and tantalum over an extended range of temperatures. Elastic constants are consequently determined for b-HMX. Sound speeds are calculated for tantalum, from known elastic constants, and compare favorably with the results presented here. ISLS time-domain fits of tantalum records allowed for thermal diffusion determinations and, correspondingly, thermal conductivity. Measurements of the speed of sound and of the thermal diffusivities of fluid oxygen up to pressures of 13 GPa and at several temperatures are presented. Between 0.1 and 13 GPa the fluid's density increases by a factor of three. Thermal diffusivities rise slowly over this range, and are substantially smaller than those previously measured for the solid b-phase. Additional sound speed measurements were made along the 250 C isotherm in a 1:1 molar ratio mixture of liquid oxygen and nitrogen. These experiments demonstrate the versatility and potential application of a new laboratory within the U. S. DOD and DOE complex. 1
NASA Astrophysics Data System (ADS)
Hayes, Dennis
1999-06-01
Prior accurate measurements of sound speed on the Hugoniot for copper and 316-SS are used to construct complete equations of state for solid and liquid phases. Differences between calculated bulk and observed elastic sound-speed in the solid are used to infer high-pressure elastic constants. At higher pressures, where the shocked state is entirely liquid, data are sufficient to construct the EOS including an accurate estimate for Grüneisen's ratio. The liquid EOS also reasonably describes some low-pressure, high-temperature properties, including density, sound speed, variation of sound speed with temperature, and thermal expansion, lending confidence to its accuracy. Results are comparable for each metal: the shear modulus increases along the Hugoniot and then drops precipitously toward zero as the pressure nears the liquid-phase boundary. In the liquid, Grüneisen's ratio is observed to be constant and agrees with the value measured for the liquid at zero pressure. The state below which this constancy holds is identified as the smallest pressure on the Hugoniot at which melting is complete. The gap between pure solid and pure liquid is identified as the mixed-phase region and in the case of copper, its size and location are in reasonable agreement with published ab initio calculations of Moriarty. Confidence in calculated temperature and entropy is less then that in pressure, volume and energy owing to uncertainties in specific heats.
Adiabatic Compression of Oxygen: Real Fluid Temperatures
NASA Technical Reports Server (NTRS)
Barragan, Michelle; Wilson, D. Bruce; Stoltzfus, Joel M.
2000-01-01
The adiabatic compression of oxygen has been identified as an ignition source for systems operating in enriched oxygen atmospheres. Current practice is to evaluate the temperature rise on compression by treating oxygen as an ideal gas with constant heat capacity. This paper establishes the appropriate thermodynamic analysis for the common occurrence of adiabatic compression of oxygen and in the process defines a satisfactory equation of state (EOS) for oxygen. It uses that EOS to model adiabatic compression as isentropic compression and calculates final temperatures for this system using current approaches for comparison.
Bounds and self-consistent estimates for elastic constants of polycrystals of hcp solid He ${}^{4}$
Berryman, James G.
2012-03-01
Recent advances in methods for computing both Hashin-Shtrikman bounds and related selfconsistent (or CPA) estimates of elastic constants for polycrystals composed of randomly oriented crystals can be applied successfully to hexagonal close packed solid He{sup 4}. In particular, since the shear modulus C{sub 44} of hexagonal close-packed solid He is known to undergo large temperature variations when 20 mK {<=} T {<=} 200 mK, bounds and estimates computed with this class of effective medium methods, while using C{sub 44} {r_arrow} 0 as a proxy for melting, are found to be both qualitatively and quantitatively very similar to prior results obtained using Monte Carlo methods. Hashin- Shtrikman bounds provide significantly tighter constraints on the polycrystal behavior than do the traditional Voigt and Reuss bounds.
Adiabatic approximation for nucleus-nucleus scattering
Johnson, R.C.
2005-10-14
Adiabatic approximations to few-body models of nuclear scattering are described with emphasis on reactions with deuterons and halo nuclei (frozen halo approximation) as projectiles. The different ways the approximation should be implemented in a consistent theory of elastic scattering, stripping and break-up are explained and the conditions for the theory's validity are briefly discussed. A formalism which links few-body models and the underlying many-body system is outlined and the connection between the adiabatic and CDCC methods is reviewed.
Yang, X X; Li, J W; Zhou, Z F; Wang, Y; Yang, L W; Zheng, W T; Sun, Chang Q
2012-01-21
From the perspective of bond relaxation and bond vibration, we have formulated the Raman phonon relaxation of graphene, under the stimuli of the number-of-layers, the uni-axial strain, the pressure, and the temperature, in terms of the response of the length and strength of the representative bond of the entire specimen to the applied stimuli. Theoretical unification of the measurements clarifies that: (i) the opposite trends of the Raman shifts, which are due to the number-of-layers reduction, of the G-peak shift and arises from the vibration of a pair of atoms, while the D- and the 2D-peak shifts involve the z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C(3v) bond geometry to the C(2v) uni-axial bond elongation; (iii) the thermal softening of the phonons originates from bond expansion and weakening; and (iv) the pressure stiffening of the phonons results from bond compression and work hardening. Reproduction of the measurements has led to quantitative information about the referential frequencies from which the Raman frequencies shift as well as the length, energy, force constant, Debye temperature, compressibility and elastic modulus of the C-C bond in graphene, which is of instrumental importance in the understanding of the unusual behavior of graphene. PMID:22105904
Lucchinetti, E; Stüssi, E
2004-01-01
Measuring the elasticity constants of biological materials often sets important constraints, such as the limited size or the irregular geometry of the samples. In this paper, the identification approach as applied to the specific problem of accurately retrieving the material properties of small bone samples from a measured displacement field is discussed. The identification procedure can be formulated as an optimization problem with the goal of minimizing the difference between computed and measured displacements by searching for an appropriate set of material parameters using dedicated algorithms. Alternatively, the backcalculation of the material properties from displacement maps can be implemented using artificial neural networks. In a practical situation, however, measurement errors strongly affect the identification results, calling for robust optimization approaches in order accurately to retrieve the material properties from error-polluted sample deformation maps. Using a simple model problem, the performances of both classical and neural network driven optimization are compared. When performed before the collection of experimental data, this evaluation can be very helpful in pinpointing potential problems with the envisaged experiments such as the need for a sufficient signal-to-noise ratio, particularly important when working with small tissue samples such as specimens cut from rodent bones or single bone trabeculae. PMID:15648663
NASA Astrophysics Data System (ADS)
Tarumi, Ryuichi; Matsuhisa, Tomohiro; Shibutani, Yoji
2012-07-01
The complete sets of elastic constants Cij and piezoelectric coefficients eij for LiNbO3 and LiTaO3 single crystals have been determined by resonant ultrasound spectroscopy (RUS) from ambient temperature to 6 K. Both Cij(T) and eij(T) of the two crystals monotonically increased as the temperature decreased. The Einstein temperature estimated from Varshni's equation revealed that e15 and e22 of LiNbO3 have remarkably low values compared with the acoustic Debye temperature. In addition, the lattice anharmonicity of these piezoelectric coefficients was also extraordinarily low. An analysis based on the group theory and lattice dynamics revealed that both LiNbO3 and LiTaO3 crystals have three types of internal displacement modes: A1, A2, and E, and only the E mode affects e15 and e22. Therefore, it is reasonable to suppose that the E mode internal displacement is responsible for the unusual behaviors of the tow piezoelectric coefficients.
