Peru, S.; Goutte, H.
2008-04-15
Fully consistent axially-symmetric-deformed quasiparticle random phase approximation (QRPA) calculations have been performed, in which the same Gogny D1S effective force has been used for both the Hartree-Fock-Bogolyubov mean field and the QRPA approaches. Giant resonances calculated in deformed {sup 26-28}Si and {sup 22-24}Mg nuclei as well as in the spherical {sup 30}Si and {sup 28}Mg isotopes are presented. Theoretical results for isovector-dipole and isoscalar monopole, quadrupole, and octupole responses are presented and the impact of the intrinsic nuclear deformation is discussed.
NASA Astrophysics Data System (ADS)
Martini, M.; Péru, S.; Hilaire, S.; Goriely, S.; Lechaftois, F.
2016-07-01
Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the E 1 γ -ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cutoff energy introduced in the 2-quasiparticle (2 -q p ) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the E 1 strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically ˜2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2 -q p QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to somewhat similar predictions of the E 1 strength, both at low energies and for exotic neutron-rich nuclei. Predictions of γ -ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.
NASA Astrophysics Data System (ADS)
Fang, Dong-Liang
2016-03-01
In this work, I take into consideration the Pauli exclusion principle (PEP) in the quasiparticle random-phase approximation (QRPA) calculations for the deformed systems by replacing the traditional quasiboson approximation (QBA) with the renormalized one. With this new formalism, the parametrization of QRPA calculations has been changed and the collapse of QRPA solutions could be avoid for realistic gp p values. I further find that the necessity of the renormalization parameter of particle-particle residual interaction gp p in QRPA calculations is due to the exclusion of PEP. So with the inclusion of PEP, I could easily extend the deformed QRPA calculations to the less-explored region where lack of experimental data prevent effective parametrization of gp p for QRPA methods. With this theoretical improvement, I give predictions of weak decay rates for even-even isotopes in the rare-earth region and compare the results with existing calculations.
NASA Astrophysics Data System (ADS)
Ha, Eunja; Cheoun, Myung-Ki
2016-11-01
We investigate effects of neutron-proton (n p ) pairing correlations on the Gamow-Teller (GT) transition of Mg,2624 by explicitly taking into account deformation effects. Our calculation is performed by a deformed quasiparticle random phase approximation (DQRPA) which includes the deformation at the Bardeen-Cooper-Schrieffer and RPA stage. In this paper, we include the n p pairing as well as neutron-neutron (n n ) and proton-proton (p p ) paring correlations to the DQRPA. Our new formalism is applied to the GT transition of well-known deformed Mg isotopes. The n p pairing effect is found to affect more or less the GT distribution of 24Mg and 26Mg. But the deformation effect turns out to be much larger than the n p paring effect because the Fermi surfaces smear more widely by the deformation rather than the n p pairing correlations. Correlations between the deformation and the n p pairing effects and their ambiguities are also discussed with the comparison to experimental GT strength data by triton and 3He beams.
Finite amplitude method for the quasiparticle random-phase approximation
Avogadro, Paolo; Nakatsukasa, Takashi
2011-07-15
We present the finite amplitude method (FAM), originally proposed in Ref. [17], for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasiparticle-random-phase approximation (QRPA) with simple modifications. This technique has advantages over the conventional QRPA calculations, such as coding feasibility and computational cost. We perform the fully self-consistent linear-response calculation for the spherical neutron-rich nucleus {sup 174}Sn, modifying the hfbrad code, to demonstrate the accuracy, feasibility, and usefulness of the FAM.
Peru, S.; Gosselin, G.; Martini, M.; Dupuis, M.; Hilaire, S.
2011-01-15
Fully consistent axially-symmetric deformed quasiparticle random-phase approximation (QRPA) calculations have been performed, using the same Gogny D1S effective force for both the Hartree-Fock-Bogolyubov mean field and QRPA matrix. New implementation of this approach leads to the applicability of QRPA to heavy deformed nuclei. Giant resonances and low-energy collective states for monopole, dipole, quadrupole, and octupole modes are predicted for the heavy deformed nucleus {sup 238}U and compared with experimental data.
Extended proton-neutron quasiparticle random-phase approximation in a boson expansion method
NASA Astrophysics Data System (ADS)
Civitarese, O.; Montani, F.; Reboiro, M.
1999-08-01
The proton-neutron quasiparticle random phase approximation (pn-QRPA) is extended to include next to leading order terms of the QRPA harmonic expansion. The procedure is tested for the case of a separable Hamiltonian in the SO(5) symmetry representation. The pn-QRPA equation of motion is solved by using a boson expansion technique adapted to the treatment of proton-neutron correlations. The resulting wave functions are used to calculate the matrix elements of double-Fermi transitions.
Self-consistent quasiparticle random-phase approximation for a multilevel pairing model
Hung, N. Quang; Dang, N. Dinh
2007-11-15
Particle-number projection within the Lipkin-Nogami (LN) method is applied to the self-consistent quasiparticle random-phase approximation (SCQRPA), which is tested in an exactly solvable multilevel pairing model. The SCQRPA equations are numerically solved to find the energies of the ground and excited states at various numbers {omega} of doubly degenerate equidistant levels. The use of the LN method allows one to avoid the collapse of the BCS (QRPA) to obtain the energies of the ground and excited states as smooth functions of the interaction parameter G. The comparison between results given by different approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA, and LNSCQRPA is carried out. Although the use of the LN method significantly improves the agreement with the exact results in the intermediate coupling region, we found that in the strong coupling region the SCQRPA results are closest to the exact ones.
NASA Astrophysics Data System (ADS)
Matsuo, Masayuki
2015-03-01
I formulate a many-body theory to calculate the cross section of direct radiative neutron capture reaction by means of the Hartree-Fock-Bogoliubov mean-field model and the continuum quasiparticle random-phase approximation (QRPA). A focus is put on very-neutron-rich nuclei and low-energy neutron kinetic energy in the range from 1 keV to several MeV, which is relevant to the rapid neutron capture process of nucleosynthesis. I begin with the photoabsorption cross section and the E 1 strength function. Next, in order to apply the reciprocity theorem, I decompose the cross section into partial cross sections corresponding to different channels of one- and two-neutron emission decays of photo-excited states. A numerical example is shown for the photo-absorption of 142Sn and the neutron capture of 141Sn .
NASA Astrophysics Data System (ADS)
Goriely, S.; Hilaire, S.; Péru, S.; Martini, M.; Deloncle, I.; Lechaftois, F.
2016-10-01
Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we extend our large-scale calculations of the E 1 γ -ray strength function, obtained in the framework of the axially- symmetric-deformed quasiparticle random phase approximation (QRPA) based on the finite-range D1M Gogny force, to the calculation of the M 1 strength function. We compare our QRPA prediction of the M 1 strength with available experimental data and show that a relatively good agreement is obtained provided the strength is shifted globally by about 2 MeV and increased by an empirical factor of 2. Predictions of the M 1 strength function for spherical and deformed nuclei within the valley of β stability as well as in the neutron-rich region are discussed. Its impact on the radiative neutron capture cross section is also analyzed.
Spin-isospin transitions in chromium isotopes within the quasiparticle random phase approximation
NASA Astrophysics Data System (ADS)
Cakmak, Sadiye; Nabi, Jameel-Un; Babacan, Tahsin; Maras, Ismail
2015-01-01
Beta decay and electron capture on isotopes of chromium are advocated to play a key role in the stellar evolution process. In this paper we endeavor to study charge-changing transitions for 24 isotopes of chromium (42-65Cr). These include neutron-rich and neutron-deficient isotopes of chromium. Three different models from the QRPA genre, namely the pn-QRPA, the Pyatov method (PM) and the Schematic model (SM), were selected to calculate and study the Gamow-Teller (GT) transitions in chromium isotopes. The SM was employed separately in the particle-particle (pp) and pp + particle-hole (ph) channels. To study the effect of deformation, the SM was first used assuming the nuclei to be spherical and later to be deformed. The PM was used both in pp and pp + ph channels but only for the case of spherical nuclei. The pn-QRPA calculation was done by considering both pp and ph forces and taking deformation of nucleus into consideration. A recent study proved this version of pn-QRPA to be the best for calculation of GT strength distributions amongst the QRPA models. The pn-QRPA model calculated GT distributions had low-lying centroids and small widths as compared to other QRPA models. Our calculation results were also compared with other theoretical models and measurements wherever available. Our results are in decent agreement with previous measurements and shell model calculations.
NASA Astrophysics Data System (ADS)
Scuseria, Gustavo E.; Henderson, Thomas M.; Bulik, Ireneusz W.
2013-09-01
We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a "correct bosonization" in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call "crossed-ring" whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call "mosaic" terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.
Scuseria, Gustavo E; Henderson, Thomas M; Bulik, Ireneusz W
2013-09-14
We establish a formal connection between the particle-particle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our previous formal proof on the connection between particle-hole (ph) RPA and ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a "correct bosonization" in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call "crossed-ring" whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call "mosaic" terms which can be absorbed into defining a new effective one-body Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The pp-RPA and qp-RPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.
Martini, M.; Peru, S.; Dupuis, M.
2011-03-15
Low-energy dipole excitations in neon isotopes and N=16 isotones are calculated with a fully consistent axially-symmetric-deformed quasiparticle random phase approximation (QRPA) approach based on Hartree-Fock-Bogolyubov (HFB) states. The same Gogny D1S effective force has been used both in HFB and QRPA calculations. The microscopical structure of these low-lying resonances, as well as the behavior of proton and neutron transition densities, are investigated in order to determine the isoscalar or isovector nature of the excitations. It is found that the N=16 isotones {sup 24}O, {sup 26}Ne, {sup 28}Mg, and {sup 30}Si are characterized by a similar behavior. The occupation of the 2s{sub 1/2} neutron orbit turns out to be crucial, leading to nontrivial transition densities and to small but finite collectivity. Some low-lying dipole excitations of {sup 28}Ne and {sup 30}Ne, characterized by transitions involving the {nu}1d{sub 3/2} state, present a more collective behavior and isoscalar transition densities. A collective proton low-lying excitation is identified in the {sup 18}Ne nucleus.
Ansari, A.; Ring, P.
2006-11-15
The excitation energies and electric multipole decay rates of the lowest lying 2{sup +} and 3{sup -} vibrational states in Pb, Sn, and Ni nuclei are calculated following relativistic quasiparticle random-phase approximation formalism based on the relativistic Hartree-Bogoliubov mean field. Two sets of Lagrangian parameters, NL1 and NL3, are used to investigate the effect of the nuclear force. Overall there is good agreement with the available experimental data for a wide range of mass numbers considered here, and the NL3 set seems to be a better choice. However, strictly speaking, these studies point toward the need of a new set of force parameters that could produce more realistic single-particle levels, at least in vicinity of the Fermi surface, of a wide range of nuclear masses.
NASA Astrophysics Data System (ADS)
Deppisch, Frank F.; Suhonen, Jouni
2016-11-01
We perform a Markov chain Monte Carlo (MCMC) statistical analysis of a number of measured ground-state-to-ground-state single β+/electron-capture and β- decays in the nuclear mass range of A =62 -142 . The corresponding experimental comparative half-lives (logf t values) are compared with the theoretical ones obtained by the use of the proton-neutron quasiparticle random-phase approximation (p n QRPA ) with G -matrix-based effective interactions. The MCMC analysis is performed separately for 47 isobaric triplets and 28 more extended isobaric chains of nuclei to extract values and uncertainties for the effective axial-vector coupling constant gA in nuclear-structure calculations performed in the p n QRPA framework. As far as available, measured half-lives for two-neutrino β β- decays occurring in the studied isobaric chains are analyzed as well.
Raduta, C. M.; Raduta, A. A.
2010-12-15
A many-body Hamiltonian involving the mean field for a projected spherical single-particle basis, the pairing interactions for alike nucleons, and the dipole-dipole proton-neutron interactions in the particle-hole (ph) channel and the ph dipole pairing potential is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation approach. The resulting wave functions and energies for the mother and daughter nuclei are used to calculate the 2{nu}{beta}{beta} decay rate and the process half-life. For illustration, the formalism is applied for the decay {sup 100}Mo{yields}{sup 100}Ru. The calculated half-life is in agreement with the corresponding experimental data. The Ikeda sum rule is obeyed.
NASA Astrophysics Data System (ADS)
Kostensalo, Joel; Suhonen, Jouni
2017-01-01
Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), MpnQRPA, and a two-quasiparticle (two-qp) model, Mqp, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) 1+ and first-forbidden spin-dipole (SD) 2- transitions. The present calculations are done using realistic single-particle model spaces and G -matrix based microscopic two-body interactions. In terms of the ratio k =MpnQRPA/Mqp the studied decays fall into two groups: for GROUP 1, which consists of transitions involving non-magic nuclei, the ratio turns out to be k =0.29 ±0.15 . For GROUP 2, consisting of transitions involving semimagic nuclei, the ratio is 0.5-0.8 for half of the decays and less than 5 ×10-3 for the other half. The magnitudes of the NMEs for several nuclei of GROUP 2 depend sensitively on the size of the used single-particle space and the energies of few key single-particle orbitals used in the pnQRPA calculation, while no such dependence is found for the transitions involving nuclei of GROUP 1. Comparing the NME ratios k of GROUP 1 with those of the earlier GT and SD calculations, where also experimental data are available, the expected "experimental" half-lives for the decays between the 0+ ground state of the even-even reference nuclei and the Jπ=3+,4-,5+,6-,7+,8- states of the neighboring odd-odd nuclei are derived for possible experimental verification. The present results could also shed light to the magnitudes of the NMEs corresponding to the high-forbidden unique 0+→Jπ=3+,4-,5+,6-,7+,8- virtual transitions taking part in the neutrinoless double beta decays.
QRPA Calculations for Spherical and Deformed Nuclei With the Gogny Force
Peru, S.
2009-08-26
Fully consistent axially-symmetric-deformed Quasi-particle Random Phase Approximation (QRPA) calculations have been performed with the D1S Gogny force. Dipole responses have been calculated in Ne isotopes to study the existence of soft dipole modes in exotic nuclei. A comparison between QRPA and generator coordinate method with Gaussian overlap approximation results is done for low lying 2{sup +} states in N = 16 isotones and Ni isotopes.
Igashov, S. Yu.; Urin, M. H.; Rodin, Vadim; Faessler, Amand
2011-04-15
An isospin-self-consistent pn-continuum-QRPA approach is formulated and applied to describe the Gamow-Teller strength distributions for {beta}{beta}-decaying open-shell nuclei. Calculation results obtained for the pairs of nuclei {sup 76}Ge-Se, {sup 100}Mo-Ru, {sup 116}Cd-Sn, and {sup 130}Te-Xe are compared with available experimental data.
Exotic modes of excitation in deformed neutron-rich nuclei
Yoshida, Kenichi
2011-05-06
Low-lying dipole excitation mode in neutron-rich Mg isotopes close to the drip line is investigated in the framework of the Hartree-Fock-Bogoliubov and the quasiparticle random-phase approximation employing the Skyrme and the pairing energy-density functionals. It is found that the low-lying dipole-strength distribution splits into the K{sup {pi}} = 0{sup -} and 1{sup -} components due to the nuclear deformation. The low-lying dipole strength increases as the neutron drip-line is approached.
NASA Astrophysics Data System (ADS)
Nabi, J.-U.; Klapdor-Kleingrothaus, H. V.
1999-03-01
Allowed weak interaction rates for sd-shell nuclei in stellar environment are calculated using a generalized form of proton-neutron quasi-particle RPA model with separable Gamow-Teller forces. The calculated capture and decay rates take into consideration the latest experimental energy levels and ft-value compilations. Weak rates calculated are tabulated at the same points of density and temperature as those of Oda et al. [Atomic Data and Nuclear Data Tables 56, 231 (1994)]. The results are also compared with earlier works. Particle emission processes from excited states, previously ignored, are taken into account and are found to significantly affect some β decay rates.
Neutron-Proton Pairing Effects on the Gamow-Teller Transitions in 24,26Mg by Using the Deformed QRPA
NASA Astrophysics Data System (ADS)
Ha, Eunja; Cheoun, Myung-Ki
We investigated the effects of the neutron-proton (np) pairing correlations on the Gamow-Teller (GT) transition of 24,26Mg by taking into account the deformation. Our calculations is performed within the deformed quasi-particle random phase approximation (DQRPA) which explicitly includes the deformation at the BCS and RPA stage. In this work, we include the np pairing as well as the nn and pp paring correlations to the DQRPA. Our new formalism is applied to the GT transition of the well known deformed Mg isotopes. The np pairing effect is found to affect the GT distribution of 24Mg and 26Mg. Correlations between the deformation and the np pairing are also discussed with the comparison to the experimental GT transition data by triton and 3He beams.
Charge-exchange QRPA with the Gogny Force for Axially-symmetric Deformed Nuclei
Martini, M.; Goriely, S.; Péru, S.
2014-06-15
In recent years fully consistent quasiparticle random-phase approximation (QRPA) calculations using finite range Gogny force have been performed to study electromagnetic excitations of several axially-symmetric deformed nuclei up to the {sup 238}U. Here we present the extension of this approach to the charge-exchange nuclear excitations (pnQRPA). In particular we focus on the Isobaric Analog and Gamow-Teller resonances. A comparison of the predicted GT strength distribution with existing experimental data is presented. The role of nuclear deformation is shown. Special attention is paid to β-decay half-lives calculations for which experimental data exist and for specific isotone chains of relevance for the r-process nucleosynthesis.
Projected shell model for Gamow-Teller transitions in heavy, deformed nuclei
NASA Astrophysics Data System (ADS)
Wang, Long-Jun; Sun, Yang; Gao, Zao-Chun; Kiran Ghorui, Surja
2016-02-01
Calculations of Gamow-Teller (GT) transition rates for heavy, deformed nuclei, which are useful input for nuclear astrophysics studies, are usually done with the quasiparticle random-phase approximation. We propose a shell-model method by applying the Projected Shell Model (PSM) based on deformed bases. With this method, it is possible to perform a state-by-state calculation for nuclear matrix elements for β-decay and electron-capture in heavy nuclei. Taking β- decay from 168Dy to 168Ho as an example, we show that the known experimental B(GT) from the ground state of the mother nucleus to the low-lying states of the daughter nucleus could be well described. Moreover, strong transitions to high-lying states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.
Raduta, C. M.; Raduta, A. A.
2007-10-15
The Gamow-Teller transition operator is written as a polynomial in the dipole proton-neutron and quadrupole charge-conserving quasiparticle random-phase approximation boson operators, using the prescription of the boson expansion technique. Then, the 2{nu}{beta}{beta} process ending on the first 2{sup +} state in the daughter nucleus is allowed through one-, two-, and three-boson states describing the odd-odd intermediate nucleus. The approach uses a single particle basis that is obtained by projecting out the good angular momentum from an orthogonal set of deformed functions. The basis for mother and daughter nuclei may have different deformations. The GT transition amplitude as well as the half-lives were calculated for 18 transitions. Results are compared with the available data as well as with the predictions obtained with other methods.
Onset of deformation in polonium nuclei
Younes, W.; Cizewski, J.A.
1996-12-31
The authors have been able to reproduce the systematics of the positive-parity states in {sup 192-208}Po within the framework of the Particle-Core Model. The wave-functions of the 2{sup +}{sub 1} states have been extracted using the Quasiparticle Random Phase Approximation. The increase in the collective motion of the lighter isotopes comes from the increased proton-neutron interaction when the neutrons and protons both occupy high-j orbitals.
Pygmy dipole mode in deformed neutron-rich Mg isotopes close to the drip line
NASA Astrophysics Data System (ADS)
Yoshida, Kenichi
2009-10-01
We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich Mg36,38,40 close to the drip line by means of the deformed quasiparticle random-phase approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at Ex<10 MeV exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule in Mg40. We obtained the collective dipole modes at around 8-10 MeV in Mg isotopes, that consist of many two-quasiparticle excitations of the neutron. The transition density clearly shows an oscillation of the neutron skin against the isoscalar core. We found significant coupling effects between the dipole and octupole excitation modes due to the nuclear deformation. It is also found that the responses for the compressional dipole and isoscalar octupole excitations are much enhanced in the lower energy region.
Competition between α and β decays for heavy deformed neutron-deficient Pa, U, Np, and Pu isotopes
NASA Astrophysics Data System (ADS)
Ni, Dongdong; Ren, Zhongzhou
2017-01-01
The competition between α and β decays is investigated for neutron-deficient Pa, U, Np, and Pu isotopes. β+/electron-capture (EC) decay rates are calculated within the deformed quasiparticle random-phase approximation with realistic nucleon-nucleon (N N ) interactions. Contributions from allowed Gamow-Teller and Fermi transitions as well as first-forbidden transitions are considered. α -decay calculations are performed within the generalized density-dependent cluster model. Effects of differences between neutron and proton distributions and nuclear deformation are taken into account. In the calculations, Reid-93 N N interactions are used for β+/EC decays, while Michigan three-range Yukawa effective interactions, based on the G -matrix elements of Reid N N potentials, are used for α decay. The calculated β -decay half-lives show good agreement with the experimental data over a range of magnitude from 102 to 105 s. The resulting total half-lives including α and β contributions are found to be in good agreement with the experimental data, together with the α /β -decay branching ratios.
NASA Astrophysics Data System (ADS)
Yakut, H.; Guliyev, E.; Guner, M.; Tabar, E.; Zenginerler, Z.
2012-08-01
A new microscopic method has been developed in the framework of the Quasiparticle-Phonon Nuclear Model (QPNM) in order to investigate spin polarization effects on the magnetic properties such as magnetic moment, intrinsic magnetic moment and effective gs factor of the ground state of odd-mass 157-167Er isotopes. The calculations were performed using both Tamm-Dancoff Approximation (TDA) and Quasiparticle Random-Phase Approximation (QRPA). Reasonably good agreement has been obtained between the QRPA results and the relevant experimental data. Furthermore the variation of the intrinsic magnetic moment gK values with the mass number A exhibits similar behavior for both theoretical and experimental results. From the compression of the calculated intrinsic magnetic moment values with the experimental data the spin-spin interaction parameter has been found as χ=(30/A) MeV for odd-mass 157-167Er isotopes. Our results clarify the possibility of using this new method to describe the magnetic properties of odd-mass deformed nuclei.
QRAP: A numerical code for projected (Q)uasiparticle (RA)ndom (P)hase approximation
NASA Astrophysics Data System (ADS)
Samana, A. R.; Krmpotić, F.; Bertulani, C. A.
2010-06-01
A computer code for quasiparticle random phase approximation - QRPA and projected quasiparticle random phase approximation - PQRPA models of nuclear structure is explained in details. The residual interaction is approximated by a simple δ-force. An important application of the code consists in evaluating nuclear matrix elements involved in neutrino-nucleus reactions. As an example, cross sections for 56Fe and 12C are calculated and the code output is explained. The application to other nuclei and the description of other nuclear and weak decay processes are also discussed. Program summaryTitle of program: QRAP ( Quasiparticle RAndom Phase approximation) Computers: The code has been created on a PC, but also runs on UNIX or LINUX machines Operating systems: WINDOWS or UNIX Program language used: Fortran-77 Memory required to execute with typical data: 16 Mbytes of RAM memory and 2 MB of hard disk space No. of lines in distributed program, including test data, etc.: ˜ 8000 No. of bytes in distributed program, including test data, etc.: ˜ 256 kB Distribution format: tar.gz Nature of physical problem: The program calculates neutrino- and antineutrino-nucleus cross sections as a function of the incident neutrino energy, and muon capture rates, using the QRPA or PQRPA as nuclear structure models. Method of solution: The QRPA, or PQRPA, equations are solved in a self-consistent way for even-even nuclei. The nuclear matrix elements for the neutrino-nucleus interaction are treated as the beta inverse reaction of odd-odd nuclei as function of the transfer momentum. Typical running time: ≈ 5 min on a 3 GHz processor for Data set 1.
Aygor, H. Ali; Maras, Ismail; Cakmak, Necla; Selam, Cevad
2008-11-11
Within quasiparticle random phase approximation (QRPA), Pyatov-Salamov method for the self-consistent determination of the isovector effective interaction strength parameter, restoring a broken isotopic symmetry for the nuclear part of the Hamiltonian, is used. The isospin admixtures in the ground state of the parent nucleus, and the isospin structure of the isobar analog resonance (IAR) state are investigated by including the pairing correlations between nucleons for {sup 72-80}Kr isotopes. Our results are compared with the spherical case and with other theoretical results.
Limitations of the number self-consistent random phase approximation
NASA Astrophysics Data System (ADS)
Mariano, Alejandro; Hirsch, Jorge G.
2000-05-01
The quasiparticle random phase approximation (QRPA) equations are solved taking into account the Pauli principle at the expectation value level, and allowing changes in the mean field occupation numbers to minimize the energy while having the correct number of particles in the correlated vacuum. The study of Fermi pn excitations in 76Ge using a realistic Hilbert space shows that the pairing energy gaps in the modified mean field are diminished up to one half of the experimental value when strong proton-neutron correlations are present. Additionally, the Ikeda sum rule for Fermi transitions is violated due to the lack of scattering terms in the phonon operators. These results call for a critical revision of the double β decay half-lives estimated using the QRPA extensions when standard QRPA calculations collapse.
Deformation behaviour of Rheocast A356 Al alloy at microlevel considering approximated RVEs
NASA Astrophysics Data System (ADS)
Islam, Sk. Tanbir; Das, Prosenjit; Das, Santanu
2015-03-01
A micromechanical approach is considered here to predict the deformation behaviour of Rheocast A356 (Al-Si-Mg) alloy. Two representative volume elements (RVEs) are modelled in the finite element (FE) framework. Two dimensional approximated microstructures are generated assuming elliptic grains, based on the grain size, shape factor and area fraction of the primary Al phase of the said alloy at different processing condition. Plastic instability is shown using stress and strain distribution between the Al rich primary and Si rich eutectic phases under different boundary conditions. Boundary conditions are applied on the approximated RVEs in such a manner, so that they represent the real life situation depending on their position on a cylindrical tensile test sample. FE analysis is carried out using commercial finite element code ABAQUS without specifying any damage or failure criteria. Micro-level in-homogeneity leads to incompatible deformation between the constituent phases of the rheocast alloy and steers plastic strain localisation. Plastic stain localised regions within the RVEs are predicted as the favourable sites for void nucleation. Subsequent growth of nucleated voids leads to final failure of the materials under investigation.
Exact and approximate ensemble treatments of thermal pairing in a multilevel model
NASA Astrophysics Data System (ADS)
Hung, N. Quang; Dang, N. Dinh
2009-05-01
A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected (FTBCS1+SCQRPA) and Lipkin+Nogami projected (FTLN1+SCQRPA) theories that include the quasiparticle number fluctuation and coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations are performed for the pairing gap, total energy, heat capacity, entropy, and microcanonical temperature within the doubly folded equidistant multilevel pairing model. The FTLN1+SCQRPA predictions agree best with the exact grand-canonical results. In general, all approaches clearly show that the superfluid-normal phase transition is smoothed out in finite systems. A novel formula is suggested for extracting the empirical pairing gap in reasonable agreement with the exact canonical results.
Skyrme random-phase-approximation description of lowest Kπ=2γ+ states in axially deformed nuclei
NASA Astrophysics Data System (ADS)
Nesterenko, V. O.; Kartavenko, V. G.; Kleinig, W.; Kvasil, J.; Repko, A.; Jolos, R. V.; Reinhard, P.-G.
2016-03-01
The lowest quadrupole γ -vibrational Kπ=2+ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies Eγ and reduced transition probabilities B (E 2 ) of 2γ+ states are calculated with the Skyrme forces SV-bas and SkM*. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of Eγ by 0.3-0.5 MeV and thus in a better agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of Eγ and too weak collectivity of 2γ+ states still persist. It is shown that domains of nuclei with low and high 2γ+ collectivity are related to the structure of the lowest two-quasiparticle states and conservation of the Nilsson selection rules. The description of 2γ+ states with SV-bas and SkM* is similar in light rare-earth nuclei but deviates in heavier nuclei. However SV-bas much better reproduces the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The accuracy of SRPA is justified by comparison with exact RPA. The calculations suggest that a further development of the self-consistent calculation schemes is needed for a systematic satisfactory description of the 2γ+ states.
Alemgadmi, Khaled I. K. Suparmi; Cari; Deta, U. A.
2015-09-30
The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.
NASA Technical Reports Server (NTRS)
Hyer, M. W.; Cooper, D. E.; Cohen, D.
1985-01-01
The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.
NASA Astrophysics Data System (ADS)
Xu, Chun-Long; Zhang, Min-Cang
2017-01-01
The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.
NASA Astrophysics Data System (ADS)
Egorova, Irina A.; Litvinova, Elena
2016-09-01
New results for electric dipole strength in the chain of even-even calcium isotopes with the mass numbers A =40 -54 are presented. Starting from the covariant Lagrangian of quantum hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for J ≤6 and natural parity were computed in a self-consistent relativistic quasiparticle random-phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations (2 q ⊗phonon ) formed the model space for the calculations of the dipole response function in the relativistic quasiparticle time blocking approximation. The calculations in the latter approach were performed for the giant dipole resonance (GDR) and compared to those obtained with the RQRPA and to available data. The evolution of the dipole strength with the neutron number is investigated for both high-frequency GDRs and low-lying strengths. The development of a pygmy resonant structure on the low-energy shoulder of the GDR is traced and analyzed in terms of transition densities. A dependence of the pygmy dipole strength on the isospin asymmetry parameter is extracted.
Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert
2007-03-15
Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.
Some exploitations of the self-consistent QRPA approach with the Gogny force
Peru, S.; Martini, M.; Dupuis, M.
2012-10-20
Fully consistent axially-symmetric-deformed quasiparticle random phase approximation calculations have been performed with the D1S Gogny force. Giant resonances in exotic nuclei as well as in deformed Mg and Si isotopes have been studied. Dipole responses have been calculated in Ne isotopes and N=16 isotones to study the existence of soft dipole modes in exotic nuclei. The same formalism has been used to describe multipole responses up to octupole in the deformed and heavy nucleus {sup 238}U. Low energy spectroscopy of nickel isotopes has been studied, revealing 0{sup +} states which display a particular structure.
NASA Astrophysics Data System (ADS)
Tanaka, Y.; Ide, S.
2014-12-01
It is well known that the statistical probability of earthquake occurrence changes over the course of a day due to periodic variations in the tidal stress acting on faults. However, periodicity on a decadal scale (8.85 and 18.61 years) has been studied by relatively few researchers and clear correlations have not been obtained. In this study, by investigating historical large earthquakes that occurred over 1,000 years in Japan, it is shown that a stronger periodicity of 8.85 years and a weaker periodicity of 18.61 years appear in the seismicity along the Japan Trench and the Nankai Trough, respectively. The past strain and tilt observations conducted during the 1950s through the 1970s indicate that, nationwide, gradual compression repeated every 8-10 years in the direction of relative plate motion. These compression periods are in accordance with the periods of higher seismic activity in the area along the Japan Trench. This agreement between the phase of the increasing seismicity and the compression periods seen in the long-term cyclic crustal deformation suggests that the periodicity is not merely a coincidence and that the transient crustal movement may be relevant with the tides. Considering the seismiity in the Nankai region, periodicity of 18.61 years should be superimposed on the crustal deformation with periods of 8-10 years. However, the approximately twenty-year observation was too short to extract it. According to a recently proposed model based on the combination of the nonlinear fault rheology and oscillating tidal stress, the above transient crustal deformation with periods of approximately 9 years may be caused by long-term variations in the occurrence rate of tremors. The initiation of the past slow slip events in the Tokai area also agreed with the phase of the 9-year mode except for the largest event from the year 2000.
Skyrme RPA description of γ-vibrational states in rare-earth nuclei
NASA Astrophysics Data System (ADS)
Nesterenko, V. O.; Kartavenko, V. G.; Kleinig, W.; Kvasil, J.; Repko, A.; Jolos, R. V.; Reinhard, P.-G.
2016-01-01
The lowest γ-vibrational states with Kπ = 2+γ in well-deformed Dy, Er and Yb isotopes are investigated within the self-consistent separable quasiparticle random-phase-approximation (QRPA) approach based on the Skyrme functional. The energies Eγ and reduced transition probabilities B(E2)γ of the states are calculated with the Skyrme force SV-mas10. We demonstrate the strong effect of the pairing blocking on the energies of γ-vibrational states. It is also shown that collectivity of γ-vibrational states is strictly determined by keeping the Nilsson selection rules in the corresponding lowest 2qp configurations.
Is it possible to enhance the nuclear Schiff moment by nuclear collective modes?
Auerbach, N. Dmitriev, V. F. Flambaum, V. V. Lisetskiy, A. Sen'kov, R. A. Zelevinsky, V. G.
2007-09-15
The nuclear Schiff moment is predicted to be enhanced in nuclei with static quadrupole and octupole deformation. The analogous suggestion of the enhanced contribution to the Schiff moment from the soft collective quadrupole and octupole vibrations in spherical nuclei is tested in the framework of the quasiparticle random phase approximation with separable quadrupole and octupole forces applied to the odd {sup 217-221}Ra and {sup 217-221}Rn isotopes. In this framework, we confirm the existence of the enhancement effect due to the soft modes, but only in the limit when the frequencies of quadrupole and octupole vibrations are close to zero.
Relativistic Energy Density Functionals: Exotic modes of excitation
Vretenar, D.; Paar, N.; Marketin, T.
2008-11-11
The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of {beta}-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
β-decay properties of neutron-deficient Pt, Hg, and Pb isotopes
Sarriguren, P.; Boillos, J. M.; Moreno, O.; Moya de Guerra, E.
2015-10-15
Neutron-deficient isotopes in the lead region are well established examples of the shape coexistence phenomenon in nuclei. In this work, bulk and decay properties, including deformation energy curves, charge mean square radii, Gamow-Teller (GT) strength distributions, and β-decay half-lives, are studied in neutron-deficient Pt, Hg, and Pb isotopes. The nuclear structure involved is described microscopically from deformed quasiparticle random-phase approximation calculations with residual interactions in both particle-hole and particle-particle channels, performed on top of a self-consistent deformed quasiparticle Skyrme Hartree-Fock basis. The sensitivity to deformation of the GT strength distributions in those isotopes is proposed as an additional complementary signature of the nuclear shape. The β-decay half-lives resulting from the GT strength distributions are compared to experiment to demonstrate the ability of the method.
{beta}-decay in neutron-deficient Hg, Pb, and Po isotopes
Moreno, O.; Sarriguren, P.; Alvarez-Rodriguez, R.; Guerra, E. Moya de
2006-05-15
The effect of nuclear deformation on the energy distributions of the Gamow-Teller strength is studied in neutron-deficient Hg, Pb, and Po even isotopes. The theoretical framework is based on a self-consistent deformed Skyrme Hartree-Fock mean field with pairing correlations between like nucleons in BCS approximation and residual spin-isospin interactions treated in the proton-neutron quasiparticle random-phase approximation. After a systematic study of the Gamow-Teller strength distributions in the low-excitation-energy region, relevant for {beta}{sup +} decay, we have identified the best candidates to look for deformation signatures in their {beta}{sup +}-decay patterns. {beta}{sup +} half-lives and total Gamow-Teller strengths B(GT{sup {+-}}) are analyzed as well.
Photon Scattering from the Stable Even-Mass Mo Isotopes Below the Neutron-Separation Energy
NASA Astrophysics Data System (ADS)
Rusev, G.; Hutcheson, A.; Kwan, E.; Tonchev, A. P.; Tornow, W.; Angell, C.; Hammond, S.; Karwowski, H. J.; Kelley, J. H.; Schwengner, R.; Dönau, F.; Wagner, A.
