Single Parameter Description Research Articles

Anharmonic incommensurate structure modulation in Ni-Mn-Ga martensite exhibiting highly mobile twin boundaries

We perform neutron diffraction on a bulk Ni50.0Mn27.5Ga22.5 single crystal to investigate the evolution of its five-layered modulated (10M) martensite structure, from 300 K down to 10 K. Close to martensite transformation, the modulation is nearly commensurate, with q = 0.402 in a modulation vector (q, q, 0). Upon cooling, the shift in diffraction satellites indicates a transition to an incommensurate modulation with increasing q. However, the observed fifth-order diffraction satellites below 260 K and even more complex satellite landscape at 10 K cannot be explained by incommensurability alone. Our analysis reveals that the modulation function is highly anharmonic, encompassing Fourier components up to the eighth order. We have developed a single-parameter description of the evolution of modulation across the entire temperature interval of the 10M phase existence. Surprisingly, the structure evolution from commensurate to incommensurate modulation has no significant effect on twin boundary mobility.

Quantitative description of the quality of size exclusion chromatography separations

Size exclusion chromatography (SEC) is unique among chromatographic methods as it allows separation of non-retained analytes. However, such mechanism often put an analytical scientist in front of relatively poorly resolved set of peaks that may have strikingly different abundance. The description of such chromatograms needs a particular approach to accurately capture the overall quality of separation. Consequently, use of a single parameter description may not be accurate enough and therefore we introduce a dimensionless separation quality factor, which is based on five SEC specific measures (peak-to-valley, elution window width, peak widths, peak-positioning and recovery). Combining several factors allowed detailed differentiation of various simulated separations, clearly correlating column characteristics with specific contributions to separation quality whether they concern a single peak pair or entire peak landscape. The method could be further elaborated by the addition of normalized priority weighting allowing for flexible quality quantification of a relevant portion of real-life nucleic acid separation on different columns. With growing complexity of biotherapeutics to be separated, such a term is predicted to be a useful response function for purposes of factorial method optimization.

Chemical Exchange Rate Study by NMR CPMG Method

Analysis of the NMR CPMG method is presented that enables direct sampling of the spectral-density function of the chemical exchange processes. The approach is demonstrated on a solution of sucrose in water. The result confirms that the method can provide insight into the details of the dynamics of molecular conformations beyond a single-parameter description by an exchange rate. The results of the method are not limited to a single exchange process but can be of advantage if a large and potentially unknown number of exchange processes is contributing to the dynamics of a spin system.

Fracture resistance of shape memory alloys under thermomechanical loading

Experimental measurements of the fracture resistance of Shape Memory Alloys (SMAs) under thermomechanical loading conditions are reported. NiTi compact tension specimens are subjected to either isothermal mechanical or isobaric thermal loading; the latter loading path is an idealization of typical loading paths that utilize these alloys as actuators. A single-parameter description of the experimental data is employed on the basis of a path-independent contour integral, which is approximated by the load–load-line displacement curves recorded from the experiments. The obtained results represent the first experimental measurement of the fracture toughness of SMAs under coupled thermo-mechanical loading, and indicate that the fracture toughness enhancement associated with crack advance under isobaric thermal loading is less pronounced than the corresponding one under isothermal mechanical loading.

A unified description of mechanical and actuation fatigue crack growth in shape memory alloys

The damage tolerance approaches to fatigue rely on fracture mechanics concepts to explicitly account for the fatigue crack growth process. These approaches typically adopt the Paris equation, which relates the crack growth per cycle to the range of variation of the stress intensity factor, ΔK, during cyclic loading by means of experimentally calibrated parameters. Conditions on the validity of a single parameter description of the near crack tip stress and strain fields restrict the applicability of ΔK to fatigue crack growth resistance in Shape Memory Alloys (SMAs) under general thermomechanical loading paths. These conditions are substantially relaxed for the cyclic ΔJ–integral approach, which can achieve similitude over a wider range of loading conditions and geometric configurations. Thus, ΔJ qualifies as a potential unified descriptor of thermomechanical fatigue crack growth resistance in SMAs, an assertion, which is tested in this work for data from both purely mechanical and actuation fatigue crack growth experiments of a high temperature SMA, Ni50.3Ti29.7Hf20. In the latter, compact tension specimens are subjected to thermal cycling under constant load between an upper and a lower cycle temperature that allows for the stable phase to alternate in each cycle. It is shown here that a Paris-type power-law crack growth expression based on the ΔJ-integral can fit fatigue crack growth rate data from both types of experiments with a single set of parameters. This new analysis method for both actuation and mechanical fatigue crack growth rates provides a unified description for fatigue crack growth in SMAs and can allow estimating actuation fatigue crack growth rates, laborious and challenging to measure, from easier to detect mechanical fatigue crack growth rates.

