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.

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.

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.

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.

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.

Interfacial ion solvation: Obtaining the thermodynamic limit from molecular simulations

NASA Astrophysics Data System (ADS)

Cox, Stephen J.; Geissler, Phillip L.

2018-06-01

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting finite size effects can be substantial and may attenuate very slowly with increasing system size, as shown by previous work on dilute ions in bulk aqueous solution. Here we examine corrections for such effects, with an emphasis on solvation near interfaces. Our central assumption follows the perspective of Hünenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]: Long-wavelength solvent response underlying finite size effects should be well described by reduced models like dielectric continuum theory, whose size dependence can be calculated straightforwardly. Applied to an ion in a periodic slab of liquid coexisting with vapor, this approach yields a finite size correction for solvation free energies that differs in important ways from results previously derived for bulk solution. For a model polar solvent, we show that this new correction quantitatively accounts for the variation of solvation free energy with volume and aspect ratio of the simulation cell. Correcting periodic slab results for an aqueous system requires an additional accounting for the solvent's intrinsic charge asymmetry, which shifts electric potentials in a size-dependent manner. The accuracy of these finite size corrections establishes a simple method for a posteriori extrapolation to the thermodynamic limit and also underscores the realism of dielectric continuum theory down to the nanometer scale.

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.

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.

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.

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

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.

Finite Size Corrections to the Parisi Overlap Function in the GREM

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2018-01-01

We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use replicas, but shed some light on what the replica method should give for finite size corrections. In the gradual freezing situation, which is known to exhibit full replica symmetry breaking, we show that the finite size corrections lead to a modification of the simple relations between the sample averages of the overlaps Y_k between k configurations predicted by replica theory. This can be interpreted as fluctuations in the replica block size with a negative variance. The mechanism is similar to the one we found recently in the random energy model in Derrida and Mottishaw (J Stat Mech 2015(1): P01021, 2015). We also consider a simultaneous freezing situation, which is known to exhibit one step replica symmetry breaking. We show that finite size corrections lead to full replica symmetry breaking and give a more complete derivation of the results presented in Derrida and Mottishaw (Europhys Lett 115(4): 40005, 2016) for the directed polymer on a tree.

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.

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

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.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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.

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.

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.

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 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.

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

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-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.

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.

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.

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.

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

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.

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

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.

75 FR 48815 - Medicaid Program and Children's Health Insurance Program (CHIP); Revisions to the Medicaid...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-11

... size may be reduced by the finite population correction factor. The finite population correction is a statistical formula utilized to determine sample size where the population is considered finite rather than... program may notify us and the annual sample size will be reduced by the finite population correction...

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.

Rotational Diffusion Depends on Box Size in Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-06-07

We show that the rotational dynamics of proteins and nucleic acids determined from molecular dynamics simulations under periodic boundary conditions suffer from significant finite-size effects. We remove the box-size dependence of the rotational diffusion coefficients by adding a hydrodynamic correction k B T/6 ηV with k B Boltzmann's constant, T the absolute temperature, η the solvent shear viscosity, and V the box volume. We show that this correction accounts for the finite-size dependence of the rotational diffusion coefficients of horse-heart myoglobin and a B-DNA dodecamer in aqueous solution. The resulting hydrodynamic radii are in excellent agreement with experiment.

Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method

NASA Astrophysics Data System (ADS)

Chen, Feier; Tian, Kang; Ding, Xiaoxu; Miao, Yuqi; Lu, Chunxia

2016-11-01

Analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation. The multifractal detrended fluctuation analysis technique is employed to analyze the time series of Baltic Dry Bulk Freight Rate Index and the market trend of two bulk ship sizes, namely Capesize and Panamax for the period: March 1st 1999-February 26th 2015. In this paper, the degree of the multifractality with different fluctuation sizes is calculated. Besides, multifractal detrending moving average (MF-DMA) counting technique has been developed to quantify the components of multifractal spectrum with the finite-size effect taken into consideration. Numerical results show that both Capesize and Panamax freight rate index time series are of multifractal nature. The origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation.

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.

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

NASA Astrophysics Data System (ADS)

Xun, Zhi-Peng; Tang, Gang; Han, Kui; Hao, Da-Peng; Xia, Hui; Zhou, Wei; Yang, Xi-Quan; Wen, Rong-Ji; Chen, Yu-Ling

2010-07-01

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

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.

Effect of grid transparency and finite collector size on determining ion temperature and density by the retarding potential analyzer

NASA Technical Reports Server (NTRS)

Troy, B. E., Jr.; Maier, E. J.

1975-01-01

The effects of the grid transparency and finite collector size on the values of thermal ion density and temperature determined by the standard RPA (retarding potential analyzer) analysis method are investigated. The current-voltage curves calculated for varying RPA parameters and a given ion mass, temperature, and density are analyzed by the standard RPA method. It is found that only small errors in temperature and density are introduced for an RPA with typical dimensions, and that even when the density error is substantial for nontypical dimensions, the temperature error remains minimum.

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.

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.

Deleterious mutations and selection for sex in finite diploid populations.

PubMed

Roze, Denis; Michod, Richard E

2010-04-01

In diploid populations, indirect benefits of sex may stem from segregation and recombination. Although it has been recognized that finite population size is an important component of selection for recombination, its effects on selection for segregation have been somewhat less studied. In this article, we develop analytical two- and three-locus models to study the effect of recurrent deleterious mutations on a modifier gene increasing sex, in a finite diploid population. The model also incorporates effects of mitotic recombination, causing loss of heterozygosity (LOH). Predictions are tested using multilocus simulations representing deleterious mutations occurring at a large number of loci. The model and simulations show that excess of heterozygosity generated by finite population size is an important component of selection for sex, favoring segregation when deleterious alleles are nearly additive to dominant. Furthermore, sex tends to break correlations in homozygosity among selected loci, which disfavors sex when deleterious alleles are either recessive or dominant. As a result, we find that it is difficult to maintain costly sex when deleterious alleles are recessive. LOH tends to favor sex when deleterious mutations are recessive, but the effect is relatively weak for rates of LOH corresponding to current estimates (of the order 10(-4)-10(-5)).

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.

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.

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

Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Relefors, Johan

2017-12-01

We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

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.

Recurrence time statistics for finite size intervals

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; da Silva, Elton C.; Caldas, Iberê L.

2004-12-01

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincaré recurrence time statistics.

Linkage Disequilibrium in a Finite Population That Is Partially Selfing

PubMed Central

Golding, G. B.; Strobeck, C.

1980-01-01

The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size Ne = (1-½S)N and the effective recombination value re = (1-S)r/(1-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value. Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1-½S and the recombination value by a factor (1-S)/(1-½S). PMID:17249017

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.

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.

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

NASA Astrophysics Data System (ADS)

Rajni, Kumar, Prashant

2017-10-01

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

Stochastic gain in finite populations

NASA Astrophysics Data System (ADS)

Röhl, Torsten; Traulsen, Arne; Claussen, Jens Christian; Schuster, Heinz Georg

2008-08-01

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen , Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

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.

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.

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.

The nuclear size and mass effects on muonic hydrogen-like atoms embedded in Debye plasma

NASA Astrophysics Data System (ADS)

Poszwa, A.; Bahar, M. K.; Soylu, A.

2016-10-01

Effects of finite nuclear size and finite nuclear mass are investigated for muonic atoms and muonic ions embedded in the Debye plasma. Both nuclear charge radii and nuclear masses are taken into account with experimentally determined values. In particular, isotope shifts of bound state energies, radial probability densities, transition energies, and binding energies for several atoms are studied as functions of Debye length. The theoretical model based on semianalytical calculations, the Sturmian expansion method, and the perturbative approach has been constructed, in the nonrelativistic frame. For some limiting cases, the comparison with previous most accurate literature results has been made.

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.

Effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter

NASA Technical Reports Server (NTRS)

Ko, William L.; Olona, Timothy

1987-01-01

The effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter was investigated. Several structural performance and resizing (SPAR) thermal models and NASA structural analysis (NASTRAN) structural models were set up for the orbiter wing midspan bay 3. The thermal model was found to be the one that determines the limit of finite-element fineness because of the limitation of computational core space required for the radiation view factor calculations. The thermal stresses were found to be extremely sensitive to a slight variation of structural temperature distributions. The minimum degree of element fineness required for the thermal model to yield reasonably accurate solutions was established. The radiation view factor computation time was found to be insignificant compared with the total computer time required for the SPAR transient heat transfer analysis.

Bounds on quantum confinement effects in metal nanoparticles

NASA Astrophysics Data System (ADS)

Blackman, G. Neal; Genov, Dentcho A.

2018-03-01

Quantum size effects on the permittivity of metal nanoparticles are investigated using the quantum box model. Explicit upper and lower bounds are derived for the permittivity and relaxation rates due to quantum confinement effects. These bounds are verified numerically, and the size dependence and frequency dependence of the empirical Drude size parameter is extracted from the model. Results suggest that the common practice of empirically modifying the dielectric function can lead to inaccurate predictions for highly uniform distributions of finite-sized particles.

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

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.

Practical performance of real-time shot-noise measurement in continuous-variable quantum key distribution

NASA Astrophysics Data System (ADS)

Wang, Tao; Huang, Peng; Zhou, Yingming; Liu, Weiqi; Zeng, Guihua

2018-01-01

In a practical continuous-variable quantum key distribution (CVQKD) system, real-time shot-noise measurement (RTSNM) is an essential procedure for preventing the eavesdropper exploiting the practical security loopholes. However, the performance of this procedure itself is not analyzed under the real-world condition. Therefore, we indicate the RTSNM practical performance and investigate its effects on the CVQKD system. In particular, due to the finite-size effect, the shot-noise measurement at the receiver's side may decrease the precision of parameter estimation and consequently result in a tight security bound. To mitigate that, we optimize the block size for RTSNM under the ensemble size limitation to maximize the secure key rate. Moreover, the effect of finite dynamics of amplitude modulator in this scheme is studied and its mitigation method is also proposed. Our work indicates the practical performance of RTSNM and provides the real secret key rate under it.

Effects of Pore Distributions on Ductility of Thin-Walled High Pressure Die-Cast Magnesium

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

Choi, Kyoo Sil; Li, Dongsheng; Sun, Xin

2013-06-01

In this paper, a microstructure-based three-dimensional (3D) finite element modeling method is adopted to investigate the effects of porosity in thin-walled high pressure die-cast (HPDC) Magnesium alloys on their ductility. For this purpose, the cross-sections of AM60 casting samples are first examined using optical microscope and X-ray tomography to obtain the general information on the pore distribution features. The experimentally observed pore distribution features are then used to generate a series of synthetic microstructure-based 3D finite element models with different pore volume fractions and pore distribution features. Shear and ductile damage models are adopted in the finite element analyses tomore » induce the fracture by element removal, leading to the prediction of ductility. The results in this study show that the ductility monotonically decreases as the pore volume fraction increases and that the effect of ‘skin region’ on the ductility is noticeable under the condition of same local pore volume fraction in the center region of the sample and its existence can be beneficial for the improvement of ductility. The further synthetic microstructure-based 3D finite element analyses are planned to investigate the effects of pore size and pore size distribution.« less

Chiral crossover transition in a finite volume

NASA Astrophysics Data System (ADS)

Shi, Chao; Jia, Wenbao; Sun, An; Zhang, Liping; Zong, Hongshi

2018-02-01

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature {T}{{c}} of the crossover, showing a significant decrease in {T}{{c}} as L decreases below 3 fm. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

NASA Astrophysics Data System (ADS)

Nemoto, Takahiro; Jack, Robert L.; Lecomte, Vivien

2017-03-01

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

Size Dependence of Residual Thermal Stresses in Micro Multilayer Ceramic Capacitors by Using Finite Element Unit Cell Model Including Strain Gradient Effect

NASA Astrophysics Data System (ADS)

Jiang, W. G.; Xiong, C. A.; Wu, X. G.

2013-11-01

The residual thermal stresses induced by the high-temperature sintering process in multilayer ceramic capacitors (MLCCs) are investigated by using a finite-element unit cell model, in which the strain gradient effect is considered. The numerical results show that the residual thermal stresses depend on the lateral margin length, the thickness ratio of the dielectrics layer to the electrode layer, and the MLCC size. At a given thickness ratio, as the MLCC size is scaled down, the peak shear stress reduces significantly and the normal stresses along the length and thickness directions change slightly with the decrease in the ceramic layer thickness t d as t d > 1 μm, but as t d < 1 μm, the normal stress components increase sharply with the increase in t d. Thus, the residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices

Finite-size effects in transcript sequencing count distribution: its power-law correction necessarily precedes downstream normalization and comparative analysis.

PubMed

Wong, Wing-Cheong; Ng, Hong-Kiat; Tantoso, Erwin; Soong, Richie; Eisenhaber, Frank

2018-02-12

Though earlier works on modelling transcript abundance from vertebrates to lower eukaroytes have specifically singled out the Zip's law, the observed distributions often deviate from a single power-law slope. In hindsight, while power-laws of critical phenomena are derived asymptotically under the conditions of infinite observations, real world observations are finite where the finite-size effects will set in to force a power-law distribution into an exponential decay and consequently, manifests as a curvature (i.e., varying exponent values) in a log-log plot. If transcript abundance is truly power-law distributed, the varying exponent signifies changing mathematical moments (e.g., mean, variance) and creates heteroskedasticity which compromises statistical rigor in analysis. The impact of this deviation from the asymptotic power-law on sequencing count data has never truly been examined and quantified. The anecdotal description of transcript abundance being almost Zipf's law-like distributed can be conceptualized as the imperfect mathematical rendition of the Pareto power-law distribution when subjected to the finite-size effects in the real world; This is regardless of the advancement in sequencing technology since sampling is finite in practice. Our conceptualization agrees well with our empirical analysis of two modern day NGS (Next-generation sequencing) datasets: an in-house generated dilution miRNA study of two gastric cancer cell lines (NUGC3 and AGS) and a publicly available spike-in miRNA data; Firstly, the finite-size effects causes the deviations of sequencing count data from Zipf's law and issues of reproducibility in sequencing experiments. Secondly, it manifests as heteroskedasticity among experimental replicates to bring about statistical woes. Surprisingly, a straightforward power-law correction that restores the distribution distortion to a single exponent value can dramatically reduce data heteroskedasticity to invoke an instant increase in signal-to-noise ratio by 50% and the statistical/detection sensitivity by as high as 30% regardless of the downstream mapping and normalization methods. Most importantly, the power-law correction improves concordance in significant calls among different normalization methods of a data series averagely by 22%. When presented with a higher sequence depth (4 times difference), the improvement in concordance is asymmetrical (32% for the higher sequencing depth instance versus 13% for the lower instance) and demonstrates that the simple power-law correction can increase significant detection with higher sequencing depths. Finally, the correction dramatically enhances the statistical conclusions and eludes the metastasis potential of the NUGC3 cell line against AGS of our dilution analysis. The finite-size effects due to undersampling generally plagues transcript count data with reproducibility issues but can be minimized through a simple power-law correction of the count distribution. This distribution correction has direct implication on the biological interpretation of the study and the rigor of the scientific findings. This article was reviewed by Oliviero Carugo, Thomas Dandekar and Sandor Pongor.

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

Effect of dislocation pile-up on size-dependent yield strength in finite single-crystal micro-samples

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

Pan, Bo; Shibutani, Yoji, E-mail: sibutani@mech.eng.osaka-u.ac.jp; Zhang, Xu

2015-07-07

Recent research has explained that the steeply increasing yield strength in metals depends on decreasing sample size. In this work, we derive a statistical physical model of the yield strength of finite single-crystal micro-pillars that depends on single-ended dislocation pile-up inside the micro-pillars. We show that this size effect can be explained almost completely by considering the stochastic lengths of the dislocation source and the dislocation pile-up length in the single-crystal micro-pillars. The Hall–Petch-type relation holds even in a microscale single-crystal, which is characterized by its dislocation source lengths. Our quantitative conclusions suggest that the number of dislocation sources andmore » pile-ups are significant factors for the size effect. They also indicate that starvation of dislocation sources is another reason for the size effect. Moreover, we investigated the explicit relationship between the stacking fault energy and the dislocation “pile-up” effect inside the sample: materials with low stacking fault energy exhibit an obvious dislocation pile-up effect. Our proposed physical model predicts a sample strength that agrees well with experimental data, and our model can give a more precise prediction than the current single arm source model, especially for materials with low stacking fault energy.« less

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

NASA Astrophysics Data System (ADS)

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.

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.

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.

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.

Robustness of topological Hall effect of nontrivial spin textures

NASA Astrophysics Data System (ADS)

Jalil, Mansoor B. A.; Tan, Seng Ghee

2014-05-01

We analyze the topological Hall conductivity (THC) of topologically nontrivial spin textures like magnetic vortices and skyrmions and investigate its possible application in the readback for magnetic memory based on those spin textures. Under adiabatic conditions, such spin textures would theoretically yield quantized THC values, which are related to topological invariants such as the winding number and polarity, and as such are insensitive to fluctuations and smooth deformations. However, in a practical setting, the finite size of spin texture elements and the influence of edges may cause them to deviate from their ideal configurations. We calculate the degree of robustness of the THC output in practical magnetic memories in the presence of edge and finite size effects.

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.

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

Effects of finite spatial resolution on quantitative CBF images from dynamic PET

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

Phelps, M.E.; Huang, S.C.; Mahoney, D.K.

1985-05-01

The finite spatial resolution of PET causes the time-activity responses on pixels around the boundaries between gray and white matter regions to contain kinetic components from tissues of different CBF's. CBF values estimated from kinetics of such mixtures are underestimated because of the nonlinear relationship between the time-activity response and the estimated CBF. Computer simulation is used to investigate these effects on phantoms of circular structures and realistic brain slice in terms of object size and quantitative CBF values. The CBF image calculated is compared to the case of having resolution loss alone. Results show that the size of amore » high flow region in the CBF image is decreased while that of a low flow region is increased. For brain phantoms, the qualitative appearance of CBF images is not seriously affected, but the estimated CBF's are underestimated by 11 to 16 percent in local gray matter regions (of size 1 cm/sup 2/) with about 14 percent reduction in global CBF over the whole slice. It is concluded that the combined effect of finite spatial resolution and the nonlinearity in estimating CBF from dynamic PET is quite significant and must be considered in processing and interpreting quantitative CBF images.« less

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.

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.

The ensemble switch method for computing interfacial tensions

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

Schmitz, Fabian; Virnau, Peter

2015-04-14

We present a systematic thermodynamic integration approach to compute interfacial tensions for solid-liquid interfaces, which is based on the ensemble switch method. Applying Monte Carlo simulations and finite-size scaling techniques, we obtain results for hard spheres, which are in agreement with previous computations. The case of solid-liquid interfaces in a variant of the effective Asakura-Oosawa model and of liquid-vapor interfaces in the Lennard-Jones model are discussed as well. We demonstrate that a thorough finite-size analysis of the simulation data is required to obtain precise results for the interfacial tension.

Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1988-01-01

A scattering model for defoliated vegetation is developed by treating a layer of defoliated vegetation as a collection of randomly oriented dielectric cylinders of finite length over an irregular ground surface. Both polarized and depolarized backscattering are computed and their behavior versus the volume fraction, the incidence angle, the frequency, the angular distribution and the cylinder size are illustrated. It is found that both the angular distribution and the cylinder size have significant effects on the backscattered signal. The present theory is compared with measurements from defoliated vegetations.

Cortical bone fracture analysis using XFEM - case study.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2017-04-01

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Anomalous finite-size effects in the Battle of the Sexes

NASA Astrophysics Data System (ADS)

Cremer, J.; Reichenbach, T.; Frey, E.

2008-06-01

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.

The effects of CuO particle size on microstructure evolution of AgCuO compo-sites in plastic deformation process: finite element simulation and experimental study

NASA Astrophysics Data System (ADS)

Li, Zhiguo; Cao, Hanxing; Zhou, Xiaolong; Zhou, Zhaobo; Cao, Jianchun

2018-04-01

The effects of CuO with different particle sizes on the microstructure evolution of AgCuO composite material during plastic deformation process were investigated by finite element (FE) analysis and experiment. The results are as follows: with the decrease of CuO particle size, the degree of radial compression and axial elongation of CuO particle cluster increase gradually, as well as the dispersion of CuO also increase. Meanwhile, the shape of CuO particles is constantly transformed from polygonal to fibrous, which makes the number of linear fibrous CuO increase continuously while bent fibrous CuO reduce gradually. By comparing the simulation and experiment results we find that there are four different typical microstructure regions, which caused by the interaction between monoclinic and cubic CuO during the extrusion process.

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.

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

PubMed

Sato, Y; Teixeira, E R; Tsuga, K; Shindoi, N

1999-08-01

More validity of finite element analysis (FEA) in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To evaluate the effectiveness of a new algorithm established for more valid FEA model construction without downsizing, three-dimensional FEA bone trabeculae models with different element sizes (300, 150 and 75 micron) were constructed. Four algorithms of stepwise (1 to 4 ranks) assignment of Young's modulus accorded with bone volume in the individual cubic element was used and then stress distribution against vertical loading was analysed. The model with 300 micron element size, with 4 ranks of Young's moduli accorded with bone volume in each element presented similar stress distribution to the model with the 75 micron element size. These results show that the new algorithm was effective, and the use of the 300 micron element for bone trabeculae representation was proposed, without critical changes in stress values and for possible savings on computer memory and calculation time in the laboratory.

Finite-Size Effects on the Behavior of the Susceptibility in van der Waals Films Bounded by Strongly Absorbing Substrates

NASA Technical Reports Server (NTRS)

Dantchev, Daniel; Rudnick, Joseph; Barmatz, M.

2007-01-01

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of 3He and 4He films in the vicinity of their respective liquid-vapor critical points.

Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings

NASA Astrophysics Data System (ADS)

Azadi, Sam; Kühne, T. D.

2018-05-01

The magnitude of finite-size effects and Coulomb interactions in quantum Monte Carlo simulations of van der Waals interactions between weakly bonded benzene molecules are investigated. To that extent, two trial wave functions of the Slater-Jastrow and Backflow-Slater-Jastrow types are employed to calculate the energy-volume equation of state. We assess the impact of the backflow coordinate transformation on the nonlocal correlation energy. We found that the effect of finite-size errors in quantum Monte Carlo calculations on energy differences is particularly large and may even be more important than the employed trial wave function. In addition to the cohesive energy, the singlet excitonic energy gap and the energy gap renormalization of crystalline benzene at different densities are computed.

Electrokinetic mixing at high zeta potentials: ionic size effects on cross stream diffusion.

PubMed

Ahmadian Yazdi, Alireza; Sadeghi, Arman; Saidi, Mohammad Hassan

2015-03-15

The electrokinetic phenomena at high zeta potentials may show several unique features which are not normally observed. One of these features is the ionic size (steric) effect associated with the solutions of high ionic concentration. In the present work, attention is given to the influences of finite ionic size on the cross stream diffusion process in an electrokinetically actuated Y-shaped micromixer. The method consists of a finite difference based numerical approach for non-uniform grid which is applied to the dimensionless form of the governing equations, including the modified Poisson-Boltzmann equation. The results reveal that, neglecting the ionic size at high zeta potentials gives rise to the overestimation of the mixing length, because the steric effects retard liquid flow, thereby enhancing the mixing efficiency. The importance of steric effects is found to be more intense for channels of smaller width to height ratio. It is also observed that, in sharp contrast to the conditions that the ions are treated as point charges, increasing the zeta potential improves the cross stream diffusion when incorporating the ionic size. Moreover, increasing the EDL thickness decreases the mixing length, whereas the opposite is true for the channel aspect ratio. Copyright © 2014 Elsevier Inc. All rights reserved.

Effect of vehicular size on chain-reaction crash

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2015-11-01

We present the dynamic model of the chain-reaction crash to take account of the vehicular size. Drivers brake according to taillights of the forward vehicle. We investigate the effect of the vehicular size on the chain-reaction crash (multiple-vehicle collision) in the traffic flow controlled by taillights. In the multiple-vehicle collision, the first crash induces more collisions. We investigate how the first collision induces the chain-reaction crash numerically. We derive, analytically, the transition points and the region maps for the chain-reaction crash in the traffic flow of vehicles with finite sizes. We clarify the effect of the vehicular size on the multiple-vehicle collision.

Polymer loaded microemulsions: Changeover from finite size effects to interfacial interactions

NASA Astrophysics Data System (ADS)

Kuttich, B.; Ivanova, O.; Grillo, I.; Stühn, B.

2016-10-01

Form fluctuations of microemulsion droplets are observed in experiments using dielectric spectroscopy (DS) and neutron spin echo spectroscopy (NSE). Previous work on dioctyl sodium sulfosuccinate based water in oil microemulsions in the droplet phase has shown that adding a water soluble polymer (Polyethylene glycol M = 1500 g mol-1) modifies these fluctuations. While for small droplet sizes (water core radius rc < 37 Å) compared to the size of the polymer both methods consistently showed a reduction in the bending modulus of the surfactant shell as a result of polymer addition, dielectric spectroscopy suggests the opposite behaviour for large droplets. This observation is now confirmed by NSE experiments on large droplets. Structural changes due to polymer addition are qualitatively independent of droplet size. Dynamical properties, however, display a clear variation with the number of polymer chains per droplet, leading to the observed changes in the bending modulus. Furthermore, the contribution of structural and dynamical properties on the changes in bending modulus shifts in weight. With increasing droplet size, we initially find dominating finite size effects and a changeover to a system, where interactions between the confined polymer and the surfactant shell dominate the bending modulus.

Characterizing the surface charge of synthetic nanomembranes by the streaming potential method

PubMed Central

Datta, Subhra; Conlisk, A. T.; Kanani, Dharmesh M.; Zydney, Andrew L.; Fissell, William H.; Roy, Shuvo

2010-01-01

The inference of the surface charge of polyethylene glycol (PEG)-coated and uncoated silicon membranes with nanoscale pore sizes from streaming potential measurements in the presence of finite electric double layer (EDL) effects is studied theoretically and experimentally. The developed theoretical model for inferring the pore wall surface charge density from streaming potential measurements is applicable to arbitrary pore cross-sectional shapes and accounts for the effect of finite salt concentration on the ionic mobilities and the thickness of the deposited layer of PEG. Theoretical interpretation of the streaming potential data collected from silicon membranes having nanoscale pore sizes, with/without pore wall surface modification with PEG, indicates that finite electric double layer (EDL) effects in the pore-confined electrolyte significantly affect the interpretation of the membrane charge and that surface modification with PEG leads to a reduction in the pore wall surface charge density. The theoretical model is also used to study the relative significance of the following uniquely nanoscale factors affecting the interpretation of streaming potential in moderate to strongly charged pores: altered net charge convection by applied pressure differentials, surface-charge effects on ionic conduction, and electroosmotic convection of charges. PMID:20462592

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

NASA Technical Reports Server (NTRS)

Watson, W. R.

1977-01-01

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

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.

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

Saha, Sourabh K.

Although geometric imperfections have a detrimental effect on buckling, imperfection sensitivity has not been well studied in the past during design of sinusoidal micro and nano-scale structures via wrinkling of supported thin films. This is likely because one is more interested in predicting the shape/size of the resultant patterns than the buckling bifurcation onset strain during fabrication of such wrinkled structures. Herein, I have demonstrated that even modest geometric imperfections alter the final wrinkled mode shapes via the mode locking phenomenon wherein the imperfection mode grows in exclusion to the natural mode of the system. To study the effect ofmore » imperfections on mode locking, I have (i) developed a finite element mesh perturbation scheme to generate arbitrary geometric imperfections in the system and (ii) performed a parametric study via finite element methods to link the amplitude and period of the sinusoidal imperfections to the observed wrinkle mode shape and size. Based on this, a non-dimensional geometric parameter has been identified that characterizes the effect of imperfection on the mode locking phenomenon – the equivalent imperfection size. An upper limit for this equivalent imperfection size has been identified via a combination of analytical and finite element modeling. During compression of supported thin films, the system gets “locked” into the imperfection mode if its equivalent imperfection size is above this critical limit. For the polydimethylsiloxane/glass bilayer with a wrinkle period of 2 µm, this mode lock-in limit corresponds to an imperfection amplitude of 32 nm for an imperfection period of 5 µm and 8 nm for an imperfection period of 0.8 µm. Interestingly, when the non-dimensional critical imperfection size is scaled by the bifurcation onset strain, the scaled critical size depends solely on the ratio of the imperfection to natural periods. Furthermore, the computational data generated here can be generalized beyond the specific natural periods and bilayer systems studied to enable deterministic design of a variety of wrinkled micro and nano-scale structures.« less

A model to study finite-size and magnetic effects on the phase transition of a fermion interacting system

NASA Astrophysics Data System (ADS)

Corrêa, Emerson B. S.; Linhares, César A.; Malbouisson, Adolfo P. C.

2018-03-01

We present a model to study the effects from external magnetic field, chemical potential and finite size on the phase structures of a massive four- and six-fermion interacting systems. These effects are introduced by a method of compactification of coordinates, a generalization of the standard Matsubara prescription. Through the compactification of the z-coordinate and of imaginary time, we describe a heated system with the shape of a film of thickness L, at temperature β-1 undergoing first- or second-order phase transition. We have found a strong dependence of the temperature transition on the coupling constants λ and η. Besides inverse magnetic catalysis and symmetry breaking for both kinds of transition, we have found an inverse symmetry breaking phenomenon with respect to first-order phase transition.

