Finite element and analytical solutions for van der Pauw and four-point probe correction factors when multiple non-ideal measurement conditions coexist.

PubMed

Reveil, Mardochee; Sorg, Victoria C; Cheng, Emily R; Ezzyat, Taha; Clancy, Paulette; Thompson, Michael O

2017-09-01

This paper presents an extensive collection of calculated correction factors that account for the combined effects of a wide range of non-ideal conditions often encountered in realistic four-point probe and van der Pauw experiments. In this context, "non-ideal conditions" refer to conditions that deviate from the assumptions on sample and probe characteristics made in the development of these two techniques. We examine the combined effects of contact size and sample thickness on van der Pauw measurements. In the four-point probe configuration, we examine the combined effects of varying the sample's lateral dimensions, probe placement, and sample thickness. We derive an analytical expression to calculate correction factors that account, simultaneously, for finite sample size and asymmetric probe placement in four-point probe experiments. We provide experimental validation of the analytical solution via four-point probe measurements on a thin film rectangular sample with arbitrary probe placement. The finite sample size effect is very significant in four-point probe measurements (especially for a narrow sample) and asymmetric probe placement only worsens such effects. The contribution of conduction in multilayer samples is also studied and found to be substantial; hence, we provide a map of the necessary correction factors. This library of correction factors will enable the design of resistivity measurements with improved accuracy and reproducibility over a wide range of experimental conditions.

The effect of finite field size on classification and atmospheric correction

NASA Technical Reports Server (NTRS)

Kaufman, Y. J.; Fraser, R. S.

1981-01-01

The atmospheric effect on the upward radiance of sunlight scattered from the Earth-atmosphere system is strongly influenced by the contrasts between fields and their sizes. For a given atmospheric turbidity, the atmospheric effect on classification of surface features is much stronger for nonuniform surfaces than for uniform surfaces. Therefore, the classification accuracy of agricultural fields and urban areas is dependent not only on the optical characteristics of the atmosphere, but also on the size of the surface do not account for the nonuniformity of the surface have only a slight effect on the classification accuracy; in other cases the classification accuracy descreases. The radiances above finite fields were computed to simulate radiances measured by a satellite. A simulation case including 11 agricultural fields and four natural fields (water, soil, savanah, and forest) was used to test the effect of the size of the background reflectance and the optical thickness of the atmosphere on classification accuracy. It is concluded that new atmospheric correction methods, which take into account the finite size of the fields, have to be developed to improve significantly the classification accuracy.

Radiative nonrecoil nuclear finite size corrections of order α(Zα)5 to the Lamb shift in light muonic atoms

NASA Astrophysics Data System (ADS)

Faustov, R. N.; Martynenko, A. P.; Martynenko, F. A.; Sorokin, V. V.

2017-12-01

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order α(Zα) 5 to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using modern experimental data on the electromagnetic form factors of light nuclei.

Accuracy of topological entanglement entropy on finite cylinders.

PubMed

Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon

2013-09-06

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

Finite-size corrections in simulation of dipolar fluids

NASA Astrophysics Data System (ADS)

Belloni, Luc; Puibasset, Joël

2017-12-01

Monte Carlo simulations of dipolar fluids are performed at different numbers of particles N = 100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,Ω) is accumulated in terms of projections gmnl(r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominates in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals, and bridge functions can be derived from box sizes as small as N ≈ 100, even with existing long-range tails. In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the 1/N dependence of the gmnl(r) is shown to disagree with the, yet well-accepted, prediction of the literature.

Universal thermal corrections to single interval entanglement entropy for two dimensional conformal field theories.

PubMed

Cardy, John; Herzog, Christopher P

2014-05-02

We consider single interval Rényi and entanglement entropies for a two dimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any two dimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle.

The nature of the laning transition in two dimensions

NASA Astrophysics Data System (ADS)

Glanz, T.; Löwen, H.

2012-11-01

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures (‘lanes’) characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262 144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Nonvariational calculation of the relativistic, finite-size, and QED corrections for the 2 1S excited state of the helium atom

NASA Astrophysics Data System (ADS)

Haftel, M. I.; Mandelzweig, V. B.

1994-05-01

Relativistic and QED corrections are calculated by using a direct solution of the Schrödinger equation for the 2 1S excited state of the helium atom obtained with the correlation-function hyperspherical-harmonic method. Our extremely accurate nonvariational results for relativistic, QED, and finite-size corrections coincide exactly (up to 0.000 03 cm-1) with the values obtained in precision variational calculations of Drake [Nucl. Instrum. Methods Phys. Res. B 5, 2207 (1988)] and Baker, Hill, and Morgan [in Relativistic, Quantum Electrodynamic and Weak Interaction Effects in Atoms, edited by Walter Johnson, Peter Mohr, and Joseph Sucher, AIP Conf. Proc. No. 189 (AIP, New York, 1989), p. 123] for both infinite and finite nuclear masses. This confirms that a discrepancy of 0.0033 cm-1 between theory and experiment is not a result of an inaccuracy of variational wave functions, but is rooted in our inadequate knowledge of the QED operators. A better understanding of the different QED contributions to the operators (such as, for example, a more precise estimate of the Bethe logarithm) is therefore needed to explain the discrepancy.

Nonperturbative theory for the dispersion self-energy of atoms

NASA Astrophysics Data System (ADS)

Thiyam, Priyadarshini; Persson, C.; Brevik, I.; Sernelius, Bo E.; Boström, Mathias

2014-11-01

We go beyond the approximate series expansions used in the dispersion theory of finite-size atoms. We demonstrate that a correct, and nonperturbative, theory dramatically alters the dispersion self-energies of atoms. The nonperturbed theory gives as much as 100 % corrections compared to the traditional series-expanded theory for the smaller noble gas atoms.

1/ f noise from the laws of thermodynamics for finite-size fluctuations.

PubMed

Chamberlin, Ralph V; Nasir, Derek M

2014-07-01

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals and to show non-Gaussian fluctuations characteristic of nanoscale systems.

Predator-prey Encounter Rates in Turbulent Environments: Consequences of Inertia Effects and Finite Sizes

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

Pecseli, H. L.; Trulsen, J.

2009-10-08

Experimental as well as theoretical studies have demonstrated that turbulence can play an important role for the biosphere in marine environments, in particular also by affecting prey-predator encounter rates. Reference models for the encounter rates rely on simplifying assumptions of predators and prey being described as point particles moving passively with the local flow velocity. Based on simple arguments that can be tested experimentally we propose corrections for the standard expression for the encounter rates, where now finite sizes and Stokes drag effects are included.

Sensitivity of resistive and Hall measurements to local inhomogeneities: Finite-field, intensity, and area corrections

NASA Astrophysics Data System (ADS)

Koon, Daniel W.; Wang, Fei; Petersen, Dirch Hjorth; Hansen, Ole

2014-10-01

We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. We express these sensitivities for conductance tensor components and for other charge transport quantities. Both resistive and Hall sensitivities, for a van der Pauw specimen in a finite magnetic field, are a superposition of the zero-field sensitivities to both sheet resistance and Hall sheet resistance. Strong perturbations produce a nonlinear correction term that depends on the strength of the inhomogeneity. Solution of the specific case of a finite-sized circular inhomogeneity coaxial with a circular specimen suggests a first-order correction for the general case. Our results are confirmed by computer simulations on both a linear four-point probe array on a large circular disc and a van der Pauw square geometry. Furthermore, the results also agree well with Náhlík et al. published experimental results for physical holes in a circular copper foil disc.

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

NASA Astrophysics Data System (ADS)

Hall, J. M. M.; Leinweber, D. B.; Young, R. D.

2014-03-01

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.

Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

NASA Astrophysics Data System (ADS)

Altieri, Ada

2018-01-01

In view of the results achieved in a previously related work [A. Altieri, S. Franz, and G. Parisi, J. Stat. Mech. (2016) 093301], 10.1088/1742-5468/2016/09/093301, regarding a Plefka-like expansion of the free energy up to the second order in the perceptron model, we improve the computation here focusing on the role of third-order corrections. The perceptron model is a simple example of constraint satisfaction problem, falling in the same universality class as hard spheres near jamming and hence allowing us to get exact results in high dimensions for more complex settings. Our method enables to define an effective potential (or Thouless-Anderson-Palmer free energy), namely a coarse-grained functional, which depends on the generalized forces and the effective gaps between particles. The analysis of the third-order corrections to the effective potential reveals that, albeit irrelevant in a mean-field framework in the thermodynamic limit, they might instead play a fundamental role in considering finite-size effects. We also study the typical behavior of generalized forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. We nevertheless show that third-order corrections in the perturbative expansion vanish in the jamming limit both for the potential and the generalized forces, in agreement with the isostaticity argument proposed by Wyart and coworkers. Finally, we analyze the relevant scaling solutions emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

Higher-order corrections to the effective potential close to the jamming transition in the perceptron model.

PubMed

Altieri, Ada

2018-01-01

In view of the results achieved in a previously related work [A. Altieri, S. Franz, and G. Parisi, J. Stat. Mech. (2016) 093301]10.1088/1742-5468/2016/09/093301, regarding a Plefka-like expansion of the free energy up to the second order in the perceptron model, we improve the computation here focusing on the role of third-order corrections. The perceptron model is a simple example of constraint satisfaction problem, falling in the same universality class as hard spheres near jamming and hence allowing us to get exact results in high dimensions for more complex settings. Our method enables to define an effective potential (or Thouless-Anderson-Palmer free energy), namely a coarse-grained functional, which depends on the generalized forces and the effective gaps between particles. The analysis of the third-order corrections to the effective potential reveals that, albeit irrelevant in a mean-field framework in the thermodynamic limit, they might instead play a fundamental role in considering finite-size effects. We also study the typical behavior of generalized forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. We nevertheless show that third-order corrections in the perturbative expansion vanish in the jamming limit both for the potential and the generalized forces, in agreement with the isostaticity argument proposed by Wyart and coworkers. Finally, we analyze the relevant scaling solutions emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

Finite-size effects in simulations of electrolyte solutions under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Thompson, Jeffrey; Sanchez, Isaac

The equilibrium properties of charged systems with periodic boundary conditions may exhibit pronounced system-size dependence due to the long range of the Coulomb force. As shown by others, the leading-order finite-size correction to the Coulomb energy of a charged fluid confined to a periodic box of volume V may be derived from sum rules satisfied by the charge-charge correlations in the thermodynamic limit V -> ∞ . In classical systems, the relevant sum rule is the Stillinger-Lovett second-moment (or perfect screening) condition. This constraint implies that for large V, periodicity induces a negative bias of -kB T(2 V) - 1 in the total Coulomb energy density of a homogeneous classical charged fluid of given density and temperature. We present a careful study of the impact of such finite-size effects on the calculation of solute chemical potentials from explicit-solvent molecular simulations of aqueous electrolyte solutions. National Science Foundation Graduate Research Fellowship Program, Grant No. DGE-1610403.

Atmospheric effect on classification of finite fields. [satellite-imaged agricultural areas

NASA Technical Reports Server (NTRS)

Kaufman, Y. J.; Fraser, R. S.

1984-01-01

The atmospheric effect on the upward radiance of sunlight scattered from the earth-atmosphere system is strongly influenced by the contrasts between fields and their sizes. In this paper, the radiances above finite fields are computed to simulate radiances measured by a satellite. A simulation case including 11 agricultural fields and four natural fields (water, soil, savanah, and forest) is used to test the effect of field size, background reflectance, and optical thickness of the atmosphere on the classification accuracy. For a given atmospheric turbidity, the atmospheric effect on classification of surface features may be much stronger for nonuniform surfaces than for uniform surfaces. Therefore, the classification accuracy of agricultural fields and urban areas is dependent not only on the optical characteristics of the atmosphere, but also on the size of the surface elements to be classified and their contrasts. It is concluded that new atmospheric correction methods, which take into account the finite size of the fields, are needed.

System-size corrections for self-diffusion coefficients calculated from molecular dynamics simulations: The case of CO2, n-alkanes, and poly(ethylene glycol) dimethyl ethers

NASA Astrophysics Data System (ADS)

Moultos, Othonas A.; Zhang, Yong; Tsimpanogiannis, Ioannis N.; Economou, Ioannis G.; Maginn, Edward J.

2016-08-01

Molecular dynamics simulations were carried out to study the self-diffusion coefficients of CO2, methane, propane, n-hexane, n-hexadecane, and various poly(ethylene glycol) dimethyl ethers (glymes in short, CH3O-(CH2CH2O)n-CH3 with n = 1, 2, 3, and 4, labeled as G1, G2, G3, and G4, respectively) at different conditions. Various system sizes were examined. The widely used Yeh and Hummer [J. Phys. Chem. B 108, 15873 (2004)] correction for the prediction of diffusion coefficient at the thermodynamic limit was applied and shown to be accurate in all cases compared to extrapolated values at infinite system size. The magnitude of correction, in all cases examined, is significant, with the smallest systems examined giving for some cases a self-diffusion coefficient approximately 15% lower than the infinite system-size extrapolated value. The results suggest that finite size corrections to computed self-diffusivities must be used in order to obtain accurate results.

Finite-size scaling analysis in the two-photon Dicke model

NASA Astrophysics Data System (ADS)

Chen, Xiang-You; Zhang, Yu-Yu

2018-05-01

We perform a Schrieffer-Wolff transformation to the two-photon Dicke model by keeping the leading-order correction with a quartic term of the field, which is crucial for finite-size scaling analysis. Besides a spectral collapse as a consequence of two-photon interaction, the super-radiant phase transition is indicated by the vanishing of the excitation energy and the uniform atomic polarization. The scaling functions for the ground-state energy and the atomic pseudospin are derived analytically. The scaling exponents of the observables are the same as those in the standard Dicke model, indicating they are in the same universality class.

Full self-consistency in the Fermi-orbital self-interaction correction

NASA Astrophysics Data System (ADS)

Yang, Zeng-hui; Pederson, Mark R.; Perdew, John P.

2017-05-01

The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-Löwdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm Pederson et al., J. Chem. Phys. 140, 121103 (2014)., 10.1063/1.4869581 appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper, we demonstrate a different algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

Quadratic electroweak corrections for polarized Moller scattering

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

A. Aleksejevs, S. Barkanova, Y. Kolomensky, E. Kuraev, V. Zykunov

2012-01-01

The paper discusses the two-loop (NNLO) electroweak radiative corrections to the parity violating electron-electron scattering asymmetry induced by squaring one-loop diagrams. The calculations are relevant for the ultra-precise 11 GeV MOLLER experiment planned at Jefferson Laboratory and experiments at high-energy future electron colliders. The imaginary parts of the amplitudes are taken into consideration consistently in both the infrared-finite and divergent terms. The size of the obtained partial correction is significant, which indicates a need for a complete study of the two-loop electroweak radiative corrections in order to meet the precision goals of future experiments.

Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations.

PubMed

Salvalaglio, Matteo; Tiwary, Pratyush; Maggioni, Giovanni Maria; Mazzotti, Marco; Parrinello, Michele

2016-12-07

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated. Nucleation rates spanning a range of 10 orders of magnitude are computed at moderate supersaturation levels, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems.

Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations

NASA Astrophysics Data System (ADS)

Salvalaglio, Matteo; Tiwary, Pratyush; Maggioni, Giovanni Maria; Mazzotti, Marco; Parrinello, Michele

2016-12-01

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated. Nucleation rates spanning a range of 10 orders of magnitude are computed at moderate supersaturation levels, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems.

Adsorption of finite semiflexible polymers and their loop and tail distributions

NASA Astrophysics Data System (ADS)

Kampmann, Tobias A.; Kierfeld, Jan

2017-07-01

We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of finite length and their loop and tail distributions using both Monte Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the deflection length exceeds the contour length. In the flexible and semiflexible regimes, finite size corrections arise because the correlation length exceeds the contour length. In the rigid rod regime, however, it is essential how the global orientational or translational degrees of freedom are restricted by grafting or confinement. We discuss finite size corrections for polymers grafted to the adsorbing surface and for polymers confined by a second (parallel) hard wall. Based on these results, we obtain a method to analyze adsorption data for finite semiflexible polymers such as filamentous actin. For the loop and tail distributions, we find power laws with an exponential decay on length scales exceeding the correlation length. We derive and confirm the loop and tail power law exponents for flexible and semiflexible polymers. This allows us to explain that, close to the transition, semiflexible polymers have significantly smaller loops and both flexible and semiflexible polymers desorb by expanding their tail length. The tail distribution allows us to extract the free energy per length of adsorption for actin filaments from experimental data [D. Welch et al., Soft Matter 11, 7507 (2015)].

Renormalization-group theory for finite-size scaling in extreme statistics

NASA Astrophysics Data System (ADS)

Györgyi, G.; Moloney, N. R.; Ozogány, K.; Rácz, Z.; Droz, M.

2010-04-01

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

Correlated Debye model for atomic motions in metal nanocrystals

NASA Astrophysics Data System (ADS)

Scardi, P.; Flor, A.

2018-05-01

The Correlated Debye model for the mean square relative displacement of atoms in near-neighbour coordination shells has been extended to include the effect of finite crystal size. This correctly explains the increase in Debye-Waller coefficient observed for metal nanocrystals. A good match with Molecular Dynamics simulations of Pd nanocrystals is obtained if, in addition to the phonon confinement effect of the finite domain size, proper consideration is also given to the static disorder component caused by the undercoordination of surface atoms. The new model, which addresses the analysis of the Pair Distribution Function and powder diffraction data collected at different temperatures, was preliminarily tested on recently published experimental data on nanocrystalline Pt powders.

Stress Intensity Factor Plasticity Correction for Flaws in Stress Concentration Regions

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

Friedman, E.; Wilson, W.K.

2000-02-01

Plasticity corrections to elastically computed stress intensity factors are often included in brittle fracture evaluation procedures. These corrections are based on the existence of a plastic zone in the vicinity of the crack tip. Such a plastic zone correction is included in the flaw evaluation procedure of Appendix A to Section XI of the ASME Boiler and Pressure Vessel Code. Plasticity effects from the results of elastic and elastic-plastic explicit flaw finite element analyses are examined for various size cracks emanating from the root of a notch in a panel and for cracks located at fillet fadii. The results ofmore » these caluclations provide conditions under which the crack-tip plastic zone correction based on the Irwin plastic zone size overestimates the plasticity effect for crack-like flaws embedded in stress concentration regions in which the elastically computed stress exceeds the yield strength of the material. A failure assessment diagram (FAD) curve is employed to graphically c haracterize the effect of plasticity on the crack driving force. The Option 1 FAD curve of the Level 3 advanced fracture assessment procedure of British Standard PD 6493:1991, adjusted for stress concentration effects by a term that is a function of the applied load and the ratio of the local radius of curvature at the flaw location to the flaw depth, provides a satisfactory bound to all the FAD curves derived from the explicit flaw finite element calculations. The adjusted FAD curve is a less restrictive plasticity correction than the plastic zone correction of Section XI for flaws embedded in plastic zones at geometric stress concentrators. This enables unnecessary conservatism to be removed from flaw evaluation procedures that utilize plasticity corrections.« less

System-size corrections for self-diffusion coefficients calculated from molecular dynamics simulations: The case of CO{sub 2}, n-alkanes, and poly(ethylene glycol) dimethyl ethers

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

Moultos, Othonas A.; Economou, Ioannis G.; Zhang, Yong

Molecular dynamics simulations were carried out to study the self-diffusion coefficients of CO{sub 2}, methane, propane, n-hexane, n-hexadecane, and various poly(ethylene glycol) dimethyl ethers (glymes in short, CH{sub 3}O–(CH{sub 2}CH{sub 2}O){sub n}–CH{sub 3} with n = 1, 2, 3, and 4, labeled as G1, G2, G3, and G4, respectively) at different conditions. Various system sizes were examined. The widely used Yeh and Hummer [J. Phys. Chem. B 108, 15873 (2004)] correction for the prediction of diffusion coefficient at the thermodynamic limit was applied and shown to be accurate in all cases compared to extrapolated values at infinite system size. Themore » magnitude of correction, in all cases examined, is significant, with the smallest systems examined giving for some cases a self-diffusion coefficient approximately 15% lower than the infinite system-size extrapolated value. The results suggest that finite size corrections to computed self-diffusivities must be used in order to obtain accurate results.« less

Building a linear equation-of-state for trapped gravitons from finite size effects and the Schwarzschild black hole case

NASA Astrophysics Data System (ADS)

Viaggiu, Stefano

In this paper, we continue the investigations present in [S. Viaggiu, Physica A 473 (2017) 412; 488 (2017) 72.] concerning the spectrum of trapped gravitons in a spherical box, and in particular, inside a Schwarzschild black hole (BH). We explore the possibility that, due to finite size effects, the frequency of the radiation made of trapped gravitons can be modified in such a way that a linear equation-of-state PV = γU for the pressure P and the internal energy U arises. Firstly, we study the case with U ˜ R, where only fluids with γ > ‑1 3 are possible. If corrections ˜ 1/R are added to U, for γ ∈ [0, 1 3], we found no limitation on the allowed value for the areal radius of the trapped sphere R. Moreover, for γ > 1 3, we have a minimum allowed value for R of the order of the Planck length LP. Conversely, a fluid with P < 0 can be obtained but with a maximum allowed value for R. With the added term looking like ˜ 1/R to the BH internal energy U, the well-known logarithmic corrections to the BH entropy naturally emerge for any linear equation-of-state. The results of this paper suggest that finite size effects could modify the structure of graviton’s radiation inside, showing a possible mechanism to transform radiation into dark energy.

Spectral function of a hole in the t - J model

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

Liu, Z.; Manousakis, E.

1991-08-01

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink {ital et} {ital al}. and Kane {ital et} {ital al}. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 4{sup 2} lattice in the region of {ital J}/{ital t}{le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others changemore » due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.« less

Driven Langevin systems: fluctuation theorems and faithful dynamics

NASA Astrophysics Data System (ADS)

Sivak, David; Chodera, John; Crooks, Gavin

2014-03-01

Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Finite-Size Effects in Non-neutral Two-Dimensional Coulomb Fluids

NASA Astrophysics Data System (ADS)

Šamaj, Ladislav

2017-07-01

Thermodynamic potential of a neutral two-dimensional (2D) Coulomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature β a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number c=-1. A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary ± e charges at coupling constant Γ =β e^2, was studied in the past. It was shown that creating a non-neutrality by spreading out a charge Qe at infinity modifies the anomaly number to c(Q,Γ ) = - 1 + 3Γ Q^2. Here, we study the effect of non-neutrality on the finite-size expansion of the free energy for another Coulomb fluid, namely the 2D one-component plasma (jellium) composed of identical pointlike e-charges in a homogeneous background surface charge density. For the disk geometry of the confining domain we find that the non-neutrality induces the same change of the anomaly number in the finite-size expansion. We derive this result first at the free-fermion coupling Γ ≡ β e^2=2 and then, by using a mapping of the 2D one-component plasma onto an anticommuting field theory formulated on a chain, for an arbitrary even coupling constant.

A computational framework for automation of point defect calculations

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

Goyal, Anuj; Gorai, Prashun; Peng, Haowei

We have developed a complete and rigorously validated open-source Python framework to automate point defect calculations using density functional theory. Furthermore, the framework provides an effective and efficient method for defect structure generation, and creation of simple yet customizable workflows to analyze defect calculations. This package provides the capability to compute widely-accepted correction schemes to overcome finite-size effects, including (1) potential alignment, (2) image-charge correction, and (3) band filling correction to shallow defects. Using Si, ZnO and In2O3 as test examples, we demonstrate the package capabilities and validate the methodology.

A computational framework for automation of point defect calculations

DOE PAGES

Goyal, Anuj; Gorai, Prashun; Peng, Haowei; ...

2017-01-13

We have developed a complete and rigorously validated open-source Python framework to automate point defect calculations using density functional theory. Furthermore, the framework provides an effective and efficient method for defect structure generation, and creation of simple yet customizable workflows to analyze defect calculations. This package provides the capability to compute widely-accepted correction schemes to overcome finite-size effects, including (1) potential alignment, (2) image-charge correction, and (3) band filling correction to shallow defects. Using Si, ZnO and In2O3 as test examples, we demonstrate the package capabilities and validate the methodology.

Simulating correction of adjustable optics for an x-ray telescope

NASA Astrophysics Data System (ADS)

Aldcroft, Thomas L.; Schwartz, Daniel A.; Reid, Paul B.; Cotroneo, Vincenzo; Davis, William N.

2012-10-01

The next generation of large X-ray telescopes with sub-arcsecond resolution will require very thin, highly nested grazing incidence optics. To correct the low order figure errors resulting from initial manufacture, the mounting process, and the effects of going from 1 g during ground alignment to zero g on-orbit, we plan to adjust the shapes via piezoelectric "cells" deposited on the backs of the reflecting surfaces. This presentation investigates how well the corrections might be made. We take a benchmark conical glass element, 410×205 mm, with a 20×20 array of piezoelectric cells 19×9 mm in size. We use finite element analysis to calculate the influence function of each cell. We then simulate the correction via pseudo matrix inversion to calculate the stress to be applied by each cell, considering distortion due to gravity as calculated by finite element analysis, and by putative low order manufacturing distortions described by Legendre polynomials. We describe our algorithm and its performance, and the implications for the sensitivity of the resulting slope errors to the optimization strategy.

Lamb shift and fine structure at n =2 in a hydrogenlike muonic atom with the nuclear spin I =0

NASA Astrophysics Data System (ADS)

Korzinin, Evgeny Yu.; Shelyuto, Valery A.; Ivanov, Vladimir G.; Karshenboim, Savely G.

2018-01-01

The paper is devoted to the Lamb shift and fine structure in a hydrogenlike muonic atom with a spinless nucleus up to the order α5m with all the recoil corrections included. Enhanced contributions of a higher order are also considered. We present the results on the pure QED contribution and on the finite-nuclear-size contribution, proportional to RN2, with the higher-order corrections included. We also consider the consistency of the pure QED theory and the evaluation of the nuclear-structure effects. Most of the QED theory is the same as the theory for the case of the nuclear spin 1/2. Additional nuclear-spin-dependent terms are considered in detail. The issue of the difference for the theories with a spinor nucleus and a scalar one is discussed for the recoil contributions in the order (Zα ) 4m ,α (Zα ) 4m , and (Zα ) 5m . The numerical results are presented for the muonic atoms with two lightest scalar nuclei, helium-4 and beryllium-10. We compare the theory of those muonic atoms with theory for the muonic hydrogen. Some higher-order finite-nuclear-size corrections for the Lamb shift in muonic hydrogen are revisited.

Stiffness of frictional contact of dissimilar elastic solids

DOE PAGES

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; ...

2017-12-22

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

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

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This study gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the frictionmore » coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. Finally, the correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.« less

Stiffness of frictional contact of dissimilar elastic solids

NASA Astrophysics Data System (ADS)

Lee, Jin Haeng; Gao, Yanfei; Bower, Allan F.; Xu, Haitao; Pharr, George M.

2018-03-01

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations - adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

Revision of the documentation for a model for calculating effects of liquid waste disposal in deep saline aquifers

USGS Publications Warehouse

INTERA Environmental Consultants, Inc.

1979-01-01

The major limitation of the model arises using second-order correct (central-difference) finite-difference approximation in space. To avoid numerical oscillations in the solution, the user must restrict grid block and time step sizes depending upon the magnitude of the dispersivity.

Size distribution and volume fraction of T(1) phase precipitates from TEM images: Direct measurements and related correction.

PubMed

Dorin, Thomas; Donnadieu, Patricia; Chaix, Jean-Marc; Lefebvre, Williams; Geuser, Frédéric De; Deschamps, Alexis

2015-11-01

Transmission Electron Microscopy (TEM) can be used to measure the size distribution and volume fraction of fine scale precipitates in metallic systems. However, such measurements suffer from a number of artefacts that need to be accounted for, related to the finite thickness of the TEM foil and to the projected observation in two dimensions of the microstructure. We present a correction procedure to describe the 3D distribution of disc-like particles and apply this method to the plate-like T1 precipitates in an Al-Li-Cu alloy in two ageing conditions showing different particle morphologies. The precipitates were imaged in a High-Angular Annular Dark Field Microscope (HAADF-STEM). The corrected size distribution is further used to determine the precipitate volume fraction. Atom probe tomography (APT) is finally utilised as an alternative way to measure the precipitate volume fraction and test the validity of the electron microscopy results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Toric-boson model: Toward a topological quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Castelnovo, Claudio; Chamon, Claudio

2009-06-01

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact.

Hadron mass corrections in semi-inclusive deep-inelastic scattering

DOE PAGES

Guerrero Teran, Juan Vicente; Ethier, James J.; Accardi, Alberto; ...

2015-09-24

We found that the spin-dependent cross sections for semi-inclusive lepton-nucleon scattering are derived in the framework of collinear factorization, including the effects of masses of the target and produced hadron at finite Q 2. At leading order the cross sections factorize into products of parton distribution and fragmentation functions evaluated in terms of new, mass-dependent scaling variables. Furthermore, the size of the hadron mass corrections is estimated at kinematics relevant for current and future experiments, and the implications for the extraction of parton distributions from semi-inclusive measurements are discussed.

Non-perturbative theory of dispersion interactions

NASA Astrophysics Data System (ADS)

Boström, M.; Thiyam, P.; Persson, C.; Parsons, D. F.; Buhmann, S. Y.; Brevik, I.; Sernelius, Bo E.

2015-03-01

Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here, we present a full non-perturbative theory. In addition, we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.

Scaling laws and bulk-boundary decoupling in heat flow.

PubMed

del Pozo, Jesús J; Garrido, Pedro L; Hurtado, Pablo I

2015-03-01

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows one to measure the marginal anomaly of the heat conductivity predicted for hard disks.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Scaling analysis of the non-Abelian quasiparticle tunneling in Z}}_k FQH states

NASA Astrophysics Data System (ADS)

Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang

2018-06-01

Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge–edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read–Rezayi states for and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.

Finite-size radiation force correction for inviscid spheres in standing waves.

PubMed

Marston, Philip L

2017-09-01

Yosioka and Kawasima gave a widely used approximation for the acoustic radiation force on small liquid spheres surrounded by an immiscible liquid in 1955. Considering the liquids to be inviscid with negligible thermal dissipation, in their approximation the force on the sphere is proportional to the sphere's volume and the levitation position in a vertical standing wave becomes independent of the size. The analysis given here introduces a small correction term proportional to the square of the sphere's radius relative to the aforementioned small-sphere force. The significance of this term also depends on the relative density and sound velocity of the sphere. The improved approximation is supported by comparison with the exact partial-wave-series based radiation force for ideal fluid spheres in ideal fluids.

Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter

NASA Astrophysics Data System (ADS)

Jeong, Hyunjo; Zhang, Shuzeng; Barnard, Dan; Li, Xiongbing

2015-09-01

The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α2 ≃ 2α1.

Universality from disorder in the random-bond Blume-Capel model

NASA Astrophysics Data System (ADS)

Fytas, N. G.; Zierenberg, J.; Theodorakis, P. E.; Weigel, M.; Janke, W.; Malakis, A.

2018-04-01

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L*≈32 for the chosen parameters.

Finite-size effects on current correlation functions

NASA Astrophysics Data System (ADS)

Chen, Shunda; Zhang, Yong; Wang, Jiao; Zhao, Hong

2014-02-01

We study why the calculation of current correlation functions (CCFs) still suffers from finite-size effects even when the periodic boundary condition is taken. Two important one-dimensional, momentum-conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as ˜t-2/3 in the diatomic hard-core gas model and in a manner close to ˜t-1/2 in the Fermi-Pasta-Ulam-β model.

Transient queue-size distribution in a finite-capacity queueing system with server breakdowns and Bernoulli feedback

NASA Astrophysics Data System (ADS)

Kempa, Wojciech M.

2017-12-01

A finite-capacity queueing system with server breakdowns is investigated, in which successive exponentially distributed failure-free times are followed by repair periods. After the processing a customer may either rejoin the queue (feedback) with probability q, or definitely leave the system with probability 1 - q. The system of integral equations for transient queue-size distribution, conditioned by the initial level of buffer saturation, is build. The solution of the corresponding system written for Laplace transforms is found using the linear algebraic approach. The considered queueing system can be successfully used in modelling production lines with machine failures, in which the parameter q may be considered as a typical fraction of items demanding corrections. Morever, this queueing model can be applied in the analysis of real TCP/IP performance, where q stands for the fraction of packets requiring retransmission.

Asymmetric fluid criticality. II. Finite-size scaling for simulations.

PubMed

Kim, Young C; Fisher, Michael E

2003-10-01

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions L focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded "complete" thermodynamic (L--> infinity) scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling [Phys. Rev. E 67, 061506 (2003)] is extended to finite L, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when L--> infinity, the second temperature derivative (d2musigma/dT2) of the chemical potential along the phase boundary musigmaT diverges when T-->Tc-. The finite-size behavior of various special critical loci in the temperature-density or (T,rho) plane, in particular, the k-inflection susceptibility loci and the Q-maximal loci--derived from QL(T,L) is identical with 2L/L where m is identical with rho-L--is carefully elucidated and shown to be of value in estimating Tc and rhoc. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent nu that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

NASA Astrophysics Data System (ADS)

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

2014-02-01

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In this paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

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

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In thismore » paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.« less

The electric double layer at a metal electrode in pure water

NASA Astrophysics Data System (ADS)

Brüesch, Peter; Christen, Thomas

2004-03-01

Pure water is a weak electrolyte that dissociates into hydronium ions and hydroxide ions. In contact with a charged electrode a double layer forms for which neither experimental nor theoretical studies exist, in contrast to electrolytes containing extrinsic ions like acids, bases, and solute salts. Starting from a self-consistent solution of the one-dimensional modified Poisson-Boltzmann equation, which takes into account activity coefficients of point-like ions, we explore the properties of the electric double layer by successive incorporation of various correction terms like finite ion size, polarization, image charge, and field dissociation. We also discuss the effect of the usual approximation of an average potential as required for the one-dimensional Poisson-Boltzmann equation, and conclude that the one-dimensional approximation underestimates the ion density. We calculate the electric potential, the ion distributions, the pH-values, the ion-size corrected activity coefficients, and the dissociation constants close to the electric double layer and compare the results for the various model corrections.

Polymer nanomechanics: Separating the size effect from the substrate effect in nanoindentation

NASA Astrophysics Data System (ADS)

Li, Le; Encarnacao, Lucas M.; Brown, Keith A.