The Molecular Biophysics of Adaptation

From molecular conformations to mass migrations, adaptation is a defining feature of life that is found across time and length scales. Here, we present a theory-experiment dialogue examining how adaptive behavior is manifested at the molecular level in the context of transcriptional regulation in bacteria. Using a statistical mechanical rendering of the Monod-Wyman-Changeux model of allostery, we draw parameter-free predictions of the level of gene expression from a regulated reporter as a function of an extracellular signal across a wide variety of strains. We then derive an expression for the free energy, enabling full data collapse of our experimental measurements onto a single master curve. With this arsenal of analytic ammunition, we then explore how physiological changes (rewiring carbon metabolism and varying temperature) and evolutionary perturbations (mutations with the regulatory protein) tune the level of gene expression and ultimately, the free energy of the system. We demonstrate that the adaptive response of the system can be mapped onto changes in the free energy, providing a set of diagnostic tools that identify which biophysical parameters are modified to yield the observed adaptation by examining the phenomenology of the data alone. These results illustrate that the free energy is the “natural variable” of the system and can be treated as a quantitative trait upon which evolutionary forces act, allowing for one to reduce the high-dimensional parameter space to a single-parameter description.

Local buckling strength of steel foam sandwich panels

The objective of this paper is to provide and verify a new design method for the in-plane compressive strength of steel sandwich panels comprised of steel face sheets and foamed steel cores. Foamed steel, literally steel with internal voids, provides enhanced bending rigidity, exceptional energy dissipation, and the potential to mitigate local instability. In this work, Winter's effective width expression is generalized to the case of steel foam sandwich panels. The generalization requires modification of the elastic buckling expressions to account for panel non-composite bending rigidity and shear deformations. In addition, an equivalent yield stress is introduced to provide a single parameter description of the yielding behavior of the steel face sheets and steel foam core. The provided analytical expressions are verified with finite element simulations employing three-dimensional continuum elements and calibrated constitutive models specific to metallic foams. The developed closed-form design expressions are employed to conduct parametric studies of steel foam sandwich panels, which (a) demonstrate the significant strength improvements possible when compared with solid steel, and (b) provide insights on the optimal balance between steel face sheet thickness and density of the foamed steel core. This work is part of a larger effort to help develop steel foam as a material with relevance to civil engineering applications.

Report 86

The absorbed dose, the mean value of the energy imparted by ionizing radiation to a volume of interest divided by the mass of that volume, is often a very effective way to describe radiation exposures. For example, in radiation therapy and industrial radiation processing, the absorbed dose is usually adequate for predicting the results of the irradiation. However, in situations in which the heterogeneity of the energy deposition or of the target structure results in individual targets (often assumed to be a cell or a cell nucleus) receiving energy depositions that are dramatically different from the mean value, the absorbed dose does not provide sufficient information needed to fully understand the consequences of irradiation or for the use of radiation-response models. In some cases, such as microbeam irradiations, heterogeneous exposures have been created intentionally in order to study mechanisms of response to ionizing radiation. In other situations, such as background-radiation exposure, the heterogeneity occurs as a result of the low level of radiation exposure or of a small local concentration of a radioactive material. When the energy deposition is heterogeneous, the conventional description in terms of absorbed dose can be misleading because it suggests that neighboring structures will incur the same amount of damage, and that the amount received by an individual target can be decreased to as low a value as desired. In fact, the individual targets can receive highly variable energy depositions, with a mean and variance determined by the physical properties of the radiation and the target. Reliance on the mean values rather than the spectrum of individual energy depositions can lead to inappropriate conclusions about the relationship between energy deposited and the initiation of biological response. Even with the same amount of deposited energy, the spectrum of initial damage products depends on radiation quality (sometimes specified in terms of the linear energy transfer). However, the complex combinations of biomolecular processes occurring following irradiation make it unlikely that any single-parameter description of the radiation interaction will be satisfactory for understanding biological processes. This Report recommends that, in cases in which energy deposition is likely to be heterogeneous, a detailed description of the radiation field, with an appropriate description of the irradiated system, should be given. The complete description of the radiation is the energy distribution of the particle radiance as a function of time and particle type. However, simplified descriptions such as the distribution of fluence rate, the probability density of lineal energy, and the event rate, or even the absorbed dose rate and radiation quality are appropriate descriptions of the irradiation in many cases.