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

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.

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.

Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process

PubMed Central

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

2016-01-01

The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary. PMID:27584596

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

NASA Astrophysics Data System (ADS)

Costa, Pedro; Picano, Francesco; Brandt, Luca; Breugem, Wim-Paul

2018-05-01

We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (PRL 117, 134501), a particle-wall layer is responsible for deviations of the statistics from what is observed in the continuum limit where the suspension is modeled as a Newtonian fluid with an effective viscosity. Here we investigate the fluid and particle dynamics in this layer and in the bulk. In the particle-wall layer, the near wall inhomogeneity has an influence on the suspension micro-structure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the flow scaling laws in to second-order Eulerian statistics in the homogeneous suspension region away from the wall. Finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that 1-point dispersion is dominated by particle-turbulence (and not particle-particle) interactions, while differences in 2-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.

A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

PubMed Central

Baity-Jesi, Marco; Calore, Enrico; Cruz, Andres; Fernandez, Luis Antonio; Gil-Narvión, José Miguel; Gordillo-Guerrero, Antonio; Iñiguez, David; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor; Monforte-Garcia, Jorge; Muñoz Sudupe, Antonio; Navarro, Denis; Parisi, Giorgio; Perez-Gaviro, Sergio; Ricci-Tersenghi, Federico; Ruiz-Lorenzo, Juan Jesus; Schifano, Sebastiano Fabio; Tarancón, Alfonso; Tripiccione, Raffaele; Yllanes, David

2017-01-01

We have performed a very accurate computation of the nonequilibrium fluctuation–dissipation ratio for the 3D Edwards–Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes. PMID:28174274

A combined molecular dynamics/micromechanics/finite element approach for multiscale constitutive modeling of nanocomposites with interface effects

NASA Astrophysics Data System (ADS)

Yang, B. J.; Shin, H.; Lee, H. K.; Kim, H.

2013-12-01

We introduce a multiscale framework based on molecular dynamic (MD) simulation, micromechanics, and finite element method (FEM). A micromechanical model, which considers influences of the interface properties, nanoparticle (NP) size, and microcracks, is developed. Then, we perform MD simulations to characterize the mechanical properties of the nanocomposite system (silica/nylon 6) with varying volume fraction and size of NPs. By comparing the MD with micromechanics results, intrinsic physical properties at interfacial region are derived. Finally, we implement the developed model in the FEM code with the derived interfacial parameters, and predict the mechanical behavior of the nanocomposite at the macroscopic scale.

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

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.

Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical self-avoiding polygons.

PubMed

Shimamura, Miyuki K; Deguchi, Tetsuo

2002-05-01

Several nontrivial properties are shown for the mean-square radius of gyration R2(K) of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite size and asymptotic behaviors of the gyration radius under the topological constraint for self-avoiding polygons consisting of N cylindrical segments with radius r. We find that the average size of ring polymers with the knot K can be much larger than that of no topological constraint. The effective expansion due to the topological constraint depends strongly on the parameter r that is related to the excluded volume. The topological expansion is particularly significant for the small r case, where the simulation result is associated with that of random polygons with the knot K.

A computational study of coherent structures in the wakes of two-dimensional bluff bodies

NASA Astrophysics Data System (ADS)

Pearce, Jeffrey Alan

1988-08-01

The periodic shedding of vortices from bluff bodies was first recognized in the late 1800's. Currently, there is great interest concerning the effect of vortex shedding on structures and on vehicle stability. In the design of bluff structures which will be exposed to a flow, knowledge of the shedding frequency and the amplitude of the aerodynamic forces is critical. The ability to computationally predict parameters associated with periodic vortex shedding is thus a valuable tool. In this study, the periodic shedding of vortices from several bluff body geometries is predicted. The study is conducted with a two-dimensional finite-difference code employed on various grid sizes. The effects of the grid size and time step on the accuracy of the solution are addressed. Strouhal numbers and aerodynamic force coefficients are computed for all of the bodies considered and compared with previous experimental results. Results indicate that the finite-difference code is capable of predicting periodic vortex shedding for all of the geometries tested. Refinement of the finite-difference grid was found to give little improvement in the prediction; however, the choice of time step size was shown to be critical. Predictions of Strouhal numbers were generally accurate, and the calculated aerodynamic forces generally exhibited behavior consistent with previous studies.

Tapered holey fibers for spot-size and numerical-aperture conversion.

PubMed

Town, G E; Lizier, J T

2001-07-15

Adiabatically tapered holey fibers are shown to be potentially useful for guided-wave spot-size and numerical-aperture conversion. Conditions for adiabaticity and design guidelines are provided in terms of the effective-index model. We also present finite-difference time-domain calculations of downtapered holey fiber, showing that large spot-size conversion factors are obtainable with minimal loss by use of short, optimally shaped tapers.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

PubMed

Bonfiglio, Paolo; Pompoli, Francesco; Lionti, Riccardo

2016-04-01

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

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

Anomalous group velocity at the high energy range of real 3D photonic nanostructures

NASA Astrophysics Data System (ADS)

Botey, Muriel; Martorell, Jordi; Lozano, Gabriel; Míguez, Hernán; Dorado, Luis A.; Depine, Ricardo A.

2010-05-01

We perform a theoretical study on the group velocity for finite thin artificial opal slabs made of a reduced number of layers in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method including extinction allows us to evaluate the finite-size effects on light propagation in the ΓL and ΓX directions of fcc close-packed opal films made of dielectric spheres. The group is index determined from the phase delay introduced by the structure to the forwardly transmitted electric field. We show that for certain frequencies, light propagation can either be superluminal -positive or negative- or approach zero depending on the crystal size and absorption. Such anomalous behavior can be attributed to the finite character of the structure and provides confirmation of recently emerged experimental results.

Dynamics of DNA breathing: weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem.

PubMed

Fogedby, Hans C; Metzler, Ralf

2007-12-01

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature, the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature, the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

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

Teomy, Eial, E-mail: eialteom@post.tau.ac.il; Shokef, Yair, E-mail: shokef@tau.ac.il

2014-08-14

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10{sup 7} ×more » 10{sup 7}, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.« less

Charging and hybridization in the finite cluster model

NASA Technical Reports Server (NTRS)

Bauschlicher, C. W., Jr.; Bagus, P. S.; Nelin, C. J.

1984-01-01

Cluster wavefunctions which have appropriate hybridization and polarization lead to reasonable properties for the interaction of an adsorbate with a solid surface. However, for Al clusters, it was found that the atomic change distribution is not uniform. The finite cluster size leads to changes not representative for an extended system. This effect appears to be dependent on the particular materials being studied; it does not occur in all cases.

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

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.

Simulation of wave propagation in three-dimensional random media

NASA Astrophysics Data System (ADS)

Coles, Wm. A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1995-04-01

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of

Biology-Culture Co-evolution in Finite Populations.

PubMed

de Boer, Bart; Thompson, Bill

2018-01-19

Language is the result of two concurrent evolutionary processes: biological and cultural inheritance. An influential evolutionary hypothesis known as the moving target problem implies inherent limitations on the interactions between our two inheritance streams that result from a difference in pace: the speed of cultural evolution is thought to rule out cognitive adaptation to culturally evolving aspects of language. We examine this hypothesis formally by casting it as as a problem of adaptation in time-varying environments. We present a mathematical model of biology-culture co-evolution in finite populations: a generalisation of the Moran process, treating co-evolution as coupled non-independent Markov processes, providing a general formulation of the moving target hypothesis in precise probabilistic terms. Rapidly varying culture decreases the probability of biological adaptation. However, we show that this effect declines with population size and with stronger links between biology and culture: in realistically sized finite populations, stochastic effects can carry cognitive specialisations to fixation in the face of variable culture, especially if the effects of those specialisations are amplified through cultural evolution. These results support the view that language arises from interactions between our two major inheritance streams, rather than from one primary evolutionary process that dominates another.

Dynamical effects in Bragg coherent x-ray diffraction imaging of finite crystals

NASA Astrophysics Data System (ADS)

Shabalin, A. G.; Yefanov, O. M.; Nosik, V. L.; Bushuev, V. A.; Vartanyants, I. A.

2017-08-01

We present simulations of Bragg coherent x-ray diffractive imaging (CXDI) data from finite crystals in the frame of the dynamical theory of x-ray diffraction. The developed approach is based on a numerical solution of modified Takagi-Taupin equations and can be applied for modeling of a broad range of x-ray diffraction experiments with finite three-dimensional crystals of arbitrary shape also in the presence of strain. We performed simulations for nanocrystals of a cubic and hemispherical shape of different sizes and provided a detailed analysis of artifacts in the Bragg CXDI reconstructions introduced by the dynamical diffraction. Based on our theoretical analysis we developed an analytical procedure to treat effects of refraction and absorption in the reconstruction. Our results elucidate limitations for the kinematical approach in the Bragg CXDI and suggest a natural criterion to distinguish between kinematical and dynamical cases in coherent x-ray diffraction on a finite crystal.

Maximum likelihood estimation of finite mixture model for economic data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-06-01

Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.

Rashba and Dresselhaus spin-orbit interactions effects on electronic features of a two dimensional elliptic quantum dot

NASA Astrophysics Data System (ADS)

Mokhtari, P.; Rezaei, G.; Zamani, A.

2017-06-01

In this paper, electronic structure of a two dimensional elliptic quantum dot under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. This investigation is done computationally and to do this, at first, the effective Hamiltonian of the system by considering the spin-orbit coupling is demonstrated in the presence of applied electric and magnetic fields and afterwards the Schrödinger equation is solved using the finite difference approach. Utilizing finite element method, eigenvalues and eigenstates of the system are calculated and the effect of the external fields, the size of the dot as well as the strength of Rashba spin-orbit interaction are studied. Our results indicate that, Spin-orbit interactions, external fields and the dot size have a great influence on the electronic structure of the system.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

NASA Astrophysics Data System (ADS)

Zhao, Hanqing; Wang, Wen-ge

2018-01-01

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

Stress Distribution During Deformation of Polycrystalline Aluminum by Molecular-Dynamics and Finite-Element Modeling

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Phillips, D.; Glaessgen, E. H.

2004-01-01

In this paper, a multiscale modelling strategy is used to study the effect of grain-boundary sliding on stress localization in a polycrystalline microstructure with an uneven distribution of grain size. The development of the molecular dynamics (MD) analysis used to interrogate idealized grain microstructures with various types of grain boundaries and the multiscale modelling strategies for modelling large systems of grains is discussed. Both molecular-dynamics and finite-element (FE) simulations for idealized polycrystalline models of identical geometry are presented with the purpose of demonstrating the effectiveness of the adapted finite-element method using cohesive zone models to reproduce grain-boundary sliding and its effect on the stress distribution in a polycrystalline metal. The yield properties of the grain-boundary interface, used in the FE simulations, are extracted from a MD simulation on a bicrystal. The models allow for the study of the load transfer between adjacent grains of very different size through grain-boundary sliding during deformation. A large-scale FE simulation of 100 grains of a typical microstructure is then presented to reveal that the stress distribution due to grain-boundary sliding during uniform tensile strain can lead to stress localization of two to three times the background stress, thus suggesting a significant effect on the failure properties of the metal.

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.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence

NASA Astrophysics Data System (ADS)

Mathai, Varghese; Prakash, Vivek N.; Brons, Jon; Sun, Chao; Lohse, Detlef

2015-09-01

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multiphysics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

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

Finite size effects in ferroelectric-semiconductor thin films under open-circuit electric boundary conditions

DOE PAGES

Eliseev, Eugene A.; Kalinin, Sergei V.; Morozovska, Anna N.

2015-01-21

General features of finite size effects in the ferroelectric-semiconductor film under open-circuit electric boundary conditions are analyzed using Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The temperature dependence of the film critical thickness, spontaneous polarization and depolarization field profiles of the open-circuited films are found to be significantly different from the characteristics of short-circuited ones. In particular, we predict the re-entrant type transition boundary between the mono-domain and poly-domain ferroelectric states due to reduced internal screening efficiency and analyzed possible experimental scenarios created by this mechanism. Performed analysis is relevant for the quantitative description of free-standing ferroelectric films phase diagrams andmore » polar properties. Also our results can be useful for the explanation of the scanning-probe microscopy experiments on free ferroelectric surfaces.« less

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

PubMed

Rajesh, R; Krishnamurthy, Supriya

2002-10-01

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

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.

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.

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-size effects on the dynamic susceptibility of CoPhOMe single-chain molecular magnets in presence of a static magnetic field

NASA Astrophysics Data System (ADS)

Pini, M. G.; Rettori, A.; Bogani, L.; Lascialfari, A.; Mariani, M.; Caneschi, A.; Sessoli, R.

2011-09-01

The static and dynamic properties of the single-chain molecular magnet Co(hfac)2NITPhOMe (CoPhOMe) (hfac = hexafluoroacetylacetonate, NITPhOMe = 4'-methoxy-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) are investigated in the framework of the Ising model with Glauber dynamics, in order to take into account both the effect of an applied magnetic field and a finite size of the chains. For static fields of moderate intensity and short chain lengths, the approximation of a monoexponential decay of the magnetization fluctuations is found to be valid at low temperatures; for strong fields and long chains, a multiexponential decay should rather be assumed. The effect of an oscillating magnetic field, with intensity much smaller than that of the static one, is included in the theory in order to obtain the dynamic susceptibility χ(ω). We find that, for an open chain with N spins, χ(ω) can be written as a weighted sum of N frequency contributions, with a sum rule relating the frequency weights to the static susceptibility of the chain. Very good agreement is found between the theoretical dynamic susceptibility and the ac susceptibility measured in moderate static fields (Hdc≤2 kOe), where the approximation of a single dominating frequency for each segment length turns out to be valid. For static fields in this range, data for the relaxation time, τ versus Hdc, of the magnetization of CoPhOMe at low temperature are also qualitatively reproduced by theory, provided that finite-size effects are included.

NiMnGa/Si Shape Memory Bimorph Nanoactuation

NASA Astrophysics Data System (ADS)

Lambrecht, Franziska; Lay, Christian; Aseguinolaza, Iván R.; Chernenko, Volodymyr; Kohl, Manfred

2016-12-01

The size dependences of thermal bimorph and shape memory effect of nanoscale shape memory alloy (SMA)/Si bimorph actuators are investigated in situ in a scanning electron microscope and by finite element simulations. By combining silicon nanomachining and magnetron sputtering, freestanding NiMnGa/Si bimorph cantilever structures with film/substrate thickness of 200/250 nm and decreasing lateral dimensions are fabricated. Electrical resistance and mechanical beam bending tests upon direct Joule heating demonstrate martensitic phase transformation and reversible thermal bimorph effect, respectively. Corresponding characteristics are strongly affected by the large temperature gradient in the order of 50 K/µm forming along the nano bimorph cantilever upon electro-thermal actuation, which, in addition, depends on the size-dependent heat conductivity in the Si nano layer. Furthermore, the martensitic transformation temperatures show a size-dependent decrease by about 40 K for decreasing lateral dimensions down to 200 nm. The effects of heating temperature and stress distribution on the nanoactuation performance are analyzed by finite element simulations revealing thickness ratio of SMA/Si of 90/250 nm to achieve an optimum SME. Differential thermal expansion and thermo-elastic effects are discriminated by comparative measurements and simulations on Ni/Si bimorph reference actuators.

Computational Dynamics of Metal-Carbon Interface-- Key to Controllable Nanotube Growth

DTIC Science & Technology

2013-11-13

functionalization. 20, 21 On a finite- size particle , e.g., of radius R, the carbon nucleus has to accommodate mean curvature ~ 1/R by incorporating pentagonal...with diameter. Its length adjusting effect is not obvious at similar conditions. Yet as the precursor size increases, the bias energy also...enhance the effect of the force. Our mathematical abstraction may not precisely govern the behaviors of tubes that are not nucleated simultaneously or

Effect of carrier doping and external electric field on the optical properties of graphene quantum dots

NASA Astrophysics Data System (ADS)

Basak, Tista; Basak, Tushima

2018-02-01

In this paper, we demonstrate that the optical properties of finite-sized graphene quantum dots can be effectively controlled by doping it with different types of charge carriers (electron/hole). In addition, the role played by a suitably directed external electric field on the optical absorption of charge-doped graphene quantum dots have also been elucidated. The computations have been performed on diamond-shaped graphene quantum dot (DQD) within the framework of the Pariser-Parr-Pople (PPP) model Hamiltonian, which takes into account long-range Coulomb interactions. Our results reveal that the energy band-gap increases when the DQD is doped with holes while it decreases on doping it with electrons. Further, the optical absorption spectra of DQD exhibits red/blue-shift on doping with electrons/holes. Our computations also indicate that the application of external transverse electric field results in a substantial blue-shift of the optical spectrum for charge-doped DQD. However, it is observed that the influence of charge-doping is more prominent in tuning the optical properties of finite-sized graphene quantum dots as compared to externally applied electric field. Thus, tailoring the optical properties of finite-sized graphene quantum dots by manipulative doping with charge carriers and suitably aligned external electric field can greatly enhance its potential application in designing nano-photonic devices.

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

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

Rashidi, Reza, E-mail: reza.rashidi@srttu.edu

The effects of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane–Emden equation. It is proved that the star always has a finite size. It is then argued that the maximum mass of such an ideal white dwarf tends to infinity, as opposed to the conventional case where it has a finite value.

Analytic calculation of finite-population reproductive numbers for direct- and vector-transmitted diseases with homogeneous mixing.

PubMed

Keegan, Lindsay; Dushoff, Jonathan

2014-05-01

The basic reproductive number, R0, provides a foundation for evaluating how various factors affect the incidence of infectious diseases. Recently, it has been suggested that, particularly for vector-transmitted diseases, R0 should be modified to account for the effects of finite host population within a single disease transmission generation. Here, we use a transmission factor approach to calculate such "finite-population reproductive numbers," under the assumption of homogeneous mixing, for both vector-borne and directly transmitted diseases. In the case of vector-borne diseases, we estimate finite-population reproductive numbers for both host-to-host and vector-to-vector generations, assuming that the vector population is effectively infinite. We find simple, interpretable formulas for all three of these quantities. In the direct case, we find that finite-population reproductive numbers diverge from R0 before R0 reaches half of the population size. In the vector-transmitted case, we find that the host-to-host number diverges at even lower values of R0, while the vector-to-vector number diverges very little over realistic parameter ranges.

The deformation mechanisms and size effects of single-crystal magnesium

NASA Astrophysics Data System (ADS)

Byer, Cynthia M.

In this work, we seek to understand the deformation mechanisms and size effects of single-crystal magnesium at the micrometer scale through both microcompression experiments and finite element simulations. Microcompression experiments are conducted to investigate the impact of initial dislocation density and orientation on size effects. Micropillars are fabricated using a focused ion beam and tested in a Nanoindenter using a diamond fiat tip as a compression platen. Two different initial dislocation densities are examined for [0001] oriented micropillars. Our results demonstrate that decreasing the initial dislocation density results in an increased size effect in terms of increased strength and stochasticity. Microcompression along the [23¯14] axis results in much lower strengths than for [0001] oriented samples. Post-mortem analysis reveals basal slip in both [0001] and [23¯14] micropillars. The application of a stochastic probability model shows good agreement between theoretical predictions and experimental results for size effects with our values of initial dislocation density and micropillar dimensions. Size effects are then incorporated into a single-crystal plasticity model (modified from Zhang and Joshi [1]) implemented in ABAQUS/STANDARD as a user-material subroutine. The model successfully captures the phenomena typically associated with size effects of increasing stochasticity and strength with decreasing specimen size and also accounts for the changing trends resulting from variations in initial dislocation density that we observe in the experiments. Finally, finite element simulations are performed with the original (traditional, without size effects) crystal plasticity model [1] to investigate the relative activities of the deformation modes of single-crystal magnesium for varying degrees of misalignment in microcompression. The simulations reveal basal activity in all micropillars, even for perfectly aligned compression along the [0001] axis. Pyramidal < c + a > activity dominates until the misalignment increases to 2°, when basal slip takes over as the dominant mode. The stress-strain curves for the case of 0° misalignment agrees well with experimental curves, indicating that good alignment was achieved during the experiments. Through this investigation, we gain a better understanding of how to control the size effects, as well as the deformation mechanisms operating at the small scale in magnesium.

The dynamics of particle disks. III - Dense and spinning particle disks. [development of kinetic theory for planetary rings

NASA Technical Reports Server (NTRS)

Araki, Suguru

1991-01-01

The kinetic theory of planetary rings developed by Araki and Tremaine (1986) and Araki (1988) is extended and refined, with a focus on the implications of finite particle size: (1) nonlocal collisions and (2) finite filling factors. Consideration is given to the derivation of the equations for the local steady state, the low-optical-depth limit, and the steady state at finite filling factors (including the effects of collision inelasticity, spin degrees of freedom, and self-gravity). Numerical results are presented in extensive graphs and characterized in detail. The importance of distinguishing effects (1) and (2) at low optical depths is stressed, and the existence of vertical density profiles with layered structures at high filling factors is demonstrated.

Finite-size effects in Monte Carlo simulations of two stock market models

NASA Astrophysics Data System (ADS)

Egenter, E.; Lux, T.; Stauffer, D.

The microscopic market models of Kim-Markowitz and of Lux-Marchesi are simulated for varying number of investors. If this number goes to infinity, in some quantities nearly periodic oscillations occur.

Size effects on the structural, electronic, and optical properties of (5,0) finite-length carbon nanotube: An ab-initio electronic structure study

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

Tarighi Ahmadpour, Mahdi; Rostamnejadi, Ali; Hashemifar, S. Javad

2016-07-07

We use density functional computations to study the zero temperature structural, electronic, magnetic, and optical properties of (5,0) finite carbon nanotubes (FCNT), with length in the range of 4–44 Å. It is found that the structural and electronic properties of (5,0) FCNTs, in the ground state, converge at a length of about 30 Å, while the excited state properties exhibit long-range edge effects. We discuss that curvature effects enhance energy gap of FCNTs, in contrast to the known trend in the periodic limit. It is seen that compensation of curvature effects in two special small sizes may give rise to spontaneous magnetization.more » The obtained cohesive energies provide some insights into the effects of environment on the growth of FCNTs. The second-order difference of the total energies reveals an important magic size of about 15 Å. The optical and dynamical magnetic responses of the FCNTs to polarized electromagnetic pulses are studied by time dependent density functional theory. The results show that the static and dynamic magnetic properties mainly come from the edge carbon atoms. The optical absorption properties are described in terms of local field effects and characterized by Casida linear response method.« less

Sensitivity of the mode locking phenomenon to geometric imperfections during wrinkling of supported thin films

DOE PAGES

Saha, Sourabh K.

2017-01-11

Although geometric imperfections have a detrimental effect on buckling, imperfection sensitivity has not been well studied in the past during design of sinusoidal micro and nano-scale structures via wrinkling of supported thin films. This is likely because one is more interested in predicting the shape/size of the resultant patterns than the buckling bifurcation onset strain during fabrication of such wrinkled structures. Herein, I have demonstrated that even modest geometric imperfections alter the final wrinkled mode shapes via the mode locking phenomenon wherein the imperfection mode grows in exclusion to the natural mode of the system. To study the effect ofmore » imperfections on mode locking, I have (i) developed a finite element mesh perturbation scheme to generate arbitrary geometric imperfections in the system and (ii) performed a parametric study via finite element methods to link the amplitude and period of the sinusoidal imperfections to the observed wrinkle mode shape and size. Based on this, a non-dimensional geometric parameter has been identified that characterizes the effect of imperfection on the mode locking phenomenon – the equivalent imperfection size. An upper limit for this equivalent imperfection size has been identified via a combination of analytical and finite element modeling. During compression of supported thin films, the system gets “locked” into the imperfection mode if its equivalent imperfection size is above this critical limit. For the polydimethylsiloxane/glass bilayer with a wrinkle period of 2 µm, this mode lock-in limit corresponds to an imperfection amplitude of 32 nm for an imperfection period of 5 µm and 8 nm for an imperfection period of 0.8 µm. Interestingly, when the non-dimensional critical imperfection size is scaled by the bifurcation onset strain, the scaled critical size depends solely on the ratio of the imperfection to natural periods. Furthermore, the computational data generated here can be generalized beyond the specific natural periods and bilayer systems studied to enable deterministic design of a variety of wrinkled micro and nano-scale structures.« less

Quantum field theory on toroidal topology: Algebraic structure and applications

NASA Astrophysics Data System (ADS)

Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.

2014-05-01

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on the hadronic phase structure are investigated, taking into account density and temperature. As a final application, effects of extra spatial dimensions are addressed, by developing a quantum electrodynamics in a five-dimensional space-time, where the fifth-dimension is compactified on a torus. The formalism, initially developed for particle physics, provides results compatible with other trials of probing the existence of extra-dimensions.

Surface and finite size effect on fluctuations dynamics in nanoparticles with long-range order

NASA Astrophysics Data System (ADS)

Morozovska, A. N.; Eliseev, E. A.

2010-02-01

The influence of surface and finite size on the dynamics of the order parameter fluctuations and critical phenomena in the three-dimensional (3D)-confined systems with long-range order was not considered theoretically. In this paper, we study the influence of surface and finite size on the dynamics of the order parameter fluctuations in the particles of arbitrary shape. We consider concrete examples of the spherical and cylindrical ferroic nanoparticles within Landau-Ginzburg-Devonshire phenomenological approach. Allowing for the strong surface energy contribution in micro and nanoparticles, the analytical expressions derived for the Ornstein-Zernike correlator of the long-range order parameter spatial-temporal fluctuations, dynamic generalized susceptibility, relaxation times, and correlation radii discrete spectra are different from those known for bulk systems. Obtained analytical expressions for the correlation function of the order parameter spatial-temporal fluctuations in micro and nanosized systems can be useful for the quantitative analysis of the dynamical structural factors determined from magnetic resonance diffraction and scattering spectra. Besides the practical importance of the correlation function for the analysis of the experimental data, derived expressions for the fluctuations strength determine the fundamental limits of phenomenological theories applicability for 3D-confined systems.

(Finite) statistical size effects on compressive strength.

PubMed

Weiss, Jérôme; Girard, Lucas; Gimbert, Florent; Amitrano, David; Vandembroucq, Damien

2014-04-29

The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.

Majorana bound states in the finite-length chain

NASA Astrophysics Data System (ADS)

Zvyagin, A. A.

2015-08-01

Recent experiments investigating edge states in ferromagnetic atomic chains on superconducting substrate are analyzed. In particular, finite size effects are considered. It is shown how the energy of the Majorana bound state depends on the length of the chain, as well as on the parameters of the model. Oscillations of the energy of the bound edge state in the chain as a function of the length of the chain, and as a function of the applied voltage (or the chemical potential) are studied. In particular, it has been shown that oscillations can exist only for some values of the effective potential.

The forced sound transmission of finite single leaf walls using a variational technique.

PubMed

Brunskog, Jonas

2012-09-01

The single wall is the simplest element of concern in building acoustics, but there still remain some open questions regarding the sound insulation of this simple case. The two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size, and the fact that the wave field in the wall is consisting of two types of waves, namely forced waves due to the exciting acoustic field, and free bending waves due to reflections in the boundary. The aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size, using a variational technique based on the integral-differential equation of the fluid loaded wall. The so derived formulas are valid in the entire audible frequency range. The results are compared with full numerical calculations, measurements and alternative theory, with reasonable agreement.

Getting Things Sorted With Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team

2014-11-01

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of Lagrangian Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.

Finite size effects in epidemic spreading: the problem of overpopulated systems

NASA Astrophysics Data System (ADS)

Ganczarek, Wojciech

2013-12-01

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

Surface and finite size effects impact on the phase diagrams, polar, and dielectric properties of (Sr,Bi)Ta{sub 2}O{sub 9} ferroelectric nanoparticles

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

Eliseev, E. A.; Fomichov, Y. M.; Glinchuk, M. D.

2016-05-28

In the framework of the thermodynamic approach Landau-Ginzburg-Devonshire (LGD) combined with the equations of electrostatics, we investigated the effect of polarization surface screening on finite size effects of the phase diagrams, polar, and dielectric properties of ferroelectric nanoparticles of different shapes. We obtained and analyzed the analytical results for the dependences of the ferroelectric phase transition temperature, critical size, spontaneous polarization, and thermodynamic coercive field on the shape and size of the nanoparticles. The pronounced size effect of these characteristics on the scaling parameter, the ratio of the particle characteristic size to the length of the surface screening, was revealed.more » Also our modeling predicts a significant impact of the flexo-chemical effect (that is a joint action of flexoelectric effect and chemical pressure) on the temperature of phase transition, polar, and dielectric properties of nanoparticles when their chemical composition deviates from the stoichiometric one. We showed on the example of the stoichiometric nanosized SrBi{sub 2}Ta{sub 2}O{sub 9} particles that except the vicinity of the critical size, where the system splitting into domains has an important role, results of analytical calculation of the spontaneous polarization have a little difference from the numerical ones. We revealed a strong impact of the flexo-chemical effect on the phase transition temperature, polar, and dielectric properties of Sr{sub y}Bi{sub 2+x}Ta{sub 2}O{sub 9} nanoparticles when the ratio Sr/Bi deviates from the stoichiometric value of 0.5 within the range from 0.35 to 0.65. From the analysis of experimental data, we derived the parameters of the theory, namely, the coefficients of expansion of the LGD functional, the contribution of flexo-chemical effect, and the length of the surface screening.« less

Modeling Physical Processes at the Nanoscale—Insight into Self-Organization of Small Systems (abstract)

NASA Astrophysics Data System (ADS)

Proykova, Ana

2009-04-01

Essential contributions have been made in the field of finite-size systems of ingredients interacting with potentials of various ranges. Theoretical simulations have revealed peculiar size effects on stability, ground state structure, phases, and phase transformation of systems confined in space and time. Models developed in the field of pure physics (atomic and molecular clusters) have been extended and successfully transferred to finite-size systems that seem very different—small-scale financial markets, autoimmune reactions, and social group reactions to advertisements. The models show that small-scale markets diverge unexpectedly fast as a result of small fluctuations; autoimmune reactions are sequences of two discontinuous phase transitions; and social groups possess critical behavior (social percolation) under the influence of an external field (advertisement). Some predicted size-dependent properties have been experimentally observed. These findings lead to the hypothesis that restrictions on an object's size determine the object's total internal (configuration) and external (environmental) interactions. Since phases are emergent phenomena produced by self-organization of a large number of particles, the occurrence of a phase in a system containing a small number of ingredients is remarkable.

Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

DOE PAGES

Schuetrumpf, B.; Nazarewicz, W.

2015-10-21

Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at subsaturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100-m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite three-dimensional boxes assuming periodic boundary conditions. The resulting solutions are affected by spurious finite-size effects. To remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice quantum chromodynamics applications. In this work, we study the effectivenessmore » of TABC in the context of pasta phase simulations within nuclear density functional theory. We demonstrated that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range. Future applications will include the TABC extension of the adaptive multiresolution 3D Hartree-Fock solver and Hartree-Fock-Bogoliubov TABC applications to superfluid pasta phases and complex nucleonic topologies as in fission.« less

Thermodynamics of phase-separating nanoalloys: Single particles and particle assemblies

NASA Astrophysics Data System (ADS)

Fèvre, Mathieu; Le Bouar, Yann; Finel, Alphonse

2018-05-01

The aim of this paper is to investigate the consequences of finite-size effects on the thermodynamics of nanoparticle assemblies and isolated particles. We consider a binary phase-separating alloy with a negligible atomic size mismatch, and equilibrium states are computed using off-lattice Monte Carlo simulations in several thermodynamic ensembles. First, a semi-grand-canonical ensemble is used to describe infinite assemblies of particles with the same size. When decreasing the particle size, we obtain a significant decrease of the solid/liquid transition temperatures as well as a growing asymmetry of the solid-state miscibility gap related to surface segregation effects. Second, a canonical ensemble is used to analyze the thermodynamic equilibrium of finite monodisperse particle assemblies. Using a general thermodynamic formulation, we show that a particle assembly may split into two subassemblies of identical particles. Moreover, if the overall average canonical concentration belongs to a discrete spectrum, the subassembly concentrations are equal to the semi-grand-canonical equilibrium ones. We also show that the equilibrium of a particle assembly with a prescribed size distribution combines a size effect and the fact that a given particle size assembly can adopt two configurations. Finally, we have considered the thermodynamics of an isolated particle to analyze whether a phase separation can be defined within a particle. When studying rather large nanoparticles, we found that the region in which a two-phase domain can be identified inside a particle is well below the bulk phase diagram, but the concentration of the homogeneous core remains very close to the bulk solubility limit.

The effect of grid transparency and finite collector size on determining ion temperature and density by the retarding potential analyzer

NASA Technical Reports Server (NTRS)

Troy, B. E., Jr.; Maier, E. J.

1973-01-01

The analysis of ion data from retarding potential analyzers (RPA's) is generally done under the planar approximation, which assumes that the grid transparency is constant with angle of incidence and that all ions reaching the plane of the collectors are collected. These approximations are not valid for situations in which the ion thermal velocity is comparable to the vehicle velocity, causing ions to enter the RPA with high average transverse velocity. To investigate these effects, the current-voltage curves for H+ at 4000 K were calculated, taking into account the finite collector size and the variation of grid transparency with angle. These curves are then analyzed under the planar approximation. The results show that only small errors in temperature and density are introduced for an RPA with typical dimensions; and that even when the density error is substantial for non-typical dimensions, the temperature error remains minimal.

The Influence of Finite-size Sources in Acousto-ultrasonics

NASA Technical Reports Server (NTRS)

Pavlakovic, Brian N.; Rose, Joseph L.

1994-01-01

This work explores the effects that the finite normal axisymmetric traction loading of an infinite isotropic plate has on wave propagation in acousto-ultrasonics (AU), in which guided waves are created using two normal incidence transducers. Although the work also addresses the effects of the transducer pressure distribution and pulse shape, this thesis concentrates on two main questions: how does the transducer's diameter control the phase velocity and frequency spectrum of the response, and how does the plate thickness relate to the plate's excitability? The mathematics of the time-harmonic solution and the physical principles and the practical considerations for AU wave generation are explained. Transient sources are modeled by the linear superposition of the time-harmonic solutions found using the Hankel transform and they are then compared to experimental data to provide insight into the relation between the size of the transducer and the preferred phase velocity.

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.

Finite-size effect on optimal efficiency of heat engines.

PubMed

Tajima, Hiroyasu; Hayashi, Masahito

2017-07-01

The optimal efficiency of quantum (or classical) heat engines whose heat baths are n-particle systems is given by the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistical mechanical optimal efficiency with the macroscopic thermodynamic bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint. We also evaluate the quantum coherence effect on the optimal efficiency of the cycle processes without restricting their cycle time by comparing the classical and quantum optimal efficiencies.

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

NASA Technical Reports Server (NTRS)

Thompson, D. Muheim; Griffin, O. Hayden, Jr.

1990-01-01

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

Predicting the constitutive behavior of semi-solids via a direct finite element simulation: application to AA5182

NASA Astrophysics Data System (ADS)

Phillion, A. B.; Cockcroft, S. L.; Lee, P. D.

2009-07-01

The methodology of direct finite element (FE) simulation was used to predict the semi-solid constitutive behavior of an industrially important aluminum-magnesium alloy, AA5182. Model microstructures were generated that detail key features of the as-cast semi-solid: equiaxed-globular grains of random size and shape, interconnected liquid films, and pores at the triple-junctions. Based on the results of over fifty different simulations, a model-based constitutive relationship which includes the effects of the key microstructure features—fraction solid, grain size and fraction porosity—was derived using regression analysis. This novel constitutive equation was then validated via comparison with both the FE simulations and experimental stress/strain data. Such an equation can now be used to incorporate the effects of microstructure on the bulk semi-solid flow stress within a macro- scale process model.

Finite mixture model: A maximum likelihood estimation approach on time series data

NASA Astrophysics Data System (ADS)

Yen, Phoong Seuk; Ismail, Mohd Tahir; Hamzah, Firdaus Mohamad

2014-09-01

Recently, statistician emphasized on the fitting of finite mixture model by using maximum likelihood estimation as it provides asymptotic properties. In addition, it shows consistency properties as the sample sizes increases to infinity. This illustrated that maximum likelihood estimation is an unbiased estimator. Moreover, the estimate parameters obtained from the application of maximum likelihood estimation have smallest variance as compared to others statistical method as the sample sizes increases. Thus, maximum likelihood estimation is adopted in this paper to fit the two-component mixture model in order to explore the relationship between rubber price and exchange rate for Malaysia, Thailand, Philippines and Indonesia. Results described that there is a negative effect among rubber price and exchange rate for all selected countries.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Monte-Carlo simulation of a stochastic differential equation

NASA Astrophysics Data System (ADS)

Arif, ULLAH; Majid, KHAN; M, KAMRAN; R, KHAN; Zhengmao, SHENG

2017-12-01

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Finite-size effects of hysteretic dynamics in multilayer graphene on a ferroelectric

DOE PAGES

Morozovska, Anna N.; Pusenkova, Anastasiia S.; Varenyk, Oleksandr V.; ...

2015-06-11

The origin and influence of finite-size effects on the nonlinear dynamics of space charge stored by multilayer graphene on a ferroelectric and resistivity of graphene channel were analyzed. In this paper, we develop a self-consistent approach combining the solution of electrostatic problems with the nonlinear Landau-Khalatnikov equations for a ferroelectric. The size-dependent behaviors are governed by the relations between the thicknesses of multilayer graphene, ferroelectric film, and the dielectric layer. The appearance of charge and electroresistance hysteresis loops and their versatility stem from the interplay of polarization reversal dynamics and its incomplete screening in an alternating electric field. These featuresmore » are mostly determined by the dielectric layer thickness. The derived analytical expressions for electric fields and space-charge-density distribution in a multilayer system enable knowledge-driven design of graphene-on-ferroelectric heterostructures with advanced performance. We further investigate the effects of spatially nonuniform ferroelectric domain structures on the graphene layers’ conductivity and predict its dramatic increase under the transition from multi- to single-domain state in a ferroelectric. Finally, this intriguing effect can open possibilities for the graphene-based sensors and explore the underlying physical mechanisms in the operation of graphene field-effect transistor with ferroelectric gating.« less

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.

Stamping of Thin-Walled Structural Components with Magnesium Alloy AZ31 Sheets

NASA Astrophysics Data System (ADS)

Chen, Fuh-Kuo; Chang, Chih-Kun

2005-08-01

In the present study, the stamping process for manufacturing cell phone cases with magnesium alloy AZ31 sheets was studied using both the experimental approach and the finite element analysis. In order to determine the proper forming temperature and set up a fracture criterion, tensile tests and forming limit tests were first conducted to obtain the mechanical behaviors of AZ31 sheets at various elevated temperatures. The mechanical properties of Z31 sheets obtained from the experiments were then adopted in the finite element analysis to investigate the effects of the process parameters on the formability of the stamping process of cell phone cases. The finite element simulation results revealed that both the fracture and wrinkle defects could not be eliminated at the same time by adjusting blank-holder force or blank size. A drawbead design was then performed using the finite element simulations to determine the size and the location of drawbead required to suppress the wrinkle defect. An optimum stamping process, including die geometry, forming temperature, and blank dimension, was then determined for manufacturing the cell phone cases. The finite element analysis was validated by the good agreement between the simulation results and the experimental data. It confirms that the cell phone cases can be produced with magnesium alloy AZ31 sheet by the stamping process at elevated temperatures.

Simulations of wave propagation and disorder in 3D non-close-packed colloidal photonic crystals with low refractive index contrast.

PubMed

Glushko, O; Meisels, R; Kuchar, F

2010-03-29

The plane-wave expansion method (PWEM), the multiple-scattering method (MSM) and the 3D finite-difference time-domain method (FDTD) are applied for simulations of propagation of electromagnetic waves through 3D colloidal photonic crystals. The system investigated is not a "usual" artificial opal with close-packed fcc lattice but a dilute bcc structure which occurs due to long-range repulsive interaction between electrically charged colloidal particles during the growth process. The basic optical properties of non-close-packed colloidal PhCs are explored by examining the band structure and reflection spectra for a bcc lattice of silica spheres in an aqueous medium. Finite size effects and correspondence between the Bragg model, band structure and reflection spectra are discussed. The effects of size, positional and missing-spheres disorder are investigated. In addition, by analyzing the results of experimental work we show that the fabricated structures have reduced plane-to-plane distance probably due to the effect of gravity during growth.

Finite-size versus interface-proximity effects in thin-film epitaxial SrTiO3

NASA Astrophysics Data System (ADS)

De Souza, R. A.; Gunkel, F.; Hoffmann-Eifert, S.; Dittmann, R.

2014-06-01

The equilibrium electrical conductivity of epitaxial SrTiO3 (STO) thin films was investigated as a function of temperature, 950≤ T/K ≤1100, and oxygen partial pressure, 10-23≤ pO2/bar ≤1. Compared with single-crystal STO, nanoscale thin-film STO exhibited with decreasing film thickness an increasingly enhanced electronic conductivity under highly reducing conditions, with a corresponding decrease in the activation enthalpy of conduction. This implies substantial modification of STO's point-defect thermodynamics for nanoscale film thicknesses. We argue, however, against such a finite-size effect and for an interface-proximity effect. Indeed, assuming trapping of oxygen vacancies at the STO surface and concomitant depletion of oxygen vacancies—and accumulation of electrons—in an equilibrium surface space-charge layer, we are able to predict quantitatively the conductivity as a function of temperature, oxygen partial pressure, and film thickness. Particularly complex behavior is predicted for ultrathin films that are consumed entirely by space charge.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

A scattering model for defoliated vegetation

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1986-01-01

A scattering model for defoliated vegetation is conceived as a layer of dielectric, finite-length cylinders with specified size and orientation distributions above an irregular ground surface. The scattering phase matrix of a single cylinder is computed, then the radiative transfer technique is applied to link volume scattering from vegetation to surface scattering from the soil surface. Polarized and depolarized scattering are computed and the effects of the cylinder size and orientation distributions are illustrated. It is found that size and orientation distributions have significant effects on the backscattered signal. The model is compared with scattering from defoliated trees and agricultural crops.

Communication: Finite size correction in periodic coupled cluster theory calculations of solids.

PubMed

Liao, Ke; Grüneis, Andreas

2016-10-14

We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

Influence of local meshing size on stress intensity factor of orthopedic lag screw

NASA Astrophysics Data System (ADS)

Husain, M. N.; Daud, R.; Basaruddin, K. S.; Mat, F.; Bajuri, M. Y.; Arifin, A. K.

2017-09-01

Linear elastic fracture mechanics (LEFM) concept is generally used to study the influence of crack on the performance of structures. In order to study the LEFM concept on damaged structure, the usage of finite element analysis software is implemented to do the simulation of the structure. Mesh generation is one of the most crucial procedures in finite element method. For the structure that crack or damaged, it is very important to determine the accurate local meshing size at the crack tip of the crack itself in order to get the accurate value of stress intensity factor, KI. Pre crack will be introduced to the lag screw based on the von mises' stress result that had been performed in previous research. This paper shows the influence of local mesh arrangement on numerical value of the stress intensity factor, KI obtained by the displacement method. This study aims to simulate the effect of local meshing which is the singularity region on stress intensity factor, KI to the critical point of failure in screw. Five different set of wedges meshing size are introduced during the simulation of finite element analysis. The number of wedges used to simulate this research is 8, 10, 14, 16 and 20. There are three set of numerical equations used to validate the results which are brown and srawley, gross and brown and Tada equation. The result obtained from the finite element software (ANSYS APDL) has a positive agreement with the numerical analysis which is Brown and Srawley compared to other numerical formula. Radius of first row size of 0.014 and singularity element with 14 numbers of wedges is proved to be the best local meshing for this study.

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.

Switching times of nanoscale FePt: Finite size effects on the linear reversal mechanism

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

Ellis, M. O. A.; Chantrell, R. W.

2015-04-20

The linear reversal mechanism in FePt grains ranging from 2.316 nm to 5.404 nm has been simulated using atomistic spin dynamics, parametrized from ab-initio calculations. The Curie temperature and the critical temperature (T{sup *}), at which the linear reversal mechanism occurs, are observed to decrease with system size whilst the temperature window T{sup *}

Novel Quantum Phases at Interfaces

DTIC Science & Technology

2014-12-12

89.085122 Mehdi Kargarian, Gregory A. Fiete. Multiorbital effects on thermoelectric properties of strongly correlated materials , Physical Review B...Multi-orbital Effects on Thermoelectric Properties of Strongly Correlated Materials , ArXiv e-prints (08 2013) Joseph Maciejko, Victor Chua...Lei Wang , Gregory A. Fiete. Finite- size and interaction effects on topological phase transitions via numerically exact quantum Monte Carlo

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

Numerical Study of the Effect of Presence of Geometric Singularities on the Mechanical Behavior of Laminated Plates

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Guettala, Abdelhamid

2017-05-01

In this paper, an effort is made to understand the effects of geometric singularities on the load bearing capacity and stress distribution in thin laminated plates. Composite plates with variously shaped cutouts are frequently used in both modern and classical aerospace, mechanical and civil engineering structures. Finite element investigation is undertaken to show the effect of geometric singularities on stress distribution. In this study, the stress concentration factors (SCFs) in cross-and-angle-ply laminated as well as in isotropic plates subjected to uniaxial loading are studied using a quadrilateral finite element of four nodes with thirty-two degrees-of-freedom per element. The varying parameters such as the cutout shape and hole sizes (a/b) are considered. The numerical results obtained by the present element are compared favorably with those obtained using the finite element software Freefem++ and the analytic findings published in literature, which demonstrates the accuracy of the present element. Freefem++ is open source software based on the finite element method, which could be helpful to study and improving the analyses of the stress distribution in composite plates with cutouts. The Freefem++ and the quadrilateral finite element formulations will be given in the beginning of this paper. Finally, to show the effect of the fiber orientation angle and anisotropic modulus ratio on the (SCF), number of figures are given for various ratio (a/b).

Exact special twist method for quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Dagrada, Mario; Karakuzu, Seher; Vildosola, Verónica Laura; Casula, Michele; Sorella, Sandro

2016-12-01

We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995), 10.1103/PhysRevB.51.10591] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.

Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.

2017-01-01

This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

Length and temperature dependence of the mechanical properties of finite-size carbyne

NASA Astrophysics Data System (ADS)

Yang, Xueming; Huang, Yanhui; Cao, Bingyang; To, Albert C.

2017-09-01

Carbyne is an ideal one-dimensional conductor and the thinnest interconnection in an ultimate nano-device and it requires an understanding of the mechanical properties that affect device performance and reliability. Here, we report the mechanical properties of finite-size carbyne, obtained by a molecular dynamics simulation study based on the adaptive intermolecular reactive empirical bond order potential. To avoid confusion in assigning the effective cross-sectional area of carbyne, the value of the effective cross-sectional area of carbyne (4.148 Å2) was deduced via experiment and adopted in our study. Ends-constraints effects on the ultimate stress (maximum force) of the carbyne chains are investigated, revealing that the molecular dynamics simulation results agree very well with the experimental results. The ultimate strength, Young's Modulus and maximum strain of carbyne are rather sensitive to the temperature and all decrease with the temperature. Opposite tendencies of the length dependence of the overall ultimate strength and maximum strain of carbyne at room temperature and very low temperature have been found, and analyses show that this originates in the ends effect of carbyne.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

NASA Astrophysics Data System (ADS)

Pervishko, Anastasiia A.; Yudin, Dmitry; Shelykh, Ivan A.

2018-02-01

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

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.

A two-stage Monte Carlo approach to the expression of uncertainty with finite sample sizes.

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

Crowder, Stephen Vernon; Moyer, Robert D.

2005-05-01

Proposed supplement I to the GUM outlines a 'propagation of distributions' approach to deriving the distribution of a measurand for any non-linear function and for any set of random inputs. The supplement's proposed Monte Carlo approach assumes that the distributions of the random inputs are known exactly. This implies that the sample sizes are effectively infinite. In this case, the mean of the measurand can be determined precisely using a large number of Monte Carlo simulations. In practice, however, the distributions of the inputs will rarely be known exactly, but must be estimated using possibly small samples. If these approximatedmore » distributions are treated as exact, the uncertainty in estimating the mean is not properly taken into account. In this paper, we propose a two-stage Monte Carlo procedure that explicitly takes into account the finite sample sizes used to estimate parameters of the input distributions. We will illustrate the approach with a case study involving the efficiency of a thermistor mount power sensor. The performance of the proposed approach will be compared to the standard GUM approach for finite samples using simple non-linear measurement equations. We will investigate performance in terms of coverage probabilities of derived confidence intervals.« less

Anderson metal-insulator transitions with classical magnetic impurities

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

Jung, Daniel; Kettemann, Stefan

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition (AMIT) numerically. In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude W{sub c}, in the presence of Heisenberg impurities, W{sub c} is first increased with increasing exchange coupling strength J due to time-reversal symmetry breaking. The resulting scaling with J is compared to analytical predictions by Wegner [1]. The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [2], which is the geometric average of the local densitymore » of states. The latter can efficiently be calculated using the kernel polynomial method [3]. Although still suffering from methodical shortcomings, our method proves to deliver results close to established results for the orthogonal symmetry class [4]. We extend previous approaches [5] by combining the KPM with a finite-size scaling analysis. We also discuss the relevance of our findings for systems like phosphor-doped silicon (Si:P), which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [6].« less

A novel measure of effect size for mediation analysis.

PubMed

Lachowicz, Mark J; Preacher, Kristopher J; Kelley, Ken

2018-06-01

Mediation analysis has become one of the most popular statistical methods in the social sciences. However, many currently available effect size measures for mediation have limitations that restrict their use to specific mediation models. In this article, we develop a measure of effect size that addresses these limitations. We show how modification of a currently existing effect size measure results in a novel effect size measure with many desirable properties. We also derive an expression for the bias of the sample estimator for the proposed effect size measure and propose an adjusted version of the estimator. We present a Monte Carlo simulation study conducted to examine the finite sampling properties of the adjusted and unadjusted estimators, which shows that the adjusted estimator is effective at recovering the true value it estimates. Finally, we demonstrate the use of the effect size measure with an empirical example. We provide freely available software so that researchers can immediately implement the methods we discuss. Our developments here extend the existing literature on effect sizes and mediation by developing a potentially useful method of communicating the magnitude of mediation. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Competing Grain Boundary and Interior Deformation Mechanisms with Varying Sizes

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

Zhang, Wei; Gao, Yanfei; Nieh, T. G.

In typical coarse-grained alloys, the dominant plastic deformations are dislocation gliding or climbing, and material strengths can be tuned by dislocation interactions with grain boundaries, precipitates, solid solutions, and other defects. With the reduction of grain size, the increase of material strengths follows the classic Hall-Petch relationship up to nano-grained materials. Even at room temperatures, nano-grained materials exhibit strength softening, or called the inverse Hall-Petch effect, as grain boundary processes take over as the dominant deformation mechanisms. On the other hand, at elevated temperatures, grain boundary processes compete with grain interior deformation mechanisms over a wide range of the appliedmore » stress and grain sizes. This book chapter reviews and compares the rate equation model and the microstructure-based finite element simulations. The latter explicitly accounts for the grain boundary sliding, grain boundary diffusion and migration, as well as the grain interior dislocation creep. Therefore the explicit finite element method has clear advantages in problems where microstructural heterogeneities play a critical role, such as in the gradient microstructure in shot peening or weldment. Furthermore, combined with the Hall-Petch effect and its breakdown, the above competing processes help construct deformation mechanism maps by extending from the classic Frost-Ashby type to the ones with the dependence of grain size.« less

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.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

Iterative and variational homogenization methods for filled elastomers

NASA Astrophysics Data System (ADS)

Goudarzi, Taha

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents --- i.e., the elastomeric matrix and the filler particles --- and their microstructure --- i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly bonded or bonded through finite size interphases) at finite concentrations. Three-dimensional finite element simulations are also carried out to gain further insight into the proposed theoretical solutions. Inter alia, we make use of these solutions to examine the effects of particle concentration, mono- and poly-dispersity of the filler particle size, and the presence of finite size interphases on the macroscopic response of filled elastomers. The solutions are found able to explain and describe experimental results that to date have been understood only in part. More generally, the solutions provide a robust tool to efficiently guide the design of filled elastomers with desired macroscopic properties. The homogenization techniques developed in this work are not limited to nonlinear elasticity, but can be readily utilized to study multi-functional properties as well. For demonstration purposes, we work out a novel exact solution for the macroscopic dielectric response of filled elastomers with interphasial space charges.

Volume dependence of baryon number cumulants and their ratios

DOE PAGES

Almási, Gábor A.; Pisarski, Robert D.; Skokov, Vladimir V.

2017-03-17

Here, we explore the influence of finite-volume effects on cumulants of baryon/quark number fluctuations in a nonperturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth- to the second-order cumulant of quark number fluctuations. Finally,more » when the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.« less

Modeling the nonlinear dielectric response of glass formers

NASA Astrophysics Data System (ADS)

Buchenau, U.

2017-06-01

The recently developed pragmatical model of asymmetric double-well potentials with a finite lifetime is applied to nonlinear dielectric data in polar undercooled liquids. The viscous effects from the finite lifetime provide a crossover from the cooperative jumps of many molecules at short times to the motion of statistically independent molecules at long times. The model allows us to determine the size of cooperatively rearranging regions from nonlinear ω -data and throws new light on a known inconsistency between nonlinear ω and 3 ω -signals for glycerol and propylene carbonate.

Vacuum Energy Induced by AN Impenetrable Flux Tube of Finite Radius

NASA Astrophysics Data System (ADS)

Gorkavenko, V. M.; Sitenko, Yu. A.; Stepanov, O. B.

2011-06-01

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

Vacuum Energy Induced by AN Impenetrable Flux Tube of Finite Radius

NASA Astrophysics Data System (ADS)

Gorkavenko, V. M.; Sitenko, Yu. A.; Stepanov, O. B.

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

Finite size effects on the experimental observables of the Glauber model: a theoretical and experimental investigation

NASA Astrophysics Data System (ADS)

Vindigni, A.; Bogani, L.; Gatteschi, D.; Sessoli, R.; Rettori, A.; Novak, M. A.

2004-05-01

We investigate the relaxation time, τ, of a dilute Glauber kinetic Ising chain obtained by ac susceptibility and SQUID magnetometry on a Co(II)-organic radical Ising 1D ferrimagnet doped with Zn(II). Theoretically we predicted a crossover in the temperature-dependence of τ, when the average segment is of the same order of the correlation length. Comparing the experimental results with theory we conclude that in the investigted temperature range the correlation length exceeds the finite length also in the pure sample.

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data

PubMed Central

He, Jingjing; Ran, Yunmeng; Liu, Bin; Yang, Jinsong; Guan, Xuefei

2017-01-01

This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions. PMID:28902148

Effect of zone size on the convergence of exact solutions for diffusion in single phase systems with planar, cylindrical or spherical geometry

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.

1981-01-01

Exact solutions for diffusion in single phase binary alloy systems with constant diffusion coefficient and zero-flux boundary condition have been evaluated to establish the optimum zone size of applicability. Planar, cylindrical and spherical interface geometry, and finite, singly infinite, and doubly infinite systems are treated. Two solutions are presented for each geometry, one well suited to short diffusion times, and one to long times. The effect of zone-size on the convergence of these solutions is discussed. A generalized form of the diffusion solution for doubly infinite systems is proposed.

Gradient and size effects on spinodal and miscibility gaps

NASA Astrophysics Data System (ADS)

Tsagrakis, Ioannis; Aifantis, Elias C.

2018-05-01

A thermodynamically consistent model of strain gradient elastodiffusion is developed. Its formulation is based on the enhancement of a robust theory of gradient elasticity, known as GRADELA, to account for a Cahn-Hilliard type of diffusion. Linear stability analysis is employed to determine the influence of concentration and strain gradients on the spinodal decomposition. For finite domains, spherically symmetric conditions are considered, and size effects on spinodal and miscibility gaps are discussed. The theoretical predictions are in agreement with the experimental trends, i.e., both gaps shrink as the grain diameter decreases and they are completely eliminated for crystals smaller than a critical size.

Inertial objects in complex flows

NASA Astrophysics Data System (ADS)

Syed, Rayhan; Ho, George; Cavas, Samuel; Bao, Jialun; Yecko, Philip

2017-11-01

Chaotic Advection and Finite Time Lyapunov Exponents both describe stirring and transport in complex and time-dependent flows, but FTLE analysis has been largely limited to either purely kinematic flow models or high Reynolds number flow field data. The neglect of dynamic effects in FTLE and Lagrangian Coherent Structure studies has stymied detailed information about the role of pressure, Coriolis effects and object inertia. We present results of laboratory and numerical experiments on time-dependent and multi-gyre Stokes flows. In the lab, a time-dependent effectively two-dimensional low Re flow is used to distinguish transport properties of passive tracer from those of small paramagnetic spheres. Companion results of FTLE calculations for inertial particles in a time-dependent multi-gyre flow are presented, illustrating the critical roles of density, Stokes number and Coriolis forces on their transport. Results of Direct Numerical Simulations of fully resolved inertial objects (spheroids) immersed in a three dimensional (ABC) flow show the role of shape and finite size in inertial transport at small finite Re. We acknowledge support of NSF DMS-1418956.

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.

Micromorphic approach for gradient-extended thermo-elastic-plastic solids in the logarithmic strain space

NASA Astrophysics Data System (ADS)

Aldakheel, Fadi

2017-11-01

The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704-734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117-131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).

Ambiance-dependent agglomeration and surface-enhanced Raman spectroscopy response of self-assembled silver nanoparticles for plasmonic photovoltaic devices

NASA Astrophysics Data System (ADS)

Gwamuri, Jephias; Venkatesan, Ragavendran; Sadatgol, Mehdi; Mayandi, Jeyanthinath; Guney, Durdu O.; Pearce, Joshua M.

2017-07-01

The agglomeration/dewetting process of thin silver films provides a scalable method of obtaining self-assembled nanoparticles (SANPs) for plasmonics-based thin-film solar photovoltaic (PV) devices. We show the effect of annealing ambiance on silver SANP average size, particle/cluster finite shape, substrate area coverage/particle distribution, and how these physical parameters influence optical properties and surface-enhanced Raman scattering (SERS) responses of SANPs. Statistical analysis performed indicates that generally Ag SANPs processed in the presence of a gas (argon and nitrogen) ambiance tend to have smaller average size particles compared to those processed under vacuum. Optical properties are observed to be highly dependent on particle size, separation distance, and finite shape. The greatest SERS enhancement was observed for the argon-processed samples. There is a correlation between simulation and experimental data that indicate argon-processed AgNPs have a great potential to enhance light coupling when integrated to thin-film PV.