2008-10-01
We present results from photon-scattering experiments on the stable even-mass molybdenum isotopes below the neutron-separation energy carried out with bremsstrahlung at the superconducting electron accelerator ELBE at the Research Center Dresden-Rossendorf in Germany, and with monoenergetic photon beams at the HIγS facility at TUNL. We applied statistical methods in order to correct for the branching and cascade transitions and to determine the photoabsorption cross section. The obtained results allowed us to extend the tail of the Giant Dipole Resonance below the (,) threshold down to 4 MeV. The photoabsorption cross sections deduced from the present experiments show that the dipole strength increases with the neutron number of the Mo isotopes. The experimental results are discussed in the frame of Quasiparticle-Random-Phase-Approximation in a deformed basis which describe the increasing strength as a result of the deformation.
Magnetic dipole strength in 128Xe and 134Xe in the spin-flip resonance region
NASA Astrophysics Data System (ADS)
Massarczyk, R.; Rusev, G.; Schwengner, R.; Dönau, F.; Bhatia, C.; Gooden, M. Â. E.; Kelley, J. Â. H.; Tonchev, A. Â. P.; Tornow, W.
2014-11-01
The magnetic dipole strength in the energy region of the spin-flip resonance is investigated in 128Xe and 134Xe using quasimonoenergetic and linearly polarized γ -ray beams at the High-Intensity γ -Ray Source facility in Durham, North Carolina, USA. Absorption cross sections were deduced for the magnetic and electric and dipole strength distributions separately for various intervals of excitation energy, including the strength of states in the unresolved quasicontinuum. The magnetic dipole strength distributions show structures resembling a resonance in the spin-flip region around an excitation energy of 8 MeV. The electric dipole strength distributions obtained from the present experiments are in agreement with the ones deduced from an earlier experiment using broad-band bremsstrahlung instead of a quasimonoenergetic beam. The experimental magnetic and electric dipole strength distributions are compared with phenomenological approximations and with predictions of a quasiparticle random phase approximation in a deformed basis.
Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.
1997-01-01
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
Beta-decay spectroscopy relevant to the r-process nucleosynthesis
Nishimura, Shunji; Collaboration: RIBF Decay Collaboration
2012-11-12
A scientific program of beta-decay spectroscopy relevant to r-process nucleosynthesis has been started using high intensity U-beam at the RIBF. The first results of {beta}-decay half-lives of very neutron-rich Kr to Tc nuclides, all of which lie close to the r-process path, suggest a systematic enhancement of the the {beta}-decay rates of the Zr and Nb isotopes around A110 with respect to the predictions of the deformed quasiparticle-random-phase-approximation model (FRDM + QRPA). An impact of the results on the astrophysical r-process is discussed together with the future perspective of the {beta}-decay spectroscopy with the EURICA.
β -decay properties of neutron-rich rare-earth isotopes
NASA Astrophysics Data System (ADS)
Sarriguren, P.
2017-01-01
In this paper, β -decay properties of even-even neutron-rich isotopes in the rare-earth mass region are studied within a microscopic theoretical approach based on a proton-neutron quasiparticle random-phase approximation. The underlying mean field is constructed self-consistently from a deformed Hartree-Fock calculation with Skyrme interactions and pairing correlations to which particle-hole and particle-particle residual interactions are added. Nuclei in this mass region participate in the astrophysical rapid neutron capture process and are directly involved in the generation of the rare-earth peak in the isotopic abundance pattern centered at A ≃160 . The energy distributions of the Gamow-Teller strength as well as the β -decay half-lives and the β -delayed neutron-emission probabilities are discussed and compared with the available experimental information and with calculations based on different approaches.
Contribution of excited states to stellar weak-interaction rates in odd-A nuclei
NASA Astrophysics Data System (ADS)
Sarriguren, P.
2016-05-01
Weak-interaction rates, including β decay and electron capture, are studied in several odd-A nuclei in the p f -shell region at various densities and temperatures of astrophysical interest. Special attention is paid to the relative contribution to these rates of thermally populated excited states in the decaying nucleus. The nuclear structure involved in the weak processes is studied within a quasiparticle random-phase approximation with residual interactions in both particle-hole and particle-particle channels on top of a deformed Skyrme Hartree-Fock mean field with pairing correlations. In the range of densities and temperatures considered, it is found that the total rates do not differ much from the rates of the ground state fully populated. In any case, the changes are not larger than the uncertainties due to the nuclear-model dependence of the rates.
Self-consistent approach to beta decay and delayed neutron emission
NASA Astrophysics Data System (ADS)
Borzov, I. N.
2016-11-01
A brief overview of the recent self-consistent studies of nuclear beta decay is given including the relativistic quasi-particle random-phase approximation or QRPA and Finite Amplitude Method. The results of our self-consistent continuum QRPA model based on the density functional description of the ground states are presented. They are in a good agreement with the recent experimental beta-decay half-lives and delayed neutron emission branchings for the nuclei approaching (and beyond) the neutron closed shells N = 50 near 78Ni and N = 82 near 132Sn. A comparison with the recent calculations from relativistic QRPA model, Finite Amplitude Method and semi-microscopic finite-range droplet model is performed. An importance of the quasi-particle phonon coupling is stressed for the description of the beta decay and delayed multi-neutron emission rates. A strategy of extending our approach to the deformed nuclei and the open problems are discussed.
Crustal deformation and earthquakes
NASA Technical Reports Server (NTRS)
Cohen, S. C.
1984-01-01
The manner in which the Earth's surface deforms during the cycle of stress accumulation and release along major faults is investigated. In an investigation of the crustal deformation associated with a thin channel asthenosphere displacements are reduced from those computed for a half space asthenosphere. A previous finding by other workers that displacements are enhanced when flow is confined to a thin channel is based on several invalid approximations. The major predictions of the finite element model are that the near field postseismic displacements and strain rates are less than those for a half space asthenosphere and that the postseismic strain rates at intermediate distances are greater (in magnitude). The finite width of the asthenosphere ceases to have a significant impact on the crustal deformation pattern when its magnitude exceeds about three lithosphere thicknesses.
Bunnell, W P
1986-12-01
Spinal deformity is a relatively common disorder, particularly in teenage girls. Early detection is possible by a simple, quick visual inspection that should be a standard part of the routine examination of all preteen and teenage patients. Follow-up observation will reveal those curvatures that are progressive and permit orthotic treatment to prevent further increase in the deformity. Spinal fusion offers correction and stabilization of more severe degrees of scoliosis.
Experimental Deformation of Magnetite
NASA Astrophysics Data System (ADS)
Till, J. L.; Rybacki, E.; Morales, L. F. G.
2015-12-01
Magnetite is an important iron ore mineral and the most prominent Fe-oxide phase in the Earth's crust. The systematic occurrence of magnetite in zones of intense deformation in oceanic core complexes suggests that it may play a role in strain localization in some silicate rocks. We performed a series of high-temperature deformation experiments on synthetic magnetite aggregates and natural single crystals to characterize the rheological behavior of magnetite. As starting material, we used fine-grained magnetite powder that was hot isostatically pressed at 1100°C for several hours, resulting in polycrystalline material with a mean grain size of around 40 μm and containing 3-5% porosity. Samples were deformed to 15-20% axial strain under constant load (approximating constant stress) conditions in a Paterson-type gas apparatus for triaxial deformation at temperatures between 900 and 1100°C and 300 MPa confining pressure. The aggregates exhibit typical power-law creep behavior. At high stresses, samples deformed by dislocation creep exhibit stress exponents close to 3, revealing a transition to near-Newtonian creep with stress exponents around 1.3 at lower stresses. Natural magnetite single crystals deformed at 1 atm pressure and temperatures between 950°C and 1150 °C also exhibit stress exponents close to 3, but with lower flow stresses and a lower apparent activation energy than the aggregates. Such behavior may result from the different oxygen fugacity buffers used. Crystallographic-preferred orientations in all polycrystalline samples are very weak and corroborate numerical models of CPO development, suggesting that texture development in magnetite may be inherently slow compared with lower symmetry phases. Comparison of our results with experimental deformation data for various silicate minerals suggests that magnetite should be weaker than most silicates during ductile creep in dry igneous rocks.
Deformation mechanisms in experimentally deformed Boom Clay
NASA Astrophysics Data System (ADS)
Desbois, Guillaume; Schuck, Bernhard; Urai, Janos
2016-04-01
Bulk mechanical and transport properties of reference claystones for deep disposal of radioactive waste have been investigated since many years but little is known about microscale deformation mechanisms because accessing the relevant microstructure in these soft, very fine-grained, low permeable and low porous materials remains difficult. Recent development of ion beam polishing methods to prepare high quality damage free surfaces for scanning electron microscope (SEM) is opening new fields of microstructural investigation in claystones towards a better understanding of the deformation behavior transitional between rocks and soils. We present results of Boom Clay deformed in a triaxial cell in a consolidated - undrained test at a confining pressure of 0.375 MPa (i.e. close to natural value), with σ1 perpendicular to the bedding. Experiments stopped at 20 % strain. As a first approximation, the plasticity of the sample can be described by a Mohr-Coulomb type failure envelope with a coefficient of cohesion C = 0.117 MPa and an internal friction angle ϕ = 18.7°. After deformation test, the bulk sample shows a shear zone at an angle of about 35° from the vertical with an offset of about 5 mm. We used the "Lamipeel" method that allows producing a permanent absolutely plane and large size etched micro relief-replica in order to localize and to document the shear zone at the scale of the deformed core. High-resolution imaging of microstructures was mostly done by using the BIB-SEM method on key-regions identified after the "Lamipeel" method. Detailed BIB-SEM investigations of shear zones show the following: the boundaries between the shear zone and the host rock are sharp, clay aggregates and clastic grains are strongly reoriented parallel to the shear direction, and the porosity is significantly reduced in the shear zone and the grain size is smaller in the shear zone than in the host rock but there is no evidence for broken grains. Comparison of microstructures
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
Partially segmented deformable mirror
Bliss, Erlan S.; Smith, James R.; Salmon, J. Thaddeus; Monjes, Julio A.
1991-01-01
A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp.
Partially segmented deformable mirror
Bliss, E.S.; Smith, J.R.; Salmon, J.T.; Monjes, J.A.
1991-05-21
A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp. 5 figures.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
Cohen, Bruce E; Nicholson, Christopher W
2007-05-01
The bunionette, or tailor's bunion, is a lateral prominence of the fifth metatarsal head. Most commonly, bunionettes are the result of a widened 4-5 intermetatarsal angle with associated varus of the metatarsophalangeal joint. When symptomatic, these deformities often respond to nonsurgical treatment methods, such as wider shoes and padding techniques. When these methods are unsuccessful, surgical treatment is based on preoperative radiographs and associated lesions, such as hyperkeratoses. In rare situations, a simple lateral eminence resection is appropriate; however, the risk of recurrence or overresection is high with this technique. Patients with a lateral bow to the fifth metatarsal are treated with a distal chevron-type osteotomy. A widened 4-5 intermetatarsal angle often requires a diaphyseal osteotomy for correction.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M.
2008-07-15
The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.
Gamma-ray strength at low energies using relativistic QRPA with exact coupling to the continuum
NASA Astrophysics Data System (ADS)
Daoutidis, I.; Goriely, S.
2012-02-01
Continuum-quasiparticle random-phase Approximation (CQRPA) within the relativistic point-coupling model with density-dependent coupling constants is applied to investigate collective excitations in spherical nuclei. In particular we study the impact of the exact continuum on the giant-dipole and pygmy resonance of several Sn isotopes as well as the radiative neutron capture rates of importance for astrophysical calculations.
Low-lying Gamow-Teller transitions in spherical nuclei
Cakmak, N.; Uenlue, S.; Selam, C.
2012-01-15
The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 Less-Than-Or-Slanted-Equal-To A Less-Than-Or-Slanted-Equal-To 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying {beta} decay log(ft) values have been calculated for the nuclei under consideration.
Microscopic description of large-amplitude shape-mixing dynamics with local QRPA inertial functions
Hinohara, Nobuo; Yoshida, Kenichi; Nakatsukasa, Takashi; Sato, Koichi; Matsuo, Masayuki
2011-05-06
We introduce a microscopic approach to derive all the inertial functions in the five-dimensional quadrupole collective Hamiltonian. Local normal modes are evaluated on the constrained mean field in the quasiparticle random-phase approximation in order to derive the inertial functions. The collective Hamiltonians for neutron-rich Mg isotopes are determined with use of this approach, and the shape coexistence/mixing around the N = 20 region is analyzed.
Linear-response calculation in the time-dependent density functional theory
Nakatsukasa, Takashi; Inakura, Tsunenori; Avogadro, Paolo; Ebata, Shuichiro; Sato, Koichi; Yabana, Kazuhiro
2012-11-12
Linear response calculations based on the time-dependent density-functional theory are presented. Especially, we report results of the finite amplitude method which we have recently proposed as an alternative and feasible approach to the (quasiparticle-)random-phase approximation. Calculated properties of the giant resonances and low-energy E1 modes are discussed. We found a universal linear correlation between the low-energy E1 strength and the neutron skin thickness.
Neutral current reaction cross sections for the stable 100 Mo isotope
NASA Astrophysics Data System (ADS)
Balasi, K. G.; Kosmas, T. S.; Divari, P. C.; Ejiri, H.
2010-01-01
Motivated by the ongoing MOON neutrino experiment at Japan aiming to search for double beta and neutrinoless double beta decay events, we investigate inelastic neutrino scattering cross sections for the stable 100Mo isotope by performing state-by-state calculations. The required many body nuclear wave functions are constructed within the context of the quasi-particle random phase approximation (QRPA) tested in the reproducibility of the low-lying spectrum of the 100Mo isotope.
Low-lying dipole resonance in neutron-rich Ne isotopes
NASA Astrophysics Data System (ADS)
Yoshida, Kenichi; van Giai, Nguyen
2008-07-01
Microscopic structure of the low-lying isovector dipole excitation mode in neutron-rich Ne26,28,30 is investigated by performing deformed quasiparticle-random-phase-approximation (QRPA) calculations. The particle-hole residual interaction is derived from a Skyrme force through a Landau-Migdal approximation. We obtain the low-lying resonance in Ne26 at around 8.6 MeV. It is found that the isovector dipole strength at Ex<10 MeV exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule. This excitation mode is composed of several QRPA eigenmodes, one is generated by a ν(2s1/2-12p3/2) transition dominantly and the other mostly by a ν(2s1/2-12p1/2) transition. The neutron excitations take place outside of the nuclear surface reflecting the spatially extended structure of the 2s1/2 wave function. In Ne30, the deformation splitting of the giant resonance is large, and the low-lying resonance overlaps with the giant resonance.
Intrinsic Nilpotent Approximation.
1985-06-01
RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E T*M/O. It
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
NASA Astrophysics Data System (ADS)
Watanabe, H.; Zhang, G. X.; Yoshida, K.; Walker, P. M.; Liu, J. J.; Wu, J.; Regan, P. H.; Söderström, P.-A.; Kanaoka, H.; Korkulu, Z.; Lee, P. S.; Nishimura, S.; Yagi, A.; Ahn, D. S.; Alharbi, T.; Baba, H.; Browne, F.; Bruce, A. M.; Carroll, R. J.; Chae, K. Y.; Dombradi, Zs.; Doornenbal, P.; Estrade, A.; Fukuda, N.; Griffin, C.; Ideguchi, E.; Inabe, N.; Isobe, T.; Kanaya, S.; Kojouharov, I.; Kondev, F. G.; Kubo, T.; Kubono, S.; Kurz, N.; Kuti, I.; Lalkovski, S.; Lane, G. J.; Lee, C. S.; Lee, E. J.; Lorusso, G.; Lotay, G.; Moon, C.-B.; Nishizuka, I.; Nita, C. R.; Odahara, A.; Patel, Z.; Phong, V. H.; Podolyák, Zs.; Roberts, O. J.; Sakurai, H.; Schaffner, H.; Shand, C. M.; Shimizu, Y.; Sumikama, T.; Suzuki, H.; Takeda, H.; Terashima, S.; Vajta, Zs.; Valiente-Dóbon, J. J.; Xu, Z. Y.
2016-09-01
The level structure of 172Dy has been investigated for the first time by means of decay spectroscopy following in-flight fission of a 238U beam. A long-lived isomeric state with T1/2 = 0.71 (5) s and Kπ =8- has been identified at 1278 keV, which decays to the ground-state and γ-vibrational bands through hindered electromagnetic transitions, as well as to the daughter nucleus 172Ho via allowed β decays. The robust nature of the Kπ =8- isomer and the ground-state rotational band reveals an axially-symmetric structure for this nucleus. Meanwhile, the γ-vibrational levels have been identified at unusually low excitation energy compared to the neighboring well-deformed nuclei, indicating the significance of the microscopic effect on the non-axial collectivity in this doubly mid-shell region. The underlying mechanism of enhanced γ vibration is discussed in comparison with the deformed Quasiparticle Random-Phase Approximation based on a Skyrme energy-density functional.
Uncertainties in Astrophysical β-decay Rates from the FRDM
Bertolli, M.G.; Möller, P.; Jones, S.
2014-06-15
β{sup −}-decay rates are of crucial importance in stellar evolution and nucleosynthesis, as they are a key component in stellar processes. Tabulated values of the decay rates as functions of both temperature T and density ρ are necessary input to stellar evolution codes such as MESA, or largescale nucleosynthesis simulations such as those performed by the NuGrid collaboration. Therefore, it is interesting to know the uncertainties in these rates and the effects of these uncertainties on stellar structure and isotopic yields. We have calculated β-strength functions and reaction rates for nuclei ranging from {sup 16}O to {sup 339}136, extending from the proton drip line to the neutron drip line based on a quasi-particle random-phase approximation (QRPA) in a deformed folded-Yukawa single-particle model. Q values are determined from the finite-range droplet mass model (FRDM). We have investigated the effect of model uncertainty on astrophysical β{sup −}-decay rates calculated by the FRDM. The sources of uncertainty considered are Q values and deformation. The rates and their uncertainties are generated for a variety of temperature and density ranges, corresponding to key stellar processes. We demonstrate the effects of these rate uncertainties on isotopic abundances using the NuGrid network calculations.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
NASA Technical Reports Server (NTRS)
Clark, T. A.; Thomsen, P.
1988-01-01
A study is presented of deformations in antennas with the emphasis on their influence on VLBI measurements. The GIFTS structural analysis program has been used to model the VLBI antenna in Fairbanks (Alaska). The report identifies key deformations and studies the effect of gravity, wind, and temperature. Estimates of expected deformations are given.
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Approximate Qualitative Temporal Reasoning
2001-01-01
i.e., their boundaries can be placed in such a way that they coincide with the cell boundaries of the appropriate partition of the time-line. (Think of...respect to some appropriate partition of the time-line. For example, I felt well on Saturday. When I measured my temperature I had a fever on Monday and on...Bittner / Approximate Qualitative Temporal Reasoning 49 [27] I. A. Goralwalla, Y. Leontiev , M. T. Özsu, D. Szafron, and C. Combi. Temporal granularity for
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
Scattering problem in deformed space with minimal length
Stetsko, M. M.; Tkachuk, V. M.
2007-07-15
We investigated the elastic scattering problem with deformed Heisenberg algebra leading to the existence of a minimal length. The continuity equations for the moving particle in deformed space were constructed. We obtained the Green's function for a free particle, the scattering amplitude, and the cross section in deformed space. We also calculated the scattering amplitudes and differential cross sections for the Yukawa and the Coulomb potentials in the Born approximation.
Nuclear Deformation Effects in the Cluster Radioactivity
NASA Astrophysics Data System (ADS)
Misicu, Serban; Protopopescu, Dan
1999-01-01
We investigate the influence of the nuclear deformation on the decay rates of some cluster emission processes. The interaction between the daughter and the cluster is given by a double folding potential including quadrupole and hexadecupole deformed densities of both fragments. The nuclear part of the nucleus--nucleus interaction is density dependent and at small distances a repulsive core in the potential will occur. In the frame of the WKB-approximation the assault frequency of the cluster will depend on the geometric properties of the potential pocket whereas the penetrability will be sensitive to changes in the barrier location. The results obtained in this paper point out that various combinations of cluster and daughter deformations may account for the measured values of the decay rate. The decay rates are however more sensitive to the changes in the daughter deformation due to the large mass asymmetry of the process.
Electric dipole strength distribution below the E1 giant resonance in N = 82 nuclei
NASA Astrophysics Data System (ADS)
Guliyev, Ekber; Kuliev, Ali; Guner, Mehmet
2010-12-01
In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in 136Xe, 138Ba, 140Ce, 142Nd, 144Sm and 146Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6-8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1- excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1+ States in heavy N = 82 isotones in the energy interval 6-8 MeV which shows not all dipole excitations were of electric character in this energy range.
Electric dipole strength distribution below the E1 giant resonance in N = 82 nuclei
NASA Astrophysics Data System (ADS)
Guliyev, Ekber; Kuliev, Ali; Guner, Mehmet
2010-12-01
In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in 136Xe, 138Ba, 140Ce, 142Nd, 144Sm and 146Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6-8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B( E1) value of the 1- excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1+ States in heavy N = 82 isotones in the energy interval 6-8 MeV which shows not all dipole excitations were of electric character in this energy range.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
Approximate universal relations among tidal parameters for neutron star binaries
NASA Astrophysics Data System (ADS)
Yagi, Kent; Yunes, Nicolás
2017-01-01
One of largest uncertainties in nuclear physics is the relation between the pressure and density of supranuclear matter: the equation of state. Some of this uncertainty may be removed through future gravitational wave observations of neutron star binaries by extracting the tidal deformabilities (or Love numbers) of neutron stars, a novel way to probe nuclear physics in the high-density regime. Previous studies have shown that only a certain combination of the individual (quadrupolar) deformabilities of each body (the so-called chirp tidal deformability) can be measured with second-generation, gravitational wave interferometers, such as Adv. LIGO, due to correlations between the individual deformabilities. To overcome this, we search for approximately universal (i.e. approximately equation-of-state independent) relations between two combinations of the individual tidal deformabilities, such that once one of them has been measured, the other can be automatically obtained and the individual ones decoupled through these relations. We find an approximately universal relation between the symmetric and the anti-symmetric combination of the individual tidal deformabilities that is equation-of-state-insensitive to 20 % for binaries with masses less than 1.7{{M}⊙} . We show that these relations can be used to eliminate a combination of the tidal parameters from the list of model parameters, thus breaking degeneracies and improving the accuracy in parameter estimation. A simple (Fisher) study shows that the universal binary Love relations can improve the accuracy in the extraction of the symmetric combination of tidal parameters by as much as an order of magnitude, making the overall accuracy in the extraction of this parameter slightly better than that of the chirp tidal deformability. These new universal relations and the improved measurement accuracy on tidal parameters not only are important to astrophysics and nuclear physics, but also impact our ability to probe
Deformations of superconformal theories
NASA Astrophysics Data System (ADS)
Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
2016-11-01
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.
Strain localization during deformation of Westerly granite
NASA Technical Reports Server (NTRS)
Brodsky, N. S.; Spetzler, H. A.
1984-01-01
A specimen of Westerly granite was cyclically loaded to near failure at 50 MPa confining pressure. Holographic interferometry provided detailed measurements of localized surface deformations during loading and unloading. The data are consistent with deformation occurring primarily elastically at low differential stress; in conjunction with one incipient fault zone between approximately 350 and 520 MPa differential stress; and in conjunction with a second incipient fault zone above 580 MPa and/or during creep. During unloading only one fault zone, that which is active at the intermediate stress levels during loading, is seen to recede.
Vertex finding with deformable templates at LHC
NASA Astrophysics Data System (ADS)
Stepanov, Nikita; Khanov, Alexandre
1997-02-01
We present a novel vertex finding technique. The task is formulated as a discrete-continuous optimisation problem in a way similar to the deformable templates approach for the track finding. Unlike the track finding problem, "elastic hedgehogs" rather than elastic arms are used as deformable templates. They are initialised by a set of procedures which provide zero level approximation for vertex positions and track parameters at the vertex point. The algorithm was evaluated using the simulated events for the LHC CMS detector and demonstrated good performance.
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
An autoregulatory enhancer element of the Drosophila homeotic gene Deformed.
Bergson, C; McGinnis, W
1990-12-01
The stable determination of different anterior-posterior regions of the Drosophila embryo is controlled by the persistent expression of homeotic selector genes. One mechanism that has been proposed to explain the persistent expression of the homeotic gene Deformed is an autoactivation circuit that would be used once Deformed expression had been established by earlier acting patterning genes. Here we show that a large cis-regulatory element mapping approximately 5 kb upstream of the Deformed transcription start has the properties predicted for a Deformed autoregulatory enhancer. This element provides late, spatially localized expression in the epidermal cells of the maxillary and mandibular segments which is wholly dependent upon endogenous Deformed function. In addition, the autoregulatory enhancer can be activated ectopically in embryos and in imaginal disc cells by ectopic expression of Deformed protein. Deletion analysis of the autoregulatory element indicates that it contains compartment specific sub-elements similar to those of other homeotic loci.
Approximating the dynamic response of strain-hardening structures
Youngdahl, C.K.
1991-01-01
A mode approximation method is being developed to predict the dynamic plastic deformation of strain-hardening structures. A mode shape having time-dependent coefficients is based on quasi-static deformation profiles. Two stress fields are associated with the modal shape, one satisfying the dynamic relations and the other satisfying the constitutive equations. The application of suitable matching conditions results in a set of simultaneous differential and algebraic equations for the amplitude coefficients and plastic region size. Using the example of a simply supported beam, the effect of varying the number of matching conditions on the accuracy of the solution is presented. 5 refs., 7 figs.
Deformation Zones along Leading Edges of Thrust Faults
NASA Astrophysics Data System (ADS)
Johnsion, A. M.; Huang, W. O.
2006-12-01
Deformation zones and concomitant damage along earthquake ruptures were recognized long ago in studies of the 1906 San Francisco earthquake. Most of the previous investigations of deformation zones have been of features along strike slip earthquake ruptures. This research, in contrast, describes and analyzes deformation zones observed along leading edges of two thrusts—the 1999 Chi Chi rupture in Taiwan and the Sylmar segment of the 1971 San Fernando Valley rupture in California. Deformation zones along the leading edges of the Chi Chi and Sylmar thrusts have several features and conditions in common: Both formed over reverse faults that dip 30° to 45° at shallow depths. Both accommodated different amounts of strike slip as well as reverse, dip slip along their traces. Both had associated ground deformation zones containing various kinds of smaller structures, including low amplitude folds, small fractures such as strike slip and thrust faults and tension cracks. Both had broken and tilted dwellings and other man made structures within them. Also, both deformation zones were highly asymmetric: the deformation zone in the hanging wall was much wider than that in the footwall. We have combined a proper yielding criterion for permanent (plastic) deformation at the ground surface produced by slip on a buried dislocation that is propagating upward to the surface. The result is an approximate simulation of the growth of ground deformation zones analogous to those we see in the field. The specific phenomena we investigate with the method include: 1). Compressional deformation zones straddling earthquake thrust ruptures. 2). Asymmetric deformation zones. Compressional deformation zones are much wider in the hanging wall than the footwall of thrusts. 3). A thrust deformation zone also includes an extensional zone in the hanging wall. 4). Where there is also left lateral, strike shift across the deformation zone, a zone of left lateral distortion is sandwiched by zones
Evans, D
1975-08-01
A discussion of the essential deformity in calcaneo-valgus feet develops a theme originally put forward in 1961 on the relapsed club foot (Evans 1961). Whereas in the normal foot the medial and lateral columns are about equal in length, in talipes equino-varus the lateral column is longer and in calcaneo-valgus shorter than the medial column. The suggestion is that in the treatment of both deformities the length of the columns be made equal. A method is described of treating calcaneo-valgus deformity by inserting cortical bone grafts taken from the tibia to elongate the anterior end of the calcaneus.
Hamiltonian deformations of Gabor frames: First steps
de Gosson, Maurice A.
2015-01-01
Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed – as the title suggests – as the very first steps towards a general deformation theory for Gabor frames. PMID:25892903
Hamiltonian deformations of Gabor frames: First steps.
de Gosson, Maurice A
2015-03-01
Gabor frames can advantageously be redefined using the Heisenberg-Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed - as the title suggests - as the very first steps towards a general deformation theory for Gabor frames.
NASA Astrophysics Data System (ADS)
Green, Harry
The Third Rock Deformation Colloquium was held December 4, 1989, at the AGU Fall Meeting in San Francisco. Steve Kirby of the U.S. Geological Survey, Menlo Park, Calif., reported on actions taken by the rock deformation steering committee. Brian Wernicke of Harvard University, Cambridge, Mass., talked on the structural geology of the Great Basin.The steering committee voted for “Committee on Deformation of Earth Materials” as the name for the AGU technical committee on rock deformation, Kirby said. Considerable discussion has occurred in the steering committee over our relationship to the AGU Mineral Physics Committee. Indeed, Kirby will become chairman of that committee in 1990, underlining the overlap of the two groups. It was agreed that we will pursue closer association with Mineral Physics.
Wrist deformities after fracture.
Vanheest, Ann
2006-02-01
Wrist deformities can occur after fracture because of malunion of the fracture or injury to the growth plate leading to imbalance of growth. Prevention of malunion is paramount by early recognition with proper reduction and casting or fixation with casting. If a mal-union occurs, an osteotomy may be necessary if anticipated growth will not correct the deformity. Injury of the growth plate may lead to wrist deformity in two ways: angular growth or growth arrest. Angular growth deformities are corrected most commonly by osteotomy. Growth arrest of the radius or the ulna leads to an ulnar-positive or an ulnar-negative variance at the wrist. If the ulnar variance is symptomatic, treatment is centered on achieving a level joint. Options for joint leveling procedures include epiphysiodesis or physeal stapling of the longer bone, lengthening osteotomy of the shorter bone, or shortening osteotomy of the longer bone.
Principles of rock deformation
Nicolas, A.
1987-01-01
This text focuses on the recent achievements in the analysis of rock deformation. It gives an analytical presentation of the essential structures in terms of kinetic and dynamic interpretation. The physical properties underlying the interpretation of rock structures are exposed in simple terms. Emphasized in the book are: the role of fluids in rock fracturing; the kinematic analysis of magnetic flow structures; the application of crystalline plasticity to the kinematic and dynamic analysis of the large deformation imprinted in many metamorphic rocks.
Learning a hierarchical deformable template for rapid deformable object parsing.
Zhu, Long Leo; Chen, Yuanhao; Yuille, Alan
2010-06-01
In this paper, we address the tasks of detecting, segmenting, parsing, and matching deformable objects. We use a novel probabilistic object model that we call a hierarchical deformable template (HDT). The HDT represents the object by state variables defined over a hierarchy (with typically five levels). The hierarchy is built recursively by composing elementary structures to form more complex structures. A probability distribution--a parameterized exponential model--is defined over the hierarchy to quantify the variability in shape and appearance of the object at multiple scales. To perform inference--to estimate the most probable states of the hierarchy for an input image--we use a bottom-up algorithm called compositional inference. This algorithm is an approximate version of dynamic programming where approximations are made (e.g., pruning) to ensure that the algorithm is fast while maintaining high performance. We adapt the structure-perceptron algorithm to estimate the parameters of the HDT in a discriminative manner (simultaneously estimating the appearance and shape parameters). More precisely, we specify an exponential distribution for the HDT using a dictionary of potentials, which capture the appearance and shape cues. This dictionary can be large and so does not require handcrafting the potentials. Instead, structure-perceptron assigns weights to the potentials so that less important potentials receive small weights (this is like a "soft" form of feature selection). Finally, we provide experimental evaluation of HDTs on different visual tasks, including detection, segmentation, matching (alignment), and parsing. We show that HDTs achieve state-of-the-art performance for these different tasks when evaluated on data sets with groundtruth (and when compared to alternative algorithms, which are typically specialized to each task).
NASA Astrophysics Data System (ADS)
Antonellini, Marco; Mollema, Pauline Nella
2015-12-01
We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are shear deformation bands that developed under shallow burial conditions via strain hardening in dm-wide zones. The edges of the polygons are 1-5 m long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain <0.005). The individual shear deformation bands show abutting T-junctions, veering, curving, and merging where they mechanically interact. Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.
Combining global and local approximations
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.
1991-01-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.
Combining global and local approximations
Haftka, R.T. )
1991-09-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 6 refs.
Phenomenological applications of rational approximants
NASA Astrophysics Data System (ADS)
Gonzàlez-Solís, Sergi; Masjuan, Pere
2016-08-01
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function 1 zln(1 + z) is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract Vub from the semileptonic B → πℓνℓ decays. Finally, the π vector form factor in the TL region is explored using QAs.
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Optimal approximation of harmonic growth clusters by orthogonal polynomials
Teodorescu, Razvan
2008-01-01
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.
Interfacial Bubble Deformations
NASA Astrophysics Data System (ADS)
Seymour, Brian; Shabane, Parvis; Cypull, Olivia; Cheng, Shengfeng; Feitosa, Klebert
Soap bubbles floating at an air-water experience deformations as a result of surface tension and hydrostatic forces. In this experiment, we investigate the nature of such deformations by taking cross-sectional images of bubbles of different volumes. The results show that as their volume increases, bubbles transition from spherical to hemispherical shape. The deformation of the interface also changes with bubble volume with the capillary rise converging to the capillary length as volume increases. The profile of the top and bottom of the bubble and the capillary rise are completely determined by the volume and pressure differences. James Madison University Department of Physics and Astronomy, 4VA Consortium, Research Corporation for Advancement of Science.
Minster, B.; Prescott, W.; Royden, L.
1991-02-01
Our goal is to understand the motions of the plates, the deformation along their boundaries and within their interiors, and the processes that control these tectonic phenomena. In the broadest terms, we must strive to understand the relationships of regional and local deformation to flow in the upper mantle and the rheological, thermal and density structure of the lithosphere. The essential data sets which we require to reach our goal consist of maps of current strain rates at the earth's surface and the distribution of integrated deformation through time as recorded in the geologic record. Our success will depend on the effective synthesis of crustal kinematics with a variety of other geological and geophysical data, within a quantitative theoretical framework describing processes in the earth's interior. Only in this way can we relate the snapshot of current motions and earth structure provided by geodetic and geophysical data with long-term processes operating on the time scales relevant to most geological processes. The wide-spread use of space-based techniques, coupled with traditional geological and geophysical data, promises a revolution in our understanding of the kinematics and dynamics of plate motions over a broad range of spatial and temporal scales and in a variety of geologic settings. The space-based techniques that best address problems in plate motion and deformation are precise space-geodetic positioning -- on land and on the seafloor -- and satellite acquisition of detailed altimetric and remote sensing data in oceanic and continental areas. The overall science objectives for the NASA Solid Earth Science plan for the 1990's, are to Understand the motion and deformation of the lithosphere within and across plate boundaries'', and to understand the dynamics of the mantle, the structure and evolution of the lithosphere, and the landforms that result from local and regional deformation. 57 refs., 7 figs., 2 tabs.
Abductor pollicis longus tendon division with swan neck thumb deformity.
Zacharia, Balaji; Puthezhath, Kishore
2012-08-01
Swan neck thumb deformity can be caused by osteoarthritis, rheumatoid arthritis, systemic lupus erythematosus, tendon transfers and paralytic diseases. Abductor pollicis longus is one of the major stabilizing tendon of the carpometacarpal joint of thumb. To the best of our knowledge, swan neck thumb deformity owing to division of abductor pollicis longus tendon is rare. In this article, we describe a case of isolated division of abductor pollicis longus tendon presenting with swan-neck deformity of thumb and discuss the mechanism, management and outcome. The patient was treated by repair of the divided tendon using palmaris longus tendon graft. At approximately 107 weeks following treatment, the patient was having full range of thumb movement and the deformity completely disappeared. We also describe the unusual mechanism whereby an isolated division of abductor pollicis longus tendon results in swan neck thumb deformity. Level of clinical evidence IV.
Deformation and failure mechanisms in metal matrix composites
NASA Technical Reports Server (NTRS)
Newaz, G.; Majumdar, B. S.