Wireless adiabatic power transfer
Rangelov, A.A.; Suchowski, H.; Silberberg, Y.; Vitanov, N.V.
2011-03-15
Research Highlights: > Efficient and robust mid-range wireless energy transfer between two coils. > The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. > Wireless energy transfer is insensitive to any resonant constraints. > Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Adiabatically driven Brownian pumps.
Rozenbaum, Viktor M; Makhnovskii, Yurii A; Shapochkina, Irina V; Sheu, Sheh-Yi; Yang, Dah-Yen; Lin, Sheng Hsien
2013-07-01
We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane. PMID:23944411
Pfeiffer, Jonathan B.; Kaufman, Yaniv; Wagner, Kelvin H.; Ledbetter, Hassel
2014-05-27
We utilized both resonant ultrasound spectroscopy (RUS) and Schaefer-Bergmann diffraction patterns (SBDP) to measure the elastic stiffness coefficients of the trigonal, non-piezo-electric crystal α−BaB{sub 2}O{sub 4}. RUS determines the elastic coefficients of a sample by matching measured resonant frequencies to a model of resonances. SBDP deduces the elastic coefficients by fitting the measured shape of the acousto-optic diffraction pattern to an acoustic slowness surface cross-section. We present our measured elastic coefficients of α−BaB{sub 2}O{sub 4} from both RUS and SBDP experiments.
Parallelizable adiabatic gate teleportation
NASA Astrophysics Data System (ADS)
Nakago, Kosuke; Hajdušek, Michal; Nakayama, Shojun; Murao, Mio
2015-12-01
To investigate how a temporally ordered gate sequence can be parallelized in adiabatic implementations of quantum computation, we modify adiabatic gate teleportation, a model of quantum computation proposed by Bacon and Flammia [Phys. Rev. Lett. 103, 120504 (2009), 10.1103/PhysRevLett.103.120504], to a form deterministically simulating parallelized gate teleportation, which is achievable only by postselection. We introduce a twisted Heisenberg-type interaction Hamiltonian, a Heisenberg-type spin interaction where the coordinates of the second qubit are twisted according to a unitary gate. We develop parallelizable adiabatic gate teleportation (PAGT) where a sequence of unitary gates is performed in a single step of the adiabatic process. In PAGT, numeric calculations suggest the necessary time for the adiabatic evolution implementing a sequence of L unitary gates increases at most as O (L5) . However, we show that it has the interesting property that it can map the temporal order of gates to the spatial order of interactions specified by the final Hamiltonian. Using this property, we present a controlled-PAGT scheme to manipulate the order of gates by a control qubit. In the controlled-PAGT scheme, two differently ordered sequential unitary gates F G and G F are coherently performed depending on the state of a control qubit by simultaneously applying the twisted Heisenberg-type interaction Hamiltonians implementing unitary gates F and G . We investigate why the twisted Heisenberg-type interaction Hamiltonian allows PAGT. We show that the twisted Heisenberg-type interaction Hamiltonian has an ability to perform a transposed unitary gate by just modifying the space ordering of the final Hamiltonian implementing a unitary gate in adiabatic gate teleportation. The dynamics generated by the time-reversed Hamiltonian represented by the transposed unitary gate enables deterministic simulation of a postselected event of parallelized gate teleportation in adiabatic
Nonadiabatic exchange dynamics during adiabatic frequency sweeps
NASA Astrophysics Data System (ADS)
Barbara, Thomas M.
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.
Adiabatic cooling of antiprotons.
Gabrielse, G; Kolthammer, W S; McConnell, R; Richerme, P; Kalra, R; Novitski, E; Grzonka, D; Oelert, W; Sefzick, T; Zielinski, M; Fitzakerley, D; George, M C; Hessels, E A; Storry, C H; Weel, M; Müllers, A; Walz, J
2011-02-18
Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap to very low temperatures. Up to 3×10(6) p are cooled to 3.5 K-10(3) times more cold p and a 3 times lower p temperature than previously reported. A second cooling method cools p plasmas via the synchrotron radiation of embedded e(-) (with many fewer e(-) than p in preparation for adiabatic cooling. No p are lost during either process-a significant advantage for rare particles. PMID:21405511
Adiabatic Cooling of Antiprotons
Gabrielse, G.; Kolthammer, W. S.; McConnell, R.; Richerme, P.; Kalra, R.; Novitski, E.; Oelert, W.; Grzonka, D.; Sefzick, T.; Zielinski, M.; Fitzakerley, D.; George, M. C.; Hessels, E. A.; Storry, C. H.; Weel, M.; Muellers, A.; Walz, J.
2011-02-18
Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap to very low temperatures. Up to 3x10{sup 6} p are cooled to 3.5 K--10{sup 3} times more cold p and a 3 times lower p temperature than previously reported. A second cooling method cools p plasmas via the synchrotron radiation of embedded e{sup -} (with many fewer e{sup -} than p) in preparation for adiabatic cooling. No p are lost during either process--a significant advantage for rare particles.
Adiabatically implementing quantum gates
Sun, Jie; Lu, Songfeng Liu, Fang
2014-06-14
We show that, through the approach of quantum adiabatic evolution, all of the usual quantum gates can be implemented efficiently, yielding running time of order O(1). This may be considered as a useful alternative to the standard quantum computing approach, which involves quantum gates transforming quantum states during the computing process.
Entanglement and adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Ahrensmeier, D.
2006-06-01
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a resource is discussed.
Necessary and sufficient condition for quantum adiabatic evolution by unitary control fields
NASA Astrophysics Data System (ADS)
Wang, Zhen-Yu; Plenio, Martin B.
2016-05-01
We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided, and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.
Equations for Adiabatic but Rotational Steady Gas Flows without Friction
NASA Technical Reports Server (NTRS)
Schaefer, Manfred
1947-01-01
This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.
The dynamic instability of adiabatic blast waves
NASA Technical Reports Server (NTRS)
Ryu, Dongsu; Vishniac, Ethan T.