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: Case study of zinc selenide and zinc oxide

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

Yu, Jaehyung; Wagner, Lucas K.; Ertekin, Elif, E-mail: ertekin@illinois.edu

2015-12-14

The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total energies, atomization energies, and excited state energies is not yet fully established. Several outstanding questions remain as to the effect of pseudopotentials, the magnitude of the fixed node error, and the size of supercell finite size effects. Here, we consider in detail the semiconductors ZnSe and ZnO and carry out systematic studies to assess the magnitude of the energy differences arising from controlledmore » and uncontrolled approximations in DMC. The former include time step errors and supercell finite size effects for ground and optically excited states, and the latter include pseudopotentials, the pseudopotential localization approximation, and the fixed node approximation. We find that for these compounds, the errors can be controlled to good precision using modern computational resources and that quantum Monte Carlo calculations using Dirac-Fock pseudopotentials can offer good estimates of both cohesive energy and the gap of these systems. We do however observe differences in calculated optical gaps that arise when different pseudopotentials are used.« less

Analytical YORP torques model with an improved temperature distribution function

NASA Astrophysics Data System (ADS)

Breiter, S.; Vokrouhlický, D.; Nesvorný, D.

2010-01-01

Previous models of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect relied either on the zero thermal conductivity assumption, or on the solutions of the heat conduction equations assuming an infinite body size. We present the first YORP solution accounting for a finite size and non-radial direction of the surface normal vectors in the temperature distribution. The new thermal model implies the dependence of the YORP effect in rotation rate on asteroids conductivity. It is shown that the effect on small objects does not scale as the inverse square of diameter, but rather as the first power of the inverse.

Resonant Electromagnetic Interaction in Low Energy Nuclear Reactions

NASA Astrophysics Data System (ADS)

Chubb, Scott

2008-03-01

Basic ideas about how resonant electromagnetic interaction (EMI) can take place in finite solids are reviewed. These ideas not only provide a basis for conventional, electron energy band theory (which explains charge and heat transport in solids), but they also explain how through finite size effects, it is possible to create many of the kinds of effects envisioned by Giuliano Preparata. The underlying formalism predicts that the orientation of the external fields in the SPAWAR protocolootnotetextKrivit, Steven B., New Energy Times, 2007, issue 21, item 10. http://newenergytimes.com/news/2007/NET21.htm^,ootnotetextSzpak, S.; Mosier-Boss, P.A.; Gordon, F.E. Further evidence of nuclear reactions in the Pd lattice: emission of charged particles. Naturwissenschaften 94,511(2007)..has direct bearing on the emission of high-energy particles. Resonant EMI also implies that nano-scale solids, of a particular size, provide an optimal environment for initiating Low Energy Nuclear Reactions (LENR) in the PdD system.

Effect of Fibonacci modulation on superconductivity

NASA Astrophysics Data System (ADS)

Gupta, Sanjay; Sil, Shreekantha; Bhattacharyya, Bibhas

2006-02-01

We have studied finite-sized single band models with short-range pairing interactions between electrons in the presence of diagonal Fibonacci modulation in one dimension. Two models, namely the attractive Hubbard model and the Penson-Kolb model, have been investigated at half-filling at zero temperature by solving the Bogoliubov-de Gennes equations in real space within a mean-field approximation. The competition between 'disorder' and the pairing interaction leads to a suppression of superconductivity (of usual pairs with zero centre-of-mass momenta) in the strong-coupling limit while an enhancement of the pairing correlation is observed in the weak-coupling regime for both models. However, the dissimilarity of the pairing mechanisms in these two models brings about notable differences in the results. The extent to which the bond-ordered wave and the η-paired (of pairs with centre-of-mass momenta = π) phases of the Penson-Kolb model are affected by the disorder has also been studied in the present calculation. Some finite size effects are also identified.

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.

Finite element modelling to assess the effect of surface mounted piezoelectric patch size on vibration response of a hybrid beam

NASA Astrophysics Data System (ADS)

Rahman, N.; Alam, M. N.

2018-02-01

Vibration response analysis of a hybrid beam with surface mounted patch piezoelectric layer is presented in this work. A one dimensional finite element (1D-FE) model based on efficient layerwise (zigzag) theory is used for the analysis. The beam element has eight mechanical and a variable number of electrical degrees of freedom. The beams are also modelled in 2D-FE (ABAQUS) using a plane stress piezoelectric quadrilateral element for piezo layers and a plane stress quadrilateral element for the elastic layers of hybrid beams. Results are presented to assess the effect of size of piezoelectric patch layer on the free and forced vibration responses of thin and moderately thick beams under clamped-free and clamped-clamped configurations. The beams are subjected to unit step loading and harmonic loading to obtain the forced vibration responses. The vibration control using in phase actuation potential on piezoelectric patches is also studied. The 1D-FE results are compared with the 2D-FE results.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale m{sub IR}

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

Bornyakov, V. G.; Mitrjushkin, V. K.; Mueller-Preussker, M.

2010-03-01

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found themore » Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.« less

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels

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

Liu, Jinn-Liang, E-mail: jinnliu@mail.nhcue.edu.tw; Eisenberg, Bob, E-mail: beisenbe@rush.edu

2014-12-14

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part ofmore » the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form — called Gibbs-Fermi entropy — that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10{sup 8}-fold range of Ca{sup 2+} concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms ranging from binding, to permeation, blocking, flexibility, and charge/space competition of the channel.« less

Phonon Confinement Effect in TiO2 Nanoparticles as Thermosensor Materials

DTIC Science & Technology

2018-01-24

TiO2 or ZnO nanoparticles (NPs) have a very strong finite-size dependency in their Raman spectra or photoluminescence (PL) spectra due to the phonon...spectrometers were used to establish the particle size versus the Raman/PL peak position master curves. Systematic isothermal and temperature- dependent heat...Thermosensor Materials", Workshop on Time- Dependent Temperature Measurements in Energy Release Processes, Chicago, IL, 2012. 11 3) Ashish Kumar Mishra

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.

Numerical Large Deviation Analysis of the Eigenstate Thermalization Hypothesis

NASA Astrophysics Data System (ADS)

Yoshizawa, Toru; Iyoda, Eiki; Sagawa, Takahiro

2018-05-01

A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have thermal properties. We numerically investigate the ETH by focusing on the large deviation property, which directly evaluates the ratio of athermal energy eigenstates in the energy shell. As a consequence, we have systematically confirmed that the strong ETH is indeed true even for near-integrable systems. Furthermore, we found that the finite-size scaling of the ratio of athermal eigenstates is a double exponential for nonintegrable systems. Our result illuminates the universal behavior of quantum chaos, and suggests that a large deviation analysis would serve as a powerful method to investigate thermalization in the presence of the large finite-size effect.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

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.

Finite driving rate and anisotropy effects in landslide modeling

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

Piegari, E.; Cataudella, V.; Di Maio, R.

2006-02-15

In order to characterize landslide frequency-size distributions and individuate hazard scenarios and their possible precursors, we investigate a cellular automaton where the effects of a finite driving rate and the anisotropy are taken into account. The model is able to reproduce observed features of landslide events, such as power-law distributions, as experimentally reported. We analyze the key role of the driving rate and show that, as it is increased, a crossover from power-law to non-power-law behaviors occurs. Finally, a systematic investigation of the model on varying its anisotropy factors is performed and the full diagram of its dynamical behaviors ismore » presented.« less

Effect of Thermal Diffusivity on the Detectability of TNDE

NASA Technical Reports Server (NTRS)

Zhao, Junduo; Chu, Tsuchin; Russell, Samuel S.

2000-01-01

The effect of thermal diffusively on the defect detectability in Carbon/Epoxy composite panels by transient thermography is presented in this paper. A series of Finite Element Models were constructed and analyzed to simulate the transient heat transfer phenomenon during Thermographic Non-destructive Evaluation (TNDE) of composite panels with square defects. Six common carbon fibers were considered. The models were built for composites with various combinations of fibers and volumetric ratios. Finite Element Analysis of these models showed the trends of the detectable range and the maximum thermal contrast versus the thermal diffusivity of various composites. Additionally, the trends of defect size to depth ratio and the thermal contrast has been investigated.

Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement.

PubMed

Chen, Xiaojie; Sasaki, Tatsuya; Perc, Matjaž

2015-11-24

Monitoring with implicated punishment is common in human societies to avert freeriding on common goods. But is it effective in promoting public cooperation? We show that the introduction of monitoring and implicated punishment is indeed effective, as it transforms the public goods game to a coordination game, thus rendering cooperation viable in infinite and finite well-mixed populations. We also show that the addition of within-group enforcement further promotes the evolution of public cooperation. However, although the group size in this context has nonlinear effects on collective action, an intermediate group size is least conductive to cooperative behaviour. This contradicts recent field observations, where an intermediate group size was declared optimal with the conjecture that group-size effects and within-group enforcement are responsible. Our theoretical research thus clarifies key aspects of monitoring with implicated punishment in human societies, and additionally, it reveals fundamental group-size effects that facilitate prosocial collective action.

Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement

NASA Astrophysics Data System (ADS)

Chen, Xiaojie; Sasaki, Tatsuya; Perc, Matjaž

2015-11-01

Monitoring with implicated punishment is common in human societies to avert freeriding on common goods. But is it effective in promoting public cooperation? We show that the introduction of monitoring and implicated punishment is indeed effective, as it transforms the public goods game to a coordination game, thus rendering cooperation viable in infinite and finite well-mixed populations. We also show that the addition of within-group enforcement further promotes the evolution of public cooperation. However, although the group size in this context has nonlinear effects on collective action, an intermediate group size is least conductive to cooperative behaviour. This contradicts recent field observations, where an intermediate group size was declared optimal with the conjecture that group-size effects and within-group enforcement are responsible. Our theoretical research thus clarifies key aspects of monitoring with implicated punishment in human societies, and additionally, it reveals fundamental group-size effects that facilitate prosocial collective action.

Statistical properties and condensate fluctuation of attractive Bose gas with finite number of particles

NASA Astrophysics Data System (ADS)

Bera, Sangita; Lekala, Mantile Leslie; Chakrabarti, Barnali; Bhattacharyya, Satadal; Rampho, Gaotsiwe Joel

2017-09-01

'We study the condensate fluctuation and several statistics of weakly interacting attractive Bose gas of 7 Li atoms in harmonic trap. Using exact recursion relation we calculate canonical ensemble partition function and study the thermal evolution of the condensate. As 7 Li condensate is associated with collapse, the number of condensate atom is truly finite and it facilitates to study the condensate in mesoscopic region. Being highly correlated, we utilize the two-body correlated basis function to get the many-body effective potential which is further used to calculate the energy levels. Taking van der Waals interaction as interatomic interaction we calculate several quantities like condensate fraction N, root-mean-square fluctuation δn0 and different orders of central moments. We observe the effect of finite size on the calculation of condensate fluctuations and the effect of attractive interaction over the noninteracting limit. We observe the depletion of the condensate with increase in temperature. The calculated moments nicely exhibit the mesoscopic effect. The sharp fall in the root-mean-square fluctuation near the critical point signifies the possibility of phase transition.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Biomechanical effects of metastasis in the osteoporotic lumbar spine: A Finite Element Analysis.

PubMed

Salvatore, Giuseppe; Berton, Alessandra; Giambini, Hugo; Ciuffreda, Mauro; Florio, Pino; Longo, Umile Giuseppe; Denaro, Vincenzo; Thoreson, Andrew; An, Kai-Nan

2018-02-05

Cancer patients are likely to undergo osteoporosis as consequence of hormone manipulation and/or chemotherapy. Little is known about possible increased risk of fracture in this population. The aim of this study was to describe the biomechanical effect of a metastatic lesion in an osteoporotic lumbar spine model. A finite element model of two spinal motion segments (L3-L5) was extracted from a previously developed L3-Sacrum model and used to analyze the effect of metastasis size and bone mineral density (BMD) on Vertebral bulge (VB) and Vertebral height (VH). VB and VH represent respectively radial and axial displacement and they have been correlated to burst fracture. A total of 6 scenarios were evaluated combining three metastasis sizes (no metastasis, 15% and 30% of the vertebral body) and two BMD conditions (normal BMD and osteoporosis). 15% metastasis increased VB and VH by 178% and 248%, respectively in normal BMD model; while VB and VH increased by 134% and 174% in osteoporotic model. 30% metastasis increased VB and VH by 88% and 109%, respectively, when compared to 15% metastasis in normal BMD model; while VB and VH increased by 59% and 74% in osteoporotic model. A metastasis in the osteoporotic lumbar spine always leads to a higher risk of vertebral fracture. This risk increases with the size of the metastasis. Unexpectedly, an increment in metastasis size in the normal BMD spine produces a greater impact on vertebral stability compared to the osteoporotic spine.

Modeling of electrically actuated elastomer structures for electro-optical modulation

NASA Astrophysics Data System (ADS)

Kluge, Christian; Galler, Nicole; Ditlbacher, Harald; Gerken, Martina

2011-02-01

A transparent elastomer layer sandwiched between two metal electrodes deforms upon voltage application due to electrostatic forces. This structure can be used as tunable waveguide. We investigate structures of a polydimethylsiloxane (PDMS) layer with 1-30 μm thickness and 40 nm gold electrodes. For extended electrodes the effect size may be calculated analytically as a function of the Poisson ratio. A fully coupled finite-element method (FEM) is used for calculation of the position-dependent deformation in case of structured electrodes. Different geometries are compared concerning actuation effect size and homogeneity. Structuring of the top electrode results in high effect magnitude, but non-uniform deformation concentrated at the electrode edges. Structured bottom electrodes provide good compromise between effect size and homogeneity for electrode widths of 2.75 times the elastomer thickness.

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.

Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer.

PubMed

Lim, Jongil; Whitcomb, John; Boyd, James; Varghese, Julian

2007-01-01

A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

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.

Finite-size anomalies of the Drude weight: Role of symmetries and ensembles

NASA Astrophysics Data System (ADS)

Sánchez, R. J.; Varma, V. K.

2017-12-01

We revisit the numerical problem of computing the high temperature spin stiffness, or Drude weight, D of the spin-1 /2 X X Z chain using exact diagonalization to systematically analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero total magnetization, we find D vanishes exactly due to spin-inversion symmetry for all but the anisotropies Δ˜M N=cos(π M /N ) with N ,M ∈Z+ coprimes and N >M , provided system sizes L ≥2 N , for which states with different spin-inversion signature become degenerate due to the underlying s l2 loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on data from the system sizes and anisotropies Δ˜M N (with N

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.

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

NASA Astrophysics Data System (ADS)

Tůma, K.; Stupkiewicz, S.; Petryk, H.

2016-10-01

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.

Planetary Interiors: Parametric Modeling of Global Geophysical Properties

NASA Astrophysics Data System (ADS)

Montgomery, W.; Jeanloz, R.

2004-12-01

Taking into account a realistic form of equation of state, we parameterize the degree to which bulk geophysical properties of planets are sensitive to gravitational self-compression. For example, the normalized moment of mass of a uniform-composition planet is C/Ma2 = 0.40 only in the limit of zero planetary size or incompressible material, and decreases toward 0.32 for finite compressibility as the planetary radius increases toward a = 104 km (M is planetary mass). Central density correspondingly increases from ρ 0, the surface density, toward 10 * ρ 0. Our calculations, based on the Eulerian finite-strain equation of state, make it possible to distinguish the effects of self-compression from the effects of non-uniformity (due either to changes in bulk composition or in phase with depth) as these influence planetary mass and moment of inertia relative to size. As observations of extra-solar planets can provide estimates of their mass and diameter (hence mean density), our formulation can account for the effects of compression in modeling the internal constitution and evolution of these objects. The effects of compression are especially important for giant and super-giant planets, such as the majority that have been observed to date.

Thermal conduction in particle packs via finite elements

NASA Astrophysics Data System (ADS)

Lechman, Jeremy B.; Yarrington, Cole; Erikson, William; Noble, David R.

2013-06-01

Conductive transport in heterogeneous materials composed of discrete particles is a fundamental problem for a number of applications. While analytical results and rigorous bounds on effective conductivity in mono-sized particle dispersions are well established in the literature, the methods used to arrive at these results often fail when the average size of particle clusters becomes large (i.e., near the percolation transition where particle contact networks dominate the bulk conductivity). Our aim is to develop general, efficient numerical methods that would allow us to explore this behavior and compare to a recent microstructural description of conduction in this regime. To this end, we present a finite element analysis approach to modeling heat transfer in granular media with the goal of predicting effective bulk thermal conductivities of particle-based heterogeneous composites. Our approach is verified against theoretical predictions for random isotropic dispersions of mono-disperse particles at various volume fractions up to close packing. Finally, we present results for the probability distribution of the effective conductivity in particle dispersions generated by Brownian dynamics, and suggest how this might be useful in developing stochastic models of effective properties based on the dynamical process involved in creating heterogeneous dispersions.

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.

Magnetochromic sensing and size-dependent collective excitations in iron oxide nanoparticles

DOE PAGES

O'Neal, Kenneth R.; Patete, Jonathan M.; Chen, Peng; ...

2017-03-10

We combine optical and magneto-optical spectroscopies with complementary vibrational and magnetic property measurements to reveal finite length scale effects in nanoscale α–Fe 2O 3. Analysis of the d-to-d on-site excitations uncovers enhanced color contrast at particle sizes below approximately 75 nm due to size-induced changes in spin-charge coupling that are suppressed again below the superparamagnetic limit. These findings provide a general strategy for amplifying magnetochromism in α–Fe 2O 3 and other iron-containing nanomaterials that may be useful for advanced sensing applications. Lastly, we also unravel the size dependence of collective excitations in this iconic antiferromagnet.

Magnetochromic sensing and size-dependent collective excitations in iron oxide nanoparticles

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

O'Neal, Kenneth R.; Patete, Jonathan M.; Chen, Peng

We combine optical and magneto-optical spectroscopies with complementary vibrational and magnetic property measurements to reveal finite length scale effects in nanoscale α–Fe 2O 3. Analysis of the d-to-d on-site excitations uncovers enhanced color contrast at particle sizes below approximately 75 nm due to size-induced changes in spin-charge coupling that are suppressed again below the superparamagnetic limit. These findings provide a general strategy for amplifying magnetochromism in α–Fe 2O 3 and other iron-containing nanomaterials that may be useful for advanced sensing applications. Lastly, we also unravel the size dependence of collective excitations in this iconic antiferromagnet.

Atomistic origin of size effects in fatigue behavior of metallic glasses

NASA Astrophysics Data System (ADS)

Sha, Zhendong; Wong, Wei Hin; Pei, Qingxiang; Branicio, Paulo Sergio; Liu, Zishun; Wang, Tiejun; Guo, Tianfu; Gao, Huajian

2017-07-01

While many experiments and simulations on metallic glasses (MGs) have focused on their tensile ductility under monotonic loading, the fatigue mechanisms of MGs under cyclic loading still remain largely elusive. Here we perform molecular dynamics (MD) and finite element simulations of tension-compression fatigue tests in MGs to elucidate their fatigue mechanisms with focus on the sample size effect. Shear band (SB) thickening is found to be the inherent fatigue mechanism for nanoscale MGs. The difference in fatigue mechanisms between macroscopic and nanoscale MGs originates from whether the SB forms partially or fully through the cross-section of the specimen. Furthermore, a qualitative investigation of the sample size effect suggests that small sample size increases the fatigue life while large sample size promotes cyclic softening and necking. Our observations on the size-dependent fatigue behavior can be rationalized by the Gurson model and the concept of surface tension of the nanovoids. The present study sheds light on the fatigue mechanisms of MGs and can be useful in interpreting previous experimental results.

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.

Baryonic popcorn

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Melnikov, Dmitry; Sonnenschein, Jacob

2012-11-01

In the large N c limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities. We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an "abelian anti- ferromagnetic" straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.

Nonlocal Poisson-Fermi double-layer models: Effects of nonuniform ion sizes on double-layer structure

NASA Astrophysics Data System (ADS)

Xie, Dexuan; Jiang, Yi

2018-05-01

This paper reports a nonuniform ionic size nonlocal Poisson-Fermi double-layer model (nuNPF) and a uniform ionic size nonlocal Poisson-Fermi double-layer model (uNPF) for an electrolyte mixture of multiple ionic species, variable voltages on electrodes, and variable induced charges on boundary segments. The finite element solvers of nuNPF and uNPF are developed and applied to typical double-layer tests defined on a rectangular box, a hollow sphere, and a hollow rectangle with a charged post. Numerical results show that nuNPF can significantly improve the quality of the ionic concentrations and electric fields generated from uNPF, implying that the effect of nonuniform ion sizes is a key consideration in modeling the double-layer structure.

Stochastic Oscillation in Self-Organized Critical States of Small Systems: Sensitive Resting State in Neural Systems

NASA Astrophysics Data System (ADS)

Wang, Sheng-Jun; Ouyang, Guang; Guang, Jing; Zhang, Mingsha; Wong, K. Y. Michael; Zhou, Changsong

2016-01-01

Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems, which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli.

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.

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 .

Anisotropic failure and size effects in periodic honeycomb materials: A gradient-elasticity approach

NASA Astrophysics Data System (ADS)

Réthoré, Julien; Dang, Thi Bach Tuyet; Kaltenbrunner, Christine

2017-02-01

This paper proposes a fracture mechanics model for the analysis of crack propagation in periodic honeycomb materials. The model is based on gradient-elasticity which enables us to account for the effect of the material structure at the macroscopic scale. For simulating the propagation of cracks along an arbitrary path, the numerical implementation is elaborated based on an extended finite element method with the required level of continuity. The two main features captured by the model are directionality and size effect. The numerical predictions are consistent with experimental results on honeycomb materials but also with results reported in the literature for microstructurally short cracks in metals.

General formulation of long-range degree correlations in complex networks

NASA Astrophysics Data System (ADS)

Fujiki, Yuka; Takaguchi, Taro; Yakubo, Kousuke

2018-06-01

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One joint and four conditional probability distributions are introduced to fully describe long-range degree correlations with respect to degrees k and k' of two nodes and shortest path length l between them. We present general relations among these probability distributions and clarify the relevance to nearest-neighbor degree correlations. Unlike nearest-neighbor correlations, some of these probability distributions are meaningful only in finite-size networks. Furthermore, as a baseline to determine the existence of intrinsic long-range degree correlations in a network other than inevitable correlations caused by the finite-size effect, the functional forms of these probability distributions for random networks are analytically evaluated within a mean-field approximation. The utility of our argument is demonstrated by applying it to real-world networks.

Generalized Knudsen Number for Unsteady Fluid Flow.

PubMed

Kara, V; Yakhot, V; Ekinci, K L

2017-02-17

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Generalized Knudsen Number for Unsteady Fluid Flow

NASA Astrophysics Data System (ADS)

Kara, V.; Yakhot, V.; Ekinci, K. L.

2017-02-01

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Determination of female breast tumor and its parameter estimation by thermal simulation

NASA Astrophysics Data System (ADS)

Chen, Xin-guang; Xu, A.-qing; Yang, Hong-qin; Wang, Yu-hua; Xie, Shu-sen

2010-02-01

Thermal imaging is an emerging method for early detection of female breast tumor. The main challenge for thermal imaging used in breast clinics lies in how to detect or locate the tumor and obtain its related parameters. The purpose of this study is to apply an improved method which combined a genetic algorithm with finite element thermal analysis to determine the breast tumor and its parameters, such as the size, location, metabolic heat generation and blood perfusion rate. A finite element model for breast embedded a tumor was used to investigate the temperature distribution, and then the influences of tumor metabolic heat generation, tumor location and tumor size on the temperature were studied by use of an improved genetic algorithm. The results show that thermal imaging is a potential and effective detection tool for early breast tumor, and thermal simulation may be helpful for the explanation of breast thermograms.

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.

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.

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.

Three-dimensional finite element analysis and comparison of a new intramedullary fixation with interlocking intramedullary nail.

PubMed

Liu, Chang-cheng; Xing, Wen-zhao; Zhang, Ya-xing; Pan, Zheng-hua; Feng, Wen-ling

2015-03-01

This study was set to introduce a new intramedullary fixation, explore its biomechanical properties, and provide guidance for further biomechanical experiments. With the help of CT scans and finite element modeling software, finite element model was established for a new intramedullary fixation and intramedullary nailing of femoral shaft fractures in a volunteer adult. By finite element analysis software ANSYS 10.0, we conducted 235-2,100 N axial load, 200-1,000 N bending loads and 2-15 Nm torsional loading, respectively, and analyzed maximum stress distribution, size, and displacement of the fracture fragments of the femur and intramedullary nail. During the loading process, the maximum stress of our new intramedullary fixation were within the normal range, and the displacement of the fracture fragments was less than 1 mm. Our new intramedullary fixation exhibited mechanical reliability and unique advantages of anti-rotation, which provides effective supports during fracture recovery.

Meta-ecosystem dynamics and functioning on finite spatial networks

PubMed Central

Marleau, Justin N.; Guichard, Frédéric; Loreau, Michel

2014-01-01

The addition of spatial structure to ecological concepts and theories has spurred integration between sub-disciplines within ecology, including community and ecosystem ecology. However, the complexity of spatial models limits their implementation to idealized, regular landscapes. We present a model meta-ecosystem with finite and irregular spatial structure consisting of local nutrient–autotrophs–herbivores ecosystems connected through spatial flows of materials and organisms. We study the effect of spatial flows on stability and ecosystem functions, and provide simple metrics of connectivity that can predict these effects. Our results show that high rates of nutrient and herbivore movement can destabilize local ecosystem dynamics, leading to spatially heterogeneous equilibria or oscillations across the meta-ecosystem, with generally increased meta-ecosystem primary and secondary production. However, the onset and the spatial scale of these emergent dynamics depend heavily on the spatial structure of the meta-ecosystem and on the relative movement rate of the autotrophs. We show how this strong dependence on finite spatial structure eludes commonly used metrics of connectivity, but can be predicted by the eigenvalues and eigenvectors of the connectivity matrix that describe the spatial structure and scale. Our study indicates the need to consider finite-size ecosystems in meta-ecosystem theory. PMID:24403323

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.

High-numerical-aperture-based virtual point detectors for photoacoustic tomography

NASA Astrophysics Data System (ADS)

Li, Changhui; Wang, Lihong V.

2008-07-01

The focal point of a high-numerical-aperture (NA) ultrasonic transducer can be used as a virtual point detector. This virtual point detector detects omnidirectionally over a wide acceptance angle. It also combines a large active transducer surface and a small effective virtual detector size. Thus the sensitivity is high compared with that of a real point detector, and the aperture effect is small compared with that of a finite size transducer. We present two kinds of high-NA-based virtual point detectors and their successful application in photoacoustic tomography. They can also be applied in other ultrasound-related fields.

Energy absorption in aluminum extrusions for a spaceframe chassis

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

Logan, R.W.; Perfect, S.A.; Parkinson, R.D.

1994-09-19

This work describes the design, finite-element analysis, and verifications performed by LLNL and Kaiser Aluminum for the prototype design of the CALSTART Running Chassis purpose-built electric vehicle. Component level studies, along with our previous experimental and finite-element works, provided the confidence to study the crashworthiness of a complete aluminum spaceframe. Effects of rail geometry, size, and thickness were studied in order to achieve a controlled crush of the front end structure. These included the performance of the spaceframe itself, and the additive effects of the powertrain cradle and powertrain (motor/controller in this case) as well as suspension. Various design iterationsmore » for frontal impact at moderate and high speed are explored.« less

Stellar occultation of polarized light from circumstellar electrons. I - Flat envelopes viewed edge on

NASA Technical Reports Server (NTRS)

Brown, John C.; Fox, Geoffrey K.

1989-01-01

The depolarizing and occultation effects of a finite spherical light source on the polarization of light Thomson-scattered from a flat circumstellar envelope seen edge-on are analyzed. The analysis shows that neglect of the finite size of the light source leads to a gross overestimate of the polarization for a given disk geometry. By including occultation and depolarization, it is found that B-star envelopes are necessarily highly flattened disk-type structures. For a disk viewed edge-on, the effect of occultation reduces the polarization more than the inclusion of the depolarization factor alone. Analysis of a one-dimensional plume leads to a powerful technique that permits the electron density distribution to be explicitly obtained from the polarimetric data.

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.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

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

He Guangjun; Duan Wenshan; Tian Duoxiang

2008-04-15

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev-Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Quantum size effects in the size-temperature phase diagram of gallium: structural characterization of shape-shifting clusters.

PubMed

Steenbergen, Krista G; Gaston, Nicola

2015-02-09

Finite temperature analysis of cluster structures is used to identify signatures of the low-temperature polymorphs of gallium, based on the results of first-principle Born-Oppenheimer molecular dynamics simulations. Pre-melting structural transitions proceed from either the β- and/or the δ-phase to the γ- or δ-phase, with a size- dependent phase progression. We relate the stability of each isomer to the electronic structures of the different phases, giving new insight into the origin of polymorphism in this complicated element. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The effect of size and composition on structural transitions in monometallic nanoparticles

NASA Astrophysics Data System (ADS)

Rossi, Kevin; Pavan, Luca; Soon, YeeYeen; Baletto, Francesca

2018-02-01

Predicting the morphological stability of nanoparticles is an essential step towards the accurate modelling of their chemophysical properties. Here we investigate solid-solid transitions in monometallic clusters of 0.5-2.0 nm diameter at finite temperatures and we report the complex dependence of the rearrangement mechanism on the nanoparticle's composition and size. The concerted Lipscomb's Diamond-Square-Diamond mechanisms which connects the decahedral or the cuboctahedral to the icosahedral basins, take place only below a material dependent critical size above which surface diffusion prevails and leads to low-symmetry and defected shapes still belonging to the initial basin.

