Size Exponent Research Articles

Quantum renormalization group approach to geometric phases in spin chains

A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative and its position scales with an exponent of the system size. This exponent is directly associated with the critical properties of the model where, the exponent governing the divergence of the correlation length close to the quantum critical point.

Unified water isotherms for clayey porous materials

[1] We provide a unified model for the soil-water retention function, including the effect of bound and capillary waters for all types of soils, including clayey media. The model combines a CEC-normalized isotherm describing the sorption of the bound water (and the filling of the trapped porosity) and the van Genuchten model to describe the capillary water sorption retention but ignore capillary condensation. For the CEC-normalized isotherm, we tested both the BET and Freundlich isotherms, and we found that the Freundlich is more suitable than the BET isotherm in fitting the data. It is also easier to combine the Freundlich isotherm with the van Genuchten model. The new model accounts for (1) the different types of clay minerals, (2) the different types of ions sorbed in the Stern layer and on the basal planes of 2:1 clays, and (3) the pore size distribution. The model is validated with different data sets, including mixtures of kaolinite and bentonite. The model parameters include two exponents (the pore size exponent of the van Genuchten model and the exponent of the Freundlich isotherm), the capillary entry pressure, and two critical water contents. The first critical water content is the water content at saturation (porosity), and the second is the maximum water content associated with adsorption forces, including the trapped nonbound water.

Evaluating the Superplastic Flow of a Magnesium AZ31 Alloy Processed by Equal-Channel Angular Pressing

Experiments show that the magnesium AZ31 (Mg-3 pct Al-1 pct Zn) alloy exhibits excellent superplastic properties at 623 K (350 °C) after processing by equal-channel angular pressing using a die with a channel angle of 135 deg and a range of decreasing processing temperatures from 473 K to 413 K (200 °C to 140 °C). A maximum elongation to failure of ~1200 pct was achieved in this alloy at a tensile strain rate of 1.0 × 10−4 s−1. Microstructural inspection showed evidence for cavity formation and grain growth during tensile testing with the grain growth leading to significant strain hardening. An examination of the experimental data shows that grain boundary sliding is dominant during superplastic flow. Furthermore, a comprehensive review of the present results and extensive published data for the AZ31 alloy shows the exponent of the inverse grain size is given by p ≈ 2 which is consistent with grain boundary sliding as the rate-controlling flow mechanism.

Influence of mineral fraction on the rheological properties of forsterite + enstatite during grain‐size‐sensitive creep: 2. Deformation experiments

AbstractIn order to understand the effects of secondary minerals on the flow properties of rocks, we have conducted uniaxial compression experiments on polycrystalline forsterite (Fo) + enstatite (En) samples. At constant temperature and strain rate, the flow stress of the samples decreases with increasing enstatite volume fraction ( fEn) for samples with 0 < fEn < 0.5 and increases with increasing fEn for samples with 0.5 < fEn < 1. The values of the preexponential term, stress and grain size exponents, and activation energy in the constitutive equation for a wide range of fEn were determined. Samples with a low fEn(≤0.03) deformed at strain rates of 2 × 10−5 to 2 × 10−4/s exhibit creep characteristics that correspond to dislocation‐accommodated grain boundary sliding creep (i.e., stress exponent, n = 3), whereas diffusion‐accommodated grain boundary sliding creep is typical of high fEn samples (i.e., stress exponent, n = 1). The change of flow strength as a function of fEn during grain‐size‐sensitive creep is primarily due to changes in grain size of both phases and secondarily due to changes in the volume fraction of phases with different flow strengths. Viscosities of all samples can be reproduced in a viscosity model that takes into account (1) the grain sizes estimated by the grain growth laws established in our part 1 paper and (2) flow laws determined for the individual phases, in this case, forsterite and enstatite. Furthermore, we demonstrate that our model can be extended to make predictions of viscosity in other mineral assemblages.