Establishing the island of stability for superheavy nuclei via the dynamical cluster-decay model applied to a hot fusion reaction 48Ca + 238U → 286112*

Considering different magic shells such as Z = 126, 120 or 114, N = 184 or Z = 120, N = 172 for the superheavy mass region, the dynamical cluster-decay model (DCM), with deformation and orientation degrees of freedom of colliding nuclei or decay fragments included, is used to study the complete excitation functions of a ‘non-equatorial’ compact hot-fusion reaction 48Ca + 238U → 286112* (orientation angle θc = 72° for 238U; θc = 90° for ‘equatorial’ compact). For the higher multipole deformations taken up to hexadecapole deformations β4i and configurations with ‘compact’ orientations θci, the DCM gives a good description of the individual light-particle decay channels σxn (x = 3 and 4 neutrons), and other decay channels, the fusion–fission σff and quasi-fission σqf cross-sections, at various incident energies or compound nucleus excitation energies E*, within a single parameter description, the neck-length parameter ΔR. Within the Strutinsly renormalization procedure, in each case, the shell corrections are obtained from an ‘empirical’ formula with the corresponding liquid-drop energies adjusted to give the experimental binding energies. This is done for all the mass (and charge) fragmentations of the compound system. Of all the four choices of magic numbers considered, the evaporation residue cross-sections (σER = σ3n + σ4n, the sum of light-particle, neutron-channel cross-sections) remain the largest and nearly the same for Z = 126, N = 184 or Z = 120, N = 184, but the fusion–fission cross-sections σff are always the highest for Z = 120, N = 184. Noting that the quasi-fission process is not affected by the magicity of shells, this study supports Z = 120 and N = 184 as the strongest magic numbers for the center of an island of stability for superheavy elements.

Distribution of conductance for Anderson insulators: A theory with a single parameter

We obtain an analytic expression for the full distribution of conductance for a strongly disordered threedimensional conductor within a perturbative approach based on transfer-matrix formulation. Our results confirm the numerical evidence that the log-normal limit of the distribution is not reached even in the deeply insulating regime. We show that the variance of the logarithm of the conductance scales as a fractional power of the mean, while the skewness changes sign as one approaches the Anderson metal-insulator transition from the deeply insulating limit, all described as a function of a single parameter. The approach suggests a possible single parameter description of the Anderson transition that takes into account the full nontrivial distribution of conductance.

Feasibility of a single-parameter description of equilibrium viscous liquid dynamics

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics is described by a single parameter to a good approximation. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid, a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the alpha time scale in the constant-volume, constant-temperature ensemble; similarly, energy and volume fluctuations correlate strongly in the constant-pressure, constant-temperature ensemble.

The whitecap coverage model from breaking dissipation parametrizations of wind waves

An analytical model for whitecap coverage has been established from wave breaking dissipation models by improving the model of Kraan et al. [1996]. The similarity of three wave breaking parametrizations has been discussed and applied to develop the analytical model. The proposed model predicts an inversely quadratic dependence of whitecap coverage on wave age, after invoking the 3/2 power law. The undetermined parameter in the model is fixed with the latest published data sets. The proposed model is more consistent with the four data sets used than the other two analytical models presented more recently, which would underestimate significantly the four data sets overall. The substantiation of the field observations to inversely quadratic dependence on wave age means that the choice for the dependence of the damping rate on wave steepness by Komen et al. [1984] in quasilinear dissipation model has some support from observations of the whitecap coverage. The limitation of the single parameter description to whitecap coverage and the controversy on the nature of the dependence of wave breaking properties on wind wave status due to the single‐parameter description are discussed. It is pointed out that the multiple‐parameter scheme is expected to give rise to a consistent interpretation to the variability of whitecap coverage.