2017-01-01

While the moduli of thin polymer films are known to deviate dramatically from their bulk values, there is not a consensus regarding the nature of this size effect. In particular, indenting experiments appear to contradict results from both buckling experiments and molecular dynamics calculations. In this letter, we present a combined computational and experimental method for measuring the modulus of nanoindented soft films on rigid substrates that reconciles this discrepancy. Through extensive finite element simulation, we determine a correction to the Hertzian contact model that separates the substrate effect from the thickness-dependent modulus of the film. Interestingly, this correction only depends upon a dimensionless film thickness and the Poisson ratio of the film. To experimentally test this approach, we prepared poly(methyl methacrylate), polystyrene, and parylene films with thicknesses ranging from 20 to 300 nm and studied these films using atomic force microscope-based nanoindenting. Strikingly, when experiments were interpreted using the computationally derived substrate correction, sub-70 nm films were found to be softer than bulk, in agreement with buckling experiments and molecular dynamics studies. This correction can serve as a general method for unambiguously determining the size effect of thin polymer films and ultimately lead to the ability to quantitatively image the mechanical properties of heterogeneous materials such as composites.

Estimation After a Group Sequential Trial.

PubMed

Milanzi, Elasma; Molenberghs, Geert; Alonso, Ariel; Kenward, Michael G; Tsiatis, Anastasios A; Davidian, Marie; Verbeke, Geert

2015-10-01

Group sequential trials are one important instance of studies for which the sample size is not fixed a priori but rather takes one of a finite set of pre-specified values, dependent on the observed data. Much work has been devoted to the inferential consequences of this design feature. Molenberghs et al (2012) and Milanzi et al (2012) reviewed and extended the existing literature, focusing on a collection of seemingly disparate, but related, settings, namely completely random sample sizes, group sequential studies with deterministic and random stopping rules, incomplete data, and random cluster sizes. They showed that the ordinary sample average is a viable option for estimation following a group sequential trial, for a wide class of stopping rules and for random outcomes with a distribution in the exponential family. Their results are somewhat surprising in the sense that the sample average is not optimal, and further, there does not exist an optimal, or even, unbiased linear estimator. However, the sample average is asymptotically unbiased, both conditionally upon the observed sample size as well as marginalized over it. By exploiting ignorability they showed that the sample average is the conventional maximum likelihood estimator. They also showed that a conditional maximum likelihood estimator is finite sample unbiased, but is less efficient than the sample average and has the larger mean squared error. Asymptotically, the sample average and the conditional maximum likelihood estimator are equivalent. This previous work is restricted, however, to the situation in which the the random sample size can take only two values, N = n or N = 2 n . In this paper, we consider the more practically useful setting of sample sizes in a the finite set { n 1 , n 2 , …, n L }. It is shown that the sample average is then a justifiable estimator , in the sense that it follows from joint likelihood estimation, and it is consistent and asymptotically unbiased. We also show why simulations can give the false impression of bias in the sample average when considered conditional upon the sample size. The consequence is that no corrections need to be made to estimators following sequential trials. When small-sample bias is of concern, the conditional likelihood estimator provides a relatively straightforward modification to the sample average. Finally, it is shown that classical likelihood-based standard errors and confidence intervals can be applied, obviating the need for technical corrections.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

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

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Ab initio structures and polarizabilities of sodium clusters

NASA Astrophysics Data System (ADS)

Kronik, Leeor; Vasiliev, Igor; Jain, Manish; Chelikowsky, James R.

2001-09-01

We present quantitative ab initio calculations for Na cluster structures and polarizabilities, for all cluster sizes up to 20 atoms. Our calculations are performed by combining an ab initio core-corrected pseudopotential and a gradient-corrected density functional within a real space approach. We find the cluster bonding to be very floppy and catalog a host of low-energy quasi-degenerate isomers for all second-decade clusters. The existence of these isomers results in a band of polarizability values for each cluster size even at zero temperature. This eliminates any finer structure in the polarizability curve. We further show that the experimental polarizability values are consistently underestimated by calculations at zero temperature. By computing the effects of structure expansion and distortion due to a finite temperature we arrive at a quantitative agreement between theory and experiment.

A piece of cake: the ground-state energies in γ i -deformed = 4 SYM theory at leading wrapping order

NASA Astrophysics Data System (ADS)

Fokken, Jan; Sieg, Christoph; Wilhelm, Matthias

2014-09-01

In the non-supersymmetric γi-deformed = 4 SYM theory, the scaling dimensions of the operators tr[ Z L ] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L ≥ 3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Lüscher corrections, TBA and Y-system equations. At L = 2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing β-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken — even in the 't Hooft limit. [Figure not available: see fulltext.

Modal density of rectangular structures in a wide frequency range

NASA Astrophysics Data System (ADS)

Parrinello, A.; Ghiringhelli, G. L.

2018-04-01

A novel approach to investigate the modal density of a rectangular structure in a wide frequency range is presented. First, the modal density is derived, in the whole frequency range of interest, on the basis of sound transmission through the infinite counterpart of the structure; then, it is corrected by means of the low-frequency modal behavior of the structure, taking into account actual size and boundary conditions. A statistical analysis reveals the connection between the modal density of the structure and the transmission of sound through its thickness. A transfer matrix approach is used to compute the required acoustic parameters, making it possible to deal with structures having arbitrary stratifications of different layers. A finite element method is applied on coarse grids to derive the first few eigenfrequencies required to correct the modal density. Both the transfer matrix approach and the coarse grids involved in the finite element analysis grant high efficiency. Comparison with alternative formulations demonstrates the effectiveness of the proposed methodology.

Gapless Spin-Liquid Ground State in the S =1 /2 Kagome Antiferromagnet

NASA Astrophysics Data System (ADS)

Liao, H. J.; Xie, Z. Y.; Chen, J.; Liu, Z. Y.; Xie, H. D.; Huang, R. Z.; Normand, B.; Xiang, T.

2017-03-01

The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S =1 /2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

GPS/INS Sensor Fusion Using GPS Wind up Model

NASA Technical Reports Server (NTRS)

Williamson, Walton R. (Inventor)

2013-01-01

A method of stabilizing an inertial navigation system (INS), includes the steps of: receiving data from an inertial navigation system; and receiving a finite number of carrier phase observables using at least one GPS receiver from a plurality of GPS satellites; calculating a phase wind up correction; correcting at least one of the finite number of carrier phase observables using the phase wind up correction; and calculating a corrected IMU attitude or velocity or position using the corrected at least one of the finite number of carrier phase observables; and performing a step selected from the steps consisting of recording, reporting, or providing the corrected IMU attitude or velocity or position to another process that uses the corrected IMU attitude or velocity or position. A GPS stabilized inertial navigation system apparatus is also described.

Discrete Thermodynamics

DOE PAGES

Margolin, L. G.; Hunter, A.

2017-10-18

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of ourmore » results both in theory and as applied to numerical simulation.« less

Discrete Thermodynamics

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

Margolin, L. G.; Hunter, A.

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of ourmore » results both in theory and as applied to numerical simulation.« less

Correcting intensity loss errors in the absence of texture-free reference samples during pole figure measurement

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

Saleh, Ahmed A., E-mail: asaleh@uow.edu.au

Even with the use of X-ray polycapillary lenses, sample tilting during pole figure measurement results in a decrease in the recorded X-ray intensity. The magnitude of this error is affected by the sample size and/or the finite detector size. These errors can be typically corrected by measuring the intensity loss as a function of the tilt angle using a texture-free reference sample (ideally made of the same alloy as the investigated material). Since texture-free reference samples are not readily available for all alloys, the present study employs an empirical procedure to estimate the correction curve for a particular experimental configuration.more » It involves the use of real texture-free reference samples that pre-exist in any X-ray diffraction laboratory to first establish the empirical correlations between X-ray intensity, sample tilt and their Bragg angles and thereafter generate correction curves for any Bragg angle. It will be shown that the empirically corrected textures are in very good agreement with the experimentally corrected ones. - Highlights: •Sample tilting during X-ray pole figure measurement leads to intensity loss errors. •Texture-free reference samples are typically used to correct the pole figures. •An empirical correction procedure is proposed in the absence of reference samples. •The procedure relies on reference samples that pre-exist in any texture laboratory. •Experimentally and empirically corrected textures are in very good agreement.« less

Scaling analysis of the non-Abelian quasiparticle tunneling in [Formula: see text] FQH states.

PubMed

Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang

2018-06-27

Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge-edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read-Rezayi [Formula: see text] states for [Formula: see text] and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.

Novel Infrared Dynamics of Cold Atoms on Hot Graphene

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri; Clougherty, Dennis

The low-energy dynamics of cold atoms interacting with macroscopic graphene membranes exhibits severe infrared divergences when treated perturbatively. These infrared problems are even more pronounced at finite temperature due to the (infinitely) many flexural phonons excited in graphene. We have devised a technique to take account (resummation) of such processes in the spirit of the well-known exact solution of the independent boson model. Remarkably, there is also similarity to the infrared problems and their treatment (via the Bloch-Nordsieck scheme) in finite temperature ``hot'' quantum electrodynamics and chromodynamics due to the long-range, unscreened nature of gauge interactions. The method takes into account correctly the strong damping provided by the many emitted phonons at finite temperature. In our case, the inverse membrane size plays the role of an effective low-energy scale, and, unlike the above mentioned field theories, there remains an unusual, highly nontrivial dependence on that scale due to the 2D nature of the problem. We present detailed results for the sticking (atomic damping rate) rate of cold atomic hydrogen as a function of the membrane temperature and size. We find that the rate is very strongly dependent on both quantities.

Reduction of the discretization stencil of direct forcing immersed boundary methods on rectangular cells: The ghost node shifting method

NASA Astrophysics Data System (ADS)

Picot, Joris; Glockner, Stéphane

2018-07-01

We present an analytical study of discretization stencils for the Poisson problem and the incompressible Navier-Stokes problem when used with some direct forcing immersed boundary methods. This study uses, but is not limited to, second-order discretization and Ghost-Cell Finite-Difference methods. We show that the stencil size increases with the aspect ratio of rectangular cells, which is undesirable as it breaks assumptions of some linear system solvers. To circumvent this drawback, a modification of the Ghost-Cell Finite-Difference methods is proposed to reduce the size of the discretization stencil to the one observed for square cells, i.e. with an aspect ratio equal to one. Numerical results validate this proposed method in terms of accuracy and convergence, for the Poisson problem and both Dirichlet and Neumann boundary conditions. An improvement on error levels is also observed. In addition, we show that the application of the chosen Ghost-Cell Finite-Difference methods to the Navier-Stokes problem, discretized by a pressure-correction method, requires an additional interpolation step. This extra step is implemented and validated through well known test cases of the Navier-Stokes equations.

Integrable subsectors from holography

NASA Astrophysics Data System (ADS)

de Mello Koch, Robert; Kim, Minkyoo; Van Zyl, Hendrik J. R.

2018-05-01

We consider operators in N=4 super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large N limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large N dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argues that the net effect of summing the huge set of non-planar diagrams, is a simple rescaling of the 't Hooft coupling. We carry out some nontrivial checks of this proposal. Using the su(2|2)2 symmetry we determine the two magnon S-matrix and demonstrate that it agrees, up to two loops, with a weak coupling computation performed in the CFT. We also compute the first finite size corrections to both the magnon and the dyonic magnon by constructing solutions to the Nambu-Goto action that carry finite angular momentum. These finite size computations constitute a strong coupling confirmation of the proposal.

On the genealogy of branching random walks and of directed polymers

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2016-08-01

It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.

A Computational Framework for Automation of Point Defect Calculations

NASA Astrophysics Data System (ADS)

Goyal, Anuj; Gorai, Prashun; Peng, Haowei; Lany, Stephan; Stevanovic, Vladan; National Renewable Energy Laboratory, Golden, Colorado 80401 Collaboration

A complete and rigorously validated open-source Python framework to automate point defect calculations using density functional theory has been developed. The framework provides an effective and efficient method for defect structure generation, and creation of simple yet customizable workflows to analyze defect calculations. The package provides the capability to compute widely accepted correction schemes to overcome finite-size effects, including (1) potential alignment, (2) image-charge correction, and (3) band filling correction to shallow defects. Using Si, ZnO and In2O3as test examples, we demonstrate the package capabilities and validate the methodology. We believe that a robust automated tool like this will enable the materials by design community to assess the impact of point defects on materials performance. National Renewable Energy Laboratory, Golden, Colorado 80401.

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

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

Chakrabarty, Aurab, E-mail: aurab.chakrabarty@qatar.tamu.edu; Bouhali, Othmane; Mousseau, Normand

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structuralmore » defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.« less

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

NASA Astrophysics Data System (ADS)

Chakrabarty, Aurab; Bouhali, Othmane; Mousseau, Normand; Becquart, Charlotte S.; El-Mellouhi, Fedwa

2016-08-01

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.

Interface-Resolving Simulation of Collision Efficiency of Cloud Droplets

NASA Astrophysics Data System (ADS)

Wang, Lian-Ping; Peng, Cheng; Rosa, Bodgan; Onishi, Ryo

2017-11-01

Small-scale air turbulence could enhance the geometric collision rate of cloud droplets while large-scale air turbulence could augment the diffusional growth of cloud droplets. Air turbulence could also enhance the collision efficiency of cloud droplets. Accurate simulation of collision efficiency, however, requires capture of the multi-scale droplet-turbulence and droplet-droplet interactions, which has only been partially achieved in the recent past using the hybrid direct numerical simulation (HDNS) approach. % where Stokes disturbance flow is assumed. The HDNS approach has two major drawbacks: (1) the short-range droplet-droplet interaction is not treated rigorously; (2) the finite-Reynolds number correction to the collision efficiency is not included. In this talk, using two independent numerical methods, we will develop an interface-resolved simulation approach in which the disturbance flows are directly resolved numerically, combined with a rigorous lubrication correction model for near-field droplet-droplet interaction. This multi-scale approach is first used to study the effect of finite flow Reynolds numbers on the droplet collision efficiency in still air. Our simulation results show a significant finite-Re effect on collision efficiency when the droplets are of similar sizes. Preliminary results on integrating this approach in a turbulent flow laden with droplets will also be presented. This work is partially supported by the National Science Foundation.

Comment on “Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution”

DOE PAGES

Arrington, J.

2016-02-23

In a recent study, Hagelstein and Pascalutsa [F. Hagelstein and V. Pascalutsa, Phys. Rev. A 91, 040502 (2015)] examine the error associated with an expansion of proton structure corrections to the Lamb shift in terms of moments of the charge distribution. They propose a small modification to a conventional parametrization of the proton's charge form factor and show that this can resolve the proton radius puzzle. However, while the size of the bump they add to the form factor is small, it is large compared to the total proton structure effects in the initial parametrization, yielding a final form factormore » that is unphysical. Reducing their modification to the point where the resulting form factor is physical does not allow for a resolution of the radius puzzle.« less

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

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

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

Better band gaps with asymptotically corrected local exchange potentials

NASA Astrophysics Data System (ADS)

Singh, Prashant; Harbola, Manoj K.; Hemanadhan, M.; Mookerjee, Abhijit; Johnson, D. D.

2016-02-01

We formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to the local density approximation (LDA) exchange potential [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994), 10.1103/PhysRevA.49.2421] that enforces the ionization potential (IP) theorem following T. Stein et al. [Phys. Rev. Lett. 105, 266802 (2010), 10.1103/PhysRevLett.105.266802]. For electronic-structure problems, the vLB correction replicates the behavior of exact-exchange potentials, with improved scaling and well-behaved asymptotics, but with the computational cost of semilocal functionals. The vLB + IP correction produces a large improvement in the eigenvalues over those from the LDA due to correct asymptotic behavior and atomic shell structures, as shown in rare-gas, alkaline-earth, zinc-based oxides, alkali halides, sulfides, and nitrides. In half-Heusler alloys, this asymptotically corrected LDA reproduces the spin-polarized properties correctly, including magnetism and half-metallicity. We also consider finite-sized systems [e.g., ringed boron nitride (B12N12 ) and graphene (C24)] to emphasize the wide applicability of the method.

Better band gaps with asymptotically corrected local exchange potentials

DOE PAGES

Singh, Prashant; Harbola, Manoj K.; Hemanadhan, M.; ...

2016-02-22

In this study, we formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to the local density approximation (LDA) exchange potential [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994)] that enforces the ionization potential (IP) theorem following T. Stein et al. [Phys. Rev. Lett. 105, 266802 (2010)]. For electronic-structure problems, the vLB correction replicates the behavior of exact-exchange potentials, with improved scaling and well-behaved asymptotics, but with the computational cost of semilocal functionals. The vLB + IP correction produces a large improvement in the eigenvalues over those from the LDA due to correct asymptotic behaviormore » and atomic shell structures, as shown in rare-gas, alkaline-earth, zinc-based oxides, alkali halides, sulfides, and nitrides. In half-Heusler alloys, this asymptotically corrected LDA reproduces the spin-polarized properties correctly, including magnetism and half-metallicity. We also consider finite-sized systems [e.g., ringed boron nitride (B 12N 12) and graphene (C 24)] to emphasize the wide applicability of the method.« less

Principles of Considering the Effect of the Limited Volume of a System on Its Thermodynamic State

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

The features of a system with a finite volume that affect its thermodynamic state are considered in comparison to describing small bodies in macroscopic phases. Equations for unary and pair distribution functions are obtained using difference derivatives of a discrete statistical sum. The structure of the equation for the free energy of a system consisting of an ensemble of volume-limited regions with different sizes and a full set of equations describing a macroscopic polydisperse system are discussed. It is found that the equations can be applied to molecular adsorption on small faces of microcrystals, to bound and isolated pores of a polydisperse material, and to describe the spinodal decomposition of a fluid in brief periods of time and high supersaturations of the bulk phase when each local region functions the same on average. It is shown that as the size of a system diminishes, corrections must be introduced for the finiteness of the system volume and fluctuations of the unary and pair distribution functions.

Exact combinatorial approach to finite coagulating systems

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Entanglement scaling at first order quantum phase transitions

NASA Astrophysics Data System (ADS)

Yuste, A.; Cartwright, C.; De Chiara, G.; Sanpera, A.

2018-04-01

First order quantum phase transitions (1QPTs) are signalled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations. When a 1QPT is crossed in the vicinity of a second order one, due to the correlation length divergence of the latter, the corresponding ground state is modified and it becomes increasingly difficult to determine the order of the transition when the size of the system is finite. Here we show that, in such situations, it is possible to apply finite size scaling (FSS) to entanglement measures, as it has recently been done for the order parameters and the energy gap, in order to recover the correct thermodynamic limit (Campostrini et al 2014 Phys. Rev. Lett. 113 070402). Such a FSS can unambiguously discriminate between first and second order phase transitions in the vicinity of multicritical points even when the singularities displayed by entanglement measures lead to controversial results.

Finite-size effects in Luther-Emery phases of Holstein and Hubbard models

NASA Astrophysics Data System (ADS)

Greitemann, J.; Hesselmann, S.; Wessel, S.; Assaad, F. F.; Hohenadler, M.

2015-12-01

The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin gap significantly complicates finite-size numerical studies, and explains inconsistent previous results for Luttinger parameters and phase boundaries. On the other hand, no such complications arise in spinless models. The correct low-energy theory of the spinful Holstein model is argued to be that of singlet bipolarons with a repulsive, mutual interaction. This picture naturally explains the existence of a metallic phase, but also implies that gapless Luttinger liquid theory is not applicable.

Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

DOE PAGES

Dornheim, Tobias; Groth, Simon; Sjostrom, Travis; ...

2016-10-07

Here we perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F xc of the macroscopic electron gas withmore » an unprecedented accuracy of | Δ V | / | V | , | Δ F xc | / | F | xc ~ 10 $-$3. Finally, a comparison of our new data to the recent parametrization of F xc by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.« less

Thermodynamics of quasideterministic digital computers

NASA Astrophysics Data System (ADS)

Chu, Dominique

2018-02-01

A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes. Concretely, we consider the entropy production of stochastic (Markovian) systems that behave like and and a not gates. Combinations of these gates can implement any logical function. We require that these gates return the correct result with a probability that is very close to 1, and additionally, that they do so within finite time. The central component of the model is a machine that can read and write binary tapes. We find that the error probability of the computation of these gates falls with the power of the system size, whereas the cost only increases linearly with the system size.

Forwardscattering corrections for optical extinction measurements in aerosol media. II - Polydispersions

NASA Technical Reports Server (NTRS)

Deepak, A.; Box, M. A.

1978-01-01

The paper presents a parametric study of the forwardscattering corrections for experimentally measured optical extinction coefficients in polydisperse particulate media, since some forward scattered light invariably enters, along with the direct beam, into the finite aperture of the detector. Forwardscattering corrections are computed by two methods: (1) using the exact Mie theory, and (2) the approximate Rayleigh diffraction formula for spherical particles. A parametric study of the dependence of the corrections on mode radii, real and imaginary parts of the complex refractive index, and half-angle of the detector's view cone has been carried out for three different size distribution functions of the modified gamma type. In addition, a study has been carried out to investigate the range of these parameters in which the approximate formulation is valid. The agreement is especially good for small-view cone angles and large particles, which improves significantly for slightly absorbing aerosol particles. Also discussed is the dependence of these corrections on the experimental design of the transmissometer systems.

Finite Element Analysis of Denosumab Treatment Effects on Vertebral Strength in Ovariectomized Cynomolgus Monkeys.

PubMed

Lee, David C; Varela, Aurore; Kostenuik, Paul J; Ominsky, Michael S; Keaveny, Tony M

2016-08-01

Finite element analysis has not yet been validated for measuring changes in whole-bone strength at the hip or spine in people after treatment with an osteoporosis agent. Toward that end, we assessed the ability of a clinically approved implementation of finite element analysis to correctly quantify treatment effects on vertebral strength, comparing against direct mechanical testing, in cynomolgus monkeys randomly assigned to one of three 16-month-long treatments: sham surgery with vehicle (Sham-Vehicle), ovariectomy with vehicle (OVX-Vehicle), or ovariectomy with denosumab (OVX-DMAb). After treatment, T12 vertebrae were retrieved, scanned with micro-CT, and mechanically tested to measure compressive strength. Blinded to the strength data and treatment codes, the micro-CT images were coarsened and homogenized to create continuum-type finite element models, without explicit porosity. With clinical translation in mind, these models were then analyzed for strength using the U.S. Food and Drug Administration (FDA)-cleared VirtuOst software application (O.N. Diagnostics, Berkeley, CA, USA), developed for analysis of human bones. We found that vertebral strength by finite element analysis was highly correlated (R(2)  = 0.97; n = 52) with mechanical testing, independent of treatment (p = 0.12). Further, the size of the treatment effect on strength (ratio of mean OVX-DMAb to mean OVX-Vehicle, as a percentage) was large and did not differ (p = 0.79) between mechanical testing (+57%; 95% CI [26%, 95%]) and finite element analysis (+51% [20%, 88%]). The micro-CT analysis revealed increases in cortical thickness (+45% [19%, 73%]) and trabecular bone volume fraction (+24% [8%, 42%]). These results show that a preestablished clinical finite element analysis implementation-developed for human bone and clinically validated in fracture-outcome studies-correctly quantified the observed treatment effects of denosumab on vertebral strength in cynomolgus monkeys. One implication is that the treatment effects in this study are well explained by the features contained within these finite element models, namely, the bone geometry and mass and the spatial distribution of bone mass. © 2016 American Society for Bone and Mineral Research. © 2016 American Society for Bone and Mineral Research.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

Shaping plasmon beams via the controlled illumination of finite-size plasmonic crystals

PubMed Central

Bouillard, J.-S.; Segovia, P.; Dickson, W.; Wurtz, G. A.; Zayats, A. V.

2014-01-01

Plasmonic crystals provide many passive and active optical functionalities, including enhanced sensing, optical nonlinearities, light extraction from LEDs and coupling to and from subwavelength waveguides. Here we study, both experimentally and numerically, the coherent control of SPP beam excitation in finite size plasmonic crystals under focussed illumination. The correct combination of the illuminating spot size, its position relative to the plasmonic crystal, wavelength and polarisation enables the efficient shaping and directionality of SPP beam launching. We show that under strongly focussed illumination, the illuminated part of the crystal acts as an antenna, launching surface plasmon waves which are subsequently filtered by the surrounding periodic lattice. Changing the illumination conditions provides rich opportunities to engineer the SPP emission pattern. This offers an alternative technique to actively modulate and control plasmonic signals, either via micro- and nano-electromechanical switches or with electro- and all-optical beam steering which have direct implications for the development of new integrated nanophotonic devices, such as plasmonic couplers and switches and on-chip signal demultiplexing. This approach can be generalised to all kinds of surface waves, either for the coupling and discrimination of light in planar dielectric waveguides or the generation and control of non-diffractive SPP beams. PMID:25429786

A new DFT approach to model small polarons in oxides with proper account for long-range polarization

NASA Astrophysics Data System (ADS)

Kokott, Sebastian; Levchenko, Sergey V.; Scheffler, Matthias; Theory Department Team

In this work, we address two important challenges in the DFT description of small polarons (excess charges localized within one unit cell): sensitivity to the errors in exchange-correlation (XC) treatment and finite-size effects in supercell calculations. The polaron properties are obtained using a modified neutral potential-energy surface (PES). Using the hybrid HSE functional and considering the whole range 0 <= α <= 1 , we show that the modified PES model significantly reduces the dependence of the polaron level and binding energy in MgO and TiO2 on the XC functional. It does not eliminate the dependence on supercell size. Based on Pekar's model, we derive the proper long-range behavior of the polaron and a finite-size correction that allows to obtain the polaron properties in the dilute limit (tested for supercells containing up to 1,000 atoms). The developed approach reduces drastically the computational time for exploring the polaron PES, and gives a consistent description of polarons for the whole range of α. It allowed us to find a self-trapped hole in MgO that is noticeably more stable than reported previously. partially supported by UniCat (Deutsche Forschungsgemeinschaft).

Skewness and kurtosis analysis for non-Gaussian distributions

NASA Astrophysics Data System (ADS)

Celikoglu, Ahmet; Tirnakli, Ugur

2018-06-01

In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0 < q < 3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.

Modulated error diffusion CGHs for neural nets

NASA Astrophysics Data System (ADS)

Vermeulen, Pieter J. E.; Casasent, David P.

1990-05-01

New modulated error diffusion CGHs (computer generated holograms) for optical computing are considered. Specific attention is given to their use in optical matrix-vector, associative processor, neural net and optical interconnection architectures. We consider lensless CGH systems (many CGHs use an external Fourier transform (FT) lens), the Fresnel sampling requirements, the effects of finite CGH apertures (sample and hold inputs), dot size correction (for laser recorders), and new applications for this novel encoding method (that devotes attention to quantization noise effects).

Bias correction of risk estimates in vaccine safety studies with rare adverse events using a self-controlled case series design.

PubMed

Zeng, Chan; Newcomer, Sophia R; Glanz, Jason M; Shoup, Jo Ann; Daley, Matthew F; Hambidge, Simon J; Xu, Stanley

2013-12-15

The self-controlled case series (SCCS) method is often used to examine the temporal association between vaccination and adverse events using only data from patients who experienced such events. Conditional Poisson regression models are used to estimate incidence rate ratios, and these models perform well with large or medium-sized case samples. However, in some vaccine safety studies, the adverse events studied are rare and the maximum likelihood estimates may be biased. Several bias correction methods have been examined in case-control studies using conditional logistic regression, but none of these methods have been evaluated in studies using the SCCS design. In this study, we used simulations to evaluate 2 bias correction approaches-the Firth penalized maximum likelihood method and Cordeiro and McCullagh's bias reduction after maximum likelihood estimation-with small sample sizes in studies using the SCCS design. The simulations showed that the bias under the SCCS design with a small number of cases can be large and is also sensitive to a short risk period. The Firth correction method provides finite and less biased estimates than the maximum likelihood method and Cordeiro and McCullagh's method. However, limitations still exist when the risk period in the SCCS design is short relative to the entire observation period.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

Scaling in the vicinity of the four-state Potts fixed point

NASA Astrophysics Data System (ADS)

Blöte, H. W. J.; Guo, Wenan; Nightingale, M. P.

2017-08-01

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.

Efficiency at maximum power of a chemical engine.

PubMed

Hooyberghs, Hans; Cleuren, Bart; Salazar, Alberto; Indekeu, Joseph O; Van den Broeck, Christian

2013-10-07

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power η(mp) [corrected] takes the form 1/2+cΔμ+O(Δμ(2)), with 1∕2 a universal constant and Δμ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in η(mp) [corrected] is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model, we obtain η(mp) = 1/(θ + 1) [corrected], with θ > 0 the power of Δμ in the transport equation.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

NASA Astrophysics Data System (ADS)

Boffi, Nicholas M.; Jain, Manish; Natan, Amir

2016-02-01

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations.

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

NASA Astrophysics Data System (ADS)

Collell, Julien; Galliero, Guillaume

2014-05-01

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

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

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

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

2014-05-21

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

Measuring nanometre-scale electric fields in scanning transmission electron microscopy using segmented detectors.

PubMed

Brown, H G; Shibata, N; Sasaki, H; Petersen, T C; Paganin, D M; Morgan, M J; Findlay, S D

2017-11-01

Electric field mapping using segmented detectors in the scanning transmission electron microscope has recently been achieved at the nanometre scale. However, converting these results to quantitative field measurements involves assumptions whose validity is unclear for thick specimens. We consider three approaches to quantitative reconstruction of the projected electric potential using segmented detectors: a segmented detector approximation to differential phase contrast and two variants on ptychographical reconstruction. Limitations to these approaches are also studied, particularly errors arising from detector segment size, inelastic scattering, and non-periodic boundary conditions. A simple calibration experiment is described which corrects the differential phase contrast reconstruction to give reliable quantitative results despite the finite detector segment size and the effects of plasmon scattering in thick specimens. A plasmon scattering correction to the segmented detector ptychography approaches is also given. Avoiding the imposition of periodic boundary conditions on the reconstructed projected electric potential leads to more realistic reconstructions. Copyright © 2017 Elsevier B.V. All rights reserved.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

An analysis of the nucleon spectrum from lattice partially-quenched QCD

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

W. Armour; Allton, C. R.; Leinweber, Derek B.

2010-09-01

The chiral extrapolation of the nucleon mass, Mn, is investigated using data coming from 2-flavour partially-quenched lattice simulations. The leading one-loop corrections to the nucleon mass are derived for partially-quenched QCD. A large sample of lattice results from the CP-PACS Collaboration is analysed, with explicit corrections for finite lattice spacing artifacts. The extrapolation is studied using finite range regularised chiral perturbation theory. The analysis also provides a quantitative estimate of the leading finite volume corrections. It is found that the discretisation, finite-volume and partial quenching effects can all be very well described in this framework, producing an extrapolated value ofmore » Mn in agreement with experiment. This procedure is also compared with extrapolations based on polynomial forms, where the results are less encouraging.« less

Flow adjustment inside large finite-size wind farms approaching the infinite wind farm regime

NASA Astrophysics Data System (ADS)

Wu, Ka Ling; Porté-Agel, Fernando

2017-04-01

Due to the increasing number and the growing size of wind farms, the distance among them continues to decrease. Thus, it is necessary to understand how these large finite-size wind farms and their wakes could interfere the atmospheric boundary layer (ABL) dynamics and adjacent wind farms. Fully-developed flow inside wind farms has been extensively studied through numerical simulations of infinite wind farms. The transportation of momentum and energy is only vertical and the advection of them is neglected in these infinite wind farms. However, less attention has been paid to examine the length of wind farms required to reach such asymptotic regime and the ABL dynamics in the leading and trailing edges of the large finite-size wind farms. Large eddy simulations are performed in this study to investigate the flow adjustment inside large finite-size wind farms in conventionally-neutral boundary layer with the effect of Coriolis force and free-atmosphere stratification from 1 to 5 K/km. For the large finite-size wind farms considered in the present work, when the potential temperature lapse rate is 5 K/km, the wind farms exceed the height of the ABL by two orders of magnitude for the incoming flow inside the farms to approach the fully-developed regime. An entrance fetch of approximately 40 times of the ABL height is also required for such flow adjustment. At the fully-developed flow regime of the large finite-size wind farms, the flow characteristics match those of infinite wind farms even though they have different adjustment length scales. The role of advection at the entrance and exit regions of the large finite-size wind farms is also examined. The interaction between the internal boundary layer developed above the large finite-size wind farms and the ABL under different potential temperature lapse rates are compared. It is shown that the potential temperature lapse rate plays a role in whether the flow inside the large finite-size wind farms adjusts to the fully-developed flow regime. The flow characteristics of the wake of these large finite-size wind farms are reported to forecast the effect of large finite-size wind farms on adjacent wind farms. A power deficit as large as 8% is found at a distance of 10 km downwind from the large finite-size wind farms.

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

NASA Astrophysics Data System (ADS)

Zhang, Xueying; Zhang, Yichen; Zhao, Yijia; Wang, Xiangyu; Yu, Song; Guo, Hong

2017-10-01

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

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

NASA Astrophysics Data System (ADS)

Shi, Jing-xian; Fan, Jiang

2018-03-01

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

Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Zhang, L.

1994-01-01

The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.

On the two-loop virtual QCD corrections to Higgs boson pair production in the standard model

DOE PAGES

Degrassi, Giuseppe; Giardino, Pier Paolo; Gröber, Ramona

2016-07-21

Here, we compute the next-to-leading order virtual QCD corrections to Higgs-pair production via gluon fusion. We also present analytic results for the two-loop contributions to the spin-0 and spin-2 form factors in the amplitude. The reducible contributions, given by the double-triangle diagrams, are evaluated exactly while the two-loop irreducible diagrams are evaluated by an asymptotic expansion in heavy top-quark mass up to and including terms of O(1/mmore » $$8\\atop{t}$$). We estimate that mass effects can reduce the hadronic cross section by at most 10 %, assuming that the finite top-quark mass effects are of similar size in the entire range of partonic energies.« less

Maximum efficiency of ideal heat engines based on a small system: correction to the Carnot efficiency at the nanoscale.

PubMed

Quan, H T

2014-06-01

We study the maximum efficiency of a heat engine based on a small system. It is revealed that due to the finiteness of the system, irreversibility may arise when the working substance contacts with a heat reservoir. As a result, there is a working-substance-dependent correction to the Carnot efficiency. We derive a general and simple expression for the maximum efficiency of a Carnot cycle heat engine in terms of the relative entropy. This maximum efficiency approaches the Carnot efficiency asymptotically when the size of the working substance increases to the thermodynamic limit. Our study extends Carnot's result of the maximum efficiency to an arbitrary working substance and elucidates the subtlety of thermodynamic laws in small systems.

Long Range Debye-Hückel Correction for Computation of Grid-based Electrostatic Forces Between Biomacromolecules

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

Mereghetti, Paolo; Martinez, M.; Wade, Rebecca C.

Brownian dynamics (BD) simulations can be used to study very large molecular systems, such as models of the intracellular environment, using atomic-detail structures. Such simulations require strategies to contain the computational costs, especially for the computation of interaction forces and energies. A common approach is to compute interaction forces between macromolecules by precomputing their interaction potentials on three-dimensional discretized grids. For long-range interactions, such as electrostatics, grid-based methods are subject to finite size errors. We describe here the implementation of a Debye-Hückel correction to the grid-based electrostatic potential used in the SDA BD simulation software that was applied to simulatemore » solutions of bovine serum albumin and of hen egg white lysozyme.« less

Polyelectrolyte Bundles: Finite size at thermodynamic equilibrium?