1991-01-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as t(sup q) and propagate through a preshock medium with a density rho(sub E) varies as r(sup -omega) are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
The dynamic instability of adiabatic blast waves
NASA Astrophysics Data System (ADS)
Ryu, Dongsu; Vishniac, Ethan T.
1991-02-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as tq and propagate through a preshock medium with a density rhoE varies as r-omega are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
The dynamic instability of adiabatic blastwaves
NASA Astrophysics Data System (ADS)
Ryu, Dongsu; Vishniac, Ethan T.
1990-05-01
Adiabatic blastwaves, which have a total energy injected from the center E varies as t(sup q) and propagate through a preshock medium with a density rho(sub E) varies as r(sup -omega) are described by a family of similarity solutions. Previous work has shown that adiabatic blastwaves with increasing or constant postshock entropy behind the shock front are susceptible to an oscillatory instability, caused by the difference between the nature of the forces on the two sides of the dense shell behind the shock front. This instability sets in if the dense postshock layer is sufficiently thin. The stability of adiabatic blastwaves with a decreasing postshock entropy is considered. Such blastwaves, if they are decelerating, always have a region behind the shock front which is subject to convection. Some accelerating blastwaves also have such region, depending on the values of q, omega, and gamma where gamma is the adiabatic index. However, since the shock interface stabilizes dynamically induced perturbations, blastwaves become convectively unstable only if the convective zone is localized around the origin or a contact discontinuity far from the shock front. On the other hand, the contact discontinuity of accelerating blastwaves is subject to a strong Rayleigh-Taylor instability. The frequency spectra of the nonradial, normal modes of adiabatic blastwaves have been calculated. The results have been applied to the shocks propagating through supernovae envelopes. It is shown that the metal/He and He/H interfaces are strongly unstable against the Rayleigh-Taylor instability. This instability will induce mixing in supernovae envelopes. In addition the implications of this work for the evolution of planetary nebulae is discussed.
Bazzani, A.; Turchetti, G.; Benedetti, C.; Rambaldi, S.; Servizi, G.
2005-06-08
In a high intensity circular accelerator the synchrotron dynamics introduces a slow modulation in the betatronic tune due to the space-charge tune depression. When the transverse motion is non-linear due to the presence of multipolar effects, resonance islands move in the phase space and change their amplitude. This effect introduces the trapping and detrapping phenomenon and a slow diffusion in the phase space. We apply the neo-adiabatic theory to describe this diffusion mechanism that can contribute to halo formation.
Arbitrary qudit gates by adiabatic passage
NASA Astrophysics Data System (ADS)
Rousseaux, B.; Guérin, S.; Vitanov, N. V.
2013-03-01
We derive an adiabatic technique that implements the most general SU(d) transformation in a quantum system of d degenerate states, featuring a qudit. This technique is based on the factorization of the SU(d) transformation into d generalized quantum Householder reflections, each of which is implemented by a two-shot stimulated Raman adiabatic passage with appropriate static phases. The energy of the lasers needed to synthesize a single Householder reflection is shown to be remarkably constant as a function of d. This technique is directly applicable to a linear trapped ion system with d+1 ions. We implement the quantum Fourier transform numerically in a qudit with d=4 (defined as a quartit) as an example.
NASA Astrophysics Data System (ADS)
Landahl, Andrew
2012-10-01
Quantum computers promise to exploit counterintuitive quantum physics principles like superposition, entanglement, and uncertainty to solve problems using fundamentally fewer steps than any conventional computer ever could. The mere possibility of such a device has sharpened our understanding of quantum coherent information, just as lasers did for our understanding of coherent light. The chief obstacle to developing quantum computer technology is decoherence--one of the fastest phenomena in all of physics. In principle, decoherence can be overcome by using clever entangled redundancies in a process called fault-tolerant quantum error correction. However, the quality and scale of technology required to realize this solution appears distant. An exciting alternative is a proposal called ``adiabatic'' quantum computing (AQC), in which adiabatic quantum physics keeps the computer in its lowest-energy configuration throughout its operation, rendering it immune to many decoherence sources. The Adiabatic Quantum Architectures In Ultracold Systems (AQUARIUS) Grand Challenge Project at Sandia seeks to demonstrate this robustness in the laboratory and point a path forward for future hardware development. We are building devices in AQUARIUS that realize the AQC architecture on up to three quantum bits (``qubits'') in two platforms: Cs atoms laser-cooled to below 5 microkelvin and Si quantum dots cryo-cooled to below 100 millikelvin. We are also expanding theoretical frontiers by developing methods for scalable universal AQC in these platforms. We have successfully demonstrated operational qubits in both platforms and have even run modest one-qubit calculations using our Cs device. In the course of reaching our primary proof-of-principle demonstrations, we have developed multiple spinoff technologies including nanofabricated diffractive optical elements that define optical-tweezer trap arrays and atomic-scale Si lithography commensurate with placing individual donor atoms with
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Peng, Qing; De, Suvranu
2014-10-21
Silicane is a fully hydrogenated silicene-a counterpart of graphene-having promising applications in hydrogen storage with capacities larger than 6 wt%. Knowledge of its elastic limit is critical in its applications as well as tailoring its electronic properties by strain. Here we investigate the mechanical response of silicane to various strains using first-principles calculations based on density functional theory. We illustrate that non-linear elastic behavior is prominent in two-dimensional nanomaterials as opposed to bulk materials. The elastic limits defined by ultimate tensile strains are 0.22, 0.28, and 0.25 along armchair, zigzag, and biaxial directions, respectively, an increase of 29%, 33%, and 24% respectively in reference to silicene. The in-plane stiffness and Poisson ratio are reduced by a factor of 16% and 26%, respectively. However, hydrogenation/dehydrogenation has little effect on its ultimate tensile strengths. We obtained high order elastic constants for a rigorous continuum description of the nonlinear elastic response. The limitation of second, third, fourth, and fifth order elastic constants are in the strain range of 0.02, 0.08, and 0.13, and 0.21, respectively. The pressure effect on the second order elastic constants and Poisson's ratio were predicted from the third order elastic constants. Our results could provide a safe guide for promising applications and strain-engineering the functions and properties of silicane monolayers. PMID:25190587
Erba, Alessandro
2016-05-18
Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients. PMID:27150599
Liu, Xiaozhou; Zhang, Shujun; Luo, Jun; Shrout, Thomas R.; Cao, Wenwu
2010-01-01
Through second harmonic measurements, the ultrasonic nonlinearity parameters of [001]c and [111]c polarized 0.70Pb(Mg1∕3Nb2∕3)O3–0.30PbTiO3(PMN–0.3PT) single crystals have been measured as a function of bias electric field. It was found that the nonlinearity parameter increases almost linearly with field at low field but shows a drastic increase near the coercive field. The [111]c polarized single domain crystal has much smaller nonlinearity parameter than that of the [001]c polarized multidomain crystal. Based on effective symmetries of these crystals, we were able to derive the field dependence of several third order elastic constants, which are important parameters for high field applications. PMID:20198132
Adiabatic evolution of plasma equilibrium
Grad, H.; Hu, P. N.; Stevens, D. C.