Effective diffusion distance for isothermal sintering of hydroxyapatite

The microstructural evolution of hydroxyapatite (HAp) was quantified for isothermal sintering at 1100°C. The aggregated state of the powder particles is thought to be responsible for the relatively high value of the average pore separation throughout isothermal sintering. The measured grain size exponent of 6·7 is not compatible with the values expected for volume diffusion or grain boundary diffusion under the assumptions of the Combined Stage Sintering Model and hence the Master Sintering Curve. The measured exponent for a previously defined flux weighted effective diffusion distance gave a more reasonable value of 3·4. The theoretical exponent in the Combined Stage Sintering Model was then corrected to accommodate a non-linear relationship between the effective diffusion length and pore size. The results demonstrate how the effective lengthscale in the Combined Stage Sintering Model can be corrected to accommodate aggregation in the microstructure.

Transient-regime grain growth in nanocrystalline yttria-stabilized zirconia annealed without and with a DC electric field

Grain size exponents considerably larger than normally reported occurred for grain growth in nanoscale 3 mol.% yttria-stabilized zirconia annealed without and with a DC electric field at 1300 and 1400 °C. It is shown that the large exponents correspond to the transition regime predicted by solute drag theory. The observed smaller grain growth rate with an electric field compared to without is in keeping with a reduction in the capillary driving force.

Experimental and computational modelling of solid particle erosion in a pipe annular cavity

Pipe annular cavities are present in equipment related to the oil and gas and other process industries. The flow in a pipe initially expands into an annular cavity of a given length with a larger pipe diameter before suddenly contracting into a smaller pipe. In this work, air-suspended sands flow through an aluminium pipe annular cavity (diameter ratios, 1.25 and 0.8; cavity length, 10.25 step-heights) in which multi-layer paint erosion and parent material loss information were obtained. It was found that:•the highest erosion rate occurs on the leading edge of the forward-facing step;•the forward-facing step shoulder erodes more than the backward-facing step;•the maximum depth of erosion per unit mass on the curved cavity surface is approximately one third that of the material loss on the pipe surface;•more material is removed in the downstream half of the cavity than in the upstream half;•negligible erosion occurs up to 1.7 step-heights downstream from the backward-facing step;•198μm-sized particles remove twice as much material from the pipe surface as 38μm-sized particles, and value of the particle size exponent is 0.36.A complementary computational fluid dynamics study using a Lagrangian approach predicted erosion rate at the forward-facing step by the 198μm-sized particles to within ±30% of experimental values, while that for 38μm-sized particles are over predicted by up to 100%. It was observed that erosion rate is most accurately predicted on surfaces that experience direct impact with particles compared to erosion predictions on surfaces where erosion is caused by secondary or higher order impacts.

Entanglement and quantum phase transition in the Heisenberg—Ising model

We use the quantum renormalization-group (QRG) method to study the entanglement and quantum phase transition (QPT) in the one-dimensional spin-1/2 Heisenberg—Ising model [Lieb E, Schultz T and Mattis D 1961 Ann. Phys. (N.Y.) 16 407]. We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations. We also investigate the scaling behavior of the system close to the quantum critical point, which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size. Also, the first derivative of concurrence between two blocks diverges at the quantum critical point, which is directly associated with the divergence of the correlation length.

Aerobic Fitness, Maturation, and Training Experience in Youth Basketball

Relationships among chronological age (CA), maturation, training experience, and body dimensions with peak oxygen uptake (VO2max) were considered in male basketball players 14-16 y of age. Data for all players included maturity status estimated as percentage of predicted adult height attained at the time of the study (Khamis-Roche protocol), years of training, body dimensions, and VO2max (incremental maximal test on a treadmill). Proportional allometric models derived from stepwise regressions were used to incorporate either CA or maturity status and to incorporate years of formal training in basketball. Estimates for size exponents (95% CI) from the separate allometric models for VO2max were height 2.16 (1.23-3.09), body mass 0.65 (0.37-0.93), and fat-free mass 0.73 (0.46-1.02). Body dimensions explained 39% to 44% of variance. The independent variables in the proportional allometric models explained 47% to 60% of variance in VO2max. Estimated maturity status (11-16% of explained variance) and training experience (7-11% of explained variance) were significant predictors with either body mass or estimated fat-free mass (P ≤ .01) but not with height. Biological maturity status and training experience in basketball had a significant contribution to VO2max via body mass and fat-free fat mass and also had an independent positive relation with aerobic performance. The results highlight the importance of considering variation associated with biological maturation in aerobic performance of late-adolescent boys.