NASA Astrophysics Data System (ADS)

Sayar, Mehmet

2005-03-01

Experimental observation of finite size aggregates formed by polyelectrolytes such as DNA and F-actin, as well as synthetic polymers like poly(p-phenylene), has created a lot of attention in recent years. Here, bundle formation in rigid rod-like polyelectrolytes is studied via computer simulations. For the case of hydrophobically modified polyelectrolytes finite size bundles are observed even in the presence of only monovalent counterions. Furthermore, in the absence of a hydrophobic backbone, we have also observed formation of finite size aggregates via multivalent counterion condensation. The size distribution of such aggregates and the stability is analyzed in this study.

Finite size effects in the thermodynamics of a free neutral scalar field

NASA Astrophysics Data System (ADS)

Parvan, A. S.

2018-04-01

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume

DOE PAGES

Hansen, Maxwell; Briceno, Raul

2015-10-01

We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore » $$\\textbf{0}\\rightarrow\\textbf{2}$$ and $$\\textbf{1}\\rightarrow\\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\\mathcal{J}~\\rightarrow~(N\\pi,N\\eta,N\\eta',\\Sigma K,\\Lambda K)$$ transitions, where $$\\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.« less

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

DOE PAGES

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

2015-06-24

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

Assessment of Cracks in Stress Concentration Regions with Localized Plastic Zones

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

Friedman, E.

1998-11-25

Marty brittle fracture evaluation procedures include plasticity corrections to elastically computed stress intensity factors. These corrections, which are based on the existence of a plastic zone in the vicinity of the crack tip, can overestimate the plasticity effect for a crack embedded in a stress concentration region in which the elastically computed stress exceeds the yield strength of the material in a localized zone. The interactions between the crack, which acts to relieve the high stresses driving the crack, plasticity effects in the stress concentration region, and the nature and source of the loading are examined by formulating explicit flawmore » finite element models for a crack emanating from the root of a notch located in a panel subject to an applied tensile stress. The results of these calculations provide conditions under which a crack-tip plasticity correction based on the Irwin plastic zone size overestimates the plasticity effect. A failure assessment diagram (FAD) curve is used to characterize the effect of plasticity on the crack driving force and to define a less restrictive plasticity correction for cracks at notch roots when load-controlled boundary conditions are imposed. The explicit flaw finite element results also demonstrate that stress intensity factors associated with load-controlled boundary conditions, such as those inherent in the ASME Boiler and Pressure Vessel Code as well as in most handbooks of stress intensity factors, can be much higher than those associated with displacement-controlled conditions, such as those that produce residual or thermal stresses. Under certain conditions, the inclusion of plasticity effects for cracks loaded by displacement-controlled boundary conditions reduces the crack driving force thus justifying the elimination of a plasticity correction for such loadings. The results of this study form the basis for removing unnecessary conservatism from flaw evaluation procedures that utilize plasticity corrections.« less

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

Entanglement, replicas, and Thetas

NASA Astrophysics Data System (ADS)

Mukhi, Sunil; Murthy, Sameer; Wu, Jie-Qiang

2018-01-01

We compute the single-interval Rényi entropy (replica partition function) for free fermions in 1+1d at finite temperature and finite spatial size by two methods: (i) using the higher-genus partition function on the replica Riemann surface, and (ii) using twist operators on the torus. We compare the two answers for a restricted set of spin structures, leading to a non-trivial proposed equivalence between higher-genus Siegel Θ-functions and Jacobi θ-functions. We exhibit this proposal and provide substantial evidence for it. The resulting expressions can be elegantly written in terms of Jacobi forms. Thereafter we argue that the correct Rényi entropy for modular-invariant free-fermion theories, such as the Ising model and the Dirac CFT, is given by the higher-genus computation summed over all spin structures. The result satisfies the physical checks of modular covariance, the thermal entropy relation, and Bose-Fermi equivalence.

Dynamic properties of epidemic spreading on finite size complex networks

NASA Astrophysics Data System (ADS)

Li, Ying; Liu, Yang; Shan, Xiu-Ming; Ren, Yong; Jiao, Jian; Qiu, Ben

2005-11-01

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS (susceptible-infected-susceptible) model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.

Sampling errors in the measurement of rain and hail parameters

NASA Technical Reports Server (NTRS)

Gertzman, H. S.; Atlas, D.

1977-01-01

Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.

Finite-size scaling and integer-spin Heisenberg chains

NASA Astrophysics Data System (ADS)

Bonner, Jill C.; Müller, Gerhard

1984-03-01

Finite-size scaling (phenomenological renormalization) techniques are trusted and widely applied in low-dimensional magnetism and, particularly, in lattice gauge field theory. Recently, investigations have begun which subject the theoretical basis to systematic and intensive scrutiny to determine the validity of finite-size scaling in a variety of situations. The 2D ANNNI model is an example of a situation where finite-size scaling methods encounter difficulty, related to the occurrence of a disorder line (one-dimensional line). A second example concerns the behavior of the spin-1/2 antiferromagnetic XXZ model where the T=0 critical behavior is exactly known and features an essential singularity at the isotropic Heisenberg point. Standard finite-size scaling techniques do not convincingly reproduce the exact phase behavior and this is attributable to the essential singularity. The point is relevant in connection with a finite-size scaling analysis of a spin-one antiferromagnetic XXZ model, which claims to support a conjecture by Haldane that the T=0 phase behavior of integer-spin Heisenberg chains is significantly different from that of half-integer-spin Heisenberg chains.

Numerical investigation of finite-volume effects for the HVP

NASA Astrophysics Data System (ADS)

Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher

2018-03-01

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Finite coupling corrections to holographic predictions for hot QCD

DOE PAGES

Waeber, Sebastian; Schafer, Andreas; Vuorinen, Aleksi; ...

2015-11-13

Finite ’t Hooft coupling corrections to multiple physical observables in strongly coupled N=4 supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the ’t Hooft coupling λ. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Furthermore large λ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity of the results to the value of λ.

Finite-volume effects and the electromagnetic contributions to kaon and pion masses

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

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

Topological quantum error correction in the Kitaev honeycomb model

NASA Astrophysics Data System (ADS)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

Atmospheric turbulence compensation with laser phase shifting interferometry

NASA Astrophysics Data System (ADS)

Rabien, S.; Eisenhauer, F.; Genzel, R.; Davies, R. I.; Ott, T.

2006-04-01

Laser guide stars with adaptive optics allow astronomical image correction in the absence of a natural guide star. Single guide star systems with a star created in the earth's sodium layer can be used to correct the wavefront in the near infrared spectral regime for 8-m class telescopes. For possible future telescopes of larger sizes, or for correction at shorter wavelengths, the use of a single guide star is ultimately limited by focal anisoplanatism that arises from the finite height of the guide star. To overcome this limitation we propose to overlap coherently pulsed laser beams that are expanded over the full aperture of the telescope, traveling upwards along the same path which light from the astronomical object travels downwards. Imaging the scattered light from the resultant interference pattern with a camera gated to a certain height above the telescope, and using phase shifting interferometry we have found a method to retrieve the local wavefront gradients. By sensing the backscattered light from two different heights, one can fully remove the cone effect, which can otherwise be a serious handicap to the use of laser guide stars at shorter wavelengths or on larger telescopes. Using two laser beams multiconjugate correction is possible, resulting in larger corrected fields. With a proper choice of laser, wavefront correction could be expanded to the visible regime and, due to the lack of a cone effect, the method is applicable to any size of telescope. Finally the position of the laser spot could be imaged from the side of the main telescope against a bright background star to retrieve tip-tilt information, which would greatly improve the sky coverage of the system.

Absorption and scattering of light by nonspherical particles. [in atmosphere

NASA Technical Reports Server (NTRS)

Bohren, C. F.

1986-01-01

Using the example of the polarization of scattered light, it is shown that the scattering matrices for identical, randomly ordered particles and for spherical particles are unequal. The spherical assumptions of Mie theory are therefore inconsistent with the random shapes and sizes of atmospheric particulates. The implications for corrections made to extinction measurements of forward scattering light are discussed. Several analytical methods are examined as potential bases for developing more accurate models, including Rayleigh theory, Fraunhoffer Diffraction theory, anomalous diffraction theory, Rayleigh-Gans theory, the separation of variables technique, the Purcell-Pennypacker method, the T-matrix method, and finite difference calculations.

Atomic states in optical traps near a planar surface

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

Messina, Riccardo; Pelisson, Sophie; Angonin, Marie-Christine

2011-05-15

In this paper, we discuss the atomic states in a vertical optical lattice in proximity of a surface. We study the modifications to the ordinary Wannier-Stark states in the presence of a surface, and we characterize the energy shifts produced by the Casimir-Polder interaction between atom and mirror. In this context, we introduce an effective model describing the finite size of the atom in order to regularize the energy corrections. In addition, the modifications to the energy levels due to a hypothetical non-Newtonian gravitational potential as well as their experimental observability are investigated.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

PubMed

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

2017-06-01

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.

Predicting Long-term Temperature Increase for Time-Dependent SAR Levels with a Single Short-term Temperature Response

PubMed Central

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M.

2015-01-01

Purpose Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). Methods After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and Impulse-Response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes’ bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. Results The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time, and can be adjusted to be more or less conservative than the corresponding finite difference simulation. Conclusion With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. (200/200 words) PMID:26096947

Predicting long-term temperature increase for time-dependent SAR levels with a single short-term temperature response.

PubMed

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M

2016-05-01

Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and impulse-response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes' bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time and can be adjusted to be more or less conservative than the corresponding finite difference simulation. With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. © 2015 Wiley Periodicals, Inc.

Finite barrier corrections to the PGH solution of Kramers' turnover theory

NASA Astrophysics Data System (ADS)

Pollak, Eli; Ianconescu, Reuven

2014-04-01

Kramers [Physica 7, 284 (1940)], in his seminal paper, derived expressions for the rate of crossing a barrier in the underdamped limit of weak friction and the moderate to strong friction limit. The challenge of obtaining a uniform expression for the rate, valid for all damping strengths is known as Kramers turnover theory. Two different solutions have been presented. Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)] (MM) considered the motion of the particle, treating the friction as a perturbation parameter. Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] (PGH), considered the motion along the unstable mode which is separable from the bath in the barrier region. In practice, the two theories differ in the way an energy loss parameter is estimated. In this paper, we show that previous numerical attempts to resolve the quality of the two approaches were incomplete and that at least for a cubic potential with Ohmic friction, the quality of agreement of both expressions with numerical simulation is similar over a large range of friction strengths and temperatures. Mel'nikov [Phys. Rev. E 48, 3271 (1993)], in a later paper, improved his theory by introducing finite barrier corrections. In this paper we note that previous numerical tests of the finite barrier corrections were also incomplete. They did not employ the exact rate expression, but a harmonic approximation to it. The central part of this paper, is to include finite barrier corrections also within the PGH formalism. Tests on a cubic potential demonstrate that finite barrier corrections significantly improve the agreement of both MM and PGH theories when compared with numerical simulations.

Development of a Detailed Volumetric Finite Element Model of the Spine to Simulate Surgical Correction of Spinal Deformities

PubMed Central

Driscoll, Mark; Mac-Thiong, Jean-Marc; Labelle, Hubert; Parent, Stefan

2013-01-01

A large spectrum of medical devices exists; it aims to correct deformities associated with spinal disorders. The development of a detailed volumetric finite element model of the osteoligamentous spine would serve as a valuable tool to assess, compare, and optimize spinal devices. Thus the purpose of the study was to develop and initiate validation of a detailed osteoligamentous finite element model of the spine with simulated correction from spinal instrumentation. A finite element of the spine from T1 to L5 was developed using properties and geometry from the published literature and patient data. Spinal instrumentation, consisting of segmental translation of a scoliotic spine, was emulated. Postoperative patient and relevant published data of intervertebral disc stress, screw/vertebra pullout forces, and spinal profiles was used to evaluate the models validity. Intervertebral disc and vertebral reaction stresses respected published in vivo, ex vivo, and in silico values. Screw/vertebra reaction forces agreed with accepted pullout threshold values. Cobb angle measurements of spinal deformity following simulated surgical instrumentation corroborated with patient data. This computational biomechanical analysis validated a detailed volumetric spine model. Future studies seek to exploit the model to explore the performance of corrective spinal devices. PMID:23991426

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Two-point correlation function for Dirichlet L-functions

NASA Astrophysics Data System (ADS)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Spin-resolved correlations in the warm-dense homogeneous electron gas

NASA Astrophysics Data System (ADS)

Arora, Priya; Kumar, Krishan; Moudgil, R. K.

2017-04-01

We have studied spin-resolved correlations in the warm-dense homogeneous electron gas by determining the linear density and spin-density response functions, within the dynamical self-consistent mean-field theory of Singwi et al. The calculated spin-resolved pair-correlation function gσσ'(r) is compared with the recent restricted path-integral Monte Carlo (RPIMC) simulations due to Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)], while interaction energy Eint and exchange-correlation free energy Fxc with the RPIMC and very recent ab initio quantum Monte Carlo (QMC) simulations by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. g↑↓(r) is found to be in good agreement with the RPIMC data, while a mismatch is seen in g↑↑(r) at small r where it becomes somewhat negative. As an interesting result, it is deduced that a non-monotonic T-dependence of g(0) is driven primarily by g↑↓(0). Our results of Eint and Fxc exhibit an excellent agreement with the QMC study due to Dornheim et al., which deals with the finite-size correction quite accurately. We observe, however, a visible deviation of Eint from the RPIMC data for high densities ( 8% at rs = 1). Further, we have extended our study to the fully spin-polarized phase. Again, with the exception of high density region, we find a good agreement of Eint with the RPIMC data. This points to the need of settling the problem of finite-size correction in the spin-polarized phase also. Interestingly, we also find that the thermal effects tend to oppose spatial localization as well as spin polarization of electrons. Supplementary material in the form of one zip file available from the Journal web page at http://https://doi.org/10.1140/epjb/e2017-70532-y

Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems

NASA Astrophysics Data System (ADS)

Koh, Yang Wei

2018-03-01

In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.

Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions. Numerical Analysis in Continuous Time

NASA Astrophysics Data System (ADS)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. However, such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. Using the continuous-time cloning algorithm, we analyze the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. We use these scalings in order to propose a numerical approach which allows to extract the infinite-time and infinite-size limit of these estimators.

Role of relaxation and time-dependent formation of x-ray spectra

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

A fundamental problem of x-ray spectroscopy is the role of relaxation of the electronic subsystem in the field of the transient core hole. The main intention of the present study is to explore the dynamics due to core-hole relaxation in the whole time domain, and to find out how it is manifested in finite molecular systems in comparison with solids. A technique is developed based on a reduction of the Noziéres-De Dominicis equation to a set of linear algebraic equations. The developed time-dependent formalism is applied to a numerical investigation of a one-dimensional tight-binding model. The formation of the x-ray profiles is explored on the real time scale, and the role of interaction with the core hole, band filling, and the final-state rule are investigated for systems of different size. The formation of spectra of the infinite translational invariant system is studied by extensions of the finite systems. We found that the dynamics of finite systems, like molecules, differs qualitatively from solids: Contrary to the latter the time lapse of the Noziéres-De Dominicis domain for finite systems is squeezed between the inverse bandwidth and the revival time, which is proportional to the system size. For small molecules this means that there is no time for a ``Mahan-Noziéres-De Dominicis singularity'' to develop. Comparison with the strict solution of the Noziéres-De Dominicis equation shows that the adiabatic approximation describes x-ray absorption and emission considerably better than the fast approximation. This explains the suppression of the relaxation effects in x-ray emission of, e.g., gas phase and surface adsorbed molecules, but also that these effects are essential for the absorption case. There is still a quantitative distinction between the adiabatic approximation and the strict approach, which becomes more important for larger systems. Adopting the so-called finite state rule by von Barth and Grossman also for molecules, an almost complete numerical agreement between this rule and the strict x-ray-absorption and emission profiles for systems of different sizes is obtained. The simulations indicate that the final-state rule correction is important mainly near the absorption edge and at the top of the emission band.

Stochastic evaluation of second-order many-body perturbation energies.

PubMed

Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So

2012-11-28

With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.

Thermoelectricity near Anderson localization transitions

NASA Astrophysics Data System (ADS)

Yamamoto, Kaoru; Aharony, Amnon; Entin-Wohlman, Ora; Hatano, Naomichi

2017-10-01

The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies and find universal approximants which allow us to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at nonzero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Corrections to the leading power-law singularity in the zero-temperature conductivity are shown to introduce nonuniversal temperature-dependent corrections to the otherwise universal functions which describe the Seebeck coefficient, the figure of merit, and the Wiedemann-Franz ratio. Next, the thermoelectric coefficients are shown to have interesting dependences on the system size. While the Seebeck coefficient decreases with decreasing size, the figure of merit first decreases but then increases, while the Wiedemann-Franz ratio first increases but then decreases as the size decreases. Small (but finite) samples may thus have larger thermoelectric efficiencies. In the last part we study thermoelectricity in systems with a pair of localization edges, the ubiquitous situation in random systems near the centers of electronic energy bands. As the disorder increases, the two thresholds approach each other, and then the Seebeck coefficient and the figure of merit increase significantly, as expected from the general arguments of Mahan and Sofo [J. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. USA 93, 7436 (1996), 10.1073/pnas.93.15.7436] for a narrow energy range of the zero-temperature metallic behavior.

Improved Algorithm For Finite-Field Normal-Basis Multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1989-01-01

Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.

Feasibility of self-correcting quantum memory and thermal stability of topological order

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

Yoshida, Beni, E-mail: rouge@mit.edu

2011-10-15

Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that themore » model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions. - Highlights: > We define a class of physically realizable quantum codes. > We determine their coding and physical properties completely. > We establish the connection between topological order and self-correcting memory. > We find they do not work as self-correcting quantum memory. > We find they do not have thermally stable topological order.« less

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

NASA Technical Reports Server (NTRS)

Arya, V. K.; Kaufman, A.

1989-01-01

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

NASA Technical Reports Server (NTRS)

Arya, V. K.; Kaufman, A.

1987-01-01

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Theoretical and Experimental Evaluation of the Bond Strength Under Peeling Loads

NASA Technical Reports Server (NTRS)

Nayeb-Hashemi, Hamid; Jawad, Oussama Cherkaoui

1997-01-01

Reliable applications of adhesively bonded joints require understanding of the stress distribution along the bond-line and the stresses that are responsible for the joint failure. To properly evaluate factors affecting peel strength, effects of defects such as voids on the stress distribution in the overlap region must be understood. In this work, the peel stress distribution in a single lap joint is derived using a strength of materials approach. The bonded joint is modeled as Euler-Bernoulli beams, bonded together with an adhesive. which is modeled as an elastic foundation which can resist both peel and shear stresses. It is found that for certain adhesive and adherend geometries and properties, a central void with the size up to 50 percent of the overlap length has negligible effect on the peak peel and shear stresses. To verify the solutions obtained from the model, the problem is solved again by using the finite element method and by treating the adherends and the adhesive as elastic materials. It is found that the model used in the analysis not only predicts the correct trend for the peel stress distribution but also gives rather surprisingly close results to that of the finite element analysis. It is also found that both shear and peel stresses can be responsible for the joint performance and when a void is introduced, both of these stresses can contribute to the joint failure as the void size increases. Acoustic emission (AE) activities of aluminum-adhesive-aluminum specimens with different void sizes were monitored. The AE ringdown counts and energy were very sensitive and decreased significantly with the void size. It was observed that the AE events were shifting towards the edge of the overlap where the maximum peeling and shearing stresses were occurring as the void size increased.

γ-Particle coincidence technique for the study of nuclear reactions

NASA Astrophysics Data System (ADS)

Zagatto, V. A. B.; Oliveira, J. R. B.; Allegro, P. R. P.; Chamon, L. C.; Cybulska, E. W.; Medina, N. H.; Ribas, R. V.; Seale, W. A.; Silva, C. P.; Gasques, L. R.; Zahn, G. S.; Genezini, F. A.; Shorto, J. M. B.; Lubian, J.; Linares, R.; Toufen, D. L.; Silveira, M. A. G.; Rossi, E. S.; Nobre, G. P.

2014-06-01

The Saci-Perere γ ray spectrometer (located at the Pelletron AcceleratorLaboratory - IFUSP) was employed to implement the γ-particle coincidence technique for the study of nuclear reaction mechanisms. For this, the 18O+110Pd reaction has been studied in the beam energy range of 45-54 MeV. Several corrections to the data due to various effects (energy and angle integrations, beam spot size, γ detector finite size and the vacuum de-alignment) are small and well controlled. The aim of this work was to establish a proper method to analyze the data and identify the reaction mechanisms involved. To achieve this goal the inelastic scattering to the first excited state of 110Pd has been extracted and compared to coupled channel calculations using the São Paulo Potential (PSP), being reasonably well described by it.

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume-Capel model in a transverse crystal field

NASA Astrophysics Data System (ADS)

Roberto Viana, J.; Rodriguez Salmon, Octavio D.; Neto, Minos A.; Carvalho, Diego C.

2018-02-01

A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.

Conformal partition functions of critical percolation from D 3 thermodynamic Bethe Ansatz equations

NASA Astrophysics Data System (ADS)

Morin-Duchesne, Alexi; Klümper, Andreas; Pearce, Paul A.

2017-08-01

Using the planar Temperley-Lieb algebra, critical bond percolation on the square lattice can be reformulated as a loop model. In this form, it is incorporated as {{ L}}{{ M}}(2, 3) in the Yang-Baxter integrable family of logarithmic minimal models {{ L}}{{ M}}( p, p\\prime) . We consider this model of percolation in the presence of boundaries and with periodic boundary conditions. Inspired by Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite Y-system of functional equations. In this way, we obtain nonlinear integral equations in the form of a closed finite set of TBA equations described by a D 3 Dynkin diagram. Following the methods of Klümper and Pearce, we solve the TBA equations for the conformal finite-size corrections. For the ground states of the standard modules on the strip, these agree with the known central charge c  =  0 and conformal weights Δ1, s for \\renewcommand≥≥slant} s\\in {{ Z}≥slant 1} with Δr, s=\\big((3r-2s){\\hspace{0pt}}^2-1\\big)/24 . For the periodic case, the finite-size corrections agree with the conformal weights Δ0, s , Δ1, s with \\renewcommand{≥{≥slant} s\\in\\frac{1}{2}{{ Z}≥slant 0} . These are obtained analytically using Rogers dilogarithm identities. We incorporate all finite excitations by formulating empirical selection rules for the patterns of zeros of all the eigenvalues of the standard modules. We thus obtain the conformal partition functions on the cylinder and the modular invariant partition function (MIPF) on the torus. By applying q-binomial and q-Narayana identities, it is shown that our refined finitized characters on the strip agree with those of Pearce, Rasmussen and Zuber. For percolation on the torus, the MIPF is a non-diagonal sesquilinear form in affine u(1) characters given by the u(1) partition function Z2, 3(q)=Z2, 3{Circ}(q) . The u(1) operator content is {{ N}}Δ, \\barΔ=1 for Δ=\\barΔ=-\\frac{1}{24}, \\frac{35}{24} and {{ N}}Δ, \\barΔ=2 for Δ=\\barΔ=\\frac{1}{8}, \\frac{1}{3}, \\frac{5}{8} and (Δ, \\barΔ)=(0, 1), (1, 0) . This result is compatible with the general conjecture of Pearce and Rasmussen, namely Zp, p\\prime(q)=Z{Proj}p, p\\prime(q)+np, p\\prime Z{Min}p, p\\prime(q) with np, p\\prime\\in {{ Z}} , where the minimal partition function is Z{Min}2, 3(q)=1 and the lattice derivation fixes n 2,3  =  -1.

Environmental corrections of a dual-induction logging while drilling tool in vertical wells

NASA Astrophysics Data System (ADS)

Kang, Zhengming; Ke, Shizhen; Jiang, Ming; Yin, Chengfang; Li, Anzong; Li, Junjian

2018-04-01

With the development of Logging While Drilling (LWD) technology, dual-induction LWD logging is not only widely applied in deviated wells and horizontal wells, but it is used commonly in vertical wells. Accordingly, it is necessary to simulate the response of LWD tools in vertical wells for logging interpretation. In this paper, the investigation characteristics, the effects of the tool structure, skin effect and drilling environment of a dual-induction LWD tool are simulated by the three-dimensional (3D) finite element method (FEM). In order to closely simulate the actual situation, real structure of the tool is taking into account. The results demonstrate that the influence of the background value of the tool structure can be eliminated. The values of deducting the background of a tool structure and analytical solution have a quantitative agreement in homogeneous formations. The effect of measurement frequency could be effectively eliminated by chart of skin effect correction. In addition, the measurement environment, borehole size, mud resistivity, shoulder bed, layer thickness and invasion, have an effect on the true resistivity. To eliminate these effects, borehole correction charts, shoulder bed correction charts and tornado charts are computed based on real tool structure. Based on correction charts, well logging data can be corrected automatically by a suitable interpolation method, which is convenient and fast. Verified with actual logging data in vertical wells, this method could obtain the true resistivity of formation.

Extremal optimization for Sherrington-Kirkpatrick spin glasses

NASA Astrophysics Data System (ADS)

Boettcher, S.

2005-08-01

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using ±J bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of ω=2/3 for the finite-size correction exponent, and of ρ=3/4 for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent.

Finite-size analysis of a continuous-variable quantum key distribution

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

Leverrier, Anthony; Grosshans, Frederic; Grangier, Philippe

2010-06-15

The goal of this paper is to extend the framework of finite-size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite-size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully securemore » secret keys in the finite-size scenario, over distances larger than 50 km.« less

Time series ARIMA models for daily price of palm oil

NASA Astrophysics Data System (ADS)

Ariff, Noratiqah Mohd; Zamhawari, Nor Hashimah; Bakar, Mohd Aftar Abu

2015-02-01

Palm oil is deemed as one of the most important commodity that forms the economic backbone of Malaysia. Modeling and forecasting the daily price of palm oil is of great interest for Malaysia's economic growth. In this study, time series ARIMA models are used to fit the daily price of palm oil. The Akaike Infromation Criterion (AIC), Akaike Infromation Criterion with a correction for finite sample sizes (AICc) and Bayesian Information Criterion (BIC) are used to compare between different ARIMA models being considered. It is found that ARIMA(1,2,1) model is suitable for daily price of crude palm oil in Malaysia for the year 2010 to 2012.

Archimedes force on Casimir apparatus

NASA Astrophysics Data System (ADS)

Shevchenko, Vladimir; Shevrin, Efim

2016-08-01

This paper addresses a problem of Casimir apparatus in dense medium, put in weak gravitational field. The falling of the apparatus has to be governed by the equivalence principle with proper account for contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general expression for the corresponding force in metric with cylindrical symmetry. By way of example, we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.

Corrections of the finite relativistic contributions to the synodic month period Earth-Moon range oscillations: Agreement between the geocentric and the solar-system barycentric inertial-frame calculations

NASA Astrophysics Data System (ADS)

Nordtvedt, Ken

1993-04-01

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result x(t)~=(3gSr2/c2) cos(ω-Ω)t agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

Characterization methodology for lead zirconate titanate thin films with interdigitated electrode structures

NASA Astrophysics Data System (ADS)

Nigon, R.; Raeder, T. M.; Muralt, P.

2017-05-01

The accurate evaluation of ferroelectric thin films operated with interdigitated electrodes is quite a complex task. In this article, we show how to correct the electric field and the capacitance in order to obtain identical polarization and CV loops for all geometrical variants. The simplest model is compared with corrections derived from Schwartz-Christoffel transformations, and with finite element simulations. The correction procedure is experimentally verified, giving almost identical curves for a variety of gaps and electrode widths. It is shown that the measured polarization change corresponds to the average polarization change in the center plane between the electrode fingers, thus at the position where the electric field is most homogeneous with respect to the direction and size. The question of maximal achievable polarization in the various possible textures, and compositional types of polycrystalline lead zirconate titanate thin films is revisited. In the best case, a soft (110) textured thin film with the morphotropic phase boundary composition should yield a value of 0.95Ps, and in the worst case, a rhombohedral (100) textured thin film should deliver a polarization of 0.74Ps.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

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

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Volume dependence of N-body bound states

NASA Astrophysics Data System (ADS)

König, Sebastian; Lee, Dean

2018-04-01

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

SU-E-T-101: Determination and Comparison of Correction Factors Obtained for TLDs in Small Field Lung Heterogenous Phantom Using Acuros XB and EGSnrc

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

Soh, R; Lee, J; Harianto, F

Purpose: To determine and compare the correction factors obtained for TLDs in 2 × 2cm{sup 2} small field in lung heterogenous phantom using Acuros XB (AXB) and EGSnrc. Methods: This study will simulate the correction factors due to the perturbation of TLD-100 chips (Harshaw/Thermoscientific, 3 × 3 × 0.9mm{sup 3}, 2.64g/cm{sup 3}) in small field lung medium for Stereotactic Body Radiation Therapy (SBRT). A physical lung phantom was simulated by a 14cm thick composite cork phantom (0.27g/cm{sup 3}, HU:-743 ± 11) sandwiched between 4cm thick Plastic Water (CIRS,Norfolk). Composite cork has been shown to be a good lung substitute materialmore » for dosimetric studies. 6MV photon beam from Varian Clinac iX (Varian Medical Systems, Palo Alto, CA) with field size 2 × 2cm{sup 2} was simulated. Depth dose profiles were obtained from the Eclipse treatment planning system Acuros XB (AXB) and independently from DOSxyznrc, EGSnrc. Correction factors was calculated by the ratio of unperturbed to perturbed dose. Since AXB has limitations in simulating actual material compositions, EGSnrc will also simulate the AXB-based material composition for comparison to the actual lung phantom. Results: TLD-100, with its finite size and relatively high density, causes significant perturbation in 2 × 2cm{sup 2} small field in a low lung density phantom. Correction factors calculated by both EGSnrc and AXB was found to be as low as 0.9. It is expected that the correction factor obtained by EGSnrc wlll be more accurate as it is able to simulate the actual phantom material compositions. AXB have a limited material library, therefore it only approximates the composition of TLD, Composite cork and Plastic water, contributing to uncertainties in TLD correction factors. Conclusion: It is expected that the correction factors obtained by EGSnrc will be more accurate. Studies will be done to investigate the correction factors for higher energies where perturbation may be more pronounced.« less

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

PubMed

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

2004-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

A theoretical consideration of ion size effects on the electric double layer and voltammetry of nanometer-sized disk electrodes.

PubMed

Gao, Yu; Liu, Yuwen; Chen, Shengli

2016-12-12

Considering that an electric-double-layer (EDL) structure may significantly impact on the mass transport and charge transfer kinetics at the interfaces of nanometer-sized electrodes, while EDL structures could be altered by the finite sizes of electrolyte and redox ions, the possible effects of ion sizes on EDL structures and voltammetric responses of nanometer-sized disk (nanodisk) electrodes are investigated. Modified Boltzmann and Nernst-Planck (NP) equations, which include the influence of the finite ion volumes, are combined with the Poisson equation and modified Butler-Volmer equation to gain knowledge on how the finite sizes of ions and the nanometer sizes of electrodes may couple with each other to affect the structures and reactivities of a nanoscale electrochemical interface. Two typical ion radii, 0.38 nm and 0.68 nm, which could represent the sizes of the commonly used aqueous electrolyte ions (e.g., the solvated K + ) and the organic electrolyte ions (e.g., the solvated TEA + ) respectively, are considered. The finite size of ions can result in decreased screening of electrode charges, therefore magnifying EDL effects on the ion transport and the electron transfer at electrochemical interfaces. This finite size effect of ions becomes more pronounced for larger ions and at smaller electrodes as the electrode radii is larger than 10 nm. For electrodes with radii smaller than 10 nm, however, the ion size effect may be less pronounced with decreasing the electrode size. This can be explained in terms of the increased edge effect of disk electrodes at nanometer scales, which could relax the ion crowding at/near the outer Helmholtz plane. The conditions and situations under which the ion sizes may have a significant effect on the voltammetry of electrodes are discussed.

Indispensable finite time corrections for Fokker-Planck equations from time series data.

PubMed

Ragwitz, M; Kantz, H

2001-12-17

The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply these methods to time series data of local surface wind velocities, where the dependence of the diffusion constant on the state variable shows a different behavior than previously suggested.

A new approach to fluid-structure interaction within graphics hardware accelerated smooth particle hydrodynamics considering heterogeneous particle size distribution

NASA Astrophysics Data System (ADS)

Eghtesad, Adnan; Knezevic, Marko

2018-07-01

A corrective smooth particle method (CSPM) within smooth particle hydrodynamics (SPH) is used to study the deformation of an aircraft structure under high-velocity water-ditching impact load. The CSPM-SPH method features a new approach for the prediction of two-way fluid-structure interaction coupling. Results indicate that the implementation is well suited for modeling the deformation of structures under high-velocity impact into water as evident from the predicted stress and strain localizations in the aircraft structure as well as the integrity of the impacted interfaces, which show no artificial particle penetrations. To reduce the simulation time, a heterogeneous particle size distribution over a complex three-dimensional geometry is used. The variable particle size is achieved from a finite element mesh with variable element size and, as a result, variable nodal (i.e., SPH particle) spacing. To further accelerate the simulations, the SPH code is ported to a graphics processing unit using the OpenACC standard. The implementation and simulation results are described and discussed in this paper.

A new approach to fluid-structure interaction within graphics hardware accelerated smooth particle hydrodynamics considering heterogeneous particle size distribution

NASA Astrophysics Data System (ADS)

Eghtesad, Adnan; Knezevic, Marko

2017-12-01

A corrective smooth particle method (CSPM) within smooth particle hydrodynamics (SPH) is used to study the deformation of an aircraft structure under high-velocity water-ditching impact load. The CSPM-SPH method features a new approach for the prediction of two-way fluid-structure interaction coupling. Results indicate that the implementation is well suited for modeling the deformation of structures under high-velocity impact into water as evident from the predicted stress and strain localizations in the aircraft structure as well as the integrity of the impacted interfaces, which show no artificial particle penetrations. To reduce the simulation time, a heterogeneous particle size distribution over a complex three-dimensional geometry is used. The variable particle size is achieved from a finite element mesh with variable element size and, as a result, variable nodal (i.e., SPH particle) spacing. To further accelerate the simulations, the SPH code is ported to a graphics processing unit using the OpenACC standard. The implementation and simulation results are described and discussed in this paper.

Asymmetric finite size of ions and orientational ordering of water in electric double layer theory within lattice model.

PubMed

Gongadze, Ekaterina; Kralj-Iglic, Veronika; Iglic, Ales

2018-06-25

In the present short communication, a brief historical survey of the mean-field theoretical description of electric double layer (EDL) is presented. A special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble.