1991-01-01
An investigation was undertaken to determine the key deformation mechanisms and their interaction leading to failure of both 0 degree and 90 degree Ti 15-3/SCS-6 laminae under monotonic loading. The experimental results suggest that inelastic deformation in the 0-degree lamina is dominated by plastic deformation and that in the 90-degree lamina is dominated by both fiber-matrix debonding and plasticity. The loading-unloading response, monitoring of Poisson's ratio and microscopy were utilized to identify the key deformation mechanisms. The sequence of deformation mechanisms leading to failure are identified for both the 0 and the 90-degree specimens. The threshold strains for plasticity or damage which are referred to as 'microdeformation' in the 0 deg and 90 deg laminae are approximately 0.004 and 0.002, respectively, at room temperature. These strain levels may be considered critical in initiation based structural design with these composites.
Approximating subtree distances between phylogenies.
Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina
2006-10-01
We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results.
Nanolaminate deformable mirrors
Papavasiliou, Alexandros P.; Olivier, Scot S.
2009-04-14
A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.
Nanolaminate deformable mirrors
Papavasiliou, Alexandros P.; Olivier, Scot S.
2010-04-06
A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.
Micromachined, Electrostatically Deformable Reflectors
NASA Technical Reports Server (NTRS)
Bartman, Randall K.; Wang, Paul K. C.; Miller, Linda M.; Kenny, Thomas W.; Kaiser, William J.; Hadaegh, Fred Y.; Agronin, Michael L.
1995-01-01
Micromachined, closed-loop, electrostatically actuated reflectors (microCLEARs) provide relatively simple and inexpensive alternatives to large, complex, expensive adaptive optics used to control wavefronts of beams of light in astronomy and in experimental laser weapons. Micromachining used to make deformable mirror, supporting structure, and actuation circuitry. Development of microCLEARs may not only overcome some of disadvantages and limitations of older adaptive optics but may also satisfy demands of potential market for small, inexpensive deformable mirrors in electronically controlled film cameras, video cameras, and other commercial optoelectronic instruments.
Many-body correlations of QRPA in nuclear matrix elements of double-beta decay
Terasaki, J.
2015-10-28
We present two new ideas on the quasiparticle random-phase approximation (QRPA) approach for calculating nuclear matrix elements of double-beta decay. First, it is necessary to calculate overlaps of the QRPA states obtained on the basis of the ground states of different nuclei. We calculate this overlap using quasiboson vacua as the QRPA ground states. Second, we show that two-particle transfer paths are possible to use for the calculation under the closure approximation. A calculation is shown for {sup 150}Nd→{sup 150}Sm using these two new ideas, and their implication is discussed.
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Explosive loading of deformable gas-permeable axisymmetric structural elements
NASA Astrophysics Data System (ADS)
Glazova, E. G.; Konstantinov, A. Yu.; Kochetkov, A. V.; Krylov, S. V.
2016-09-01
A mathematical model is proposed which describes the interrelated processes of unsteady elastoplastic deformation of stacks of woven metal wire mesh and wave processes in pore gas in a two-dimensional axisymmetric approximation. The nonlinear equations of the dynamics of two interpenetrating continua are solved numerically using a modified Godunov's scheme. The problem of explosive loading of a multilayer shell with an internal permeable deformable layer is solved. The results of numerical solutions are compared with experimental data. The influence of the gas-permeable layer on shell deformation is determined.
Dense deformation field estimation for brain intraoperative images registration
NASA Astrophysics Data System (ADS)
De Craene, Mathieu S.; du Bois d'Aische, Aloys; Talos, Ion-Florin; Ferrant, Matthieu; Black, Peter M.; Jolesz, Ferenc; Kikinis, Ron; Macq, Benoit; Warfield, Simon K.
2004-05-01
A new fast non rigid registration algorithm is presented. The algorithm estimates a dense deformation field by optimizing a criterion that measures image similarity by mutual information and regularizes with a linear elastic energy term. The optimal deformation field is found using a Simultaneous Perturbation Stochastic Approximation to the gradient. The implementation is parallelized for symmetric multi-processor architectures. This algorithm was applied to capture non-rigid brain deformations that occur during neurosurgery. Segmentation of the intra-operative data is not required but preoperative segmentation of the brain allows the algorithm to be robust to artifacts due to the craniotomy.
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
Shear deformation in thick auxetic plates
NASA Astrophysics Data System (ADS)
Lim, Teik-Cheng
2013-08-01
This paper aims to understand the effect of auxeticity on shear deformation in thick plates. Three models for the shear correction factor of plates as a function of Poisson’s ratio were proposed: an analytical model, a cubic fit model and a modified model. Of these three, the cubic fit model exhibits the best accuracy over the entire range of Poisson’s ratio from -1 to 0.5. The extent of shear deformation is herein investigated using the example of uniformly loaded circular plates. It was found that the maximum deformation of such plates based on Mindlin theory approximates to those according to Kirchhoff theory when the Poisson’s ratio of the plate material is highly negative. When the Poisson’s ratio of the plate material is -1 and the edge of the plate is simply supported, the calculation of the maximum deflection by Mindlin theory simplifies into that by Kirchhoff theory. These results suggest that auxeticity reduces shear deformation in thick plates, permitting the use of classical plate theory for thick plates only if the plate material is highly auxetic.
Deformation and seismicity of Taiwan.
Vita-Finzi, C
2000-10-10
14C-dated Holocene coastal uplift, conventional and satellite geodetic measurements, and coseismic and aseismic fault slip reveal the pattern of distributed deformation at Taiwan resulting from convergence between the Philippine Sea plate and Eurasia; as in other subduction orogenic settings, the locus of strain release and accumulation is strongly influenced by changes in fault geometry across strike. Uplift evidence from the islands of Lutao and Lanhsu is consistent with progressive oblique collision between the Luzon arc and the Chinese continental margin. In the Coastal Range, geodetic and seismic records show that shortening is taken up serially by discontinuous slip on imbricate faults. The geodetic data point to net extension across the Central Range, but deformed Holocene shorelines in the Hengchun Peninsula at its southern extremity suggest that the extension is a superficial effect partly caused by blind reverse faulting. The fastest shortening rates indicated by geodesy are recorded on the Longitudinal Valley fault and across the Chukou fault within the fold-and-thrust belt. In the former, the strain is dissipated mainly as aseismic reverse and strike-slip displacement. In contrast, the fold-and-thrust belt has witnessed five earthquakes with magnitudes of 6.5 or above in the 20th century, including the 1999.9.21 Chi-Chi earthquake (magnitude approximately 7.6) on a branch of the Chukou fault. The neotectonic and geodetic data for Taiwan as a whole suggest that the fold-and-thrust belt will continue to host the majority of great earthquakes on the island.
Rational approximations for tomographic reconstructions
NASA Astrophysics Data System (ADS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-06-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image.
Gadgets, approximation, and linear programming
Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P.
1996-12-31
We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
Adaptive approximation models in optimization
Voronin, A.N.
1995-05-01
The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions.
Approximating spatially exclusive invasion processes
NASA Astrophysics Data System (ADS)
Ross, Joshua V.; Binder, Benjamin J.
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
Heat pipe transient response approximation.
Reid, R. S.
2001-01-01
A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.
Second Approximation to Conical Flows
1950-12-01
Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . $O’/ + (8) Introducing Eqs
Metabolic dependence of red cell deformability
Weed, Robert I.; LaCelle, Paul L.; Merrill, Edward W.
1969-01-01
The contribution of the metabolic state of human erythrocytes to maintenance of cellular deformability was studied during and after in vitro incubation in serum for periods up to 28 hr. An initial loss of membrane deformability became apparent between 4 and 6 hr when cellular adenosine triphosphate (ATP) levels were approximately 70% of initial values. Membrane deformability then remained stable between 6 and 10 hr. After 10 hr, when cellular ATP had decreased to < 15% of initial values, progressive parallel changes occurred in red cell calcium which increased 400% by 24 hr and in the viscosity of red cell suspensions which had risen 500-750% at 24 hr. A further progressive decrease in membrane deformability also occurred and was reflected by a 1000% increase in negative pressure required to deform the membrane. Red cell filterability decreased to zero as the disc-sphere shape transformation ensued. These changes were accompanied by an increase in ghost residual hemoglobin and nonhemoglobin protein. Regeneration of ATP in depleted cells by incubation with adenosine produced significant reversal of these changes, even in the presence of ouabain. Introduction of calcium into reconstituted ghosts prepared from fresh red cells mimicked the depleted state, and introduction of ATP, ethylenediamine tetraacetate (EDTA), and magnesium into depleted cells mimicked the adenosine effects in intact depleted cells. ATP added externally to 24-hr depleted cells was without effect. Simultaneous introduction of EDTA, ATP, or magnesium along with calcium into reconstituted ghosts prevented the marked decrease in deformability produced by calcium alone. Incorporation of adenosine diphosphate (ADP), nicotinamide adenine dinucleotide (NAD), NAD phosphate (NADP), NADP, reduced form (NADPH), glutatione, reduced form (GSH), inosine triphosphate (ITP), guanosine triphosphate (GTP), and uridine triphosphate (UTP) was without effect. These data suggest that a major role of ATP in maintenance
Nanoscale deformation mechanisms in bone.
Gupta, Himadri S; Wagermaier, Wolfgang; Zickler, Gerald A; Raz-Ben Aroush, D; Funari, Sérgio S; Roschger, Paul; Wagner, H Daniel; Fratzl, Peter
2005-10-01
Deformation mechanisms in bone matrix at the nanoscale control its exceptional mechanical properties, but the detailed nature of these processes is as yet unknown. In situ tensile testing with synchrotron X-ray scattering allowed us to study directly and quantitatively the deformation mechanisms at the nanometer level. We find that bone deformation is not homogeneous but distributed between a tensile deformation of the fibrils and a shearing in the interfibrillar matrix between them.
Probing deformed quantum commutators
NASA Astrophysics Data System (ADS)
Rossi, Matteo A. C.; Giani, Tommaso; Paris, Matteo G. A.
2016-07-01
Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.
[Babies with cranial deformity].
Feijen, Michelle M W; Claessens, Edith A W M Habets; Dovens, Anke J Leenders; Vles, Johannes S; van der Hulst, Rene R W J
2009-01-01
Plagiocephaly was diagnosed in a baby aged 4 months and brachycephaly in a baby aged 5 months. Positional or deformational plagio- or brachycephaly is characterized by changes in shape and symmetry of the cranial vault. Treatment options are conservative and may include physiotherapy and helmet therapy. During the last two decades the incidence of positional plagiocephaly has increased in the Netherlands. This increase is due to the recommendation that babies be laid on their backs in order to reduce the risk of sudden infant death syndrome. We suggest the following: in cases of positional preference of the infant, referral to a physiotherapist is indicated. In cases of unacceptable deformity of the cranium at the age 5 months, moulding helmet therapy is a possible treatment option.
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Crustal deformation in Great California Earthquake cycles
NASA Technical Reports Server (NTRS)
Li, Victor C.; Rice, James R.
1987-01-01
A model in which coupling is described approximately through a generalized Elsasser model is proposed for computation of the periodic crustal deformation associated with repeated strike-slip earthquakes. The model is found to provide a more realistic physical description of tectonic loading than do simpler kinematic models. Parameters are chosen to model the 1857 and 1906 San Andreas ruptures, and predictions are found to be consistent with data on variations of contemporary surface strain and displacement rates as a function of distance from the 1857 and 1906 rupture traces. Results indicate that the asthenosphere appropriate to describe crustal deformation on the earthquake cycle time scale lies in the lower crust and perhaps the crust-mantle transition zone.
Osteotomies for bunionette deformity.
Weil, Lowell; Weil, Lowell Scott
2011-12-01
A variety of surgical osteotomy procedures have been described for the bunionette deformity.Metatarsal osteotomies narrow the forefoot, maintain the length of the metatarsal, and preserve function of the metatarsophalangeal joint. Distal metatarsal osteotomies produce less correction and reduce postoperative disability; however, they pose a risk of inadequate correction because of the small width of the fifth metatarsal head and transfer lesions if shortened or dorsiflexed excessively. The sliding oblique metaphyseal osteotomy described by Smith and Weil (without fixation) and later by Steinke (with fixation) is easy to perform and provides good cancellous bone contact. Fixation is sometimes difficult and bone healing can take a few months owing to the unstable construct of this osteotomy. Kitaoka described a distal chevron osteotomy, which provides lateral pressure relief and reduced plantar pressure. This osteotomy is currently the most common procedure used; however, it may prove difficult to perform if the deformity is large and the bone is narrow. Diaphyseal osteotomies are indicated when greater correction is needed; however, they require more dissection and there is greater postoperative convalescence with non–weight bearing for several weeks. Proximal base osteotomies may be used to address significantly increased 4–5 IMAs or when a large degree of sagittal plane correction is required. Approaches that have been described include opening and closing base wedges and basal chevrons. Advantages to this approach are the ability to avoid epiphyseal plates in pediatric patients and maintain function of the MTPJ, while disadvantages include inherent instability of the location of the osteotomy, embarrassment of intraosseous and extraosseus blood supply of the metatarsal, and technical demand. Non–weight bearing is essential for several weeks. The Scarfette procedure is a combination head–shaft procedure, which is indicated to treat mild to moderate
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Advanced Curvature Deformable Mirrors
2010-09-01
designs using just a glass wafer and a wafer of Carbon Fiber Reinforced Polymer ( CFRP ). In both cases minimum bend radius decreases and the resonant... matrix is consequently nearly diagonal. The long actuators at the outer edge of the deformable mirror are largely outside the working pupil so their...formal reconstruction of the wave front either explicitly or implicitly in the control matrix . The WFS-DM combination is acting like an analog computer
Deformation of Wrinkled Graphene
2015-01-01
The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the exfoliated material. This unusual deformation behavior has been modeled in terms of mechanically isolated graphene islands separated by the graphene wrinkles, with the strain distribution in each graphene island determined using shear lag analysis. The effect of the size and position of the Raman laser beam spot has also been incorporated in the model. The predictions fit well with the behavior observed experimentally for the Raman band shifts and broadening of the wrinkled CVD graphene. The effect of wrinkles upon the efficiency of graphene to reinforce nanocomposites is also discussed. PMID:25765609
Deformable micro torque swimmer
NASA Astrophysics Data System (ADS)
Ishikawa, Takuji; Tanaka, Tomoyuki; Omori, Toshihiro; Imai, Yohsuke
2015-11-01
We investigated the deformation of a ciliate swimming freely in a fluid otherwise at rest. The cell body was modeled as a capsule with a hyper elastic membrane enclosing Newtonian fluid. Thrust forces due to the ciliary beat were modeled as torques distributed above the cell body. Effects of the membrane elasticity, the aspect ratio of cell's reference shape and the density difference between the cell and the surrounding fluid were investigated. The results showed that the cell deformed like heart shape when Capillary number (Ca) was sufficiently large, and the swimming velocity decreased as Ca was increased. The gravity effect on the membrane tension suggested that the upwards and downwards swimming velocities of Paramecium might be reglated by the calcium ion channels distributed locally around the anterior end. Moreover, the gravity induced deformation made a cell directed vertically downwards, which resulted in a positive geotaxis like behavior with physical origin. These results are important to understand physiology of ciliate's biological responses to mechanical stimuli.
[Neurogenic foot deformities].
Senst, S
2010-01-01
There is a multitude of neurological diseases which may lead to neuro-orthopaedic problems and subsequently to neurogenic foot deformities. For this reason the diagnostician will be consistently surprised that there is a great multitude of different foot abnormalities and that not only the typical spastic talipes equines dominates. Of particular significance here is that these deformities almost always develop progressively, whereas most diseases persist per se, cerebral palsy being a typical case in point. However, in MMC (myelomeningocele) patients, there is also the danger of a worsening of the basic problem in the case of tethered cord syndrome. Unlike congenital talipes equinovarus, neuro-orthopaedic talipes equinovarus often shows over- or undercorrection postoperatively due to a shift in muscle imbalance. It is important, therefore, that the basis of conservative therapy include regular physiotherapy and orthoses during the day and, if necessary, at night. Botulinum toxin has been established as an additional measure for spasticity; however, this cannot always prevent surgical intervention, but is able to delay this to a better point in the development of the child/patient. The present article describes the diversity of neurological deformities and presents conservative as well as surgical therapeutic approaches.
Civitarese, Osvaldo; Suhonen, Jouni
2013-12-30
In this work we report on general properties of the nuclear matrix elements involved in the neutrinoless double β{sup −} decays (0νβ{sup −}β{sup −} decays) of several nuclei. A summary of the values of the NMEs calculated along the years by the Jyväskylä-La Plata collaboration is presented. These NMEs, calculated in the framework of the quasiparticle random phase approximation (QRPA), are compared with those of the other available calculations, like the Shell Model (ISM) and the interacting boson model (IBA-2)
Calculation of delayed-neutron energy spectra in a QRPA-Hauser-Feshbach model
Kawano, Toshihiko; Moller, Peter; Wilson, William B
2008-01-01
Theoretical {beta}-delayed-neutron spectra are calculated based on the Quasiparticle Random-Phase Approximation (QRPA) and the Hauser-Feshbach statistical model. Neutron emissions from an excited daughter nucleus after {beta} decay to the granddaughter residual are more accurately calculated than in previous evaluations, including all the microscopic nuclear structure information, such as a Gamow-Teller strength distribution and discrete states in the granddaughter. The calculated delayed-neutron spectra agree reasonably well with those evaluations in the ENDF decay library, which are based on experimental data. The model was adopted to generate the delayed-neutron spectra for all 271 precursors.
On the neutrinoless double β{sup +}/EC decays
Suhonen, Jouni
2013-12-30
The neutrinoless double positron-emission/electron-capture (0νβ{sup +}/EC) decays are studied for the magnitudes of the involved nuclear matrix elements (NMEs). Decays to the ground state, 0{sub gs}{sup +}, and excited 0{sup +} states are discussed. The participant many-body wave functions are evaluated in the framework of the quasiparticle random-phase approximation (QRPA). Effective, G-matrix-derived nuclear forces are used in realistic single-particle model spaces. The channels β{sup +}β{sup +}, β{sup +}EC, and the resonant neutrinoless double electron capture (R0νECEC) are discussed.
NASA Astrophysics Data System (ADS)
Birch, M.; Singh, B.; Abriola, D.; Dillmann, I.; Johnson, T. D.; McCutchan, E. A.; Sonzogni, A. A.
2014-06-01
A comprehensive compilation and evaluation of beta-delayed neutron (β- n) emission probabilities, Pn, and associated half-lives for A ≤ 72 nuclei has been performed for the first time. The recommended values have been used to analyze the systematics of β- n emission in this region. The ratio Pn /T1/2 is better correlated with the Q-value of the β- n decay mode than the previously proposed Kratz-Herrmann Formula (KHF). The recommended values are also compared with theoretical quasi-particle random phase approximation (QRPA) calculations.
Static and dynamic aspect of covariant density functional theory in proton rich nuclei
Ring, P.; Lalazissis, G. A.; Paar, N.; Vretenar, D.
2007-11-30
Proton rich nuclei are investigated in the framework of Covariant Density Functional Theory (CDFT). The Relativistic Hartree Bogoliubov (RHB) model is used to study the proton drip line in the region of heavy and superheavy nuclei. The dynamical behavior of nuclei with a large proton excess is studied within the Relativistic Quasiparticle Random Phase Approximation (RQRPA). Low lying El-strength is observed and it is shown that it corresponds to an oscillation of the proton skin against the isospin saturated neutron-proton core. This mode is in full analogy to the neutron pygmy resonances found in many nuclei with neutron excess.
The 2νβ-β- decay rates within Pyatov's restoration method
NASA Astrophysics Data System (ADS)
Ünlü, Serdar; Çakmak, Neçla; Selam, Cevad
2017-01-01
We try to give a detailed analysis of the 2 νβ-β- decay rates to the final ground states for decay emitters: 70Zn, 80Se, 86Kr, 94Zr, 104Ru, 110Pd, 114Cd and 124Sn. The nucleon-nucleon residual interaction potential is defined according to Pyatov's restoration method. The nuclear matrix element for 2 νβ-β- decay is obtained by including the virtual contributions coming from the isobar analogue excitations within the framework of proton-neutron quasi-particle random phase approximation (pnQRPA). The calculated decay rates are compared with mean field, schematic model and other calculations.
Inelastic neutrino scattering off stable even-even Mo isotopes at low and intermediate energies
NASA Astrophysics Data System (ADS)
Balasi, K. G.; Kosmas, T. S.; Divari, P. C.
2010-04-01
Inelastic neutrino scattering cross sections for the even-even Mo isotopes (contents of the MOON detector at Japan), at low and intermediate electron neutrino energies ( ɛi≤100 MeV), are calculated. MOON is a next-generation double beta and neutrino-less double-beta-decay experiment which is also a promising facility for low-energy neutrino detection. The nuclear wave functions required in this work have been constructed in the context of the quasi-particle random phase approximation (QRPA) and the results presented refer to 92Mo, 94Mo, 96Mo, 98Mo and 100Mo isotopes.
Contributions of unique first-forbidden transitions to two-neutrino double-β-decay half-lives
NASA Astrophysics Data System (ADS)
Civitarese, O.; Suhonen, J.
1996-02-01
The two-neutrino double-β-decay transition of 76Ge to the ground state of 76Se is calculated using a realistic proton-neutron force and including unique first-forbidden single-β-decay transitions to virtual 2 - intermediate states. The corresponding nuclear matrix elements are computed by using the proton-neutron quasiparticle random-phase approximation (pn-QRPA). From the results of the present study it is concluded that the inclusion of virtual unique first-forbidden transitions, as possible "new" steps contributing to the half-life of the two-neutrino double-β-decay mode, can be disregarded.
NASA Technical Reports Server (NTRS)
Strauss, Karl F.; Sheldon, Douglas J.
2011-01-01
Several missions and instruments in the conceptual design phase rely on the technique of interferometry to create detectable fringe patterns. The intimate emplacement of reflective material upon electron device cells based upon chalcogenide material technology permits high-speed, predictable deformation of the reflective surface to a subnanometer or finer resolution with a very high degree of accuracy. In this innovation, a layer of reflective material is deposited upon a wafer containing (perhaps in the millions) chalcogenic memory cells with the reflective material becoming the front surface of a mirror and the chalcogenic material becoming a means of selectively deforming the mirror by the application of heat to the chalcogenic material. By doing so, the mirror surface can deform anywhere from nil to nanometers in spots the size of a modern day memory cell, thereby permitting realtime tuning of mirror focus and reflectivity to mitigate aberrations caused elsewhere in the optical system. Modern foundry methods permit the design and manufacture of individual memory cells having an area of or equal to the Feature (F) size of the design (assume 65 nm). Fabrication rules and restraints generally require the instantiation of one memory cell to another no closer than 1.5 F, or, for this innovation, 90 nm from its neighbor in any direction. Chalcogenide is a semiconducting glass compound consisting of a combination of chalcogen ions, the ratios of which vary according to properties desired. It has been shown that the application of heat to cells of chalcogenic material cause a large alteration in resistance to the range of 4 orders of magnitude. It is this effect upon which chalcogenidebased commercial memories rely. Upon removal of the heat source, the chalcogenide rapidly cools and remains frozen in the excited state. It has also been shown that the chalcogenide expands in volume because of the applied heat, meaning that the coefficient of expansion of chalcogenic
Gamow-Teller strength and lepton captures rates on 66‑71Ni in stellar matter
NASA Astrophysics Data System (ADS)
Nabi, Jameel-Un; Majid, Muhammad
Charge-changing transitions play a significant role in stellar weak-decay processes. The fate of the massive stars is decided by these weak-decay rates including lepton (positron and electron) captures rates, which play a consequential role in the dynamics of core collapse. As per previous simulation results, weak interaction rates on nickel (Ni) isotopes have significant influence on the stellar core vis-à-vis controlling the lepton content of stellar matter throughout the silicon shell burning phases of high mass stars up to the presupernova stages. In this paper, we perform a microscopic calculation of Gamow-Teller (GT) charge-changing transitions, in the β-decay and electron capture (EC) directions, for neutron-rich Ni isotopes (66‑71Ni). We further compute the associated weak-decay rates for these selected Ni isotopes in stellar environment. The computations are accomplished by employing the deformed proton-neutron quasiparticle random phase approximation (pn-QRPA) model. A recent study showed that the deformed pn-QRPA theory is well suited for the estimation of GT transitions. The astral weak-decay rates are determined over densities in the range of 10-1011g/cm3 and temperatures in the range of 0.01 × 109-30 × 109K. The calculated lepton capture rates are compared with the previous calculation of Pruet and Fuller (PF). The overall comparison demonstrates that, at low stellar densities and high temperatures, our EC rates are bigger by as much as two orders of magnitude. Our results show that, at higher temperatures, the lepton capture rates are the dominant mode for the stellar weak rates and the corresponding lepton emission rates may be neglected.
Testing the frozen flow approximation
NASA Technical Reports Server (NTRS)
Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro
1993-01-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.
Ab initio dynamical vertex approximation
NASA Astrophysics Data System (ADS)
Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten
2017-03-01
Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.
Potential of the approximation method
Amano, K.; Maruoka, A.
1996-12-31
Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.
Nonlinear Filtering and Approximation Techniques
1991-09-01
Shwartz), Academic Press (1991). [191 M.Cl. ROUTBAUD, Fiting lindairc par morceaux avec petit bruit d’obserration, These. Universit6 de Provence ( 1990...Kernel System (GKS), Academic Press (1983). 181 H.J. KUSHNER, Probability methods for approximations in stochastic control and for elliptic equations... Academic Press (1977). [9] F. LE GLAND, Time discretization of nonlinear filtering equations, in: 28th. IEEE CDC, Tampa, pp. 2601-2606. IEEE Press (1989
Reliable Function Approximation and Estimation
2016-08-16
Journal on Mathematical Analysis 47 (6), 2015. 4606-4629. (P3) The Sample Complexity of Weighted Sparse Approximation. B. Bah and R. Ward. IEEE...solving systems of quadratic equations. S. Sanghavi, C. White, and R. Ward. Results in Mathematics , 2016. (O5) Relax, no need to round: Integrality of...Theoretical Computer Science. (O6) A unified framework for linear dimensionality reduction in L1. F Krahmer and R Ward. Results in Mathematics , 2014. 1-23
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
NASA Technical Reports Server (NTRS)
Stenholm, Stig
1993-01-01
A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.
NASA Astrophysics Data System (ADS)
Milton, Graeme Walter
2013-07-01
A complete characterization is given of the possible macroscopic deformations of periodic non-linear affine unimode metamaterials constructed from rigid bars and pivots. The materials are affine in the sense that their macroscopic deformations can only be affine deformations: on a local level the deformation may vary from cell to cell. Unimode means that macroscopically the material can only deform along a one dimensional trajectory in the six dimensional space of invariants describing the deformation (excluding translations and rotations). We show by explicit construction that any continuous trajectory is realizable to an arbitrarily high degree of approximation provided at all points along the trajectory the geometry does not collapse to a lower dimensional one. In particular, we present two and three dimensional dilational materials having an arbitrarily large flexibility window. These are perfect auxetic materials for which a dilation is the only easy mode of deformation. They are free to dilate to arbitrarily large strain with zero bulk modulus.
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-15
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Improved non-approximability results
Bellare, M.; Sudan, M.
1994-12-31
We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones.
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-10-01
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
Approximate transferability in conjugated polyalkenes
NASA Astrophysics Data System (ADS)
Eskandari, Keiamars; Mandado, Marcos; Mosquera, Ricardo A.
2007-03-01
QTAIM computed atomic and bond properties, as well as delocalization indices (obtained from electron densities computed at HF, MP2 and B3LYP levels) of several linear and branched conjugated polyalkenes and O- and N-containing conjugated polyenes have been employed to assess approximate transferable CH groups. The values of these properties indicate the effects of the functional group extend to four CH groups, whereas those of the terminal carbon affect up to three carbons. Ternary carbons also modify significantly the properties of atoms in α, β and γ.
The Zeldovich & Adhesion approximations and applications to the local universe
NASA Astrophysics Data System (ADS)
Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei
2016-10-01
The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.
Adiabatic approximation via hodograph translation and zero-curvature equations
NASA Astrophysics Data System (ADS)
Karasev, M. V.
2014-04-01
For quantum as well classical slow-fast systems, we develop a general method which allows one to compute the adiabatic invariant (approximate integral of motion), its symmetries, the adiabatic guiding center coordinates and the effective scalar Hamiltonian in all orders of a small parameter. The scheme does not exploit eigenvectors or diagonalization, but is based on the ideas of isospectral deformation and zero-curvature equations, where the role of "time" is played by the adiabatic (quantization) parameter. The algorithm includes the construction of the zero-curvature adiabatic connection and its splitting generated by averaging up to an arbitrary order in the small parameter.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Laguerre approximation of random foams
NASA Astrophysics Data System (ADS)
Liebscher, André
2015-09-01
Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam's cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.
Geodynamics of Cenozoic deformation in central Asia
NASA Technical Reports Server (NTRS)
Liu, H.-S.
1981-01-01
This paper presents a study of the tectonic stresses in central Asia based on an interpretation of satellite gravity data for mantle convection and supplemented with published fault plane solutions of earthquakes. Northwest-southeast to north-south compressional stresses exist in the Tien Shan region where reverse faulting dominates. The maximum compressive stress is oriented approximately northeast-southwest in the regions of Altai and southern Mongolia. Farther north, compressive stress gives way to tensional stress which causes normal faulting in the Baikal rift system. It is also shown that all of the tectonic stresses in the Tibetan plateau and Himalayan frontal thrust are related to the convection-generated stress patterns inferred from satellite gravity data. These results suggest that the complex crustal deformation in central Asia can be convincingly described by the deformation of the lithosphere on top of the up- and down-welling asthenospheric material beneath it. This observational fact may not only upset the simple view of the fluid crustal model of the Tibetan plateau, but also provide some useful constraints for the future development of deformation theory of continental crust.
Deformation behaviour of a large underground cavern
NASA Astrophysics Data System (ADS)
Mizukoshi, Tatsuo; Mimaki, Youichi
1985-10-01
The Imaichi underground power station, with a cross sectional area of 1420 m2, which is now under construction by Tokyo Electric Power Co., Inc., is one of the largest underground caverns in the world. Due to the considerable depth of the over-burden of 400 m, the horseshoe-shaped section was adopted for the first time in Japan to minimize excesive stress concentration on the surrounding bedrock and keep loosened zones to a minimum. The bedrock consists of sandstone, slate, siliceous sandstone and breccia. The rock is generally hard and compact, with few fractured zones which may have an adverse influence on the excavation of the cavern. The supporting system of the cavern consists of prestressed rock anchors, rock bolts and shotcrete. Approximately 800 instruments, mainly multiple stage extensometers, were used to monitor behaviour of the surrounding rock during excavation of the cavern. With the exception of some cracks which occurred in a portion of the shotcrete when about half the height of the cavern had been excavated, excavation work was completed without any major trouble. In spite of the symmetrical shape of the cavern, the deformation behaviour of the surrounding rock during excavation was remarkedly asymmetric. The reason for this was concluded to be the peculiar deformation behaviour exhibited by Breccia during stress relief, as shown by in-situ rock tests, etc., and analysis of deformation data after completion of the excavation work.
Algorithmic deformation of matrix factorisations
NASA Astrophysics Data System (ADS)
Carqueville, Nils; Dowdy, Laura; Recknagel, Andreas
2012-04-01
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these algorithms and apply them to several examples. Apart from explicit results in concrete cases, this leads to a novel way to generate new matrix factorisations via nilpotent substitutions, and to criteria whether boundary obstructions can be lifted by bulk deformations.
Global feedforward and glocal feedback control of large deformable mirrors
NASA Astrophysics Data System (ADS)
Ruppel, Thomas; Sawodny, Oliver
2011-09-01
With an increasing demand for high spatial resolution and fast temporal response of AO components for ELTs, the need for actively controlled, electronically damped deformable mirrors is evident. With typically more than 1000 actuators and collocated sensors, the evolving multi-input multi-output control task for shaping the deformable mirror requires sophisticated control concepts. Although global position control of the mirror would be the most promising solution, the computational complexity for high order spatial control of the deformable element typically exceeds available computing power. Due to this reason, existing deformable membrane mirrors for large telescopes incorporate local feedback instead of global feedback control and neglect some of the global dynamics of the deformable mirror. As a side effect, coupling of the separately controlled actuators through the deformable membrane can lead to instability of the individually stable loops and draws the need for carefully designing the control parameters of the local feedback loops. In this presentation, the computational demands for global position control of deformable mirrors are revisited and a less demanding model-based modal control concept for large deformable membrane mirrors with distributed force actuators and collocated position sensors is presented. Both global feedforward and glocal feedback control is employed in a two-degree-of-freedom control structure allowing for separately designing tracking performance and disturbance rejection. In order to implement state feedback control, non-measureable state information is reconstructed by using model-based distributed state observers. By taking into account the circular symmetry of the deformable mirror geometry, the computational complexity of the algorithms is discussed and model reduction techniques with quasi-static state approximation are presented. As an example, the geometric layout of required sensor / actuator wiring and computational
Analytical approximations for spiral waves
Löber, Jakob Engel, Harald
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase.
Analytical approximations for spiral waves.
Löber, Jakob; Engel, Harald
2013-12-01
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects.
Dynamic soft tissue deformation estimation based on energy analysis
NASA Astrophysics Data System (ADS)
Gao, Dedong; Lei, Yong; Yao, Bin
2016-10-01
The needle placement accuracy of millimeters is required in many needle-based surgeries. The tissue deformation, especially that occurring on the surface of organ tissue, affects the needle-targeting accuracy of both manual and robotic needle insertions. It is necessary to understand the mechanism of tissue deformation during needle insertion into soft tissue. In this paper, soft tissue surface deformation is investigated on the basis of continuum mechanics, where a geometry model is presented to quantitatively approximate the volume of tissue deformation. The energy-based method is presented to the dynamic process of needle insertion into soft tissue based on continuum mechanics, and the volume of the cone is exploited to quantitatively approximate the deformation on the surface of soft tissue. The external work is converted into potential, kinetic, dissipated, and strain energies during the dynamic rigid needle-tissue interactive process. The needle insertion experimental setup, consisting of a linear actuator, force sensor, needle, tissue container, and a light, is constructed while an image-based method for measuring the depth and radius of the soft tissue surface deformations is introduced to obtain the experimental data. The relationship between the changed volume of tissue deformation and the insertion parameters is created based on the law of conservation of energy, with the volume of tissue deformation having been obtained using image-based measurements. The experiments are performed on phantom specimens, and an energy-based analytical fitted model is presented to estimate the volume of tissue deformation. The experimental results show that the energy-based analytical fitted model can predict the volume of soft tissue deformation, and the root mean squared errors of the fitting model and experimental data are 0.61 and 0.25 at the velocities 2.50 mm/s and 5.00 mm/s. The estimating parameters of the soft tissue surface deformations are proven to be useful
Approximate analytic solutions to the NPDD: Short exposure approximations
NASA Astrophysics Data System (ADS)
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Approximate Stress Analysis of Multistringer Beams with Shear Deformation of the Flanges
NASA Technical Reports Server (NTRS)
Kuhn, Paul
1938-01-01
The problem of the skin-stringer combinations used as axially loaded panels or as covers for box beams is considered from the point of view of the practical stress analyst. By a simple substitution the problem is reduced to the problem of the single-stringer structure, which has been treated in NACA Report no. 608. The method of making this substitution is essentially empirical; in order to justify it, comparisons are shown between calculations and strain-gage tests of three beams tested by the author and of one compression panel and three beams tested and reported elsewhere.
NASA Astrophysics Data System (ADS)
Price, C. E.; Shepard, J. R.
1991-04-01
We compute properties of the nucleon in a hybrid chiral model based on the linear σ-model with quark degrees of freedom treated explicity. In contrast to previous calculations, we do not use the hedgehog ansatz. Instead we solve self-consistently for a state with well defined spin and isospin projections. We allow this state to be deformed and find that, although d- and g-state admixtures in the predominantly s-state single quark wave functions are not large, they have profound effects on many nucleon properties including magnetic moments and gA. Our best fit parameters provide excellent agreement with experiment but are much different from those determined in hedgehog calculations.