1975-01-01
A new theory of plasma equilibrium is introduced in which adiabatic constraints are specified. This leads to a mathematically nonstandard structure, as compared to the usual equilibrium theory, in which prescription of pressure and current profiles leads to an elliptic partial differential equation. Topologically complex configurations require further generalization of the concept of adiabaticity to allow irreversible mixing of plasma and magnetic flux among islands. Matching conditions across a boundary layer at the separatrix are obtained from appropriate conservation laws. Applications are made to configurations with planned islands (as in Doublet) and accidental islands (as in Tokamaks). Two-dimensional, axially symmetric, helically symmetric, and closed line equilibria are included. PMID:16578729
Geometric Adiabatic Transport in Quantum Hall States
NASA Astrophysics Data System (ADS)
Klevtsov, S.; Wiegmann, P.
2015-08-01
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.
Geometric Adiabatic Transport in Quantum Hall States.
Klevtsov, S; Wiegmann, P
2015-08-21
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states. PMID:26340197
Pressure Oscillations in Adiabatic Compression
ERIC Educational Resources Information Center
Stout, Roland
2011-01-01
After finding Moloney and McGarvey's modified adiabatic compression apparatus, I decided to insert this experiment into my physical chemistry laboratory at the last minute, replacing a problematic experiment. With insufficient time to build the apparatus, we placed a bottle between two thick textbooks and compressed it with a third textbook forced…
Adiabatic dynamics of magnetic vortices
NASA Astrophysics Data System (ADS)
Papanicolaou, N.
1994-03-01
We formulate a reasonably detailed adiabatic conjecture concerning the dynamics of skew deflection of magnetic vortices in a field gradient, which is expected to be valid at sufficiently large values of the winding number. The conjecture is consistent with the golden rule used to describe the dynamics of realistic magnetic bubbles and is verified here numerically within the 2-D isotropic Heisenberg model.
Transitionless driving on adiabatic search algorithm
Oh, Sangchul; Kais, Sabre
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Transitionless driving on adiabatic search algorithm
NASA Astrophysics Data System (ADS)
Oh, Sangchul; Kais, Sabre
2014-12-01
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Transitionless driving on adiabatic search algorithm.
Oh, Sangchul; Kais, Sabre
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics. PMID:25494733
Studies in Chaotic adiabatic dynamics
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the {open_quotes}goodness{close_quotes} of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees).
On the anisotropic elastic properties of hydroxyapatite.
NASA Technical Reports Server (NTRS)
Katz, J. L.; Ukraincik, K.
1971-01-01
Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are given. The anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.
Robust adiabatic sum frequency conversion.
Suchowski, Haim; Prabhudesai, Vaibhav; Oron, Dan; Arie, Ady; Silberberg, Yaron
2009-07-20
We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems. PMID:19654679
Adiabaticity in open quantum systems
NASA Astrophysics Data System (ADS)
Venuti, Lorenzo Campos; Albash, Tameem; Lidar, Daniel A.; Zanardi, Paolo
2016-03-01
We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian L (t ) . We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of L (t ) will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time T . In the case of a finite number of level crossings, the scaling becomes T-η with an exponent η that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time T should be long compared to the corresponding minimum inverse gap squared of L (t ) . Our results are illustrated with several examples.
Does temperature increase or decrease in adiabatic decompression of magma?
NASA Astrophysics Data System (ADS)
Kilinc, A. I.; Ghiorso, M. S.; Khan, T.
2011-12-01
We have modeled adiabatic decompression of an andesitic and a basaltic magma as an isentropic process using the Melts algorithm. Our modeling shows that during adiabatic decompression temperature of andesitic magma increases but temperature of basaltic magma decreases. In an isentropic process entropy is constant so change of temperature with pressure can be written as dT/dP=T (dV/dT)/Cp where T (dV/dT)/Cp is generally positive. If delta P is negative so is delta T. In general, in the absence of phase change, we expect the temperature to decrease with adiabatic decompression. The effect of crystallization is to turn a more entropic phase (liquid) into a less entropic phase (solid), which must be compensated by raising the temperature. If during adiabatic decompression there is small amount or no crystallization, T (dV/dT)/Cp effect which lowers the temperature overwhelms the small amount of crystallization, which raises the temperature, and overall system temperature decreases.
Andronesi, Ovidiu C.; Ramadan, Saadallah; Mountford, Carolyn E.; Sorensen, A. Gregory
2011-01-01
Novel low-power adiabatic sequences are demonstrated for in-vivo localized two-dimensional (2D) correlated MR spectroscopy, such as COSY (Correlated Spectroscopy) and TOCSY (Total Correlated Spectroscopy). The design is based on three new elements for in-vivo 2D MRS: the use of gradient modulated constant adiabaticity GOIA-W(16,4) pulses for i) localization (COSY and TOCSY) and ii) mixing (TOCSY), and iii) the use of longitudinal mixing (z-filter) for magnetization transfer during TOCSY. GOIA-W(16,4) provides accurate signal localization, and more importantly, lowers the SAR for both TOCSY mixing and localization. Longitudinal mixing improves considerably (five-folds) the efficiency of TOCSY transfer. These are markedly different from previous 1D editing TOCSY sequences using spatially non-selective pulses and transverse mixing. Fully adiabatic (adiabatic mixing with adiabatic localization) and semi-adiabatic (adiabatic mixing with non-adiabatic localization) methods for 2D TOCSY are compared. Results are presented for simulations, phantoms, and in-vivo 2D spectra from healthy volunteers and patients with brain tumors obtained on 3T clinical platforms equipped with standard hardware. To the best of our knowledge this is the first demonstration of in-vivo adiabatic 2D TOCSY and fully adiabatic 2D COSY. It is expected that these methodological developments will advance the in-vivo applicability of multi(spectrally)dimensional MRS to reliably identify metabolic biomarkers. PMID:20890988
NASA Astrophysics Data System (ADS)
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
Adiabatic Wankel type rotary engine
NASA Technical Reports Server (NTRS)
Kamo, R.; Badgley, P.; Doup, D.