PubMed

Gross, Markus; Gambassi, Andrea; Dietrich, S

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

NASA Astrophysics Data System (ADS)

Gross, Markus; Gambassi, Andrea; Dietrich, S.

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

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

Kaothekar, Sachin, E-mail: sackaothekar@gmail.com

I have studied the effects of finite electron inertia, finite ion Larmor radius (FLR) corrections, and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effect of thermal conductivity for star formation in interstellar medium (ISM). A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instabilitymore » criterion is get modified into radiative instability criterion by inclusion of radiative heat-loss functions with thermal conductivity. The viscosity of medium removes the effect of FLR corrections from the condition of radiative instability. Numerical calculation shows stabilizing effect of heat-loss function, viscosity and FLR corrections, and destabilizing effect of finite electron inertia on the thermal instability. Results carried out in this paper shows that stars are formed in interstellar medium mainly due to thermal instability.« less

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.

2010-06-01

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

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

PubMed

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

2014-11-01

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

Predicting the effectiveness of viscoelastic damping pockets in beams

NASA Astrophysics Data System (ADS)

Butler, Nigel D.; Oyadiji, S. O.

2005-05-01

This paper looks at the use of viscoelastic damping pockets in the suppression of structural vibration. These are in the form of cavities filled with a viscoelastic material. The benefits and uses of these designed-in damping treatments are highlighted. The vibration responses of viscoelastically-damped beams are predicted using the finite element method. A series of cantilevered beams are considered and the damping performance of several configurations of designed-in dampers are predicted and compared to that of a traditional CLD treatment. It is shown that the effectiveness of the damping pockets and sinks depends on their location and size with respect to the highly stressed regions of the beams. Although there is a practical limit on the sizes of the geometrical features that can be designed-in, it is shown that if located correctly the damping pockets and sinks can be more effective at suppressing structural vibration than traditional CLD treatments.

Finite-size scaling of survival probability in branching processes

NASA Astrophysics Data System (ADS)

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro

2015-04-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G (y ) =2 y ey /(ey-1 ) , with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.

Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals. I. Nanoparticle size-dependent tetragonal phase stability

NASA Astrophysics Data System (ADS)

Akdogan, E. K.; Safari, A.

2007-03-01

We propose a phenomenological intrinsic finite-size effect model for single domain, mechanically free, and surface charge compensated ΔG-P ⃗s-ξ space, which describes the decrease in tetragonal phase stability with decreasing ξ rigorously.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

NASA Astrophysics Data System (ADS)

Forssén, C.; Carlsson, B. D.; Johansson, H. T.; Sääf, D.; Bansal, A.; Hagen, G.; Papenbrock, T.

2018-03-01

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 1010 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to Nmax=22 and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

Does a Single Eigenstate Encode the Full Hamiltonian?

NASA Astrophysics Data System (ADS)

Garrison, James R.; Grover, Tarun

2018-04-01

The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

Size-dependent chemical transformation, structural phase-change, and optical properties of nanowires

PubMed Central

Piccione, Brian; Agarwal, Rahul; Jung, Yeonwoong; Agarwal, Ritesh

2013-01-01

Nanowires offer a unique approach for the bottom up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5 – 300 nm range, where finite size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well controlled geometries, dimensions and functionality, which can then be used for understanding novel processes in finite-sized systems and devices. PMID:23997656

High precision analytical description of the allowed β spectrum shape

NASA Astrophysics Data System (ADS)

Hayen, Leendert; Severijns, Nathal; Bodek, Kazimierz; Rozpedzik, Dagmara; Mougeot, Xavier

2018-01-01

A fully analytical description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. Particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. The need for an accurate evaluation of weak magnetism contributions was stressed, and the possible significance of the oft-neglected induced pseudoscalar interaction was noted. Together with improved atomic corrections, an analytical description was presented of the allowed β spectrum shape accurate to a few parts in 10-4 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Jeans instability of magnetized quantum plasma: Effect of viscosity, rotation and finite Larmor radius corrections

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

Jain, Shweta, E-mail: jshweta09@gmail.com; Sharma, Prerana; Chhajlani, R. K.

2015-07-31

The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.

Finite-size effects for anisotropic 2D Ising model with various boundary conditions

NASA Astrophysics Data System (ADS)

Izmailian, N. Sh

2012-12-01

We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Multifractal analysis with the probability density function at the three-dimensional anderson transition.

PubMed

Rodriguez, Alberto; Vasquez, Louella J; Römer, Rudolf A

2009-03-13

The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.

Archimedes force on Casimir apparatus

NASA Astrophysics Data System (ADS)

Shevchenko, V.; Shevrin, E.

2016-11-01

The talk addresses a problem of Casimir apparatus in weak gravitational field, surrounded by a dense medium. The falling of the apparatus has to be governed by the equivalence principle, taking into account proper contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general ex pression for the corresponding force in terms of the effective action. By way of example we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.

Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

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

Lemarie, Gabriel; Delande, Dominique; Chabe, Julien

Using a cold atomic gas exposed to laser pulses - a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies - we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent {nu}=1.59{+-}0.01, which is found to be equal to the one previously computed for themore » Anderson model.« less

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

Zardecki, A.

The effect of multiple scattering on the validity of the Beer-Lambert law is discussed for a wide range of particle-size parameters and optical depths. To predict the amount of received radiant power, appropriate correction terms are introduced. For particles larger than or comparable to the wavelength of radiation, the small-angle approximation is adequate; whereas for small densely packed particles, the diffusion theory is advantageously employed. These two approaches are used in the context of the problem of laser-beam propagation in a dense aerosol medium. In addition, preliminary results obtained by using a two-dimensional finite-element discrete-ordinates transport code are described. Multiple-scatteringmore » effects for laser propagation in fog, cloud, rain, and aerosol cloud are modeled.« less

Finite-size effects on the radiative energy loss of a fast parton in hot and dense strongly interacting matter

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

Caron-Huot, Simon; Gale, Charles

2010-12-15

We consider finite-size effects on the radiative energy loss of a fast parton moving in a finite-temperature, strongly interacting medium, using the light-cone path integral formalism put forward by B. G. Zakharov [JETP Lett. 63, 952 (1996); 65, 615 (1997)]. We present a convenient reformulation of the problem that makes possible its exact numerical analysis. This is done by introducing the concept of a radiation rate in the presence of finite-size effects. This effectively extends the finite-temperature approach of Arnold, Moore, and Yaffe [J. High Energy Phys. 11 (2001) 057; 12 (2001) 009; 06 (2001) 030] (AMY) to include interferencemore » between vacuum and medium radiation. We compare results with those obtained in the regime considered by AMY, with those obtained at leading order in an opacity expansion, and with those obtained deep in the Landau-Pomeranchuk-Migdal regime.« less

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

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

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

Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

NASA Astrophysics Data System (ADS)

Kim, Isaac H.

2011-05-01

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

The principle of finiteness - a guideline for physical laws

NASA Astrophysics Data System (ADS)

Sternlieb, Abraham

2013-04-01

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

Rank-based permutation approaches for non-parametric factorial designs.

PubMed

Umlauft, Maria; Konietschke, Frank; Pauly, Markus

2017-11-01

Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null. To bridge these gaps, a novel permutation approach is proposed which can be seen as a flexible generalization of the Kruskal-Wallis test to all kinds of factorial designs with independent observations. It is proven that the permutation principle is asymptotically correct while keeping its finite exactness property when data are exchangeable. The results of extensive simulation studies foster these theoretical findings. A real data set exemplifies its applicability. © 2017 The British Psychological Society.

Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure

NASA Astrophysics Data System (ADS)

Beloy, Kyle; Derevianko, Andrei

2008-09-01

The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V.M. Shabaev et al., Phys. Rev. Lett. 93 (2004) 130405] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely-employed approach of Notre Dame (ND) group [W.R. Johnson, S.A. Blundell, J. Sapirstein, Phys. Rev. A 37 (1988) 307-315]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the 6s-7s transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach. In addition, we present a strategy for optimizing the size of the basis sets by choosing progressively smaller number of basis functions for increasingly higher partial waves. This strategy exploits suppression of contributions of high partial waves to typical many-body correlation corrections.

The effects of dielectric decrement and finite ion size on differential capacitance of electrolytically gated graphene

NASA Astrophysics Data System (ADS)

Daniels, Lindsey; Scott, Matthew; Mišković, Z. L.

2018-06-01

We analyze the effects of dielectric decrement and finite ion size in an aqueous electrolyte on the capacitance of a graphene electrode, and make comparisons with the effects of dielectric saturation combined with finite ion size. We first derive conditions for the cross-over from a camel-shaped to a bell-shaped capacitance of the diffuse layer. We show next that the total capacitance is dominated by a V-shaped quantum capacitance of graphene at low potentials. A broad peak develops in the total capacitance at high potentials, which is sensitive to the ion size with dielectric saturation, but is stable with dielectric decrement.

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

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

Methods for the computation of detailed geoids and their accuracy

NASA Technical Reports Server (NTRS)

Rapp, R. H.; Rummel, R.

1975-01-01

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants.

Analytical treatment of the deformation behavior of EUVL masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-03-01

A new analytical approach is presented to predict mask deformation during electro-static chucking in next generation extreme-ultraviolet-lithography (EUVL). Given an arbitrary profile measurement of the mask and chuck non-flatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern-distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Analytical treatment of the deformation behavior of extreme-ultraviolet-lithography masks during electrostatic chucking

NASA Astrophysics Data System (ADS)

Brandstetter, Gerd; Govindjee, Sanjay

2012-10-01

A new analytical approach is presented to predict mask deformation during electrostatic chucking in next-generation extreme-ultraviolet-lithography. Given an arbitrary profile measurement of the mask and chuck nonflatness, this method has been developed as an alternative to time-consuming finite element simulations for overlay error correction algorithms. We consider the feature transfer of each harmonic component in the profile shapes via linear elasticity theory and demonstrate analytically how high spatial frequencies are filtered. The method is compared to presumably more accurate finite element simulations and has been tested successfully in an overlay error compensation experiment, where the residual error y-component could be reduced by a factor of 2. As a side outcome, the formulation provides a tool to estimate the critical pin-size and -pitch such that the distortion on the mask front-side remains within given tolerances. We find for a numerical example that pin-pitches of less than 5 mm will result in a mask pattern distortion of less than 1 nm if the chucking pressure is below 30 kPa.

Evaluation of different screw fixation techniques and screw diameters in sagittal split ramus osteotomy: finite element analysis method.

PubMed

Sindel, A; Demiralp, S; Colok, G

2014-09-01

Sagittal split ramus osteotomy (SSRO) is used for correction of numerous congenital or acquired deformities in facial region. Several techniques have been developed and used to maintain fixation and stabilisation following SSRO application. In this study, the effects of the insertion formations of the bicortical different sized screws to the stresses generated by forces were studied. Three-dimensional finite elements analysis (FEA) and static linear analysis methods were used to investigate difference which would occur in terms of forces effecting onto the screws and transmitted to bone between different application areas. No significant difference was found between 1·5- and 2-mm screws used in SSRO fixation. Besides, it was found that 'inverted L' application was more successful compared to the others and that was followed by 'L' and 'linear' formations which showed close rates to each other. Few studies have investigated the effect of thickness and application areas of bicortical screws. This study was performed on both advanced and regressed jaws positions. © 2014 John Wiley & Sons Ltd.

Adaptive Mesh Refinement for Microelectronic Device Design

NASA Technical Reports Server (NTRS)

Cwik, Tom; Lou, John; Norton, Charles

1999-01-01

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

Safe and sensible preprocessing and baseline correction of pupil-size data.

PubMed

Mathôt, Sebastiaan; Fabius, Jasper; Van Heusden, Elle; Van der Stigchel, Stefan

2018-02-01

Measurement of pupil size (pupillometry) has recently gained renewed interest from psychologists, but there is little agreement on how pupil-size data is best analyzed. Here we focus on one aspect of pupillometric analyses: baseline correction, i.e., analyzing changes in pupil size relative to a baseline period. Baseline correction is useful in experiments that investigate the effect of some experimental manipulation on pupil size. In such experiments, baseline correction improves statistical power by taking into account random fluctuations in pupil size over time. However, we show that baseline correction can also distort data if unrealistically small pupil sizes are recorded during the baseline period, which can easily occur due to eye blinks, data loss, or other distortions. Divisive baseline correction (corrected pupil size = pupil size/baseline) is affected more strongly by such distortions than subtractive baseline correction (corrected pupil size = pupil size - baseline). We discuss the role of baseline correction as a part of preprocessing of pupillometric data, and make five recommendations: (1) before baseline correction, perform data preprocessing to mark missing and invalid data, but assume that some distortions will remain in the data; (2) use subtractive baseline correction; (3) visually compare your corrected and uncorrected data; (4) be wary of pupil-size effects that emerge faster than the latency of the pupillary response allows (within ±220 ms after the manipulation that induces the effect); and (5) remove trials on which baseline pupil size is unrealistically small (indicative of blinks and other distortions).

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Applications and error correction for adiabatic quantum optimization

NASA Astrophysics Data System (ADS)

Pudenz, Kristen

Adiabatic quantum optimization (AQO) is a fast-developing subfield of quantum information processing which holds great promise in the relatively near future. Here we develop an application, quantum anomaly detection, and an error correction code, Quantum Annealing Correction (QAC), for use with AQO. The motivation for the anomaly detection algorithm is the problematic nature of classical software verification and validation (V&V). The number of lines of code written for safety-critical applications such as cars and aircraft increases each year, and with it the cost of finding errors grows exponentially (the cost of overlooking errors, which can be measured in human safety, is arguably even higher). We approach the V&V problem by using a quantum machine learning algorithm to identify charateristics of software operations that are implemented outside of specifications, then define an AQO to return these anomalous operations as its result. Our error correction work is the first large-scale experimental demonstration of quantum error correcting codes. We develop QAC and apply it to USC's equipment, the first and second generation of commercially available D-Wave AQO processors. We first show comprehensive experimental results for the code's performance on antiferromagnetic chains, scaling the problem size up to 86 logical qubits (344 physical qubits) and recovering significant encoded success rates even when the unencoded success rates drop to almost nothing. A broader set of randomized benchmarking problems is then introduced, for which we observe similar behavior to the antiferromagnetic chain, specifically that the use of QAC is almost always advantageous for problems of sufficient size and difficulty. Along the way, we develop problem-specific optimizations for the code and gain insight into the various on-chip error mechanisms (most prominently thermal noise, since the hardware operates at finite temperature) and the ways QAC counteracts them. We finish by showing that the scheme is robust to qubit loss on-chip, a significant benefit when considering an implemented system.

Gravity/Topography Admittances and Lithospheric Evolution on Mars: The Importance of Finite-Amplitude Topography

NASA Technical Reports Server (NTRS)

McGovern, Patrick J.; Solomon, Sean C.; Smith, David E.; Zuber, Maria T.; Neumann, Gregory A.; Head, J. W., III; Phillips, Roger J.; Simons, Mark

2001-01-01

We calculate localized gravity/topography admittances for Mars, in order to estimate elastic lithosphere thickness. A finite-amplitude correction to modeled gravity is required to properly interpret admittances in high-relief regions of Mars. Additional information is contained in the original extended abstract.

Finite element design procedure for correcting the coining die profiles

NASA Astrophysics Data System (ADS)

Alexandrino, Paulo; Leitão, Paulo J.; Alves, Luis M.; Martins, Paulo A. F.

2018-05-01

This paper presents a new finite element based design procedure for correcting the coining die profiles in order to optimize the distribution of pressure and the alignment of the resultant vertical force at the end of the die stroke. The procedure avoids time consuming and costly try-outs, does not interfere with the creative process of the sculptors and extends the service life of the coining dies by significantly decreasing the applied pressure and bending moments. The numerical simulations were carried out in a computer program based on the finite element flow formulation that is currently being developed by the authors in collaboration with the Portuguese Mint. A new experimental procedure based on the stack compression test is also proposed for determining the stress-strain curve of the materials directly from the coin blanks.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

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

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Interference assembly and fretting wear analysis of hollow shaft.

PubMed

Han, Chuanjun; Zhang, Jie

2014-01-01

Fretting damage phenomenon often appears in the interference fit assembly. The finite element model of hollow shaft and shaft sleeve was established, and the equivalent stress and contact stress were computed after interference assembly. The assembly body of hollow shaft and shaft sleeve was in whirling bending load, and the contact status (sticking, sliding, and opening) and the distribution of stress along one typical contact line were computed under different loads, interferences, hollow degrees, friction coefficient, and wear quantity. Judgment formula of contact state was fixed by introducing the corrected coefficient k. The computation results showed that the "edge effect" appears in the contact surface after interference fit. The size of slip zone is unchanged along with the increase of bending load. The greater the interference value, the bigger the wear range. The hollow degree does not influence the size of stick zone but controls the position of the junction point of slip-open. Tangential contact stress increases with the friction coefficient, which has a little effect on normal contact stress. The relationship between open size and wear capacity is approximately linear.

Relationship of forces acting on implant rods and degree of scoliosis correction.

PubMed

Salmingo, Remel Alingalan; Tadano, Shigeru; Fujisaki, Kazuhiro; Abe, Yuichiro; Ito, Manabu

2013-02-01

Adolescent idiopathic scoliosis is a complex spinal pathology characterized as a three-dimensional spine deformity combined with vertebral rotation. Various surgical techniques for correction of severe scoliotic deformity have evolved and became more advanced in applying the corrective forces. The objective of this study was to investigate the relationship between corrective forces acting on deformed rods and degree of scoliosis correction. Implant rod geometries of six adolescent idiopathic scoliosis patients were measured before and after surgery. An elasto-plastic finite element model of the implant rod before surgery was reconstructed for each patient. An inverse method based on Finite Element Analysis was used to apply forces to the implant rod model such that it was deformed the same after surgery. Relationship between the magnitude of corrective forces and degree of correction expressed as change of Cobb angle was evaluated. The effects of screw configuration on the corrective forces were also investigated. Corrective forces acting on rods and degree of correction were not correlated. Increase in number of implant screws tended to decrease the magnitude of corrective forces but did not provide higher degree of correction. Although greater correction was achieved with higher screw density, the forces increased at some level. The biomechanics of scoliosis correction is not only dependent to the corrective forces acting on implant rods but also associated with various parameters such as screw placement configuration and spine stiffness. Considering the magnitude of forces, increasing screw density is not guaranteed as the safest surgical strategy. Copyright © 2012 Elsevier Ltd. All rights reserved.

Fault-tolerant measurement-based quantum computing with continuous-variable cluster states.

PubMed

Menicucci, Nicolas C

2014-03-28

A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.

Higgs decays to Z Z and Z γ in the standard model effective field theory: An NLO analysis

NASA Astrophysics Data System (ADS)

Dawson, S.; Giardino, P. P.

2018-05-01

We calculate the complete one-loop electroweak corrections to the inclusive H →Z Z and H →Z γ decays in the dimension-6 extension of the Standard Model Effective Field Theory (SMEFT). The corrections to H →Z Z are computed for on-shell Z bosons and are a precursor to the physical H →Z f f ¯ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite next-to-leading-order contributions to the decay widths. As a byproduct of our calculation, we obtain the first complete result for the finite corrections to Gμ in the SMEFT.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

NASA Astrophysics Data System (ADS)

Brell, Courtney G.

2016-01-01

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in {{{R}}}3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

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

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

Finite-size scaling of eigenstate thermalization

NASA Astrophysics Data System (ADS)

Beugeling, W.; Moessner, R.; Haque, Masudul

2014-04-01

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

NASA Astrophysics Data System (ADS)

Zschocke, Fabian; Vojta, Matthias

2015-07-01

Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011), 10.1103/PhysRevB.84.165414]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A; Reddy, S.; Handschuh, R.

1995-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator’s spatial size and shape

NASA Astrophysics Data System (ADS)

Jeknić-Dugić, Jasmina; Petrović, Igor; Arsenijević, Momir; Dugić, Miroljub

2018-05-01

We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator’s stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.

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

Setyawan, Wahyu; Nandipati, Giridhar; Kurtz, Richard J.

The stability of tungsten self-interstitial atom (SIA) clusters is studied using first-principles methods. Clusters from one to seven SIAs are systematically explored from 1264 unique configurations. Finite-size effect of the simulation cell is corrected based on the scaling of formation energy versus inverse volume cell. Furthermore, the accuracy of the calculations is improved by treating the 5p semicore states as valence states. Configurations of the three most stable clusters in each cluster size n are presented, which consist of parallel [111] dumbbells. The evolution of these clusters leading to small dislocation loops is discussed. The binding energy of size-n clustersmore » is analyzed relative to an n → (n-1) + 1 dissociation and is shown to increase with size. Extrapolation for n > 7 is presented using a dislocation loop model. In addition, the interaction of these clusters with a substitutional Re, Os, or Ta solute is explored by replacing one of the dumbbells with the solute. Re and Os strongly attract these clusters, but Ta strongly repels. The strongest interaction is found when the solute is located on the periphery of the cluster rather than in the middle. The magnitude of this interaction decreases with cluster size. Empirical fits to describe the trend of the solute binding energy are presented.« less

Non-thermal transitions in a model inspired by moral decisions

NASA Astrophysics Data System (ADS)

Alamino, Roberto C.

2016-08-01

This work introduces a model in which agents of a network act upon one another according to three different kinds of moral decisions. These decisions are based on an increasing level of sophistication in the empathy capacity of the agent, a hierarchy which we name Piaget’s ladder. The decision strategy of the agents is non-rational, in the sense they are arbitrarily fixed, and the model presents quenched disorder given by the distribution of its defining parameters. An analytical solution for this model is obtained in the large system limit as well as a leading order correction for finite-size systems which shows that typical realisations of the model develop a phase structure with both continuous and discontinuous non-thermal transitions.

The random fractional matching problem

NASA Astrophysics Data System (ADS)

Lucibello, Carlo; Malatesta, Enrico M.; Parisi, Giorgio; Sicuro, Gabriele

2018-05-01

We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. In the other one, on the contrary, such a link is forbidden. Both problems have the same asymptotic average optimal cost of the random-link matching problem on the complete graph. Using a replica approach and previous results of Wästlund (2010 Acta Mathematica 204 91–150), we analytically derive the finite-size corrections to the asymptotic optimal cost. We compare our results with numerical simulations and we discuss the main differences between random-link fractional matching problems and the random-link matching problem.

An Engineering Solution for Solving Mesh Size Effects in the Simulation of Delamination with Cohesive Zone Models

NASA Technical Reports Server (NTRS)

Turon, A.; Davila, C. G.; Camanho, P. P.; Costa, J.

2007-01-01

This paper presents a methodology to determine the parameters to be used in the constitutive equations of Cohesive Zone Models employed in the simulation of delamination in composite materials by means of decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is also proposed. The procedure ensures that the energy dissipated by the fracture process is computed correctly. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used for the simulation of fracture processes.

A lattice calculation of the hadronic vacuum polarization contribution to (g - 2)µ

NASA Astrophysics Data System (ADS)

Della Morte, M.; Francis, A.; Gérardin, A.; Gülpers, V.; Herdoíza, G.; von Hippel, G.; Horch, H.; Jäger, B.; Meyer, H. B.; Nyffeler, A.; Wittig, H.

2018-03-01

We present results of calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. Specifically, we focus on controlling the infrared regime of the vacuum polarisation function. Our results are corrected for finite-size effects by combining the Gounaris-Sakurai parameterisation of the timelike pion form factor with the Lüscher formalism. The impact of quark-disconnected diagrams and the precision of the scale determination is discussed and included in our final result in two-flavour QCD, which carries an overall uncertainty of 6%. We present preliminary results computed on ensembles with Nf = 2 + 1 dynamical flavours and discuss how the long-distance contribution can be accurately constrained by a dedicated spectrum calculation in the iso-vector channel.

Many-body localization in a long range XXZ model with random-field

NASA Astrophysics Data System (ADS)

Li, Bo

2016-12-01

Many-body localization (MBL) in a long range interaction XXZ model with random field are investigated. Using the exact diagonal method, the MBL phase diagram with different tuning parameters and interaction range is obtained. It is found that the phase diagram of finite size results supplies strong evidence to confirm that the threshold interaction exponent α = 2. The tuning parameter Δ can efficiently change the MBL edge in high energy density stats, thus the system can be controlled to transfer from thermal phase to MBL phase by changing Δ. The energy level statistics data are consistent with result of the MBL phase diagram. However energy level statistics data cannot detect the thermal phase correctly in extreme long range case.

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

Can a pseudo-Nambu-Goldstone Higgs lead to symmetry non-restoration?

NASA Astrophysics Data System (ADS)

Kilic, Can; Swaminathan, Sivaramakrishnan

2016-01-01

The calculation of finite temperature contributions to the scalar potential in a quantum field theory is similar to the calculation of loop corrections at zero temperature. In natural extensions of the Standard Model where loop corrections to the Higgs potential cancel between Standard Model degrees of freedom and their symmetry partners, it is interesting to contemplate whether finite temperature corrections also cancel, raising the question of whether a broken phase of electroweak symmetry may persist at high temperature. It is well known that this does not happen in supersymmetric theories because the thermal contributions of bosons and fermions do not cancel each other. However, for theories with same spin partners, the answer is less obvious. Using the Twin Higgs model as a benchmark, we show that although thermal corrections do cancel at the level of quadratic divergences, subleading corrections still drive the system to a restored phase. We further argue that our conclusions generalize to other well-known extensions of the Standard Model where the Higgs is rendered natural by being the pseudo-Nambu-Goldstone mode of an approximate global symmetry.

The Effects of Finite Sampling on State Assessment Sample Requirements. NAEP Validity Studies. Working Paper Series.

ERIC Educational Resources Information Center

Chromy, James R.

This study addressed statistical techniques that might ameliorate some of the sampling problems currently facing states with small populations participating in State National Assessment of Educational Progress (NAEP) assessments. The study explored how the application of finite population correction factors to the between-school component of…

Finite temperature corrections to tachyon mass in intersecting D-branes

NASA Astrophysics Data System (ADS)

Sethi, Varun; Chowdhury, Sudipto Paul; Sarkar, Swarnendu

2017-04-01

We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in [1]. In this paper we extend the computation to the case of intersecting D3 branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8 branes in D4 brane background was proposed in [2]. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1 branes obtained in [1] as well as those for intersecting D2 branes.

Updating finite element dynamic models using an element-by-element sensitivity methodology

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Hemez, Francois M.

1993-01-01

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.

Criticality in finite dynamical networks

NASA Astrophysics Data System (ADS)

Rohlf, Thimo; Gulbahce, Natali; Teuscher, Christof

2007-03-01

It has been shown analytically and experimentally that both random boolean and random threshold networks show a transition from ordered to chaotic dynamics at a critical average connectivity Kc in the thermodynamical limit [1]. By looking at the statistical distributions of damage spreading (damage sizes), we go beyond this extensively studied mean-field approximation. We study the scaling properties of damage size distributions as a function of system size N and initial perturbation size d(t=0). We present numerical evidence that another characteristic point, Kd exists for finite system sizes, where the expectation value of damage spreading in the network is independent of the system size N. Further, the probability to obtain critical networks is investigated for a given system size and average connectivity k. Our results suggest that, for finite size dynamical networks, phase space structure is very complex and may not exhibit a sharp order-disorder transition. Finally, we discuss the implications of our findings for evolutionary processes and learning applied to networks which solve specific computational tasks. [1] Derrida, B. and Pomeau, Y. (1986), Europhys. Lett., 1, 45-49

Eisenstein series for infinite-dimensional U-duality groups

NASA Astrophysics Data System (ADS)

Fleig, Philipp; Kleinschmidt, Axel

2012-06-01

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Asta, Adelchi J.; Levesque, Maximilien; Vuilleumier, Rodolphe; Rotenberg, Benjamin

2017-06-01

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t-3 /2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Electrical four-point probing of spherical metallic thin films coated onto micron sized polymer particles

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

Pettersen, Sigurd R., E-mail: sigurd.r.pettersen@ntnu.no, E-mail: jianying.he@ntnu.no; Stokkeland, August Emil; Zhang, Zhiliang

Micron-sized metal-coated polymer spheres are frequently used as filler particles in conductive composites for electronic interconnects. However, the intrinsic electrical resistivity of the spherical thin films has not been attainable due to deficiency in methods that eliminate the effect of contact resistance. In this work, a four-point probing method using vacuum compatible piezo-actuated micro robots was developed to directly investigate the electric properties of individual silver-coated spheres under real-time observation in a scanning electron microscope. Poly(methyl methacrylate) spheres with a diameter of 30 μm and four different film thicknesses (270 nm, 150 nm, 100 nm, and 60 nm) were investigated. By multiplying the experimental resultsmore » with geometrical correction factors obtained using finite element models, the resistivities of the thin films were estimated for the four thicknesses. These were higher than the resistivity of bulk silver.« less

Finite-size correction scheme for supercell calculations in Dirac-point two-dimensional materials.

PubMed

Rocha, C G; Rocha, A R; Venezuela, P; Garcia, J H; Ferreira, M S

2018-06-19

Modern electronic structure calculations are predominantly implemented within the super cell representation in which unit cells are periodically arranged in space. Even in the case of non-crystalline materials, defect-embedded unit cells are commonly used to describe doped structures. However, this type of computation becomes prohibitively demanding when convergence rates are sufficiently slow and may require calculations with very large unit cells. Here we show that a hitherto unexplored feature displayed by several 2D materials may be used to achieve convergence in formation- and adsorption-energy calculations with relatively small unit-cell sizes. The generality of our method is illustrated with Density Functional Theory calculations for different 2D hosts doped with different impurities, all of which providing accuracy levels that would otherwise require enormously large unit cells. This approach provides an efficient route to calculating the physical properties of 2D systems in general but is particularly suitable for Dirac-point materials doped with impurities that break their sublattice symmetry.

Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements

NASA Technical Reports Server (NTRS)

Kalinowski, A. J.; Wagner, C. A.

1983-01-01

Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.

Random sequential adsorption of straight rigid rods on a simple cubic lattice

NASA Astrophysics Data System (ADS)

García, G. D.; Sanchez-Varretti, F. O.; Centres, P. M.; Ramirez-Pastor, A. J.

2015-10-01

Random sequential adsorption of straight rigid rods of length k (k-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The k-mers were irreversibly and isotropically deposited into the lattice. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for k ranging from 2 to 64, revealed that (i) the jamming coverage for dimers (k = 2) is θj = 0.918388(16) . Our result corrects the previously reported value of θj = 0.799(2) (Tarasevich and Cherkasova, 2007); (ii) θj exhibits a decreasing function when it is plotted in terms of the k-mer size, being θj(∞) = 0.4045(19) the value of the limit coverage for large k's; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing to zero with increasing k.

Temperature behaviour of the average size of nanoparticle lattices co-deposited with an amorphous matrix. Analysis of Ge + Al2O3 and Ni + Al2O3 thin films

NASA Astrophysics Data System (ADS)

Mezzasalma, Stefano A.; Car, Tihomir; Nekić, Nikolina; Jerčinović, Marko; Buljan, Maja

2017-11-01

We theoretically interpret the thermal behaviour of the average radius versus substrate temperature of regular quantum dot/nanocluster arrays formed by sputtering semiconductor/metal atoms with oxide molecules. The analysis relies on a continuum theory for amorphous films with given surface quantities, perturbed by a nanoparticle lattice. An account of the basic thermodynamic contributions is given in terms of force-flux phenomenological coefficients of each phase (Ge, Ni, Al2O3). Average radii turn out to be expressible by a characteristic length scale and a dimensionless parameter, which mainly depend upon temperature through diffusion lengths, film pressures and finite-size corrections to interfacial tensions. The numerical agreement is good in both Ge (4 % ) and Ni (15.4 % ) lattices grown at temperatures ≤slant 800 K, despite the lower temperature behaviour of quantum dots seeming to suggest further driving forces taking part in such processes.

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

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

Preston, Leiph

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

The uniform electron gas at warm dense matter conditions

NASA Astrophysics Data System (ADS)

Dornheim, Tobias; Groth, Simon; Bonitz, Michael

2018-05-01

Motivated by the current high interest in the field of warm dense matter research, in this article we review the uniform electron gas (UEG) at finite temperature and over a broad density range relevant for warm dense matter applications. We provide an exhaustive overview of different simulation techniques, focusing on recent developments in the dielectric formalism (linear response theory) and quantum Monte Carlo (QMC) methods. Our primary focus is on two novel QMC methods that have recently allowed us to achieve breakthroughs in the thermodynamics of the warm dense electron gas: Permutation blocking path integral MC (PB-PIMC) and configuration path integral MC (CPIMC). In fact, a combination of PB-PIMC and CPIMC has allowed for a highly accurate description of the warm dense UEG over a broad density-temperature range. We are able to effectively avoid the notorious fermion sign problem, without invoking uncontrolled approximations such as the fixed node approximation. Furthermore, a new finite-size correction scheme is presented that makes it possible to treat the UEG in the thermodynamic limit without loss of accuracy. In addition, we in detail discuss the construction of a parametrization of the exchange-correlation free energy, on the basis of these data - the central thermodynamic quantity that provides a complete description of the UEG and is of crucial importance as input for the simulation of real warm dense matter applications, e.g., via thermal density functional theory. A second major aspect of this review is the use of our ab initio simulation results to test previous theories, including restricted PIMC, finite-temperature Green functions, the classical mapping by Perrot and Dharma-wardana, and various dielectric methods such as the random phase approximation, or the Singwi-Tosi-Land-Sjölander (both in the static and quantum versions), Vashishta-Singwi and the recent Tanaka scheme for the local field correction. Thus, for the first time, thorough benchmarks of the accuracy of important approximation schemes regarding various quantities such as different energies, in particular the exchange-correlation free energy, and the static structure factor, are possible. In the final part of this paper, we outline a way how to rigorously extend our QMC studies to the inhomogeneous electron gas. We present first ab initio data for the static density response and for the static local field correction.

Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

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

Sommer, A., E-mail: a.sommer@lte.uni-saarland.de; Farle, O., E-mail: o.farle@lte.uni-saarland.de; Dyczij-Edlinger, R., E-mail: edlinger@lte.uni-saarland.de

2015-10-15

This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline–online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.

Mean-cluster approach indicates cell sorting time scales are determined by collective dynamics

NASA Astrophysics Data System (ADS)

Beatrici, Carine P.; de Almeida, Rita M. C.; Brunnet, Leonardo G.