[Rheumatic forefoot deformities].
Fuhrmann, R
2014-11-01
The frequency and extent of rheumatic forefoot deformities have been greatly reduced since the introduction of disease-modifying antirheumatic drugs (DMARD). The accompanying reduction in arthritic destruction of joints opens up new treatment options whereby priority is given to joint preservation. This is true for the first middle foot ray as well as for the small toe rays. Whereas resection arthroplasty of the metatarsophalangeal joints II-V was previously considered the gold standard treatment, joint-preserving operative procedures (e.g. metatarsal osteotomy and periarticular soft tissue interventions) are now being increasingly more propagated. Resection arthroplasty of the first midfoot ray has major biomechanical disadvantages so that it is not surprising that reconstructive procedures are given priority. In patients with severe arthritic destruction of the first metatarsophalangeal joint, arthrodesis has substantial biomechanical advantages compared to resection arthroplasty. Nevertheless, it has not yet been confirmed that fusion leads to superior clinical results.
NASA Astrophysics Data System (ADS)
Limat, Laurent; de Pascalis, Riccardo; Dervaux, Julien; Ionescu, Ioan; Perthame, Benoit
2016-11-01
Wetting on soft compounds is still imperfectly understood, especially when the dry and wetted parts of the substrate have two different values of surface energies (contact angle different than 90 degrees). The problem is made very complex by geometrical non-linearities arising from finite slope of the substrate and finite deformations, that must be absolutely considered, to distinguish at second order between Young law and Neuman equilibrium of surface tensions. We have developed a numerical, finite element, code that allows one to minimize surface and bulk energies, with finite deformations and asymmetry of the surface energies. The results are compared to a linear theory based on Green function theory and Fredholm integrals, and with recent experiments using X-ray visualization. The non-linear numerics reproduce very well the observed profiles, while the linear approach gives helpful analytical approximates.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Femtolensing: Beyond the semiclassical approximation
NASA Technical Reports Server (NTRS)
Ulmer, Andrew; Goodman, Jeremy
1995-01-01
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.
Fine-grid calculations for stellar electron and positron capture rates on Fe isotopes
Nabi, Jameel-Un; Tawfik, Abdel Nasser
2013-03-15
The acquisition of precise and reliable nuclear data is a prerequisite to success for stellar evolution and nucleosynthesis studies. Core-collapse simulators find it challenging to generate an explosion from the collapse of the core of massive stars. It is believed that a better understanding of the microphysics of core-collapse can lead to successful results. The weak interaction processes are able to trigger the collapse and control the lepton-to-baryon ratio (Y{sub e}) of the corematerial. It is suggested that the temporal variation of Y{sub e} within the core of a massive star has a pivotal role to play in the stellar evolution and a fine-tuning of this parameter at various stages of presupernova evolution is the key to generate an explosion. During the presupernova evolution of massive stars, isotopes of iron, mainly {sup 54-56}Fe, are considered to be key players in controlling Y{sub e} ratio via electron capture on these nuclides. Recently an improved microscopic calculation of weak-interaction-mediated rates for iron isotopes was introduced using the proton-neutron quasiparticle random-phase-approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic state-by-state calculation of stellar capture rates which greatly increases the reliability of calculated rates. The results were suggestive of some fine-tuning of the Y{sub e} ratio during various phases of stellar evolution. Here we present for the first time the fine-grid calculation of the electron and positron capture rates on {sup 54-56}Fe. The sensitivity of the pn-QRPA calculated capture rates to the deformation parameter is also studied in this work. Core-collapse simulators may find this calculation suitable for interpolation purposes and for necessary incorporation in the stellar evolution codes.
NASA Astrophysics Data System (ADS)
Nabi, Jameel-Un
2008-09-01
A few white dwarfs, located in binary systems, may acquire sufficiently high mass-accretion rates resulting in the burning of carbon and oxygen under nondegenerate conditions forming an O+Ne+Mg core. These O+Ne+Mg cores are gravitationally less bound than more massive progenitor stars and can release more energy due to the nuclear burning. They are also amongst the probable candidates for low entropy r-process sites. Recent observations of subluminous Type II-P supernovae (e.g. 2005cs, 2003gd, 1999br and 1997D) were able to rekindle the interest in 8-10 Modot which develop O+Ne+Mg cores. Microscopic calculations of capture rates on 24Mg, which may contribute significantly to the collapse of O+Ne+Mg cores, using the shell model and the proton-neutron quasiparticle random-phase approximation (pn-QRPA) theory, were performed earlier and comparisons made. Simulators, however, may require these capture rates on a fine scale. For the first time, a detailed microscopic calculation of the electron and positron capture rates on 24Mg on an extensive temperature-density scale is presented here. This type of scale is more appropriate for interpolation purposes and of greater utility for simulation codes. The calculations are done using the pn-QRPA theory using a separable interaction. The deformation parameter, believed to be a key parameter in QRPA calculations, is adopted from experimental data to increase the reliability of the QRPA results further. The resulting calculated rates are up to a factor of 14 or more enhanced as compared to shell model rates and may lead to some interesting scenarios for core collapse simulators.
Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach
NASA Astrophysics Data System (ADS)
Camassa, R.; Falqui, G.; Ortenzi, G.
2017-02-01
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.
Deformation and paleomagnetism
NASA Astrophysics Data System (ADS)
Borradaile, Graham J.
We may use tectonic structures to confirm the primary age of a paleomagnetic remanence component but only if we know how to undo the natural strain history. It is normally insufficient to untilt fold limbs, as in the original version of Graham''s Fold Test. One may need to remove also the bulk or local strain and account for strain heterogeneities, achieved by grain-strain and the more elusive intergranular flow. Most important, one must know the sequence of strains and tilts that occurred through geological history because the order of these noncommutative events critically affects the final orientation of the remanence component.In many non-metamorphic rocks, strain-rotation of a remanence component approximates a simple formula, although the actual rotation mechanism is complex. This simple, passive line approximation is confirmed experimentally for strains up to 45% oblate shortening. The passive line hypothesis has permitted successful paleomagnetic restorations in several natural case studies.
[Spectrum research on metamorphic and deformation of tectonically deformed coals].
Li, Xiao-Shi; Ju, Yi-Wen; Hou, Quan-Lin; Lin, Hong
2011-08-01
The structural and compositive evolution of tectonically deformed coals (TDCs) and their influencing factors were investigated and analyzed in detail through Fourier transform infrared spectroscopy (FTIR) and laser Raman spectra analysis. The TDC samples (0.7% < Ro,max <3.1%) were collected from Huaibei coalfield with different deformation mechanisms and intensity. The FTIR of TDCs shows that the metamorphism and the deformation affect the degradation and polycondensation process of macromolecular structure to different degree. The Raman spectra analysis indicates that secondary structure defects can be produced mainly by structural deformation, also the metamorphism influences the secondary structure defects and aromatic structure. Through comprehensive analysis, it was discussed that the ductile deformation could change to strain energy through the increase and accumulation of dislocation in molecular structure units of TDC, and it could make an obvious influence on degradation and polycondensation. While the brittle deformation could change to frictional heat energy and promote the metamorphism and degradation of TDC structure, but has less effect on polycondensation. Furthermore, degradation is the main reason for affecting the structural evolution of coal in lower metamorphic stage, and polycondensation is the most important controlling factor in higher metamorphic stage. Under metamorphism and deformation, the small molecules which break and fall off from the macromolecular tructure of TDC are preferentially replenished and embedded into the secondary structure defects or the residual aromatic rings were formed into aromatic structure by polycondensation. This process improved the stability of coal structure. It is easier for ductile deformation of coal to induce the secondary structure defects than brittle deformation.
Perceptual transparency from image deformation
Kawabe, Takahiro; Maruya, Kazushi; Nishida, Shin’ya
2015-01-01
Human vision has a remarkable ability to perceive two layers at the same retinal locations, a transparent layer in front of a background surface. Critical image cues to perceptual transparency, studied extensively in the past, are changes in luminance or color that could be caused by light absorptions and reflections by the front layer, but such image changes may not be clearly visible when the front layer consists of a pure transparent material such as water. Our daily experiences with transparent materials of this kind suggest that an alternative potential cue of visual transparency is image deformations of a background pattern caused by light refraction. Although previous studies have indicated that these image deformations, at least static ones, play little role in perceptual transparency, here we show that dynamic image deformations of the background pattern, which could be produced by light refraction on a moving liquid’s surface, can produce a vivid impression of a transparent liquid layer without the aid of any other visual cues as to the presence of a transparent layer. Furthermore, a transparent liquid layer perceptually emerges even from a randomly generated dynamic image deformation as long as it is similar to real liquid deformations in its spatiotemporal frequency profile. Our findings indicate that the brain can perceptually infer the presence of “invisible” transparent liquids by analyzing the spatiotemporal structure of dynamic image deformation, for which it uses a relatively simple computation that does not require high-level knowledge about the detailed physics of liquid deformation. PMID:26240313
A simulation study of planar swaging deformation
NASA Astrophysics Data System (ADS)
Zhang, Cheng-Gen; Jen, Gwang-Shen; Su, Gwang-Huei
1992-08-01
Planar swaging deformation was studied with a photoplastic method. The domestic polycarbonate was used as a simulation material. The full-field strain distribution for planar swaging deformation was obtained. The average error of the calculated strain was less than 7 percent. The deformation area and the effect of friction on deformation area were studied with the characteristics of photoplasticity. This paper points out the special features of planar swaging deformation and the effect of lubrication on deformation flow.
Femoral deformity planning: intentional placement of the apex of deformity.
Fabricant, Peter D; Camara, James M; Rozbruch, S Robert
2013-05-01
Traditionally, correction of femoral deformity has been performed with osteotomies through the center of rotation of angulation (CORA), but the CORA location is not always practical. If the osteotomy is created at a site adjacent to the CORA, an additional translation must be performed to accurately correct the deformity. However, at times, the ideal osteotomy site may require an unfeasible amount of translation. Multiple osteotomies may also be problematic, and when overcorrection of the mechanical axis is planned, the CORA method is not practical.This article describes a novel method by which the surgeon may choose the location of the osteotomy regardless of the location of the CORA and may consolidate a multiapical deformity into a single corrective osteotomy. Furthermore, intentional mechanical axis overcorrection may be performed to unload knee joint arthritis. Simple, complex, and multiapical deformities may now be corrected via a single familiar surgical procedure, such as a distal femoral osteotomy, and the need for translation is eliminated.
Global organization of tectonic deformation on Venus
NASA Technical Reports Server (NTRS)
Bilotti, Frank; Connors, Chris; Suppe, John
1993-01-01
The geographic organization of surface deformation on Venus as on Earth is a key to understanding the global tectonic system. To date we have mapped the distribution of three unambiguous tectonic land forms on Venus: (1) linear foldbelts analogous to those at plate margins of the Earth; (2) linear rift zones, analogous to continental rifts on the Earth; and (3) distributed plains deformation in the form of wrinkle ridges and extensional faults and fractures. The linear foldbelts are the dominant structural style in the Northern Hemisphere; ninety percent of the planet's foldbelts lie above the equator. In contrast, compressive deformation in the Southern Hemisphere is dominated by two large, sweeping patterns of wrinkle ridges. The two hemispheres are divided by an equatorial region that is largely covered by rift zones and several large tessera blocks. A tectonic model of generally poleward convergence of the Northern Hemisphere explains the distribution of foldbelts and rift zones. In our model, a northern hemispherical plate (or system of plates) moves poleward and deforms along discrete, predominately longitudinal bands. We recognize four types of foldbelts based on their relationships to other large-scale tectonic features on Venus. There are foldbelts that lie within the low plains, foldbelts associated with coronae, novae and chasmata, foldbelts that lie at the margins of poly-deformed tessera plateaus, and the folded mountain belts around Lakshmi Planum. We see a geometric increase in the area of fold belts when normalized to percent area at a given latitude. This increase is consistent with our model of poleward convergence. Also, the orientations of most foldbelts are either approximately north-south or parallel to lines of latitude in the northern hemisphere. This observation is also consistent with the model in that the longitudinal bands are the result of the decreasing area of the sphere as the plate moves poleward and the latitudinal belts are the
Continuum calculations of continental deformation in transcurrent environments
NASA Technical Reports Server (NTRS)
Sonder, L. J.; England, P. C.; Houseman, G. A.
1986-01-01
A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.
Videogrammetric Model Deformation Measurement Technique
NASA Technical Reports Server (NTRS)
Burner, A. W.; Liu, Tian-Shu
2001-01-01
The theory, methods, and applications of the videogrammetric model deformation (VMD) measurement technique used at NASA for wind tunnel testing are presented. The VMD technique, based on non-topographic photogrammetry, can determine static and dynamic aeroelastic deformation and attitude of a wind-tunnel model. Hardware of the system includes a video-rate CCD camera, a computer with an image acquisition frame grabber board, illumination lights, and retroreflective or painted targets on a wind tunnel model. Custom software includes routines for image acquisition, target-tracking/identification, target centroid calculation, camera calibration, and deformation calculations. Applications of the VMD technique at five large NASA wind tunnels are discussed.
Control of micromachined deformable mirrors
NASA Technical Reports Server (NTRS)
Agronin, M. L.; Bartman, R.; Hadaegh, F. Y.; Kaiser, W.; Wang, P. K. C.
1993-01-01
A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.
Variable focal length deformable mirror
Headley, Daniel; Ramsey, Marc; Schwarz, Jens
2007-06-12
A variable focal length deformable mirror has an inner ring and an outer ring that simply support and push axially on opposite sides of a mirror plate. The resulting variable clamping force deforms the mirror plate to provide a parabolic mirror shape. The rings are parallel planar sections of a single paraboloid and can provide an on-axis focus, if the rings are circular, or an off-axis focus, if the rings are elliptical. The focal length of the deformable mirror can be varied by changing the variable clamping force. The deformable mirror can generally be used in any application requiring the focusing or defocusing of light, including with both coherent and incoherent light sources.
ROCK DEFORMATION. Final Progress Report
2002-05-24
The Gordon Research Conference (GRC) on ROCK DEFORMATION was held at II Ciocco from 5/19/02 thru 5/24/02. Emphasis was placed on current unpublished research and discussion of the future target areas in this field.
Taylor, W. C.
1965-01-01
Ten children with gross deformity of the external ear were observed. In six the facial bones were underdeveloped on the same side as the deformed ear. In all six there was a congenital abnormality of the kidney or upper urinary tract, usually on the same side as the deformed ear. In addition there were usually other associated congenital defects in each case. In the remaining four children the facial bones appeared normal, and pyelography showed no abnormality of the urinary tract. In these four children there were no other associated defects. These observations emphasize the importance of investigating the urinary tract in children with gross deformity of the external ear, especially where there is an associated underdevelopment of the facial bones. PMID:14317453
Anisotropic ripple deformation in phosphorene
Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; ...
2015-04-07
Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticitymore » theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.« less
Anisotropic ripple deformation in phosphorene
Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; Chen, Changfeng
2015-04-07
Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS_{2}. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.
Anisotropic Ripple Deformation in Phosphorene.
Kou, Liangzhi; Ma, Yandong; Smith, Sean C; Chen, Changfeng
2015-05-07
Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.
Gauge Mechanics of Deformable Bodies: a Theory of Something.
NASA Astrophysics Data System (ADS)
Shapere, Alfred Dudley
The treatment of the motion of deformable bodies requires a specification of axes for each shape. We present a natural kinematic formulation of this problem in terms of a gauge structure over the space of shapes that the body may assume. Our first and simplest application is to a freely -falling self-deforming body. We show how deformations of a body with angular momentum zero can result in a change in orientation, and we give a general expression for the gauge potential describing the net rotation due to an arbitrary change of shape. The problem of swimming at low Reynolds number may also be formulated in terms of a gauge potential. Effective methods for computing it, by solving a linear boundary value problem, are described. We employ conformal mapping techniques to calculate swimming motions for cylinders with a variety of cross-sections. We also determine the net translational motions due to arbitrary infinitesimal deformations of the sphere and the circular cylinder. The solution is compactly expressed in terms of the field strength tensor of the gauge potential. Having solved for all cyclic swimming motions of a nearly spherical body, it makes sense to ask which motions are the best. We define a notion of efficiency and use it to determine optimal swimming strokes. These strokes are composed of propagating waves, symmetric about the axis of propulsion. Qualitatively, they resemble the swimming strokes of ciliated micro-organisms, such as the Paramecium. The solution of Stokes' equations is not feasible analytically, except for the simplest shapes. Two approximation schemes may help in studying more general swimming strokes. We discuss and test a short-wavelength analytic approximation, valid when the scales associated with a deformation are small relative to the radius of curvature of the average shape. The complementary domain of large deformations is probably best dealt with on a computer. We sketch a general method for solving Stokes' equations numerically.
Plastic Deformation of Granular Materials
1993-01-25
discontinuities. These result will be important in our granular flow work, when considering viscoplastic constitutive relations (i.e. relaxation systems...5 CUNDN( NUMRES Plastic Deformation of Granular Materials (U) 61102F 6. AUTHOR(S) 2304/A4 Dr. E. Bruce Pitman 7 PERFORMING ORGANIZATION NA .h • 8...lose hyperbolicity. 98 3 81 061! SUBJECT TERMS 15. NUMBER OF PAGES granular material ; plastic deformation; hyperbolic 12 equations 16. PRICE CODE 17
Cleft Nasal Deformity and Rhinoplasty
Kaufman, Yoav; Buchanan, Edward P.; Wolfswinkel, Erik M.; Weathers, William M.; Stal, Samuel
2012-01-01
The cleft nasal deformity is a complex challenge in plastic surgery involving the skin, cartilage, mucosa, and skeletal platform. Ever since Blair and Brown first described the intricacies of the cleft pathology in 1931, the appropriate approach has been extensively debated in the literature with respect to timing, technique, and extent of surgical intervention. In this article, the authors review the literature and summarize the various modalities for achieving a successful rhinoplasty in the patient with a cleft nasal deformity. PMID:24179452
Advanced materials characterization based on full field deformation measurements
NASA Astrophysics Data System (ADS)
Carpentier, A. Paige
approximation must be independent of the deformation measurements, independent of the material properties (geometric stress approximation), and be simple for use in the industry. A remarkable benefit of the full-field deformation measurement is that it lets us observe the physical phenomena of the deformation which enables the derivation of simple and accurate geometric stress approximations. In particular, linear axial through the thickness strain distributions consistently measured in composite short-beam specimens allow a rigorous derivation of extremely simple stress approximations. The observation of linear through the thickness axial strain distributions has become the basis for eliminating the need of using Bernoulli-Euler kinematic assumptions of the rigid cross sections remaining perpendicular to the beam neutral axis throughout the deformation. Such assumptions are not consistent with the deformation mechanisms and therefore are arguable as a rigorous basis for stress approximation. Simple stress approximations are derived in this work based on the observations from the full-field deformation measurements; accuracy of such approximations are verified; and their limitations determined.
Remanent magnetism and ductile deformation in an experimentally deformed magnetite-bearing limestone
NASA Astrophysics Data System (ADS)
Borradaile, Graham J.
1991-07-01
A limestone with pseudo-single-domain (PSD) pure magnetite is given an isothermal remanent magnetization (IRM). Samples are deformed triaxially at 200 MPa (2 kbar) confining pressure at room temperature and at a strain-rate of 10 -5 s -1. The limestone deforms in a ductile manner by twinning to produce sufficiently homogeneously strained specimens up to about 20% shortening. The uniform, saturation IRM rotates away from the shortening axis, approximately by an amount expected for the homogeneous strain of a non-material line marker. Hydrostatic compaction alone shows that this is time-dependent and compatible with progressive damage of the ferrimagnetic grains. Strain produces an increase in coercivity of the magnetite, an increase in its saturation remanence, and an increase in its anisotropy of magnetization (with respect to IRM). These observations are compatible with reduction in effective grain size and change of shape of magnetite. Experimental deformation reduces the intensity of magnetisation, chiefly by the removal of low-coercivity components of remanence when there is a pure IRM vector.
Signal Approximation with a Wavelet Neural Network
1992-12-01
specialized electronic devices like the Intel Electronically Trainable Analog Neural Network (ETANN) chip. The WNN representation allows the...accurately approximated with a WNN trained with irregularly sampled data. Signal approximation, Wavelet neural network .
Rough Set Approximations in Formal Concept Analysis
NASA Astrophysics Data System (ADS)
Yamaguchi, Daisuke; Murata, Atsuo; Li, Guo-Dong; Nagai, Masatake
Conventional set approximations are based on a set of attributes; however, these approximations cannot relate an object to the corresponding attribute. In this study, a new model for set approximation based on individual attributes is proposed for interval-valued data. Defining an indiscernibility relation is omitted since each attribute value itself has a set of values. Two types of approximations, single- and multiattribute approximations, are presented. A multi-attribute approximation has two solutions: a maximum and a minimum solution. A maximum solution is a set of objects that satisfy the condition of approximation for at least one attribute. A minimum solution is a set of objects that satisfy the condition for all attributes. The proposed set approximation is helpful in finding the features of objects relating to condition attributes when interval-valued data are given. The proposed model contributes to feature extraction in interval-valued information systems.
Deformation analysis of rotary combustion engine housings
NASA Technical Reports Server (NTRS)
Vilmann, Carl
1991-01-01
This analysis of the deformation of rotary combustion engine housings targeted the following objectives: (1) the development and verification of a finite element model of the trochoid housing, (2) the prediction of the stress and deformation fields present within the trochoid housing during operating conditions, and (3) the development of a specialized preprocessor which would shorten the time necessary for mesh generation of a trochoid housing's FEM model from roughly one month to approximately two man hours. Executable finite element models were developed for both the Mazda and the Outboard Marine Corporation trochoid housings. It was also demonstrated that a preprocessor which would hasten the generation of finite element models of a rotary engine was possible to develop. The above objectives are treated in detail in the attached appendices. The first deals with finite element modeling of a Wankel engine center housing, and the second with the development of a preprocessor that generates finite element models of rotary combustion engine center housings. A computer program, designed to generate finite element models of user defined rotary combustion engine center housing geometries, is also included.
Kink's dynamics for a deformable substrate potential
NASA Astrophysics Data System (ADS)
Tchofo Dinda, P.; Willis, C. R.
1994-01-01
We study the static and dynamic properties of a kink in a chain of harmonically coupled atoms subjected to a deformable double-well substrate potential. We treat intrinsically the lattice discreteness without approximation and show that in some deformation-parameter ranges each period of the PN (Peierls-Nabarro) potential consists of two wells whose minima are located respectively on a lattice site and midway between two adjacent sites of the chain. In some other parameter ranges each period of the PN potential posseses a single well whose minimum is located either on a lattice site or midway between two adjacent lattice sites. We examine the kink's dynamics by using a multiple-collective-variable treatment, that is, we derive the exact equations of motion for the collective variables X and Y - which describe respectively the center-of-mass mode and the internal mode of the kink. We numerically solve the collective variable equations of motion for the trapped and untrapped regimes of the discrete-kink motion, and show that the presence of a nonlinear internal mode makes a contribution of particular importance in the discrete-kink's dynamics. Indeed, we show that during its untrapped regime, the discrete kink can undergo one or more temporary trappings and even a reflection back over several PN wells, and relate such behaviours to the effects of the excitations of the internal mode of the kink.
Surface deformation in Houston, Texas using GPS
NASA Astrophysics Data System (ADS)
Engelkemeir, Richard; Khan, Shuhab D.; Burke, Kevin
2010-07-01
Surface deformation in the Houston area has been quantified by using a variety of methods including LIDAR, InSAR, extensometers, drilling (to approximately 100 m), and Ground Penetrating Radar. In this paper we report on GPS data acquired during the period between 1995 and 2005 that found evidence of ongoing subsidence (up to - 56 mm/year) in northwestern Houston and of possible horizontal surface movement towards the Gulf of Mexico (up to 6 mm/year). We describe the methods of data-processing used in the study and speculate on the possibility that the active elevation of salt domes, mainly at the south and east of the city, may indirectly influence other surface movements including fault movements and subsidence over areas > 1 km 2. Making use of our observations and analysis could help in natural hazard mitigation in the Houston area and possibly also indicate approaches to surface subsidence study that might be used in other urban areas.
An approximation technique for jet impingement flow
Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H.
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
Postural & striatal deformities in Parkinson's disease: Are these rare?
Pandey, Sanjay; Garg, Hitesh
2016-01-01
Parkinson's disease (PD) is the most common neurodegenerative disease and is characterized by tremor, rigidity and akinesia. Diagnosis is clinical in the majority of the patients. Patients with PD may have stooped posture but some of them develop different types of postural and striatal deformities. Usually these deformities are more common in atypical parkinsonian disorders such as progressive supranuclear palsy and multisystem atrophy. But in many studies it has been highlighted that these may also be present in approximately one third of PD patients leading to severe disability. These include antecollis or dropped head, camptocormia, Pisa syndrome, scoliosis, striatal hands and striatal toes. The pathogenesis of these deformities is a complex combination of central and peripheral influences such as rigidity, dystonia and degenerative skeletal changes. Duration of parkinsonism symptoms is an important risk factor and in majority of the patients these deformities are seen in advanced statge of the disease. The patients with such symptoms may initially respond to dopaminergic medications but if not intervened they may become fixed and difficult to treat. Pain and restriction of movement are most common clinical manifestations and these may mimick symptoms of musculoskeletal disorders like rheumatoid arthritis. Early diagnosis is important as the patients may respond to adjustment in dopaminergic medications. Recent advances such as deep brain stimulation (DBS) and ultrasound guided botulinum toxin injection are helpful in management of these deformities in patients with PD. PMID:26997007
Two-temperature continuum thermomechanics of deforming amorphous solids
NASA Astrophysics Data System (ADS)
Kamrin, Ken; Bouchbinder, Eran
2014-12-01
There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material - the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations - are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables, that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.
Analysis of Mining Terrain Deformation Characteristics with Deformation Information System
NASA Astrophysics Data System (ADS)
Blachowski, Jan; Milczarek, Wojciech; Grzempowski, Piotr
2014-05-01
Mapping and prediction of mining related deformations of the earth surface is an important measure for minimising threat to surface infrastructure, human population, the environment and safety of the mining operation itself arising from underground extraction of useful minerals. The number of methods and techniques used for monitoring and analysis of mining terrain deformations is wide and increasing with the development of geographical information technologies. These include for example: terrestrial geodetic measurements, global positioning systems, remote sensing, spatial interpolation, finite element method modelling, GIS based modelling, geological modelling, empirical modelling using the Knothe theory, artificial neural networks, fuzzy logic calculations and other. The aim of this paper is to introduce the concept of an integrated Deformation Information System (DIS) developed in geographic information systems environment for analysis and modelling of various spatial data related to mining activity and demonstrate its applications for mapping and visualising, as well as identifying possible mining terrain deformation areas with various spatial modelling methods. The DIS concept is based on connected modules that include: the spatial database - the core of the system, the spatial data collection module formed by: terrestrial, satellite and remote sensing measurements of the ground changes, the spatial data mining module for data discovery and extraction, the geological modelling module, the spatial data modeling module with data processing algorithms for spatio-temporal analysis and mapping of mining deformations and their characteristics (e.g. deformation parameters: tilt, curvature and horizontal strain), the multivariate spatial data classification module and the visualization module allowing two-dimensional interactive and static mapping and three-dimensional visualizations of mining ground characteristics. The Systems's functionality has been presented on
Compressive Imaging via Approximate Message Passing
2015-09-04
We propose novel compressive imaging algorithms that employ approximate message passing (AMP), which is an iterative signal estimation algorithm that...Approved for Public Release; Distribution Unlimited Final Report: Compressive Imaging via Approximate Message Passing The views, opinions and/or findings...Research Triangle Park, NC 27709-2211 approximate message passing , compressive imaging, compressive sensing, hyperspectral imaging, signal reconstruction
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
NASA Astrophysics Data System (ADS)
Kaercher, P. M.; Zepeda-Alarcon, E.; Prakapenka, V.; Kanitpanyacharoen, W.; Smith, J.; Sinogeikin, S. V.; Wenk, H. R.
2014-12-01
The crystal structure of the high pressure SiO2 polymorph stishovite has been studied in detail, yet little is known about its deformation mechanisms. Information about how stishovite deforms under stress is important for understanding subduction of quartz-bearing crustal rocks into the mantle. Particularly, stishovite is elastically anisotropic and thus development of crystallographic preferred orientation (CPO) during deformation may contribute to seismic anomalies in the mantle. We converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. Diffraction patterns were collected in situ in radial geometry at the Advanced Light Source (ALS) and the Advanced Photon Source (APS) to examine development of CPO during deformation. We find that (001) poles preferentially align with the compression direction and infer deformation mechanisms leading to the observed CPO with visco-plastic self consistent (VPSC) polycrystal plasticity models. Our results show pyramidal and basal slip are most likely active at high pressure and ambient temperature, in agreement with transmission electron microscopy (TEM) studies of rutile (TiO2) and paratellurite (TeO2), which are isostructural to stishovite. Conversely other TEM studies of stishovite done at higher temperature suggest dominant prismatic slip. This indicates that a variety of slip systems may be active in stishovite, depending on conditions. As a result, stishovite's contribution to the seismic signature in the mantle may vary as a function of pressure and temperature and thus depth.
Finite deformation analysis of geomaterials
NASA Astrophysics Data System (ADS)
Jeremi, Boris; Runesson, Kenneth; Sture, Stein
2001-07-01
The mathematical structure and numerical analysis of classical small deformation elasto-plasticity is generally well established. However, development of large deformation elastic-plastic numerical formulation for dilatant, pressure sensitive material models is still a research area.In this paper we present development of the finite element formulation and implementation for large deformation, elastic-plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process.The algorithm is tested in conjunction with the novel hyperelasto-plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto-plastic problems in geomechanics.We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS-89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching.
Bilateral cleft lip nasal deformity
Singh, Arun Kumar; Nandini, R.
2009-01-01
Bilateral cleft lip nose deformity is a multi-factorial and complex deformity which tends to aggravate with growth of the child, if not attended surgically. The goals of primary bilateral cleft lip nose surgery are, closure of the nasal floor and sill, lengthening of the columella, repositioning of the alar base, achieving nasal tip projection, repositioning of the lower lateral cartilages, and reorienting the nares from horizontal to oblique position. The multiplicity of procedures in the literature for correction of this deformity alludes to the fact that no single procedure is entirely effective. The timing for surgical intervention and its extent varies considerably. Early surgery on cartilage may adversely affect growth and development; at the same time, allowing the cartilage to grow in an abnormal position and contributing to aggravation of deformity. Some surgeons advocate correction of deformity at an early age. However, others like the cartilages to grow and mature before going in for surgery. With peer pressure also becoming an important consideration during the teens, the current trend is towards early intervention. There is no unanimity in the extent of nasal dissection to be done at the time of primary lip repair. While many perform limited nasal dissection for the fear of growth retardation, others opt for full cartilage correction at the time of primary surgery itself. The value of naso-alveolar moulding (NAM) too is not universally accepted and has now more opponents than proponents. Also most centres in the developing world have neither the personnel nor the facilities for the same. The secondary cleft nasal deformity is variable and is affected by the extent of the original abnormality, any prior surgeries performed and alteration due to nasal growth. This article reviews the currently popular methods for correction of nasal deformity associated with bilateral cleft lip, it's management both at the time of cleft lip repair and also secondarily
Deformation of second and third quantization
NASA Astrophysics Data System (ADS)
Faizal, Mir
2015-03-01
In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler-DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.
Nuclear energy surfaces at high-spin in the A{approximately}180 mass region
Chasman, R.R.; Egido, J.L.; Robledo, L.M.
1995-08-01
We are studying nuclear energy surfaces at high spin, with an emphasis on very deformed shapes using two complementary methods: (1) the Strutinsky method for making surveys of mass regions and (2) Hartree-Fock calculations using a Gogny interaction to study specific nuclei that appear to be particularly interesting from the Strutinsky method calculations. The great advantage of the Strutinsky method is that one can study the energy surfaces of many nuclides ({approximately}300) with a single set of calculations. Although the Hartree-Fock calculations are quite time-consuming relative to the Strutinsky calculations, they determine the shape at a minimum without being limited to a few deformation modes. We completed a study of {sup 182}Os using both approaches. In our cranked Strutinsky calculations, which incorporate a necking mode deformation in addition to quadrupole and hexadecapole deformations, we found three well-separated, deep, strongly deformed minima. The first is characterized by nuclear shapes with axis ratios of 1.5:1; the second by axis ratios of 2.2:1 and the third by axis ratios of 2.9:1. We also studied this nuclide with the density-dependent Gogny interaction at I = 60 using the Hartree-Fock method and found minima characterized by shapes with axis ratios of 1.5:1 and 2.2:1. A comparison of the shapes at these minima, generated in the two calculations, shows that the necking mode of deformation is extremely useful for generating nuclear shapes at large deformation that minimize the energy. The Hartree-Fock calculations are being extended to larger deformations in order to further explore the energy surface in the region of the 2.9:1 minimum.
Transition from frictional to viscous deformation in granitoid fault rocks
NASA Astrophysics Data System (ADS)
Peč, M.; Heilbronner, R.; Stünitz, H.
2009-04-01
Fracturing of rocks in natural fault zones increases the permeability and produces extremely small grain sizes (< 0.1 μm). This fine grain size is a potential precursor to viscous deformation by diffusion creep, even at low temperatures if fluids are present. The aim of this study is to test the potential transition from frictional to viscous deformation in very fine-grained gouge material. We have performed a series of simple shear deformation experiments on fault gouge in a Griggs deformation apparatus. Crushed Verzasca gneiss powder (< 200 μm) with 0.2 wt% water added was placed between Verzasca Gneiss forcing blocks cut at 45 degrees and weld-sealed in a gold jackets. Before deformation, the gouge material needs to be compacted. This is achieved by a set 1 of frictional deformation experiments at different temperatures (T = 24 °C, 300 °C, 500 °C, Pc = 500 MPa, strain rate = 10ˆ-4) to shear strains of approximately gamma = 2.5. In the subsequent experiments (set 2), potential viscous deformation processes are tested in the pre-deformed gouge. After initial frictional deformation (set 1) the samples are left at peak differential stress conditions for one week. Finally, in a third type of experiments (set 3), the peak differential stress was lowered after frictional deformation to a level similar to the confining pressure and held constant for one week. In set 1, the peak shear stresses are temperature independent (given the limited stress resolution of the Griggs apparatus; 300° C = 780 - 870 MPa, 500° C = 760 - 820 MPa). In set 2, the stress relaxation after frictional deformation is clearly temperature dependent (after one week at 300° C, the shear stress is approx. 370 MPa; at 500° C, approx. 230 MPa). In set 3, no creep was observed. Further investigation of this phenomenon is required but probably the differential stress was too low. Microstructural observations show a striking difference between samples of set 1 and set 2. The samples deformed by
An approximate yield criterion for anisotropic porous media
NASA Astrophysics Data System (ADS)
Keralavarma, Shyam M.; Benzerga, A. Amine
2008-09-01
We derive a new yield function for materials containing spheroidal voids embedded in a perfectly-plastic anisotropic Hill-type matrix. Using approximate limit-analysis and a restricted set of trial velocity fields, analytical yield loci are derived for a hollow, spheroidal volume element containing a confocal spheroidal void. Alternatively, the yield loci are determined through numerical limit-analysis, i.e., employing a larger set of velocity fields. The numerical results are quasi-exact for transversely isotropic materials under axisymmetric loading. We show that an enhanced description of admissible microscopic deformation fields results in a close agreement between analytical and numerical macroscopic yield loci. To cite this article: S.M. Keralavarma, A.A. Benzerga, C. R. Mecanique 336 (2008).