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.

Influence of surface and finite size effects on the structural and magnetic properties of nanocrystalline lanthanum strontium perovskite manganites

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

Žvátora, Pavel; Veverka, Miroslav; Veverka, Pavel

2013-08-15

Syntheses of nanocrystalline perovskite phases of the general formula La{sub 1−x}Sr{sub x}MnO{sub 3+δ} were carried out employing sol–gel technique followed by thermal treatment at 700–900 °C under oxygen flow. The prepared samples exhibit a rhombohedral structure with space group R3{sup ¯}c in the whole investigated range of composition 0.20≤x≤0.45. The studies were aimed at the chemical composition including oxygen stoichiometry and extrinsic properties, i.e. size of the particles, both influencing the resulting structural and magnetic properties. The oxygen stoichiometry was determined by chemical analysis revealing oxygen excess in most of the studied phases. The excess was particularly high for themore » samples with the smallest crystallites (12–28 nm) while comparative bulk materials showed moderate non-stoichiometry. These differences are tentatively attributed to the surface effects in view of the volume fraction occupied by the upper layer whose atomic composition does not comply with the ideal bulk stoichiometry. - Graphical abstract: Evolution of the particle size with annealing temperature in the nanocrystalline La{sub 0.70}Sr{sub 0.30}MnO{sub 3+δ} phase. Display Omitted - Highlights: • The magnetic behaviour of nanocrystalline La{sub 1−x}Sr{sub x}MnO{sub 3+δ} phases was analyzed on the basis of their crystal structure, chemical composition and size of the particles. • Their Curie temperature and magnetization are markedly affected by finite size and surface effects. • The oxygen excess observed in the La{sub 1−x}Sr{sub x}MnO{sub 3+δ} nanoparticles might be generated by the surface layer with deviated oxygen stoichiometry.« less

Clinical Biomechanics of Wear in Total Hip Arthroplasty

PubMed Central

Callaghan, John J; Pedersen, Douglas R; Johnston, Richard C; Brown, Thomas D

2003-01-01

Complementary clinical and laboratory studies were performed to identify variables associated with polyethylene wear following total hip replacement, and to elucidate the mechanisms responsible for accelerated wear in the total hip arthroplasty construct. Observational cohort studies were performed using a prospective clinical database of more than 4000 consecutive primary total hip arthroplasties performed by a single surgeon, to identify wear-related variables. These variables included head size, acetabular/femoral component impingement, and third body debris. Novel digital edge detection techniques were developed and employed to accurately measure wear, and to determine the relationships of head size and third body debris to acceleration of wear. A novel slidingdistance-coupled finite element model was formulated and employed to examine the mechanisms responsible for wear. The long-term cohort studies demonstrated smaller head sizes to be associated with less wear. Third body debris generated from cable fretting was associated with an increase in wear, osteolysis, and acetabular loosening, especially with larger head sizes. The sliding-distance-coupled finite element model replicated the wear rates occurring in vitro and in vivo, demonstrating the importance of sliding distance on polyethylene wear following total hip arthroplasty. It also demonstrated substantial increases in wear associated with femoral head scratching from third body debris. Further extension of the finite element formulation demonstrated the potential for acetabular component rim damage from impingement wear, and the enhanced potential for third body ingress to the bearing surface with larger head sizes. Edge detection wear measurement techniques demonstrated that early wear rates were predictive of long-term wear rates. These complementary clinical and laboratory investigations have provided insight into 1) the significance of sliding distance and physiologic loci of motion as contributing factors in minimizing wear, 2) the deleterious effects of third body particulates in accelerating wear, 3) the potential for, and factors related to, impingement wear, and 4) the potential advantages and compromises related to the use of larger head sizes in the bearing surface construct. PMID:14575243

Effect of shape and size of lung and chest wall on stresses in the lung

NASA Technical Reports Server (NTRS)

Vawter, D. L.; Matthews, F. L.; West, J. B.

1975-01-01

To understand better the effect of shape and size of lung and chest wall on the distribution of stresses, strains, and surface pressures, we analyzed a theoretical model using the technique of finite elements. First we investigated the effects of changing the chest wall shape during expansion, and second we studied lungs of a variety of inherent shapes and sizes. We found that, in general, the distributions of alveolar size, mechanical stresses, and surface pressures in the lungs were dominated by the weight of the lung and that changing the shape of the lung or chest wall had relatively little effect. Only at high states of expansion where the lung was very stiff did changing the shape of the chest wall cause substantial changes. Altering the inherent shape of the lung generally had little effect but the topographical differences in stresses and surface pressures were approximately proportional to lung height. The results are generally consistent with those found in the dog by Hoppin et al (1969).

Finite element analysis of fretting contact for nonhomogenous materials

NASA Astrophysics Data System (ADS)

Korkmaz, Y. M.; Coker, D.

2018-01-01

Fretting problem arises in the case of relatively small sliding motion between contacting surfaces. Fatigue life of the components that are in contact with each other, especially in rotorcraft may be significantly reduced due to fretting. The purpose of this study is to investigate material inhomogeneity near the contact region on the fretting problem in a cylindrical on flat contact configuration. A finite element (FE) model was constructed by using commercial finite element package ABAQUSTMto study partial sliding and stress concentrations. In order to investigate the effect of material inhomogeneity, the fretting contact is analyzed by introducing voids near the contact region. The void size and an array of voids is introduced into the substrate. The results are compared in terms of pressure, shear traction, tangential stress magnitudes and relative slip between the contacting materials.

High precision determination of the melting points of water TIP4P/2005 and water TIP4P/Ice models by the direct coexistence technique

NASA Astrophysics Data System (ADS)

Conde, M. M.; Rovere, M.; Gallo, P.

2017-12-01

An exhaustive study by molecular dynamics has been performed to analyze the factors that enhance the precision of the technique of direct coexistence for a system of ice and liquid water. The factors analyzed are the stochastic nature of the method, the finite size effects, and the influence of the initial ice configuration used. The results obtained show that the precision of estimates obtained through the technique of direct coexistence is markedly affected by the effects of finite size, requiring systems with a large number of molecules to reduce the error bar of the melting point. This increase in size causes an increase in the simulation time, but the estimate of the melting point with a great accuracy is important, for example, in studies on the ice surface. We also verified that the choice of the initial ice Ih configuration with different proton arrangements does not significantly affect the estimate of the melting point. Importantly this study leads us to estimate the melting point at ambient pressure of two of the most popular models of water, TIP4P/2005 and TIP4P/Ice, with the greatest precision to date.

Stabilizing Selection, Purifying Selection, and Mutational Bias in Finite Populations

PubMed Central

Charlesworth, Brian

2013-01-01

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size. PMID:23709636

Numerical Analysis of Stress Concentration in Isotropic and Laminated Plates with Inclined Elliptical Holes

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Belarbi, Mohamed Ouejdi; Guettala, Abdelhamid

2018-03-01

The design of high-performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. Understanding the behavior of perforated laminates is necessary for structural design. In the current work, stress concentrations taking place in laminated and isotropic plates subjected to tensile load are investigated. The stress concentrations are obtained using a recent quadrilateral finite element of four nodes with 32 DOFs. The present finite element (PE) is a combination of two finite elements. The first finite element is a linear isoparametric membrane element and the second is a high precision Hermitian element. One of the essential objectives of the current investigation is to confirm the capability and efficiency of the PE for stress determination in perforated laminates. Different geometric parameters, such as the cutout form, sizes and cutout orientations, which have a considerable effect on the stress values, are studied. Using the present finite element formulation, the obtained results are found to be in good agreement with the analytical findings, which validates the capability and the efficiency of the proposed formulation. Finally, to understand the material parameters effect such as the orientation of fibers and degree of orthotropy ratio on the stress values, many figures are presented using different ellipse major to minor axis ratio. The stress concentration values are considerably affected by increasing the orientation angle of the fibers and degree of orthotropy.

SPIREs: A Finite-Difference Frequency-Domain electromagnetic solver for inhomogeneous magnetized plasma cylinders

NASA Astrophysics Data System (ADS)

Melazzi, D.; Curreli, D.; Manente, M.; Carlsson, J.; Pavarin, D.

2012-06-01

We present SPIREs (plaSma Padova Inhomogeneous Radial Electromagnetic solver), a Finite-Difference Frequency-Domain (FDFD) electromagnetic solver in one dimension for the rapid calculation of the electromagnetic fields and the deposited power of a large variety of cylindrical plasma problems. The two Maxwell wave equations have been discretized using a staggered Yee mesh along the radial direction of the cylinder, and Fourier transformed along the other two dimensions and in time. By means of this kind of discretization, we have found that mode-coupling of fast and slow branches can be fully resolved without singularity issues that flawed other well-established methods in the past. Fields are forced by an antenna placed at a given distance from the plasma. The plasma can be inhomogeneous, finite-temperature, collisional, magnetized and multi-species. Finite-temperature Maxwellian effects, comprising Landau and cyclotron damping, have been included by means of the plasma Z dispersion function. Finite Larmor radius effects have been neglected. Radial variations of the plasma parameters are taken into account, thus extending the range of applications to a large variety of inhomogeneous plasma systems. The method proved to be fast and reliable, with accuracy depending on the spatial grid size. Two physical examples are reported: fields in a forced vacuum waveguide with the antenna inside, and forced plasma oscillations in the helicon radiofrequency range.

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.

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

NASA Astrophysics Data System (ADS)

Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent

2016-04-01

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

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

PubMed

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

2016-10-01

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

Finite element modeling of sound transmission with perforations of tympanic membrane

PubMed Central

Gan, Rong Z.; Cheng, Tao; Dai, Chenkai; Yang, Fan; Wood, Mark W.

2009-01-01

A three-dimensional finite element (FE) model of human ear with structures of the external ear canal, middle ear, and cochlea has been developed recently. In this paper, the FE model was used to predict the effect of tympanic membrane (TM) perforations on sound transmission through the middle ear. Two perforations were made in the posterior-inferior quadrant and inferior site of the TM in the model with areas of 1.33 and 0.82 mm2, respectively. These perforations were also created in human temporal bones with the same size and location. The vibrations of the TM (umbo) and stapes footplate were calculated from the model and measured from the temporal bones using laser Doppler vibrometers. The sound pressure in the middle ear cavity was derived from the model and measured from the bones. The results demonstrate that the TM perforations can be simulated in the FE model with geometrical visualization. The FE model provides reasonable predictions on effects of perforation size and location on middle ear transfer function. The middle ear structure-function relationship can be revealed with multi-field coupled FE analysis. PMID:19603881

Permeability-Selectivity Analysis of Microfiltration and Ultrafiltration Membranes: Effect of Pore Size and Shape Distribution and Membrane Stretching.

PubMed

Siddiqui, Muhammad Usama; Arif, Abul Fazal Muhammad; Bashmal, Salem

2016-08-06

We present a modeling approach to determine the permeability-selectivity tradeoff for microfiltration and ultrafiltration membranes with a distribution of pore sizes and pore shapes. Using the formulated permeability-selectivity model, the effect of pore aspect ratio and pore size distribution on the permeability-selectivity tradeoff of the membrane is analyzed. A finite element model is developed to study the effect of membrane stretching on the distribution of pore sizes and shapes in the stretched membrane. The effect of membrane stretching on the permeability-selectivity tradeoff of membranes is also analyzed. The results show that increasing pore aspect ratio improves membrane performance while increasing the width of pore size distribution deteriorates the performance. It was also found that the effect of membrane stretching on the permeability-selectivity tradeoff is greatly affected by the uniformity of pore distribution in the membrane. Stretching showed a positive shift in the permeability-selectivity tradeoff curve of membranes with well-dispersed pores while in the case of pore clustering, a negative shift in the permeability-selectivity tradeoff curve was observed.

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

Lu, Dingjie; Xie, Yi Min; Huang, Xiaodong

Analytical studies on the size effects of a simply-shaped beam fixed at both ends have successfully explained the sudden changes of effective Young's modulus as its diameter decreases below 100 nm. Yet they are invalid for complex nanostructures ubiquitously existing in nature. In accordance with a generalized Young-Laplace equation, one of the representative size effects is transferred to non-uniformly distributed pressure against an external surface due to the imbalance of inward and outward loads. Because the magnitude of pressure depends on the principal curvatures, iterative steps have to be adopted to gradually stabilize the structure in finite element analysis. Computational resultsmore » are in good agreement with both experiment data and theoretical prediction. Furthermore, the investigation on strengthened and softened Young's modulus for two complex nanostructures demonstrates that the proposed computational method provides a general and effective approach to analyze the size effects for nanostructures in arbitrary shape.« less

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Transferable Coarse-Grained Models for Ionic Liquids.

PubMed

Wang, Yanting; Feng, Shulu; Voth, Gregory A

2009-04-14

The effective force coarse-graining (EF-CG) method was applied to the imidazolium-based nitrate ionic liquids with various alkyl side-chain lengths. The nonbonded EF-CG forces for the ionic liquid with a short side chain were extended to generate the nonbonded forces for the ionic liquids with longer side chains. The EF-CG force fields for the ionic liquids exhibit very good transferability between different systems at various temperatures and are suitable for investigating the mesoscopic structural properties of this class of ionic liquids. The good additivity and ease of manipulation of the EF-CG force fields can allow for an inverse design methodology of ionic liquids at the coarse-grained level. With the EF-CG force field, the molecular dynamics (MD) simulation at a very large scale has been performed to check the significance of finite size effects on the structural properties. From these MD simulation results, it can be concluded that the finite size effect on the phenomenon of ionic liquid spatial heterogeneity (Wang, Y.; Voth, G. A. J. Am. Chem. Soc. 2005, 127, 12192) is small and that this phenomenon is indeed a nanostructural behavior which leads to the experimentally observed mesoscopic heterogeneous structure of ionic liquids.

Taming axial dispersion in hydrodynamic chromatography columns through wall patterning

NASA Astrophysics Data System (ADS)

Adrover, Alessandra; Cerbelli, Stefano; Giona, Massimiliano

2018-04-01

A well-known limitation of hydrodynamic chromatography arises from the synergistic interaction between transverse diffusion and streamwise convection, which enhances axial dispersion through the Taylor-Aris mechanism. We show that a periodic sequence of slip/no-slip conditions at the channel walls (e.g., representing wall indentations hosting stable air pockets) can significantly reduce axial dispersion, thus enhancing separation performance. The theoretical/numerical analysis is based on a generalization of Brenner's macrotransport approach to solute transport, here modified to account for the finite-size of the suspended particles. The most effective dispersion-taming outcome is observed when the alternating sequence of slip/no-slip conditions yields non-vanishing cross-sectional flow components. The combination of these components with the hindering interaction between the channel boundaries and the finite-sized particles gives rise to a non-trivial solution of Brenner's problem on the unit periodic cell, where the cross-sectional particle number density departs from the spatially homogeneous condition. In turn, this effect impacts upon the solution of the so-called b-field defining the large-scale dispersion tensor, with an overall decremental effect on the axial dispersion coefficient and on the Height Equivalent of a Theoretical Plate.

Damage Accumulation in Silica Glass Nanofibers.

PubMed

Bonfanti, Silvia; Ferrero, Ezequiel E; Sellerio, Alessandro L; Guerra, Roberto; Zapperi, Stefano

2018-06-06

The origin of the brittle-to-ductile transition, experimentally observed in amorphous silica nanofibers as the sample size is reduced, is still debated. Here we investigate the issue by extensive molecular dynamics simulations at low and room temperatures for a broad range of sample sizes, with open and periodic boundary conditions. Our results show that small sample-size enhanced ductility is primarily due to diffuse damage accumulation, that for larger samples leads to brittle catastrophic failure. Surface effects such as boundary fluidization contribute to ductility at room temperature by promoting necking, but are not the main driver of the transition. Our results suggest that the experimentally observed size-induced ductility of silica nanofibers is a manifestation of finite-size criticality, as expected in general for quasi-brittle disordered networks.

Effect of cell-size on the energy absorption features of closed-cell aluminium foams

NASA Astrophysics Data System (ADS)

Nammi, S. K.; Edwards, G.; Shirvani, H.

2016-11-01

The effect of cell-size on the compressive response and energy absorption features of closed-cell aluminium (Al) foam were investigated by finite element method. Micromechanical models were constructed with a repeating unit-cell (RUC) which was sectioned from tetrakaidecahedra structure. Using this RUC, three Al foam models with different cell-sizes (large, medium and small) and all of same density, were built. These three different cell-size pieces of foam occupy the same volume and their domains contained 8, 27 and 64 RUCs respectively. However, the smaller cell-size foam has larger surface area to volume ratio compared to other two. Mechanical behaviour was modelled under uniaxial loading. All three aggregates (3D arrays of RUCs) of different cell-sizes showed an elastic region at the initial stage, then followed by a plateau, and finally, a densification region. The smaller cell size foam exhibited a higher peak-stress and a greater densification strain comparing other two cell-sizes investigated. It was demonstrated that energy absorption capabilities of smaller cell-size foams was higher compared to the larger cell-sizes examined.

A hybrid LBG/lattice vector quantizer for high quality image coding

NASA Technical Reports Server (NTRS)

Ramamoorthy, V.; Sayood, K.; Arikan, E. (Editor)

1991-01-01

It is well known that a vector quantizer is an efficient coder offering a good trade-off between quantization distortion and bit rate. The performance of a vector quantizer asymptotically approaches the optimum bound with increasing dimensionality. A vector quantized image suffers from the following types of degradations: (1) edge regions in the coded image contain staircase effects, (2) quasi-constant or slowly varying regions suffer from contouring effects, and (3) textured regions lose details and suffer from granular noise. All three of these degradations are due to the finite size of the code book, the distortion measures used in the design, and due to the finite training procedure involved in the construction of the code book. In this paper, we present an adaptive technique which attempts to ameliorate the edge distortion and contouring effects.

Effects of welding technology on welding stress based on the finite element method

NASA Astrophysics Data System (ADS)

Fu, Jianke; Jin, Jun

2017-01-01

Finite element method is used to simulate the welding process under four different conditions of welding flat butt joints. Welding seams are simulated with birth and death elements. The size and distribution of welding residual stress is obtained in the four kinds of welding conditions by Q345 manganese steel plate butt joint of the work piece. The results shown that when using two-layers welding,the longitudinal and transverse residual stress were reduced;When welding from Middle to both sides,the residual stress distribution will change,and the residual stress in the middle of the work piece was reduced.

Temporal and spatiotemporal correlation functions for trapped Bose gases

NASA Astrophysics Data System (ADS)

Kohnen, M.; Nyman, R. A.

2015-03-01

Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into account the effects of finite-size and -duration measurements made by light beams passing through the atom cloud. We specialize to the case of Bose gases in harmonic traps above critical temperature, for weakly perturbative measurements. For overlapping measurement regions, shot-noise correlations revive after a trap oscillation period. For nonoverlapping regions, bosonic correlations dominate at long times, and propagate at finite speeds. Finally, we give a realistic measurement protocol for performing such experiments.

DNA bubble dynamics as a quantum Coulomb problem.

PubMed

Fogedby, Hans C; Metzler, Ralf

2007-02-16

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution W(t). Below Tm, W(t) is associated with the continuum of scattering states of the repulsive Coulomb potential. At Tm, the Coulomb potential vanishes and W(t) assumes a power-law tail with nontrivial dynamic exponents: the critical exponent of the entropy loss factor may cause a finite mean lifetime. Above Tm (attractive potential), the long-time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

A study of delamination buckling of laminates

NASA Technical Reports Server (NTRS)

Mukherjee, Yu-Xie; Xie, Zhi-Cheng; Ingraffea, Anthony

1990-01-01

The subject of this paper is the buckling of laminated plates, with a preexisting delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results are presented for several examples. The effects of the shape, size, and position of the delamination on the buckling load are studied through these examples.

Application of micropolar plasticity to post failure analysis in geomechanics

NASA Astrophysics Data System (ADS)

Manzari, Majid T.

2004-08-01

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy-Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright

Coevolutionary dynamics in large, but finite populations

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph

2006-07-01

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number |C |>1

NASA Astrophysics Data System (ADS)

Andrews, Bartholomew; Möller, Gunnar

2018-01-01

We study the stability of composite fermion fractional quantum Hall states in Harper-Hofstadter bands with Chern number |C |>1 . From composite fermion theory, states are predicted to be found at filling factors ν =r /(k r |C |+1 ),r ∈Z , with k =1 for bosons and k =2 for fermions. Here, we closely analyze these series in both cases, with contact interactions for bosons and nearest-neighbor interactions for (spinless) fermions. In particular, we analyze how the many-body gap scales as the bands are tuned to the effective continuum limit of Chern number |C | bands, realized near flux density nϕ=1 /|C | . Near these points, the Hofstadter model requires large magnetic unit cells that yield bands with perfectly flat dispersion and Berry curvature. We exploit the known scaling of energies in the effective continuum limit in order to maintain a fixed square aspect ratio in finite-size calculations. Based on exact diagonalization calculations of the band-projected Hamiltonian for these lattice geometries, we show that for both bosons and fermions, the vast majority of finite-size spectra yield the ground-state degeneracy predicted by composite fermion theory. For the chosen interactions, we confirm that states with filling factor ν =1 /(k |C |+1 ) are the most robust and yield a clear gap in the thermodynamic limit. For bosons with contact interactions in |C |=2 and |C |=3 bands, our data for the composite fermion states are compatible with a finite gap in the thermodynamic limit. We also report new evidence for gapped incompressible states stabilized for fermions with nearest-neighbor interactions in |C |>1 bands. For cases with a clear gap, we confirm that the thermodynamic limit commutes with the effective continuum limit within finite-size error bounds. We analyze the nature of the correlation functions for the Abelian composite fermion states and find that the correlation functions for |C |>1 states are smooth functions for positions separated by |C | sites along both axes, giving rise to |C| 2 sheets; some of which can be related by inversion symmetry. We also comment on two cases which are associated with a bosonic integer quantum Hall effect (BIQHE): For ν =2 in |C |=1 bands, we find a strong competing state with a higher ground-state degeneracy, so no clear BIQHE is found in the band-projected Hofstadter model; for ν =1 in |C |=2 bands, we present additional data confirming the existence of a BIQHE state.

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

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

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

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.

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 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.

Influence of Finite Element Size in Residual Strength Prediction of Composite Structures

NASA Technical Reports Server (NTRS)

Satyanarayana, Arunkumar; Bogert, Philip B.; Karayev, Kazbek Z.; Nordman, Paul S.; Razi, Hamid

2012-01-01

The sensitivity of failure load to the element size used in a progressive failure analysis (PFA) of carbon composite center notched laminates is evaluated. The sensitivity study employs a PFA methodology previously developed by the authors consisting of Hashin-Rotem intra-laminar fiber and matrix failure criteria and a complete stress degradation scheme for damage simulation. The approach is implemented with a user defined subroutine in the ABAQUS/Explicit finite element package. The effect of element size near the notch tips on residual strength predictions was assessed for a brittle failure mode with a parametric study that included three laminates of varying material system, thickness and stacking sequence. The study resulted in the selection of an element size of 0.09 in. X 0.09 in., which was later used for predicting crack paths and failure loads in sandwich panels and monolithic laminated panels. Comparison of predicted crack paths and failure loads for these panels agreed well with experimental observations. Additionally, the element size vs. normalized failure load relationship, determined in the parametric study, was used to evaluate strength-scaling factors for three different element sizes. The failure loads predicted with all three element sizes provided converged failure loads with respect to that corresponding with the 0.09 in. X 0.09 in. element size. Though preliminary in nature, the strength-scaling concept has the potential to greatly reduce the computational time required for PFA and can enable the analysis of large scale structural components where failure is dominated by fiber failure in tension.

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.

Transition to collective oscillations in finite Kuramoto ensembles

NASA Astrophysics Data System (ADS)

Peter, Franziska; Pikovsky, Arkady

2018-03-01

We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.

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

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.

Microvascular stress analysis. Part I: simulation of microvascular anastomoses using finite element analysis.

PubMed

Al-Sukhun, Jehad; Lindqvist, Christian; Ashammakhi, Nureddin; Penttilä, Heikki

2007-03-01

To develop a finite element model (FEM) to study the effect of the stress and strain, in microvascular anastomoses that result from the geometrical mismatch of anastomosed vessels. FEMs of end-to-end and end-to-side anastomoses were constructed. Simulations were made using finite element software (NISA). We investigated the angle of inset in the end-to-side anastomosis and the discrepancy in the size of the opening in the vessel between the host and recipient vessels. The FEMs were used to predict principal and shear stress and strain at the position of each node. Two types of vascular deformation were predicted during different simulations: longitudinal distortion, and rotational distortion. Stress values ranged from 151.1 to 282.4MPa for the maximum principal stress, from -122.9 to -432.2MPa for the minimum principal stress, and from 122.1 to 333.1MPa for the maximum shear stress. The highest values were recorded when there was a 50% mismatch in the diameter of the vessels at the site of the end-to-end anastomosis. The effect of the vessel's size discrepancy on the blood flow and deformation was remarkable in the end-to-end anastomosis. End-to-side anastomosis was superior to end-to-end anastomosis. FEM is a powerful tool to study vascular deformation, as it predicts deformation and biomechanical processes at sites where physical measurements are likely to remain impossible in living humans.

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

DOE PAGES

Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...

2015-06-05

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Kinetic theory of coupled oscillators.

PubMed

Hildebrand, Eric J; Buice, Michael A; Chow, Carson C

2007-02-02

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.

Finite element computation on nearest neighbor connected machines

NASA Technical Reports Server (NTRS)

Mcaulay, A. D.

1984-01-01

Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.

A model of mesons in finite extra-dimension

NASA Astrophysics Data System (ADS)

Lahkar, Jugal; Choudhury, D. K.; Roy, S.; Bordoloi, N. S.

2018-05-01

Recently,problem of stability of H-atom has been reported in extra-finite dimension,and found out that it is stable in extra-finite dimension of size,$R\\leq\\frac{a_0}{4}$,where,$a_0$ is the Bohr radius.Assuming that,the heavy flavoured mesons have also such stability controlled by the scale of coupling constant,we obtain corresponding QCD Bohr radius and it is found to be well within the present theoretical and experimental limit of higher dimension.We then study its consequences in their masses using effective string inspired potential model in higher dimension pursued by us.Within the uncertainty of masses of known Heavy Flavoured mesons the allowed range of extra dimension is $L\\leq10^{-16}m$,which is well below the present theoretical and experimental limit,and far above the Planck length $\\simeq1.5\\times10^{-35}$ m.

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.

A Preliminary Comparison of the Effectiveness of Cluster Analysis Weighting Procedures for Within-Group Covariance Structure.

ERIC Educational Resources Information Center

Donoghue, John R.

A Monte Carlo study compared the usefulness of six variable weighting methods for cluster analysis. Data were 100 bivariate observations from 2 subgroups, generated according to a finite normal mixture model. Subgroup size, within-group correlation, within-group variance, and distance between subgroup centroids were manipulated. Of the clustering…

Nature of solidification of nanoconfined organic liquid layers.

PubMed

Lang, X Y; Zhu, Y F; Jiang, Q

2007-01-30

A simple model is established for solidification of a nanoconfined liquid under nonequilibrium conditions. In terms of this model, the nature of solidification is the conjunct finite size and interface effects, which is directly related to the cooling rate or the relaxation time of the undercooled liquid. The model predictions are consistent with available experimental results.

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

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.

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 .

A size-dependent constitutive model of bulk metallic glasses in the supercooled liquid region

PubMed Central

Yao, Di; Deng, Lei; Zhang, Mao; Wang, Xinyun; Tang, Na; Li, Jianjun

2015-01-01

Size effect is of great importance in micro forming processes. In this paper, micro cylinder compression was conducted to investigate the deformation behavior of bulk metallic glasses (BMGs) in supercooled liquid region with different deformation variables including sample size, temperature and strain rate. It was found that the elastic and plastic behaviors of BMGs have a strong dependence on the sample size. The free volume and defect concentration were introduced to explain the size effect. In order to demonstrate the influence of deformation variables on steady stress, elastic modulus and overshoot phenomenon, four size-dependent factors were proposed to construct a size-dependent constitutive model based on the Maxwell-pulse type model previously presented by the authors according to viscosity theory and free volume model. The proposed constitutive model was then adopted in finite element method simulations, and validated by comparing the micro cylinder compression and micro double cup extrusion experimental data with the numerical results. Furthermore, the model provides a new approach to understanding the size-dependent plastic deformation behavior of BMGs. PMID:25626690

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model.

PubMed

Usami, Satoshi

2017-03-01

Behavioral and psychological researchers have shown strong interests in investigating contextual effects (i.e., the influences of combinations of individual- and group-level predictors on individual-level outcomes). The present research provides generalized formulas for determining the sample size needed in investigating contextual effects according to the desired level of statistical power as well as width of confidence interval. These formulas are derived within a three-level random intercept model that includes one predictor/contextual variable at each level to simultaneously cover various kinds of contextual effects that researchers can show interest. The relative influences of indices included in the formulas on the standard errors of contextual effects estimates are investigated with the aim of further simplifying sample size determination procedures. In addition, simulation studies are performed to investigate finite sample behavior of calculated statistical power, showing that estimated sample sizes based on derived formulas can be both positively and negatively biased due to complex effects of unreliability of contextual variables, multicollinearity, and violation of assumption regarding the known variances. Thus, it is advisable to compare estimated sample sizes under various specifications of indices and to evaluate its potential bias, as illustrated in the example.