2017-03-01

Cell migration is essential to cell segregation, playing a central role in tissue formation, wound healing, and tumor evolution. Considering random mixtures of two cell types, it is still not clear which cell characteristics define clustering time scales. The mass of diffusing clusters merging with one another is expected to grow as td /d +2 when the diffusion constant scales with the inverse of the cluster mass. Cell segregation experiments deviate from that behavior. Explanations for that could arise from specific microscopic mechanisms or from collective effects, typical of active matter. Here we consider a power law connecting diffusion constant and cluster mass to propose an analytic approach to model cell segregation where we explicitly take into account finite-size corrections. The results are compared with active matter model simulations and experiments available in the literature. To investigate the role played by different mechanisms we considered different hypotheses describing cell-cell interaction: differential adhesion hypothesis and different velocities hypothesis. We find that the simulations yield normal diffusion for long time intervals. Analytic and simulation results show that (i) cluster evolution clearly tends to a scaling regime, disrupted only at finite-size limits; (ii) cluster diffusion is greatly enhanced by cell collective behavior, such that for high enough tendency to follow the neighbors, cluster diffusion may become independent of cluster size; (iii) the scaling exponent for cluster growth depends only on the mass-diffusion relation, not on the detailed local segregation mechanism. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed certainly have deep implications in biological evolution as a selection mechanism.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

DOE PAGES

Burr, P. A.; Cooper, M. W. D.

2017-09-15

Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover,more » the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.« less

Importance of elastic finite-size effects: Neutral defects in ionic compounds

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

Burr, P. A.; Cooper, M. W. D.

Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover,more » the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.« less

Importance of elastic finite-size effects: Neutral defects in ionic compounds

NASA Astrophysics Data System (ADS)

Burr, P. A.; Cooper, M. W. D.

2017-09-01

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Stabilised finite-element methods for solving the level set equation with mass conservation

NASA Astrophysics Data System (ADS)

Kabirou Touré, Mamadou; Fahsi, Adil; Soulaïmani, Azzeddine

2016-01-01

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier-Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position.

Finite element analyses of thin film active grazing incidence x-ray optics

NASA Astrophysics Data System (ADS)

Davis, William N.; Reid, Paul B.; Schwartz, Daniel A.

2010-09-01

The Chandra X-ray Observatory, with its sub-arc second resolution, has revolutionized X-ray astronomy by revealing an extremely complex X-ray sky and demonstrating the power of the X-ray window in exploring fundamental astrophysical problems. Larger area telescopes of still higher angular resolution promise further advances. We are engaged in the development of a mission concept, Generation-X, a 0.1 arc second resolution x-ray telescope with tens of square meters of collecting area, 500 times that of Chandra. To achieve these two requirements of imaging and area, we are developing a grazing incidence telescope comprised of many mirror segments. Each segment is an adjustable mirror that is a section of a paraboloid or hyperboloid, aligned and figure corrected in situ on-orbit. To that end, finite element analyses of thin glass mirrors are performed to determine influence functions for each actuator on the mirrors, in order to develop algorithms for correction of mirror deformations. The effects of several mirror mounting schemes are also studied. The finite element analysis results, combined with measurements made on prototype mirrors, will be used to further refine the correction algorithms.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

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

Altabet, Y. Elia; Debenedetti, Pablo G., E-mail: pdebene@princeton.edu; Stillinger, Frank H.

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρ{sub S}. The tensile limit at ρ{sub S} is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρ{sub S} is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherentmore » structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.« less

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

PubMed

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

1999-04-01

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

A method of selecting grid size to account for Hertz deformation in finite element analysis of spur gears

NASA Technical Reports Server (NTRS)

Coy, J. J.; Chao, C. H. C.

1981-01-01

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

Finite-size polyelectrolyte bundles at thermodynamic equilibrium

NASA Astrophysics Data System (ADS)

Sayar, M.; Holm, C.

2007-01-01

We present the results of extensive computer simulations performed on solutions of monodisperse charged rod-like polyelectrolytes in the presence of trivalent counterions. To overcome energy barriers we used a combination of parallel tempering and hybrid Monte Carlo techniques. Our results show that for small values of the electrostatic interaction the solution mostly consists of dispersed single rods. The potential of mean force between the polyelectrolyte monomers yields an attractive interaction at short distances. For a range of larger values of the Bjerrum length, we find finite-size polyelectrolyte bundles at thermodynamic equilibrium. Further increase of the Bjerrum length eventually leads to phase separation and precipitation. We discuss the origin of the observed thermodynamic stability of the finite-size aggregates.

Finite-size effects on bacterial population expansion under controlled flow conditions

NASA Astrophysics Data System (ADS)

Tesser, Francesca; Zeegers, Jos C. H.; Clercx, Herman J. H.; Brunsveld, Luc; Toschi, Federico

2017-03-01

The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra, advection induced, dispersal factor. We designed and assembled a dedicated microfluidic device to control and quantify the expansion of populations of E. coli bacteria under both co-flowing and counter-flowing conditions, measuring the front speed at varying intensity of the imposed flow. At variance with respect to the case of classic advective-reactive-diffusive chemical fronts, we measure that almost irrespective of the counter-flow velocity, the front speed remains finite at a constant positive value. A simple model incorporating growth, dispersion and drift on finite-size hard beads allows to explain this finding as due to a finite volume effect of the bacteria. This indicates that models based on the Fisher-Kolmogorov-Petrovsky-Piscounov equation (FKPP) that ignore the finite size of organisms may be inaccurate to describe the physics of spatial growth dynamics of bacteria.

Exact Electromagnetic Fields Produced by a Finite Wire with Constant Current

ERIC Educational Resources Information Center

Jimenez, J. L.; Campos, I.; Aquino, N.

2008-01-01

We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…

An improved radiation metric. [for radiation pressure in strong gravitational fields

NASA Technical Reports Server (NTRS)

Noerdlinger, P. D.

1976-01-01

An improved radiation metric is obtained in which light rays make a small nonzero angle with the radius, thus representing a source of finite size. Kaufmann's previous solution is criticized. The stabilization of a scatterer near a source of gravitational field and radiation is slightly enhanced for sources of finite size.

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

PubMed Central

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-01-01

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

Global-Local Finite Element Analysis of Bonded Single-Lap Joints

NASA Technical Reports Server (NTRS)

Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.

2004-01-01

Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

The empirical Bayes estimators of fine-scale population structure in high gene flow species.

PubMed

Kitada, Shuichi; Nakamichi, Reiichiro; Kishino, Hirohisa

2017-11-01

An empirical Bayes (EB) pairwise F ST estimator was previously introduced and evaluated for its performance by numerical simulation. In this study, we conducted coalescent simulations and generated genetic population structure mechanistically, and compared the performance of the EBF ST with Nei's G ST , Nei and Chesser's bias-corrected G ST (G ST_NC ), Weir and Cockerham's θ (θ WC ) and θ with finite sample correction (θ WC_F ). We also introduced EB estimators for Hedrick' G' ST and Jost' D. We applied these estimators to publicly available SNP genotypes of Atlantic herring. We also examined the power to detect the environmental factors causing the population structure. Our coalescent simulations revealed that the finite sample correction of θ WC is necessary to assess population structure using pairwise F ST values. For microsatellite markers, EBF ST performed the best among the present estimators regarding both bias and precision under high gene flow scenarios (FST≤0.032). For 300 SNPs, EBF ST had the highest precision in all cases, but the bias was negative and greater than those for G ST_NC and θ WC_F in all cases. G ST_NC and θ WC_F performed very similarly at all levels of F ST . As the number of loci increased up to 10 000, the precision of G ST_NC and θ WC_F became slightly better than for EBF ST for cases with FST≥0.004, even though the size of the bias remained constant. The EB estimators described the fine-scale population structure of the herring and revealed that ~56% of the genetic differentiation was caused by sea surface temperature and salinity. The R package finepop for implementing all estimators used here is available on CRAN. © 2017 The Authors. Molecular Ecology Resources Published by John Wiley & Sons Ltd.

Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling

NASA Astrophysics Data System (ADS)

Ito, Kosuke; Hayashi, Masahito

2018-01-01

In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.

Are extreme events (statistically) special? (Invited)

NASA Astrophysics Data System (ADS)

Main, I. G.; Naylor, M.; Greenhough, J.; Touati, S.; Bell, A. F.; McCloskey, J.

2009-12-01

We address the generic problem of testing for scale-invariance in extreme events, i.e. are the biggest events in a population simply a scaled model of those of smaller size, or are they in some way different? Are large earthquakes for example ‘characteristic’, do they ‘know’ how big they will be before the event nucleates, or is the size of the event determined only in the avalanche-like process of rupture? In either case what are the implications for estimates of time-dependent seismic hazard? One way of testing for departures from scale invariance is to examine the frequency-size statistics, commonly used as a bench mark in a number of applications in Earth and Environmental sciences. Using frequency data however introduces a number of problems in data analysis. The inevitably small number of data points for extreme events and more generally the non-Gaussian statistical properties strongly affect the validity of prior assumptions about the nature of uncertainties in the data. The simple use of traditional least squares (still common in the literature) introduces an inherent bias to the best fit result. We show first that the sampled frequency in finite real and synthetic data sets (the latter based on the Epidemic-Type Aftershock Sequence model) converge to a central limit only very slowly due to temporal correlations in the data. A specific correction for temporal correlations enables an estimate of convergence properties to be mapped non-linearly on to a Gaussian one. Uncertainties closely follow a Poisson distribution of errors across the whole range of seismic moment for typical catalogue sizes. In this sense the confidence limits are scale-invariant. A systematic sample bias effect due to counting whole numbers in a finite catalogue makes a ‘characteristic’-looking type extreme event distribution a likely outcome of an underlying scale-invariant probability distribution. This highlights the tendency of ‘eyeball’ fits to unconsciously (but wrongly in this case) assume Gaussian errors. We develop methods to correct for these effects, and show that the current best fit maximum likelihood regression model for the global frequency-moment distribution in the digital era is a power law, i.e. mega-earthquakes continue to follow the Gutenberg-Richter trend of smaller earthquakes with no (as yet) observable cut-off or characteristic extreme event. The results may also have implications for the interpretation of other time-limited geophysical time series that exhibit power-law scaling.

Testing for scale-invariance in extreme events, with application to earthquake occurrence

NASA Astrophysics Data System (ADS)

Main, I.; Naylor, M.; Greenhough, J.; Touati, S.; Bell, A.; McCloskey, J.

2009-04-01

We address the generic problem of testing for scale-invariance in extreme events, i.e. are the biggest events in a population simply a scaled model of those of smaller size, or are they in some way different? Are large earthquakes for example ‘characteristic', do they ‘know' how big they will be before the event nucleates, or is the size of the event determined only in the avalanche-like process of rupture? In either case what are the implications for estimates of time-dependent seismic hazard? One way of testing for departures from scale invariance is to examine the frequency-size statistics, commonly used as a bench mark in a number of applications in Earth and Environmental sciences. Using frequency data however introduces a number of problems in data analysis. The inevitably small number of data points for extreme events and more generally the non-Gaussian statistical properties strongly affect the validity of prior assumptions about the nature of uncertainties in the data. The simple use of traditional least squares (still common in the literature) introduces an inherent bias to the best fit result. We show first that the sampled frequency in finite real and synthetic data sets (the latter based on the Epidemic-Type Aftershock Sequence model) converge to a central limit only very slowly due to temporal correlations in the data. A specific correction for temporal correlations enables an estimate of convergence properties to be mapped non-linearly on to a Gaussian one. Uncertainties closely follow a Poisson distribution of errors across the whole range of seismic moment for typical catalogue sizes. In this sense the confidence limits are scale-invariant. A systematic sample bias effect due to counting whole numbers in a finite catalogue makes a ‘characteristic'-looking type extreme event distribution a likely outcome of an underlying scale-invariant probability distribution. This highlights the tendency of ‘eyeball' fits unconsciously (but wrongly in this case) to assume Gaussian errors. We develop methods to correct for these effects, and show that the current best fit maximum likelihood regression model for the global frequency-moment distribution in the digital era is a power law, i.e. mega-earthquakes continue to follow the Gutenberg-Richter trend of smaller earthquakes with no (as yet) observable cut-off or characteristic extreme event. The results may also have implications for the interpretation of other time-limited geophysical time series that exhibit power-law scaling.

Long range Debye-Hückel correction for computation of grid-based electrostatic forces between biomacromolecules

PubMed Central

2014-01-01

Background Brownian dynamics (BD) simulations can be used to study very large molecular systems, such as models of the intracellular environment, using atomic-detail structures. Such simulations require strategies to contain the computational costs, especially for the computation of interaction forces and energies. A common approach is to compute interaction forces between macromolecules by precomputing their interaction potentials on three-dimensional discretized grids. For long-range interactions, such as electrostatics, grid-based methods are subject to finite size errors. We describe here the implementation of a Debye-Hückel correction to the grid-based electrostatic potential used in the SDA BD simulation software that was applied to simulate solutions of bovine serum albumin and of hen egg white lysozyme. Results We found that the inclusion of the long-range electrostatic correction increased the accuracy of both the protein-protein interaction profiles and the protein diffusion coefficients at low ionic strength. Conclusions An advantage of this method is the low additional computational cost required to treat long-range electrostatic interactions in large biomacromolecular systems. Moreover, the implementation described here for BD simulations of protein solutions can also be applied in implicit solvent molecular dynamics simulations that make use of gridded interaction potentials. PMID:25045516

Hydrophone area-averaging correction factors in nonlinearly generated ultrasonic beams

NASA Astrophysics Data System (ADS)

Cooling, M. P.; Humphrey, V. F.; Wilkens, V.

2011-02-01

The nonlinear propagation of an ultrasonic wave can be used to produce a wavefield rich in higher frequency components that is ideally suited to the calibration, or inter-calibration, of hydrophones. These techniques usually use a tone-burst signal, limiting the measurements to harmonics of the fundamental calibration frequency. Alternatively, using a short pulse enables calibration at a continuous spectrum of frequencies. Such a technique is used at PTB in conjunction with an optical measurement technique to calibrate devices. Experimental findings indicate that the area-averaging correction factor for a hydrophone in such a field demonstrates a complex behaviour, most notably varying periodically between frequencies that are harmonics of the centre frequency of the original pulse and frequencies that lie midway between these harmonics. The beam characteristics of such nonlinearly generated fields have been investigated using a finite difference solution to the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a focused field. The simulation results are used to calculate the hydrophone area-averaging correction factors for 0.2 mm and 0.5 mm devices. The results clearly demonstrate a number of significant features observed in the experimental investigations, including the variation with frequency, drive level and hydrophone element size. An explanation for these effects is also proposed.

Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

NASA Astrophysics Data System (ADS)

Hong, Hyunsuk

2017-07-01

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984), 10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν ¯=5 /4 . Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ =1 /4 , which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007), 10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν ¯=5 /2 . On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν ¯=5 /4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature

NASA Astrophysics Data System (ADS)

Leschke, Hajo; Sobolev, Alexander V.; Spitzer, Wolfgang

2016-07-01

The leading asymptotic large-scale behaviour of the spatially bipartite entanglement entropy (EE) of the free Fermi gas infinitely extended in multidimensional Euclidean space at zero absolute temperature, T = 0, is by now well understood. Here, we present and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at T> 0. The leading large-scale term of this thermal EE turns out to be twice the first-order finite-size correction to the infinite-volume thermal entropy (density). Not surprisingly, this correction is just the thermal entropy on the interface of the bipartition. However, it is given by a rather complicated integral derived from a semiclassical trace formula for a certain operator on the underlying one-particle Hilbert space. But in the zero-temperature limit T\\downarrow 0, the leading large-scale term of the thermal EE considerably simplifies and displays a {ln}(1/T)-singularity which one may identify with the known logarithmic enhancement at T = 0 of the so-called area-law scaling. birthday of the ideal Fermi gas.

Toward one-loop tunneling rates of near-extremal magnetic black hole pair production

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

Yi, P.

Pair production of magnetic Reissner-Nordstroem black holes (of charges [plus minus][ital q]) was recently studied in the leading WKB approximation. Here we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behavior of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for a sufficiently weak field [ital B], the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renormalization procedures, typical one-loop contributions to themore » WKB exponent are shown to be inversely proportional to [ital B], as [ital B][r arrow]0, indicating that the leading Schwinger term is corrected by a small fraction [similar to][h bar]/[ital q][sup 2]. We demonstrate that this correction to the Schwinger term is actually due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. Finally we discuss a few loose ends.« less

Numerical investigation of diffraction of acoustic waves by phononic crystals

NASA Astrophysics Data System (ADS)

Moiseyenko, Rayisa P.; Declercq, Nico F.; Laude, Vincent

2012-05-01

Diffraction as well as transmission of acoustic waves by two-dimensional phononic crystals (PCs) composed of steel rods in water are investigated in this paper. The finite element simulations were performed in order to compute pressure fields generated by a line source that are incident on a finite size PC. Such field maps are analyzed based on the complex band structure for the infinite periodic PC. Finite size computations indicate that the exponential decrease of the transmission at deaf frequencies is much stronger than that in Bragg band gaps.

Strength of Screw Propellers

DTIC Science & Technology

1975-07-07

development depends not, only on the ability of the material to resist hydraulic impacts in cavitation, but also on the correct design of the propeller. Study...9) z where k - correction of Goldstein-Prandtl, which takes into considera- tion the effect of the finite number of propeller blades on the amount... correction of Goldztcin-Prwxidtl is deteri~inedi by graphs in Fig. 10. An example of the calculation of hydrodynamic forces distribu- tion along a

Repulsion Between Finite Charged Plates with Strongly Overlapped Electric Double Layers.

PubMed

Ghosal, Sandip; Sherwood, John D

2016-09-20

Screened Coulomb interactions between uniformly charged flat plates are considered at very small plate separations for which the Debye layers are strongly overlapped, in the limit of small electrical potentials. If the plates are of infinite length, the disjoining pressure between the plates decays as an inverse power of the plate separation. If the plates are of finite length, we show that screening Debye layer charges close to the edge of the plates are no longer constrained to stay between the plates, but instead spill out into the surrounding electrolyte. The resulting change in the disjoining pressure is calculated analytically: the force between the plates is reduced by this edge correction when the charge density is uniform over the surface of the plates, and is increased when the surface is at constant potential. A similar change in disjoining pressure due to loss of lateral confinement of the Debye layer charges should occur whenever the sizes of the interacting charged objects become small enough to approach the Debye scale. We investigate the effect here in the context of a two-dimensional model problem that is sufficiently simple to yield analytical results.

Electrodiffusion of lipids on membrane surfaces.

PubMed

Zhou, Y C

2012-05-28

Lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when the random lateral motion is mediated by the electrostatic interactions and membrane curvature. Although the lateral diffusion rates of lipids on membranes of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain largely undetermined. Here we propose an electrodiffusion model, based on the variational principle of the free energy functional, for the self-consistent lateral drift-diffusion of multiple species of charged lipids on membrane surfaces. Finite sizes of lipids are modeled to enforce the geometrical constraint of the lipid concentration on membrane surfaces. A surface finite element method is developed to appropriate the Laplace-Beltrami operators in the partial differential equations of the model. Our model properly describes the saturation of lipids on membrane surfaces, and correctly predicts that the MARCKS peptide can consistently sequester three multivalent phosphatidylinositol 4,5-bisphosphate lipids through its basic amino acid residues, regardless of a wide range of the percentage of monovalent phosphatidylserine in the membrane.

Electrodiffusion of lipids on membrane surfaces

NASA Astrophysics Data System (ADS)

Zhou, Y. C.

2012-05-01

Lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when the random lateral motion is mediated by the electrostatic interactions and membrane curvature. Although the lateral diffusion rates of lipids on membranes of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain largely undetermined. Here we propose an electrodiffusion model, based on the variational principle of the free energy functional, for the self-consistent lateral drift-diffusion of multiple species of charged lipids on membrane surfaces. Finite sizes of lipids are modeled to enforce the geometrical constraint of the lipid concentration on membrane surfaces. A surface finite element method is developed to appropriate the Laplace-Beltrami operators in the partial differential equations of the model. Our model properly describes the saturation of lipids on membrane surfaces, and correctly predicts that the MARCKS peptide can consistently sequester three multivalent phosphatidylinositol 4,5-bisphosphate lipids through its basic amino acid residues, regardless of a wide range of the percentage of monovalent phosphatidylserine in the membrane.

The effect of finite Larmor radius corrections on Jeans instability of quantum plasma

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

Sharma, Prerana; Chhajlani, R. K.

2013-09-15

The influence of finite Larmor radius (FLR) effects on the Jeans instability of infinitely conducting homogeneous quantum plasma is investigated. The quantum magnetohydrodynamic (QMHD) model is used to formulate the problem. The contribution of FLR is incorporated to the QMHD set of equations in the present analysis. The general dispersion relation is obtained analytically using the normal mode analysis technique which is modified due to the contribution of FLR corrections. From general dispersion relation, the condition of instability is obtained and it is found that Jeans condition is modified due to quantum effect. The general dispersion relation is reduced formore » both transverse and longitudinal mode of propagations. The condition of gravitational instability is modified due to the presence of both FLR and quantum corrections in the transverse mode of propagation. In longitudinal case, it is found to be unaffected by the FLR effects but modified due to the quantum corrections. The growth rate of Jeans instability is discussed numerically for various values of quantum and FLR corrections of the medium. It is found that the quantum parameter and FLR effects have stabilizing influence on the growth rate of instability of the system.« less

Deterministic figure correction of piezoelectrically adjustable slumped glass optics

NASA Astrophysics Data System (ADS)

DeRoo, Casey T.; Allured, Ryan; Cotroneo, Vincenzo; Hertz, Edward; Marquez, Vanessa; Reid, Paul B.; Schwartz, Eric D.; Vikhlinin, Alexey A.; Trolier-McKinstry, Susan; Walker, Julian; Jackson, Thomas N.; Liu, Tianning; Tendulkar, Mohit

2018-01-01

Thin x-ray optics with high angular resolution (≤ 0.5 arcsec) over a wide field of view enable the study of a number of astrophysically important topics and feature prominently in Lynx, a next-generation x-ray observatory concept currently under NASA study. In an effort to address this technology need, piezoelectrically adjustable, thin mirror segments capable of figure correction after mounting and on-orbit are under development. We report on the fabrication and characterization of an adjustable cylindrical slumped glass optic. This optic has realized 100% piezoelectric cell yield and employs lithographically patterned traces and anisotropic conductive film connections to address the piezoelectric cells. In addition, the measured responses of the piezoelectric cells are found to be in good agreement with finite-element analysis models. While the optic as manufactured is outside the range of absolute figure correction, simulated corrections using the measured responses of the piezoelectric cells are found to improve 5 to 10 arcsec mirrors to 1 to 3 arcsec [half-power diameter (HPD), single reflection at 1 keV]. Moreover, a measured relative figure change which would correct the figure of a representative slumped glass piece from 6.7 to 1.2 arcsec HPD is empirically demonstrated. We employ finite-element analysis-modeled influence functions to understand the current frequency limitations of the correction algorithm employed and identify a path toward achieving subarcsecond corrections.

Entanglement entropy in a boundary impurity model.

PubMed

Levine, G C

2004-12-31

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

Accurate analytic solution of chemical master equations for gene regulation networks in a single cell

NASA Astrophysics Data System (ADS)

Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun

2018-01-01

Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015), 10.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media

PubMed Central

Morales Cruzado, Beatriz; y Montiel, Sergio Vázquez; Atencio, José Alberto Delgado

2013-01-01

In this paper, we present and validate a new method for optical properties recovery of turbid media with slab geometry. This method is an iterative method that compares diffuse reflectance and transmittance, measured using integrating spheres, with those obtained using the known algorithm MCML. The search procedure is based in the evolution of a population due to selection of the best individual, i.e., using a genetic algorithm. This new method includes several corrections such as non-linear effects in integrating spheres measurements and loss of light due to the finite size of the sample. As a potential application and proof-of-principle experiment of this new method, we use this new algorithm in the recovery of optical properties of blood samples at different degrees of coagulation. PMID:23504404

Scattering of Acoustic Waves from Ocean Boundaries

DTIC Science & Technology

2015-09-30

of buried mines and improve SONAR performance in shallow water. OBJECTIVES 1) Determination of the correct physical model of acoustic propagation... acoustic parameters in the ocean. APPROACH 1) Finite Element Modeling for Range Dependent Waveguides: Finite element modeling is applied to a...roughness measurements for reverberation modeling . GLISTEN data provide insight into the role of biology on acoustic propagation and scattering

Cement bond evaluation method in horizontal wells using segmented bond tool

NASA Astrophysics Data System (ADS)

Song, Ruolong; He, Li

2018-06-01

Most of the existing cement evaluation technologies suffer from tool eccentralization due to gravity in highly deviated wells and horizontal wells. This paper proposes a correction method to lessen the effects of tool eccentralization on evaluation results of cement bond using segmented bond tool, which has an omnidirectional sonic transmitter and eight segmented receivers evenly arranged around the tool 2 ft from the transmitter. Using 3-D finite difference parallel numerical simulation method, we investigate the logging responses of centred and eccentred segmented bond tool in a variety of bond conditions. From the numerical results, we find that the tool eccentricity and channel azimuth can be estimated from measured sector amplitude. The average of the sector amplitude when the tool is eccentred can be corrected to the one when the tool is centred. Then the corrected amplitude will be used to calculate the channel size. The proposed method is applied to both synthetic and field data. For synthetic data, it turns out that this method can estimate the tool eccentricity with small error and the bond map is improved after correction. For field data, the tool eccentricity has a good agreement with the measured well deviation angle. Though this method still suffers from the low accuracy of calculating channel azimuth, the credibility of corrected bond map is improved especially in horizontal wells. It gives us a choice to evaluate the bond condition for horizontal wells using existing logging tool. The numerical results in this paper can provide aids for understanding measurements of segmented tool in both vertical and horizontal wells.

A cavitation transition in the energy landscape of simple cohesive liquids and glasses

NASA Astrophysics Data System (ADS)

Altabet, Y. Elia; Stillinger, Frank H.; Debenedetti, Pablo G.

2016-12-01

In particle systems with cohesive interactions, the pressure-density relationship of the mechanically stable inherent structures sampled along a liquid isotherm (i.e., the equation of state of an energy landscape) will display a minimum at the Sastry density ρS. The tensile limit at ρS is due to cavitation that occurs upon energy minimization, and previous characterizations of this behavior suggested that ρS is a spinodal-like limit that separates all homogeneous and fractured inherent structures. Here, we revisit the phenomenology of Sastry behavior and find that it is subject to considerable finite-size effects, and the development of the inherent structure equation of state with system size is consistent with the finite-size rounding of an athermal phase transition. What appears to be a continuous spinodal-like point at finite system sizes becomes discontinuous in the thermodynamic limit, indicating behavior akin to a phase transition. We also study cavitation in glassy packings subjected to athermal expansion. Many individual expansion trajectories averaged together produce a smooth equation of state, which we find also exhibits features of finite-size rounding, and the examples studied in this work give rise to a larger limiting tension than for the corresponding landscape equation of state.

Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves.

PubMed

Planková, Barbora; Vinš, Václav; Hrubý, Jan

2017-10-28

Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.

Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves

NASA Astrophysics Data System (ADS)

Planková, Barbora; Vinš, Václav; Hrubý, Jan

2017-10-01

Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.

Fast synthesis of topographic mask effects based on rigorous solutions

NASA Astrophysics Data System (ADS)

Yan, Qiliang; Deng, Zhijie; Shiely, James

2007-10-01

Topographic mask effects can no longer be ignored at technology nodes of 45 nm, 32 nm and beyond. As feature sizes become comparable to the mask topographic dimensions and the exposure wavelength, the popular thin mask model breaks down, because the mask transmission no longer follows the layout. A reliable mask transmission function has to be derived from Maxwell equations. Unfortunately, rigorous solutions of Maxwell equations are only manageable for limited field sizes, but impractical for full-chip optical proximity corrections (OPC) due to the prohibitive runtime. Approximation algorithms are in demand to achieve a balance between acceptable computation time and tolerable errors. In this paper, a fast algorithm is proposed and demonstrated to model topographic mask effects for OPC applications. The ProGen Topographic Mask (POTOMAC) model synthesizes the mask transmission functions out of small-sized Maxwell solutions from a finite-difference-in-time-domain (FDTD) engine, an industry leading rigorous simulator of topographic mask effect from SOLID-E. The integral framework presents a seamless solution to the end user. Preliminary results indicate the overhead introduced by POTOMAC is contained within the same order of magnitude in comparison to the thin mask approach.

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

NASA Astrophysics Data System (ADS)

Flores-Sola, Emilio J.; Berche, Bertrand; Kenna, Ralph; Weigel, Martin

2015-01-01

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

Selection for sex in finite populations.

PubMed

Roze, D

2014-07-01

Finite population size generates interference between selected loci, which has been shown to favour increased rates of recombination. In this article, I present different analytical models exploring selection acting on a 'sex modifier locus' (that affects the relative investment into asexual and sexual reproduction) in a finite population. Two forms of selective forces act on the modifier: direct selection due to intrinsic costs associated with sexual reproduction and indirect selection generated by one or two other loci affecting fitness. The results show that indirect selective forces differ from those acting on a recombination modifier even in the case of a haploid population: in particular, a single selected locus generates indirect selection for sex, while two loci are required in the case of a recombination modifier. This effect stems from the fact that modifier alleles increasing sex escape more easily from low-fitness genetic backgrounds than alleles coding for lower rates of sex. Extrapolating the results from three-locus models to a large number of loci at mutation-selection balance indicates that in the parameter range where indirect selection is strong enough to outweigh a substantial cost of sex, interactions between selected loci have a stronger effect than the sum of individual effects of each selected locus. Comparisons with multilocus simulation results show that such extrapolations may provide correct predictions for the evolutionarily stable rate of sex, unless the cost of sex is high. © 2014 The Author. Journal of Evolutionary Biology © 2014 European Society For Evolutionary Biology.

Ab initio thermodynamic results for warm dense matter

NASA Astrophysics Data System (ADS)

Bonitz, Michael

2016-10-01

Warm dense matter (WDM) - an exotic state where electrons are quantum degenerate and ions may be strongly correlated - is ubiquitous in dense astrophysical plasmas and highly compressed laboratory systems including inertial fusion. Accurate theoretical predictions require precision thermodynamic data for the electron gas at high density and finite temperature around the Fermi temperature. First such data have been obtained by restricted path integral Monte Carlo (restricted PIMC) simulations and transformed into analytical fits for the free energy. Such results are also key input for novel finite temperature density functional theory. However, the RPIMC data of Ref. 1 are limited to moderate densities, and even there turned out to be surprisingly inaccurate, which is a consequence of the fermion sign problem. These problems were recently overcome by the development of alternative QMC approaches in Kiel (configuration PIMC and permutation blocking PIMC) and Imperial College (Density matrix QMC). The three methods have their strengths and limitations in complementary parameter regions and provide highly accurate thermodynamic data for the electronic contributions in WDM. While the original results were obtained for small particle numbers, recently accurate finite size corrections were derived allowing to compute ab initio thermodynamic data with an unprecedented accuracy of better than 0.3 percent. This provides the final step for the use as benchmark data for experiments and models of Warm dense matter. Co-authors: T. Schoof, S. Groth, T. Dornheim, F. D. Malone, M. Foulkes, and T. Sjostroem, Funded by: DFG via SFB-TR24 and project BO1366-10.

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Budrikis, Zoe; Zapperi, Stefano; Fernandez Castellanos, David

2015-02-01

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

Lack of a thermodynamic finite-temperature spin-glass phase in the two-dimensional randomly coupled ferromagnet

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Ochoa, Andrew J.; Katzgraber, Helmut G.

2018-05-01

The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasiplanar topologies. We have performed large-scale finite-temperature Monte Carlo simulations of a two-dimensional square-lattice bimodal spin glass with next-nearest ferromagnetic interactions claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest interactions [Phys. Rev. Lett. 76, 4616 (1996), 10.1103/PhysRevLett.76.4616]. Our results show that the system is in a paramagnetic state in the thermodynamic limit, despite zero-temperature simulations [Phys. Rev. B 63, 094423 (2001), 10.1103/PhysRevB.63.094423] suggesting the existence of a finite-temperature spin-glass transition. Therefore, deducing the finite-temperature behavior from zero-temperature simulations can be dangerous when corrections to scaling are large.

Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

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

Nafari, F.; Ghoranneviss, M., E-mail: ghoranneviss@gmail.com

2016-08-15

In thermal interaction of laser pulse with a deuterium-tritium (DT) plane, the thermal waves of electrons are generated instantly. Since the thermal conductivity of electron is a nonlinear function of temperature, a nonlinear heat conduction equation is used to investigate the propagation of waves in solid DT. This paper presents a self-similar analytic solution for the nonlinear heat conduction equation in a planar geometry. The thickness of the target material is finite in numerical computation, and it is assumed that the laser energy is deposited at a finite initial thickness at the initial time which results in a finite temperaturemore » for electrons at initial time. Since the required temperature range for solid DT ignition is higher than the critical temperature which equals 35.9 eV, the effects of quantum correction in thermal conductivity should be considered. This letter investigates the effects of quantum correction on characteristic features of nonlinear thermal wave, including temperature, penetration depth, velocity, heat flux, and heating and cooling domains. Although this effect increases electron temperature and thermal flux, penetration depth and propagation velocity are smaller. This effect is also applied to re-evaluate the side-on laser ignition of uncompressed DT.« less

Bose–Einstein condensation temperature of finite systems

NASA Astrophysics Data System (ADS)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

NASA Astrophysics Data System (ADS)

Lucini, B.; Patella, A.; Ramos, A.; Tantalo, N.

2016-02-01

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C⋆ boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C⋆ boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

NASA Astrophysics Data System (ADS)

Torre, Emanuele G. Dalla; Diehl, Sebastian; Lukin, Mikhail D.; Sachdev, Subir; Strack, Philipp

2013-02-01

We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number N of atoms. For finite N, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms’ depolarization due to dissipative dephasing.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

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

Repeatability and heritability of reproductive traits in free-ranging snakes.

PubMed

Brown, G P; Shine, R

2007-03-01

The underlying genetic basis of life-history traits in free-ranging animals is critical to the effects of selection on such traits, but logistical constraints mean that such data are rarely available. Our long-term ecological studies on free-ranging oviparous snakes (keelbacks, Tropidonophis mairii (Gray, 1841), Colubridae) on an Australian floodplain provide the first such data for any tropical reptile. All size-corrected reproductive traits (egg mass, clutch size, clutch mass and post-partum maternal mass) were moderately repeatable between pairs of clutches produced by 69 female snakes after intervals of 49-1152 days, perhaps because maternal body condition was similar between clutches. Parent-offspring regression of reproductive traits of 59 pairs of mothers and daughters revealed high heritability for egg mass (h2= 0.73, SE=0.24), whereas heritability for the other three traits was low (< 0.37). The estimated heritability of egg mass may be inflated by maternal effects such as differential allocation of yolk steroids to different-sized eggs. High heritability of egg size may be maintained (rather than eroded by stabilizing selection) because selection acts on a trait (hatchling size) that is determined by the interaction between egg size and incubation substrate rather than by egg size alone. Variation in clutch size was mainly because of environmental factors (h2=0.04), indicating that one component of the trade-off between egg size and clutch size is under much tighter genetic control than the other. Thus, the phenotypic trade-off between egg size and egg number in keelback snakes occurs because each female snake must allocate a finite amount of energy into eggs of a genetically determined size.