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Transverse deformations of extreme horizons
NASA Astrophysics Data System (ADS)
Li, Carmen; Lucietti, James
2016-04-01
We consider the inverse problem of determining all extreme black hole solutions to the Einstein equations with a prescribed near-horizon geometry. We investigate this problem by considering infinitesimal deformations of the near-horizon geometry along transverse null geodesics. We show that, up to a gauge transformation, the linearised Einstein equations reduce to an elliptic PDE for the extrinsic curvature of a cross-section of the horizon. We deduce that for a given near-horizon geometry there exists a finite dimensional moduli space of infinitesimal transverse deformations. We then establish a uniqueness theorem for transverse deformations of the extreme Kerr horizon. In particular, we prove that the only smooth axisymmetric transverse deformation of the near-horizon geometry of extreme Kerr, such that cross-sections of the horizon are marginally trapped surfaces, corresponds to that of the extreme Kerr black hole. Furthermore, we determine all smooth and biaxisymmetric transverse deformations of the near-horizon geometry of the five-dimensional extreme Myers-Perry black hole with equal angular momenta. We find a three parameter family of solutions such that cross-sections of the horizon are marginally trapped, which is more general than the known black hole solutions. We discuss the possibility that they correspond to new five-dimensional vacuum black holes.
Forecasting volcanic eruptions: the control of elastic-brittle deformation
NASA Astrophysics Data System (ADS)
Kilburn, Christopher; Robertson, Robert; Wall, Richard; Steele, Alexander
2016-04-01
At volcanoes reawakening after long repose, patterns of unrest normally reflect the elastic-brittle deformation of crust above a magma reservoir. Local fault movements, detected as volcano-tectonic (VT) earthquakes, increase in number with surface deformation, at first approximately exponentially and then linearly. The trends describe how crustal behaviour evolves from quasi-elastic deformation under an increasing stress to inelastic deformation under a constant stress. They have been quantified and verified against experiments for deformation in compression [1]. We have extended the analysis to extensional deformation. The results agree well with field data for crust being stretched by a pressurizing magmatic system [2]. They also provide new criteria for enhancing the definitions of alert levels and preferred times to eruption. The VT-deformation sequence is a field proxy for changes in deformation with applied stress. The transition from quasi-elastic to inelastic behaviour is characterised in extension by the ratio of differential failure stress SF to tensile strength σT. Unrest data from at least basaltic to andesitic stratovolcanoes, as well as large calderas, yield preferred values for SF/σT ≤ 4, coinciding with the range for tensile failure expected from established theoretical constraints (from Mohr-Coulomb-Griffiths failure). We thus associate the transition with the approach to tensile rupture at the wall of a pressurized magma reservoir. In particular, values of about 2 are consistent with the rupture of a cylindrical reservoir, such as a closed conduit within a volcanic edifice, whereas values of about 3 suggest an approximately spherical reservoir, such as may exist at deeper levels. The onset of inelastic behaviour reflects the emergence of self-accelerating crack growth under a constant stress. Applied to forecasting eruptions, it provides a new and objective criterion for raising alert levels during an emergency; it yields the classic linear
Chaetal deformities in aquatic oligochaeta
Brinkhurst, R.O.; Wetzel, M.J.
1994-12-31
Gross deformities in the chaetae of specimens of the tubificid Potamothrix hammoniensis were described by Milbrink from Lake Vaenern, Sweden. This lake is one of the most mercury-polluted major lakes of the world. Statistical tests showed a highly significant correlation between the incidence of deformities and the mercury concentration in the sediments. Changes in the pulp and paper mill process led to marked reduction in specimens with deformities. Similarly modified specimens of various species have been observed at a number of sites contaminated with heavy metals or oil residues in North America. Experimental work on chaetal form has demonstrated changes due to conductivity which have also been observed in saline inland waters. These experiments suggest that chaetae may be shed and replaced by worms every few days. EDX observation of chaetae indicated that metals may accumulate in them, and so provide a potential depuration mechanism. Independent physiological studies suggest that worms may be capable of regulating their metal levels.
Finite Deformation of Magnetoelastic Film
Barham, Matthew Ian
2011-05-31
A nonlinear two-dimensional theory is developed for thin magnetoelastic lms capable of large deformations. This is derived directly from three-dimensional theory. Signi cant simpli cations emerge in the descent from three dimensions to two, permitting the self eld generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic eld. An instability is inferred and investigated for the weak magnetization material model.
Deformed Richardson-Gaudin model
NASA Astrophysics Data System (ADS)
Kulish, P.; Stolin, A.; Johannesson, L. H.
2014-09-01
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this work we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
Deformation of Unentangled Swollen Gels
NASA Astrophysics Data System (ADS)
Sariyer, Ozan; Panyukov, Sergey; Rubinstein, Michael
2014-03-01
We study the deformation characteristics (Poisson's ratios and stress-strain relations) of unentangled gels swollen and uniaxially or biaxially deformed in excess solvent by considering the balance of osmotic pressure and elastic stress in unconstrained dimensions. Our scaling theory predicts a crossover from theta solvent behavior to marginal solvent behavior upon stretching gels that are in concentrated regime at swelling equilibrium - a phenomenon that was experimentally observed long ago, but not understood theoretically. For gels that are in the semidilute good solvent regime at swelling equilibrium, we predict a crossover to theta solvent behavior upon compression and a crossover to marginal solvent behavior upon stretching. Our theory reproduces the previously known results for equilibrium swelling degree as well as known deformation characteristics in theta and athermal solvents.
Shock metamorphism of deformed quartz
NASA Technical Reports Server (NTRS)
Gratz, Andrew J.; Christie, John; Tyburczy, James; Ahrens, Thomas; Pongratz, Peter
1988-01-01
The effect produced by shock loading (to peak pressures of 12 and 24) on deformed synthetic quartz containing a dislocation and abundant bubbles and small inclusions was investigated, and the relationships between preexisting dislocation density shock lamellae in the target material were examined. The resultant material was found to be inhomogeneously deformed and extremely fractured. Results of TEM examinations indicate that no change in dislocation density was caused by shock loading except in regions containing shock lamellae, where the dislocation density was lowered. The shock-induced defects tend to nucleate on and be controlled by preexisting stress concentrators; shock lamellae, glassy veins, and most curviplanar defects form in tension, presumably during release. An extremely mobile silica fluid is formed and injected into fractures during release, which forcibly removes crystalline fragments from vein walls. It is concluded that shock deformation in quartz is dominated by fracture and melting.
Deformation processes in forging ceramics
NASA Technical Reports Server (NTRS)
Cannon, R. M.; Rhodes, W. H.
1973-01-01
The deformation processes involved in the forging of refractory ceramic oxides were investigated. A combination of mechanical testing and forging was utilized to investigate both the flow and fracture processes involved. Deformation studies of very fine grain Al203 revealed an apparent transition in behavior, characterized by a shift in the strain rate sensitivity from 0.5 at low stresses to near unity at higher stresses. The behavior is indicative of a shift in control between two dependent mechanisms, one of which is indicated to be cation limited diffusional creep with significant boundary enhancement. The possible contributions of slip, indicated by crystallographic texture, interface control of the diffusional creep and inhomogeneous boundary sliding are also discussed. Additional experiments indicated an independence of deformation behavior on MgO doping and retained hot pressing impurities, at least for ultrafine grained material, and also an independence of test atmosphere.
Microstructure of deformed graywacke sandstones
Dengler, L.A.
1980-03-05
Microsctures in low-permeability graywacke sandstones were studied by optical and scanning electron microscopy (SEM). SEM specimens were prepared by ion-bombardment of thick polished samples. The undeformed rock contains grains in a matrix composed primarily of authigenic chlorite and kaolinite. Chlorite platelets are randomly arranged in face-to-edge relation to one another. Kaolinite occurs as pseudohexagonal crystals stacked face-to-face in pore filling books. Uniaxial-stress experiments covered a range of confining pressures from .1 to 600 MPa. Below 50 MPa confining pressure, intergranular fracturing occurs within the fault zone and near the sample's cylindrical surface. Between 100 and 300 MPa confining pressure, fault zones contain highly fractured grains, gauge and slickensides on grain surfaces. At 600 MPa, the sample contains a diffuse shear zone of highly fractured grains and no well-defined fault. In all samples, the distribution of microcracks is heterogeneous. Different clay minerals exhibit different modes of deformation. Chlorite structure responds to applied stress by compaction, reducing both pore size and volume. Chlorite platelets are plastically deformed in even the least strained samples. Kaolinite does not deform plastically in any of the samples examined. Deformation of kaolinite is restricted to toppling of the book structure. Dilatant crack growth was studied in two samples unloaded prior to failure. Uniaxially-strained samples deform primarily along grain boundaries, producing intergranular cracks and realignment of chlorite platelets. Intragranular crack density is linearly related to axial-strain, although grains are less fractured than in uniaxially-stressed samples tested at equivalent mean pressures. Cracks are rarely longer than a grain diameter. Nuclear-explosively deformed samples were recovered after the Rio Blanco gas stimulation experiment. (JGB)
Controllable objective with deformable mirrors
Agafonov, V V; Safronov, A G
2004-03-31
A new optical device - an objective with deformable mirrors and parameters controlled in the dynamic regime is proposed. The computer simulation of the objective is performed. The dependences of some parameters of the objective on the control voltage are determined. The simulation showed that the ranges of control of the rear focal segment and the focal distance for the objective with the focal distance 602 mm were 1057 and 340 mm, respectively, which is substantially greater than in the control of an equivalent deformable mirror. (laser applications and other topics in quantum electronics)
Analytical volcano deformation source models
Lisowski, Michael; Dzurisin, Daniel
2007-01-01
Primary volcanic landforms are created by the ascent and eruption of magma. The ascending magma displaces and interacts with surrounding rock and fluids as it creates new pathways, flows through cracks or conduits, vesiculates, and accumulates in underground reservoirs. The formation of new pathways and pressure changes within existing conduits and reservoirs stress and deform the surrounding rock. Eruption products load the crust. The pattern and rate of surface deformation around volcanoes reflect the tectonic and volcanic processes transmitted to the surface through the mechanical properties of the crust.
Ilizarov principles of deformity correction.
Spiegelberg, B; Parratt, T; Dheerendra, S K; Khan, W S; Jennings, R; Marsh, D R
2010-03-01
Ilizarov frames provide a versatile fixation system for the management of bony deformities, fractures and their complications. The frames give stability, soft tissue preservation, adjustability and functionality allowing bone to realise its full osteogenic potential. It is important that we have a clear and concise understanding of the Ilizarov principles of deformity correction to best make use of this fixation system. In this review article, the history of Ilizarov frame, the basic sciences behind it, the mechanical principles governing its use and the clinical use of the fixation system are discussed.
Ilizarov principles of deformity correction
Spiegelberg, B; Parratt, T; Dheerendra, SK; Khan, WS; Jennings, R; Marsh, DR
2010-01-01
Ilizarov frames provide a versatile fixation system for the management of bony deformities, fractures and their complications. The frames give stability, soft tissue preservation, adjustability and functionality allowing bone to realise its full osteogenic potential. It is important that we have a clear and concise understanding of the Ilizarov principles of deformity correction to best make use of this fixation system. In this review article, the history of Ilizarov frame, the basic sciences behind it, the mechanical principles governing its use and the clinical use of the fixation system are discussed. PMID:20353638
Cavity coalescence in superplastic deformation
Stowell, M.J.; Livesey, D.W.; Ridley, N.
1984-01-01
An analysis of the probability distribution function of particles randomly dispersed in a solid has been applied to cavitation during superplastic deformation and a method of predicting cavity coalescence developed. Cavity size distribution data were obtained from two microduplex nickel-silver alloys deformed superplastically to various extents at elevated temperature, and compared to theoretical predictions. Excellent agreement occurred for small void sizes but the model underestimated the number of voids in the largest size groups. It is argued that the discrepancy results from a combination of effects due to non-random cavity distributions and to enhanced growth rates and incomplete spheroidization of the largest cavities.
The JWKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David; Singh, Parampreet
2017-01-01
We explore the JWKB approximation in loop quantum cosmology in a flat universe with a scalar matter source. Exact solutions of the quantum constraint are studied at small volume in the JWKB approximation in order to assess the probability of tunneling to small or zero volume. Novel features of the approximation are discussed which appear due to the fact that the model is effectively a two-dimensional dynamical system. Based on collaborative work with Parampreet Singh.
Approximate dynamic model of a turbojet engine
NASA Technical Reports Server (NTRS)
Artemov, O. A.
1978-01-01
An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion.
Bent approximations to synchrotron radiation optics
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors.
Feasibility of Multimodal Deformable Registration for Head and Neck Tumor Treatment Planning
Fortunati, Valerio; Verhaart, René F.; Angeloni, Francesco; Lugt, Aad van der; Niessen, Wiro J.; Veenland, Jifke F.; Paulides, Margarethus M.; Walsum, Theo van
2014-09-01
Purpose: To investigate the feasibility of using deformable registration in clinical practice to fuse MR and CT images of the head and neck for treatment planning. Method and Materials: A state-of-the-art deformable registration algorithm was optimized, evaluated, and compared with rigid registration. The evaluation was based on manually annotated anatomic landmarks and regions of interest in both modalities. We also developed a multiparametric registration approach, which simultaneously aligns T1- and T2-weighted MR sequences to CT. This was evaluated and compared with single-parametric approaches. Results: Our results show that deformable registration yielded a better accuracy than rigid registration, without introducing unrealistic deformations. For deformable registration, an average landmark alignment of approximatively 1.7 mm was obtained. For all the regions of interest excluding the cerebellum and the parotids, deformable registration provided a median modified Hausdorff distance of approximatively 1 mm. Similar accuracies were obtained for the single-parameter and multiparameter approaches. Conclusions: This study demonstrates that deformable registration of head-and-neck CT and MR images is feasible, with overall a significanlty higher accuracy than for rigid registration.
Highly deformable nanofilaments in flow
NASA Astrophysics Data System (ADS)
Pawłowska, S.
2016-10-01
Experimental analysis of hydrogel nanofilaments conveyed by flow is conducted to help in understanding physical phenomena responsible for transport properties and shape deformations of long bio-objects, like DNA or proteins. Investigated hydrogel nanofilaments exhibit typical macromolecules-like behavior, as spontaneous conformational changes and cross-flow migration. Results of the experiments indicate critical role of thermal fluctuations behavior of single filaments.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Computing Functions by Approximating the Input
ERIC Educational Resources Information Center
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Approximate methods for equations of incompressible fluid
NASA Astrophysics Data System (ADS)
Galkin, V. A.; Dubovik, A. O.; Epifanov, A. A.
2017-02-01
Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out.
Quirks of Stirling's Approximation
ERIC Educational Resources Information Center
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
Inversion and approximation of Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
An approximation for inverse Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1981-01-01
Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.
Cosca, Michael; Stunitz, Holger; Bourgiex, Anne-Lise; Lee, John P.
2011-01-01
The effects of deformation on radiogenic argon (40Ar*) retentivity in mica are described from high pressure experiments performed on rock samples of peraluminous granite containing euhedral muscovite and biotite. Cylindrical cores, ~15 mm in length and 6.25 mm in diameter, were drilled from granite collected from the South Armorican Massif in northwestern France, loaded into gold capsules, and weld-sealed in the presence of excess water. The samples were deformed at a pressure of 10 kb and a temperature of 600 degrees C over a period 29 of hours within a solid medium assembly in a Griggs-type triaxial hydraulic deformation apparatus. Overall shortening in the experiments was approximately 10%. Transmitted light and secondary and backscattered electron imaging of the deformed granite samples reveals evidence of induced defects and for significant physical grain size reduction by kinking, cracking, and grain segmentation of the micas.
Experimental Deformation of Dehydrating Antigorite: Challenging Models of Dehydration Embrittlement
NASA Astrophysics Data System (ADS)
Hirth, Greg; Chernak, Linda
2010-05-01
To test the hypothesis that intermediate depth earthquakes in subduction zones are caused by the dehydration of hydrous phases, we conducted temperature-ramping experiments on antigorite serpentinite. Cold-pressed powdered samples of antigorite were deformed to a high differential stress at 400°C and 1.0 GPa, within the antigorite stability field, where we have shown that deformation localizes. Temperature was then increased at different rates, 1800°C/hr and 180°C/hr, to cross the reaction boundary while the sample continued to deform; samples were deformed at strain rates of 10-4 s-1, 10-5 s-1 and 10-6 s-1. Two additional experiments were conducted in a similar manner at 300°C, 1.5 GPa and 10-5 s-1 but samples remained 'statically' at high stress during the temperature increase. Our results show that although the decrease in stress during temperature ramping is large, stress relaxes stably, even after dehydration. We find that the slopes of the unloading curves are approximately the same for constant values of the ratio (strain rate/ramp rate) and that the unloading slope is greater for higher values of this ratio. In addition, we find that the unloading curves with the greatest slopes are similar to the apparatus compliance, suggesting that we are generating 'slow earthquakes' in our experiments over the course 5 to 10s of minutes. A strain rate stepping experiment indicates that antigorite has velocity strengthening behavior at 700°C and 1.5 GPa suggesting that as soon as an instability develops in the antigorite, the material strengthens sufficiently to not go unstable. Our results thus suggest that antigorite dehydration does not result in 'dehydration embrittlement' but that it may promote slow earthquakes. We have also conducted a preliminary experiment to study the role of effective pressure on deformation behavior after dehydration. A cold-pressed powdered sample of antigorite with a small core of coarse-grained olivine at one end was deformed at 700
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
Approximating maximum clique with a Hopfield network.
Jagota, A
1995-01-01
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic.
The Tamm-Dancoff Approximation as the Contraction Limit of the Richardson-Gaudin Equations
NASA Astrophysics Data System (ADS)
de Baerdemacker, S.
2013-03-01
A connection is made between the exact eigenstates of the level-independent Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and its Tamm-Dancoff Approximation (TDA). This is done by means of a deformation of the quasi-spin algebra, which connects the Bethe Ansatz states with a unique multi-phonon mode of the TDA. The procedure is illustrated with a model describing neutron superluidity in 56Fe.
Prediction of Soil Deformation in Tunnelling Using Artificial Neural Networks
Lai, Jinxing
2016-01-01
In the past few decades, as a new tool for analysis of the tough geotechnical problems, artificial neural networks (ANNs) have been successfully applied to address a number of engineering problems, including deformation due to tunnelling in various types of rock mass. Unlike the classical regression methods in which a certain form for the approximation function must be presumed, ANNs do not require the complex constitutive models. Additionally, it is traced that the ANN prediction system is one of the most effective ways to predict the rock mass deformation. Furthermore, it could be envisaged that ANNs would be more feasible for the dynamic prediction of displacements in tunnelling in the future, especially if ANN models are combined with other research methods. In this paper, we summarized the state-of-the-art and future research challenges of ANNs on the tunnel deformation prediction. And the application cases as well as the improvement of ANN models were also presented. The presented ANN models can serve as a benchmark for effective prediction of the tunnel deformation with characters of nonlinearity, high parallelism, fault tolerance, learning, and generalization capability. PMID:26819587
Three saints with deformed extremities in an Italian Renaissance altarpiece.
Albury, W R; Weisz, G M
2017-03-01
A fifteenth-century Florentine altarpiece painted by the Pollaiuolo brothers, Antonio (1433-1498) and Piero (1443-1496), shows three saints with evident deformities of the hands and feet. The pathologies concerned are tentatively identified, and various rationales for their presence in the painting are discussed. Of particular importance is the location of the altarpiece in a chapel which houses the tomb of the Cardinal of Portugal, Prince James of Lusitania (1433-1459). It is argued that both the artistic style of the day and the religious symbolism of the Cardinal's funeral chapel contributed to the artists' decision to portray the saints with deformities. An unnatural curvature of the fifth finger was apparently considered elegant in fifteenth-century paintings, and the depiction of bare feet with hallux valgus gave them a shape which approximated and could have been caused by fashionable pointed shoes. But in addition, deformities in religious art could be symbolic of suffering and martyrdom, a theme which the Cardinal's chapel emphasised in a number of ways. It is suggested therefore that the Pollaiuolo altarpiece reconciles these two disparate factors, portraying genuine deformities in a way that was artistically stylish and symbolically meaningful.
Beak deformities in Northwestern Crows: evidence of a multispecies epizootic
Van Hemert, Caroline; Handel, Colleen M.
2010-01-01
Beak abnormalities are rare among adult birds and, typically, are not widespread in a given population, within a region, or across multiple species. A high concentration of beak deformities was recently documented in Black-capped Chickadees (Poecile atricapillus) and other resident avian species in Alaska. We describe a parallel condition in Northwestern Crows (Corvus caurinus) that signals the emergence of a multispecies epizootic. On the basis of 186 Northwestern Crows captured at six sites in Alaska during 2007 and 2008, we estimated the prevalence of beak deformities in adults to be 16.9 ± 5.3%, the highest rate of gross deformities ever recorded in a wild bird population. Prevalence varied among sites and was as high as 36% on the Kenai Peninsula, which suggests possible epizootic clusters. We also documented beak abnormalities in an additional 148 Northwestern Crows in south-central and southeastern Alaska and in 64 crows near Vancouver, British Columbia, and Puget Sound, Washington, a region where both Northwestern Crows and American Crows (C. brachyrhynchos) occur. The increase in frequency and distribution of crows observed with abnormal beaks throughout the Pacific Northwest since the late 1990s indicates a geographic expansion of this problem. Affected crows exhibited elongated and often crossed beaks that were morphologically similar to deformities documented in Black-capped Chickadees and other species in Alaska over approximately the same period. Additional research is needed to determine the etiology and potential adverse effects on bird populations affected by this disorder.
Studies of normal deformation in {sup 151}Dy
Nisius, D.; Janssens, R.V.F.; Crowell, B.
1995-08-01
The wealth of data collected in the study of superdeformation in {sup 151}Dy allowed for new information to be obtained on the normally deformed structures in this nucleus. At high spin several new yrast states have been identified for the first time. They were associated with single-particle excitations. Surprisingly, a sequence was identified with energy spacings characteristic of a rotational band of normal ({beta}2 {approximately} 0.2) deformation. The bandhead spin appears to be 15/2{sup -} and the levels extend up to a spin of 87/2{sup -}. A clear backbend is present at intermediate spins. While a similar band based on a bandhead of 6{sup +} is known in {sup 152}Dy, calculations suggest that this collective prolate band should not be seen in {sup 151}Dy. In the experiment described earlier in this report that is aimed at determining the deformations associated with the SD bands in this nucleus and {sup 152}Dy, the deformation associated with this band will be determined. This will provide further insight into the origin of this band.
Large Deformation Constitutive Laws for Isotropic Thermoelastic Materials
Plohr, Bradley J.; Plohr, Jeeyeon N.
2012-07-25
We examine the approximations made in using Hooke's law as a constitutive relation for an isotropic thermoelastic material subjected to large deformation by calculating the stress evolution equation from the free energy. For a general thermoelastic material, we employ the volume-preserving part of the deformation gradient to facilitate volumetric/shear strain decompositions of the free energy, its first derivatives (the Cauchy stress and entropy), and its second derivatives (the specific heat, Grueneisen tensor, and elasticity tensor). Specializing to isotropic materials, we calculate these constitutive quantities more explicitly. For deformations with limited shear strain, but possibly large changes in volume, we show that the differential equations for the stress components involve new terms in addition to the traditional Hooke's law terms. These new terms are of the same order in the shear strain as the objective derivative terms needed for frame indifference; unless the latter terms are negligible, the former cannot be neglected. We also demonstrate that accounting for the new terms requires that the deformation gradient be included as a field variable
Structural Deformation of Sm@C88 under High Pressure.
Cui, Jinxing; Yao, Mingguang; Yang, Hua; Liu, Ziyang; Ma, Fengxian; Li, Quanjun; Liu, Ran; Zou, Bo; Cui, Tian; Liu, Zhenxian; Sundqvist, Bertil; Liu, Bingbing
2015-08-25
We have studied the structural transformation of Sm@C88 under pressure up to 18 GPa by infrared spectroscopy combined with theoretical simulations. The infrared-active vibrational modes of Sm@C88 at ambient conditions have been assigned for the first time. Pressure-induced blue and red shifts of the corresponding vibrational modes indicate an anisotropic deformation of the carbon cage upon compression. We propose that the carbon cage changes from ellipsoidal to approximately spherical around 7 GPa. A smaller deformation of the carbon bonds in the area close to the Sm atom in the cage suggests that the trapped Sm atom plays a role in minimizing the compression of the adjacent bonds. Pressure induced a significant reduction of the band gap of the crystal. The HOMO-LUMO gap of the Sm@C88 molecule decreases remarkably at 7 GPa as the carbon cage is deformed. Also, compression enhances intermolecular interactions and causes a widening of the energy bands. Both effects decrease the band gap of the sample. The carbon cage deforms significantly above 7 GPa, from spherical to a peanut-like shape and collapses at 18 GPa.
Structural Deformation of Sm@C88 under High Pressure
Cui, Jinxing; Yao, Mingguang; Yang, Hua; Liu, Ziyang; Ma, Fengxian; Li, Quanjun; Liu, Ran; Zou, Bo; Cui, Tian; Liu, Zhenxian; Sundqvist, Bertil; Liu, Bingbing
2015-01-01
We have studied the structural transformation of Sm@C88 under pressure up to 18 GPa by infrared spectroscopy combined with theoretical simulations. The infrared-active vibrational modes of Sm@C88 at ambient conditions have been assigned for the first time. Pressure-induced blue and red shifts of the corresponding vibrational modes indicate an anisotropic deformation of the carbon cage upon compression. We propose that the carbon cage changes from ellipsoidal to approximately spherical around 7 GPa. A smaller deformation of the carbon bonds in the area close to the Sm atom in the cage suggests that the trapped Sm atom plays a role in minimizing the compression of the adjacent bonds. Pressure induced a significant reduction of the band gap of the crystal. The HOMO-LUMO gap of the Sm@C88 molecule decreases remarkably at 7 GPa as the carbon cage is deformed. Also, compression enhances intermolecular interactions and causes a widening of the energy bands. Both effects decrease the band gap of the sample. The carbon cage deforms significantly above 7 GPa, from spherical to a peanut-like shape and collapses at 18 GPa. PMID:26303867
Finite deformations of an electroelastic circular cylindrical tube
NASA Astrophysics Data System (ADS)
Melnikov, Andrey; Ogden, Ray W.
2016-12-01
In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load.
On the influence of a geothermal system on ground deformation during a volcanic eruption
NASA Astrophysics Data System (ADS)
Zarin, G. A.; Melnik, O. E.; Tsvetkova, Yu. D.; Afanasyev, A. A.
2016-12-01
The measurement of ground deformation during a volcanic eruption is one of the main tools for the monitoring of active volcanoes. The deformation is caused by processes that are occurring in the chamber-conduit system, as well as in the geothermal systems that are heated by ascending magma. The influence of the magma chamber and, to a lesser degree, of the conduit on deformation in host rocks is sufficiently well known theoretically, but no studies have been made to investigate the effects of a hydrothermal system on measurable ground deformation during a volcanic eruption. We made a comparative study of the ground deformation due to two deformation-initiating sources: a fissure conduit with a specified excess pressure and a hydrothermal system that was heated by magma flow. We show that the vertical deformation due to the activity of a geothermal system can exceed that due to magma flow by factors of several times. The spatial distributions of the deformation are also substantially different. The vertical displacement due to a geothermal system has its maximum above the fissure conduit, while when the pressure varies in the conduit it induces a local subsidence of the ground; the maximum ground uplift is at a distance of approximately twice the depth to the top of the conduit. The influence of the geothermal system should be incorporated in interpretations of data that come from the monitoring of active volcanoes.
Literature survey on cements for remediation of deformed casing in geothermal wells
Allan, M.L.; Philippacopoulos, A.J.
1998-12-31
Brookhaven National Laboratory was requested to conduct a literature survey for the best available cement to use in the proposed casing patch as part of the Geothermal Drilling Organization (GDO) project on remediation of deformed casings. A total of 50 wells have been identified with deformed production casing in Unocal`s portion of The Geysers geothermal field. A procedure to address the casing deformation and avoid abandonment of these wells has been developed as described in the Geysers Deformed Casing Remediation Proposal. The proposed remediation procedure involves isolation of the zone of interest with an inflatable packer, milling the deformed casing and cementing a 7 inch diameter liner to extend approximately 100 ft above and 100 ft below the milled zone. During the milling operation it is possible that the original cement and surrounding formation may slough away. In order to specify a suitable cement formulation for the casing patch it is first necessary to identify and understand the deformation mechanism/s operating in The Geysers field. Subsequently, the required cement mechanical properties to withstand further deformation of the repaired system must be defined. From this information it can be determined whether available cement formulations meet these requirements. In addition to The Geysers, other geothermal fields are at possible risk of casing deformation due to subsidence, seismic activity, lateral and vertical formation movement or other processes. Therefore, the proposed remediation procedure may have applications in other fields.
Ion induced deformation of soft tissue.
Myers, T G; Aldis, G K; Naili, S
1995-01-01
In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; ...
2014-11-07
Although the crystal structure of the high pressure SiO2 polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation andmore » find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.« less
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
NASA Astrophysics Data System (ADS)
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; Kanitpanyacharoen, Waruntorn; Smith, Jesse S.; Sinogeikin, Stanislav; Wenk, Hans-Rudolf
2015-04-01
Although the crystal structure of the high-pressure SiO2 polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser-heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation and find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.
Highly deformable bones: unusual deformation mechanisms of seahorse armor.
Porter, Michael M; Novitskaya, Ekaterina; Castro-Ceseña, Ana Bertha; Meyers, Marc A; McKittrick, Joanna
2013-06-01
Multifunctional materials and devices found in nature serve as inspiration for advanced synthetic materials, structures and robotics. Here, we elucidate the architecture and unusual deformation mechanisms of seahorse tails that provide prehension as well as protection against predators. The seahorse tail is composed of subdermal bony plates arranged in articulating ring-like segments that overlap for controlled ventral bending and twisting. The bony plates are highly deformable materials designed to slide past one another and buckle when compressed. This complex plate and segment motion, along with the unique hardness distribution and structural hierarchy of each plate, provide seahorses with joint flexibility while shielding them against impact and crushing. Mimicking seahorse armor may lead to novel bio-inspired technologies, such as flexible armor, fracture-resistant structures or prehensile robotics.
Preferred orientation in experimentally deformed stishovite: implications for deformation mechanisms
Kaercher, Pamela M.; Zepeda-Alarcon, Eloisa; Prakapenka, Vitali B.; Kanitpanyacharoen, Waruntorn; Smith, Jesse S.; Sinogeikin, Stanislav; Wenk, Hans-Rudolf
2014-11-07
Although the crystal structure of the high pressure SiO_{2} polymorph stishovite has been studied in detail, little is known about the development of crystallographic preferred orientation (CPO) during deformation in stishovite. Insight into CPO and associated deformation mechanics of stishovite would provide important information for understanding subduction of quartz-bearing crustal rocks into the mantle. To study CPO development, we converted a natural sample of flint to stishovite in a laser heated diamond anvil cell and compressed the stishovite aggregate up to 38 GPa. We collected diffraction patterns in radial geometry to examine in situ development of crystallographic preferred orientation and find that (001) poles preferentially align with the compression direction. Viscoplastic self-consistent modeling suggests the most likely slip systems at high pressure and ambient temperature are pyramidal and basal slip.
Using the deformable mirror as a spatial filter: application to circular beams.
Tyson, R K
1982-03-01
Adaptive optics correction of a wave front by a deformable mirror that acts as a lossless spatial filter is studied. The decomposition of the wave front into Zernike polynomials provides a means for deriving the rms error of a corrected wave front in analytic form. The spatial filter is given in a functional form related to deformable mirror characteristics. A step filter approximation is derived and the conditions where the approximation holds are examined. An example is provided to demonstrate the utility of the spatial filtering concept for adaptive optics systems analysis.
Clusterization and quadrupole deformation in nuclei
Cseh, J.; Algora, A.; Antonenko, N. V.; Jolos, R. V.; Scheid, W.; Darai, J.; Hess, P. O.
2006-04-26
We study the interrelation of the clusterization and quadrupole deformation of atomic nuclei, by applying cluster models. Both the energetic stability and the exclusion principle is investigated. Special attention is paid to the relative orientations of deformed clusters.
Deformed special relativity and deformed symmetries in a canonical framework
Ghosh, Subir; Pal, Probir
2007-05-15
In this paper we have studied the nature of kinematical and dynamical laws in {kappa}-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of {kappa}-Minkowski phase space algebra that yields the {kappa}-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative {kappa}-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not {kappa}-Minkowski) phase space algebra and special relativity Lorentz transformation (and not {kappa}-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical {kappa}-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the {kappa}-particle.
Lesuer, D R; Syn, C K; Sherby, O D
2004-07-06
The mechanical response of a pearlitic UHCS-1.3C steel deformed at approximately 4000 s{sup -1} to large strains ({var_epsilon} = -0.9) has been studied. Failure, at both the macroscopic and the microscopic levels has been evaluated, and the ability of the material to absorb energy in compression has been examined. Failure occurred by the development of a shear band. However before failure, extensive buckling of the carbide plates was observed and the UHCS-1.3C material exhibited significant potential for compressive ductility and energy absorption due to the distributed buckling of these plates. Strain localization during adiabatic shear band development resulted in the formation of austenite. Subsequent cooling produced a divorced-eutectoid transformation with associated deformation, which resulted in a microstructure consisting of 50 to 100 nm sized grains. The stress-strain behavior within the shear band has also been determined. The results are used to critically evaluate the maximum shear stress criterion of shear band development. New criteria for the development of shear bands are developed based on a strain energy concept.
APPROXIMATING LIGHT RAYS IN THE SCHWARZSCHILD FIELD
Semerák, O.
2015-02-10
A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various ''low-order competitors'', namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise.
Approximate Bruechner orbitals in electron propagator calculations
Ortiz, J.V.
1999-12-01
Orbitals and ground-state correlation amplitudes from the so-called Brueckner doubles approximation of coupled-cluster theory provide a useful reference state for electron propagator calculations. An operator manifold with hold, particle, two-hole-one-particle and two-particle-one-hole components is chosen. The resulting approximation, third-order algebraic diagrammatic construction [2ph-TDA, ADC (3)] and 3+ methods. The enhanced versatility of this approximation is demonstrated through calculations on valence ionization energies, core ionization energies, electron detachment energies of anions, and on a molecule with partial biradical character, ozone.
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A method for space frame synthesis based on the application of a full gamut of approximation concepts is presented. It is found that with the thoughtful selection of design space, objective function approximation, constraint approximation and mathematical programming problem formulation options it is possible to obtain near minimum mass designs for a significant class of space frame structural systems while requiring fewer than 10 structural analyses. Example problems are presented which demonstrate the effectiveness of the method for frame structures subjected to multiple static loading conditions with limits on structural stiffness and strength.
Information geometry of mean-field approximation.
Tanaka, T
2000-08-01
I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
Deformation of noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
Variational approach and deformed derivatives
NASA Astrophysics Data System (ADS)
Weberszpil, J.; Helayël-Neto, J. A.
2016-05-01
Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler-Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved Noether current is worked out.
A Survey of Techniques for Approximate Computing
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less
Approximate probability distributions of the master equation.
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
AN APPROXIMATE EQUATION OF STATE OF SOLIDS.
research. By generalizing experimental data and obtaining unified relations describing the thermodynamic properties of solids, and approximate equation of state is derived which can be applied to a wide class of materials. (Author)
Approximation concepts for efficient structural synthesis
NASA Technical Reports Server (NTRS)
Schmit, L. A., Jr.; Miura, H.
1976-01-01
It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.
Approximation methods in gravitational-radiation theory
NASA Astrophysics Data System (ADS)
Will, C. M.
1986-02-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913+16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
A Survey of Techniques for Approximate Computing
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is to provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Computational aspects of pseudospectral Laguerre approximations
NASA Technical Reports Server (NTRS)
Funaro, Daniele
1989-01-01
Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena.