1988-01-01
This SBIR Phase program accomplished the objective of advancing the technology of the Wankel type rotary engine for aircraft applications through the use of adiabatic engine technology. Based on the results of this program, technology is in place to provide a rotor and side and intermediate housings with thermal barrier coatings. A detailed cycle analysis of the NASA 1007R Direct Injection Stratified Charge (DISC) rotary engine was performed which concluded that applying thermal barrier coatings to the rotor should be successful and that it was unlikely that the rotor housing could be successfully run with thermal barrier coatings as the thermal stresses were extensive.
Ghaderi, Nima
2016-03-28
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ∼0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere. PMID:27036434
NASA Astrophysics Data System (ADS)
Ghaderi, Nima
2016-03-01
Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the krec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high pressure limit expressions). Ozone and its formation from O + O2 are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ˜0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O3 will be presented elsewhere.
NASA Astrophysics Data System (ADS)
Saadaoui, Fatiha; Driss Khodja, Fatima Zohra; Kadoun, Abd-Ed-Daïm; Driss Khodja, Mohammed; Elias, Abdelkader; Boudali, Abdelkader
2015-12-01
We have performed first-principles calculations of structural, elastic, thermodynamic, and electronic properties of anti-perovskites AIIICNi3 (AIII = Al, Ga, In), by using the full-potential linearized augmented plane wave (FP-LAPW) method combined with the quasi-harmonic Debye model. We carried out our calculations within the local density approximation (LDA) and the generalized gradient approximation (GGA-PBE and GGA-PBEsol functionals). Our results constitute interesting first predictions in the case of many elastic parameters of the anti-perovskites AIIICNi3, among them elastic parameters of AlCNi3 and GaCNi3 and some polycrystalline elastic parameters of InCNi3. We also report for the first time calculated values, at ambient conditions, of Grüneisen parameter, thermal expansion coefficient, specific heat at constant pressure, specific heat at constant volume, isothermal bulk modulus, and adiabatic bulk modulus for AlCNi3, GaCNi3, and InCNi3. Band structure, total and partial densities of states, and charge density have been obtained and analyzed. Electronic structure results show metallic behavior for the three compounds. Ni 3 d states play dominant role near the Fermi level and there is a strong hybridization between Ni 3 d and C 2 p states. In addition, as AIIICNi3 synthesized samples are expected to be carbon-deficient, we calculated structural, elastic, and thermodynamic properties of sub-stoichiometric AlC x Ni3 materials.
Degenerate adiabatic perturbation theory: Foundations and applications
NASA Astrophysics Data System (ADS)
Rigolin, Gustavo; Ortiz, Gerardo
2014-08-01
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010), 10.1103/PhysRevLett.104.170406], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions [given in Phys. Rev. A 85, 062111 (2012), 10.1103/PhysRevA.85.062111]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-Abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth-order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power-series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed-form time-dependent wave function is derived exactly, and also to other nonexactly solvable Hamiltonians whose solutions are numerically computed.
Shortcut to adiabatic gate teleportation
NASA Astrophysics Data System (ADS)
Santos, Alan C.; Silva, Raphael D.; Sarandy, Marcelo S.
2016-01-01
We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n -qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian HSA for an arbitrary n -qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n -qubit state teleportation. This result is rather general, with the speed of the evolution only dictated by the quantum speed limit. In particular, we analyze the energetic cost for different Hamiltonian interpolations in the context of the energy-time complementarity.
Quantum gates with controlled adiabatic evolutions
NASA Astrophysics Data System (ADS)
Hen, Itay
2015-02-01
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary "adiabatic circuits," analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that while these adiabatic algorithms fail to exhibit certain aspects of the inherent fault tolerance of traditional quantum adiabatic algorithms, they may have certain other experimental advantages acting as quantum gates.
On a Nonlinear Model in Adiabatic Evolutions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Norris, Andrew N.
2014-01-01
We consider a periodic lattice structure in d=2 or 3 dimensions with unit cell comprising Z thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the effective elasticity of such frameworks. The method yields the effective cubic elastic constants for three-dimensional space-filling lattices with Z=4, 6, 8, 12 and 14, the last being the ‘stiffest’ lattice proposed by Gurtner & Durand (Gurtner & Durand 2014 Proc. R. Soc. A 470, 20130611. (doi:10.1098/rspa.2013.0611)). The analytical expressions provide explicit formulae for the effective properties of pentamode materials, both isotropic and anisotropic, obtained from the general formulation in the stretch-dominated limit for Z=d+1. PMID:25484608
Plasma heating via adiabatic magnetic compression-expansion cycle
NASA Astrophysics Data System (ADS)
Avinash, K.; Sengupta, M.; Ganesh, R.
2016-06-01
Heating of collisionless plasmas in closed adiabatic magnetic cycle comprising of a quasi static compression followed by a non quasi static constrained expansion against a constant external pressure is proposed. Thermodynamic constraints are derived to show that the plasma always gains heat in cycles having at least one non quasi static process. The turbulent relaxation of the plasma to the equilibrium state at the end of the non quasi static expansion is discussed and verified via 1D Particle in Cell (PIC) simulations. Applications of this scheme to heating plasmas in open configurations (mirror machines) and closed configurations (tokamak, reverse field pinche) are discussed.
Heating and cooling in adiabatic mixing process
NASA Astrophysics Data System (ADS)
Zhou, Jing; Cai, Zi; Zou, Xu-Bo; Guo, Guang-Can
2010-12-01
We study the effect of interaction on the temperature change in the process of adiabatic mixing of two components of Fermi gases using the real-space Bogoliubov-de Gennes method. We find that in the process of adiabatic mixing, the competition between the adiabatic expansion and the attractive interaction makes it possible to cool or heat the system depending on the strength of the interaction and the initial temperature of the system. The changes of the temperature in a bulk system and in a trapped system are investigated.
Multisurface Adiabatic Reactive Molecular Dynamics.
Nagy, Tibor; Yosa Reyes, Juvenal; Meuwly, Markus
2014-04-01
Adiabatic reactive molecular dynamics (ARMD) simulation method is a surface-crossing algorithm for modeling chemical reactions in classical molecular dynamics simulations using empirical force fields. As the ARMD Hamiltonian is time dependent during crossing, it allows only approximate energy conservation. In the current work, the range of applicability of conventional ARMD is explored, and a new multisurface ARMD (MS-ARMD) method is presented, implemented in CHARMM and applied to the vibrationally induced photodissociation of sulfuric acid (H2SO4) in the gas phase. For this, an accurate global potential energy surface (PES) involving 12 H2SO4 and 4 H2O + SO3 force fields fitted to MP2/6-311G++(2d,2p) reference energies is employed. The MS-ARMD simulations conserve total energy and feature both intramolecular H-transfer reactions and water elimination. An analytical treatment of the dynamics in the crossing region finds that conventional ARMD can approximately conserve total energy for limiting cases. In one of them, the reduced mass of the system is large, which often occurs for simulations of solvated biomolecular systems. On the other hand, MS-ARMD is a general approach for modeling chemical reactions including gas-phase, homogeneous, heterogeneous, and enzymatic catalytic reactions while conserving total energy in atomistic simulations. PMID:26580356
Adiabatic limits on Riemannian Heisenberg manifolds
Yakovlev, A A
2008-02-28
An asymptotic formula is obtained for the distribution function of the spectrum of the Laplace operator, in the adiabatic limit for the foliation defined by the orbits of an invariant flow on a compact Riemannian Heisenberg manifold. Bibliography: 21 titles.