Quantum decoration transformation for spin models

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

Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de

2016-09-15

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models.more » To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.« less

Quantum decoration transformation for spin models

NASA Astrophysics Data System (ADS)

Braz, F. F.; Rodrigues, F. C.; de Souza, S. M.; Rojas, Onofre

2016-09-01

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the "classical" limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising-Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

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

2003-12-01

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

Many-body localization in disorder-free systems: The importance of finite-size constraints

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

Papić, Z., E-mail: zpapic@perimeterinstitute.ca; Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5; Stoudenmire, E. Miles

2015-11-15

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that variousmore » bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.« less

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Origin of Non-Gaussian Spectra Observed via the Charge Exchange Recombination Spectroscopy Diagnostic in the DIII-D Tokamak

NASA Astrophysics Data System (ADS)

Sulyman, Alex; Chrystal, Colin; Haskey, Shaun; Burrell, Keith; Grierson, Brian

2017-10-01

The possible observation of non-Maxwellian ion distribution functions in the pedestal of DIII-D will be investigated with a synthetic diagnostic that accounts for the effect of finite neutral beam size. Ion distribution functions in tokamak plasmas are typically assumed to be Maxwellian, however non-Gaussian features observed in impurity charge exchange spectra have challenged this concept. Two possible explanations for these observations are spatial averaging over a finite beam size and a local ion distribution that is non-Maxwellian. Non-Maxwellian ion distribution functions could be driven by orbit loss effects in the edge of the plasma, and this has implications for momentum transport and intrinsic rotation. To investigate the potential effect of finite beam size on the observed spectra, a synthetic diagnostic has been created that uses FIDAsim to model beam and halo neutral density. Finite beam size effects are investigated for vertical and tangential views in the core and pedestal region with varying gradient scale lengths. Work supported in part by US DoE under the Science Undergraduate Laboratory Internship (SULI) program, DE-FC02-04ER54698, and DE-AC02-09CH11466.

Finite-data-size study on practical universal blind quantum computation

NASA Astrophysics Data System (ADS)

Zhao, Qiang; Li, Qiong

2018-07-01

The universal blind quantum computation with weak coherent pulses protocol is a practical scheme to allow a client to delegate a computation to a remote server while the computation hidden. However, in the practical protocol, a finite data size will influence the preparation efficiency in the remote blind qubit state preparation (RBSP). In this paper, a modified RBSP protocol with two decoy states is studied in the finite data size. The issue of its statistical fluctuations is analyzed thoroughly. The theoretical analysis and simulation results show that two-decoy-state case with statistical fluctuation is closer to the asymptotic case than the one-decoy-state case with statistical fluctuation. Particularly, the two-decoy-state protocol can achieve a longer communication distance than the one-decoy-state case in this statistical fluctuation situation.

Electrostatic Estimation of Intercalant Jump-Diffusion Barriers Using Finite-Size Ion Models.

PubMed

Zimmermann, Nils E R; Hannah, Daniel C; Rong, Ziqin; Liu, Miao; Ceder, Gerbrand; Haranczyk, Maciej; Persson, Kristin A

2018-02-01

We report on a scheme for estimating intercalant jump-diffusion barriers that are typically obtained from demanding density functional theory-nudged elastic band calculations. The key idea is to relax a chain of states in the field of the electrostatic potential that is averaged over a spherical volume using different finite-size ion models. For magnesium migrating in typical intercalation materials such as transition-metal oxides, we find that the optimal model is a relatively large shell. This data-driven result parallels typical assumptions made in models based on Onsager's reaction field theory to quantitatively estimate electrostatic solvent effects. Because of its efficiency, our potential of electrostatics-finite ion size (PfEFIS) barrier estimation scheme will enable rapid identification of materials with good ionic mobility.

The effect of a finite focal spot size on location dependent detectability in a fan beam CT system

NASA Astrophysics Data System (ADS)

Kim, Byeongjoon; Baek, Jongduk

2017-03-01

A finite focal spot size is one of the sources to degrade the resolution performance in a fan beam CT system. In this work, we investigated the effect of the finite focal spot size on signal detectability. For the evaluation, five spherical objects with diameters of 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm were used. The optical focal spot size viewed at the iso-center was a 1 mm (height) × 1 mm (width) with a target angle of 7 degrees, corresponding to an 8.21 mm (i.e., 1 mm / sin (7°)) focal spot length. Simulated projection data were acquired using 8 × 8 source lets, and reconstructed by Hanning weighted filtered backprojection. For each spherical object, the detectability was calculated at (0 mm, 0 mm) and (0 mm, 200 mm) using two image quality metrics: pixel signal to noise ratio (SNR) and detection SNR. For all signal sizes, the pixel SNR is higher at the iso-center since the noise variance at the off-center is much higher than that at the iso-center due to the backprojection weightings used in direct fan beam reconstruction. In contrast, detection SNR shows similar values for different spherical objects except 1 mm and 2 mm diameter spherical objects. Overall, the results indicate the resolution loss caused by the finite focal spot size degrades the detection performance, especially for small objects with less than 2 mm diameter.

Tension fracture of laminates for transport fuselage. Part 1: Material screening

NASA Technical Reports Server (NTRS)

Walker, T. H.; Avery, W. B.; Ilcewicz, L. B.; Poe, C. C., Jr.; Harris, C. E.

1992-01-01

Transport fuselage structures are designed to contain pressure following a large penetrating damage event. Applications of composites to fuselage structures require a database and supporting analysis on tension damage tolerance. Tests with 430 fracture specimens were used to accomplish the following: (1) identify critical material and laminate variables affecting notch sensitivity; (2) evaluate composite failure criteria; and (3) recommend a screening test method. Variables studied included fiber type, matrix toughness, lamination manufacturing process, and intraply hybridization. The laminates found to have the lowest notch sensitivity were manufactured using automated tow placement. This suggests a possible relationship between the stress distribution and repeatable levels of material inhomogeneity that are larger than found in traditional tape laminates. Laminates with the highest notch sensitivity consisted of toughened matrix materials that were resistant to a splitting phenomena that reduces stress concentrations in major load bearing plies. Parameters for conventional fracture criteria were found to increase with crack length for the smallest notch sizes studied. Most material and laminate combinations followed less than a square root singularity for the largest crack sizes studied. Specimen geometry, notch type, and notch size were evaluated in developing a screening test procedure. Traitional methods of correcting for specimen finite width were found to be lacking. Results indicate that a range of notch sizes must be tested to determine notch sensitivity. Data for a single small notch size (0.25 in. diameter) was found to give no indication of the sensitivity of a particular material and laminate layup to larger notch sizes.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

NASA Technical Reports Server (NTRS)

Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.

1996-01-01

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Managing numerical errors in random sequential adsorption

NASA Astrophysics Data System (ADS)

Cieśla, Michał; Nowak, Aleksandra

2016-09-01

Aim of this study is to examine the influence of a finite surface size and a finite simulation time on a packing fraction estimated using random sequential adsorption simulations. The goal of particular interest is providing hints on simulation setup to achieve desired level of accuracy. The analysis is based on properties of saturated random packing of disks on continuous and flat surfaces of different sizes.

Calculation of flexoelectric deformations of finite-size bodies

NASA Astrophysics Data System (ADS)

Yurkov, A. S.

2015-03-01

The previously developed approximate theory of flexoelectric deformations of finite-size bodies has been considered as applied to three special cases: a uniformly polarized ball, a uniformly polarized circular rod, and a uniformly polarized thin circular plate of an isotropic material. For these cases simple algebraic formulas have been derived. In the case of the ball, the solution is compared with the previously obtained exact solution.

Bipolar radiofrequency ablation with 2 × 2 electrodes as a building block for matrix radiofrequency ablation: Ex vivo liver experiments and finite element method modelling.

PubMed

Mulier, Stefaan; Jiang, Yansheng; Jamart, Jacques; Wang, Chong; Feng, Yuanbo; Marchal, Guy; Michel, Luc; Ni, Yicheng

2015-01-01

Size and geometry of the ablation zone obtained by currently available radiofrequency (RF) electrodes is highly variable. Reliability might be improved by matrix radiofrequency ablation (MRFA), in which the whole tumour volume is contained within a cage of x × y parallel electrodes. The aim of this study was to optimise the smallest building block for matrix radiofrequency ablation: a recently developed bipolar 2 × 2 electrode system. In ex vivo bovine liver, the parameters of the experimental set-up were changed one by one. In a second step, a finite element method (FEM) modelling of the experiment was performed to better understand the experimental findings. The optimal power to obtain complete ablation in the shortest time was 50-60 W. Performing an ablation until impedance rise was superior to ablation for a fixed duration. Increasing electrode diameter improved completeness of ablation due to lower temperature along the electrodes. A chessboard pattern of electrode polarity was inferior to a row pattern due to an electric field void in between the electrodes. Variability of ablation size was limited. The FEM correctly simulated and explained the findings in ex vivo liver. These experiments and FEM modelling allowed a better insight in the factors influencing the ablation zone in a bipolar 2 × 2 electrode RF system. With optimal parameters, complete ablation was obtained quickly and with limited variability. This knowledge will be useful to build a larger system with x × y electrodes for MRFA.

Critical scaling of the mutual information in two-dimensional disordered Ising models

NASA Astrophysics Data System (ADS)

Sriluckshmy, P. V.; Mandal, Ipsita

2018-04-01

Rényi mutual information, computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the ‘zero temperature only’ phase transitions are identified when there is no consistent finite-size scaling of the Rényi mutual information curves, while for finite temperature critical points, the curves can identify the critical temperature T c by their crossings at T c and 2 Tc .

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Effects of the finite size of the ion (dd{mu}){sup +} on the energy levels of the molecules (dd{mu})e and (dd{mu})dee

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

Harston, M.R.; Hara, S.; Kino, Y.

1997-10-01

The energy shift due to the finite size of the pseudonucleus (dd{mu}){sub 11}{sup +} in the molecules (dd{mu}){sub 11}e and (dd{mu}){sub 11}dee, the subscripts indicating the first excited state with total angular momentum of one unit, is of importance in the theoretical estimation of the rate of d-d fusion catalyzed by negative muons. The energy shift in the molecule (dd{mu}){sub 11}e is calculated using perturbation theory up to second order. The finite-size shift is found to be 1.46 meV. This is significantly larger than the value of 0.7 meV for this energy shift calculated by Bakalov [Muon Catalyzed Fusion {boldmore » 3}, 321 (1988)] by a method similar to the present method; recently found excellent agreement of theory with experimental results for the formation rate of the molecule (dd{mu}){sub 11}dee was based on Bakalov{close_quote}s value with some modifications. The results of a direct calculation of the finite-size energy shifts in (dd{mu}){sub 11}dee using first-order perturbation theory are presented. The contribution from the quadrupole component of the (dd{mu}){sub 11} charge distribution, which is not taken into account in the conventional scaling procedure based on the finite-size energy shifts of (dd{mu}){sub 11}e, is found to be of the order of 1 meV and to depend on the angular-momentum states of (dd{mu}){sub 11}dee. Sources of uncertainty in the current theoretical estimates are also discussed. {copyright} {ital 1997} {ital The American Physical Society}« less

Preliminary structural sizing of a Mach 3.0 high-speed civil transport model

NASA Technical Reports Server (NTRS)

Blackburn, Charles L.

1992-01-01

An analysis has been performed pertaining to the structural resizing of a candidate Mach 3.0 High Speed Civil Transport (HSCT) conceptual design using a computer program called EZDESIT. EZDESIT is a computer program which integrates the PATRAN finite element modeling program to the COMET finite element analysis program for the purpose of calculating element sizes or cross sectional dimensions. The purpose of the present report is to document the procedure used in accomplishing the preliminary structural sizing and to present the corresponding results.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

Multicategory nets of single-layer perceptrons: complexity and sample-size issues.

PubMed

Raudys, Sarunas; Kybartas, Rimantas; Zavadskas, Edmundas Kazimieras

2010-05-01

The standard cost function of multicategory single-layer perceptrons (SLPs) does not minimize the classification error rate. In order to reduce classification error, it is necessary to: 1) refuse the traditional cost function, 2) obtain near to optimal pairwise linear classifiers by specially organized SLP training and optimal stopping, and 3) fuse their decisions properly. To obtain better classification in unbalanced training set situations, we introduce the unbalance correcting term. It was found that fusion based on the Kulback-Leibler (K-L) distance and the Wu-Lin-Weng (WLW) method result in approximately the same performance in situations where sample sizes are relatively small. The explanation for this observation is by theoretically known verity that an excessive minimization of inexact criteria becomes harmful at times. Comprehensive comparative investigations of six real-world pattern recognition (PR) problems demonstrated that employment of SLP-based pairwise classifiers is comparable and as often as not outperforming the linear support vector (SV) classifiers in moderate dimensional situations. The colored noise injection used to design pseudovalidation sets proves to be a powerful tool for facilitating finite sample problems in moderate-dimensional PR tasks.

Infrared/microwave (IR/MW) micromirror array beam combiner design and analysis.

PubMed

Tian, Yi; Lv, Lijun; Jiang, Liwei; Wang, Xin; Li, Yanhong; Yu, Haiming; Feng, Xiaochen; Li, Qi; Zhang, Li; Li, Zhuo

2013-08-01

We investigated the design method of an infrared (IR)/microwave (MW) micromirror array type of beam combiner. The size of micromirror is in microscopic levels and comparable to MW wavelengths, so that the MW will not react in these dimensions, whereas the much shorter optical wavelengths will be reflected by them. Hence, the MW multilayered substrate was simplified and designed using transmission line theory. The beam combiner used an IR wavefront-division imaging technique to reflect the IR radiation image to the unit under test (UUT)'s pupil in a parallel light path. In addition, the boresight error detected by phase monopulse radar was analyzed using a moment-of method (MoM) and multilevel fast multipole method (MLFMM) acceleration technique. The boresight error introduced by the finite size of the beam combiner was less than 1°. Finally, in order to verify the wavefront-division imaging technique, a prototype of a micromirror array was fabricated, and IR images were tested. The IR images obtained by the thermal imager verified the correctness of the wavefront-division imaging technique.

A perspective on the interfacial properties of nanoscopic liquid drops.

PubMed

Malijevský, Alexandr; Jackson, George

2012-11-21

The structural and interfacial properties of nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the macroscopic level and the microscopic level of density functional theory (DFT). With a novel analysis we show that a purely macroscopic (static) mechanical treatment can lead to a qualitatively reasonable description of the surface tension and the Tolman length of a liquid drop; the latter parameter, which characterizes the curvature dependence of the tension, is found to be negative and has a magnitude of about a half of the molecular dimension. A mechanical slant cannot, however, be considered satisfactory for small finite-size systems where fluctuation effects are significant. From the opposite perspective, a curvature expansion of the macroscopic thermodynamic properties (density and chemical potential) is then used to demonstrate that a purely thermodynamic approach of this type cannot in itself correctly account for the curvature correction of the surface tension of liquid drops. We emphasize that any approach, e.g., classical nucleation theory, which is based on a purely macroscopic viewpoint, does not lead to a reliable representation when the radius of the drop becomes microscopic. The description of the enhanced inhomogeneity exhibited by small drops (particularly in the dense interior) necessitates a treatment at the molecular level to account for finite-size and surface effects correctly. The so-called mechanical route, which corresponds to a molecular-level extension of the macroscopic theory of elasticity and is particularly popular in molecular dynamics simulation, also appears to be unreliable due to the inherent ambiguity in the definition of the microscopic pressure tensor, an observation which has been known for decades but is frequently ignored. The union of the theory of capillarity (developed in the nineteenth century by Gibbs and then promoted by Tolman) with a microscopic DFT treatment allows for a direct and unambiguous description of the interfacial properties of drops of arbitrary size; DFT provides all of the bulk and surface characteristics of the system that are required to uniquely define its thermodynamic properties. In this vein, we propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine drops of varying size. A comparison of the predictions of our DFT with recent simulation data based on a second-order fluctuation analysis (Sampayo et al 2010 J. Chem. Phys. 132 141101) reveals the consistency of the two treatments. This observation highlights the significance of fluctuation effects in small drops, which give rise to additional entropic (thermal non-mechanical) contributions, in contrast to what one observes in the case of planar interfaces which are governed by the laws of mechanical equilibrium. A small negative Tolman length (which is found to be about a tenth of the molecular diameter) and a non-monotonic behaviour of the surface tension with the drop radius are predicted for the LJ fluid. Finally, the limits of the validity of the Tolman approach, the effect of the range of the intermolecular potential, and the behaviour of bubbles are briefly discussed.

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

An analytic treatment of gravitational microlensing for sources of finite size at large optical depths

NASA Technical Reports Server (NTRS)

Deguchi, Shuji; Watson, William D.

1988-01-01

Statistical methods are developed for gravitational lensing in order to obtain analytic expressions for the average surface brightness that include the effects of microlensing by stellar (or other compact) masses within the lensing galaxy. The primary advance here is in utilizing a Markoff technique to obtain expressions that are valid for sources of finite size when the surface density of mass in the lensing galaxy is large. The finite size of the source is probably the key consideration for the occurrence of microlensing by individual stars. For the intensity from a particular location, the parameter which governs the importance of microlensing is determined. Statistical methods are also formulated to assess the time variation of the surface brightness due to the random motion of the masses that cause the microlensing.

Investigating the dominant corrections to the strong-stretching theory for dry polymeric brushes.

PubMed

Matsen, M W

2004-07-22

The accuracy of strong-stretching theory (SST) is examined against a detailed comparison to self-consistent field theory (SCFT) on dry polymeric brushes with thicknesses of up to approximately 17 times the natural chain extension. The comparison provides the strongest evidence to date that SST represents the exact thick-brush limit of SCFT. More importantly, it allows us to assess the effectiveness of proposed finite-stretching corrections to SST. Including the entropy of the free ends is shown to rectify the most severe inaccuracies in SST. The proximal layer proposed by Likhtman and Semenov provides another significant improvement, and we identify one further effect of similar importance for which there is not yet an accurate treatment. Furthermore, our study provides a valuable means of rejecting mistaken refinements to SST, and indeed one such example is revealed. A proper treatment of finite-stretching corrections is vital to a wide range of phenomena that depend on a small excess free energy, such as autophobic dewetting and the interaction between opposing brushes.

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals

NASA Astrophysics Data System (ADS)

Hasan, Shakeeb Bin; Mosk, Allard P.; Vos, Willem L.; Lagendijk, Ad

2018-06-01

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size L of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a 1 /L scale dependence for crystals in one, two and three dimensions.

Finite-size effect on the dynamic and sensing performances of graphene resonators: the role of edge stress.

PubMed

Kim, Chang-Wan; Dai, Mai Duc; Eom, Kilho

2016-01-01

We have studied the finite-size effect on the dynamic behavior of graphene resonators and their applications in atomic mass detection using a continuum elastic model such as modified plate theory. In particular, we developed a model based on von Karman plate theory with including the edge stress, which arises from the imbalance between the coordination numbers of bulk atoms and edge atoms of graphene. It is shown that as the size of a graphene resonator decreases, the edge stress depending on the edge structure of a graphene resonator plays a critical role on both its dynamic and sensing performances. We found that the resonance behavior of graphene can be tuned not only through edge stress but also through nonlinear vibration, and that the detection sensitivity of a graphene resonator can be controlled by using the edge stress. Our study sheds light on the important role of the finite-size effect in the effective design of graphene resonators for their mass sensing applications.

Quantum Hall states and conformal field theory on a singular surface

NASA Astrophysics Data System (ADS)

Can, T.; Wiegmann, P.

2017-12-01

In Can et al (2016 Phys. Rev. Lett. 117), quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone (Cardy and Peschel 1988 Nucl. Phys. B 300 377-92), and the known results for critical systems on polyhedra and flat branched Riemann surfaces.

Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2012-10-01

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures TFK(p) and TDS(p) are studied on random-bond Ising models of dimensions 2-5 and as functions of the ferromagnetic interaction probability p; the conjecture that TDS(p)˜TFK(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn TFK(p) transition line and the Nishimori line [pNL,FK,TNL,FK]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [pNL,FK], the damage spreading TDS(p) is found to be equal to TFK(p) to within 0.1%. For the other dimensions, however, TDS(p) is observed to be systematically a few percent lower than TFK(p).

Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment

NASA Astrophysics Data System (ADS)

Huveneers, François

2018-04-01

We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D . We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.

Duality of two pairs of double-walled nanotubes consisting of S=1 and S=3/2 spins probed by means of a quantum simulation approach

NASA Astrophysics Data System (ADS)

Liu, Zhaosen; Ian, Hou

2017-01-01

Using a quantum simulation approach, we investigate in the present work the spontaneous magnetic properties of two pairs of double-walled cylindrical nanotubes consisting of different spins. Our simulated magnetic and thermodynamic properties for each pair of them are precisely identical, exhibiting a fascinating property of the nature world and demonstrating the correctness of our simulation approach. The second pair of nanotubes are frustrated, two magnetic phases of distinct spin configurations appear in the low temperature region, but only the inner layer consisting of small spins is frustrated evidently, its magnetization is considerably suppressed in the high temperature phase. Moreover, the nanosystems exhibit typical Ising-like behavior due to the uniaxial anisotropy along the z-direction, and evident finite-size effects as well.

Investigation of the Statistics of Pure Tone Sound Power Injection from Low Frequency, Finite Sized Sources in a Reverberant Room

NASA Technical Reports Server (NTRS)

Smith, Wayne Farrior

1973-01-01

The effect of finite source size on the power statistics in a reverberant room for pure tone excitation was investigated. Theoretical results indicate that the standard deviation of low frequency, pure tone finite sources is always less than that predicted by point source theory and considerably less when the source dimension approaches one-half an acoustic wavelength or greater. A supporting experimental study was conducted utilizing an eight inch loudspeaker and a 30 inch loudspeaker at eleven source positions. The resulting standard deviation of sound power output of the smaller speaker is in excellent agreement with both the derived finite source theory and existing point source theory, if the theoretical data is adjusted to account for experimental incomplete spatial averaging. However, the standard deviation of sound power output of the larger speaker is measurably lower than point source theory indicates, but is in good agreement with the finite source theory.

Finite element analysis of helicopter structures

NASA Technical Reports Server (NTRS)

Rich, M. J.

1978-01-01

Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.

Effect of curvature squared corrections to gravitational action on viscosity-to-entropy ratio of the dual gauge theory

NASA Astrophysics Data System (ADS)

Petrov, Pavel

In this thesis we study the properties of strongly-coupled large-N conformal field theories (CFT's) using AdS/CFT correspondence. Chapter 1 serves as an introduction. In Chapter 2 we study the shear viscosity of strongly-coupled large-N conformal field theories. We find that it is affected by R2 corrections to the AdS action and present an example of 4D theory in which the the conjectured universal lower bound on viscosity-to-entropy ratio η/s > 1/4π is violated by 1/N corrections. This fact proves that there is no universal lower bound of 1/4π on viscosity-to-entropy ratio and may be relevant for the studies of QCD quark-gluon plasma for which this ratio is experimentally found to be close to 1/4π. In Chapter 3 we study the formation of the electron star in 4D AdS space. We show that in a gravity theory with charged fermions a layer of charged fermion fluid may form at a finite distance from the charged black hole. We show that these “electron stars” are candidate gravity duals for strongly interacting fermion systems at finite density and finite temperature. Entropy density for such systems scales as s ˜ T2/z at low temperatures as expected from IR criticality of electron stars solutions.

Apse-Alignment of the Uranian Rings

NASA Technical Reports Server (NTRS)

Mosqueira, I.; Estrada, P. R.

2000-01-01

An explanation of the dynamical mechanism for apse-alignment of the eccentric Uranian rings is necessary before observations can be used to determine properties such as ring masses, particle sizes, and elasticities. The leading model relies on the ring self-gravity to accomplish this task, yet it yields equilibrium masses which are not in accord with Voyager radio measurements. We explore possible solutions such that the self-gravity and the collisional terms are both involved in the process of apse-alignment. We consider limits that correspond to a hot and a cold ring, and show that pressure terms may play a significant role in the equilibrium conditions for the narrow Uranian rings. In the cold ring case, where the scale height of the ring near periapse is comparable to the ring particle size, we introduce a new pressure correction pertaining to a region of the ring where the particles are locked in their relative positions and jammed against their neighbors, and the velocity dispersion is so low that the collisions are nearly elastic. In this case, we find a solution such that the ring self-gravity maintains apse-alignment against both differential precession (m = 1 mode) and the fluid pressure. We apply this model to the Uranian alpha ring, and show that, compared to the previous self-gravity model, the mass estimate for this ring increases by an order of magnitude. In the case of a hot ring, where the scale height can reach a value as much as fifty times larger than a particle size, we find velocity dispersion profiles that result in pressure forces which act in such a way as to alter the ring equilibrium conditions, again leading to a ring mass increase of an order of magnitude; however, such a velocity dispersion profile would require a different mechanism than is currently envisioned for establishing heating/cooling balance in a finite-sized, inelastic particle ring. Finally, we introduce an important correction to the model of Chiang and Goldreich.

SU-F-T-490: Separating Effects Influencing Detector Response in Small MV Photon Fields

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

Wegener, S; Sauer, O

2016-06-15

Purpose: Different detector properties influence their responses especially in field sizes below the lateral electron range. Due to the finite active volume, the detector density and electron perturbation at other structural parts, the response factor is in general field size dependent. We aimed to visualize and separate the main effects contributing to detector behavior for a variety of detector types. This was achieved in an experimental setup, shielding the field center. Thus, effects caused by scattered radiation could be examined separately. Methods: Signal ratios for field sizes down to 8 mm (SSD 90 cm, water depth 10 cm) of amore » 6MV beam from a Siemens Primus LINAC were recorded with several detectors: PTW microDiamond and PinPoint ionization chamber, shielded diodes (PTW P-60008, IBA PFD and SNC Edge) and unshielded diodes (PTW E-60012 and IBA SFD). Measurements were carried out in open fields and with an aluminum pole of 4 mm diameter as a central block. The geometric volume effect was calculated from profiles obtained with Gafchromic EBT3 film, evaluated using FilmQA Pro software (Ashland, USA). Results: Volume corrections were 1.7% at maximum. After correction, in small open fields, unshielded diodes showed a lower response than the diamond, i.e. diamond detector over-response seems to be higher than that for unshielded diodes. Beneath the block, this behavior was amplified by a factor of 2. For the shielded diodes, the overresponse for small open fields could be confirmed. However their lateral response behavior was strongly type dependent, e.g. the signal ratio dropped from 1.02 to 0.98 for the P-60008 diode. Conclusion: The lateral detector response was experimentally examined. Detector volume and density alone do not fully account for the field size dependence of detector response. Detector construction details play a major role, especially for shielded diodes.« less

Pion properties at finite isospin chemical potential with isospin symmetry breaking

NASA Astrophysics Data System (ADS)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

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

Research on Finite Element Model Generating Method of General Gear Based on Parametric Modelling

NASA Astrophysics Data System (ADS)

Lei, Yulong; Yan, Bo; Fu, Yao; Chen, Wei; Hou, Liguo

2017-06-01

Aiming at the problems of low efficiency and poor quality of gear meshing in the current mainstream finite element software, through the establishment of universal gear three-dimensional model, and explore the rules of unit and node arrangement. In this paper, a finite element model generation method of universal gear based on parameterization is proposed. Visual Basic program is used to realize the finite element meshing, give the material properties, and set the boundary / load conditions and other pre-processing work. The dynamic meshing analysis of the gears is carried out with the method proposed in this pape, and compared with the calculated values to verify the correctness of the method. The method greatly shortens the workload of gear finite element pre-processing, improves the quality of gear mesh, and provides a new idea for the FEM pre-processing.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Sensitivity Analysis of Flutter Response of a Wing Incorporating Finite-Span Corrections

NASA Technical Reports Server (NTRS)

Issac, Jason Cherian; Kapania, Rakesh K.; Barthelemy, Jean-Francois M.

1994-01-01

Flutter analysis of a wing is performed in compressible flow using state-space representation of the unsteady aerodynamic behavior. Three different expressions are used to incorporate corrections due to the finite-span effects of the wing in estimating the lift-curve slope. The structural formulation is based on a Rayleigh-Pitz technique with Chebyshev polynomials used for the wing deflections. The aeroelastic equations are solved as an eigen-value problem to determine the flutter speed of the wing. The flutter speeds are found to be higher in these cases, when compared to that obtained without accounting for the finite-span effects. The derivatives of the flutter speed with respect to the shape parameters, namely: aspect ratio, area, taper ratio and sweep angle, are calculated analytically. The shape sensitivity derivatives give a linear approximation to the flutter speed curves over a range of values of the shape parameter which is perturbed. Flutter and sensitivity calculations are performed on a wing using a lifting-surface unsteady aerodynamic theory using modules from a system of programs called FAST.

Effect of Multiple Scattering on the Compton Recoil Current Generated in an EMP, Revisited

DOE PAGES

Farmer, William A.; Friedman, Alex

2015-06-18

Multiple scattering has historically been treated in EMP modeling through the obliquity factor. The validity of this approach is examined here. A simplified model problem, which correctly captures cyclotron motion, Doppler shifting due to the electron motion, and multiple scattering is first considered. The simplified problem is solved three ways: the obliquity factor, Monte-Carlo, and Fokker-Planck finite-difference. Because of the Doppler effect, skewness occurs in the distribution. It is demonstrated that the obliquity factor does not correctly capture this skewness, but the Monte-Carlo and Fokker-Planck finite-difference approaches do. Here, the obliquity factor and Fokker-Planck finite-difference approaches are then compared inmore » a fuller treatment, which includes the initial Klein-Nishina distribution of the electrons, and the momentum dependence of both drag and scattering. It is found that, in general, the obliquity factor is adequate for most situations. However, as the gamma energy increases and the Klein-Nishina becomes more peaked in the forward direction, skewness in the distribution causes greater disagreement between the obliquity factor and a more accurate model of multiple scattering.« less

Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution

NASA Astrophysics Data System (ADS)

Olsen, Jógvan Magnus Haugaard; Hedegård, Erik Donovan

The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed for quantum-chemical methods over the last decades. Its correct description requires highly-correlated multiconfigurational methods, which are incompatible with the inclusion of finite-temperature and solvent effects due to their high computational demands. Therefore, implicit solvent models are usually employed. Here we show that implicit solvent models are not sufficiently accurate to model the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of their failure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueous solution by employing the polarizable embedding (PE) model combined with a range-separated complete active space short-range density functional theory method (CAS-srDFT). Finite-temperature effects are taken into account by averaging over structures obtained from ab initio molecular dynamics simulations. The explicit treatment of finite-temperature and solvent effects facilitates the interpretation of the bands in the low-energy region of the MnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.

Method for calculating internal radiation and ventilation with the ADINAT heat-flow code

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

Butkovich, T.R.; Montan, D.N.

1980-04-01

One objective of the spent fuel test in Climax Stock granite (SFTC) is to correctly model the thermal transport, and the changes in the stress field and accompanying displacements from the application of the thermal loads. We have chosen the ADINA and ADINAT finite element codes to do these calculations. ADINAT is a heat transfer code compatible to the ADINA displacement and stress analysis code. The heat flow problem encountered at SFTC requires a code with conduction, radiation, and ventilation capabilities, which the present version of ADINAT does not have. We have devised a method for calculating internal radiation andmore » ventilation with the ADINAT code. This method effectively reproduces the results from the TRUMP multi-dimensional finite difference code, which correctly models radiative heat transport between drift surfaces, conductive and convective thermal transport to and through air in the drifts, and mass flow of air in the drifts. The temperature histories for each node in the finite element mesh calculated with ADINAT using this method can be used directly in the ADINA thermal-mechanical calculation.« less

Size Distribution of Sea-Salt Emissions as a Function of Relative Humidity

NASA Astrophysics Data System (ADS)

Zhang, K. M.; Knipping, E. M.; Wexler, A. S.; Bhave, P. V.; Tonnesen, G. S.

2004-12-01

Here we introduced a simple method for correcting sea-salt particle-size distributions as a function of relative humidity. Distinct from previous approaches, our derivation uses particle size at formation as the reference state rather than dry particle size. The correction factors, corresponding to the size at formation and the size at 80% RH, are given as polynomial functions of local relative humidity which are straightforward to implement. Without major compromises, the correction factors are thermodynamically accurate and can be applied between 0.45 and 0.99 RH. Since the thermodynamic properties of sea-salt electrolytes are weakly dependent on ambient temperature, these factors can be regarded as temperature independent. The correction factor w.r.t. to the size at 80% RH is in excellent agreement with those from Fitzgerald's and Gerber's growth equations; while the correction factor w.r.t. the size at formation has the advantage of being independent of dry size and relative humidity at formation. The resultant sea-salt emissions can be used directly in atmospheric model simulations at urban, regional and global scales without further correction. Application of this method to several common open-ocean and surf-zone sea-salt-particle source functions is described.

Dynamic ductile fracture of a central crack

NASA Technical Reports Server (NTRS)

Tsai, Y. M.

1976-01-01

A central crack, symmetrically growing at a constant speed in a two dimensional ductile material subject to uniform tension at infinity, is investigated using the integral transform methods. The crack is assumed to be the Dugdale crack, and the finite stress condition at the crack tip is satisfied during the propagation of the crack. Exact expressions of solution are obtained for the finite stress condition at the crack tip, the crack shape, the crack opening displacement, and the energy release rate. All those expressions are written as the product of explicit dimensional quantities and a nondimensional dynamic correction function. The expressions reduce to the associated static results when the crack speed tends to zero, and the nondimensional dynamic correction functions were calculated for various values of the parameter involved.

Nonlocal gradient corrections to the exchange free energy of an inhomogeneous many-fermion system at finite temperature

NASA Astrophysics Data System (ADS)

Geldart, D. J. W.; Dunlap, E.; Glasser, M. L.; Shegelski, Mark R. A.

1993-10-01

A general exact result is derived for the coefficient B x( n; T) which determines the first gradient correction to the leading exchange contribution to the free energy at finite temperature of a weakly inhomogeneous extended many fermion system having arbitrary two-body interactions. Explicit analytical results are given in the case of bare Coulomb interactions, and the case of statically screened Coulomb interactions is studied numerically. It is shown that nonanalytical structure leads to different limiting values of B x( n; T) when the inverse screening length and the temperature are both small. Some implications for physical many-electron systems are discussed, including the reasons for discrepancies between the first principles and semiempirical gradient coefficients for atomic exchange energies.

Radiation Diffusion:. AN Overview of Physical and Numerical Concepts

NASA Astrophysics Data System (ADS)

Graziani, Frank

2005-12-01

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

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Higgs boson pair production at NNLO with top quark mass effects

NASA Astrophysics Data System (ADS)

Grazzini, M.; Heinrich, G.; Jones, S.; Kallweit, S.; Kerner, M.; Lindert, J. M.; Mazzitelli, J.