Finite element modeling of the deformation of magnetoelastic film
Barham, Matthew I.; White, Daniel A.; Steigmann, David J.
2010-09-01
Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a magnetoelastic polymer, has been developed. This engineered material is formed into a thin film using spin casting. An applied magnetic field will deform the film. The magnetic deformation of this film has many possible applications, particularly in microfluidic pumps and pressure regulators. In this paper a finite element method suitable for the transient simulation of arbitrarily shaped three-dimensional magnetoelastic polymers subjected to time-varying magnetic fields is developed. The approach is similar to that employed in finite elment magnetohydrodynamic simulations, the key difference is a more complex hyperelastic material model. In order to confirm the validity of the approach, finite element solutions for an axially symmetric thin film are compared to an analytical solution based on the membrane (infinitely thin) approximation. For this particular problem the two approaches give qualitatively similar results and converge as the film thickness approaches zero.
Investigation of Optimal Digital Image Correlation Patterns for Deformation Measurement
NASA Technical Reports Server (NTRS)
Bomarito, G. F.; Ruggles, T. J.; Hochhalter, J. D.; Cannon, A. H.
2016-01-01
Digital image correlation (DIC) relies on the surface texture of a specimen to measure deformation. When the specimen itself has little or no texture, a pattern is applied to the surface which deforms with the specimen and acts as an artificial surface texture. Because the applied pattern has an effect on the accuracy of DIC, an ideal pattern is sought for which the error introduced into DIC measurements is minimal. In this work, a study is performed in which several DIC pattern quality metrics from the literature are correlated to DIC measurement error. The resulting correlations give insight on the optimality of DIC patterns in general. Optimizations are then performed to produce patterns which are well suited for DIC. These patterns are tested to show their relative benefits. Chief among these benefits are a reduction in error of approximately 30 with respect to a randomly generated pattern.
Deformation processes in forging ceramics
NASA Technical Reports Server (NTRS)
Cannon, R. M.; Rhodes, W. H.
1972-01-01
The deformation processes involved in the forging of refractory ceramic oxides were investigated. A combination of mechanical testing and forging are utilized to investigate both the flow and fracture processes involved. An additional hemisphere forging was done which failed prematurely. Analysis and comparison with available fracture data for AL2O3 indicated possible causes of the failure. Examination of previous forgings indicated an increase in grain boundary cavitation with increasing strain.
The closure approximation in the hierarchy equations.
NASA Technical Reports Server (NTRS)
Adomian, G.
1971-01-01
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.
Approximate String Matching with Reduced Alphabet
NASA Astrophysics Data System (ADS)
Salmela, Leena; Tarhio, Jorma
We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate Boyer-Moore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster than earlier algorithms for English data with small values of k.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-04-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Computing functions by approximating the input
NASA Astrophysics Data System (ADS)
Goldberg, Mayer
2012-12-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their output. Our approach assumes only the most rudimentary knowledge of algebra and trigonometry, and makes no use of calculus.
Graviton resonances on deformed branes
NASA Astrophysics Data System (ADS)
Cruz, W. T.; Gomes, A. R.; Almeida, C. A. S.
2011-11-01
Plane-wave solutions of Schrödinger-like equations obtained from the metric perturbations in 5D braneworld scenarios can present resonant modes. The search for those structures is important because they can provide us with massive modes with not suppressed couplings with the membrane. We propose in this paper the study of graviton Kaluza-Klein spectrum in a special kind of membrane that possesses internal structure. The interest in the study of these deformed defects is due to the fact that they have a richer internal structure that has implications in the matter energy density along the extra dimensions and this produces a space-time background whose curvature has a splitting, if compared to the usual kink-like models. Such models arise from (4, 1)-branes constructed with one scalar field coupled with gravity where we find two-kink solutions from deformations of a phi4 potential. The main objective of this work is to observe the effects of deformation process in the resonant modes as well as in the coupling between the graviton massive modes and the brane.
An improved proximity force approximation for electrostatics
Fosco, Cesar D.; Lombardo, Fernando C.; Mazzitelli, Francisco D.
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
NASA Astrophysics Data System (ADS)
Titus, Sarah J.
The San Andreas fault system is a transpressional plate boundary characterized by sub-parallel dextral strike-slip faults separating internally deformed crustal blocks in central California. Both geodetic and geologic tools were used to understand the short- and long-term partitioning of deformation in both the crust and the lithospheric mantle across the plate boundary system. GPS data indicate that the short-term discrete deformation rate is ˜28 mm/yr for the central creeping segment of the San Andreas fault and increases to 33 mm/yr at +/-35 km from the fault. This gradient in deformation rates is interpreted to reflect elastic locking of the creeping segment at depth, distributed off-fault deformation, or some combination of these two mechanisms. These short-term fault-parallel deformation rates are slower than the expected geologic slip rate and the relative plate motion rate. Structural analysis of folds and transpressional kinematic modeling were used to quantify long-term distributed deformation adjacent to the Rinconada fault. Folding accommodates approximately 5 km of wrench deformation, which translates to a deformation rate of ˜1 mm/yr since the start of the Pliocene. Integration with discrete offset on the Rinconada fault indicates that this portion of the San Andreas fault system is approximately 80% strike-slip partitioned. This kinematic fold model can be applied to the entire San Andreas fault system and may explain some of the across-fault gradient in deformation rates recorded by the geodetic data. Petrologic examination of mantle xenoliths from the Coyote Lake basalt near the Calaveras fault was used to link crustal plate boundary deformation at the surface with models for the accommodation of deformation in the lithospheric mantle. Seismic anisotropy calculations based on xenolith petrofabrics suggest that an anisotropic mantle layer thickness of 35-85 km is required to explain the observed shear wave splitting delay times in central
NASA Technical Reports Server (NTRS)
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Validity of the thin viscous sheet approximation in models of continental collision
NASA Astrophysics Data System (ADS)
Garthwaite, Matthew C.; Houseman, Gregory A.
2011-02-01
The two-dimensional thin viscous sheet approximation is widely used to describe large-scale continental deformation. It treats the lithosphere as a fluid layer in which deformation results from a balance between buoyancy forces and tectonic boundary conditions. Comparisons between two-dimensional thin sheet and full three-dimensional solutions of a simple indenter model show that appreciable differences exist, especially when the indenter half width, D, is of the same order as the thickness of the deforming layer, L (i.e., D/L ≈ 1). These differences are amplified by increasing the power law exponent of the viscous constitutive law (n) but decrease as the Argand number (Ar) is increased. The greatest differences between two-dimensional and three-dimensional solutions are found at the indenter corner, where the thin sheet consistently overestimates vertical strain rates. Differences between strain rates at the corner may be 50% or greater for small Argand numbers. Other differences arise because a lithospheric root zone is formed in the three-dimensional solutions and vertically averaged strain rate is decreased in regions close to the indenter. This effect is absent from thin sheet calculations since the thickness of the load-bearing layer is assumed constant. In general, the thin viscous sheet approximation provides a reasonably accurate estimate of long wavelength deformation for D/L as low as 1 if n is less than ˜3. However, even at large D/L the solutions may be inaccurate close to strain rate concentrations at the indenter corners where horizontal gradients of deformation are large.
Integrable Deformations of T -Dual σ Models
NASA Astrophysics Data System (ADS)
Borsato, Riccardo; Wulff, Linus
2016-12-01
We present a method to deform (generically non-Abelian) T duals of two-dimensional σ models, which preserves classical integrability. The deformed models are identified by a linear operator ω on the dualized subalgebra, which satisfies the 2-cocycle condition. We prove that the so-called homogeneous Yang-Baxter deformations are equivalent, via a field redefinition, to our deformed models when ω is invertible. We explain the details for deformations of T duals of principal chiral models, and present the corresponding generalization to the case of supercoset models.
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2011-09-01
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Occurrence of oral deformities in larval anurans
Drake, D.L.; Altig, R.; Grace, J.B.; Walls, S.C.
2007-01-01
We quantified deformities in the marginal papillae, tooth rows, and jaw sheaths of tadpoles from 13 population samples representing three families and 11 sites in the southeastern United States. Oral deformities were observed in all samples and in 13.5-98% of the specimens per sample. Batrachochytrium dendrobatidis (chytrid) infections were detected in three samples. There was high variability among samples in the pattern and number of discovered deformities. Pairwise associations between oral structures containing deformities were nonrandom for several populations, especially those with B. dendrobatidis infections or high total numbers of deformities. Comparisons of deformities among samples using multivariate analyses revealed that tadpole samples grouped together by family. Analyses of ordination indicated that three variables, the number of deformities, the number of significant associations among deformity types within populations, and whether populations were infected with B. dendrobatidis, were significantly correlated with the pattern of deformities. Our data indicate that the incidence of oral deformities can be high in natural populations and that phylogeny and B. dendrobatidis infection exert a strong influence on the occurrence and type of oral deformities in tadpoles. ?? by the American Society of Ichthyologists and Herperologists.
Mesh deformation based on artificial neural networks
NASA Astrophysics Data System (ADS)
Stadler, Domen; Kosel, Franc; Čelič, Damjan; Lipej, Andrej
2011-09-01
In the article a new mesh deformation algorithm based on artificial neural networks is introduced. This method is a point-to-point method, meaning that it does not use connectivity information for calculation of the mesh deformation. Two already known point-to-point methods, based on interpolation techniques, are also presented. In contrast to the two known interpolation methods, the new method does not require a summation over all boundary nodes for one displacement calculation. The consequence of this fact is a shorter computational time of mesh deformation, which is proven by different deformation tests. The quality of the deformed meshes with all three deformation methods was also compared. Finally, the generated and the deformed three-dimensional meshes were used in the computational fluid dynamics numerical analysis of a Francis water turbine. A comparison of the analysis results was made to prove the applicability of the new method in every day computation.
Helium release during shale deformation: Experimental validation
NASA Astrophysics Data System (ADS)
Bauer, Stephen J.; Gardner, W. Payton; Heath, Jason E.
2016-07-01
This work describes initial experimental results of helium tracer release monitoring during deformation of shale. Naturally occurring radiogenic 4He is present in high concentration in most shales. During rock deformation, accumulated helium could be released as fractures are created and new transport pathways are created. We present the results of an experimental study in which confined reservoir shale samples, cored parallel and perpendicular to bedding, which were initially saturated with helium to simulate reservoir conditions, are subjected to triaxial compressive deformation. During the deformation experiment, differential stress, axial, and radial strains are systematically tracked. Release of helium is dynamically measured using a helium mass spectrometer leak detector. Helium released during deformation is observable at the laboratory scale and the release is tightly coupled to the shale deformation. These first measurements of dynamic helium release from rocks undergoing deformation show that helium provides information on the evolution of microstructure as a function of changes in stress and strain.
On improvements of Double Beta Decay using FQTDA Model
NASA Astrophysics Data System (ADS)
de Oliveira, L.; Samana, A. R.; Krmpotic, F.; Mariano, A. E.; Barbero, C. A.
2015-07-01
The Quasiparticle Tamm-Dancoff Approximation (QTDA) is applied to describe the nuclear double beta decay with two neutrinos. Several serious inconveniences found in the Quasiparticle Random Phase Approximation (QRPA) are not present in the QTDA, as such as the ambiguity in treating the intermediary states, and further approximations necessary for evaluation of the nuclear matrix elements (NMEs) or, the extreme sensitivity of NME with the ratio between the pn and pp + nn pairings. Some years ago, the decay 48Ca → 48Ti was discussed within the particle-hole limit of QTDA. We found some mismatch in the numerical calculations when the full QTDA was being implemented, and a new performance in the particle-hole limit of QTDA is required to guarantee the fidelity of the approximation.
Geometrical study of the deformations of a thin spherical shell inspired by pollen grains.
NASA Astrophysics Data System (ADS)
Couturier, Etienne; Katifori, Eleni; Dumais, Jacques; Cerda, Enrique
2013-03-01
Various monocotyledon pollen grains have a geometric design. They are constituted by a stiff thin shell with an n-fold rotationally symmetric softer sector. The mechanic response of these inhomogeneous shells can be approximated as an open shell. Isometric modes are known to be energetically favorable for thin shells when they are possible. Although the literature for the complete sphere, for which these modes are impossible, is extensive, analyses of the deformation of open shells whose isometric deformations are not inhibited, are much more scarce. We focus on the isometric deformation of spheres with n-fold rotationally symmetric openings. The isometric deformation means that the surface remains a constant gaussian curvature surface. Using differential geometry, we obtained an integrable family of surfaces whose gaussian curvature remains approximatively constant. We performed both simulations by tethered mesh methods and experiments with cut ping-pong balls. We observe that first the shell surface deforms without any stretching and is very well described as a part of an approximative constant gaussian curvature surface whose singularities remain outside the shell surface and get closer to the shell surface as the load increases.
On uniform approximation of elliptic functions by Padé approximants
NASA Astrophysics Data System (ADS)
Khristoforov, Denis V.
2009-06-01
Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.
Time dependent deformation of Kilauea Volcano, Hawaii
NASA Astrophysics Data System (ADS)
Montgomery-Brown, Emily Kvietka Desmarais
In 1997 the continuous Global Positioning System (GPS) network was completed on Kilauea, providing the first network of daily position measurements during eruptions and earthquakes on Kilauea. Kilauea has been studied for many decades with continuous seismic and tilt instruments. Other geodetic data (e.g., campaign GPS, leveling, electronic distance measurements) are also available although they contain only sparse data. Data analysis methods used here include inverting multiple data sets for optimal source parameters and the spatio-temporal distribution of magma volume and fault slip, and combining GPS and seismic observations to understand flank tectonics. The field area for this study, Kilauea Volcano, was chosen because of its frequent activity and potential hazards. The 1997 East Rift Zone eruption (Episode 54) was the first major event to occur after the completion of the continuous GPS network. The event lasted 2 days, but transient deformation continued for six months. This long-duration transient allowed the first spatio-temporal study of transient dike deformation on Kilauea from daily GPS positions. Slow-slip events were discovered on Kilauea during which the southern flank of the volcano would accelerate seaward for approximately 2 days. The discovery was made possible because of the continuously operating GPS network. These slip events were also observed to correlate with small swarms of microearthquakes found to follow temporal pattern consistent with them being co- and aftershocks of the slow-slip event (Segall, 2006). Half-space models of geodetic data favor a shallow fault plane (˜ 5 km), which is much too shallow to have increased the Coulomb stress at the depths of the co- and aftershocks. However, optimizations for the slow-slip source parameters including a layered elastic structure and a topographic correction favor deeper models within the range of the co- and aftershocks. Additionally, the spatial distribution of seaward fault slip, fixed
Estimation of distribution algorithms with Kikuchi approximations.
Santana, Roberto
2005-01-01
The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables.
Approximation of Bivariate Functions via Smooth Extensions
Zhang, Zhihua
2014-01-01
For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316
Using surface deformation to image reservoir dynamics
Vasco, D.W.; Karasaki, K.; Doughty, C.
2000-02-01
The inversion of surface deformation data such as tilt, displacement, or strain provides a noninvasive method for monitoring subsurface volume change. Reservoir volume change is related directly to processes such as pressure variations induced by injection and withdrawal. The inversion procedure is illustrated by an application to tiltmeter data from the Hijiori test site in Japan. An inversion of surface tilt data allows one to image flow processes in a fractured granodiorite. Approximately 650 barrels of water, injected 2 km below the surface, produces a peak surface tilt of the order of 0.8 microradians. The authors find that the pattern of volume change in the granodiorite is very asymmetrical, elongated in a north-northwesterly direction, and the maximum volume change is offset by more than 0.7 km to the east of the pumping well. The inversion of a suite of leveling data from the Wilmington oil field in Long Beach, California, images large-scale reservoir volume changes in 12 one- to two-year increments from 1976 to 1996. The influence of various production strategies is seen in the reservoir volume changes. In particular, a steam flood in fault block 2 in the northwest portion of the field produced a sudden decrease in reservoir volume.
Crustal deformation in great California earthquake cycles
NASA Technical Reports Server (NTRS)
Li, Victor C.; Rice, James R.
1986-01-01
Periodic crustal deformation associated with repeated strike slip earthquakes is computed for the following model: A depth L (less than or similiar to H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity V sub pl after each lapse of earthquake cycle time T sub cy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep seated mantle motions, compatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. It is argued that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress build up throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone.
Causal Poisson bracket via deformation quantization
NASA Astrophysics Data System (ADS)
Berra-Montiel, Jasel; Molgado, Alberto; Palacios-García, César D.
2016-06-01
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through an appropriate causal Green’s functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls-DeWitt bracket that has been analyzed in the multisymplectic context. Once our star-product is defined, we are able to apply the Wigner-Weyl map in order to introduce a generalized version of Wick’s theorem. Finally, we include some examples to explicitly test our method: the real scalar field, the bosonic string and a physically motivated nonlinear particle model. For the field theoretic models, we have encountered causal generalizations of the creation/annihilation relations, and also a causal generalization of the Virasoro algebra for the bosonic string. For the nonlinear particle case, we use the approximate solution in terms of the Green’s function, in order to construct a well-behaved causal bracket.
Ancilla-approximable quantum state transformations
Blass, Andreas; Gurevich, Yuri
2015-04-15
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.
Fast wavelet based sparse approximate inverse preconditioner
Wan, W.L.
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
The Cell Cycle Switch Computes Approximate Majority
NASA Astrophysics Data System (ADS)
Cardelli, Luca; Csikász-Nagy, Attila
2012-09-01
Both computational and biological systems have to make decisions about switching from one state to another. The `Approximate Majority' computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.
Separable approximations of two-body interactions
NASA Astrophysics Data System (ADS)
Haidenbauer, J.; Plessas, W.
1983-01-01
We perform a critical discussion of the efficiency of the Ernst-Shakin-Thaler method for a separable approximation of arbitrary two-body interactions by a careful examination of separable 3S1-3D1 N-N potentials that were constructed via this method by Pieper. Not only the on-shell properties of these potentials are considered, but also a comparison is made of their off-shell characteristics relative to the Reid soft-core potential. We point out a peculiarity in Pieper's application of the Ernst-Shakin-Thaler method, which leads to a resonant-like behavior of his potential 3SD1D. It is indicated where care has to be taken in order to circumvent drawbacks inherent in the Ernst-Shakin-Thaler separable approximation scheme. NUCLEAR REACTIONS Critical discussion of the Ernst-Shakin-Thaler separable approximation method. Pieper's separable N-N potentials examined on shell and off shell.
Eight-moment approximation solar wind models
NASA Technical Reports Server (NTRS)
Olsen, Espen Lyngdal; Leer, Egil
1995-01-01
Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.
Approximate solutions of the hyperbolic Kepler equation
NASA Astrophysics Data System (ADS)
Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge
2015-12-01
We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,∞ ). We prove, by using Smale's α -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S( g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then |S_n-S|≤ 0.5^{2^n-1}|widetilde{S}-S|. The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,∞ ) that exclude a small neighborhood of g=1, L=0, we also provide a method to construct simpler starters involving only constants.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Appraisal of transport and deformation in shale reservoirs using natural noble gas tracers
Heath, Jason E.; Kuhlman, Kristopher L.; Robinson, David G.; Bauer, Stephen J.; Gardner, William Payton
2015-09-01
This report presents efforts to develop the use of in situ naturally-occurring noble gas tracers to evaluate transport mechanisms and deformation in shale hydrocarbon reservoirs. Noble gases are promising as shale reservoir diagnostic tools due to their sensitivity of transport to: shale pore structure; phase partitioning between groundwater, liquid, and gaseous hydrocarbons; and deformation from hydraulic fracturing. Approximately 1.5-year time-series of wellhead fluid samples were collected from two hydraulically-fractured wells. The noble gas compositions and isotopes suggest a strong signature of atmospheric contribution to the noble gases that mix with deep, old reservoir fluids. Complex mixing and transport of fracturing fluid and reservoir fluids occurs during production. Real-time laboratory measurements were performed on triaxially-deforming shale samples to link deformation behavior, transport, and gas tracer signatures. Finally, we present improved methods for production forecasts that borrow statistical strength from production data of nearby wells to reduce uncertainty in the forecasts.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Deformation and recrystallization mechanisms in naturally deformed sillimanites
NASA Astrophysics Data System (ADS)
Lambregts, P. J.; van Roermund, H. L. M.
1990-07-01
Prismatic sillimanite (Al 2SiO 5), with a length between 0.3 and 2.5 mm, was obtained from a garnet migmatite. The sillimanite, naturally deformed at a temperature of 750 ° C and a confining pressure of 6 kbar, has been studied using optical and transmission electron microscopy techniques. Optical and universal stage measurements reveal undulatory extinction, "sharp" deformation-induced subgrain boundaries (subparallel to (001) and (010)) and minor recrystallization. Transmission electron microscopy shows free dislocations, dislocation loops, (110) planar defects and tiltwalls parallel to (001). Dislocations have Burgers vectors of [001] and [100]. All isolated
Leukocyte deformability: finite element modeling of large viscoelastic deformation.
Dong, C; Skalak, R
1992-09-21
An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.
Very fast approximate reconstruction of MR images.
Angelidis, P A
1998-11-01
The ultra fast Fourier transform (UFFT) provides the means for a very fast computation of a magnetic resonance (MR) image, because it is implemented using only additions and no multiplications at all. It achieves this by approximating the complex exponential functions involved in the Fourier transform (FT) sum with computationally simpler periodic functions. This approximation introduces erroneous spectrum peaks of small magnitude. We examine the performance of this transform in some typical MRI signals. The results show that this transform can very quickly provide an MR image. It is proposed to be used as a replacement of the classically used FFT whenever a fast general overview of an image is required.
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Bronchopulmonary segments approximation using anatomical atlas
NASA Astrophysics Data System (ADS)
Busayarat, Sata; Zrimec, Tatjana
2007-03-01
Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters.
Approximate learning algorithm in Boltzmann machines.
Yasuda, Muneki; Tanaka, Kazuyuki
2009-11-01
Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments.
Plastic Deformation of Accreted Planetesimals
NASA Astrophysics Data System (ADS)
Kadish, J.
2005-08-01
The early stages of planetesimal growth follow an accretion model (Weidenschilling, Icarus 2000), which influences the intrinsic strength of a body and may control how its shape evolves after growth. In previous work we have determined the stress field of an accreted planetesimal accounting for possible variation in the object's spin as it accretes (Kadish et al., IJSS In Press) At the end of growth, these objects are subject to transport mechanisms that can distribute them throughout the solar system. As they are transported these objects can be spun-up by tidal forces (Scheeres et al, Icarus 2000), YORP (Bottke et al., Asteroids III 2002), and collisions (Binzel et al., Asteroids II 1989). Such an increase of spin will cause perturbations to the initial stress field and may lead to failure. We are able to show analytically that failure is initiated on the object's surface and a plastic zone propagates inward as the object's spin is increased. If we model an accreted body as a conglomeration of rocks similar to a gravel or sand, the deformation in the region of failure is characterized using a Mohr-Coulomb failure criterion with negligible cohesion and zero hardening(e.g. Holsapple, Icarus 2001). Such a response is highly non-linear and must be solved using finite elements and iterative methods (Simo and Hughes, Computational Inelasticity 1998). Using the commercial finite element code ABAQUS, we present the shape deformation resulting from an elasto-plastic analysis of a spinning, self-gravitating accreted sphere that is spun-up after growth is complete. The methodology can be extended to model plastic deformation due to local failure for more complex planetesimal shapes, such as for the asteroid Kleopatra. This work has implications for the evolution of planetesimal shapes, the creation of binary and contact binary asteroids, and for the maximum spin rate of small planetary bodies.
Approximations in seismic interferometry and their effects on surface waves
NASA Astrophysics Data System (ADS)
Kimman, W. P.; Trampert, J.
2010-07-01
We investigate common approximations and assumptions in seismic interferometry. The interferometric equation, valid for the full elastic wavefield, gives the Green's function between two arbitrary points by cross-correlating signals recorded at each point. The relation is exact, even for complicated lossless media, provided the signals are generated on a closed surface surrounding the two points and are from both unidirectional point-forces and deformation-rate-tensor sources. A necessary approximation to the exact interferometric equation is the use of signals from point-force sources only. Even in simple layered media, the Green's function retrieval can then be imperfect, especially for waves other than fundamental mode surface waves. We show that this is due to cross terms between different modes that occur even if a full source boundary is present. When sources are located at the free surface only, a realistic scenario for ambient noise, the cross terms can overwhelm the higher mode surface waves. Sources then need to be very far away, or organized in a band rather than a surrounding surface to overcome this cross-term problem. If sources are correlated, convergence of higher modes is very hard to achieve. In our examples of simultaneously acting sources, the phase of the higher modes only converges correctly towards the true solution if sources are acting in the stationary phase regions. This offers an explanation for some recent body wave observations, where only interstation paths in-line with the prevailing source direction were considered. The phase error resulting from incomplete distributions around the stationary phase region generally leads to an error smaller than 1 per cent for realistic applications.
Formation Flying and Deformable Instruments
NASA Astrophysics Data System (ADS)
Rio, Yvon
2009-05-01
Astronomers have always attempted to build very stable instruments. They fight all that can cause mechanical deformation or image motion. This has led to well established technologies (autoguide, active optics, thermal control, tip/tilt correction), as well as observing methods based on the use of controlled motion (scanning, micro scanning, shift and add, chopping and nodding). Formation flying disturbs this practice. It is neither possible to reduce the relative motion to very small amplitudes, nor to control it at will. Some impacts on Simbol-X instrument design, and operation are presented.
Formation Flying and Deformable Instruments
Rio, Yvon
2009-05-11
Astronomers have always attempted to build very stable instruments. They fight all that can cause mechanical deformation or image motion. This has led to well established technologies (autoguide, active optics, thermal control, tip/tilt correction), as well as observing methods based on the use of controlled motion (scanning, micro scanning, shift and add, chopping and nodding). Formation flying disturbs this practice. It is neither possible to reduce the relative motion to very small amplitudes, nor to control it at will. Some impacts on Simbol-X instrument design, and operation are presented.
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Deformational characteristics of thermoplastic elastomers
NASA Astrophysics Data System (ADS)
Indukuri, Kishore K.
This thesis focuses primarily on the structure-property relationships of poly (styrene-ethylene-butylene-styrene) triblock copolymer TPEs. First evidence for strain-induced crystallization occurring in certain SEBS block copolymers has been established using unique techniques like deformation calorimetry, combined in-situ small angle X-ray and wide angle X-ray diffraction (SAXD/WAXD). Also the ramifications of such strain-induced crystallization on the mechanical properties like cyclic hysteresis, stress relaxation/creep retention of these SEBS systems have been studied. In addition, the structural changes in the morphology of these systems on deformation have been investigated using combined SAXD/WAXD setup. Small angle X-ray diffraction probed the changes at the nano-scale of polystyrene (PS) cylinders, while wide angle X-ray diffraction probed the changes at molecular length scales of the amorphous/crystalline domains of the elastomeric mid-block in these systems. New structural features at both these length scales have been observed and incorporated into the overall deformation mechanisms of the material. Continuous processing techniques like extrusion have been used to obtain ultra long-range order and orientation in these SEBS systems. Thus well ordered crystal like hexagonal packing of cylinders, where in each element in this hexagonal lattice can be individually addressed without any grain boundaries can be realized using these robust techniques. The effect of long-range order/orientation on the mechanical properties has been studied. In addition, these well ordered systems serve as model systems for evaluating deformation mechanisms of these SEBS systems, where the relative contributions of each of the phases can be estimated. EPDM/i-PP thermoplastic vulcanizates (TPVs) have micron size scale phase separated morphologies of EPDM rubber dispersed in a semicrystalline i-PP matrix as a result of the dynamic vulcanization process. Confocal microscopy studies
Tectonic deformation in southern California
NASA Technical Reports Server (NTRS)
Jackson, David D.
1993-01-01
Our objectives were to use modem geodetic data, especially those derived from space techniques like Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), and the Global Positioning System (GPS) to infer crustal deformation in southern California and relate it to plate tectonics and earthquake hazard. To do this, we needed to collect some original data, write computer programs to determine positions of survey markers from geodetic observables, interpret time dependent positions in terms of velocity and earthquake caused episodic displacements, and construct a model to explain these velocities and displacements in terms of fault slip and plate movements.
Deformable Mirrors Correct Optical Distortions
NASA Technical Reports Server (NTRS)
2010-01-01
By combining the high sensitivity of space telescopes with revolutionary imaging technologies consisting primarily of adaptive optics, the Terrestrial Planet Finder is slated to have imaging power 100 times greater than the Hubble Space Telescope. To this end, Boston Micromachines Corporation, of Cambridge, Massachusetts, received Small Business Innovation Research (SBIR) contracts from the Jet Propulsion Laboratory for space-based adaptive optical technology. The work resulted in a microelectromechanical systems (MEMS) deformable mirror (DM) called the Kilo-DM. The company now offers a full line of MEMS DMs, which are being used in observatories across the world, in laser communication, and microscopy.
Practical solution of plastic deformation problems in elastic-plastic range
NASA Technical Reports Server (NTRS)
Mendelson, A; Manson, S
1957-01-01
A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.
A two-dimensional deformable phantom for quantitatively verifying deformation algorithms
Kirby, Neil; Chuang, Cynthia; Pouliot, Jean
2011-08-15
Purpose: The incorporation of deformable image registration into the treatment planning process is rapidly advancing. For this reason, the methods used to verify the underlying deformation algorithms must evolve equally fast. This manuscript proposes a two-dimensional deformable phantom, which can objectively verify the accuracy of deformation algorithms, as the next step for improving these techniques. Methods: The phantom represents a single plane of the anatomy for a head and neck patient. Inflation of a balloon catheter inside the phantom simulates tumor growth. CT and camera images of the phantom are acquired before and after its deformation. Nonradiopaque markers reside on the surface of the deformable anatomy and are visible through an acrylic plate, which enables an optical camera to measure their positions; thus, establishing the ground-truth deformation. This measured deformation is directly compared to the predictions of deformation algorithms, using several similarity metrics. The ratio of the number of points with more than a 3 mm deformation error over the number that are deformed by more than 3 mm is used for an error metric to evaluate algorithm accuracy. Results: An optical method of characterizing deformation has been successfully demonstrated. For the tests of this method, the balloon catheter deforms 32 out of the 54 surface markers by more than 3 mm. Different deformation errors result from the different similarity metrics. The most accurate deformation predictions had an error of 75%. Conclusions: The results presented here demonstrate the utility of the phantom for objectively verifying deformation algorithms and determining which is the most accurate. They also indicate that the phantom would benefit from more electron density heterogeneity. The reduction of the deformable anatomy to a two-dimensional system allows for the use of nonradiopaque markers, which do not influence deformation algorithms. This is the fundamental advantage of this
Approximate model for laser ablation of carbon
NASA Astrophysics Data System (ADS)
Shusser, Michael
2010-08-01
The paper presents an approximate kinetic theory model of ablation of carbon by a nanosecond laser pulse. The model approximates the process as sublimation and combines conduction heat transfer in the target with the gas dynamics of the ablated plume which are coupled through the boundary conditions at the interface. The ablated mass flux and the temperature of the ablating material are obtained from the assumption that the ablation rate is restricted by the kinetic theory limitation on the maximum mass flux that can be attained in a phase-change process. To account for non-uniform distribution of the laser intensity while keeping the calculation simple the quasi-one-dimensional approximation is used in both gas and solid phases. The results are compared with the predictions of the exact axisymmetric model that uses the conservation relations at the interface derived from the momentum solution of the Boltzmann equation for arbitrary strong evaporation. It is seen that the simpler approximate model provides good accuracy.
Large Hierarchies from Approximate R Symmetries
Kappl, Rolf; Ratz, Michael; Schmidt-Hoberg, Kai; Nilles, Hans Peter; Ramos-Sanchez, Saul; Vaudrevange, Patrick K. S.
2009-03-27
We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales.
Approximating a nonlinear MTFDE from physiology
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-12-01
This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.
Padé approximations and diophantine geometry
Chudnovsky, D. V.; Chudnovsky, G. V.
1985-01-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552
Block Addressing Indices for Approximate Text Retrieval.
ERIC Educational Resources Information Center
Baeza-Yates, Ricardo; Navarro, Gonzalo
2000-01-01
Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW)
Approximations of Two-Attribute Utility Functions
1976-09-01
Introduction to Approximation Theory, McGraw-Hill, New York, 1966. Faber, G., Uber die interpolatorische Darstellung stetiger Funktionen, Deutsche...Management Review 14 (1972b) 37-50. Keeney, R. L., A decision analysis with multiple objectives: the Mexico City airport, Bell Journal of Economics
Can Distributional Approximations Give Exact Answers?
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…
Kravchuk functions for the finite oscillator approximation
NASA Technical Reports Server (NTRS)
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
An approximate classical unimolecular reaction rate theory
NASA Astrophysics Data System (ADS)
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Sensing Position With Approximately Constant Contact Force
NASA Technical Reports Server (NTRS)
Sturdevant, Jay
1996-01-01
Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.
Approximate Solution to the Generalized Boussinesq Equation
NASA Astrophysics Data System (ADS)
Telyakovskiy, A. S.; Mortensen, J.
2010-12-01
The traditional Boussinesq equation describes motion of water in groundwater flows. It models unconfined groundwater flow under the Dupuit assumption that the equipotential lines are vertical, making the flowlines horizontal. The Boussinesq equation is a nonlinear diffusion equation with diffusivity depending linearly on water head. Here we analyze a generalization of the Boussinesq equation, when the diffusivity is a power law function of water head. For example polytropic gases moving through porous media obey this equation. Solving this equation usually requires numerical approximations, but for certain classes of initial and boundary conditions an approximate analytical solution can be constructed. This work focuses on the latter approach, using the scaling properties of the equation. We consider one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in case of cylindrical symmetry. Such situation represents the case of an injection well. Solutions would propagate with the finite speed. We construct an approximate scaling function, and we compare the approximate solution with the direct numerical solutions obtained by using the scaling properties of the equations.
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.
Quickly Approximating the Distance Between Two Objects
NASA Technical Reports Server (NTRS)
Hammen, David
2009-01-01
A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions.
Approximation algorithms for planning and control
NASA Technical Reports Server (NTRS)
Boddy, Mark; Dean, Thomas
1989-01-01
A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.
Approximating Confidence Intervals for Factor Loadings.
ERIC Educational Resources Information Center
Lambert, Zarrel V.; And Others
1991-01-01
A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…
Approximated integrability of the Dicke model
NASA Astrophysics Data System (ADS)
Relaño, A.; Bastarrachea-Magnani, M. A.; Lerma-Hernández, S.
2016-12-01
A very approximate second integral of motion of the Dicke model is identified within a broad energy region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born-Oppenheimer approximation, classifies the whole regular part of the spectrum in bands, coming from different semi-classical energy surfaces, and labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree-of-freedom integrable model for a wide range of energies and values of the external parameters.
Local discontinuous Galerkin approximations to Richards’ equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Dawson, C. N.; Miller, C. T.
2007-03-01
We consider the numerical approximation to Richards' equation because of its hydrological significance and intrinsic merit as a nonlinear parabolic model that admits sharp fronts in space and time that pose a special challenge to conventional numerical methods. We combine a robust and established variable order, variable step-size backward difference method for time integration with an evolving spatial discretization approach based upon the local discontinuous Galerkin (LDG) method. We formulate the approximation using a method of lines approach to uncouple the time integration from the spatial discretization. The spatial discretization is formulated as a set of four differential algebraic equations, which includes a mass conservation constraint. We demonstrate how this system of equations can be reduced to the solution of a single coupled unknown in space and time and a series of local constraint equations. We examine a variety of approximations at discontinuous element boundaries, permeability approximations, and numerical quadrature schemes. We demonstrate an optimal rate of convergence for smooth problems, and compare accuracy and efficiency for a wide variety of approaches applied to a set of common test problems. We obtain robust and efficient results that improve upon existing methods, and we recommend a future path that should yield significant additional improvements.