Size effects and realiability of barium strontium titanate thin films

NASA Astrophysics Data System (ADS)

Parker, Charles Bernard

Thin films of (Ba,Sr)TiO3 (BST) deposited by Liquid Source MOCVD were investigated. BST is a candidate dielectric for future-generation DRAM and as a tunable dielectric. Two areas of both scientific and commercial interest were investigated. The first area is the effect of decreasing dimension on ferroelectric properties. Several theories of size effects in ferroelectrics were evaluated. The dielectric response of a set of BST films of thicknesses from 15 to 580 nm was measured from 85 to 580 K. These films were extensively characterized and the boundary conditions that often influence size effects measurements were considered, including strain, finite screening length in the electrode, depolarization fields in the ferroelectric, atmospheric effects, control of stochiometry, and others. The data set was compared to the theoretical predictions and it was determined that Finite Size Scaling provided the best fit to the data. Using this theory, the predicted dielectric response was compared to the requirements of future generations of DRAM and was found to be sufficient, if film strain can be controlled. The second area is reliability. The types of lifetime-limiting electrical failure observed in BST are resistance degradation, time dependant dielectric breakdown (tddb), and noisy breakdown. Previous work on BST reliability has largely focused on resistance degradation at high temperature. This condition is only a small subset of experimental space. This work extends the understanding of BST failure into the low temperature regime and evaluates the effects of both DC and AC stress. It was found that tddb is the dominant failure mode at low temperature and resistance degradation is the dominant failure modes at high temperature. Synthesizing this work with previous work on resistance degradation allowed a failure framework to be developed. Rigorous extrapolation of resistance degradation and tddb lifetimes was compared to the requirements of future generations of DRAM and was found that while resistance degradation will not limit device lifetimes, tddb will. Refinement of BST processing will be necessary to reduce the defect causing tddb failure.

Finite element analysis of true and pseudo surface acoustic waves in one-dimensional phononic crystals

NASA Astrophysics Data System (ADS)

Graczykowski, B.; Alzina, F.; Gomis-Bresco, J.; Sotomayor Torres, C. M.

2016-01-01

In this paper, we report a theoretical investigation of surface acoustic waves propagating in one-dimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection, and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe.

Acoustic Resonator Optimisation for Airborne Particle Manipulation

NASA Astrophysics Data System (ADS)

Devendran, Citsabehsan; Billson, Duncan R.; Hutchins, David A.; Alan, Tuncay; Neild, Adrian

Advances in micro-electromechanical systems (MEMS) technology and biomedical research necessitate micro-machined manipulators to capture, handle and position delicate micron-sized particles. To this end, a parallel plate acoustic resonator system has been investigated for the purposes of manipulation and entrapment of micron sized particles in air. Numerical and finite element modelling was performed to optimise the design of the layered acoustic resonator. To obtain an optimised resonator design, careful considerations of the effect of thickness and material properties are required. Furthermore, the effect of acoustic attenuation which is dependent on frequency is also considered within this study, leading to an optimum operational frequency range. Finally, experimental results demonstrated good particle levitation and capture of various particle properties and sizes ranging to as small as 14.8 μm.

Phase transition dynamics for hot nuclei

NASA Astrophysics Data System (ADS)

Borderie, B.; Le Neindre, N.; Rivet, M. F.; Désesquelles, P.; Bonnet, E.; Bougault, R.; Chbihi, A.; Dell'Aquila, D.; Fable, Q.; Frankland, J. D.; Galichet, E.; Gruyer, D.; Guinet, D.; La Commara, M.; Lombardo, I.; Lopez, O.; Manduci, L.; Napolitani, P.; Pârlog, M.; Rosato, E.; Roy, R.; St-Onge, P.; Verde, G.; Vient, E.; Vigilante, M.; Wieleczko, J. P.; Indra Collaboration

2018-07-01

An abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation in the Fermi energy domain. On the other hand finite size effects are predicted to strongly reduce this abnormal production. High statistics quasifusion hot nuclei produced in central collisions between Xe and Sn isotopes at 32 and 45 A MeV incident energies have been used to definitively establish, through the experimental measurement of charge correlations, the presence of spinodal instabilities. N/Z influence was also studied.

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

NASA Astrophysics Data System (ADS)

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

1992-09-01

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

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.

The effect of gap fluctuations on interacting and non-interacting polarization for nano-superconducting grains in electron- and hole-doped cuprates

NASA Astrophysics Data System (ADS)

Afzali, R.; Alizadeh, A.

2017-12-01

The behavior of non-interacting and interacting polarization under influence of fluctuations of the superconducting gap with D-wave symmetry and under consideration of the gap dependence on nano- grain size is obtained in terms of the frequency, temperature and the size at zero and finite temperatures for rectangular cuprate nano-superconducting grains. By using Eliashberg equations and applying the relations of the fermionic dispersion for the hole-doped and electron-doped cuprates, we numerically compute the real part of size-dependent polarization for both types of cuprates. We show that the peak of real part of polarization moves to higher frequency by including the additional fluctuating part of gap (or the nano-size effect). Also, we obtain the temperatures for different frequencies, in which the effect of gap fluctuations fades. In the case of size-dependent gap, there is a critical frequency; for frequencies lower (higher) than the critical frequency, the nano-effect weakens (improves) the superconducting state. Moreover, it is concluded that the real part of polarization for hole- doped cuprates in terms of the grain size has more significant amount in comparison with electron-doped ones.

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.

Load concentration due to missing members in planar faces of a large space truss

NASA Technical Reports Server (NTRS)

Waltz, J. E.

1979-01-01

A large space structure with members missing was investigated using a finite element analysis. The particular structural configuration was the tetrahedral truss, with attention restricted to one of its planar faces. Initially the finite element model of a complete face was verified by comparing it with known results for some basic loadings. Then an analysis was made of the structure with members near the center removed. Some calculations were made on the influence of the mesh size of a structure containing a hexagonal hole, and an analysis was also made of a structure with a rigid hexagonal insert. In general, load concentration effects in these trusses were significantly lower than classical stress concentration effects in an infinitely wide isotropic plate with a circular rigid inclusion, although larger effects were obtained when a hole extended over several rings of elements.

Wetting layer effect on impurity-related electronic properties of different (In,Ga)N QD-shapes

NASA Astrophysics Data System (ADS)

El Ghazi, Haddou; Jorio, Anouar; Zorkani, Izeddine; Feddi, El Mustapha; El Mouchtachi, Ahmed

2018-05-01

In this paper, we have investigated the electronic properties of (In,Ga)N/GaN coupled wetting layer-quantum dot system using the numerical approach. The finite element method code is used to solve the Schrödinger equation, in the presence of the impurity. In our model, parallelepiped-shape, circular and square based-pyramidal and their wetting layers embedded in GaN matrix were considered. Based on the single band parabolic and the effective mass approximations, the envelop function and its corresponding energy eigenvalue are obtained assuming a finite potential barrier. Our results reveal that: (1) the wetting layer has a great influence on the electronic properties especially for a small quantum dot and acts in the opposite sense of the geometrical confinement, (2) a wetting layer-dependent critical QD-size is obtained limiting two different behaviors and (3) its effect is strongly-dependent on the quantum dot-shape.

Magnitude of finite-nucleus-size effects in relativistic density functional computations of indirect NMR nuclear spin-spin coupling constants.

PubMed

Autschbach, Jochen

2009-09-14

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

Nucleon axial charge in (2+1)-flavor dynamical-lattice QCD with domain-wall fermions.

PubMed

Yamazaki, T; Aoki, Y; Blum, T; Lin, H W; Lin, M F; Ohta, S; Sasaki, S; Tweedie, R J; Zanotti, J M

2008-05-02

We present results for the nucleon axial charge g{A} at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16;{3} x 32 and 24;{3} x 64 lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_{pi} is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m{pi}=330 MeV. We also find a scaling with the single variable m{pi}L which can also be seen in previous two-flavor domain wall and Wilson fermion calculations. Using this scaling to eliminate the finite-volume effect, we obtain g{A}=1.20(6)(4) at the physical pion mass, m_{pi}=135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when V>or=(2.4 fm);{3}. We argue this is a dynamical quark effect.

Crystallization in a model glass: Influence of the boundary conditions

NASA Astrophysics Data System (ADS)

Jund, P.; Jullien, R.

1998-06-01

Using molecular dynamics calculations and the Voronoï tessellation, we study the evolution of the local structure of a soft-sphere glass vs. temperature starting from the liquid phase at different quenching rates. This study is done for different sizes and for two different boundary conditions, namely the usual cubic periodic boundary conditions and the isotropic hyperspherical boundary conditions for which the particles evolve on the surface of a hypersphere in four dimensions. Our results show that for small system sizes, crystallization can indeed be induced by the cubic boundary conditions. On the other hand, we show that finite-size effects are more pronounced on the hypersphere and that crystallization is artificially inhibited even for large system sizes.

Eddy Current Testing and Sizing of Deep Cracks in a Thick Structure

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

Huang, H.; Endo, H.; Uchimoto, T.

2004-02-26

Due to the skin effect of eddy current testing, target of ECT restricts to thin structure such as steam generator tubes with 1.27mm thickness. Detecting and sizing of a deep crack in a thick structure remains a problem. In this paper, an ECT probe is presented to solve this problem with the help of numerical analysis. The parameters such as frequency, coil size etc. are discussed. The inverse problem of crack sizing is solved by applying a fast simulator of ECT based on an edge based finite element method and steepest descent method, and reconstructed results of 5, 10 andmore » 15mm depth cracks from experimental signals are shown.« 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.

Finite size induces crossover temperature in growing spin chains

NASA Astrophysics Data System (ADS)

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A.

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Finite size induces crossover temperature in growing spin chains.

PubMed

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Analysis of Vertebral Bone Strength, Fracture Pattern, and Fracture Location: A Validation Study Using a Computed Tomography-Based Nonlinear Finite Element Analysis

PubMed Central

Imai, Kazuhiro

2015-01-01

Finite element analysis (FEA) is an advanced computer technique of structural stress analysis developed in engineering mechanics. Because the compressive behavior of vertebral bone shows nonlinear behavior, a nonlinear FEA should be utilized to analyze the clinical vertebral fracture. In this article, a computed tomography-based nonlinear FEA (CT/FEA) to analyze the vertebral bone strength, fracture pattern, and fracture location is introduced. The accuracy of the CT/FEA was validated by performing experimental mechanical testing with human cadaveric specimens. Vertebral bone strength and the minimum principal strain at the vertebral surface were accurately analyzed using the CT/FEA. The experimental fracture pattern and fracture location were also accurately simulated. Optimization of the element size was performed by assessing the accuracy of the CT/FEA, and the optimum element size was assumed to be 2 mm. It is expected that the CT/FEA will be valuable in analyzing vertebral fracture risk and assessing therapeutic effects on osteoporosis. PMID:26029476

Irreversible opinion spreading on scale-free networks

NASA Astrophysics Data System (ADS)

Candia, Julián

2007-02-01

We study the dynamical and critical behavior of a model for irreversible opinion spreading on Barabási-Albert (BA) scale-free networks by performing extensive Monte Carlo simulations. The opinion spreading within an inhomogeneous society is investigated by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. The deposition dynamics, which is studied as a function of the degree of the occupied sites, shows evidence for the leading role played by hubs in the growth process. Systems of finite size grow either ordered or disordered, depending on the temperature. By means of standard finite-size scaling procedures, the effective order-disorder phase transitions are found to persist in the thermodynamic limit. This critical behavior, however, is absent in related equilibrium spin systems such as the Ising model on BA scale-free networks, which in the thermodynamic limit only displays a ferromagnetic phase. The dependence of these results on the degree exponent is also discussed for the case of uncorrelated scale-free networks.

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)].

Hydro-mechanically coupled finite-element analysis of the stability of a fractured-rock slope using the equivalent continuum approach: a case study of planned reservoir banks in Blaubeuren, Germany

NASA Astrophysics Data System (ADS)

Song, Jie; Dong, Mei; Koltuk, Serdar; Hu, Hui; Zhang, Luqing; Azzam, Rafig

2018-05-01

Construction works associated with the building of reservoirs in mountain areas can damage the stability of adjacent valley slopes. Seepage processes caused by the filling and drawdown operations of reservoirs also affect the stability of the reservoir banks over time. The presented study investigates the stability of a fractured-rock slope subjected to seepage forces in the lower basin of a planned pumped-storage hydropower (PSH) plant in Blaubeuren, Germany. The investigation uses a hydro-mechanically coupled finite-element analyses. For this purpose, an equivalent continuum model is developed by using a representative elementary volume (REV) approach. To determine the minimum required REV size, a large number of discrete fracture networks are generated using Monte Carlo simulations. These analyses give a REV size of 28 × 28 m, which is sufficient to represent the equivalent hydraulic and mechanical properties of the investigated fractured-rock mass. The hydro-mechanically coupled analyses performed using this REV size show that the reservoir operations in the examined PSH plant have negligible effect on the adjacent valley slope.

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).

Magnetic Nanoparticles: Surface Effects and Properties Related to Biomedicine Applications

PubMed Central

Issa, Bashar; Obaidat, Ihab M.; Albiss, Borhan A.; Haik, Yousef

2013-01-01

Due to finite size effects, such as the high surface-to-volume ratio and different crystal structures, magnetic nanoparticles are found to exhibit interesting and considerably different magnetic properties than those found in their corresponding bulk materials. These nanoparticles can be synthesized in several ways (e.g., chemical and physical) with controllable sizes enabling their comparison to biological organisms from cells (10–100 μm), viruses, genes, down to proteins (3–50 nm). The optimization of the nanoparticles’ size, size distribution, agglomeration, coating, and shapes along with their unique magnetic properties prompted the application of nanoparticles of this type in diverse fields. Biomedicine is one of these fields where intensive research is currently being conducted. In this review, we will discuss the magnetic properties of nanoparticles which are directly related to their applications in biomedicine. We will focus mainly on surface effects and ferrite nanoparticles, and on one diagnostic application of magnetic nanoparticles as magnetic resonance imaging contrast agents. PMID:24232575

Indentation size effects in single crystal copper as revealed by synchrotron x-ray microdiffraction

NASA Astrophysics Data System (ADS)

Feng, G.; Budiman, A. S.; Nix, W. D.; Tamura, N.; Patel, J. R.

2008-08-01

For a Cu single crystal, we find that indentation hardness increases with decreasing indentation depth, a phenomenon widely observed before and called the indentation size effect (ISE). To understand the underlying mechanism, we measure the lattice rotations in indentations of different sizes using white beam x-ray microdiffraction (μXRD); the indentation-induced lattice rotations are directly measured by the streaking of x-ray Laue spots associated with the indentations. The magnitude of the lattice rotations is found to be independent of indentation size, which is consistent with the basic tenets of the ISE model. Using the μXRD data together with an ISE model, we can estimate the effective radius of the indentation plastic zone, and the estimate is consistent with the value predicted by a finite element analysis. Using these results, an estimate of the average dislocation densities within the plastic zones has been made; the findings are consistent with the ISE arising from a dependence of the dislocation density on the depth of indentation.

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.

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

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.

A-Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Problems Coupled Through a Boundary with Non-Matching Grids

DTIC Science & Technology

2013-08-01

both MFE and GFV, are often similar in size. As a gross measure of the effect of geometric projection and of the use of quadrature, we also report the...interest MFE ∑(e,ψ) or GFV ∑(e,ψ). Tables 1 and 2 show this using coarse and fine forward solutions. Table 1. The forward problem with solution (4.1) is run...adjoint data components ψu and ψp are constant everywhere and ψξ = 0. adj. grid MFE ∑(e,ψ) ∑MFEi ratio GFV ∑(e,ψ) ∑GFV i ratio 20x20 : 32x32 1.96E−3

Designing pinhole vacancies in graphene towards functionalization: Effects on critical buckling load

NASA Astrophysics Data System (ADS)

Georgantzinos, S. K.; Markolefas, S.; Giannopoulos, G. I.; Katsareas, D. E.; Anifantis, N. K.

2017-03-01

The effect of size and placement of pinhole-type atom vacancies on Euler's critical load on free-standing, monolayer graphene, is investigated. The graphene is modeled by a structural spring-based finite element approach, in which every interatomic interaction is approached as a linear spring. The geometry of graphene and the pinhole size lead to the assembly of the stiffness matrix of the nanostructure. Definition of the boundary conditions of the problem leads to the solution of the eigenvalue problem and consequently to the critical buckling load. Comparison to results found in the literature illustrates the validity and accuracy of the proposed method. Parametric analysis regarding the placement and size of the pinhole-type vacancy, as well as the graphene geometry, depicts the effects on critical buckling load. Non-linear regression analysis leads to empirical-analytical equations for predicting the buckling behavior of graphene, with engineered pinhole-type atom vacancies.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Particle-in-cell simulations of the critical ionization velocity effect in finite size clouds

NASA Technical Reports Server (NTRS)

Moghaddam-Taaheri, E.; Lu, G.; Goertz, C. K.; Nishikawa, K. - I.

1994-01-01

The critical ionization velocity (CIV) mechanism in a finite size cloud is studied with a series of electrostatic particle-in-cell simulations. It is observed that an initial seed ionization, produced by non-CIV mechanisms, generates a cross-field ion beam which excites a modified beam-plasma instability (MBPI) with frequency in the range of the lower hybrid frequency. The excited waves accelerate electrons along the magnetic field up to the ion drift energy that exceeds the ionization energy of the neutral atoms. The heated electrons in turn enhance the ion beam by electron-neutral impact ionization, which establishes a positive feedback loop in maintaining the CIV process. It is also found that the efficiency of the CIV mechanism depends on the finite size of the gas cloud in the following ways: (1) Along the ambient magnetic field the finite size of the cloud, L (sub parallel), restricts the growth of the fastest growing mode, with a wavelength lambda (sub m parallel), of the MBPI. The parallel electron heating at wave saturation scales approximately as (L (sub parallel)/lambda (sub m parallel)) (exp 1/2); (2) Momentum coupling between the cloud and the ambient plasma via the Alfven waves occurs as a result of the finite size of the cloud in the direction perpendicular to both the ambient magnetic field and the neutral drift. This reduces exponentially with time the relative drift between the ambient plasma and the neutrals. The timescale is inversely proportional to the Alfven velocity. (3) The transvers e charge separation field across the cloud was found to result in the modulation of the beam velocity which reduces the parallel heating of electrons and increases the transverse acceleration of electrons. (4) Some energetic electrons are lost from the cloud along the magnetic field at a rate characterized by the acoustic velocity, instead of the electron thermal velocity. The loss of energetic electrons from the cloud seems to be larger in the direction of plasma drift relative to the neutrals, where the loss rate is characterized by the neutral drift velocity. It is also shown that a factor of 4 increase in the ambient plasma density, increases the CIV ionization yield by almost 2 orders of magnitude at the end of a typical run. It is concluded that a larger ambient plasma density can result in a larger CIV yield because of (1) larger seed ion production by non-CIV mechanisms, (2) smaller Alfven velocity and hence weak momentum coupling, and (3) smaller ratio of the ion beam density to the ambient ion density, and therefore a weaker modulation of the beam velocity. The simulation results are used to interpret various chemical release experiments in space.

Kinetic-Scale Magnetic Turbulence and Finite Larmor Radius Effects at Mercury

NASA Technical Reports Server (NTRS)

Uritsky, V. M.; Slavin, J. A.; Khazanov, G. V.; Donovan, E. F.; Boardsen, S. A.; Anderson, B. J.; Korth, H.

2011-01-01

We use a nonstationary generalization of the higher-order structure function technique to investigate statistical properties of the magnetic field fluctuations recorded by MESSENGER spacecraft during its first flyby (01/14/2008) through the near-Mercury space environment, with the emphasis on key boundary regions participating in the solar wind - magnetosphere interaction. Our analysis shows, for the first time, that kinetic-scale fluctuations play a significant role in the Mercury's magnetosphere up to the largest resolvable timescale (approx.20 s) imposed by the signal nonstationariry, suggesting that turbulence at this plane I is largely controlled by finite Larmor radius effects. In particular, we report the presence of a highly turbulent and extended foreshock system filled with packets of ULF oscillations, broad-band intermittent fluctuations in the magnetosheath, ion-kinetic turbulence in the central plasma sheet of Mercury's magnetotail, and kinetic-scale fluctuations in the inner current sheet encountered at the outbound (dawn-side) magnetopause. Overall, our measurements indicate that the Hermean magnetosphere, as well as the surrounding region, are strongly affected by non-MHD effects introduced by finite sizes of cyclotron orbits of the constituting ion species. Physical mechanisms of these effects and their potentially critical impact on the structure and dynamics of Mercury's magnetic field remain to be understood.

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.

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.

Particle sizes in Saturn's rings from UVIS stellar occultations 1. Variations with ring region

NASA Astrophysics Data System (ADS)

Colwell, J. E.; Esposito, L. W.; Cooney, J. H.

2018-01-01

The Cassini spacecraft's Ultraviolet Imaging Spectrograph (UVIS) includes a high speed photometer (HSP) that has observed stellar occultations by Saturn's rings with a radial resolution of ∼10 m. In the absence of intervening ring material, the time series of measurements by the HSP is described by Poisson statistics in which the variance equals the mean. The finite sizes of the ring particles occulting the star lead to a variance that is larger than the mean due to correlations in the blocking of photons due to finite particle size and due to random variations in the number of individual particles in each measurement area. This effect was first exploited by Showalter and Nicholson (1990) with the stellar occultation observed by Voyager 2. At a given optical depth, a larger excess variance corresponds to larger particles or clumps that results in greater variation of the signal from measurement to measurement. Here we present analysis of the excess variance in occultations observed by Cassini UVIS. We observe differences in the best-fitting particle size in different ring regions. The C ring plateaus show a distinctly smaller effective particle size, R, than the background C ring, while the background C ring itself shows a positive correlation between R and optical depth. The innermost 700 km of the B ring has a distribution of excess variance with optical depth that is consistent with the C ring ramp and C ring but not with the remainder of the B1 region. The Cassini Division, while similar to the C ring in spectral and structural properties, has different trends in effective particle size with optical depth. There are discrete jumps in R on either side of the Cassini Division ramp, while the C ring ramp shows a smooth transition in R from the C ring to the B ring. The A ring is dominated by self-gravity wakes whose shadow size depends on the occultation geometry. The spectral ;halo; regions around the strongest density waves in the A ring correspond to decreases in R. There is also a pronounced dip in R at the Mimas 5:3 bending wave corresponding to an increase in optical depth there, suggesting that at these waves small particles are liberated from clumps or self-gravity wakes leading to a reduction in effective particle size and an increase in optical depth.

Effect of the size of silver nanoparticles on SERS signal enhancement

NASA Astrophysics Data System (ADS)

He, Rui Xiu; Liang, Robert; Peng, Peng; Norman Zhou, Y.

2017-08-01

The localized surface plasmon resonance arising from plasmonic materials is beneficial in solution-based and thin-film sensing applications, which increase the sensitivity of the analyte being tested. Silver nanoparticles from 35 to 65 nm in diameter were synthesized using a low-temperature method and deposited in a monolayer on a (3-aminopropyl)triethoxysilane (APTES)-functionalized glass slide. The effect of particle size on monolayer structure, optical behavior, and surface-enhanced Raman scattering (SERS) is studied. While increasing particle size decreases particle coverage, it also changes the localized surface plasmon resonance and thus the SERS activity of individual nanoparticles. Using a laser excitation wavelength of 633 nm, the stronger localized surface plasmon resonance coupling to this excitation wavelength at larger particle sizes trumps the loss in surface coverage, and greater SERS signals are observed. The SERS signal enhancement accounts for the higher SERS signal, which was verified using a finite element model of a silver nanoparticle dimer with various nanoparticle sizes and separation distances.

Finite size of hadrons and Bose-Einstein correlations in pp collisions at 7 TeV

NASA Astrophysics Data System (ADS)

Bialas, Andrzej; Florkowski, Wojciech; Zalewski, Kacper

2015-09-01

Space-time correlations between produced particles, induced by the composite nature of hadrons, imply specific changes in the properties of the correlation functions for identical particles. The expected magnitude of these effects is evaluated using the recently published blast-wave model analysis of the data for pp collisions at √{ s} = 7 TeV.

Size, Shape and Impurity Effects on Superconducting critical temperature.

NASA Astrophysics Data System (ADS)

Umeda, Masaki; Kato, Masaru; Sato, Osamu

Bulk superconductors have their own critical temperatures Tc. However, for a nano-structured superconductor, Tc depends on size and shape of the superconductor. Nishizaki showed that the high pressure torsion on bulks of Nb makes Tc higher, because the torsion makes many nano-sized fine grains in the bulks. However the high pressure torsion on bulks of V makes Tc lower, and Nishizaki discussed that the decrease of Tc is caused by impurities in the bulks of V. We studied size, shape, and impurity effects on Tc, by solving the Gor'kov equations, using the finite element method. We found that smaller and narrower superconductors show higher Tc. We found how size and shape affects Tc by studying spacial order parameter distributions and quasi-particle eigen-energies. Also we studied the impurity effects on Tc, and found that Tc decreases with increase of scattering rate by impurities. This work was supported in part of KAKENHI Grant Number JP26400367 and JP16K05460, and program for leading graduate schools of ministry of education, culture, sports, science and technology-Japan.

Finite Element Simulation and Experimental Verification of Internal Stress of Quenched AISI 4140 Cylinders

NASA Astrophysics Data System (ADS)

Liu, Yu; Qin, Shengwei; Hao, Qingguo; Chen, Nailu; Zuo, Xunwei; Rong, Yonghua

2017-03-01

The study of internal stress in quenched AISI 4140 medium carbon steel is of importance in engineering. In this work, the finite element simulation (FES) was employed to predict the distribution of internal stress in quenched AISI 4140 cylinders with two sizes of diameter based on exponent-modified (Ex-Modified) normalized function. The results indicate that the FES based on Ex-Modified normalized function proposed is better consistent with X-ray diffraction measurements of the stress distribution than FES based on normalized function proposed by Abrassart, Desalos and Leblond, respectively, which is attributed that Ex-Modified normalized function better describes transformation plasticity. Effect of temperature distribution on the phase formation, the origin of residual stress distribution and effect of transformation plasticity function on the residual stress distribution were further discussed.

Influence of fractal substructures of the percolating cluster on transferring processes in macroscopically disordered environments

NASA Astrophysics Data System (ADS)

Kolesnikov, B. P.

2017-11-01

The presented work belongs to the issue of searching for the effective kinetic properties of macroscopically disordered environments (MDE). These properties characterize MDE in general on the sizes which significantly exceed the sizes of macro inhomogeneity. The structure of MDE is considered as a complex of interpenetrating percolating and finite clusters consolidated from homonymous components, topological characteristics of which influence on the properties of the whole environment. The influence of percolating clusters’ fractal substructures (backbone, skeleton of backbone, red bonds) on the transfer processes during crossover (a structure transition from fractal to homogeneous condition) is investigated based on the offered mathematical approach for finding the effective conductivity of MDEs and on the percolating cluster model. The nature of the change of the critical conductivity index t during crossover from the characteristic value for the area close to percolation threshold to the value corresponded to homogeneous condition is demonstrated. The offered model describes the transfer processes in MDE with the finite conductivity relation of «conductive» and «low conductive» phases above and below percolation threshold and in smearing area (an analogue of a blur area of the second-order phase transfer).

Two-dimensional Anderson-Hubbard model in the DMFT + {Sigma} approximation

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

Kuchinskii, E. Z., E-mail: kuchinsk@iep.uran.ru; Kuleeva, N. A.; Nekrasov, I. A.

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + {Sigma} approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular 'bare' density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The 'correlated metal,' Mott insulator, and correlated Anderson insulator phases are identified from the evolution ofmore » the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.« less

Limiting similarity and functional diversity along environmental gradients

USGS Publications Warehouse

Schwilk, D.W.; Ackerly, D.D.

2005-01-01

Recent developments in community models emphasize the importance of incorporating stochastic processes (e.g. ecological drift) in models of niche-structured community assembly. We constructed a finite, spatially explicit, lottery model to simulate the distribution of species in a one-dimensional landscape with an underlying gradient in environmental conditions. Our framework combines the potential for ecological drift with environmentally-mediated competition for space in a heterogeneous environment. We examined the influence of niche breadth, dispersal distances, community size (total number of individuals) and the breadth of the environmental gradient on levels of species and functional trait diversity (i.e. differences in niche optima). Three novel results emerge from this model: (1) niche differences between adjacent species (e.g. limiting similarity) increase in smaller communities, because of the interaction of competitive effects and finite population sizes; (2) immigration from a regional species pool, stochasticity and niche-assembly generate a bimodal distribution of species residence times ('transient' and 'resident') under a heterogeneous environment; and (3) the magnitude of environmental heterogeneity has a U-shaped effect on diversity, because of shifts in species richness of resident vs. transient species. These predictions illustrate the potential importance of stochastic (although not necessarily neutral) processes in community assembly. ??2005 Blackwell Publishing Ltd/CNRS.

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.