2018-05-01

We consider QCD radiative corrections to Higgs boson pair production through gluon fusion in proton collisions. We combine the exact next-to-leading order (NLO) contribution, which features two-loop virtual amplitudes with the full dependence on the top quark mass M t , with the next-to-next-to-leading order (NNLO) corrections computed in the large- M t approximation. The latter are improved with different reweighting techniques in order to account for finite- M t effects beyond NLO. Our reference NNLO result is obtained by combining one-loop double-real corrections with full M t dependence with suitably reweighted real-virtual and double-virtual contributions evaluated in the large- M t approximation. We present predictions for inclusive cross sections in pp collisions at √{s} = 13, 14, 27 and 100 TeV and we discuss their uncertainties due to missing M t effects. Our approximated NNLO corrections increase the NLO result by an amount ranging from +12% at √{s}=13 TeV to +7% at √{s}=100 TeV, and the residual uncertainty of the inclusive cross section from missing M t effects is estimated to be at the few percent level. Our calculation is fully differential in the Higgs boson pair and the associated jet activity: we also present predictions for various differential distributions at √{s}=14 and 100 TeV, and discuss the size of the missing M t effects, which can be larger, especially in the tails of certain observables. Our results represent the most advanced perturbative prediction available to date for this process.

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.

PubMed

Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan

2015-08-01

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

A Correction to the Stress-Strain Curve During Multistage Hot Deformation of 7150 Aluminum Alloy Using Instantaneous Friction Factors

NASA Astrophysics Data System (ADS)

Jiang, Fulin; Tang, Jie; Fu, Dinfa; Huang, Jianping; Zhang, Hui

2018-04-01

Multistage stress-strain curve correction based on an instantaneous friction factor was studied for axisymmetric uniaxial hot compression of 7150 aluminum alloy. Experimental friction factors were calculated based on continuous isothermal axisymmetric uniaxial compression tests at various deformation parameters. Then, an instantaneous friction factor equation was fitted by mathematic analysis. After verification by comparing single-pass flow stress correction with traditional average friction factor correction, the instantaneous friction factor equation was applied to correct multistage stress-strain curves. The corrected results were reasonable and validated by multistage relative softening calculations. This research provides a broad potential for implementing axisymmetric uniaxial compression in multistage physical simulations and friction optimization in finite element analysis.

A generalized algorithm to design finite field normal basis multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1986-01-01

Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

SU-F-T-428: An Optimization-Based Commissioning Tool for Finite Size Pencil Beam Dose Calculations

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

Li, Y; Tian, Z; Song, T

Purpose: Finite size pencil beam (FSPB) algorithms are commonly used to pre-calculate the beamlet dose distribution for IMRT treatment planning. FSPB commissioning, which usually requires fine tuning of the FSPB kernel parameters, is crucial to the dose calculation accuracy and hence the plan quality. Yet due to the large number of beamlets, FSPB commissioning could be very tedious. This abstract reports an optimization-based FSPB commissioning tool we have developed in MatLab to facilitate the commissioning. Methods: A FSPB dose kernel generally contains two types of parameters: the profile parameters determining the dose kernel shape, and a 2D scaling factors accountingmore » for the longitudinal and off-axis corrections. The former were fitted using the penumbra of a reference broad beam’s dose profile with Levenberg-Marquardt algorithm. Since the dose distribution of a broad beam is simply a linear superposition of the dose kernel of each beamlet calculated with the fitted profile parameters and scaled using the scaling factors, these factors could be determined by solving an optimization problem which minimizes the discrepancies between the calculated dose of broad beams and the reference dose. Results: We have commissioned a FSPB algorithm for three linac photon beams (6MV, 15MV and 6MVFFF). Dose of four field sizes (6*6cm2, 10*10cm2, 15*15cm2 and 20*20cm2) were calculated and compared with the reference dose exported from Eclipse TPS system. For depth dose curves, the differences are less than 1% of maximum dose after maximum dose depth for most cases. For lateral dose profiles, the differences are less than 2% of central dose at inner-beam regions. The differences of the output factors are within 1% for all the three beams. Conclusion: We have developed an optimization-based commissioning tool for FSPB algorithms to facilitate the commissioning, providing sufficient accuracy of beamlet dose calculation for IMRT optimization.« less

Astrophysical Applications of Quantum Corrections to the Equation of State of a Plasma

NASA Technical Reports Server (NTRS)

Heckler, Andrew F.

1994-01-01

The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.

Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two p electrons using all-electron explicitly correlated Gaussian basis functions

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

Sharkey, Keeper L.; Pavanello, Michele; Bubin, Sergiy

2009-12-15

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

The Chiral Separation Effect in quenched finite-density QCD

NASA Astrophysics Data System (ADS)

Puhr, Matthias; Buividovich, Pavel

2018-03-01

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coeffcient for the CSE in the confining and deconfining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coeffcient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

Finite element simulation of crack depth measurements in concrete using diffuse ultrasound

NASA Astrophysics Data System (ADS)

Seher, Matthias; Kim, Jin-Yeon; Jacobs, Laurence J.

2012-05-01

This research simulates the measurements of crack depth in concrete using diffuse ultrasound. The finite element method is employed to simulate the ultrasonic diffusion process around cracks with different geometrical shapes, with the goal of gaining physical insight into the data obtained from experimental measurements. The commercial finite element software Ansys is used to implement the two-dimensional concrete model. The model is validated with an analytical solution and experimental results. It is found from the simulation results that preliminary knowledge of the crack geometry is required to interpret the energy evolution curves from measurements and to correctly determine the crack depth.

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

Jain, Shweta; Sharma, Prerana; Kaothekar, Sachin

The thermal instability of an infinite homogeneous, thermally conducting, and rotating plasma, incorporating finite electrical resistivity, finite electron inertia, and an arbitrary radiative heat-loss function in the presence of finite Larmor radius corrections and Hall current, has been studied. Analysis has been made with the help of linearized magnetohydrodynamics (MHD) equations. A general dispersion relation is obtained using the normal mode analysis method, and the dispersion relation is discussed for longitudinal propagation and transverse propagation separately. The dispersion relation has been solved numerically to obtain the dependence of the growth rate on the various parameters involved. The conditions of modifiedmore » thermal instability and stability are discussed in the different cases of interest.« less

Olber's Paradox Revisited in a Static and Finite Universe

ERIC Educational Resources Information Center

Couture, Gilles

2012-01-01

Building a Universe populated by stars identical to our Sun and taking into consideration the wave-particle duality of light, the biological limits of the human eye, the finite size of stars and the finiteness of our Universe, we conclude that the sky could very well be dark at night. Besides the human eye, the dominant parameter is the finite…

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

Wiley, J.C.

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

System-size convergence of point defect properties: The case of the silicon vacancy

NASA Astrophysics Data System (ADS)

Corsetti, Fabiano; Mostofi, Arash A.

2011-07-01

We present a comprehensive study of the vacancy in bulk silicon in all its charge states from 2+ to 2-, using a supercell approach within plane-wave density-functional theory, and systematically quantify the various contributions to the well-known finite size errors associated with calculating formation energies and stable charge state transition levels of isolated defects with periodic boundary conditions. Furthermore, we find that transition levels converge faster with respect to supercell size when only the Γ-point is sampled in the Brillouin zone, as opposed to a dense k-point sampling. This arises from the fact that defect level at the Γ-point quickly converges to a fixed value which correctly describes the bonding at the defect center. Our calculated transition levels with 1000-atom supercells and Γ-point only sampling are in good agreement with available experimental results. We also demonstrate two simple and accurate approaches for calculating the valence band offsets that are required for computing formation energies of charged defects, one based on a potential averaging scheme and the other using maximally-localized Wannier functions (MLWFs). Finally, we show that MLWFs provide a clear description of the nature of the electronic bonding at the defect center that verifies the canonical Watkins model.

The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory

PubMed Central

Bosbach, Wolfram A.

2015-01-01

Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Finite-size scaling for discontinuous nonequilibrium phase transitions

NASA Astrophysics Data System (ADS)

de Oliveira, Marcelo M.; da Luz, M. G. E.; Fiore, Carlos E.

2018-06-01

A finite-size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E 92, 062126 (2015), 10.1103/PhysRevE.92.062126], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities such as response functions, reduced cumulants, and equal area probability distributions are derived from phenomenological arguments. Irrespective of system details, all these quantities scale with the volume, establishing the dependence on size. The approach generality is illustrated through the analysis of different models. The present results are a relevant step in trying to unify the scaling behavior description of nonequilibrium transition processes.

Structural weights analysis of advanced aerospace vehicles using finite element analysis

NASA Technical Reports Server (NTRS)

Bush, Lance B.; Lentz, Christopher A.; Rehder, John J.; Naftel, J. Chris; Cerro, Jeffrey A.

1989-01-01

A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

Dynamic finite element method modeling of the upper shelf energy of precracked Charpy specimens of neutron irradiated weld metal 72W

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

Kumar, A.S.; Sidener, S.E.; Hamilton, M.L.

1999-10-01

Dynamic finite element modeling of the fracture behavior of fatigue-precracked Charpy specimens in both unirradiated and irradiated conditions was performed using a computer code, ABAQUS Explicit, to predict the upper shelf energy of precracked specimens of a given size from experimental data obtained for a different size. A tensile fracture-strain based method for modeling crack extension and propagation was used. It was found that the predicted upper shelf energies of full and half size precracked specimens based on third size data were in reasonable agreement with their respective experimental values. Similar success was achieved for predicting the upper shelf energymore » of subsize precracked specimens based on full size data.« less

Thermodynamic theory of intrinsic finite size effects in PbTiO3 nanocrystals. II. Dielectric and piezoelectric properties

NASA Astrophysics Data System (ADS)

Akdogan, E. K.; Safari, A.

2007-03-01

We compute the intrinsic dielectric and piezoelectric properties of single domain, mechanically free, and surface charge compensated PbTiO3 nanocrystals (n-Pt) with no depolarization fields, undergoing a finite size induced first order tetragonal→cubic ferrodistortive phase transition. By using a Landau-Devonshire type free energy functional, in which Landau coefficients are a function of nanoparticle size, we demonstrate substantial deviations from bulk properties in the range <150 nm. We find a decrease in dielectric susceptibility at the transition temperature with decreasing particle size, which we verify to be in conformity with predictions of lattice dynamics considerations. We also find an anomalous increase in piezocharge coefficients near ˜15 nm , the critical size for n-Pt.

77 FR 32013 - Truck Size and Weight; Technical Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-05-31

...-2012-0037] RIN 2125-AF45 Truck Size and Weight; Technical Correction AGENCY: Federal Highway...: This rule makes a technical correction to the regulations that govern Longer Combination Vehicles (LCV... INFORMATION CONTACT: John Nicholas, Truck Size and Weight Program Manager, Office of Freight Management and...

Particle Size Distributions in Atmospheric Clouds

NASA Technical Reports Server (NTRS)

Paoli, Roberto; Shariff, Karim

2003-01-01

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.

Finite-Size Scaling for the Baxter-Wu Model Using Block Distribution Functions

NASA Astrophysics Data System (ADS)

Velonakis, Ioannis N.; Hadjiagapiou, Ioannis A.

2018-05-01

In the present work, we present an alternative way of applying the well-known finite-size scaling (FSS) theory in the case of a Baxter-Wu model using Binder-like blocks. Binder's ideas are extended to estimate phase transition points and the corresponding scaling exponents not only for magnetic but also for energy properties, saving computational time and effort. The vast majority of our conclusions can be easily generalized to other models.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

NASA Astrophysics Data System (ADS)

Bijnens, Johan

2018-03-01

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

Evaluation of Kirkwood-Buff integrals via finite size scaling: a large scale molecular dynamics study

NASA Astrophysics Data System (ADS)

Dednam, W.; Botha, A. E.

2015-01-01

Solvation of bio-molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to very large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. For example, it is useful know the conformational transitions that occur in protein structures. Although such an understanding can be obtained through large-scale molecular dynamic simulations, it is often the case that such simulations would require excessively large simulation times. In this context, Kirkwood-Buff theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique, called finite size scaling, may provide a better method to reduce system sizes, and hence also the computational times. In this paper, we present molecular dynamics trial simulations of biologically relevant low-concentration solvents, solvated by aqueous co-solvent solutions. In particular we compare two different methods of calculating the relevant Kirkwood-Buff integrals. The first (traditional) method computes running integrals over the radial distribution functions, which must be obtained from large system-size NVT or NpT simulations. The second, newer method, employs finite size scaling to obtain the Kirkwood-Buff integrals directly by counting the particle number fluctuations in small, open sub-volumes embedded within a larger reservoir that can be well approximated by a much smaller simulation cell. In agreement with previous studies, which made a similar comparison for aqueous co-solvent solutions, without the additional solvent, we conclude that the finite size scaling method is also applicable to the present case, since it can produce computationally more efficient results which are equivalent to the more costly radial distribution function method.

The Intensity Modulation of the Fluorescent Line by a Finite Light Speed Effect in Accretion-powered X-Ray Pulsars

NASA Astrophysics Data System (ADS)

Yoshida, Yuki; Kitamoto, Shunji; Hoshino, Akio

2017-11-01

The X-ray line diagnostic method is a powerful tool for an investigation of plasma around accretion-powered X-ray pulsars. We point out an apparent intensity modulation of emission lines, with their rotation period of neutron stars, due to the finite speed of light (we call this effect the “finite light speed effect”) if the line emission mechanism is a kind of reprocessing, such as fluorescence or recombination after ionization by X-ray irradiation from pulsars. The modulation amplitude is determined by the size of the emission region, which is in competition with the smearing effect by the light crossing time in the emission region. This is efficient if the size of the emission region is roughly comparable to that of the rotation period multiplied by the speed of light. We apply this effect to a symbiotic X-ray pulsar, GX 1+4, where a spin modulation of the intense iron line of which has been reported. The finite light speed effect can explain the observed intensity modulation if its fluorescent region is the size of ˜ {10}12 cm.

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

Universal scaling for the quantum Ising chain with a classical impurity

NASA Astrophysics Data System (ADS)

Apollaro, Tony J. G.; Francica, Gianluca; Giuliano, Domenico; Falcone, Giovanni; Palma, G. Massimo; Plastina, Francesco

2017-10-01

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ ≠1 . In the homogeneous chain limit at μ =1 , we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ =0 , we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ , finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ .

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

On the ab initio calculation of vibrational formation entropy of point defect: the case of the silicon vacancy

NASA Astrophysics Data System (ADS)

Seeberger, Pia; Vidal, Julien

2017-08-01

Formation entropy of point defects is one of the last crucial elements required to fully describe the temperature dependence of point defect formation. However, while many attempts have been made to compute them for very complicated systems, very few works have been carried out such as to assess the different effects of finite size effects and precision on such quantity. Large discrepancies can be found in the literature for a system as primitive as the silicon vacancy. In this work, we have proposed a systematic study of formation entropy for silicon vacancy in its 3 stable charge states: neutral, +2 and -2 for supercells with size not below 432 atoms. Rationalization of the formation entropy is presented, highlighting importance of finite size error and the difficulty to compute such quantities due to high numerical requirement. It is proposed that the direct calculation of formation entropy of VSi using first principles methods will be plagued by very high computational workload (or large numerical errors) and finite size dependent results.

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Drag Corrections in High-Speed Wind Tunnels

NASA Technical Reports Server (NTRS)

Ludwieg, H.

1947-01-01

In the vicinity of a body in a wind tunnel the displacement effect of the wake, due to the finite dimensions of the stream, produces a pressure gradient which evokes a change of drag. In incompressible flow this change of drag is so small, in general, that one does not have to take it into account in wind-tunnel measurements; however, in compressible flow it beoomes considerably larger, so that a correction factor is necessary for measured values. Correction factors for a closed tunnel and an open jet with circular cross sections are calculated and compared with the drag - corrections already bown for high-speed tunnnels.

Work extraction from quantum systems with bounded fluctuations in work.

PubMed

Richens, Jonathan G; Masanes, Lluis

2016-11-25

In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.

Work extraction from quantum systems with bounded fluctuations in work

PubMed Central

Richens, Jonathan G.; Masanes, Lluis

2016-01-01

In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations. PMID:27886177

Work extraction from quantum systems with bounded fluctuations in work

NASA Astrophysics Data System (ADS)

Richens, Jonathan G.; Masanes, Lluis

2016-11-01

In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.

Anomalous bulk behavior in the free parafermion Z (N ) spin chain

NASA Astrophysics Data System (ADS)

Alcaraz, Francisco C.; Batchelor, Murray T.

2018-06-01

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z (N ) model for N ≥3 for which the model Hamiltonian is non-Hermitian. For N =2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z (N ) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N . Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

Computational Aeroacoustics: An Overview

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

2003-01-01

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Interaction quench dynamics in the Kondo model in the presence of a local magnetic field.

PubMed

Heyl, M; Kehrein, S

2010-09-01

In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in the presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present non-equilibrium setting. The transient dynamics are studied by analyzing exact analytical results for the local spin dynamics. The timescale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.

Ubiquity of non-geometry in heterotic compactifications

DOE PAGES

García-Etxebarria, Iñaki; Lüst, Dieter; Massai, Stefano; ...

2017-03-08

Here, we study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest nontrivial elliptic fibration the effect is quite dramatic: the I 1 degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the T 2. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety duemore » to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.« less

Evaluation of attenuation and scatter correction requirements in small animal PET and SPECT imaging

NASA Astrophysics Data System (ADS)

Konik, Arda Bekir

Positron emission tomography (PET) and single photon emission tomography (SPECT) are two nuclear emission-imaging modalities that rely on the detection of high-energy photons emitted from radiotracers administered to the subject. The majority of these photons are attenuated (absorbed or scattered) in the body, resulting in count losses or deviations from true detection, which in turn degrades the accuracy of images. In clinical emission tomography, sophisticated correction methods are often required employing additional x-ray CT or radionuclide transmission scans. Having proven their potential in both clinical and research areas, both PET and SPECT are being adapted for small animal imaging. However, despite the growing interest in small animal emission tomography, little scientific information exists about the accuracy of these correction methods on smaller size objects, and what level of correction is required. The purpose of this work is to determine the role of attenuation and scatter corrections as a function of object size through simulations. The simulations were performed using Interactive Data Language (IDL) and a Monte Carlo based package, Geant4 application for emission tomography (GATE). In IDL simulations, PET and SPECT data acquisition were modeled in the presence of attenuation. A mathematical emission and attenuation phantom approximating a thorax slice and slices from real PET/CT data were scaled to 5 different sizes (i.e., human, dog, rabbit, rat and mouse). The simulated emission data collected from these objects were reconstructed. The reconstructed images, with and without attenuation correction, were compared to the ideal (i.e., non-attenuated) reconstruction. Next, using GATE, scatter fraction values (the ratio of the scatter counts to the total counts) of PET and SPECT scanners were measured for various sizes of NEMA (cylindrical phantoms representing small animals and human), MOBY (realistic mouse/rat model) and XCAT (realistic human model) digital phantoms. In addition, PET projection files for different sizes of MOBY phantoms were reconstructed in 6 different conditions including attenuation and scatter corrections. Selected regions were analyzed for these different reconstruction conditions and object sizes. Finally, real mouse data from the real version of the same small animal PET scanner we modeled in our simulations were analyzed for similar reconstruction conditions. Both our IDL and GATE simulations showed that, for small animal PET and SPECT, even the smallest size objects (˜2 cm diameter) showed ˜15% error when both attenuation and scatter were not corrected. However, a simple attenuation correction using a uniform attenuation map and object boundary obtained from emission data significantly reduces this error in non-lung regions (˜1% for smallest size and ˜6% for largest size). In lungs, emissions values were overestimated when only attenuation correction was performed. In addition, we did not observe any significant improvement between the uses of uniform or actual attenuation map (e.g., only ˜0.5% for largest size in PET studies). The scatter correction was not significant for smaller size objects, but became increasingly important for larger sizes objects. These results suggest that for all mouse sizes and most rat sizes, uniform attenuation correction can be performed using emission data only. For smaller sizes up to ˜ 4 cm, scatter correction is not required even in lung regions. For larger sizes if accurate quantization needed, additional transmission scan may be required to estimate an accurate attenuation map for both attenuation and scatter corrections.

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

NASA Technical Reports Server (NTRS)

Knudsen, William C.

1992-01-01

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.

An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods.

PubMed

Frank, Florian; Liu, Chen; Scanziani, Alessio; Alpak, Faruk O; Riviere, Beatrice

2018-08-01

We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from μCT (micro computed tomography) imaging of porous rock and approximate a (on μm scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90°, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90° on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method. However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. Copyright © 2018 Elsevier Inc. All rights reserved.

Effect of finite size in magnetic properties of BaFe12O19

NASA Astrophysics Data System (ADS)

Kumar, A. Sendil; Bhatnagar, Anil K.

2018-05-01

BaFe12O19 Nanoparticles are prepared through auto ignition method and structure, microstructure and magnetic properties are characterized. Samples having spherical shapes and elongated nanorods are chosen to investigate the role of finite size effect in magnetic properties. Magnetization studies show superparamagnetic, antiferromagnetic and ferrimagnetic behaviors depending on the size and shape. Very small coercive field of around 200 Oe is observed for spherical nanoparticles and a large coercive field of around 7000 Oe for nanorods is found. The shape and size plays an important role in magnetic properties of BaFe12O19 nanoparticles. Shape anisotropy has significant value compared to other anisotropies. Therefore shape of nanoparticles influences the magnetic order.

Predict the fatigue life of crack based on extended finite element method and SVR

NASA Astrophysics Data System (ADS)

Song, Weizhen; Jiang, Zhansi; Jiang, Hui

2018-05-01

Using extended finite element method (XFEM) and support vector regression (SVR) to predict the fatigue life of plate crack. Firstly, the XFEM is employed to calculate the stress intensity factors (SIFs) with given crack sizes. Then predicetion model can be built based on the function relationship of the SIFs with the fatigue life or crack length. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Because of the accuracy of the forward Euler method only ensured by the small step size, a new prediction method is presented to resolve the issue. The numerical examples were studied to demonstrate the proposed method allow a larger step size and have a high accuracy.

Exact Length Distribution of Filamentous Structures Assembled from a Finite Pool of Subunits.

PubMed

Harbage, David; Kondev, Jané

2016-07-07

Self-assembling filamentous structures made of protein subunits are ubiquitous in cell biology. These structures are often highly dynamic, with subunits in a continuous state of flux, binding to and falling off of filaments. In spite of this constant turnover of their molecular parts, many cellular structures seem to maintain a well-defined size over time, which is often required for their proper functioning. One widely discussed mechanism of size regulation involves the cell maintaining a finite pool of protein subunits available for assembly. This finite pool mechanism can control the length of a single filament by having assembly proceed until the pool of free subunits is depleted to the point when assembly and disassembly are balanced. Still, this leaves open the question of whether the same mechanism can provide size control for multiple filamentous structures that are assembled from a common pool of protein subunits, as is often the case in cells. We address this question by solving the steady-state master equation governing the stochastic assembly and disassembly of multifilament structures made from a shared finite pool of subunits. We find that, while the total number of subunits within a multifilament structure is well-defined, individual filaments within the structure have a wide, power-law distribution of lengths. We also compute the phase diagram for two multifilament structures competing for the same pool of subunits and identify conditions for coexistence when both have a well-defined size. These predictions can be tested in cell experiments in which the size of the subunit pool or the number of filament nucleators is tuned.

Practical wavelength calibration considerations for UV-visible Fourier-transform spectroscopy.

PubMed

Salit, M L; Travis, J C; Winchester, M R

1996-06-01

The intrinsic wavelength scale in a modern reference laser-controlled Michelson interferometer-sometimes referred to as the Connes advantage-offers excellent wavelength accuracy with relative ease. Truly superb wavelength accuracy, with total relative uncertainty in line position of the order of several parts in 10(8), should be within reach with single-point, multiplicative calibration. The need for correction of the wavelength scale arises from two practical effects: the use of a finite aperture, from which off-axis rays propagate through the interferometer, and imperfect geometric alignment of the sample beam with the reference beam and the optical axis of the moving mirror. Although an analytical correction can be made for the finite-aperture effect, calibration with a trusted wavelength standard is typically used to accomplish both corrections. Practical aspects of accurate calibration of an interferometer in the UV-visible region are discussed. Critical issues regarding accurate use of a standard external to the sample source and the evaluation and selection of an appropriate standard are addressed. Anomalous results for two different potential wavelength standards measured by Fabry-Perot interferometry (Ar II and (198)Hg I) are observed.

Finite-size effects in surface-enhanced Raman scattering in noble-metal nanoparticles: a semiclassical approach.

PubMed

Pustovit, Vitaliy N; Shahbazyan, Tigran V

2006-06-01

We study finite-size effects in surface-enhanced Raman scattering (SERS) from molecules adsorbed on small metal particles. Within an electromagnetic description of SERS, the enhancement of the Raman signal originates from the local field of the surface plasmon resonance in a nanoparticle. With decreasing particle sizes, this enhancement is reduced due to the size-dependent Landau damping of the surface plasmon. We show that, in small noble-metal particles, the reduction of interband screening in the surface layer leads to an additional increase in the local field acting on a molecule close to the metal surface. The overall size dependence of Raman signal enhancement is determined by the interplay between Landau damping and underscreening effects. Our calculations, based on a two-region model, show that the role of the surface layer increases for smaller nanoparticle sizes due to a larger volume fraction of the underscreened region.

Finite Element Analysis of Walking Beam of a New Compound Adjustment Balance Pumping Unit

NASA Astrophysics Data System (ADS)

Wu, Jufei; Wang, Qian; Han, Yunfei

2017-12-01

In this paper, taking the designer of the new compound balance pumping unit beam as our research target, the three-dimensional model is established by Solid Works, the load and the constraint are determined. ANSYS Workbench is used to analyze the tail and the whole of the beam, the stress and deformation are obtained to meet the strength requirements. The finite element simulation and theoretical calculation of the moment of the center axis beam are carried out. The finite element simulation results are compared with the calculated results of the theoretical mechanics model to verify the correctness of the theoretical calculation. Finally, the finite element analysis is consistent with the theoretical calculation results. The theoretical calculation results are preferable, and the bending moment value provides the theoretical reference for the follow-up optimization and research design.

Spatio-temporal correlations in the Manna model in one, three and five dimensions

NASA Astrophysics Data System (ADS)

Willis, Gary; Pruessner, Gunnar

2018-02-01

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

Consideration of Kaolinite Interference Correction for Quartz Measurements in Coal Mine Dust

PubMed Central

Lee, Taekhee; Chisholm, William P.; Kashon, Michael; Key-Schwartz, Rosa J.; Harper, Martin

2015-01-01

Kaolinite interferes with the infrared analysis of quartz. Improper correction can cause over- or underestimation of silica concentration. The standard sampling method for quartz in coal mine dust is size selective, and, since infrared spectrometry is sensitive to particle size, it is intuitively better to use the same size fractions for quantification of quartz and kaolinite. Standard infrared spectrometric methods for quartz measurement in coal mine dust correct interference from the kaolinite, but they do not specify a particle size for the material used for correction. This study compares calibration curves using as-received and respirable size fractions of nine different examples of kaolinite in the different correction methods from the National Institute for Occupational Safety and Health Manual of Analytical Methods (NMAM) 7603 and the Mine Safety and Health Administration (MSHA) P-7. Four kaolinites showed significant differences between calibration curves with as-received and respirable size fractions for NMAM 7603 and seven for MSHA P-7. The quartz mass measured in 48 samples spiked with respirable fraction silica and kaolinite ranged between 0.28 and 23% (NMAM 7603) and 0.18 and 26% (MSHA P-7) of the expected applied mass when the kaolinite interference was corrected with respirable size fraction kaolinite. This is termed “deviation,” not bias, because the applied mass is also subject to unknown variance. Generally, the deviations in the spiked samples are larger when corrected with the as-received size fraction of kaolinite than with the respirable size fraction. Results indicate that if a kaolinite correction with reference material of respirable size fraction is applied in current standard methods for quartz measurement in coal mine dust, the quartz result would be somewhat closer to the true exposure, although the actual mass difference would be small. Most kinds of kaolinite can be used for laboratory calibration, but preferably, the size fraction should be the same as the coal dust being collected. PMID:23767881

Consideration of kaolinite interference correction for quartz measurements in coal mine dust.

PubMed

Lee, Taekhee; Chisholm, William P; Kashon, Michael; Key-Schwartz, Rosa J; Harper, Martin

2013-01-01

Kaolinite interferes with the infrared analysis of quartz. Improper correction can cause over- or underestimation of silica concentration. The standard sampling method for quartz in coal mine dust is size selective, and, since infrared spectrometry is sensitive to particle size, it is intuitively better to use the same size fractions for quantification of quartz and kaolinite. Standard infrared spectrometric methods for quartz measurement in coal mine dust correct interference from the kaolinite, but they do not specify a particle size for the material used for correction. This study compares calibration curves using as-received and respirable size fractions of nine different examples of kaolinite in the different correction methods from the National Institute for Occupational Safety and Health Manual of Analytical Methods (NMAM) 7603 and the Mine Safety and Health Administration (MSHA) P-7. Four kaolinites showed significant differences between calibration curves with as-received and respirable size fractions for NMAM 7603 and seven for MSHA P-7. The quartz mass measured in 48 samples spiked with respirable fraction silica and kaolinite ranged between 0.28 and 23% (NMAM 7603) and 0.18 and 26% (MSHA P-7) of the expected applied mass when the kaolinite interference was corrected with respirable size fraction kaolinite. This is termed "deviation," not bias, because the applied mass is also subject to unknown variance. Generally, the deviations in the spiked samples are larger when corrected with the as-received size fraction of kaolinite than with the respirable size fraction. Results indicate that if a kaolinite correction with reference material of respirable size fraction is applied in current standard methods for quartz measurement in coal mine dust, the quartz result would be somewhat closer to the true exposure, although the actual mass difference would be small. Most kinds of kaolinite can be used for laboratory calibration, but preferably, the size fraction should be the same as the coal dust being collected.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

On the delay analysis of a TDMA channel with finite buffer capacity

NASA Technical Reports Server (NTRS)

Yan, T.-Y.

1982-01-01

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.

Security of continuous-variable quantum key distribution against general attacks.

PubMed

Leverrier, Anthony; García-Patrón, Raúl; Renner, Renato; Cerf, Nicolas J

2013-01-18

We prove the security of Gaussian continuous-variable quantum key distribution with coherent states against arbitrary attacks in the finite-size regime. In contrast to previously known proofs of principle (based on the de Finetti theorem), our result is applicable in the practically relevant finite-size regime. This is achieved using a novel proof approach, which exploits phase-space symmetries of the protocols as well as the postselection technique introduced by Christandl, Koenig, and Renner [Phys. Rev. Lett. 102, 020504 (2009)].

Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control.

PubMed

Liu, Xiwei; Chen, Tianping

2018-01-01

In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.

Anomalous DC Hall response in noncentrosymmetric tilted Weyl semimetals

NASA Astrophysics Data System (ADS)

Mukherjee, S. P.; Carbotte, J. P.

2018-03-01

Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by {Q} and the anomalous DC Hall conductivity σxy is proportional to {Q} at charge neutrality. For finite doping there are additive corrections to σxy which depend on the chemical potential as well as on the tilt (C ) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount Q0 . This introduces further changes in σxy and we provide simple analytic formulas for these modifications for both type I (C<1 ) and type II (C>1 , overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to σxy is proportional to the chemical potential μ and completely independent of the energy shift Q0 . When instead the tilts are parallel, the correction is linear in Q0 and μ drops out. For type II the corrections involve both μ and Q0 , are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite Q0 .

Implementation of Coupled Skin Temperature Analysis and Bias Correction in a Global Atmospheric Data Assimilation System

NASA Technical Reports Server (NTRS)

Radakovich, Jon; Bosilovich, M.; Chern, Jiun-dar; daSilva, Arlindo

2004-01-01

The NASA/NCAR Finite Volume GCM (fvGCM) with the NCAR CLM (Community Land Model) version 2.0 was integrated into the NASA/GMAO Finite Volume Data Assimilation System (fvDAS). A new method was developed for coupled skin temperature assimilation and bias correction where the analysis increment and bias correction term is passed into the CLM2 and considered a forcing term in the solution to the energy balance. For our purposes, the fvDAS CLM2 was run at 1 deg. x 1.25 deg. horizontal resolution with 55 vertical levels. We assimilate the ISCCP-DX (30 km resolution) surface temperature product. The atmospheric analysis was performed 6-hourly, while the skin temperature analysis was performed 3-hourly. The bias correction term, which was updated at the analysis times, was added to the skin temperature tendency equation at every timestep. In this presentation, we focus on the validation of the surface energy budget at the in situ reference sites for the Coordinated Enhanced Observation Period (CEOP). We will concentrate on sites that include independent skin temperature measurements and complete energy budget observations for the month of July 2001. In addition, MODIS skin temperature will be used for validation. Several assimilations were conducted and preliminary results will be presented.

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Augmented wedge-shaped glenoid component for the correction of glenoid retroversion: a finite element analysis.

PubMed

Hermida, Juan C; Flores-Hernandez, Cesar; Hoenecke, Heinz R; D'Lima, Darryl D

2014-03-01

This study undertook a computational analysis of a wedged glenoid component for correction of retroverted glenoid arthritic deformity to determine whether a wedge-shaped glenoid component design with a built-in correction for version reduces excessive stresses in the implant, cement, and glenoid bone. Recommendations for correcting retroversion deformity are asymmetric reaming of the anterior glenoid, bone grafting of the posterior glenoid, or a glenoid component with posterior augmentation. Eccentric reaming has the disadvantages of removing normal bone, reducing structural support for the glenoid component, and increasing the risk of bone perforation by the fixation pegs. Bone grafting to correct retroverted deformity does not consistently generate successful results. Finite element models of 2 scapulae models representing a normal and an arthritic retroverted glenoid were implanted with a standard glenoid component (in retroversion or neutral alignment) or a wedged component. Glenohumeral forces representing in vivo loading were applied and stresses and strains computed in the bone, cement, and glenoid component. The retroverted glenoid components generated the highest compressive stresses and decreased cyclic fatigue life predictions for trabecular bone. Correction of retroversion by the wedged glenoid component significantly decreased stresses and predicted greater bone fatigue life. The cement volume estimated to survive 10 million cycles was the lowest for the retroverted components and the highest for neutrally implanted glenoid components and for wedged components. A wedged glenoid implant is a viable option to correct severe arthritic retroversion, reducing the need for eccentric reaming and the risk for implant failure. Copyright © 2014 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Mosby, Inc. All rights reserved.

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

NASA Astrophysics Data System (ADS)

Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.

2016-10-01

We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.

Excitations in the Yang–Gaudin Bose gas

DOE PAGES

Robinson, Neil J.; Konik, Robert M.

2017-06-01

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

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

Robinson, Neil J.; Konik, Robert M.

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold.