Experimental demonstration of composite adiabatic passage
NASA Astrophysics Data System (ADS)
Schraft, Daniel; Halfmann, Thomas; Genov, Genko T.; Vitanov, Nikolay V.
2013-12-01
We report an experimental demonstration of composite adiabatic passage (CAP) for robust and efficient manipulation of two-level systems. The technique represents a altered version of rapid adiabatic passage (RAP), driven by composite sequences of radiation pulses with appropriately chosen phases. We implement CAP with radio-frequency pulses to invert (i.e., to rephase) optically prepared spin coherences in a Pr3+:Y2SiO5 crystal. We perform systematic investigations of the efficiency of CAP and compare the results with conventional π pulses and RAP. The data clearly demonstrate the superior features of CAP with regard to robustness and efficiency, even under conditions of weakly fulfilled adiabaticity. The experimental demonstration of composite sequences to support adiabatic passage is of significant relevance whenever a high efficiency or robustness of coherent excitation processes need to be maintained, e.g., as required in quantum information technology.
An Adiabatic Architecture for Linear Signal Processing
NASA Astrophysics Data System (ADS)
Vollmer, M.; Götze, J.
2005-05-01
Using adiabatic CMOS logic instead of the more traditional static CMOS logic can lower the power consumption of a hardware design. However, the characteristic differences between adiabatic and static logic, such as a four-phase clock, have a far reaching influence on the design itself. These influences are investigated in this paper by adapting a systolic array of CORDIC devices to be implemented adiabatically. We present a means to describe adiabatic logic in VHDL and use it to define the systolic array with precise timing and bit-true calculations. The large pipeline bubbles that occur in a naive version of this array are identified and removed to a large degree. As an example, we demonstrate a parameterization of the CORDIC array that carries out adaptive RLS filtering.
General conditions for quantum adiabatic evolution
Comparat, Daniel
2009-07-15
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution [H({epsilon}t),{epsilon}{yields}0], are insufficient to describe an evolution driven by the Hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian H(t). As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions)
Adiabatic invariance of oscillons/I -balls
NASA Astrophysics Data System (ADS)
Kawasaki, Masahiro; Takahashi, Fuminobu; Takeda, Naoyuki
2015-11-01
Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or I -balls. We prove the adiabatic invariance of the oscillons/I -balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such a potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/I -balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/I -balls are only quasistable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the I -balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/I -balls is due to the adiabatic invariance.
Improved Indentation Test for Measuring Nonlinear Elasticity
NASA Technical Reports Server (NTRS)
Eldridge, Jeffrey I.
2004-01-01
A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.
Symmetry of the Adiabatic Condition in the Piston Problem
ERIC Educational Resources Information Center
Anacleto, Joaquim; Ferreira, J. M.
2011-01-01
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be…
NASA Astrophysics Data System (ADS)
Moraru, Gheorghe; Mursa, Condrat
2006-12-01
In this book we present the basic concepts of the theory of elasticity: stress and deformation states (plane and three-dimensional) and generalized Hooke's law. We present a number of problems which have applications in strength analysis. The book includes a synthesis of the theory of elasticity and modern methods of applied mathematics. This book is designed for students, post graduate students and specialists in strength analysis. the book contains a number of appendixes which includes: elements of matrix-calculation, concepts of tensorial calculation, the Fourier transform, the notion of improper integrals,singular and hypersingular integrals, generalized functions, the Dirac Delta function
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-02-01
In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G →G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap Δ (N) separating the ground and first-excited states in the limit of large problem size N ≫1. Calculating Δ (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.
Accurate adiabatic correction in the hydrogen molecule
Pachucki, Krzysztof; Komasa, Jacek
2014-12-14
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10{sup −12} at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H{sub 2}, HD, HT, D{sub 2}, DT, and T{sub 2} has been determined. For the ground state of H{sub 2} the estimated precision is 3 × 10{sup −7} cm{sup −1}, which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels.
Accurate adiabatic correction in the hydrogen molecule
NASA Astrophysics Data System (ADS)
Pachucki, Krzysztof; Komasa, Jacek
2014-12-01
A new formalism for the accurate treatment of adiabatic effects in the hydrogen molecule is presented, in which the electronic wave function is expanded in the James-Coolidge basis functions. Systematic increase in the size of the basis set permits estimation of the accuracy. Numerical results for the adiabatic correction to the Born-Oppenheimer interaction energy reveal a relative precision of 10-12 at an arbitrary internuclear distance. Such calculations have been performed for 88 internuclear distances in the range of 0 < R ⩽ 12 bohrs to construct the adiabatic correction potential and to solve the nuclear Schrödinger equation. Finally, the adiabatic correction to the dissociation energies of all rovibrational levels in H2, HD, HT, D2, DT, and T2 has been determined. For the ground state of H2 the estimated precision is 3 × 10-7 cm-1, which is almost three orders of magnitude higher than that of the best previous result. The achieved accuracy removes the adiabatic contribution from the overall error budget of the present day theoretical predictions for the rovibrational levels.
Symmetry-Protected Quantum Adiabatic Transistors
NASA Astrophysics Data System (ADS)
Williamson, Dominic J.; Bartlett, Stephen D.
2014-03-01
An essential development in the history of computing was the invention of the transistor as it allowed logic circuits to be implemented in a robust and modular way. The physical characteristics of semiconductor materials were the key to building these devices. We aim to present an analogous development for quantum computing by showing that quantum adiabatic transistors (as defined by Flammia et al.) are built upon the essential qualities of symmetry-protected (SP) quantum ordered phases in one dimension. Flammia et al. and Renes et al. have demonstrated schemes for universal adiabatic quantum computation using quantum adiabatic transistors described by interacting spin chain models with specifically chosen Hamiltonian terms. We show that these models can be understood as specific examples of the generic situation in which all SP phases lead to quantum computation on encoded edge degrees of freedom by adiabatically traversing a symmetric phase transition into a trivial symmetric phase. This point of view is advantageous as it allows us to readily see that the computational properties of a quantum adiabatic transistor arise from a phase of matter rather than due to carefully tuned interactions.