Fostering Formal Commutativity Knowledge with Approximate Arithmetic
Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert
2015-01-01
How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311
Multidimensional stochastic approximation using locally contractive functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Approximating the efficiency characteristics of blade pumps
NASA Astrophysics Data System (ADS)
Shekun, G. D.
2007-11-01
Results from a statistical investigation into the experimental efficiency characteristics of commercial type SD centrifugal pumps and type SDS swirl flow pumps are presented. An exponential function for approximating the efficiency characteristics of blade pumps is given. The versatile nature of this characteristic is confirmed by the fact that the use of different systems of relative units gives identical results.
Counting independent sets using the Bethe approximation
Chertkov, Michael; Chandrasekaran, V; Gamarmik, D; Shah, D; Sin, J
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Deformation During Friction Stir Welding
NASA Technical Reports Server (NTRS)
White, Henry J.
2002-01-01
Friction Stir Welding (FSW) is a solid state welding process that exhibits characteristics similar to traditional metal cutting processes. The plastic deformation that occurs during friction stir welding is due to the superposition of three flow fields: a primary rotation of a radially symmetric solid plug of metal surrounding the pin tool, a secondary uniform translation, and a tertiary ring vortex flow (smoke rings) surrounding the tool. If the metal sticks to the tool, the plug surface extends down into the metal from the outer edge of the tool shoulder, decreases in diameter like a funnel, and closes up beneath the pin. Since its invention, ten years have gone by and still very little is known about the physics of the friction stir welding process. In this experiment, an H13 steel weld tool (shoulder diameter, 0.797 in; pin diameter, 0.312 in; and pin length, 0.2506 in) was used to weld three 0.255 in thick plates. The deformation behavior during friction stir welding was investigated by metallographically preparing a plan view sections of the weldment and taking Vickers hardness test in the key-hole region.
Thermocapillary motion of deformable drops
NASA Astrophysics Data System (ADS)
Haj-Hariri, Hossein; Shi, Qingping; Borhan, Ali
1994-08-01
The thermocapillary motion of initially spherical drops/bubbles driven by a constant temperature gradient in an unbounded liquid medium is simulated numerically. Effects of convection of momentum and energy, as well as shape deformations, are addressed. The method used is based on interface tracking on a base cartesian grid, and uses a smeared color or indicator function for the determination of the surface topology. Quad-tree adaptive refinement of the cartesian grid is implemented to enhance the fidelity of the surface tracking. It is shown that convection of energy results in a slowing of the drop, as the isotherms get wrapped around the front of the drop. Shape deformation resulting from inertial effects affect the migration velocity. The physical results obtained are in agreement with the existing literature. Furthermore, remarks are made on the sensitivity of the calculated solutions to the smearing of the fluid properties. Analysis and simulations show that the migration velocity depends very strongly on the smearing of the interfacial force whereas it is rather insensitive to the smearing of other properties, hence the adaptive grid.
Deformable human body model development
Wray, W.O.; Aida, T.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). A Deformable Human Body Model (DHBM) capable of simulating a wide variety of deformation interactions between man and his environment has been developed. The model was intended to have applications in automobile safety analysis, soldier survivability studies and assistive technology development for the disabled. To date, we have demonstrated the utility of the DHBM in automobile safety analysis and are currently engaged in discussions with the U.S. military involving two additional applications. More specifically, the DHBM has been incorporated into a Virtual Safety Lab (VSL) for automobile design under contract to General Motors Corporation. Furthermore, we have won $1.8M in funding from the U.S. Army Medical Research and Material Command for development of a noninvasive intracranial pressure measurement system. The proposed research makes use of the detailed head model that is a component of the DHBM; the project duration is three years. In addition, we have been contacted by the Air Force Armstrong Aerospace Medical Research Laboratory concerning possible use of the DHBM in analyzing the loads and injury potential to pilots upon ejection from military aircraft. Current discussions with Armstrong involve possible LANL participation in a comparison between DHBM and the Air Force Articulated Total Body (ATB) model that is the current military standard.
Deformation parameters influencing prepreg tack
Ahn, K.J.; Seferis, J.C. ); Pelton, T.; Wilhelm, M. )
1992-01-01
A compression to tension apparatus and a methodology capable of measuring prepreg tack have been analyzed in detail in order to establish fundamental material and operating characteristics. Both intrinsic and extrinsic parameters influencing prepreg tack were identified and analyzed using commercially available carbon fiber/epoxy prepregs and mechanical testing equipment. Two different factors, (1) contact (or wetting) area of adjacent prepreg plies and (2) viscoelastic properties of the prepreg, were found to control prepreg tack. At low temperatures, contact area was the main deformation controlling step, while at high temperatures, the viscoelastic property of the prepreg was found to be dominant. Both interlaminar and intralaminar deformations were observed depending on the prepreg systems examined as well as the operating conditions of the test. In addition, hold time, hold pressure, loading rate, resin content, and out-time were also found to affect prepreg tack. Energy of separation, which may be viewed as a descriptor of prepreg tack, was observed to increase with increasing hold time, hold pressure, and loading rate. Energy of separation also showed a maximum value at a specific resin content for a specific prepreg system, while it decreased with increasing prepreg out-time due to prepreg surface characteristic change rather than bulk physical aging. Conclusively, it was observed that prepreg tack must be viewed as an extrinsic, bulk, but surface-sensitive, viscoelastic property which depends on material as well as operating conditions.
Protein transfer to membranes upon shape deformation
NASA Astrophysics Data System (ADS)
Sagis, L. M. C.; Bijl, E.; Antono, L.; de Ruijter, N. C. A.; van Valenberg, H.
2013-05-01
Red blood cells, milk fat droplets, or liposomes all have interfaces consisting of lipid membranes. These particles show significant shape deformations as a result of flow. Here we show that these shape deformations can induce adsorption of proteins to the membrane. Red blood cell deformability is an important factor in several diseases involving obstructions of the microcirculatory system, and deformation induced protein adsorption will alter the rigidity of their membranes. Deformation induced protein transfer will also affect adsorption of cells onto implant surfaces, and the performance of liposome based controlled release systems. Quantitative models describing this phenomenon in biomaterials do not exist. Using a simple quantitative model, we provide new insight in this phenomenon. We present data that show convincingly that for cells or droplets with diameters upwards of a few micrometers, shape deformations induce adsorption of proteins at their interface even at moderate flow rates.
Deformable mirrors development program at ESO
NASA Astrophysics Data System (ADS)
Stroebele, Stefan; Vernet, Elise; Brinkmann, Martin; Jakob, Gerd; Lilley, Paul; Casali, Mark; Madec, Pierre-Yves; Kasper, Markus
2016-07-01
Over the last decade, adaptive optics has become essential in different fields of research including medicine and industrial applications. With this new need, the market of deformable mirrors has expanded a lot allowing new technologies and actuation principles to be developed. Several E-ELT instruments have identified the need for post focal deformable mirrors but with the increasing size of the telescopes the requirements on the deformable mirrors become more demanding. A simple scaling up of existing technologies from few hundred actuators to thousands of actuators will not be sufficient to satisfy the future needs of ESO. To bridge the gap between available deformable mirrors and the future needs for the E-ELT, ESO started a development program for deformable mirror technologies. The requirements and the path to get the deformable mirrors for post focal adaptive optics systems for the E-ELT is presented.
Plastic deformation mechanisms in SiC-whisker-reinforced alumina
Arellano-Lopez, A.R. de; Dominguez-Rodriguez, A. )
1993-06-01
SiC-whisker-reinforced Al[sub 2]O[sub 3] samples (SiC[sub w]/Al[sub 2]O[sub 3]), obtained from three different manufacturers, containing 0-30 vol% SiC have been crept under compression at 1,400 C in flowing argon. Compressive creep tests and microstructural observations have been used to characterize the plastic deformation mechanisms. The presence of whiskers decreased the creep rate by reducing grain-boundary sliding. Damage formation was increased, however, because the whiskers acted as stress concentration sites. For specimens with whisker loadings greater than 15%, the absolute creep rate was not strongly dependent on whisker concentration, and the formation of cavitation damage was negligible below a critical stress that depended on the fabrication procedure of the specimen. This creep regime was characterized by a stress exponent of approximately 1, in which deformation occurred primarily by diffusional flow. For the materials with less SiC, the deformation occurred primarily by grain boundary sliding.
Nuclear ground-state masses and deformations: FRDM(2012)
Moller, P.; Sierk, A. J.; Ichikawa, T.; Sagawa, H.
2016-03-25
Here, we tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from ^{16}O to A=339. The calculations are based on the finite-range droplet macroscopic and the folded-Yukawa single-particle microscopic nuclear-structure models, which are completely specified. Relative to our FRDM(1992) mass table in Möller et al. (1995), the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensive and more accurate experimental mass data base now available allow us to determine one additional macroscopic-model parameter, the density-symmetry coefficient LL, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some highly deformed shapes occurring in fission, because some effects are derived in terms of perturbations around a sphere, we only adjust its macroscopic parameters to ground-state masses.
Nuclear ground-state masses and deformations: FRDM(2012)
Moller, P.; Sierk, A. J.; Ichikawa, T.; ...
2016-03-25
Here, we tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from 16O to A=339. The calculations are based on the finite-range droplet macroscopic and the folded-Yukawa single-particle microscopic nuclear-structure models, which are completely specified. Relative to our FRDM(1992) mass table in Möller et al. (1995), the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensivemore » and more accurate experimental mass data base now available allow us to determine one additional macroscopic-model parameter, the density-symmetry coefficient LL, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some highly deformed shapes occurring in fission, because some effects are derived in terms of perturbations around a sphere, we only adjust its macroscopic parameters to ground-state masses.« less
Plastic Deformation Modes of CuZr/Cu Multilayers
Cui, Yan; Abad, Oscar Torrents; Wang, Fei; Huang, Ping; Lu, Tian-Jian; Xu, Ke-Wei; Wang, Jian
2016-01-01
We synthesized CuZr/Cu multilayers and performed nanoindentation testing to explore the dependence of plastic deformation modes on the thickness of CuZr layers. The Cu layers were 18 nm thick and the CuZr layers varied in thickness from 4 nm to 100 nm. We observed continuous plastic co-deformation in the 4 nm and 10 nm CuZr − 18 nm Cu multilayers and plastic-induced shear instability in thick CuZr layers (>20 nm). The plastic co-deformation is ascribed to the nucleation and interaction of shear transformation zones in CuZr layers at the adjacent interfaces, while the shear instability is associated with the nucleation and propagation of shear bands in CuZr layers. Shear bands are initialized in the CuZr layers due to the accumulated glide dislocations along CuZr-Cu interfaces, and propagate into adjacent Cu layers via slips on {111} plane non-parallel to the interface. Due to crystallographic constraint of the Cu layers, shear bands are approximately parallel to {111} plane in the Cu layer. PMID:26984537
Temperature Dependent Cyclic Deformation Mechanisms in Haynes 188 Superalloy
NASA Technical Reports Server (NTRS)
Rao, K. Bhanu Sankara; Castelli, Michael G.; Allen, Gorden P.; Ellis, John R.
1995-01-01
The cyclic deformation behavior of a wrought cobalt-base superalloy, Haynes 188, has been investigated over a range of temperatures between 25 and 1000 C under isothermal and in-phase thermomechanical fatigue (TMF) conditions. Constant mechanical strain rates (epsilon-dot) of 10(exp -3)/s and 10(exp -4)/s were examined with a fully reversed strain range of 0.8%. Particular attention was given to the effects of dynamic strain aging (DSA) on the stress-strain response and low cycle fatigue life. A correlation between cyclic deformation behavior and microstructural substructure was made through detailed transmission electron microscopy. Although DSA was found to occur over a wide temperature range between approximately 300 and 750 C the microstructural characteristics and the deformation mechanisms responsible for DSA varied considerably and were dependent upon temperature. In general, the operation of DSA processes led to a maximum of the cyclic stress amplitude at 650 C and was accompanied by pronounced planar slip, relatively high dislocation density, and the generation of stacking faults. DSA was evidenced through a combination of phenomena, including serrated yielding, an inverse dependence of the maximum cyclic hardening with epsilon-dot, and an instantaneous inverse epsilon-dot sensitivity verified by specialized epsilon-dot -change tests. The TMF cyclic hardening behavior of the alloy appeared to be dictated by the substructural changes occuring at the maximum temperature in the TMF cycle.
Plastically deformed region around indentations on Si angle crystal
NASA Astrophysics Data System (ADS)
Yoshioka, M.
1994-12-01
Expansion of a hemispherical shell by inner pressure has been widely applied for the model of the deformation by an indentation on a flat surface; however, the deformed region is not necessarily spherically symmetric, especially in anisotropic materials such as single crystals. Therefore, whether the spherical model is applicable in an indentation process for objective materials must always be kept in mind. Indentations have been made on the (111) surface of silicon crystal at various temperatures. The three-dimensional shape of the plastically deformed region was experimentally measured by means of an etching technique and its difference from the hemisphere was observed. It was never spherical but much more complicated, similar to a bottle gourd. The slip mechanism, which resulted in the observed shape of the plastic region, is discussed further. The plastic region was analytically obtained also on the assumption that the stress distribution was spherically symmetrical. The result is approximately in accordance with the observed shape. It is therefore concluded that the stress distribution is nearly spherical although the plastic region is far from it. The yield strength of silicon crystals and their temperature dependence were obtained based on the spherical model.
Thermally induced stresses and deformations in layered composite tubes
NASA Technical Reports Server (NTRS)
Cooper, D. E.; Cohen, D.; Rousseau, C. Q.; Hyer, M. W.; Tompkins, S. S.
1985-01-01
The thermally induced stresses and deformations in layered, orthotropic tubes are studied. The motivation for studying tubes is their likely application for use in space structures. Tubes are a strong candidate for this application because of their high structural efficiency, as measured by stiffness per unit weight, and their relative ease of fabrication. Also, tubes have no free edges to deteriorate or delaminate. An anticipated thermal condition for tubes in space is a circumferential temperature gradient. This type of gradient will introduce dimensional changes into the structure and may cause stresses large enough to cause damage to the material. There are potentially large differences in temperatures at different circumferential locations on the tube. Because of this, the effects of temperature dependent material properties on the stresses and deformations may be important. The study is composed of three parts: experiments to determine the functional form of the circumferential gradient and to measure tube deflections; an elasticity solution to compute the stresses and deformations; and an approximate approach to determine the effects of temperature dependent material properties.
Sound Emission of Rotor Induced Deformations of Generator Casings
NASA Technical Reports Server (NTRS)
Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)
2001-01-01
The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.
Patterns of brittle deformation under extension on Venus
NASA Technical Reports Server (NTRS)
Neumann, G. A.; Zuber, M. T.
1994-01-01
The development of fractures at regular length scales is a widespread feature of Venusian tectonics. Models of lithospheric deformation under extension based on non-Newtonian viscous flow and brittle-plastic flow develop localized failure at preferred wavelengths that depend on lithospheric thickness and stratification. The characteristic wavelengths seen in rift zones and tessera can therefore provide constraints on crustal and thermal structure. Analytic solutions were obtained for growth rates in infinitesimal perturbations imposed on a one-dimensional, layered rheology. Brittle layers were approximated by perfectly-plastic, uniform strength, overlying ductile layers exhibiting thermally-activated power-law creep. This study investigates the formation of faults under finite amounts of extension, employing a finite-element approach. Our model incorporates non-linear viscous rheology and a Coulomb failure envelope. An initial perturbation in crustal thickness gives rise to necking instabilities. A small amount of velocity weakening serves to localize deformation into planar regions of high strain rate. Such planes are analogous to normal faults seen in terrestrial rift zones. These 'faults' evolve to low angle under finite extension. Fault spacing, orientation and location, and the depth to the brittle-ductile transition, depend in a complex way on lateral variations in crustal thickness. In general, we find that multiple wavelengths of deformation can arise from the interaction of crustal and mantle lithosphere.
Nuclear ground-state masses and deformations: FRDM(2012)
NASA Astrophysics Data System (ADS)
Möller, P.; Sierk, A. J.; Ichikawa, T.; Sagawa, H.
2016-05-01
We tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from 16O to A = 339. The calculations are based on the finite-range droplet macroscopic and the folded-Yukawa single-particle microscopic nuclear-structure models, which are completely specified. Relative to our FRDM(1992) mass table in Möller et al. (1995), the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensive and more accurate experimental mass data base now available allow us to determine one additional macroscopic-model parameter, the density-symmetry coefficient L, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some highly deformed shapes occurring in fission, because some effects are derived in terms of perturbations around a sphere, we only adjust its macroscopic parameters to ground-state masses.
Thermocapillary deformation in a locally heated layer of silicone oil
NASA Astrophysics Data System (ADS)
Barakhovskaia, E. V.; Marchuk, I. V.; Fedorets, A. A.
2016-10-01
The processes of heat and mass transfer in systems with liquid-gas interface are of interest to a wide range of problems. Thermocapillary flows have an important role in such systems. Thermocapillary deformation of silicone oil layer was investigated using laser scanning confocal microscope Zeiss LSM 510 Meta. The numerical solution of the problem was obtained in the lubrication approximation theory for two-dimensional axisymmetric thermocapillary flow. The model takes into account the surface tension, viscosity, gravity and heat transfer in the substrate. Evaporation is neglected. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the liquid layer thickness has been developed. Stationary solutions have been obtained by the establishment method. The dependences of the depth of thermocapillary deformation on the layer thickness were obtained for silicone oils of different viscosities. It was found that the value of the relative deformation decreases nonlinearly with increasing the initial layer thickness. There is a good qualitative agreement of numerical results and experimental data.
Self-adjointness of deformed unbounded operators
Much, Albert
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
Regularities of bainitic steel deformation transition
NASA Astrophysics Data System (ADS)
Gromov, V. E.; Nikitina, E. N.; Ivanov, Yu F.; Aksenova, K. V.
2016-09-01
Quantitative analysis of defect and carbide subsystems evolution in medium-carbon bainitic steel subjected to compressive strain up to 36% was performed by means of transmission electron diffraction microscopy. Dislocation substructure and carbide phase parameters dependence on degree of deformation are identified, possible reasons of staging in their changes are discussed. It is suggested that the reason for bainitic steel softening at high (over 15%) degrees of deformation is activation of deformation microtwinning process.
Finite difference methods for approximating Heaviside functions
NASA Astrophysics Data System (ADS)
Towers, John D.
2009-05-01
We present a finite difference method for discretizing a Heaviside function H(u(x→)), where u is a level set function u:Rn ↦ R that is positive on a bounded region Ω⊂Rn. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [J.D. Towers, Two methods for discretizing a delta function supported on a level set, J. Comput. Phys. 220 (2007) 915-931; J.D. Towers, Discretizing delta functions via finite differences and gradient normalization, Preprint at http://www.miracosta.edu/home/jtowers/; J.D. Towers, A convergence rate theorem for finite difference approximations to delta functions, J. Comput. Phys. 227 (2008) 6591-6597]. We consider our approximate Heaviside functions as they are used to approximate integrals over Ω. We prove that our first approximate Heaviside function leads to second order accurate quadrature algorithms. Numerical experiments verify this second order accuracy. For our second algorithm, numerical experiments indicate at least third order accuracy if the integrand f and ∂Ω are sufficiently smooth. Numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations. We mostly focus on smooth f and u. By this we mean that f is smooth in a neighborhood of Ω, u is smooth in a neighborhood of ∂Ω, and the level set u(x)=0 is a manifold of codimension one. However, our algorithms still give reasonable results if either f or u has jumps in its derivatives. Numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way, assuming that the level set u(x)=0 is a manifold. Numerical experiments indicate that dependence on the placement of Ω with respect to the grid is quite small for our algorithms. Specifically, a grid shift results in an O(hp) change in the computed solution
Consecutive Rosochatius deformations of the Neumann system
NASA Astrophysics Data System (ADS)
Xia, Baoqiang; Zhou, Ruguang
2013-10-01
Consecutive Rosochatius deformations of the Neumann system are investigated. It is first shown that different realizations of a classical sl(2) Gaudin magnet model yield different integrable Hamiltonian systems. Then an algorithm of constructing infinitely many symplectic realizations of sl(2) algebra from a known one is presented and thus the Neumann system can be deformed consecutively. The second Rosochatius deformation of the Neumann system is taken as an illustrative example to show that the deformed systems admit separations of variables and may be linearized on the Jacobi variety.
Origami-enabled deformable silicon solar cells
Tang, Rui; Huang, Hai; Liang, Hanshuang; Liang, Mengbing; Tu, Hongen; Xu, Yong; Song, Zeming; Jiang, Hanqing; Yu, Hongyu
2014-02-24
Deformable electronics have found various applications and elastomeric materials have been widely used to reach flexibility and stretchability. In this Letter, we report an alternative approach to enable deformability through origami. In this approach, the deformability is achieved through folding and unfolding at the creases while the functional devices do not experience strain. We have demonstrated an example of origami-enabled silicon solar cells and showed that this solar cell can reach up to 644% areal compactness while maintaining reasonable good performance upon cyclic folding/unfolding. This approach opens an alternative direction of producing flexible, stretchable, and deformable electronics.
Deformation twinning: Influence of strain rate
Gray, G.T. III
1993-11-01
Twins in most crystal structures, including advanced materials such as intermetallics, form more readily as the temperature of deformation is decreased or the rate of deformation is increased. Both parameters lead to the suppression of thermally-activated dislocation processes which can result in stresses high enough to nucleate and grow deformation twins. Under high-strain rate or shock-loading/impact conditions deformation twinning is observed to be promoted even in high stacking fault energy FCC metals and alloys, composites, and ordered intermetallics which normally do not readily deform via twinning. Under such conditions and in particular under the extreme loading rates typical of shock wave deformation the competition between slip and deformation twinning can be examined in detail. In this paper, examples of deformation twinning in the intermetallics TiAl, Ti-48Al-lV and Ni{sub 3}A as well in the cermet Al-B{sub 4}C as a function of strain rate will be presented. Discussion includes: (1) the microstructural and experimental variables influencing twin formation in these systems and twinning topics related to high-strain-rate loading, (2) the high velocity of twin formation, and (3) the influence of deformation twinning on the constitutive response of advanced materials.
Analysis of deformation bands in the Aztec Sandstone, Valley of Fire State Park, Nevada
Hill, R.E. )
1993-04-01
This research concerns two types of deformation structures, deformation bands and low-angle slip surfaces, that occur in the Aztec Sandstone in the Valley of Fire State Park, Nevada. Deformation bands were analyzed by mapping and describing over 500 of the structures on a bedding surface of about 560 square meters. Deformation bands are narrow zones of reduced porosity which form resistant ribs in the sandstone. Three sets of deformation bands are present at the study site (type 1,2, and 3). Type 1 and 2 bands are interpreted as coeval and form a conjugate set with a dihedral angle of 90 degrees. These sets are usually composed of multiple bands. A third set is interpreted to be subsidiary to the older set, and intersections angles with the earlier formed sets are approximately 45 degrees. In contrast with the older sets, the third set is nearly always a single band which is sinuous or jagged along its length. All three sets of deformation bands are crosscut and sometimes offset by low-angle slip surfaces. These faults have reverse dip slip displacement and locally have mullions developed. Displacements indicate eastward movement of the hanging wall which is consistent with the inferred movements of major Mesozoic thrust faults in the vicinity. The change of deformation style from deformation bands to low-angle slip surfaces may document a change in the stress regime. Paleostress interpretation of the deformation band geometry indicates the intermediate stress axis is vertical. The low-angle slip surfaces indicate the least compressive stress axis is vertical. This possible change in stress axes may be the result of increasing pore pressure associated with tectonic loading from emplacement of the Muddy Mountain thrust.
NASA Technical Reports Server (NTRS)
Morgan, Julia K.; McGovern, Patrick J.
2005-01-01
We have carried out two-dimensional particle dynamics simulations of granular piles subject to frictional Coulomb failure criteria to gain a first-order understanding of different modes of gravitational deformation within volcanoes. Under uniform basal and internal strength conditions, granular piles grow self-similarly, developing distinctive stratigraphies, morphologies, and structures. Piles constructed upon cohesive substrates exhibit particle avalanching, forming outward dipping strata and angle of repose slopes. Systematic decreases in basal strength lead to progressively deeper and steeper internal detachment faults and slip along a basal decollement; landslide forms grade from shallow slumps to deep-seated landslide and, finally, to axial subsidence and outward flank displacements, or volcanic spreading. Surface slopes decrease and develop concave up morphologies with decreasing decollement strength; depositional layers tilt progressively inward. Spatial variations in basal strength cause lateral transitions in pile structure, stratigraphy, and morphology. This approximation of volcanoes as Coulomb granular piles reproduces the richness of deformational structures and surface morphologies in many volcanic settings. The gentle slopes of Hawaiian volcanoes and Olympus Mons on Mars suggest weak basal decollements that enable volcanic spreading. High-angle normal faults, favored above weak decollements, are interpreted in both settings and may explain catastrophic sector collapse in Hawaii and broad aureole deposits surrounding Olympus Mons. In contrast, steeper slopes and shallow detachment faults predominate in the Canary Islands, thought to lack a weak decollement, favoring smaller, more frequent slope failures than predicted for Hawaii. The numerical results provide a useful predictive tool for interpreting dynamic behavior and associated geologic hazards of active volcanoes.
Planetary ephemerides approximation for radar astronomy
NASA Technical Reports Server (NTRS)
Sadr, R.; Shahshahani, M.
1991-01-01
The planetary ephemerides approximation for radar astronomy is discussed, and, in particular, the effect of this approximation on the performance of the programmable local oscillator (PLO) used in Goldstone Solar System Radar is presented. Four different approaches are considered and it is shown that the Gram polynomials outperform the commonly used technique based on Chebyshev polynomials. These methods are used to analyze the mean square, the phase error, and the frequency tracking error in the presence of the worst case Doppler shift that one may encounter within the solar system. It is shown that in the worst case the phase error is under one degree and the frequency tracking error less than one hertz when the frequency to the PLO is updated every millisecond.
Approximated solutions to Born-Infeld dynamics
NASA Astrophysics Data System (ADS)
Ferraro, Rafael; Nigro, Mauro
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Multiwavelet neural network and its approximation properties.
Jiao, L; Pan, J; Fang, Y
2001-01-01
A model of multiwavelet-based neural networks is proposed. Its universal and L(2) approximation properties, together with its consistency are proved, and the convergence rates associated with these properties are estimated. The structure of this network is similar to that of the wavelet network, except that the orthonormal scaling functions are replaced by orthonormal multiscaling functions. The theoretical analyses show that the multiwavelet network converges more rapidly than the wavelet network, especially for smooth functions. To make a comparison between both networks, experiments are carried out with the Lemarie-Meyer wavelet network, the Daubechies2 wavelet network and the GHM multiwavelet network, and the results support the theoretical analysis well. In addition, the results also illustrate that at the jump discontinuities, the approximation performance of the two networks are about the same.
Flow past a porous approximate spherical shell
NASA Astrophysics Data System (ADS)
Srinivasacharya, D.
2007-07-01
In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Approximate inverse preconditioners for general sparse matrices
Chow, E.; Saad, Y.
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Approximation techniques of a selective ARQ protocol
NASA Astrophysics Data System (ADS)
Kim, B. G.
Approximations to the performance of selective automatic repeat request (ARQ) protocol with lengthy acknowledgement delays are presented. The discussion is limited to packet-switched communication systems in a single-hop environment such as found with satellite systems. It is noted that retransmission of errors after ARQ is a common situation. ARQ techniques, e.g., stop-and-wait and continuous, are outlined. A simplified queueing analysis of the selective ARQ protocol shows that exact solutions with long delays are not feasible. Two approximation models are formulated, based on known exact behavior of a system with short delays. The buffer size requirements at both ends of a communication channel are cited as significant factor for accurate analysis, and further examinations of buffer overflow and buffer lock-out probability and avoidance are recommended.
Deformation of the central Andes (15-27 deg S) derived from a flow model of subduction zones
NASA Technical Reports Server (NTRS)
Wdowinski, Shimon; O'Connell, Richard J.
1991-01-01
A simple viscous flow model of a subduction zone is used to calculate the deformation within continental lithosphere above a subducting slab. This formulation accounts for two forces that dominate the deformation in the overriding lithosphere: tectonic forces and buoyancy forces. Numerical solutions, obtained by using a finite element technique, are compared with observations from the central Andes (15-27 deg S). The model predicts the observed deformation pattern of extension in the forearc, compression in the Western Monocline (corresponding to magmatic activity), extension in the Altiplano, compression in the Eastern Monocline and Subandes, and no deformation in the Brazilian Shield. By comparing the calculated solutions with the large-scale tectonic observations, the forces that govern the deformation in the central Andes are evaluated. The approximately constant subduction velocity in the past 26 million years suggests that the rate of crustal shortening in the Andes has decreased with time due to the thickening of the crust.
Approximate active fault detection and control
NASA Astrophysics Data System (ADS)
Škach, Jan; Punčochář, Ivo; Šimandl, Miroslav
2014-12-01
This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit.
An Approximation Scheme for Delay Equations.
1980-06-16
C(-r,0. R) IR defined by m 10 D( ) 0 (O) - I B (-rj- B(s) b(s)ds, I(* A ,(-r ) + A(s) (s)ds, where 0 =r 0 < rI < ... < rm r. ’AJ,B are n x n matrices ...Approximations of delays by ordinary differen- tial equations, INCREST - Institutul de Matematica , Preprint series in Mathematics No. 22/1978. [14] F
Solving Math Problems Approximately: A Developmental Perspective
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224
Oscillation of boson star in Newtonian approximation
NASA Astrophysics Data System (ADS)
Jarwal, Bharti; Singh, S. Somorendro
2017-03-01
Boson star (BS) rotation is studied under Newtonian approximation. A Coulombian potential term is added as perturbation to the radial potential of the system without disturbing the angular momentum. The results of the stationary states of these ground state, first and second excited state are analyzed with the correction of Coulombian potential. It is found that the results with correction increased in the amplitude of oscillation of BS in comparison to potential without perturbation correction.
Approximation methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay
Three Definitions of Best Linear Approximation
1976-04-01
Three definitions of best (in the least squares sense) linear approximation to given data points are presented. The relationships between these three area discussed along with their relationship to basic statistics such as mean values, the covariance matrix, and the (linear) correlation coefficient . For each of the three definitions, and best line is solved in closed form in terms of the data centroid and the covariance matrix.
Nonlinear amplitude approximation for bilinear systems
NASA Astrophysics Data System (ADS)
Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I.
2014-06-01
An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
Empirical progress and nomic truth approximation revisited.
Kuipers, Theo A F
2014-06-01
In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of truth and falsity content, that the analysis already applies when, in line with scientific common sense, nomic theories are merely assumed to exclude certain conceptual possibilities as nomic possibilities.
Numerical quadratures for approximate computation of ERBS
NASA Astrophysics Data System (ADS)
Zanaty, Peter
2013-12-01
In the ground-laying paper [3] on expo-rational B-splines (ERBS), the default numerical method for approximate computation of the integral with C∞-smooth integrand in the definition of ERBS is Romberg integration. In the present work, a variety of alternative numerical quadrature methods for computation of ERBS and other integrals with smooth integrands are studied, and their performance is compared on several benchmark examples.
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values.
Capacitor-Chain Successive-Approximation ADC
NASA Technical Reports Server (NTRS)
Cunningham, Thomas
2003-01-01
A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise.
Space-Time Approximation with Sparse Grids
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
Variational Bayesian Approximation methods for inverse problems
NASA Astrophysics Data System (ADS)
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Ranking Support Vector Machine with Kernel Approximation
Dou, Yong
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256
Ranking Support Vector Machine with Kernel Approximation.
Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
Strong washout approximation to resonant leptogenesis
NASA Astrophysics Data System (ADS)
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ɛ=Xsin(2varphi)/(X2+sin2varphi), where X=8πΔ/(|Y1|2+|Y2|2), Δ=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2gg Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
An Origami Approximation to the Cosmic Web
NASA Astrophysics Data System (ADS)
Neyrinck, Mark C.
2016-10-01
The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.
Approximation abilities of neuro-fuzzy networks
NASA Astrophysics Data System (ADS)
Mrówczyńska, Maria
2010-01-01
The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
CMB-lensing beyond the Born approximation
NASA Astrophysics Data System (ADS)
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Green-Ampt approximations: A comprehensive analysis
NASA Astrophysics Data System (ADS)
Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.
2016-04-01
Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.
A coastal ocean model with subgrid approximation
NASA Astrophysics Data System (ADS)
Walters, Roy A.
2016-06-01
A wide variety of coastal ocean models exist, each having attributes that reflect specific application areas. The model presented here is based on finite element methods with unstructured grids containing triangular and quadrilateral elements. The model optimizes robustness, accuracy, and efficiency by using semi-implicit methods in time in order to remove the most restrictive stability constraints, by using a semi-Lagrangian advection approximation to remove Courant number constraints, and by solving a wave equation at the discrete level for enhanced efficiency. An added feature is the approximation of the effects of subgrid objects. Here, the Reynolds-averaged Navier-Stokes equations and the incompressibility constraint are volume averaged over one or more computational cells. This procedure gives rise to new terms which must be approximated as a closure problem. A study of tidal power generation is presented as an example of this method. A problem that arises is specifying appropriate thrust and power coefficients for the volume averaged velocity when they are usually referenced to free stream velocity. A new contribution here is the evaluation of three approaches to this problem: an iteration procedure and two mapping formulations. All three sets of results for thrust (form drag) and power are in reasonable agreement.
Using Approximations to Accelerate Engineering Design Optimization
NASA Technical Reports Server (NTRS)
Torczon, Virginia; Trosset, Michael W.
1998-01-01
Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.
Deformed ellipsoidal diffraction grating blank
NASA Technical Reports Server (NTRS)
Decew, Alan E., Jr.
1994-01-01
The Deformed Ellipsoidal Grating Blank (DEGB) is the primary component in an ultraviolet spectrometer. Since one of the major concerns for these instruments is throughput, significant efforts are made to reduce the number of components and subsequently reflections. Each reflection results in losses through absorption and scattering. It is these two sources of photon loss that dictated the requirements for the DEGB. The first goal is to shape the DEGB in such a way that the energy at the entrance slit is focused as well as possible on the exit slit. The second goal is to produce a surface smooth enough to minimize the photon loss due to scattering. The program was accomplished in three phases. The first phase was the fabrication planning. The second phase was the actual fabrication and initial testing. The last phase was the final testing of the completed DEGB.
Deformation in the continental lithosphere
NASA Astrophysics Data System (ADS)
The Physical Properties of Earth Materials Committee, a technical committee of AGU's Tectonophysics Section, is organizing a dinner/colloquium as part of the Fall Meeting in San Francisco, Calif. This event will be held Monday, December 3rd, in the Gold Rush Room of the Holiday Inn Golden Gateway Hotel at 1500 Van Ness St. There will be a no-host bar from 6:30 to 7:30 P.M., followed by dinner from 7:30 to 8:30 P.M. Paul Tapponnier will deliver the after-dinner talk, “Large-Scale Deformation Mechanisms in the Continental Lithosphere: Where Do We Stand?” It will start at 8:30 P.M. and a business meeting will follow at 9:30 P.M.
Deformation quantization of fermi fields
Galaviz, I. Garcia-Compean, H. Przanowski, M. Turrubiates, F.J.
2008-04-15
Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal *-product and the Wigner functional are obtained by extending the formalism proposed recently in [I. Galaviz, H. Garcia-Compean, M. Przanowski, F.J. Turrubiates, Weyl-Wigner-Moyal Formalism for Fermi Classical Systems, arXiv:hep-th/0612245] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal *-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.
Compound dislocation models (CDMs) for volcano deformation analyses
NASA Astrophysics Data System (ADS)
Nikkhoo, Mehdi; Walter, Thomas R.; Lundgren, Paul R.; Prats-Iraola, Pau
2017-02-01
Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is significantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid interpretation of deformation data.
Monitoring Building Deformation with InSAR: Experiments and Validation.