PubMed

Ottino-Löffler, Bertrand; Strogatz, Steven H

2016-06-01

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N≫1. The leading correction to the infinite-N result scales like either N^{-3/2} or N^{-1}, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005)PLEEE81539-375510.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

Gap Size Uncertainty Quantification in Advanced Gas Reactor TRISO Fuel Irradiation Experiments

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

Pham, Binh T.; Einerson, Jeffrey J.; Hawkes, Grant L.

The Advanced Gas Reactor (AGR)-3/4 experiment is the combination of the third and fourth tests conducted within the tristructural isotropic fuel development and qualification research program. The AGR-3/4 test consists of twelve independent capsules containing a fuel stack in the center surrounded by three graphite cylinders and shrouded by a stainless steel shell. This capsule design enables temperature control of both the fuel and the graphite rings by varying the neon/helium gas mixture flowing through the four resulting gaps. Knowledge of fuel and graphite temperatures is crucial for establishing the functional relationship between fission product release and irradiation thermal conditions.more » These temperatures are predicted for each capsule using the commercial finite-element heat transfer code ABAQUS. Uncertainty quantification reveals that the gap size uncertainties are among the dominant factors contributing to predicted temperature uncertainty due to high input sensitivity and uncertainty. Gap size uncertainty originates from the fact that all gap sizes vary with time due to dimensional changes of the fuel compacts and three graphite rings caused by extended exposure to high temperatures and fast neutron irradiation. Gap sizes are estimated using as-fabricated dimensional measurements at the start of irradiation and post irradiation examination dimensional measurements at the end of irradiation. Uncertainties in these measurements provide a basis for quantifying gap size uncertainty. However, lack of gap size measurements during irradiation and lack of knowledge about the dimension change rates lead to gap size modeling assumptions, which could increase gap size uncertainty. In addition, the dimensional measurements are performed at room temperature, and must be corrected to account for thermal expansion of the materials at high irradiation temperatures. Uncertainty in the thermal expansion coefficients for the graphite materials used in the AGR-3/4 capsules also increases gap size uncertainty. This study focuses on analysis of modeling assumptions and uncertainty sources to evaluate their impacts on the gap size uncertainty.« less

The square lattice Ising model on the rectangle II: finite-size scaling limit

NASA Astrophysics Data System (ADS)

Hucht, Alfred

2017-06-01

Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor. 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L, M\\to∞ , T\\to Tc , with fixed temperature scaling variable x\\propto(T/Tc-1)M and fixed aspect ratio ρ\\propto L/M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T=Tc we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys. B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen. 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.

Stretching Diagnostics and Mixing Properties In The Stratosphere

NASA Astrophysics Data System (ADS)

Legras, B.; Shuckburgh, E.

The "finite size Lyapunov exponent" and the "effective diffusivity" are two diagnos- tics of mixing which have been recently introduced to investigate atmospheric flows. Both have been used to successfully identify the barriers to transport, for instance at the edge of the stratospheric polar vortex. Here we compare the two diagnostics in detail. The equivalent length has the advantage of arising as a mixing quantification from a rigid theoretical framework, however it has the disadvantage of being an aver- age quantity (the average around a tracer contour). The finite size Lyapunov exponent may be defined at any point in the flow, and quantifies the stretching properties expe- rienced by a fluid parcel both in its past and future evolution. In particular, the lines of maximum stretching at any time delineate the building blocks of the chaotic stirring. However the interpretation of the finite size Lyapunov exponent as a mixing time is less direct and depends on the alignment of tracer contours with the stretching lines.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres.

PubMed

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L A; Yodh, A G; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Optimization Issues with Complex Rotorcraft Comprehensive Analysis

NASA Technical Reports Server (NTRS)

Walsh, Joanne L.; Young, Katherine C.; Tarzanin, Frank J.; Hirsh, Joel E.; Young, Darrell K.

1998-01-01

This paper investigates the use of the general purpose automatic differentiation (AD) tool called Automatic Differentiation of FORTRAN (ADIFOR) as a means of generating sensitivity derivatives for use in Boeing Helicopter's proprietary comprehensive rotor analysis code (VII). ADIFOR transforms an existing computer program into a new program that performs a sensitivity analysis in addition to the original analysis. In this study both the pros (exact derivatives, no step-size problems) and cons (more CPU, more memory) of ADIFOR are discussed. The size (based on the number of lines) of the VII code after ADIFOR processing increased by 70 percent and resulted in substantial computer memory requirements at execution. The ADIFOR derivatives took about 75 percent longer to compute than the finite-difference derivatives. However, the ADIFOR derivatives are exact and are not functions of step-size. The VII sensitivity derivatives generated by ADIFOR are compared with finite-difference derivatives. The ADIFOR and finite-difference derivatives are used in three optimization schemes to solve a low vibration rotor design problem.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres

NASA Astrophysics Data System (ADS)

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L. A.; Yodh, A. G.; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Fatigue response of perforated titanium for application in laminar flow control

NASA Technical Reports Server (NTRS)

Johnson, W. Steven; Miller, Jennifer L.; Newman, Jr., James

1996-01-01

The room temperature tensile and fatigue response of non-perforated and perforated titanium for laminar flow control application was investigated both experimentally and analytically. Results showed that multiple perforations did not affect the tensile response, but did reduce the fatigue life. A two dimensional finite element stress analysis was used to determine that the stress fields from adjacent perforations did not influence one another. The stress fields around the holes did not overlap one another, allowing the materials to be modeled as a plate with a center hole. Fatigue life was predicted using an equivalent MW flow size approach to relate the experimental results to microstructural features of the titanium. Predictions using flaw sizes ranging from 1 to 15 microns correlated within a factor of 2 with the experimental results by using a flow stress of 260 MPa. By using two different flow stresses in the crack closure model and correcting for plasticity, the experimental results were bounded by the predictions for high applied stresses. Further analysis of the complex geometry of the perforations and the local material chemistry is needed to further understand the fatigue behavior of the perforated titanium.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor

2016-06-01

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Modified stochastic fragmentation of an interval as an ageing process

NASA Astrophysics Data System (ADS)

Fortin, Jean-Yves

2018-02-01

We study a stochastic model based on modified fragmentation of a finite interval. The mechanism consists of cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve the interval length. This leads to a set of segments of random sizes, with the accumulation of small fragments near the origin. This model is an example of record dynamics, with the presence of ‘quakes’ and slow dynamics. The fragment size distribution is a universal inverse power law with logarithmic corrections. The exact distribution for the fragment number as function of time is simply related to the unsigned Stirling numbers of the first kind. Two-time correlation functions are defined, and computed exactly. They satisfy scaling relations, and exhibit aging phenomena. In particular, the probability that the same number of fragments is found at two different times t>s is asymptotically equal to [4πlog(s)]-1/2 when s\\gg 1 and the ratio t/s is fixed, in agreement with the numerical simulations. The same process with a reset impedes the aging phenomenon-beyond a typical time scale defined by the reset parameter.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap

NASA Technical Reports Server (NTRS)

Rapp, R. H.

1981-01-01

Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.

SU-F-207-05: Excess Heat Corrections in a Prototype Calorimeter for Direct Realization of CT Absorbed Dose to Phantom

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

Chen-Mayer, H; Tosh, R

2015-06-15

Purpose: To reconcile air kerma and calorimetry measurements in a prototype calorimeter for obtaining absorbed dose in diagnostic CT beams. While corrections for thermal artifacts are routine and generally small in calorimetry of radiotherapy beams, large differences in relative stopping powers of calorimeter materials at the lower energies typical of CT beams greatly magnify their effects. Work-to-date on the problem attempts to reconcile laboratory measurements with modeling output from Monte Carlo and finite-element analysis of heat transfer. Methods: Small thermistor beads were embedded in a polystyrene (PS) core element of 1 cm diameter, which was inserted into a cylindrical HDPEmore » phantom of 30 cm diameter and subjected to radiation in a diagnostic CT x-ray imaging system. Resistance changes in the thermistors due to radiation heating were monitored via lock-in amplifier. Multiple 3-second exposures were recorded at 8 different dose-rates from the CT system, and least-squares fits to experimental data were compared to an expected thermal response obtained by finite-element analysis incorporating source terms based on semi-empirical modeling and Monte Carlo simulation. Results: Experimental waveforms exhibited large thermal artifacts with fast time constants, associated with excess heat in wires and glass, and smaller steps attributable to radiation heating of the core material. Preliminary finite-element analysis follows the transient component of the signal qualitatively, but predicts a slower decay of temperature spikes. This was supplemented by non-linear least-squares fits incorporating semi-empirical formulae for heat transfer, which were used to obtain dose-to-PS in reasonable agreement with the output of Monte Carlo calculations that converts air kerma to absorbed dose. Conclusion: Discrepancies between the finite-element analysis and our experimental data testify to the very significant heat transfer correction required for absorbed dose calorimetry of diagnostic CT beams. The results obtained here are being used to refine both simulations and design of calorimeter core components.« less

Temperature equilibration rate with Fermi-Dirac statistics.

PubMed

Brown, Lowell S; Singleton, Robert L

2007-12-01

We calculate analytically the electron-ion temperature equilibration rate in a fully ionized, weakly to moderately coupled plasma, using an exact treatment of the Fermi-Dirac electrons. The temperature is sufficiently high so that the quantum-mechanical Born approximation to the scattering is valid. It should be emphasized that we do not build a model of the energy exchange mechanism, but rather, we perform a systematic first principles calculation of the energy exchange. At the heart of this calculation lies the method of dimensional continuation, a technique that we borrow from quantum field theory and use in a different fashion to regulate the kinetic equations in a consistent manner. We can then perform a systematic perturbation expansion and thereby obtain a finite first-principles result to leading and next-to-leading order. Unlike model building, this systematic calculation yields an estimate of its own error and thus prescribes its domain of applicability. The calculational error is small for a weakly to moderately coupled plasma, for which our result is nearly exact. It should also be emphasized that our calculation becomes unreliable for a strongly coupled plasma, where the perturbative expansion that we employ breaks down, and one must then utilize model building and computer simulations. Besides providing different and potentially useful results, we use this calculation as an opportunity to explain the method of dimensional continuation in a pedagogical fashion. Interestingly, in the regime of relevance for many inertial confinement fusion experiments, the degeneracy corrections are comparable in size to the subleading quantum correction below the Born approximation. For consistency, we therefore present this subleading quantum-to-classical transition correction in addition to the degeneracy correction.

Compression failure mechanisms of uni-ply composite plates with a circular cutout

NASA Technical Reports Server (NTRS)

Khamseh, A. R.; Waas, A. M.

1992-01-01

The effect of circular-hole size on the failure mode of uniply graphite-epoxy composite plates is investigated experimentally and analytically for uniaxial compressive loading. The test specimens are sandwiched between polyetherimide plastic for nondestructive evaluations of the uniply failure mechanisms associated with a range of hole sizes. Finite-element modeling based on classical lamination theory is conducted for the corresponding materials and geometries to reproduce the experimental results analytically. The type of compressive failure is found to be a function of hole size, with fiber buckling/kinking at the hole being the dominant failure mechanism for hole diam/plate width ratios exceeding 0.062. The results of the finite-element analysis supported the experimental data for these failure mechanisms and for those corresponding to smaller hole sizes.

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

DOE PAGES

Burgess, C. P.; Holman, R.; Tasinato, G.

2016-01-26

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. Here we adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochasticmore » Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, P(Φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.« less

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

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

Burgess, C. P.; Holman, R.; Tasinato, G.

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. Here we adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochasticmore » Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, P(Φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.« less

Nanoengineering Testbed for Nanosolar Cell and Piezoelectric Compounds

DTIC Science & Technology

2012-02-29

element mesh. The third model was a 3D finite element mesh that included complete geometric representation of Berkovich tip. This model allows for a...height of the specimen. These simulations suggest the proper specimen size to approximate a body of semi-infinite extent for a given indentation depth...tip nanoindentation model was the third and final finite element mesh created for analysis and comparison. The material model and the finite element

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

Development and application of a technique for reducing airframe finite element models for dynamics analysis

NASA Technical Reports Server (NTRS)

Hashemi-Kia, Mostafa; Toossi, Mostafa

1990-01-01

A computational procedure for the reduction of large finite element models was developed. This procedure is used to obtain a significantly reduced model while retaining the essential global dynamic characteristics of the full-size model. This reduction procedure is applied to the airframe finite element model of AH-64A Attack Helicopter. The resulting reduced model is then validated by application to a vibration reduction study.

Finite-size analysis of the detectability limit of the stochastic block model

NASA Astrophysics Data System (ADS)

Young, Jean-Gabriel; Desrosiers, Patrick; Hébert-Dufresne, Laurent; Laurence, Edward; Dubé, Louis J.

2017-06-01

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

CatSim: a new computer assisted tomography simulation environment

NASA Astrophysics Data System (ADS)

De Man, Bruno; Basu, Samit; Chandra, Naveen; Dunham, Bruce; Edic, Peter; Iatrou, Maria; McOlash, Scott; Sainath, Paavana; Shaughnessy, Charlie; Tower, Brendon; Williams, Eugene

2007-03-01

We present a new simulation environment for X-ray computed tomography, called CatSim. CatSim provides a research platform for GE researchers and collaborators to explore new reconstruction algorithms, CT architectures, and X-ray source or detector technologies. The main requirements for this simulator are accurate physics modeling, low computation times, and geometrical flexibility. CatSim allows simulating complex analytic phantoms, such as the FORBILD phantoms, including boxes, ellipsoids, elliptical cylinders, cones, and cut planes. CatSim incorporates polychromaticity, realistic quantum and electronic noise models, finite focal spot size and shape, finite detector cell size, detector cross-talk, detector lag or afterglow, bowtie filtration, finite detector efficiency, non-linear partial volume, scatter (variance-reduced Monte Carlo), and absorbed dose. We present an overview of CatSim along with a number of validation experiments.

Toward transient finite element simulation of thermal deformation of machine tools in real-time

NASA Astrophysics Data System (ADS)

Naumann, Andreas; Ruprecht, Daniel; Wensch, Joerg

2018-01-01

Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit-explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand.

Orbital relaxation effects on Kohn–Sham frontier orbital energies in density functional theory

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

Zhang, DaDi; Zheng, Xiao, E-mail: xz58@ustc.edu.cn; Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026

2015-04-21

We explore effects of orbital relaxation on Kohn–Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn–Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn–Sham frontier orbital energies by Hartree–Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scalingmore » correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.« less

Higher order cumulants in colorless partonic plasma

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

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

Emergence of jams in the generalized totally asymmetric simple exclusion process

NASA Astrophysics Data System (ADS)

Derbyshev, A. E.; Povolotsky, A. M.; Priezzhev, V. B.

2015-02-01

The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014, 10.1088/1742-5468/2012/05/P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter λ controlling the interaction. We study the stationary state correlations, the cluster size distribution, and the large-time fluctuations of integrated particle current. When λ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When λ grows with the system size, so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.

Universality and tails of long-range interactions in one dimension

NASA Astrophysics Data System (ADS)

Valiente, Manuel; Öhberg, Patrik

2017-07-01

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s -wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalization of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalization. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multichannel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation.

PubMed

Xie, Yang; Ying, Jinyong; Xie, Dexuan

2017-03-30

SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a PBE web server. SMPBS is designed with a dynamic, mobile-friendly user interface, and features easily accessible help text, asynchronous data submission, and an interactive, hardware-accelerated molecular visualization viewer based on the 3Dmol.js library. In particular, the viewer allows computed electrostatics to be directly mapped onto an irregular triangular mesh of a molecular surface. Due to this functionality and the fast SMPBE finite element solvers, the web server is very efficient in the calculation and visualization of electrostatics. In addition, SMPBE is reconstructed using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by SMPBE are optimal in the sense of minimizing the objective electrostatic free energy. SMPBS is available at the URL: smpbs.math.uwm.edu © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.

2018-02-01

We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.

The Root Cause of the Overheating Problem

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2017-01-01

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Second look at the spread of epidemics on networks

NASA Astrophysics Data System (ADS)

Kenah, Eben; Robins, James M.

2007-09-01

In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.

Simulation of reflecting surface deviations of centimeter-band parabolic space radiotelescope (SRT) with the large-size mirror

NASA Astrophysics Data System (ADS)

Kotik, A.; Usyukin, V.; Vinogradov, I.; Arkhipov, M.

2017-11-01

he realization of astrophysical researches requires the development of high-sensitive centimeterband parabolic space radiotelescopes (SRT) with the large-size mirrors. Constructively such SRT with the mirror size more than 10 m can be realized as deployable rigid structures. Mesh-structures of such size do not provide the reflector reflecting surface accuracy which is necessary for the centimeter band observations. Now such telescope with the 10 m diameter mirror is developed in Russia in the frame of "SPECTR - R" program. External dimensions of the telescope is more than the size of existing thermo-vacuum chambers used to prove SRT reflecting surface accuracy parameters under the action of space environment factors. That's why the numerical simulation turns out to be the basis required to accept the taken designs. Such modeling should be based on experimental working of the basic constructive materials and elements of the future reflector. In the article computational modeling of reflecting surface deviations of a centimeter-band of a large-sized deployable space reflector at a stage of his orbital functioning is considered. The analysis of the factors that determines the deviations - both determined (temperatures fields) and not-determined (telescope manufacturing and installation faults; the deformations caused by features of composite materials behavior in space) is carried out. The finite-element model and complex of methods are developed. They allow to carry out computational modeling of reflecting surface deviations caused by influence of all factors and to take into account the deviations correction by space vehicle orientation system. The results of modeling for two modes of functioning (orientation at the Sun) SRT are presented.

Vacancies and Vacancy-Mediated Self Diffusion in Cr 2 O 3 : A First-Principles Study

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

Medasani, Bharat; Sushko, Maria L.; Rosso, Kevin M.

Charged and neutral vacancies and vacancy mediated self diffusion in alpha-Cr2O3 were investigated using first principles density functional theory (DFT) and periodic supercell formalism. The vacancy formation energies of charged defects were calculated using the electrostatic finite-size corrections to account for electrostatic interactions between supercells and the corrections for the bandgap underestimation in DFT. Calculations predict that neutral oxygen (O) vacancies are predominant in chromium (Cr)-rich conditions and Cr vacancies with -2 charge state are the dominant defects in O-rich conditions. The charge transition levels of both O and Cr vacancies are deep within the bandgap indicating the stability ofmore » these defects. Transport calculations indicate that vacancy mediated diffusion along the basal plane has lower energy barriers for both O and Cr ions. The most favorable vacancy mediated self diffusion processes correspond to the diffusion of Cr ion in 3+ charge state and O ion in 2- state, respectively. Our calculations reveal that Cr triple defects comprised of Cr in octahedral interstitial sites with two adjacent Cr vacancies along the c-axis have a lower formation energy compared to that of charged Cr vacancies. The formation of such triple defects facilitate Cr self diffusion along the c-axis.« less

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Temperature Scaling Law for Quantum Annealing Optimizers.

PubMed

Albash, Tameem; Martin-Mayor, Victor; Hen, Itay

2017-09-15

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

NASA Technical Reports Server (NTRS)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Finite-Size Effects in Single Chain Magnets: An Experimental and Theoretical Study

NASA Astrophysics Data System (ADS)

Bogani, L.; Caneschi, A.; Fedi, M.; Gatteschi, D.; Massi, M.; Novak, M. A.; Pini, M. G.; Rettori, A.; Sessoli, R.; Vindigni, A.

2004-05-01

The problem of finite-size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co2+-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spin reversal has also been investigated.

Figures of Merit for Magnetic Recording Media

NASA Astrophysics Data System (ADS)

Skomski, Ralph; Sellmyer, D. J.

2007-03-01

Since the first nucleation-field calculations for hard-soft nanostructures with multilayered [1] and arbitrary [2] geometries, exchange-spring magnets have attracted much attention in various areas of magnetism, including magnetic recording. Ultrahigh storage densities correspond to the strong-coupling limit, realized on small length scales and described by volume-averaged anisotropies. Second-order perturbation theory yields finite-size corrections that describe a partial decoupling of the phases. Since soft phases reduce the nucleation field, nanostructuring can be used to reduce the coercivity Hc while maintaining the energy barrier EB. However, the ratio EB/Hc is an ill-defined figure of merit, because the comparison with the Stoner-Wohlfarth model requires the introduction of a particle volume, as contrasted to an area. By using elongated particles with a continuous anisotropy gradient, it is possible to reduce the coercivity by a factor scaling as the bit size divided by the domain-wall width of the hard phase. However, with decreasing bit size this effect becomes less pronounced. In the strong-coupling limit, thermal stability yields a maximum storage density of order γ/kBT, where γ is the domain-wall energy of the hard phase. - This research is supported by NSF MRSEC, INSIC, and NCMN. [1] S. Nieber and H. Kronm"uller, phys. stat. sol. (b) 153, 367 (1989). [2] R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993).

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

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

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

Stochastic properties of radiation-induced DSB: DSB distributions in large scale chromatin loops, the HPRT gene and within the visible volumes of DNA repair foci.

PubMed

Ponomarev, Artem L; Costes, Sylvain V; Cucinotta, Francis A

2008-11-01

We computed probabilities to have multiple double-strand breaks (DSB), which are produced in DNA on a regional scale, and not in close vicinity, in volumes matching the size of DNA damage foci, of a large chromatin loop, and in the physical volume of DNA containing the HPRT (human hypoxanthine phosphoribosyltransferase) locus. The model is based on a Monte Carlo description of DSB formation by heavy ions in the spatial context of the entire human genome contained within the cell nucleus, as well as at the gene sequence level. We showed that a finite physical volume corresponding to a visible DNA repair focus, believed to be associated with one DSB, can contain multiple DSB due to heavy ion track structure and the DNA supercoiled topography. A corrective distribution was introduced, which was a conditional probability to have excess DSB in a focus volume, given that there was already one present. The corrective distribution was calculated for 19.5 MeV/amu N ions, 3.77 MeV/amu alpha-particles, 1000 MeV/amu Fe ions, and X-rays. The corrected initial DSB yield from the experimental data on DNA repair foci was calculated. The DSB yield based on the corrective function converts the focus yield into the DSB yield, which is comparable with the DSB yield based on the earlier PFGE experiments. The distribution of DSB within the physical limits of the HPRT gene was analyzed by a similar method as well. This corrective procedure shows the applicability of the model and empowers the researcher with a tool to better analyze focus statistics. The model enables researchers to analyze the DSB yield based on focus statistics in real experimental situations that lack one-to-one focus-to-DSB correspondance.

Content analysis in information flows

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

Grusho, Alexander A.; Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow; Grusho, Nick A.

The paper deals with architecture of content recognition system. To analyze the problem the stochastic model of content recognition in information flows was built. We proved that under certain conditions it is possible to solve correctly a part of the problem with probability 1, viewing a finite section of the information flow. That means that good architecture consists of two steps. The first step determines correctly certain subsets of contents, while the second step may demand much more time for true decision.

Thin wing corrections for phase-change heat-transfer data.

NASA Technical Reports Server (NTRS)

Hunt, J. L.; Pitts, J. I.

1971-01-01

Since no methods are available for determining the magnitude of the errors incurred when the semiinfinite slab assumption is violated, a computer program was developed to calculate the heat-transfer coefficients to both sides of a finite, one-dimensional slab subject to the boundary conditions ascribed to the phase-change coating technique. The results have been correlated in the form of correction factors to the semiinfinite slab solutions in terms of parameters normally used with the technique.

Effects of Scan Resolutions and Element Sizes on Bovine Vertebral Mechanical Parameters from Quantitative Computed Tomography-Based Finite Element Analysis

PubMed Central

Zhang, Meng; Gao, Jiazi; Huang, Xu; Zhang, Min; Liu, Bei

2017-01-01

Quantitative computed tomography-based finite element analysis (QCT/FEA) has been developed to predict vertebral strength. However, QCT/FEA models may be different with scan resolutions and element sizes. The aim of this study was to explore the effects of scan resolutions and element sizes on QCT/FEA outcomes. Nine bovine vertebral bodies were scanned using the clinical CT scanner and reconstructed from datasets with the two-slice thickness, that is, 0.6 mm (PA resolution) and 1 mm (PB resolution). There were significantly linear correlations between the predicted and measured principal strains (R2 > 0.7, P < 0.0001), and the predicted vertebral strength and stiffness were modestly correlated with the experimental values (R2 > 0.6, P < 0.05). Two different resolutions and six different element sizes were combined in pairs, and finite element (FE) models of bovine vertebral cancellous bones in the 12 cases were obtained. It showed that the mechanical parameters of FE models with the PB resolution were similar to those with the PA resolution. The computational accuracy of FE models with the element sizes of 0.41 × 0.41 × 0.6 mm3 and 0.41 × 0.41 × 1 mm3 was higher by comparing the apparent elastic modulus and yield strength. Therefore, scan resolution and element size should be chosen optimally to improve the accuracy of QCT/FEA. PMID:29065624

Efficient Z gates for quantum computing

NASA Astrophysics Data System (ADS)

McKay, David C.; Wood, Christopher J.; Sheldon, Sarah; Chow, Jerry M.; Gambetta, Jay M.

2017-08-01

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary virtual Z gates, which, combined with two Xπ /2 gates, can generate any SU(2) gate. Here we show how to best utilize these virtual Z gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and Z gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration X and Y gates. Z gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse-shaping techniques such as derivative removal by adiabatic gate (DRAG). We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and Z gates to correct rotation errors realizes a 13.3 ns Xπ /2 gate characterized by low error [1.95 (3 ) ×10-4] and low leakage [3.1 (6 ) ×10-6] . Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders of magnitude smaller than pulse errors due to decoherence.

Elastic collapse in disordered isostatic networks

NASA Astrophysics Data System (ADS)

Moukarzel, C. F.

2012-02-01

Isostatic networks are minimally rigid and therefore have, generically, nonzero elastic moduli. Regular isostatic networks have finite moduli in the limit of large sizes. However, numerical simulations show that all elastic moduli of geometrically disordered isostatic networks go to zero with system size. This holds true for positional as well as for topological disorder. In most cases, elastic moduli decrease as inverse power laws of system size. On directed isostatic networks, however, of which the square and cubic lattices are particular cases, the decrease of the moduli is exponential with size. For these, the observed elastic weakening can be quantitatively described in terms of the multiplicative growth of stresses with system size, giving rise to bulk and shear moduli of order e-bL. The case of sphere packings, which only accept compressive contact forces, is considered separately. It is argued that these have a finite bulk modulus because of specific correlations in contact disorder, introduced by the constraint of compressivity. We discuss why their shear modulus, nevertheless, is again zero for large sizes. A quantitative model is proposed that describes the numerically measured shear modulus, both as a function of the loading angle and system size. In all cases, if a density p>0 of overconstraints is present, as when a packing is deformed by compression or when a glass is outside its isostatic composition window, all asymptotic moduli become finite. For square networks with periodic boundary conditions, these are of order \\sqrt{p} . For directed networks, elastic moduli are of order e-c/p, indicating the existence of an "isostatic length scale" of order 1/p.

Apical stress distribution under vertical compaction of gutta-percha and occlusal loads in canals with varying apical sizes: a three-dimensional finite element analysis.

PubMed

Yuan, K; Niu, C; Xie, Q; Jiang, W; Gao, L; Ma, R; Huang, Z

2018-02-01

To investigate and compare the effects of two apical canal instrumentation protocols on apical stress distribution at the root apex under vertical compaction of gutta-percha and occlusal loads using finite element analysis. Three finite element analysis models of a mandibular first premolar were reconstructed: an original canal model, a size 35, .04 taper apical canal enlargement model and a Lightspeed size 60 apical canal enlargement model. A 15 N compaction force was applied vertically to the gutta-percha 5 mm from the apex. A 175 N occlusal load in two directions (vertical and 45° to the longitudinal axis of the tooth) was simulated. Stresses in the apical 2 mm of the root were calculated and compared among the three models. Under vertical compaction, stresses in the apical canal instrumented by Lightspeed size 60 (maximal 3.3 MPa) were higher than that of the size 35, .04 taper model (maximal 1.3 MPa). In the case of the two occlusal forces, the Lightspeed size 60 apical enlargement was associated with the greatest stress distribution in the apical region. The greatest stress and the most obvious stress difference between the models appeared at the tip of the root when occlusal and vertical compaction loads were applied. Apical enlargement caused stress distribution changes in the apical region of roots. The larger apical size led to higher stress concentration at the root apex. © 2017 International Endodontic Journal. Published by John Wiley & Sons Ltd.

Finite-block-length analysis in classical and quantum information theory.

PubMed

Hayashi, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.

Effects of finite ground plane on the radiation characteristics of a circular patch antenna

NASA Astrophysics Data System (ADS)

Bhattacharyya, Arun K.

1990-02-01

An analytical technique to determine the effects of finite ground plane on the radiation characteristics of a microstrip antenna is presented. The induced currents on the ground plane and on the upper surface of the patch are determined from the discontinuity of the near field produced by the equivalent magnetic current source on the physical aperture of the patch. The radiated fields contributed by the induced current on the ground plane and the equivalent sources on the physical aperture yield the radiation pattern of the antenna. Radiation patterns of the circular patch with finite ground plane size are computed and compared with the experimental data, and the agreement is found to be good. The radiation pattern, directive gain, and input impedance are found to vary widely with the ground plane size.

Finite-block-length analysis in classical and quantum information theory

PubMed Central

HAYASHI, Masahito

2017-01-01

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects. PMID:28302962

Pairing mechanism in Bi-O superconductors: A finite-size chain calculation

NASA Astrophysics Data System (ADS)

Aligia, A. A.; Nuez Regueiro, M. D.; Gagliano, E. R.

1989-09-01

We have studied the pairing mechanism in BiO3 systems by calculating the binding energy of a pair of holes in finite Bi-O chains, for parameters that simulate three-dimensional behavior. In agreement with previous results using perturbation theory in the hopping t, for covalent Bi-O binding and parameters for which the parent compound has a disproportionate ground state, pairing induced by the presence of biexcitons is obtained for sufficiently large interatomic Coulomb repulsion. The analysis of appropriate correlation functions shows a rapid metallization of the system as t and the number of holes increase. This fact shrinks the region of parameters for which the finite-size calculations can be trusted without further study. The same model for other parameters yields pairing in two other regimes: bipolaronic and magnetic excitonic.

Effects of Subscale Size and Shape on Global Energy Dissipation in a Multiscale Model of a Fiber-Reinforced Composite Exhibiting Post-Peak Strain Softening Using Abaqus and FEAMAC

NASA Technical Reports Server (NTRS)

Pineda, Evan, J.; Bednarcyk, Brett, A.; Arnold, Steven, M.

2012-01-01

A mesh objective crack band model is implemented in the generalized method of cells (GMC) micromechanics model to predict failure of a composite repeating unit cell (RUC). The micromechanics calculations are achieved using the MAC/GMC core engine within the ImMAC suite of micromechanics codes, developed at the NASA Glenn Research Center. The microscale RUC is linked to a macroscale Abaqus/Standard finite element model using the FEAMAC multiscale framework (included in the ImMAC suite). The effects of the relationship between the characteristic length of the finite element and the size of the microscale RUC on the total energy dissipation of the multiscale model are investigated. A simple 2-D composite square subjected to uniaxial tension is used to demonstrate the effects of scaling the dimensions of the RUC such that the length of the sides of the RUC are equal to the characteristic length of the finite element. These results are compared to simulations where the size of the RUC is fixed, independent of the element size. Simulations are carried out for a variety of mesh densities and element shapes, including square and triangular. Results indicate that a consistent size and shape must be used to yield preserve energy dissipation across the scales.

Lens correction algorithm based on the see-saw diagram to correct Seidel aberrations employing aspheric surfaces

NASA Astrophysics Data System (ADS)

Rosete-Aguilar, Martha

2000-06-01

In this paper a lens correction algorithm based on the see- saw diagram developed by Burch is described. The see-saw diagram describes the image correction in rotationally symmetric systems over a finite field of view by means of aspherics surfaces. The algorithm is applied to the design of some basic telescopic configurations such as the classical Cassegrain telescope, the Dall-Kirkham telescope, the Pressman-Camichel telescope and the Ritchey-Chretien telescope in order to show a physically visualizable concept of image correction for optical systems that employ aspheric surfaces. By using the see-saw method the student can visualize the different possible configurations of such telescopes as well as their performances and also the student will be able to understand that it is not always possible to correct more primary aberrations by aspherizing more surfaces.

The effect of acetabular cup size on the short-term stability of revision hip arthroplasty: a finite element investigation.

PubMed

Phillips, A T M; Pankaj; Usmani, A S; Howie, C R

2004-01-01

The study uses idealized two-dimensional finite element models to examine the behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique. The behaviour of bone graft was considered in detail, with non-linear elasticity and non-associated plasticity being adopted. Load was applied to the acetabular construct through a femoral head using smooth sliding surfaces. In particular, four models were subjected to two idealized cyclic load cases to investigate the effect of acetabular cup size on the short-term stability of the acetabular construct. The study suggests that benefits may be gained by using the largest practical size of acetabular cup.

Finite Size Effects in Submonolayer Catalysts Investigated by CO Electrosorption on PtsML/Pd(100).

PubMed

Yuan, Qiuyi; Doan, Hieu A; Grabow, Lars C; Brankovic, Stanko R

2017-10-04

A combination of scanning tunneling microscopy, subtractively normalized interfacial Fourier transform infrared spectroscopy (SNIFTIRS), and density functional theory (DFT) is used to quantify the local strain in 2D Pt clusters on the 100 facet of Pd and its effect on CO chemisorption. Good agreement between SNIFTIRS experiments and DFT simulations provide strong evidence that, in the absence of coherent strain between Pt and Pd, finite size effects introduce local compressive strain, which alters the chemisorption properties of the surface. Though this effect has been widely neglected in prior studies, our results suggest that accurate control over cluster sizes in submonolayer catalyst systems can be an effective approach to fine-tune their catalytic properties.

Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Singh, Rajiv R. P.

2015-10-01

We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.

Bacterial finite-size effects for population expansion under flow

NASA Astrophysics Data System (ADS)

Toschi, Federico; Tesser, Francesca; Zeegers, Jos C. H.; Clercx, Herman J. H.; Brunsveld, Luc

2016-11-01

For organisms living in a liquid ecosystem, flow and flow gradients have a dual role as they transport nutrient while, at the same time, dispersing the individuals. In absence of flow and under homogeneous conditions, the growth of a population towards an empty region is usually described by a reaction-diffusion equation. The effect of fluid flow is not yet well understood and the interplay between transport of individuals and growth opens a wide scenario of possible behaviors. In this work, we study experimentally the dynamics of non-motile E. coli bacteria colonies spreading inside rectangular channels, in PDMS microfluidic devices. By use of a fluorescent microscope we analyze the dynamics of the population density subjected to different co- and counter-flow conditions and shear rates. A simple model incorporating growth, dispersion and drift of finite size beads is able to explain the experimental findings. This indicates that models based on the Fisher-Kolmogorov-Petrovsky-Piscounov equation (FKPP) may have to be supplemented with bacterial finite-size effects in order to be able to accurately reproduce experimental results for population spatial growth.