Influence of viscosity and the adiabatic index on planetary migration
NASA Astrophysics Data System (ADS)
Bitsch, B.; Boley, A.; Kley, W.
2013-02-01
Context. The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state. It has been shown that in active disks, where the internal dissipation is balanced by radiative transport, migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. Aims: In this paper we investigate the influence of different viscosity prescriptions (α-type and constant) and adiabatic indices on disk structures. We then determine how this affects the migration rate of planets embedded in such disks. Methods: We perform three-dimensional numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20 MEarth planets is studied. Results: Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. Hence, in these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. Conclusions: For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20-MEarth planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing
Elasticity of crystalline molecular explosives
Hooks, Daniel E.; Ramos, Kyle J.; Bolme, C. A.; Cawkwell, Marc J.
2015-04-14
Crystalline molecular explosives are key components of engineered explosive formulations. In precision applications a high degree of consistency and predictability is desired under a range of conditions to a variety of stimuli. Prediction of behaviors from mechanical response and failure to detonation initiation and detonation performance of the material is linked to accurate knowledge of the material structure and first stage of deformation: elasticity. The elastic response of pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), and cyclotetramethylene tetranitramine (HMX), including aspects of material and measurement variability, and computational methods are described in detail. Experimental determinations of elastic tensors are compared, andmore » an evaluation of sources of error is presented. Furthermore, computed elastic constants are also compared for these materials and for triaminotrinitrobenzene (TATB), for which there are no measurements.« less
Elasticity of crystalline molecular explosives
Hooks, Daniel E.; Ramos, Kyle J.; Bolme, C. A.; Cawkwell, Marc J.
2015-04-14
Crystalline molecular explosives are key components of engineered explosive formulations. In precision applications a high degree of consistency and predictability is desired under a range of conditions to a variety of stimuli. Prediction of behaviors from mechanical response and failure to detonation initiation and detonation performance of the material is linked to accurate knowledge of the material structure and first stage of deformation: elasticity. The elastic response of pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), and cyclotetramethylene tetranitramine (HMX), including aspects of material and measurement variability, and computational methods are described in detail. Experimental determinations of elastic tensors are compared, and an evaluation of sources of error is presented. Furthermore, computed elastic constants are also compared for these materials and for triaminotrinitrobenzene (TATB), for which there are no measurements.
Adiabatic approximation for the density matrix
NASA Astrophysics Data System (ADS)
Band, Yehuda B.
1992-05-01
An adiabatic approximation for the Liouville density-matrix equation which includes decay terms is developed. The adiabatic approximation employs the eigenvectors of the non-normal Liouville operator. The approximation is valid when there exists a complete set of eigenvectors of the non-normal Liouville operator (i.e., the eigenvectors span the density-matrix space), the time rate of change of the Liouville operator is small, and an auxiliary matrix is nonsingular. Numerical examples are presented involving efficient population transfer in a molecule by stimulated Raman scattering, with the intermediate level of the molecule decaying on a time scale that is fast compared with the pulse durations of the pump and Stokes fields. The adiabatic density-matrix approximation can be simply used to determine the density matrix for atomic or molecular systems interacting with cw electromagnetic fields when spontaneous emission or other decay mechanisms prevail.
Extensive Adiabatic Invariants for Nonlinear Chains
NASA Astrophysics Data System (ADS)
Giorgilli, Antonio; Paleari, Simone; Penati, Tiziano
2012-09-01
We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.
Anderson localization makes adiabatic quantum optimization fail
Altshuler, Boris; Krovi, Hari; Roland, Jérémie
2010-01-01
Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the quantum computer’s Hamiltonian. We show that the statistics of the gaps can be analyzed in a novel way, borrowed from the study of quantum disordered systems in statistical mechanics. It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems. This implies that unfortunately, adiabatic quantum optimization fails: The system gets trapped in one of the numerous local minima. PMID:20616043
The elastic properties of woven polymeric fabric
Warren, W.E. )
1989-01-01
The in-plane linear elastic constants of woven fabric are determined in terms of the specific fabric microstructure. The fabric is assumed to be a spatially periodic interlaced network of orthogonal yarns and the individual yarns are modeled as extensible elastica. These results indicate that a significant coupling of bending and stretching effects occurs during deformation. Results of this theoretical analysis compare favorable with measured in-plane elastic constants for Vincel yarn fabrics. 17 refs., 2 figs., 1 tab.
Petrova, A. E.; Krasnorussky, V. N.; Stishov, S. M.
2010-09-15
Measurements of the sound velocities in a single crystal of FeSi were performed in the temperature range 4-300 K. Elastic constants C{sub 11} and C{sub 44} deviate from a quasiharmonic behavior at high temperature; on the other hand, elastic constants C{sub 12} increases anomalously in the entire temperature range, indicating a change in the electron structure of this material.
Spontaneous emission in stimulated Raman adiabatic passage
Ivanov, P. A.; Vitanov, N. V.; Bergmann, K.
2005-11-15
This work explores the effect of spontaneous emission on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The approach uses adiabatic elimination of weakly coupled density matrix elements in the Liouville equation, from which a very accurate analytic approximation is derived. The loss of population transfer efficiency is found to decrease exponentially with the factor {omega}{sub 0}{sup 2}/{gamma}, where {gamma} is the spontaneous emission rate and {omega}{sub 0} is the peak Rabi frequency. The transfer efficiency increases with the pulse delay and reaches a steady value. For large pulse delay and large spontaneous emission rate STIRAP degenerates into optical pumping.
Adiabatic Hyperspherical Analysis of Realistic Nuclear Potentials
NASA Astrophysics Data System (ADS)
Daily, K. M.; Kievsky, Alejandro; Greene, Chris H.
2015-12-01
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin T = 3/2 contribution in our analysis.
On black hole spectroscopy via adiabatic invariance
NASA Astrophysics Data System (ADS)
Jiang, Qing-Quan; Han, Yan
2012-12-01
In this Letter, we obtain the black hole spectroscopy by combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon. This velocity is obtained in the tunneling framework. In particular, we declare, if requiring canonical invariance, the adiabatic invariant quantity should be of the covariant form Iadia = ∮pi dqi. Using it, the horizon area of a Schwarzschild black hole is quantized independently of the choice of coordinates, with an equally spaced spectroscopy always given by ΔA = 8 π lp2 in the Schwarzschild and Painlevé coordinates.