Stochastic Approximation Approach for Consensus and Convergence Rate Analysis of Multiagent Systems

In this note, we study the consensus problem for multiagent systems with measurement noises. Different from the existing approach, the consensus problem is converted to a root finding problem for which the stochastic approximation theory can be applied. By choosing an appropriate regression function, we propose a consensus algorithm which is applicable to systems with more general measurement noise processes, including stationary autoregressive and moving average (ARMA) processes and infinite moving average (MA) processes. Further, we establish a relationship between the convergence rate and the exponent of the step size of the algorithm. Particularly, strong convergence rate for systems with a leader-follower topology is studied.

MIXING IN COASTAL AREAS INFERRED FROM LYAPUNOV EXPONENTS: IMPLICATIONS FOR TRANSPORT

We study the horizontal surface mixing and the transport induced by waves, using local Lyapunov exponents and high resolution data from numerical simulations of waves and currents. By choosing the proper spatial (temporal) parameters we compute the Finite Size and Finite Time Lyapunov exponents (FSLE and FTLE) focussing on the local stirring and diffusion inferred from the Lagrangian Coherent Structures (LCS). The methodology is tested by deploying a set of eight lagrangian drifters and studying the path followed against LCS derived under current field and waves and currents.

Universality in shape evolution of Si1−xGex structures on high-index silicon surfaces

The shape evolution of MBE grown Si1−xGex islands on ultraclean reconstructed high-index Si(5 5 12), Si(5 5 7) and Si(5 5 3) surfaces has been studied experimentally and explained using a phenomenological kinetic Monte Carlo (kMC) simulation. We show that a self-assembled growth at optimum thickness leads to interesting shape transformations, namely spherical islands to rectangular rods up to a critical size beyond which the symmetry of the structures is broken, resulting in a shape transition to elongated trapezoidal structures. We observe a universality in the growth dynamics in terms of aspect ratio and size exponent, for all three high-index surfaces, irrespective of the actual dimensions of Ge-Si structures. The shape evolution has been simulated using kMC by introducing a deviation parameter (ϵ) in the surface barrier term (ED) to take the effect of anisotropic diffusion as one of the plausible mechanisms.

A GROMOS Parameter Set for Vicinal Diether Functions: Properties of Polyethyleneoxide and Polyethyleneglycol.

An extension 53A6OXY+D to the GROMOS 53A6OXY force field is reported that includes an accurate description of the vicinal diether function. The calibration is based on the model compound 1,2-dimethoxyethane (DXE) and involves a fitting of the relevant torsional-energy parameters against quantum-mechanical (QM) rotational energy profiles for the OCCO and CCOC dihedral angles in vacuum, followed by a validation against experimental conformer populations in the pure liquid and in aqueous mixtures. A systematic comparison between the 53A6, 56A6CARBO, 53A6OXY, and 53A6OXY+D parameter sets is also performed in terms of these properties, as well as in terms of the thermodynamic properties of dimethylether (DME), diethylether (DEE), 1-methoxypropane (MPH), and DXE. Finally, the new parameter set is further validated in the context of polyethers, namely polyethyleneoxide (PEO) and polyethylenegycol (PEG). The 53A6OXY+D set reproduces well the QM rotational profiles of DXE in vacuum (by calibration), the conformational populations of DXE in the pure liquid and in aqueous mixtures, and the experimental thermodynamic pure-liquid and (polar and nonpolar) solvation properties of DME, DEE, MPH, and DXE. In particular, it accounts appropriately for the gauche-effect, both in its solvent-independent stereoelectronic component and in its solvent-dependent dielectric-screening component. In contrast to 53A6OXY, it also suggests a higher affinity of DXE for water compared to octanol, in agreement with the experimental partition coefficient. In the context of aqueous polyethers, the calculated size (Flory) exponent (νg = 0.61) for the molecular-weight dependence of the radius of gyration and persistence length (Lp = 0.39 ± 0.04 nm) agree well with estimates based on experiment or previous simulations with other force fields. The simulations also suggest a picture of aqueous polyethers as "water sponges", in which the diether function "adsorbs" an essentially constant number of water molecules corresponding to first-shell hydrogen-bonded saturation of its oxygen atoms, with a tendency to include other ether oxygen atoms along the chain in the second shell, resulting in "water bridging".