Size-dependent structural, magnetic, and optical properties of MnCo2O4 nanocrystallites

NASA Astrophysics Data System (ADS)

Singh, S.; Pramanik, P.; Sangaraju, S.; Mallick, A.; Giebeler, L.; Thota, S.

2017-05-01

Finite-size (d = 5.4-112 nm) and surface effects on the structural, optical, and magnetic properties of ferrimagnetic inverse-spinel MnCo2O4 are reported. For d ≥ 87 nm, partial tetragonal distortion of the inverse spinel-lattice was observed. The Curie temperature TC of MnCo2O4 nanostructures, as determined by dc-magnetic susceptibility (χ) measurements, follows a finite-size scaling relation TC(d) = TC(∞)[1-(ξ0/d)λ] with a shift exponent λ = 0.75 ± 0.15 and microscopic correlation length ξ0 = 1.4 ± 0.3 nm, which is consistent with the mean field theory. For T > TC, χ(T) fits Néel's expression for the two-sublattice model with antiferromagnetic molecular field (exchange) constants NBB ˜ 85.16 (JBB ˜ 2.94 × 10-22 J), NAB ˜ 110.96 (JAB ˜ 1.91 × 10-22 J), and NAA ˜ 43.8 (JAA ˜ 1.13 × 10-22 J) and asymptotic Curie temperature Ta ˜ 717.63 K. The optical energy bandgap Eg, evaluated from the Kubelka-Munk function ( [ F ( R ∞ ) ℏ ω ] 2 = C2( ℏ ω - Eg)) is blueshifted to 2.4 eV (d ˜ 5.4 nm) from 1.73 eV (d ˜ 112 nm) due to the quantum confinement and non-stoichiometry. The role of tetragonal distortion and grain-size-effects in the intensity of crystal field transitions and variation in the magnetic ordering are further discussed and compared with Co3O4 nanostructures.

Finite Element Analysis of Reverberation Chambers

NASA Technical Reports Server (NTRS)

Bunting, Charles F.; Nguyen, Duc T.

2000-01-01

The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.

Finite size of hadrons and Bose-Einstein correlations

NASA Astrophysics Data System (ADS)

Bialas, A.; Zalewski, K.

2013-11-01

It is observed that the finite size of hadrons produced in high energy collisions implies that their positions are correlated, since the probability to find two hadrons on top of each other is highly reduced. It is then shown that this effect can naturally explain the values of the correlation function below one, observed at LEP and LHC for pairs of identical pions. to emphasize the role of inter-hadron correlations in the explanation of the observed negative values of C(p1,p2)-1 and to point out that a natural source of such inter-hadron correlations can be provided by the finite sizes of the produced hadrons. Several comments are in order.(i) Our use of the Θ-function to parametrize the excluded volume correlations is clearly only a crude approximation. For a precise description of data almost certainly a more sophisticated parametrization of the effect will be needed. In particular, note that with our parametrization the correlation in space-time does not affect the single-particle and two-particle non-symmetrized momentum distributions. The same comment applies to our use of Gaussians.(ii) It has been recently found [6,7] that in pp collisions at LHC, the volume of the system (as determined from the fitted HBT parameters) depends weakly on the multiplicity of the particles produced in the collision. This suggests that large multiplicity in an event is due to a longer emission time. If true, this should be also reflected in the HBT measurements and it may be interesting to investigate this aspect of the problem in more detail.(iii) To investigate further the space and/or time correlations between the emitted particles more information is needed. It would be interesting to study the minima in the correlation functions separately for the “side”, “out” and “long” directions. Such studies may allow to determine the size of the “excluded volume” and compare it with other estimates [14,15]. We also feel that with the present accuracy and statistics of data, measurements of three-particle B-E correlations represent the potential to provide some essential information helping to understand what is really going on.

Influence of fundamental mode fill factor on disk laser output power and laser beam quality

NASA Astrophysics Data System (ADS)

Cheng, Zhiyong; Yang, Zhuo; Shao, Xichun; Li, Wei; Zhu, Mengzhen

2017-11-01

An three-dimensional numerical model based on finite element method and Fox-Li method with angular spectrum diffraction theoy is developed to calculate the output power and power density distribution of Yb:YAG disk laser. We invest the influence of fundamental mode fill factor(the ratio of fundamental mode size and pump spot size) on the output power and laser beam quality. Due to aspherical aberration and soft aperture effect in laser disk, high beam quality can be achieve with relative lower efficiency. The highest output power of fundamental laser mode is influenced by the fundamental mode fill factor. Besides we find that optimal mode fill factor increase with pump spot size.

Law of corresponding states for open collaborations

NASA Astrophysics Data System (ADS)

Gherardi, Marco; Bassetti, Federico; Cosentino Lagomarsino, Marco

2016-04-01

We study the relation between number of contributors and product size in Wikipedia and GitHub. In contrast to traditional production, this is strongly probabilistic, but is characterized by two quantitative nonlinear laws: a power-law bound to product size for increasing number of contributors, and the universal collapse of rescaled distributions. A variant of the random-energy model shows that both laws are due to the heterogeneity of contributors, and displays an intriguing finite-size scaling property with no equivalent in standard systems. The analysis uncovers the right intensive densities, enabling the comparison of projects with different numbers of contributors on equal grounds. We use this property to expose the detrimental effects of conflicting interactions in Wikipedia.

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.

Can a microscopic stochastic model explain the emergence of pain cycles in patients?

NASA Astrophysics Data System (ADS)

Di Patti, Francesca; Fanelli, Duccio

2009-01-01

A stochastic model is introduced here to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: oscillations in the amount of bound receptors are spontaneously manifested, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations, and analytically, through a large size expansion. The claim that our findings could provide a consistent interpretative framework for explaining the emergence of cyclic behaviors in response to analgesic treatments is substantiated.

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.

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.

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.

Combined effect of cortical cytoskeleton and transmembrane proteins on domain formation in biomembranes

PubMed Central

Sikder, Md. Kabir Uddin; Stone, Kyle A.; Kumar, P. B. Sunil; Laradji, Mohamed

2014-01-01

We investigate the combined effects of transmembrane proteins and the subjacent cytoskeleton on the dynamics of phase separation in multicomponent lipid bilayers using computer simulations of a particle-based implicit solvent model for lipid membranes with soft-core interactions. We find that microphase separation can be achieved by the protein confinement by the cytoskeleton. Our results have relevance to the finite size of lipid rafts in the plasma membrane of mammalian cells. PMID:25106608

Finite Adaptation and Multistep Moves in the Metropolis-Hastings Algorithm for Variable Selection in Genome-Wide Association Analysis

PubMed Central

Peltola, Tomi; Marttinen, Pekka; Vehtari, Aki

2012-01-01

High-dimensional datasets with large amounts of redundant information are nowadays available for hypothesis-free exploration of scientific questions. A particular case is genome-wide association analysis, where variations in the genome are searched for effects on disease or other traits. Bayesian variable selection has been demonstrated as a possible analysis approach, which can account for the multifactorial nature of the genetic effects in a linear regression model. Yet, the computation presents a challenge and application to large-scale data is not routine. Here, we study aspects of the computation using the Metropolis-Hastings algorithm for the variable selection: finite adaptation of the proposal distributions, multistep moves for changing the inclusion state of multiple variables in a single proposal and multistep move size adaptation. We also experiment with a delayed rejection step for the multistep moves. Results on simulated and real data show increase in the sampling efficiency. We also demonstrate that with application specific proposals, the approach can overcome a specific mixing problem in real data with 3822 individuals and 1,051,811 single nucleotide polymorphisms and uncover a variant pair with synergistic effect on the studied trait. Moreover, we illustrate multimodality in the real dataset related to a restrictive prior distribution on the genetic effect sizes and advocate a more flexible alternative. PMID:23166669

Selected engineering properties and applications of EPS geofoam

NASA Astrophysics Data System (ADS)

Elragi, Ahmed Fouad

Expanded polystyrene (EPS) geofoam is a lightweight material that has been used in engineering applications since at least the 1950s. Its density is about a hundredth of that of soil. It has good thermal insulation properties with stiffness and compression strength comparable to medium clay. It is utilized in reducing settlement below embankments, sound and vibration damping, reducing lateral pressure on substructures, reducing stresses on rigid buried conduits and related applications. This study starts with an overview on EPS geofoam. EPS manufacturing processes are described followed by a review of engineering properties found in previous research work done so far. Standards and design manuals applicable to EPS are presented. Selected EPS geofoam-engineering applications are discussed with examples. State-of-the-art of experimental work is done on different sizes of EPS specimens under different loading rates for better understanding of the behavior of the material. The effects of creep, sample size, strain rate and cyclic loading on the stress strain response are studied. Equations for the initial modulus and the strength of the material under compression for different strain rates are presented. The initial modulus and Poisson's ratio are discussed in detail. Sample size effect on creep behavior is examined. Three EPS projects are shown in this study. The creep behavior of the largest EPS geofoam embankment fill is shown. Results from laboratory tests, mathematical modeling and field records are compared to each other. Field records of a geofoam-stabilized slope are compared to finite difference analysis results. Lateral stress reduction on an EPS backfill retaining structure is analyzed. The study ends with a discussion on two promising properties of EPS geofoam. These are the damping ability and the compressibility of this material. Finite element analysis, finite difference analysis and lab results are included in this discussion. The discussion with the rest of the study points towards the main conclusion that EPS geofoam is the future material of promise in various civil engineering applications.

The origin of dispersion of magnetoresistance of a domain wall spin valve

NASA Astrophysics Data System (ADS)

Sato, Jun; Matsushita, Katsuyoshi; Imamura, Hiroshi

2010-01-01

We theoretically study the current-perpendicular-to-plane magnetoresistance of a domain wall confined in a nanocontact which is experimentally fabricated as current-confined-path (CCP) structure in a nano-oxide-layer (NOL). We solve the non-collinear spin diffusion equation by using the finite element method and calculate the MR ratio by evaluating the additional voltage drop due to the spin accumulation. We investigate the origin of dispersion of magnetoresistance by considering the effect of randomness of the size and distribution of the nanocontacts in the NOL. It is observed that the effect of randomness of the contact size is much larger than that of the contact distribution. Our results suggest that the origin of dispersion of magnetoresistance observed in the experiments is the randomness of the size of the nanocontacts in the NOL.

Ion size effects on the electrokinetics of spherical particles in salt-free concentrated suspensions

NASA Astrophysics Data System (ADS)

Roa, Rafael; Carrique, Felix; Ruiz-Reina, Emilio

2012-02-01

In this work we study the influence of the counterion size on the electrophoretic mobility and on the dynamic mobility of a suspended spherical particle in a salt-free concentrated colloidal suspension. Salt-free suspensions contain charged particles and the added counterions that counterbalance their surface charge. A spherical cell model approach is used to take into account particle-particle electro-hydrodynamic interactions in concentrated suspensions. The finite size of the counterions is considered including an entropic contribution, related with the excluded volume of the ions, in the free energy of the suspension, giving rise to a modified counterion concentration profile. We are interested in studying the linear response of the system to an electric field, thus we solve the different electrokinetic equations by using a linear perturbation scheme. We find that the ionic size effect is quite important for moderate to high particles charges at a given particle volume fraction. In addition for such particle surface charges, both the electrophoretic mobility and the dynamic mobility suffer more important changes the larger the particle volume fraction for each ion size. The latter effects are more relevant the larger the ionic size.

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.

Application of multiphysics models to efficient design of experiments of solute transport across articular cartilage.

PubMed

Pouran, Behdad; Arbabi, Vahid; Weinans, Harrie; Zadpoor, Amir A

2016-11-01

Transport of solutes helps to regulate normal physiology and proper function of cartilage in diarthrodial joints. Multiple studies have shown the effects of characteristic parameters such as concentration of proteoglycans and collagens and the orientation of collagen fibrils on the diffusion process. However, not much quantitative information and accurate models are available to help understand how the characteristics of the fluid surrounding articular cartilage influence the diffusion process. In this study, we used a combination of micro-computed tomography experiments and biphasic-solute finite element models to study the effects of three parameters of the overlying bath on the diffusion of neutral solutes across cartilage zones. Those parameters include bath size, degree of stirring of the bath, and the size and concentration of the stagnant layer that forms at the interface of cartilage and bath. Parametric studies determined the minimum of the finite bath size for which the diffusion behavior reduces to that of an infinite bath. Stirring of the bath proved to remarkably influence neutral solute transport across cartilage zones. The well-stirred condition was achieved only when the ratio of the diffusivity of bath to that of cartilage was greater than ≈1000. While the thickness of the stagnant layer at the cartilage-bath interface did not significantly influence the diffusion behavior, increase in its concentration substantially elevated solute concentration in cartilage. Sufficient stirring attenuated the effects of the stagnant layer. Our findings could be used for efficient design of experimental protocols aimed at understanding the transport of molecules across articular cartilage. Copyright © 2016 Elsevier Ltd. All rights reserved.

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Communication—indentation of Li-ion pouch cell: Effect of material homogenization on prediction of internal short circuit

DOE PAGES

Kumar, A.; Kalnaus, Sergiy; Simunovic, Srdjan; ...

2016-09-12

We performed finite element simulations of spherical indentation of Li-ion pouch cells. Our model fully resolves different layers in the cell. The results of the layer resolved models were compared to the models available in the literature that treat the cell as an equivalent homogenized continuum material. Simulations were carried out for different sizes of the spherical indenter. Here, we show that calibration of a failure criterion for the cell in the homogenized model depends on the indenter size, whereas in the layer-resoled model, such dependency is greatly diminished.

Model-size reduction for the buckling and vibration analyses of anisotropic panels

NASA Technical Reports Server (NTRS)

Noor, A. K.; Whitworth, S. L.

1986-01-01

A computational procedure is presented for reducing the size of the model used in the buckling and vibration analyses of symmetric anisotropic panels to that of the corresponding orthotropic model. The key elements of the procedure are the application of an operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts and the use of a reduction method through successive application of the finite element method and the classical Rayleigh-Ritz technique. The effectiveness of the procedure is demonstrated by numerical examples.

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.

Finite size effect on hydrogen bond cooperativity in (Ala)n polypeptides: A DFT study using numeric atom-centered orbitals

NASA Astrophysics Data System (ADS)

Blum, Volker; Ireta, Joel; Scheffler, Matthias

2007-03-01

An accurate representation of the energetic contribution Ehb of hydrogen bonds to structure formation is paramount to understand the secondary structure stability of proteins, both qualitatively and quantitatively. However, Ehb depends strongly on its environment, and even on the surrounding peptide conformation itself. For instance, a short α-helical polypeptide (Ala)4 can not be stabilized by its single hydrogen bond, whereas an infinite α-helical chain (Ala)∞ is clearly energetically stable over a fully extended conformation. We here use all-electron density functional calculations in the PBE generalized gradient approximation by a recently developed, computationally efficient numeric atom-centered orbital based code^1 to investigate this H-bond cooperativity that is intrinsic to Alanine-based polypeptides (Ala)n (n=1-20,∞). We compare finite and infinite prototypical helical conformations (α, π, 310) on equal footing, with both neutral and ionic termination for finite (Ala)n peptides. Moderately sized NAO basis sets allow to capture Ehb with meV accuracy, revealing a clear jump in Ehb (cooperativity) when two H-bonds first appear in line, followed by slower and more continuous increase of Ehb towards n->∞. ^1 V. Blum, R. Gehrke, P. Havu, V. Havu, M. Scheffler, The FHI Ab Initio Molecular Simulations (aims) Project, Fritz-Haber-Institut, Berlin (2006).

Three-dimensional finite element analyses of four designs of a high-strength silicon nitride implant.

PubMed

Lin, S; Shi, S; LeGeros, R Z; LeGeros, J P

2000-01-01

The effects of implant shape and size on the stress distribution around high-strength silicon nitride implants under vertical and oblique forces were determined using a three-dimensional finite element analysis. Finite element models were designed using as a basis the serial sections of the mandible. Using Auto-CAD software, the model simulated the placement of implants in the molar region of the left mandible. Results of the analyses demonstrated that mainly the implant root shape and the directions of bite forces influence the stress distributions in the supporting bone around each implant. Implant size is a lesser factor. The serrated implants presented a larger surface area to the bone than either the cylindrical or tapered implants, which resulted in lower compressive stress around the serrated implants. With increasing implant diameter and length, compressive stress decreased. The mean compressive stress distribution on the serrated implants was more flat (platykurtic) than on either the cylindrical or tapered implants. Results of studies on two load directions (vertical and oblique) showed that, in either case, the compressive stress in the cortical bone around the neck of the implant was higher than in the cancellous bone along the length of the implant. The most extreme principal compressive stress was found with oblique force. This study provides the first information on the relationship between shape of the silicon nitride implant and stress on the supporting bone.

Windowed time-reversal music technique for super-resolution ultrasound imaging

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

Huang, Lianjie; Labyed, Yassin

Systems and methods for super-resolution ultrasound imaging using a windowed and generalized TR-MUSIC algorithm that divides the imaging region into overlapping sub-regions and applies the TR-MUSIC algorithm to the windowed backscattered ultrasound signals corresponding to each sub-region. The algorithm is also structured to account for the ultrasound attenuation in the medium and the finite-size effects of ultrasound transducer elements.

Estimating energy-momentum and angular momentum near null infinity

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

Helfer, Adam D.

2010-04-15

The energy-momentum and angular momentum contained in a spacelike two-surface of spherical topology are estimated by joining the two-surface to null infinity via an approximate no-incoming-radiation condition. The result is a set of gauge-invariant formulas for energy-momentum and angular momentum which should be applicable to much numerical work; it also gives estimates of the finite-size effects.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Assessment of crack growth in a space shuttle main engine first-stage, high-pressure fuel turbopump blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali

1993-01-01

A two-dimensional finite element fracture mechanics analysis of a space shuttle main engine (SSME) turbine blade firtree was performed using the MARC finite element code. The analysis was conducted under combined effects of thermal and mechanical loads at steady-state conditions. Data from a typical engine stand cycle of the SSME were used to run a heat transfer analysis and, subsequently, a thermal structural fracture mechanics analysis. Temperature and stress contours for the firtree under these operating conditions were generated. High stresses were found at the firtree lobes where crack initiation was triggered. A life assessment of the firtree was done by assuming an initial and a final crack size.

Interaction of rate- and size-effect using a dislocation density based strain gradient viscoplasticity model

NASA Astrophysics Data System (ADS)

Nguyen, Trung N.; Siegmund, Thomas; Tomar, Vikas; Kruzic, Jamie J.

2017-12-01

Size effects occur in non-uniform plastically deformed metals confined in a volume on the scale of micrometer or sub-micrometer. Such problems have been well studied using strain gradient rate-independent plasticity theories. Yet, plasticity theories describing the time-dependent behavior of metals in the presence of size effects are presently limited, and there is no consensus about how the size effects vary with strain rates or whether there is an interaction between them. This paper introduces a constitutive model which enables the analysis of complex load scenarios, including loading rate sensitivity, creep, relaxation and interactions thereof under the consideration of plastic strain gradient effects. A strain gradient viscoplasticity constitutive model based on the Kocks-Mecking theory of dislocation evolution, namely the strain gradient Kocks-Mecking (SG-KM) model, is established and allows one to capture both rate and size effects, and their interaction. A formulation of the model in the finite element analysis framework is derived. Numerical examples are presented. In a special virtual creep test with the presence of plastic strain gradients, creep rates are found to diminish with the specimen size, and are also found to depend on the loading rate in an initial ramp loading step. Stress relaxation in a solid medium containing cylindrical microvoids is predicted to increase with decreasing void radius and strain rate in a prior ramp loading step.

Can the Lateral Proximity Effect Be Used to Create the Superconducting Transition of a Micron-Sized TES?

NASA Technical Reports Server (NTRS)

Barrentine, E. M.; Brandl, D. E.; Brown, A. D.; Denis, K. L.; Fionkbeiner, F. M.; Hsieh, W. T.; Nagler, P. C.; Stevenson, T. R.; Timble, P. T.; U-Yen, K.

2012-01-01

Recent measurements of micron-sized Mo/Au bilayer Transition Edge Sensors (TESs) have demonstrated that the TES can behave like an S-S'-S weak link due to the lateral proximity effect from superconducting leads. In this regime the Tc is a function of bias current, and the effective Tc shifts from the bilayer Tc towards the lead Tc. We explore the idea that a micron-sized S-N-S weak link could provide a new method to engineer the TES Tc. This method would be particularly useful when small size requirements for a bilayer TES (such as for a hot-electron microbolometer) lead to undesirable shifts in the bilayer Te. We present measurements of a variety of micron-sized normal Au 'TES' devices with Nb leads. We find no evidence of a superconducting transition in the Au film of these devices, in dramatic contrast to the strong lateral proximity effect seen in micron-sized Mo/Au bilayer devices. The absence of a transition in these devices is also in disagreement with theoretical predictions for S-N-S weak links. We hypothesize that a finite contact resistance between the Nb and Au may be weakening the effect. We conclude that the use of the lateral proximity effect to create a superconducting transition will be difficult given current fabrication procedures.

Finite-temperature behavior of a classical spin-orbit-coupled model for YbMgGaO4 with and without bond disorder

NASA Astrophysics Data System (ADS)

Parker, Edward; Balents, Leon

2018-05-01

We present the results of finite-temperature classical Monte Carlo simulations of a strongly spin-orbit-coupled nearest-neighbor triangular-lattice model for the candidate U (1 ) quantum spin liquid YbMgGaO4 at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond disorder destroys the transition by fragmenting the system into very large domains—possibly explaining the lack of observed ordering in the real material. The Imry-Ma argument only partially explains this fragility to disorder, and we extend the argument with a physical explanation for the preservation of our system's time-reversal symmetry even under a disorder model that preserves the same symmetry.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Mass Efficiency Considerations for Thermally Insulated Structural Skin of an Aerospace Vehicle

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An approximate equation was derived to predict the mass of insulation required to limit the maximum temperature reached by an insulated structure subjected to a transient heating pulse. In the course of the derivation two figures of merit were identified. One figure of merit correlates to the effectiveness of the heat capacity of the underlying structural material in reducing the amount of required insulation. The second figure of merit provides an indicator of the mass efficiency of the insulator material. An iterative, one dimensional finite element analysis was used to size the external insulation required to protect the structure at a single location on the Space Shuttle Orbiter and a reusable launch vehicle. Required insulation masses were calculated for a range of different materials for both structure and insulator. The required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10 to 20 percent over the range of parameters studied. Finite element results closely followed the trends indicated by both figures of merit.

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Glaessgen, E. H.

2008-01-01

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

Finite element analysis of true and pseudo surface acoustic waves in one-dimensional phononic crystals

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

Graczykowski, B., E-mail: bartlomiej.graczykowski@icn.cat; Alzina, F.; Gomis-Bresco, J.

In this paper, we report a theoretical investigation of surface acoustic waves propagating in one-dimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection,more » and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe.« less

Modeling of nanostructured porous thermoelastic composites with surface effects

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.; Nasedkina, A. A.; Kornievsky, A. S.

2017-01-01

The paper presents an integrated approach for determination of effective properties of anisotropic porous thermoelastic materials with a nanoscale stochastic porosity structure. This approach includes the effective moduli method for composite me-chanics, the simulation of representative volumes and the finite element method. In order to take into account nanoscale sizes of pores, the Gurtin-Murdoch model of surface stresses and the highly conducting interface model are used at the borders between material and pores. The general methodology for determination of effective properties of porous composites is demonstrated for a two-phase composite with special conditions for stresses and heat flux discontinuities at the phase interfaces. The mathematical statements of boundary value problems and the resulting formulas to determine the complete set of effective constants of the two-phase composites with arbitrary anisotropy and with surface properties are described; the generalized statements are formulated and the finite element approximations are given. It is shown that the homogenization procedures for porous composites with surface effects can be considered as special cases of the corresponding procedures for the two-phase composites with interphase stresses and heat fluxes if the moduli of nanoinclusions are negligibly small. These approaches have been implemented in the finite element package ANSYS for a model of porous material with cubic crystal system for various values of surface moduli, porosity and number of pores. It has been noted that the magnitude of the area of the interphase boundaries has influence on the effective moduli of the porous materials with nanosized structure.

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.

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.

3D finite element modeling of epiretinal stimulation: Impact of prosthetic electrode size and distance from the retina.

PubMed

Sui, Xiaohong; Huang, Yu; Feng, Fuchen; Huang, Chenhui; Chan, Leanne Lai Hang; Wang, Guoxing

2015-05-01

A novel 3-dimensional (3D) finite element model was established to systematically investigate the impact of the diameter (Φ) of disc electrodes and the electrode-to-retina distance on the effectiveness of stimulation. The 3D finite element model was established based on a disc platinum stimulating electrode and a 6-layered retinal structure. The ground electrode was placed in the extraocular space in direct attachment with sclera and treated as a distant return electrode. An established criterion of electric-field strength of 1000 Vm-1 was adopted as the activation threshold for RGCs. The threshold current (TC) increased linearly with increasing Φ and electrode-to-retina distance and remained almost unchanged with further increases in diameter. However, the threshold charge density (TCD) increased dramatically with decreasing electrode diameter. TCD exceeded the electrode safety limit for an electrode diameter of 50 µm at an electrode-to-retina distance of 50 to 200 μm. The electric field distributions illustrated that smaller electrode diameters and shorter electrode-to-retina distances were preferred due to more localized excitation of RGC area under stimulation of different threshold currents in terms of varied electrode size and electrode-to-retina distances. Under the condition of same-amplitude current stimulation, a large electrode exhibited an improved potential spatial selectivity at large electrode-to-retina distances. Modeling results were consistent with those reported in animal electrophysiological experiments and clinical trials, validating the 3D finite element model of epiretinal stimulation. The computational model proved to be useful in optimizing the design of an epiretinal stimulating electrode for prosthesis.

Free and forced vibrations of a tyre using a wave/finite element approach

NASA Astrophysics Data System (ADS)

Waki, Y.; Mace, B. R.; Brennan, M. J.

2009-06-01

Free and forced vibrations of a tyre are predicted using a wave/finite element (WFE) approach. A short circumferential segment of the tyre is modelled using conventional finite element (FE) methods, a periodicity condition applied and the mass and stiffness matrices post-processed to yield wave properties. Since conventional FE methods are used, commercial FE packages and existing element libraries can be utilised. An eigenvalue problem is formulated in terms of the transfer matrix of the segment. Zhong's method is used to improve numerical conditioning. The eigenvalues and eigenvectors give the wavenumbers and wave mode shapes, which in turn define transformations between the physical and wave domains. A method is described by which the frequency dependent material properties of the rubber components of the tyre can be included without the need to remesh the structure. Expressions for the forced response are developed which are numerically well-conditioned. Numerical results for a smooth tyre are presented. Dispersion curves for real, imaginary and complex wavenumbers are shown. The propagating waves are associated with various forms of motion of the tread supported by the stiffness of the side wall. Various dispersion phenomena are observed, including curve veering, non-zero cut-off and waves for which the phase velocity and the group velocity have opposite signs. Results for the forced response are compared with experimental measurements and good agreement is seen. The forced response is numerically determined for both finite area and point excitations. It is seen that the size of area of the excitation is particularly important at high frequencies. When the size of the excitation area is small enough compared to the tread thickness, the response at high frequencies becomes stiffness-like (reactive) and the effect of shear stiffness becomes important.

Development and verification of global/local analysis techniques for laminated composites

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.

1991-01-01

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.

Scalable Computing of the Mesh Size Effect on Modeling Damage Mechanics in Woven Armor Composites

DTIC Science & Technology

2008-12-01

manner of a user defined material subroutine to provide overall stress increments to, the parallel LS-DYNA3D a Lagrangian explicit code used in...finite element code, as a user defined material subroutine . The ability of this subroutine to model the effect of the progressions of a select number...is added as a user defined material subroutine to parallel LS-DYNA3D. The computations of the global mesh are handled by LS-DYNA3D and are spread

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

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).

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Efficient FEM simulation of static and free vibration behavior of single walled boron nitride nanotubes

NASA Astrophysics Data System (ADS)

Giannopoulos, Georgios I.; Kontoni, Denise-Penelope N.; Georgantzinos, Stylianos K.

2016-08-01

This paper describes the static and free vibration behavior of single walled boron nitride nanotubes using a structural mechanics based finite element method. First, depending on the type of nanotube under investigation, its three dimensional nanostructure is developed according to the well-known corresponding positions of boron and nitride atoms as well as boron nitride bonds. Then, appropriate point masses are assigned to the atomic positions of the developed space frame. Next, these point masses are suitably interconnected with two-noded, linear, spring-like, finite elements. In order to simulate effectively the interactions observed between boron and nitride atoms within the nanotube, appropriate potential energy functions are introduced for these finite elements. In this manner, various atomistic models for both armchair and zigzag nanotubes with different aspect ratios are numerically analyzed and their effective elastic modulus as well as their natural frequencies and corresponding mode shapes are obtained. Regarding the free vibration analysis, the computed results reveal bending, breathing and axial modes of vibration depending on the nanotube size and chirality as well as the applied boundary support conditions. The longitudinal stiffness of the boron nitride nanotubes is found also sensitive to their geometric characteristics.

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.