Complexity of the Quantum Adiabatic Algorithm
NASA Technical Reports Server (NTRS)
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
AB INITIO SIMULATIONS FOR MATERIAL PROPERTIES ALONG THE JUPITER ADIABAT
French, Martin; Becker, Andreas; Lorenzen, Winfried; Nettelmann, Nadine; Bethkenhagen, Mandy; Redmer, Ronald; Wicht, Johannes
2012-09-15
We determine basic thermodynamic and transport properties of hydrogen-helium-water mixtures for the extreme conditions along Jupiter's adiabat via ab initio simulations, which are compiled in an accurate and consistent data set. In particular, we calculate the electrical and thermal conductivity, the shear and longitudinal viscosity, and diffusion coefficients of the nuclei. We present results for associated quantities like the magnetic and thermal diffusivity and the kinematic shear viscosity along an adiabat that is taken from a state-of-the-art interior structure model. Furthermore, the heat capacities, the thermal expansion coefficient, the isothermal compressibility, the Grueneisen parameter, and the speed of sound are calculated. We find that the onset of dissociation and ionization of hydrogen at about 0.9 Jupiter radii marks a region where the material properties change drastically. In the deep interior, where the electrons are degenerate, many of the material properties remain relatively constant. Our ab initio data will serve as a robust foundation for applications that require accurate knowledge of the material properties in Jupiter's interior, e.g., models for the dynamo generation.
The effect of adiabaticity on strongly quenched Bose Einstein Condensates
NASA Astrophysics Data System (ADS)
Ling, Hong; Kain, Ben
2015-05-01
We study the properties of a Bose-Einstein condensate following a deep quench to a large scattering length during which the condensate fraction nc changes with time. We construct a closed set of equations that highlight the role of the adiabaticity or equivalently, dnc/dt, the rate change of nc, which is to induce an (imaginary) effective interaction between quasiparticles. We show analytically that such a system supports a steady state characterized by a constant condensate density and a steady but periodically changing momentum distribution, whose time average is described exactly by the generalized Gibbs ensemble. We discuss how the nc -induced effective interaction, which cannot be ignored on the grounds of the adiabatic approximation for modes near the gapless Goldstone mode, can significantly affect condensate populations and Tan's contact for a Bose gas that has undergone a deep quench. In particular, we find that even when the Bose gas is quenched to unitarity, nc(t) does not completely deplete, approaching, instead, to a steady state with a finite condensate fraction. ITAMP, Harvard-Smithsonian Center for Astrophysics; KITP, University of Santa Barbara.
NASA Astrophysics Data System (ADS)
Merk, D.; Deneke, H.; Pospichal, B.; Seifert, P.
2016-01-01
Cloud properties from both ground-based as well as from geostationary passive satellite observations have been used previously for diagnosing aerosol-cloud interactions. In this investigation, a 2-year data set together with four selected case studies are analyzed with the aim of evaluating the consistency and limitations of current ground-based and satellite-retrieved cloud property data sets. The typically applied adiabatic cloud profile is modified using a sub-adiabatic factor to account for entrainment within the cloud. Based on the adiabatic factor obtained from the combination of ground-based cloud radar, ceilometer and microwave radiometer, we demonstrate that neither the assumption of a completely adiabatic cloud nor the assumption of a constant sub-adiabatic factor is fulfilled (mean adiabatic factor 0.63 ± 0.22). As cloud adiabaticity is required to estimate the cloud droplet number concentration but is not available from passive satellite observations, an independent method to estimate the adiabatic factor, and thus the influence of mixing, would be highly desirable for global-scale analyses. Considering the radiative effect of a cloud described by the sub-adiabatic model, we focus on cloud optical depth and its sensitivities. Ground-based estimates are here compared vs. cloud optical depth retrieved from the Meteosat SEVIRI satellite instrument resulting in a bias of -4 and a root mean square difference of 16. While a synergistic approach based on the combination of ceilometer, cloud radar and microwave radiometer enables an estimate of the cloud droplet concentration, it is highly sensitive to radar calibration and to assumptions about the moments of the droplet size distribution. Similarly, satellite-based estimates of cloud droplet concentration are uncertain. We conclude that neither the ground-based nor satellite-based cloud retrievals applied here allow a robust estimate of cloud droplet concentration, which complicates its use for the study of
Romero-Redondo, C.; Garrido, E.; Barletta, P.; Kievsky, A.; Viviani, M.
2011-02-15
In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. With this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative s partial waves, and with applicability in multichannel reactions. The convergence of the K matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a {sup 4}He atom on a {sup 4}He{sub 2} dimer (only the elastic channel open), and for collisions involving a {sup 6}Li and two {sup 4}He atoms (two channels open).
Adiabatic quantum-flux-parametron cell library adopting minimalist design
NASA Astrophysics Data System (ADS)
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-05-01
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Multiphoton Raman Atom Optics with Frequency-Swept Adiabatic Passage
NASA Astrophysics Data System (ADS)
Kotru, Krish; Butts, David; Kinast, Joseph; Stoner, Richard
2016-05-01
Light-pulse atom interferometry is a promising candidate for future inertial navigators, gravitational wave detectors, and measurements of fundamental physical constants. The sensitivity of this technique, however, is often limited by the small momentum separations created between interfering atom wave packets (typically ~ 2 ℏk) . We address this issue using light-pulse atom optics derived from stimulated Raman transitions and frequency-swept adiabatic rapid passage (ARP). In experiments, these Raman ARP atom optics have generated up to 30 ℏk photon recoil momenta in an acceleration-sensitive atom interferometer, thereby enhancing the phase shift per unit acceleration by a factor of 15. Since this approach forgoes evaporative cooling and velocity selection, it could enable large-area atom interferometry at higher data rates, while also lowering the atom shot-noise-limited measurement uncertainty.
Adiabatic entanglement in two-atom cavity QED
Lazarou, C.; Garraway, B. M.
2008-02-15
We analyze the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time-dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behavior which can be mapped onto the single atom Jaynes-Cummings model. Exploring the main features of this system we propose simple and fairly robust methods for entangling atoms independently of the cavity, for quantum state mapping, and for implementing SWAP and controlled-NOT (CNOT) gates with atomic qubits.
Adiabatic quantum-flux-parametron cell library adopting minimalist design
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-05-07
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Adiabatic Compression in a Fire Syringe.
ERIC Educational Resources Information Center
Hayn, Carl H.; Baird, Scott C.
1985-01-01
Suggests using better materials in fire syringes to obtain more effective results during demonstrations which show the elevation in temperature upon a very rapid (adiabatic) compression of air. Also describes an experiment (using ignition temperatures) which introduces students to the use of thermocouples for high temperature measurements. (DH)
Apparatus to Measure Adiabatic and Isothermal Processes.
ERIC Educational Resources Information Center
Lamb, D. W.; White, G. M.
1996-01-01
Describes a simple manual apparatus designed to serve as an effective demonstration of the differences between isothermal and adiabatic processes for the general or elementary physics student. Enables students to verify Boyle's law for slow processes and identify the departure from this law for rapid processes and can also be used to give a clear…