A peculiar class of debris disks fromHerschel/DUNES

Aims. We present photometric data of debris disks around HIP 103389 (HD 199260), HIP 107350 (HN Peg, HD206860), and HIP 114948 (HD 219482), obtained in the context of our Herschel Open Time Key Program DUNES (DUst around NEarby Stars). Methods. We used Herschel/PACS to detect the thermal emission of the three debris disks with a 3 sigma sensitivity of a few mJy at 100 um and 160 um. In addition, we obtained Herschel/PACS photometric data at 70 um for HIP 103389. Two different approaches are applied to reduce the Herschel data to investigate the impact of data reduction on the photometry. We fit analytical models to the available spectral energy distribution (SED) data. Results. The SEDs of the three disks potentially exhibit an unusually steep decrease at wavelengths > 70 um. We investigate the significance of the peculiar shape of these SEDs and the impact on models of the disks provided it is real. Our modeling reveals that such a steep decrease of the SEDs in the long wavelength regime is inconsistent with a power-law exponent of the grain size distribution -3.5 expected from a standard equilibrium collisional cascade. In contrast, a very distinct range of grain sizes is implied to dominate the thermal emission of such disks. However, we demonstrate that the understanding of the data of faint sources obtained with Herschel is still incomplete and that the significance of our results depends on the version of the data reduction pipeline used. Conclusions. A new mechanism to produce the dust in the presented debris disks, deviations from the conditions required for a standard equilibrium collisional cascade (grain size exponent of -3.5), and/or significantly different dust properties would be necessary to explain the potentially steep SED shape of the three debris disks presented. (abridged)

Competition of strength and stress disorder in creep rupture

Based on a fiber bundle model of subcritical fracture with localized load sharing, we show that the interplay of threshold disorder and the inhomogeneous stress field gives rise to a rich dynamics with intriguing aspects. In the model, fibers fail either due to immediate breaking or to a slow damage process. When the disorder is strong, a large amount of damage occurs, which is randomly diffused over the system; however, for weak disorder, a single growing crack is formed, which proceeds in a large number of localized bursts. The microstructure of cracks is characterized by a power-law size distribution, which is analogous to percolation in the regime of diffusive damage; however, it becomes significantly steeper when a single crack dominates. Simulations showed that the size distribution of breaking bursts and of the waiting times in between have a power-law functional form with a load-dependent cutoff. The burst size exponent proved to be independent of the damage process; however, it strongly depends on the external load with a minimum value of 1.75. The waiting time distribution is sensitive to the details of the damage process with an exponent decreasing from 2.0 to 1.4 as bursts get more and more localized to an advancing crack front.