Modeling ductile metals under large strain, pressure and high strain rate incorporating damage and microstructure evolution

NASA Astrophysics Data System (ADS)

Iannitti, Gianluca; Bonora, Nicola; Ruggiero, Andrew; Dichiaro, Simone

2012-03-01

In this work, a constitutive modeling that couples plasticity, grain size evolution (due to plastic deformation and dynamic recrystallization) and ductile damage has been developed. The effect of grain size on the material yield stress (Hall-Petch) and on the melting temperature has been considered. The model has been used to investigate computationally the behavior of high purity copper in dynamic tensile extrusion test (DTE). An extensive numerical simulation work, using implicit finite element code with direct integration, has been performed and the results have been compared with available experimental data. The major finding is that the proposed model is capable to predict most of the observed features such as the increase of material ductility with the decreasing average grain size, the overall number and size of fragments and the average grain size distribution in the fragment trapped into the dime.

Modeling ductile metals under large strain, pressure and high strain rates incorporating damage and microstructure evolution

NASA Astrophysics Data System (ADS)

Iannitti, Gianluca; Bonora, Nicola; Ruggiero, Andrew; Dichiaro, Simone

2011-06-01

In this work, a constitutive modeling that couples plasticity, grain size evolution (due to plastic deformation and dynamic recrystallization) and ductile damage has been developed. The effect of grain size on the material yield stress (Hall-Petch) and on the melting temperature has been considered. The model has been used to investigate computationally the behaviour of high purity copper in dynamic tensile extrusion test (DTE). An extensive numerical simulation work, using implicit finite element code with direct integration, has been performed and the results have been compared with available experimental data. The major finding is that the proposed model is capable to predict most of the observed features such as the increase of material ductility with the decreasing average grain size, the overall number and size of fragments and the average grain size distribution in the fragment trapped into the dime.

Effects of the underlying topology on perturbation spreading in the Axelrod model for cultural dissemination

NASA Astrophysics Data System (ADS)

Kim, Yup; Cho, Minsoo; Yook, Soon-Hyung

2011-10-01

We study the effects of the underlying topologies on a single feature perturbation imposed to the Axelrod model of consensus formation. From the numerical simulations we show that there are successive updates which are similar to avalanches in many self-organized criticality systems when a perturbation is imposed. We find that the distribution of avalanche size satisfies the finite-size scaling (FSS) ansatz on two-dimensional lattices and random networks. However, on scale-free networks with the degree exponent γ≤3 we show that the avalanche size distribution does not satisfy the FSS ansatz. The results indicate that the disordered configurations on two-dimensional lattices or on random networks are still stable against the perturbation in the limit N (network size) →∞. However, on scale-free networks with γ≤3 the perturbation always drives the disordered phase into an ordered phase. The possible relationship between the properties of phase transition of the Axelrod model and the avalanche distribution is also discussed.

Size dependent bandgap of molecular beam epitaxy grown InN quantum dots measured by scanning tunneling spectroscopy

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

Kumar, Mahesh; Roul, Basanta; Central Research Laboratory, Bharat Electronics, Bangalore-560013

InN quantum dots (QDs) were grown on Si (111) by epitaxial Stranski-Krastanow growth mode using plasma-assisted molecular beam epitaxy. Single-crystalline wurtzite structure of InN QDs was verified by the x-ray diffraction and transmission electron microscopy. Scanning tunneling microscopy has been used to probe the structural aspects of QDs. A surface bandgap of InN QDs was estimated from scanning tunneling spectroscopy (STS) I-V curves and found that it is strongly dependent on the size of QDs. The observed size-dependent STS bandgap energy shifts with diameter and height were theoretical explained based on an effective mass approximation with finite-depth square-well potential model.

Nucleation versus percolation: Scaling criterion for failure in disordered solids

NASA Astrophysics Data System (ADS)

Biswas, Soumyajyoti; Roy, Subhadeep; Ray, Purusattam

2015-05-01

One of the major factors governing the mode of failure in disordered solids is the effective range R over which the stress field is modified following a local rupture event. In a random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as R scales slower than Lζ, with ζ =2 /3 . For a faster increase in R , the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

A methodology for modeling surface effects on stiff and soft solids

NASA Astrophysics Data System (ADS)

He, Jin; Park, Harold S.

2017-09-01

We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young-Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young-Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures.

A methodology for modeling surface effects on stiff and soft solids

NASA Astrophysics Data System (ADS)

He, Jin; Park, Harold S.

2018-06-01

We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young-Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young-Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures.

Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward

2017-08-01

In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.

Equation of State of Structured Matter at Finite Temperature

NASA Astrophysics Data System (ADS)

Maruyama, T.; Yasutake, N.; Tatsumi, T.

We investigate the properties of nuclear matter at the first-order phase transitions such as liquid-gas phase transition and hadron-quark phase transition. As a general feature of the first-order phase transitions of matter consisting of many species of charged particles, there appears a mixed phases with geometrical structures called ``pasta'' due to the balance of the Coulomb repulsion and the surface tension between two phases [G.~D.~Ravenhall, C.~J.~Pethick and J.~R.~Wilson, Phys. Rev. Lett. 50 (1983), 2066. M.~Hashimoto, H.~Seki and M.~Yamada, Prog. Theor. Phys. 71 (1984), 320.] The equation of state (EOS) of mixed phase is different from the one obtained by a bulk application of the Gibbs conditions or by the Maxwell construction due to the effects of the non-uniform structure. We show that the charge screening and strong surface tension make the EOS close to that of the Maxwell construction. The thermal effects are elucidated as well as the above finite-size effects.

The constraint method: A new finite element technique. [applied to static and dynamic loads on plates

NASA Technical Reports Server (NTRS)

Tsai, C.; Szabo, B. A.

1973-01-01

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Selective mode excitation in finite size plasma crystals by diffusely reflected laser light

NASA Astrophysics Data System (ADS)

Schablinski, Jan; Block, Dietmar

2015-02-01

The possibility to use diffuse reflections of a laser beam to exert a force on levitating dust particles is studied experimentally. Measurements and theoretical predictions are found to be in good agreement. Further, the method is applied to test the selective excitation of breathing-like modes in finite dust clusters.

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

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

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

Scaling effect on the fracture toughness of bone materials using MMTS criterion.

PubMed

Akbardoost, Javad; Amirafshari, Reza; Mohsenzade, Omid; Berto, Filippo

2018-05-21

The aim of this study is to present a stress based approach for investigating the effect of specimen size on the fracture toughness of bone materials. The proposed approach is a modified form of the classical fracture criterion called maximum tangential stress (MTS). The mechanical properties of bone are different in longitudinal and transverse directions and hence the tangential stress component in the proposed approach should be determined in the orthotropic media. Since only the singular terms of series expansions were obtained in the previous studies, the tangential stress is measured from finite element analysis. In this study, the critical distance is also assumed to be size dependent and a semi-empirical formulation is used for describing the size dependency of the critical distance. By comparing the results predicted by the proposed approach and those reported in the previous studies, it is shown that the proposed approach can predict the fracture resistance of cracked bone by taking into account the effect of specimen size. Copyright © 2018 Elsevier Ltd. All rights reserved.

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

NASA Astrophysics Data System (ADS)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Spatial shape of avalanches

NASA Astrophysics Data System (ADS)

Zhu, Zhaoxuan; Wiese, Kay Jörg

2017-12-01

In disordered elastic systems, driven by displacing a parabolic confining potential adiabatically slowly, all advance of the system is in bursts, termed avalanches. Avalanches have a finite extension in time, which is much smaller than the waiting time between them. Avalanches also have a finite extension ℓ in space, i.e., only a part of the interface of size ℓ moves during an avalanche. Here we study their spatial shape 〈S(x ) 〉 ℓ given ℓ , as well as its fluctuations encoded in the second cumulant 〈S2(x ) 〉 ℓ c. We establish scaling relations governing the behavior close to the boundary. We then give analytic results for the Brownian force model, in which the microscopic disorder for each degree of freedom is a random walk. Finally, we confirm these results with numerical simulations. To do this properly we elucidate the influence of discretization effects, which also confirms the assumptions entering into the scaling ansatz. This allows us to reach the scaling limit already for avalanches of moderate size. We find excellent agreement for the universal shape and its fluctuations, including all amplitudes.

Anomalous finite-size effect due to quasidegenerate phases in triangular antiferromagnets with long-range interactions and mapping to the generalized six-state clock model

NASA Astrophysics Data System (ADS)

Nishino, Masamichi; Miyashita, Seiji

2016-11-01

The effect of long-range (LR) interactions on frustrated-spin models is an interesting problem, which provides rich ordering processes. We study the effect of LR interactions on triangular Ising antiferromagnets with the next-nearest-neighbor ferromagnetic interaction (TIAFF). In the thermodynamic limit, the LRTIAFF model should reproduce the corresponding mean-field results, in which successive phase transitions occur among various phases, i.e., the disordered paramagnetic phase, so-called partially disordered phase, three-sublattice ferrimagnetic phase, and two-sublattice ferrimagnetic phase. In the present paper we focus on the magnetic susceptibility at the transition point between the two-sublattice ferrimagnetic and the disordered paramagnetic phases at relatively large ferromagnetic interactions. In the mean-field analysis, the magnetic susceptibility shows no divergence at the transition point. In contrast, a divergencelike enhancement of the susceptibility is observed in Monte Carlo simulations in finite-size systems. We investigate the origin of this difference and find that it is attributed to a virtual degeneracy of the free energies of the partially disordered and 2-FR phases. We also exploit a generalized six-state clock model with an LR interaction, which is a more general system with Z6 symmetry. We discuss the phase diagram of this model and find that it exhibits richer transition patterns and contains the physics of the LRTIAFF model.

Thermal modeling of cogging process using finite element method

NASA Astrophysics Data System (ADS)

Khaled, Mahmoud; Ramadan, Mohamad; Fourment, Lionel

2016-10-01

Among forging processes, incremental processes are those where the work piece undergoes several thermal and deformation steps with small increment of deformation. They offer high flexibility in terms of the work piece size since they allow shaping wide range of parts from small to large size. Since thermal treatment is essential to obtain the required shape and quality, this paper presents the thermal modeling of incremental processes. The finite element discretization, spatial and temporal, is exposed. Simulation is performed using commercial software Forge 3. Results show the thermal behavior at the beginning and at the end of the process.

Generalized epidemic process on modular networks.

PubMed

Chung, Kihong; Baek, Yongjoo; Kim, Daniel; Ha, Meesoon; Jeong, Hawoong

2014-05-01

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient.

Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-03-01

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

Efficient method for the calculation of mean extinction. II. Analyticity of the complex extinction efficiency of homogeneous spheroids and finite cylinders.

PubMed

Xing, Z F; Greenberg, J M

1994-08-20

The analyticity of the complex extinction efficiency is examined numerically in the size-parameter domain for homogeneous prolate and oblate spheroids and finite cylinders. The T-matrix code, which is the most efficient program available to date, is employed to calculate the individual particle-extinction efficiencies. Because of its computational limitations in the size-parameter range, a slightly modified Hilbert-transform algorithm is required to establish the analyticity numerically. The findings concerning analyticity that we reported for spheres (Astrophys. J. 399, 164-175, 1992) apply equally to these nonspherical particles.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

New way for determining electron energy levels in quantum dots arrays using finite difference method

NASA Astrophysics Data System (ADS)

Dujardin, F.; Assaid, E.; Feddi, E.

2018-06-01

Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.

Thermal conductivity of graphene mediated by strain and size

DOE PAGES

Kuang, Youdi; Shi, Sanqiang; Wang, Xinjiang; ...

2016-06-09

Based on first-principles calculations and full iterative solution of the linearized Boltzmann–Peierls transport equation for phonons, we systematically investigate effects of strain, size and temperature on the thermal conductivity k of suspended graphene. The calculated size-dependent and temperature-dependent k for finite samples agree well with experimental data. The results show that, contrast to the convergent room-temperature k = 5450 W/m-K of unstrained graphene at a sample size ~8 cm, k of strained graphene diverges with increasing the sample size even at high temperature. Out-of-plane acoustic phonons are responsible for the significant size effect in unstrained and strained graphene due tomore » their ultralong mean free path and acoustic phonons with wavelength smaller than 10 nm contribute 80% to the intrinsic room temperature k of unstrained graphene. Tensile strain hardens the flexural modes and increases their lifetimes, causing interesting dependence of k on sample size and strain due to the competition between boundary scattering and intrinsic phonon–phonon scattering. k of graphene can be tuned within a large range by strain for the size larger than 500 μm. These findings shed light on the nature of thermal transport in two-dimensional materials and may guide predicting and engineering k of graphene by varying strain and size.« less

Polar-core spin vortex of quasi-2D ferromagnetic spin-1 condensate in a flat-bottomed optical trap with a weak magnetic field

NASA Astrophysics Data System (ADS)

Zheng, Gong-Ping; Li, Pin; Li, Ting; Xue, Ya-Jie

2018-02-01

Motivated by the recent experiments realized in a flat-bottomed optical trap (Navon et al., 2015; Chomaz et al., 2015), we study the ground state of polar-core spin vortex of quasi-2D ferromagnetic spin-1 condensate in a finite-size homogeneous trap with a weak magnetic field. The exact spatial distribution of local spin is obtained with a variational method. Unlike the fully-magnetized planar spin texture with a zero-spin core, which was schematically demonstrated in previous studies for the ideal polar-core spin vortex in a homogeneous trap with infinitely large boundary, some plateaus and two-cores structure emerge in the distribution curves of spin magnitude in the polar-core spin vortex we obtained for the larger effective spin-dependent interaction. More importantly, the spin values of the plateaus are not 1 as expected in the fully-magnetized spin texture, except for the sufficiently large spin-dependent interaction and the weak-magnetic-field limit. We attribute the decrease of spin value to the effect of finite size of the system. The spin values of the plateaus can be controlled by the quadratic Zeeman energy q of the weak magnetic field, which decreases with the increase of q.

Finite element analysis of the three different posterior malleolus fixation strategies in relation to different fracture sizes.

PubMed

Anwar, Adeel; Lv, Decheng; Zhao, Zhi; Zhang, Zhen; Lu, Ming; Nazir, Muhammad Umar; Qasim, Wasim

2017-04-01

Appropriate fixation method for the posterior malleolar fractures (PMF) according to the fracture size is still not clear. Aim of this study was to evaluate the outcomes of the different fixation methods used for fixation of PMF by finite element analysis (FEA) and to compare the effect of fixation constructs on the size of the fracture computationally. Three dimensional model of the tibia was reconstructed from computed tomography (CT) images. PMF of 30%, 40% and 50% fragment sizes were simulated through computational processing. Two antero-posterior (AP) lag screws, two postero-anterior (PA) lag screws and posterior buttress plate were analysed for three different fracture volumes. The simulated loads of 350N and 700N were applied to the proximal tibial end. Models were fixed distally in all degrees of freedom. In single limb standing condition, the posterior plate group produced the lowest relative displacement (RD) among all the groups (0.01, 0.03 and 0.06mm). Further nodal analysis of the highest RD fracture group showed a higher mean displacement of 4.77mm and 4.23mm in AP and PA lag screws model (p=0.000). The amounts of stress subjected to these implants, 134.36MPa and 140.75MPa were also significantly lower (p=0.000). There was a negative correlation (p=0.021) between implant stress and the displacement which signifies a less stable fixation using AP and PA lag screws. Progressively increasing fracture size demands more stable fixation construct because RD increases significantly. Posterior buttress plate produces superior stability and lowest RD in PMF models irrespective of the fragment size. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Size validity of plasma-metamaterial cloaking monitored by scattering wave in finite-difference time-domain method

NASA Astrophysics Data System (ADS)

Bambina, Alexandre; Yamaguchi, Shuhei; Iwai, Akinori; Miyagi, Shigeyuki; Sakai, Osamu

2018-01-01

Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD) method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.

Numerical and experimental study on multi-pass laser bending of AH36 steel strips

NASA Astrophysics Data System (ADS)

Fetene, Besufekad N.; Kumar, Vikash; Dixit, Uday S.; Echempati, Raghu

2018-02-01

Laser bending is a process of bending of plates, small sized sheets, strips and tubes, in which a moving or stationary laser beam heats the workpiece to achieve the desired curvature due to thermal stresses. Researchers studied the effects of different process parameters related to the laser source, material and workpiece geometry on laser bending of metal sheets. The studies are focused on large sized sheets. The workpiece geometry parameters like sheet thickness, length and width also affect the bend angle considerably. In this work, the effects of width and thickness on multi-pass laser bending of AH36 steel strips were studied experimentally and numerically. Finite element model using ABAQUS® was developed to investigate the size effect on the prediction of the bend angle. Microhardness and flexure tests showed an increase in the flexural strength as well as microhardness in the scanned zone. The microstructures of the bent strips also supported the physical observations.

Coarsening dynamics in condensing zero-range processes and size-biased birth death chains

NASA Astrophysics Data System (ADS)

Jatuviriyapornchai, Watthanan; Grosskinsky, Stefan

2016-05-01

Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in Godrèche (2003 J. Phys. A: Math. Gen. 36 6313) to derive effective single site dynamics which form a nonlinear birth death chain describing the coarsening behavior. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.

Brownian escape and force-driven transport through entropic barriers: Particle size effect.

PubMed

Cheng, Kuang-Ling; Sheng, Yu-Jane; Tsao, Heng-Kwong

2008-11-14

Brownian escape from a spherical cavity through small holes and force-driven transport through periodic spherical cavities for finite-size particles have been investigated by Brownian dynamic simulations and scaling analysis. The mean first passage time and force-driven mobility are obtained as a function of particle diameter a, hole radius R(H), cavity radius R(C), and external field strength. In the absence of external field, the escape rate is proportional to the exit effect, (R(H)R(C))(1-a2R(H))(32). In weak fields, Brownian diffusion is still dominant and the migration is controlled by the exit effect. Therefore, smaller particles migrate faster than larger ones. In this limit the relation between Brownian escape and force-driven transport can be established by the generalized Einstein-Smoluchowski relation. As the field strength is strong enough, the mobility becomes field dependent and grows with increasing field strength. As a result, the size selectivity diminishes.

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.

Brittle Fracture In Disordered Media: A Unified Theory

NASA Astrophysics Data System (ADS)

Shekhawat, Ashivni; Zapperi, Stefano; Sethna, James

2013-03-01

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature, as well as several experiments on materials ranging from granite to bones. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit. We present a numerical validation of our theoretical results. We acknowledge support from DOE- BES DE-FG02-07ER46393, ERC-AdG-2011 SIZEFFECT, and the NSF through TeraGrid by LONI under grant TG-DMR100025.

Full-thickness tears of the supraspinatus tendon: A three-dimensional finite element analysis.

PubMed

Quental, C; Folgado, J; Monteiro, J; Sarmento, M

2016-12-08

Knowledge regarding the likelihood of propagation of supraspinatus tears is important to allow an early identification of patients for whom a conservative treatment is more likely to fail, and consequently, to improve their clinical outcome. The aim of this study was to investigate the potential for propagation of posterior, central, and anterior full-thickness tears of different sizes using the finite element method. A three-dimensional finite element model of the supraspinatus tendon was generated from the Visible Human Project data. The mechanical behaviour of the tendon was fitted from experimental data using a transversely isotropic hyperelastic constitutive model. The full-thickness tears were simulated at the supraspinatus tendon insertion by decreasing the interface area. Tear sizes from 10% to 90%, in 10% increments, of the anteroposterior length of the supraspinatus footprint were considered in the posterior, central, and anterior regions of the tendon. For each tear, three finite element analyses were performed for a supraspinatus force of 100N, 200N, and 400N. Considering a correlation between tendon strain and the risk of tear propagation, the simulated tears were compared qualitatively and quantitatively by evaluating the volume of tendon for which a maximum strain criterion was not satisfied. The finite element analyses showed a significant impact of tear size and location not only on the magnitude, but also on the patterns of the maximum principal strains. The mechanical outcome of the anterior full-thickness tears was consistently, and significantly, more severe than that of the central or posterior full-thickness tears, which suggests that the anterior tears are at greater risk of propagating than the central or posterior tears. Copyright © 2016 Elsevier Ltd. All rights reserved.

Effects of finite-size particles on the turbulent flows in a square duct

NASA Astrophysics Data System (ADS)

Yu, Zhaosheng; Lin, Zhaowu; Shao, Xueming; Wang, Lian-Ping

2015-11-01

Fully resolved numerical simulations of the particle-laden turbulent flows in a square duct are performed with a direct-forcing fictitious domain method. The effects of the finite-size particles on the mean and root-mean-square (RMS) velocities are investigated at the friction Reynolds number of 150 (based on the friction velocity and half duct width) and the particle volume fractions ranging from 0.78% to 7.07%. For the neutrally buoyant case, our results show that the mean secondary flow is enhanced and its circulation center shifts closer to the center of the duct cross-section when the particles are added. The reason for the particle effect on the mean secondary flow is analyzed by examining the terms in the mean streamwise vorticity equation. The particles enhance the wall-tangential component of the RMS velocity (i.e. Reynolds normal stress) more than its wall-normal component in the near-wall region near the corners, resulting in the enhancement in the gradients of the normal stress difference, which we think is mainly responsible for the enhancement in the mean secondary flow. The particles accumulate preferentially in the near-corner region in the neutrally buoyant case. In addition, the effects of particle sedimentation are examined at different Shields numbers. The work was supported by the National Natural Science Foundation of China (11372275) and Research Fund for the Doctoral Program of Higher Education of China (20130101110035).

Elastic layer under axisymmetric indentation and surface energy effects

NASA Astrophysics Data System (ADS)

Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon

2018-04-01

In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin-Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green's functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.

Spread prediction model of continuous steel tube based on BP neural network

NASA Astrophysics Data System (ADS)

Zhai, Jian-wei; Yu, Hui; Zou, Hai-bei; Wang, San-zhong; Liu, Li-gang

2017-07-01

According to the geometric pass of roll and technological parameters of three-roller continuous mandrel rolling mill in a factory, a finite element model is established to simulate the continuous rolling process of seamless steel tube, and the reliability of finite element model is verified by comparing with the simulation results and actual results of rolling force, wall thickness and outer diameter of the tube. The effect of roller reduction, roller rotation speed and blooming temperature on the spread rule is studied. Based on BP(Back Propagation) neural network technology, a spread prediction model of continuous rolling tube is established for training wall thickness coefficient and spread coefficient of the continuous rolling tube, and the rapid and accurate prediction of continuous rolling tube size is realized.

Continuous and discontinuous transitions to synchronization.

PubMed

Wang, Chaoqing; Garnier, Nicolas B

2016-11-01

We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the latter is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exists at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.

Paramecium swimming in capillary tube

NASA Astrophysics Data System (ADS)

Jana, Saikat; Um, Soong Ho; Jung, Sunghwan

2012-04-01

Swimming organisms in their natural habitat need to navigate through a wide range of geometries and chemical environments. Interaction with boundaries in such situations is ubiquitous and can significantly modify the swimming characteristics of the organism when compared to ideal laboratory conditions. We study the different patterns of ciliary locomotion in glass capillaries of varying diameter and characterize the effect of the solid boundaries on the velocities of the organism. Experimental observations show that Paramecium executes helical trajectories that slowly transition to straight lines as the diameter of the capillary tubes decreases. We predict the swimming velocity in capillaries by modeling the system as a confined cylinder propagating longitudinal metachronal waves that create a finite pressure gradient. Comparing with experiments, we find that such pressure gradient considerations are necessary for modeling finite sized ciliary organisms in restrictive geometries.

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.

45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations

Code of Federal Regulations, 2012 CFR

2012-10-01

... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more than...

45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations

Code of Federal Regulations, 2014 CFR

2014-10-01

... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more than...

45 CFR Appendix C to Part 1356 - Calculating Sample Size for NYTD Follow-Up Populations

Code of Federal Regulations, 2011 CFR

2011-10-01

... Populations C Appendix C to Part 1356 Public Welfare Regulations Relating to Public Welfare (Continued) OFFICE... Follow-Up Populations 1. Using Finite Population Correction The Finite Population Correction (FPC) is applied when the sample is drawn from a population of one to 5,000 youth, because the sample is more than...

Finite element analyses of wood laminated composite poles

Treesearch

Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse

2005-01-01

Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...

Magnetic Shear Damped Polar Convective Fluid Instabilities

NASA Astrophysics Data System (ADS)

Atul, Jyoti K.; Singh, Rameswar; Sarkar, Sanjib; Kravchenko, Oleg V.; Singh, Sushil K.; Chattopadhyaya, Prabal K.; Kaw, Predhiman K.

2018-01-01

The influence of the magnetic field shear is studied on the E × B (and/or gravitational) and the Current Convective Instabilities (CCI) occurring in the high-latitude F layer ionosphere. It is shown that magnetic shear reduces the growth rate of these instabilities. The magnetic shear-induced stabilization is more effective at the larger-scale sizes (≥ tens of kilometers) while at the scintillation causing intermediate scale sizes (˜ a few kilometers), the growth rate remains largely unaffected. The eigenmode structure gets localized about a rational surface due to finite magnetic shear and has broken reflectional symmetry due to centroid shift of the mode by equilibrium parallel flow or current.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

Classical and non-classical effective medium theories: New perspectives

NASA Astrophysics Data System (ADS)

Tsukerman, Igor

2017-05-01

Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius-Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

NASA Astrophysics Data System (ADS)

Luo, Meng-Bo

2006-01-01

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n)=n-2β/ν[Φ0+Φ1n1/ν(T-Tc)+O(n2/ν(T-Tc)2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature Tc=1.784J/kB and critical exponents 2β/ν≈0.668 and ν ≈1.0. The self-diffusion constant and the chain dimensions ⟨R2⟩ and ⟨S2⟩ do not obey such a scaling law.

Finite element model of size, shape and blood pressure on rupture of intracranial saccular aneurysms

NASA Astrophysics Data System (ADS)

Rica Nabong, Jennica; David, Guido

2017-10-01

Rupture of intracranial saccular aneurysms is a primary concern for neurologists and patients because it leads to stroke and permanent disability. This paper examines the role of blood pressure, in connection with size of and wall thickness, in the rupture of saccular aneurysms. A bulb-shaped geometry of a saccular aneurysm is obtained from angiographic images of a patient and modeled using Finite Elements based on the principle of virtual work under the Fung stress-strain relationship. The numerical model is subjected to varying levels of systolic blood pressure. Rupture is assumed to occur when the wall stress exceeded its mechanical strength. The results show which sizes of this class of aneurysms are at high risk of rupture for varying levels of blood pressure.

Investigating phase transition temperatures of size separated gadolinium silicide magnetic nanoparticles

DOE PAGES

Hunagund, Shivakumar G.; Harstad, Shane M.; El-Gendy, Ahmed A.; ...

2018-01-11

Gadolinium silicide (Gd 5Si 4) nanoparticles (NPs) exhibit different properties compared to their parent bulk materials due to finite size, shape, and surface effects. NPs were prepared by high energy ball-milling of the as-cast Gd 5Si 4 ingot and size separated into eight fractions using time sensitive sedimentation in an applied dc magnetic field with average particle sizes ranging from 700 nm to 82 nm. The largest Gd 5Si 4 NPs order ferromagnetically at 316 K. A second anomaly observed at 110 K can be ascribed to a Gd 5Si 3 impurity. Here as the particle sizes decrease, the volumemore » fraction of Gd 5Si 3 phase increases at the expense of the Gd 5Si 4 phase, and the ferromagnetic transition temperature of Gd 5Si 4 is reduced from 316 K to 310 K, while the ordering of the minor phase is independent of the particle size, remaining at 110 K.« less

Investigating phase transition temperatures of size separated gadolinium silicide magnetic nanoparticles

NASA Astrophysics Data System (ADS)

Hunagund, Shivakumar G.; Harstad, Shane M.; El-Gendy, Ahmed A.; Gupta, Shalabh; Pecharsky, Vitalij K.; Hadimani, Ravi L.

2018-05-01

Gadolinium silicide (Gd5Si4) nanoparticles (NPs) exhibit different properties compared to their parent bulk materials due to finite size, shape, and surface effects. NPs were prepared by high energy ball-milling of the as-cast Gd5Si4 ingot and size separated into eight fractions using time sensitive sedimentation in an applied dc magnetic field with average particle sizes ranging from 700 nm to 82 nm. The largest Gd5Si4 NPs order ferromagnetically at 316 K. A second anomaly observed at 110 K can be ascribed to a Gd5Si3 impurity. As the particle sizes decrease, the volume fraction of Gd5Si3 phase increases at the expense of the Gd5Si4 phase, and the ferromagnetic transition temperature of Gd5Si4 is reduced from 316 K to 310 K, while the ordering of the minor phase is independent of the particle size, remaining at 110 K.

Investigating phase transition temperatures of size separated gadolinium silicide magnetic nanoparticles

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

Hunagund, Shivakumar G.; Harstad, Shane M.; El-Gendy, Ahmed A.

Gadolinium silicide (Gd 5Si 4) nanoparticles (NPs) exhibit different properties compared to their parent bulk materials due to finite size, shape, and surface effects. NPs were prepared by high energy ball-milling of the as-cast Gd 5Si 4 ingot and size separated into eight fractions using time sensitive sedimentation in an applied dc magnetic field with average particle sizes ranging from 700 nm to 82 nm. The largest Gd 5Si 4 NPs order ferromagnetically at 316 K. A second anomaly observed at 110 K can be ascribed to a Gd 5Si 3 impurity. Here as the particle sizes decrease, the volumemore » fraction of Gd 5Si 3 phase increases at the expense of the Gd 5Si 4 phase, and the ferromagnetic transition temperature of Gd 5Si 4 is reduced from 316 K to 310 K, while the ordering of the minor phase is independent of the particle size, remaining at 110 K.« less