Yang, Kui; Yan, Li; Huang, Guoman; Chen, Chu; Wu, Zhengpeng
2016-12-20
Synthetic Aperture Radar Interferometry (InSAR) techniques are increasingly applied for monitoring land subsidence. The advantages of InSAR include high accuracy and the ability to cover large areas; nevertheless, research validating the use of InSAR on building deformation is limited. In this paper, we test the monitoring capability of the InSAR in experiments using two landmark buildings; the Bohai Building and the China Theater, located in Tianjin, China. They were selected as real examples to compare InSAR and leveling approaches for building deformation. Ten TerraSAR-X images spanning half a year were used in Permanent Scatterer InSAR processing. These extracted InSAR results were processed considering the diversity in both direction and spatial distribution, and were compared with true leveling values in both Ordinary Least Squares (OLS) regression and measurement of error analyses. The detailed experimental results for the Bohai Building and the China Theater showed a high correlation between InSAR results and the leveling values. At the same time, the two Root Mean Square Error (RMSE) indexes had values of approximately 1 mm. These analyses show that a millimeter level of accuracy can be achieved by means of InSAR technique when measuring building deformation. We discuss the differences in accuracy between OLS regression and measurement of error analyses, and compare the accuracy index of leveling in order to propose InSAR accuracy levels appropriate for monitoring buildings deformation. After assessing the advantages and limitations of InSAR techniques in monitoring buildings, further applications are evaluated.
Remagnetisation of a rock analogue during experimental triaxial deformation
NASA Astrophysics Data System (ADS)
Borradaile, Graham J.
1994-05-01
Synthetic specimens containing pseudo-single-domain magnetite were given a univectorial, anhysteretic remanent magnetisation. They were deformed in a ductile manner at room temperature under a confining pressure of 150 MPa (1.5 kbar). The strain rate was 10 -5 s -1 and the maximum strain achieved was 23% shortening. A weak (0.035 mT) magnetic field was present in the pressure vessel during deformation. Hydrostatic compaction alone produced pressure demagnetisation of low-coercivity components of remanence but did not change remanence directions. Macroscopic differential stress was needed to deform the specimens, and this also permitted syndeformational remagnetisation for values of more than 20 MPa (200 bars). This added new components of piezo-remanent magnetisation (PRM) approximately parallel to the direction of the magnetic field in the pressure vessel. They were acquired in all coercivity intervals but the largest components were added below 35 mT. The final remanence orientation and its spatial distribution of vector components were dictated by the relative orientations of the remagnetising field and the initial remanence. PRM contributions almost completely masked the changes related to strain-induced grain rotation at these low strains. The directions of the externally imposed stress-strain axes may not significantly influence the direction of new remanence components. PRM acquisition occurs when differential stress exceeds a threshold value that probably depends on the previous stress-history of the magnetite grains. In part, this may explain the origin of syntectonic remagnetisation in some naturally deformed rocks where the remanence is not reset by recrystallisation, or thermal or chemical processes.
Monitoring Building Deformation with InSAR: Experiments and Validation
Yang, Kui; Yan, Li; Huang, Guoman; Chen, Chu; Wu, Zhengpeng
2016-01-01
Synthetic Aperture Radar Interferometry (InSAR) techniques are increasingly applied for monitoring land subsidence. The advantages of InSAR include high accuracy and the ability to cover large areas; nevertheless, research validating the use of InSAR on building deformation is limited. In this paper, we test the monitoring capability of the InSAR in experiments using two landmark buildings; the Bohai Building and the China Theater, located in Tianjin, China. They were selected as real examples to compare InSAR and leveling approaches for building deformation. Ten TerraSAR-X images spanning half a year were used in Permanent Scatterer InSAR processing. These extracted InSAR results were processed considering the diversity in both direction and spatial distribution, and were compared with true leveling values in both Ordinary Least Squares (OLS) regression and measurement of error analyses. The detailed experimental results for the Bohai Building and the China Theater showed a high correlation between InSAR results and the leveling values. At the same time, the two Root Mean Square Error (RMSE) indexes had values of approximately 1 mm. These analyses show that a millimeter level of accuracy can be achieved by means of InSAR technique when measuring building deformation. We discuss the differences in accuracy between OLS regression and measurement of error analyses, and compare the accuracy index of leveling in order to propose InSAR accuracy levels appropriate for monitoring buildings deformation. After assessing the advantages and limitations of InSAR techniques in monitoring buildings, further applications are evaluated. PMID:27999403
Rate-dependent deformation of rocks in the brittle regime
NASA Astrophysics Data System (ADS)
Baud, P.; Brantut, N.; Heap, M. J.; Meredith, P. G.
2013-12-01
Rate-dependent brittle deformation of rocks, a phenomenon relevant for long-term interseismic phases of deformation, is poorly understood quantitatively. Rate-dependence can arise from chemically-activated, subcritical crack growth, which is known to occur in the presence of aqueous fluids. Here we attempt to establish quantitative links between this small scale process and its macroscopic manifestations. We performed a series of brittle deformation experiments in porous sandstones, in creep (constant stress) and constant strain rate conditions, in order to investigate the relationship between their short- and long-term mechanical behaviors. Elastic wave velocities measurements indicate that the amount of microcracking follows the amount of inelastic strain in a trend which does not depend upon the timescale involved. The comparison of stress-strain curves between constant strain rate and creep tests allows us to define a stress difference between the two, which can be viewed as a difference in energy release rate. We empirically show that the creep strain rates are proportional to an exponential function of this stress difference. We then establish a general method to estimate empirical micromechanical functions relating the applied stresses to mode I stress intensity factors at microcrack tips, and we determine the relationship between creep strain rates and stress intensity factors in our sandstone creep experiments. We finally provide an estimate of the sub-critical crack growth law parameters, and find that they match -within the experimental errors and approximations of the method- the typical values observed in independent single crack tests. Our approach provides a comprehensive and unifying explanation for the origin and the macroscopic manifestation of time-dependent brittle deformation in brittle rocks.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics.
Periodic orbits and shell structure in octupole deformed potentials
Heiss, W.D. ); Nazmitdinov, R.G. ); Radu, S. )
1995-01-15
The effect of an octupole term in a quadrupole deformed single-particle potential is studied from the classical and quantum-mechanical viewpoint. Whereas the problem is nonintegrable, the quantum-mechanical spectrum nevertheless shows some shell structure in the superdeformed prolate case for particular, yet fairly large octupole strengths; for spherical or oblate deformation the shell structure disappears. This result is associated with classical periodic orbits that are found by employing the removal of resonances method; this approximation method allows determination of the shape of the orbit and of the approximate octupole coupling strength for which it occurs. The validity of the method is confirmed by solving numerically the classical equations of motion. The quantum-mechanical shell structure is analyzed using the particle-number dependence of the fluctuating part of the total energy. In accordance with the classical result, this dependence turns out to be very similar for a superdeformed prolate potential plus octupole term and a hyperdeformed prolate potential without octupole term. In this way the shell structure is explained at least for some few hundred levels. The Fourier transform of the level density further corroborates these findings.
Application of the perturbation method in mechanics of deformable solids
NASA Astrophysics Data System (ADS)
Minaeva, N. V.
2008-02-01
Although the solutions of the classical problems of continuum mechanics have been studied sufficiently well, the smallest deviations, for example, of the body boundary or of the material characteristics from the traditional values prevent one from obtaining exact solutions of these problems. In this case, one has to use approximate methods, the most common of which is the perturbation method. The problems studied in [1-6] belong to classical problems in which the perturbation method is used to study the behavior of deformable bodies. A wide survey of studies analyzing the perturbations of the body boundary shape caused by variations in its stress-strain state is given in [5, 6]. In numerous studies, it was noted that the problem on the convergence of approximate solutions and hence the studies of the continuous dependence of the solution of the original problem on the characteristics of perturbations ("imperfections") play an important role. In the present paper, we analyze the forms of mathematical models of deformable bodies by studying whether the solution of the original problem continuously depends on the characteristics of the perturbed shape of the body boundary on which the boundary conditions are posed in terms of stresses and on the characteristics of the material properties. We use the results of this analysis to conclude that, when using the perturbation method, one should state the boundary conditions in terms of stresses on the boundary of the real body in stressed state.
Elastic deformation and energy loss of flapping fly wings.
Lehmann, Fritz-Olaf; Gorb, Stanislav; Nasir, Nazri; Schützner, Peter
2011-09-01
During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m(2) near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m(2)). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.
Sun, Wei; Chaikof, Elliot L; Levenston, Marc E
2008-12-01
Finite element (FE) implementations of nearly incompressible material models often employ decoupled numerical treatments of the dilatational and deviatoric parts of the deformation gradient. This treatment allows the dilatational stiffness to be handled separately to alleviate ill conditioning of the tangent stiffness matrix. However, this can lead to complex formulations of the material tangent moduli that can be difficult to implement or may require custom FE codes, thus limiting their general use. Here we present an approach, based on work by Miehe (Miehe, 1996, "Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large Strain Computational Inelasticity," Comput. Methods Appl. Mech. Eng., 134, pp. 223-240), for an efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE codes. By perturbing the deformation gradient, the material tangent moduli from the Jaumann rate of the Kirchhoff stress are accurately approximated by a forward difference of the associated Kirchhoff stresses. The merit of this approach is that it produces a concise mathematical formulation that is not dependent on any particular material model. Consequently, once the approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and accuracy of this approach is first demonstrated with a simple neo-Hookean material. Subsequently, a fiber-reinforced structural model is applied to analyze the pressure-diameter curve during blood vessel inflation. Implementation of this approach will facilitate the incorporation of novel hyperelastic material models for a soft tissue behavior into commercial FE software.
NASA Astrophysics Data System (ADS)
Choi, Hyun-Sik; Han, Heung Nam; Lee, Dong Nyung
2017-01-01
The texture of rolled sheets is known to vary with depth from the shear texture in the surface layer to the planestrain-compression texture in the center layer. This study has interpreted the deformation and annealing textures evolved in the surface layer of a four-layered-copper sheet cold-rolled by 93% reduction in thickness without lubrication at room temperature. The surface and center layers were separated from the cold-rolled four-layered copper sheet. The deformed surface layer was annealed for 1 h at 823 K. The deformation texture of the surface layer could be simulated by straining the {112}<111> oriented fcc crystals by a true strain of 2.66 in the rolling direction at 0 ≤ | e 13/ e 11| ≤ 1.4, where eij are the displacement gradients and the subscripts 1 and 3 represent the sheet rolling and sheet surface normal directions, respectively, using a visco-plastic self-consistent scheme. The annealing texture could be approximated by the simulated shear deformation orientations plus near the {001}<100> orientation that was approximated by the recrystallization orientations calculated from the simulated deformation orientations. The recrystallization orientations were calculated by the strain-energy-release-maximization theory for the recrystallization texture evolution.
Non-collapsing renormalized QRPA with proton-neutron pairing for neutrinoless double beta decay
NASA Astrophysics Data System (ADS)
Simkovic, F.; Schwieger, J.; Veselský, M.; Pantis, G.; Faessler, Amand
1997-02-01
Using the renormalized quasiparticle random phase approximation (RQRPA), we calculate the light neutrino mass mediated mode of neutrinoless double beta decay (0νββ-decay) of 76Ge, 100Mo, 128Te and 130Te. Our results indicate that the simple quasiboson approximation is not good enough to study the 0νββ-decay, because its solutions collapse for physical values of gpp. We find that extension of the Hilbert space and inclusion of the Pauli principle in the QRPA with proton-neutron pairing, allows us to extend our calculations beyond the point of collapse, for physical values of the nuclear force strength. As a consequence one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half-life of 0νββ-decay.
Role of momentum transfer in the quenching of the Gamow-Teller strength
Marketin, T.; Martinez-Pinedo, G.; Paar, N.; Vretenar, D.
2012-10-20
A recent analysis of (p,n) and (n,p) reaction data from {sup 90}Zr was performed recently, where a significant amount of Gamow-Teller strength was found above the resonance, an energy region previously unreachable by experimental setups. The extracted strengths in the {beta}{sub -} and the {beta}{sub +} channel indicate that approximately 10% of the total strength necessary to satisfy the model independent Ikeda sum rule is missing. One possible source of this discrepancy is the treatment of the isovector spin monopole (IVSM) mode of excitation which has been found to occurr at high excitation energies. Employing the relativistic Hartree-Bogoliubov (RHB) model and the protonneutron relativistic quasiparticle random phase approximation (pn-RQRPA) to calculate the nuclear response, we explore the contribution of the IVSM mode to the total L= 0 strength and apply our results to the available data.
Role of momentum transfer in the quenching of the Gamow-Teller strength
NASA Astrophysics Data System (ADS)
Marketin, T.; Martínez-Pinedo, G.; Paar, N.; Vretenar, D.
2012-10-01
A recent analysis of (p,n) and (n,p) reaction data from 90Zr was performed recently, where a significant amount of Gamow-Teller strength was found above the resonance, an energy region previously unreachable by experimental setups. The extracted strengths in the β- and the β+ channel indicate that approximately 10% of the total strength necessary to satisfy the model independent Ikeda sum rule is missing. One possible source of this discrepancy is the treatment of the isovector spin monopole (IVSM) mode of excitation which has been found to occurr at high excitation energies. Employing the relativistic Hartree-Bogoliubov (RHB) model and the protonneutron relativistic quasiparticle random phase approximation (pn-RQRPA) to calculate the nuclear response, we explore the contribution of the IVSM mode to the total L = 0 strength and apply our results to the available data.
Deformable mirror designs for extreme AO (XAO)
NASA Astrophysics Data System (ADS)
Cavaco, Jeffrey; Wirth, Allan
2014-08-01
One of the science missions for the next generation of extremely large ground based telescopes (30-42m apertures) is the imaging and spectroscopy of exoplanets. To achieve that goal an Adaptive Optics (AO) subsystem with a very large number of corrected modes is required. To provide contrast ratios in the range of 10-9 or better for a 42m telescope an AO system with 25,000 to 60,000 channels will be needed. This is approximately an order of magnitude beyond the current state of the art. Adaptive Optics Associates Xinetics has developed the Photonex Module Deformable Mirror (DM) technology specifically to address the needs of extreme AO for high contrast applications. A Photonex Module is a monolithic block of electrostrictive ceramic in which a high density of individually addressable actuators are formed by screen printing of electrodes and partial wire saw cutting of the ceramic. The printed electrode structures also allow all electrical connections to be made at the back surface of the module via flex circuits. Actuator spacings of 1mm or less have been achieved using this approach. The individual modules can be edge butted and bonded to achieve high actuator count. The largest DMs fabricated to date have 4096 actuators in a 64X64mm array. In this paper the engineering challenges in extending this technology by a factor of ten or more in actuator count will be discussed. A conceptual design for a DM suitable for XAO will be presented. Approaches for a support structure that will maintain the low spatial frequency surface figure of this large (~0.6m) DM and for the electrical interface to the tens of thousands of actuators will be discussed. Finally, performance estimates will be presented.
Solute transport through a deforming porous medium
NASA Astrophysics Data System (ADS)
Peters, Glen P.; Smith, David W.
2002-06-01
Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co-ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non-linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers.
Measuring Viscoelastic Deformation with an Optical Mouse
ERIC Educational Resources Information Center
Ng, T. W.
2004-01-01
The feasibility of using an optical mouse to track the viscoelastic deformation of low-density polyethylene films that have a fixed attached load is presented. It is seen that using an optical mouse and with rudimentary experiment paraphernalia and arrangement, it is possible to get good measurements of viscoelastic deformation.
Plastic deformation mechanisms in nanocrystalline metallic materials
NASA Astrophysics Data System (ADS)
Ovid'ko, Ilya A.
2013-11-01
This article discusses the experiments, computer simulations, and theoretical models addressing the conventional and specific mechanisms of plastic deformation in nanocrystalline metallic materials. Particular attention is devoted to the competition between lattice dislocation slip and specific deformation mechanisms mediated by grain boundaries as well as its sensitivity to grain size and other parameters of nanocrystalline metallic structures.
Acquired nasal deformities in fighter pilots.
Schreinemakers, Joyce R C; van Amerongen, Pieter; Kon, Moshe
2010-07-01
Fighter pilots may develop slowly progressive deformities of their noses during their flying careers. The spectrum of deformities that may be acquired ranges from soft tissue to osseous changes. The main cause is the varying pressure exerted by the oxygen mask on the skin and bony pyramid of the nose during flying.
Quantification of abdominal aortic deformation after EVAR
NASA Astrophysics Data System (ADS)
Demirci, Stefanie; Manstad-Hulaas, Frode; Navab, Nassir
2009-02-01
Quantification of abdominal aortic deformation is an important requirement for the evaluation of endovascular stenting procedures and the further refinement of stent graft design. During endovascular aortic repair (EVAR) treatment, the aortic shape is subject to severe deformation that is imposed by medical instruments such as guide wires, catheters, and, the stent graft. This deformation can affect the flow characteristics and morphology of the aorta which have been shown to be elicitors for stent graft failures and be reason for reappearance of aneurysms. We present a method for quantifying the deformation of an aneurysmatic aorta imposed by an inserted stent graft device. The outline of the procedure includes initial rigid alignment of the two abdominal scans, segmentation of abdominal vessel trees, and automatic reduction of their centerline structures to one specified region of interest around the aorta. This is accomplished by preprocessing and remodeling of the pre- and postoperative aortic shapes before performing a non-rigid registration. We further narrow the resulting displacement fields to only include local non-rigid deformation and therefore, eliminate all remaining global rigid transformations. Finally, deformations for specified locations can be calculated from the resulting displacement fields. In order to evaluate our method, experiments for the extraction of aortic deformation fields are conducted on 15 patient datasets from endovascular aortic repair (EVAR) treatment. A visual assessment of the registration results and evaluation of the usage of deformation quantification were performed by two vascular surgeons and one interventional radiologist who are all experts in EVAR procedures.
Umbral Deformations on Discrete SPACE TIME
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
Given a minimum measurable length underlying spacetime, the latter may be effectively regarded as discrete, at scales of order the Planck length. A systematic discretization of continuum physics may be effected most efficiently through the umbral deformation. General functionals yielding such deformations at the level of solutions are furnished and illustrated, and broad features of discrete oscillations and wave propagation are outlined.
Exploiting Adaptive Optics with Deformable Secondary Mirrors
2007-03-08
progress in tomographic wavefront sensing and altitude conjugated adaptive correction, and is a critical step forward for adaptive optics for future large...geostationary satellites, captured at the 6.5 m MMT telescope, using the deformable secondary adaptive optics system....new technology to the unique development of deformable secondary mirrors pioneered at the University of Arizona’s Center for Astronomical Adaptive
7 CFR 51.1013 - Badly deformed.
Code of Federal Regulations, 2010 CFR
2010-01-01
... Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE REGULATIONS AND STANDARDS UNDER THE AGRICULTURAL MARKETING ACT OF 1946... Standards for Persian (Tahiti) Limes Definitions § 51.1013 Badly deformed. Badly deformed means that...
Strong washout approximation to resonant leptogenesis
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
An approximate projection method for incompressible flow
NASA Astrophysics Data System (ADS)
Stevens, David E.; Chan, Stevens T.; Gresho, Phil
2002-12-01
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.
Photoelectron spectroscopy and the dipole approximation
Hemmers, O.; Hansen, D.L.; Wang, H.
1997-04-01
Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.
Product-State Approximations to Quantum States
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Harrow, Aram W.
2016-02-01
We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.
Approximations of nonlinear systems having outputs
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1985-01-01
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
The monoenergetic approximation in stellarator neoclassical calculations
NASA Astrophysics Data System (ADS)
Landreman, Matt
2011-08-01
In 'monoenergetic' stellarator neoclassical calculations, to expedite computation, ad hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction. The error in the trapped ion fraction can be of order unity for large but experimentally realizable values of the radial electric field, suggesting some results of these codes may be unreliable in this regime. This inaccuracy is independent of any errors introduced by approximation of the collision operator.
Semiclassical approximations to quantum time correlation functions
NASA Astrophysics Data System (ADS)
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Shear viscosity in the postquasistatic approximation
Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W.
2010-05-15
We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.
Approximation concepts for numerical airfoil optimization
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1979-01-01
An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems.
Approximation of Dynamical System's Separatrix Curves
NASA Astrophysics Data System (ADS)
Cavoretto, Roberto; Chaudhuri, Sanjay; De Rossi, Alessandra; Menduni, Eleonora; Moretti, Francesca; Rodi, Maria Caterina; Venturino, Ezio
2011-09-01
In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models, like prey-predator or competition systems. In this paper we construct programs for the detection of points lying on the separatrix curve, i.e. the curve which partitions the domain. Finally, an efficient algorithm, which is based on the Partition of Unity method with local approximants given by Wendland's functions, is used for reconstructing the separatrix curve.
Approximation Algorithms for Free-Label Maximization
NASA Astrophysics Data System (ADS)
de Berg, Mark; Gerrits, Dirk H. P.
Inspired by air traffic control and other applications where moving objects have to be labeled, we consider the following (static) point labeling problem: given a set P of n points in the plane and labels that are unit squares, place a label with each point in P in such a way that the number of free labels (labels not intersecting any other label) is maximized. We develop efficient constant-factor approximation algorithms for this problem, as well as PTASs, for various label-placement models.
Analytic Approximation to Randomly Oriented Spheroid Extinction
1993-12-01
104 times faster than by the T - matrix code . Since the T-matrix scales as at least the cube of the optical size whereas the analytic approximation is...coefficient estimate, and with the Rayleigh formula. Since it is difficult estimate the accuracy near the limit of stability of the T - matrix code some...additional error due to the T - matrix code could be present. UNCLASSIFIED 30 Max Ret Error, Analytic vs T-Mat, r= 1/5 0.0 20 25 10 ~ 0.5 100 . 7.5 S-1.0
Relativistic Random Phase Approximation At Finite Temperature
Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J.
2009-08-26
The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.
Automated registration of large deformations for adaptive radiation therapy of prostate cancer
Godley, Andrew; Ahunbay, Ergun; Peng Cheng; Li, X. Allen
2009-04-15
Available deformable registration methods are often inaccurate over large organ variation encountered, for example, in the rectum and bladder. The authors developed a novel approach to accurately and effectively register large deformations in the prostate region for adaptive radiation therapy. A software tool combining a fast symmetric demons algorithm and the use of masks was developed in C++ based on ITK libraries to register CT images acquired at planning and before treatment fractions. The deformation field determined was subsequently used to deform the delivered dose to match the anatomy of the planning CT. The large deformations involved required that the bladder and rectum volume be masked with uniform intensities of -1000 and 1000 HU, respectively, in both the planning and treatment CTs. The tool was tested for five prostate IGRT patients. The average rectum planning to treatment contour overlap improved from 67% to 93%, the lowest initial overlap is 43%. The average bladder overlap improved from 83% to 98%, with a lowest initial overlap of 60%. Registration regions were set to include a volume receiving 4% of the maximum dose. The average region was 320x210x63, taking approximately 9 min to register on a dual 2.8 GHz Linux system. The prostate and seminal vesicles were correctly placed even though they are not masked. The accumulated doses for multiple fractions with large deformation were computed and verified. The tool developed can effectively supply the previously delivered dose for adaptive planning to correct for interfractional changes.
Molecular dynamics study of deformation and fracture in a tantalum nano-crystalline thin film
NASA Astrophysics Data System (ADS)
Smith, Laura; Zimmerman, Jonathan A.; Hale, Lucas M.; Farkas, Diana
2014-06-01
We present results from molecular dynamics simulations of two nano-crystalline tantalum thin films that illuminate the variety of atomic-scale mechanisms of incipient plasticity. Sample 1 contains approximately 500 K atoms and 3 grains, chosen to facilitate study at 105 s-1 strain rate; sample 2 has 4.6 M atoms and 30 grains. The samples are loaded in uniaxial tension at deformation rates of 105-109 s-1, and display phenomena including emission of perfect 1/2<1 1 1>-type dislocations and the formation and migration of twin boundaries. It was found that screw dislocation emission is the first deformation mechanism activated at strain rates below 108 s-1. Deformation twins emerge as a deformation mechanism at higher strains, with twins observed to cross grain boundaries as larger strains are reached. At high strain rates atoms are displaced with the characteristic twin vector at a ratio of 3 : 1 (108 s-1) or 4 : 1 (109 s-1) to characteristic dislocation vectors. Fracture is nucleated through a nano-void growth process. Grain boundary sliding does not scale with increasing strain rate. Detailed analysis of nano-scale deformation using these tools enhances our understanding of deformation mechanisms in tantalum.
Ghanei, Amir; Soltanian-Zadeh, Hamid
2002-12-01
In this paper, we present a new curvature-based three-dimensional (3-D) deformable surface model. The model deforms under defined force terms. Internal forces are calculated from local model curvature, using a robust method by a least-squares error (LSE) approximation to the Dupin indicatrix. External forces are calculated by applying a step expansion and restoration filter (SEF) to the image data. A solution for one of the most common problems associated with deformable models, self-cutting, has been proposed in this work. We use a principal axis analysis and reslicing of the deformable model, followed by triangulation of the slices, to remedy self-cutting. We use vertex resampling, multiresolution deformation, and refinement of the mesh grid to improve the quality of the model deformation, which leads to better results. Examples of the model application to different cases (simulation, magnetic resonance imaging (MRI), computerized tomography (CT), and ultrasound images) are presented, showing diversity and flexibility of the model.
Deformation measurements of smart aerodynamic surfaces
NASA Astrophysics Data System (ADS)
Fleming, Gary A.; Burner, Alpheus W.
1999-10-01
Video Model Deformation (VMD) and Projection Moire Interferometry (PMI) were used to acquire wind tunnel model deformation measurements of the Northrop Grumman-built Smart Wing tested in the NASA Langley Transonic Dynamics Tunnel. The F18-E/F platform Smart Wing was outfitted with embedded shape memory alloys to actuate a seamless trailing edge aileron and flat, and an embedded torque tube to generate wing twist. The VMD system was used to obtain highly accurate deformation measurements at three spanwise locations along the main body of the wing, and at spanwise locations on the flap and aileron. The PMI system was used to obtain full-field wing shape and deformation measurements over the entire wing lower surface. Although less accurate than the VMD system, the PMI system revealed deformations occurring between VMD target rows indistinguishable by VMD. This paper presents the VMD and PMI techniques and discusses their application in the Smart Wing test.
Deformation Measurements of Smart Aerodynamic Surfaces
NASA Technical Reports Server (NTRS)
Fleming, Gary A.; Burner, Alpheus
2005-01-01
Video Model Deformation (VMD) and Projection Moire Interferometry (PMI) were used to acquire wind tunnel model deformation measurements of the Northrop Grumman-built Smart Wing tested in the NASA Langley Transonic Dynamics Tunnel. The F18-E/F planform Smart Wing was outfitted with embedded shape memory alloys to actuate a seamless trailing edge aileron and flap, and an embedded torque tube to generate wing twist. The VMD system was used to obtain highly accurate deformation measurements at three spanwise locations along the main body of the wing, and at spanwise locations on the flap and aileron. The PMI system was used to obtain full-field wing shape and deformation measurements over the entire wing lower surface. Although less accurate than the VMD system, the PMI system revealed deformations occurring between VMD target rows indistinguishable by VMD. This paper presents the VMD and PMI techniques and discusses their application in the Smart Wing test.
Nilpotent deformations of N = 2 superspace
NASA Astrophysics Data System (ADS)
Ivanov, Evgeny; Zupnik, Boris; Lechtenfeld, Olaf
2004-02-01
We investigate deformations of four-dimensional N = (1,1) euclidean superspace induced by nonanticommuting fermionic coordinates. We essentially use the harmonic superspace approach and consider nilpotent bi-differential Poisson operators only. One variant of such deformations (termed chiral nilpotent) directly generalizes the recently studied chiral deformation of N = (1/2,1/2) superspace. It preserves chirality and harmonic analyticity but generically breaks N = (1,1) to N = (1,0) supersymmetry. Yet, for degenerate choices of the constant deformation matrix N = (1,1/2) supersymmetry can be retained, i.e. a fraction of 3/4. An alternative version (termed analytic nilpotent) imposes minimal nonanticommutativity on the analytic coordinates of harmonic superspace. It does not affect the analytic subspace and respects all supersymmetries, at the expense of chirality however. For a chiral nilpotent deformation, we present non(anti)commutative euclidean analogs of N = 2 Maxwell and hypermultiplet off-shell actions.
Wang, Shaobai; Xia, Qun; Passias, Peter; Li, Weishi; Wood, Kirkham; Li, Guoan
2013-01-01
Study Design Case-control study. Objective . To evaluate the effect of lumbar degenerative disc disease (DDD) on the disc deformation at the adjacent level and at the level one above the adjacent level during end ranges of lumbar motion. Summary of Background Data It has been reported that in patients with DDD, the intervertebral discs adjacent to the diseased levels have a greater tendency to degenerate. Although altered biomechanics have been suggested to be the causative factors, few data have been reported on the deformation characteristics of the adjacent discs in patients with DDD. Methods Ten symptomatic patients with discogenic low back pain between L4 and S1 and with healthy discs at the cephalic segments were involved. Eight healthy subjects recruited in our previous studies were used as a reference comparison. The in vivo kinematics of L3–L4 (the cephalic adjacent level to the degenerated discs) and L2–L3 (the level one above the adjacent level) lumbar discs of both groups were obtained using a combined magnetic resonance imaging and dual fluoroscopic imaging technique at functional postures. Deformation characteristics, in terms of areas of minimal deformation (defined as less than 5%), deformations at the center of the discs, and maximum tensile and shear deformations, were compared between the two groups at the two disc levels. Results In the patients with DDD, there were significantly smaller areas of minimal disc deformation at L3–L4 and L2–L3 than the healthy subjects (18% compared with 45% of the total disc area, on average). Both L2–L3 and L3–L4 discs underwent larger tensile and shear deformations in all postures than the healthy subjects. The maximum tensile deformations were higher by up to 23% (of the local disc height in standing) and the maximum shear deformations were higher by approximately 25% to 40% (of the local disc height in standing) compared with those of the healthy subjects. Conclusion Both the discs of the adjacent
The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation
Deta, U. A. E-mail: utamadeta@unesa.ac.id; Suparmi
2015-09-30
Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.
NASA Technical Reports Server (NTRS)
Chan, K. S.; Page, R. A.
1988-01-01
Inelastic deformation behavior of the cast Ni-base alloy, B1900 + Hf, was investigated using data from step-temperature tensile tests and thermomechanical cyclic tests in the temperature ranges 538-760 C and 760-982 C. The deformation results were correlated with the dislocation structures of deformed specimens, identified by TEM. It was found that, in the 760-982 C temperature range, there are no thermal history effects in the inelastic deformation behavior of B1900 + Hf. In the 538-760 range, anomalous cyclic hardening and, possibly, thermal history effects were observed in thermomechanically deformed alloy, caused by sessile (010) dislocations in the gamma-prime phase.
On the Validity of the Adiabatic Approximation in Compact Binary Inspirals
NASA Astrophysics Data System (ADS)
Maselli, Andrea; Gualtieri, Leonardo; Ferrari, Valeria; Pannarale, Francesco
2015-01-01
We use the post-Newtonian-Affine model to assess the validity of the adiabatic approximation in modeling tidal effects in the phase evolution of compact binary systems. We compute the dynamical evolution of the tidal tensor, which we estimate at the 2PN order, and of the quadrupole tensor, finding that their ratio, i.e. the tidal deformability, increases in the last phases of the inspiral. We derive the gravitational wave phase corrections due to this phenomenon and quantify how they affect gravitational wave detectability.
Valiev, R.Z. |; Mishral, R.S.; Grozal, J.; Mukherjee, A.K.
1996-05-01
Severe plastic deformation consolidation process of the ball-milled powder has been able to produce fully dense nanocrystalline nickel with a grain size of {approximately}20 nm. The processed samples are characterized by very high elastic strains, very likely caused by a presence of high density of extrinsic grain boundary dislocations. The combined effect of the smallest nanoscale grain size in nickel, as obtained in this study, along with the effect of high elastic strains, resulted in the high level of hardness and also the lower experimentally measured density of these severe plastic deformation consolidation samples.
Quadrupole deformation of electron shells in the lattice dynamics of compressed rare-gas crystals
NASA Astrophysics Data System (ADS)
Troitskaya, E. P.; Chabanenko, Val. V.; Zhikharev, I. V.; Gorbenko, Ie. Ie.; Pilipenko, E. A.
2012-06-01
The lattice dynamics of rare-gas crystals has been constructed taking into account the deformation of electron shells of the atoms of the dipole and quadrupole types, depending on the displacement of the nuclei. The obtained equations of lattice vibrations have been investigated in the long-wavelength approximation. The role played by the three-body interaction and the deformation of the electron shells in the violation of the Cauchy relation has been discussed. The calculated Birch elastic moduli for Xe and deviations from the Cauchy relation are in good agreement with the available experimental data over a wide range of pressures.
Large Deformations of a Soft Porous Material
NASA Astrophysics Data System (ADS)
MacMinn, Christopher W.; Dufresne, Eric R.; Wettlaufer, John S.
2016-04-01
Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy's law with Terzaghi's effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the large-deformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated with the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic
Approximate Sensory Data Collection: A Survey
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-01-01
With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximate data collection algorithms. We classify them into three categories: the model-based ones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted. PMID:28287440
Revisiting approximate dynamic programming and its convergence.
Heydari, Ali
2014-12-01
Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed.
Variational extensions of the mean spherical approximation
NASA Astrophysics Data System (ADS)
Blum, L.; Ubriaco, M.
2000-04-01
In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E- TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy.
Investigating Material Approximations in Spacecraft Radiation Analysis
NASA Technical Reports Server (NTRS)
Walker, Steven A.; Slaba, Tony C.; Clowdsley, Martha S.; Blattnig, Steve R.
2011-01-01
During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Approximation of Failure Probability Using Conditional Sampling
NASA Technical Reports Server (NTRS)
Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.
2008-01-01
In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.
Adaptive Discontinuous Galerkin Approximation to Richards' Equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Miller, C. T.
2006-12-01
Due to the occurrence of large gradients in fluid pressure as a function of space and time resulting from nonlinearities in closure relations, numerical solutions to Richards' equations are notoriously difficult for certain media properties and auxiliary conditions that occur routinely in describing physical systems of interest. These difficulties have motivated a substantial amount of work aimed at improving numerical approximations to this physically important and mathematically rich model. In this work, we build upon recent advances in temporal and spatial discretization methods by developing spatially and temporally adaptive solution approaches based upon the local discontinuous Galerkin method in space and a higher order backward difference method in time. Spatial step-size adaption, h adaption, approaches are evaluated and a so-called hp-adaption strategy is considered as well, which adjusts both the step size and the order of the approximation. Solution algorithms are advanced and performance is evaluated. The spatially and temporally adaptive approaches are shown to be robust and offer significant increases in computational efficiency compared to similar state-of-the-art methods that adapt in time alone. In addition, we extend the proposed methods to two dimensions and provide preliminary numerical results.
Perturbed kernel approximation on homogeneous manifolds
NASA Astrophysics Data System (ADS)
Levesley, J.; Sun, X.
2007-02-01
Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.
Analytic approximate radiation effects due to Bremsstrahlung
Ben-Zvi I.
2012-02-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.
Approximate solutions to fractional subdiffusion equations
NASA Astrophysics Data System (ADS)
Hristov, J.
2011-03-01
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations.
Sirenomelia apus: a rare deformity.
Kshirsagar, Vinayak Y; Ahmed, Minhajuddin; Colaco, Sylvia M
2012-07-01
Sirenomelia also known as the mermaid syndrome, is a rare congenital malformation of uncertain etiology. It is characterized by fusion of the lower limbs and commonly associated with severe urogenital and gastrointestinal malformations. There are approximately 300 cases reported in the literature, 15% of which are associated with twinning, most often monozygotic. The syndrome of caudal regression is thought to be the result of injury to the caudal mesoderm early in gestation.