Dynamic Recrystallization Mechanisms Operating under Different Processing Conditions

Dynamic recrystallization (DRX) is one of the most important mechanisms for microstructure evolution during deformation of various metals and alloys. So-called discontinuous DRX usually develops in structural materials with low to medium stacking fault energy during hot working. The local migration, i.e. bulging, of grain boundaries leads to the formation of recrystallization nuclei, which then grow out consuming work-hardened surroundings. The cyclic character of nucleation and growth of new grains during deformation results in a dynamically constant average grain size. The dynamic grain size is sensitively dependent on temperature and strain rate and can be expressed by a power law function of flow stress with a grain size exponent of about-0.7 under conditions of hot working. Recent studies on DRX phenomenon suggest that a decrease in deformation temperature changes the structural mechanism for new grain formation. As a result, the grain size exponent in the relationship between the dynamic grain size and flow stress approaches about-0.25 under warm working conditions.

Kinetics of Grain Refinement by Warm Deformation of 304-Type Stainless Steel

The dynamic process of grain evolution in an S304H-type austenitic stainless steel was studied in multiple forging tests at temperatures of 500°C, 600°C and 700°C. The deformation microstructure with a grain size of about 100 to 400 nm resulted from continuous dynamic recrystallization. The size of new grains and the recrystallization kinetics decreased with decreasing the deformation temperature. The dynamically equilibrium grain size evolved at large strains followed a power law function of the flow stress with a grain size exponent of about-0.2. The formation of new fine grains was assisted by dynamic recovery, which leads to an apparent steady state flow at large total strains.

Grain Size Dependence of Creep in Nanocrystalline Copper by Molecular Dynamics

The grain size dependence of creep is critical to understand the plastic deformation mechanism of nanoscale metals. Here we used molecular dynamics to study the stress-induced grain size exponent transition in creep of nanocrystalline copper. The grain size exponent was found to initially increase with increasing stress, then decrease after some critical stress. The derived grain size exponents are in agreement with experimental results for diffusional and grain boundary sliding creep at low stress. While, the founded decreasing grain size exponent with increasing stress for dislocation nucleation creep in nanocrystal is in contrast with conventional materials. We propose a constitutive equation for dislocation nucleation governed creep in nanocrystal to explain its grain size dependence transition with stress.

Scaling lower-limb isokinetic strength for biological maturation and body size in adolescent basketball players

The relationships between knee joint isokinetic strength, biological maturity status and body size were examined in 14-16-year-old basketball players, considering proportional allometric modeling. Biological maturity status was assessed with maturity offset protocol. Stature, body mass, sitting height, and estimated thigh volume were measured by anthropometry. Maximal moments of force of concentric and eccentric muscular actions for the knee extensors and flexors were assessed by isokinetic dynamometry at 60°s(-1). Regression analysis revealed a linear relation between maximal moments of force of the knee extensors in both muscular actions and knee flexors in concentric actions were moderately high (0.55≤r≤0.64). As for knee flexors in eccentric actions, a squared term of maturity indicator was significant indicating that the relationship with maturity offset tended to plateau approximately 2years after PHV. Incorporating maturity indicator term with body size term (body mass or thigh volume) in the allometric models revealed that the size exponents for both body mass and thigh volume were reduced compared with simple allometric modeling. The results indicate a significant inter-individual variation in lower-limb isokinetic strength performance at 60°s(-1) in concentric and eccentric muscular actions in late adolescent basketball players. The variability in performance is related to inter-individual variation in estimated time before or after peak height velocity, as well as differences in body size. Proportional allometric models indicate that the influence of estimated time from age at peak height velocity on isokinetic strength performance is mostly mediated by corresponding changes in overall body mass.

Grain boundary relaxation and grain growth in 18-carat yellow gold alloy

A high-temperature anelastic relaxation peak in the mechanical loss spectrum of 18-carat yellow gold polycrystals is analysed and interpreted as due to grain boundary sliding accommodated predominantly by elastic deformation of the grains. The characteristic time scale of the relaxation process tvaries with the grain size d, and the grain size exponent is found to be m = 1.09 +/- 0.10 which is in perfect accord with the Zener model that attributes a grain boundary relaxation to viscous sliding along the grain boundaries. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.