Three-dimensional crystal-melt Wulff-shape and interfacial stiffness in the Al-Sn binary system

The quantitative determination of the three-dimensional Wulff shape for a metallic crystal-melt system is reported here. The anisotropy of crystal-melt interfacial free energy is experimentally measured for the $\mathrm{Al}--\mathrm{Sn}$ binary system at temperatures of 300 and $500\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. Equilibrium shapes of liquid droplets entrained within the crystalline phase are measured experimentally on sequential two-dimensional sections, and the three-dimensional Wulff plot is reconstructed. For this system, it is found that a single-parameter description of anisotropy is not sufficient, and the anisotropy is reported using the leading terms of the relevant cubic harmonics. Accordingly, the anisotropy coefficients are determined to be ${\ensuremath{\epsilon}}_{1}=(1.81\ifmmode\pm\else\textpm\fi{}0.36)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${\ensuremath{\epsilon}}_{2}=(\ensuremath{-}1.12\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. In addition, the corresponding normal stiffness components as well as a generalized stiffness are quantified and compared with available predictions from atomistic simulations.

Spectral pattern complexity analysis and the quantification of voice normality in healthy and radiotherapy patient groups

Vocal fold functionality may alter in response to direct radiotherapy or indirectly by perturbation of the hypothalamic–pituitary axis. Perceptual assessment of voice quality is difficult to summarise in a single, reliable figure of normality and normality itself is undefined. In this study spectral analysis of vocal fold vibration, based on impedance variations measured across the larynx using an electro-glottogram, is used to build a single parameter description of standard vowel phonation in the normal male population. Patient data and perceptual assessment are then compared to this standard. The spectral pattern of the vowel/i/ electro-glottogram time series is analysed using approximate entropy after dynamic fundamental-harmonic frequency normalisation. The approximate entropy provides a single estimate of the spectral pattern complexity. A cohort of 89 normal males formed two statistically distinct groups, G1, with strong spectral pattern and high complexity 0.338 (±0.036), and G2 with a weak spectral pattern and low complexity 0.175 (±0.049). Membership ratio G1:G2 was 2:1. A cohort of 30 male larynx cancer cases were analysed approximately 3–6 months after irradiation, and three male prophylactic cranial irradiation cases some years after treatment. Two-thirds of patients had G2 or lower levels of complexity. The lower G2 complexity level appears to be the subjective, as well as the objective, threshold for voice normality.

The Bivariate Luminosity‐Color Distribution ofIRASGalaxies and Implications for the High‐Redshift Universe

We present a characterization of the local luminosity-color bivariate distribution of IRAS galaxies from the 1.2 Jy sample, selected at 60 μm. The R(60, 100) infrared (IR) color is used as the best single-parameter description of the IR spectral energy distribution of galaxies. We derive an analytical form of the distribution and use it to constrain the effect of the IR color distribution on evolution models for high-redshift, far-infrared (FIR)-luminous galaxies. Our adopted evolution retains the locally observed correlation between luminosity and color, such that the larger characteristic luminosities at higher redshift have a warmer characteristic color. The width of the color distribution at a given luminosity remains constant for all redshifts. We demonstrate that there is the potential for both hotter and colder sources to be missed in cosmological surveys. An evolving bivariate luminosity function coupled with the cold-source bias of submillimeter-selected surveys suggests the existence of a large population of cold sources appearing in such surveys. Likewise, a hot-source bias for most SIRTF wave bands together with a bivariate model suggests an excess of hot sources being selected. We test the evolutionary form against available data for higher redshift, FIR galaxies. The data do not reveal evidence for any strong evolution in the characteristic luminosity-color distribution as a function of redshift over 0 < z < 1. However, there is marginal evidence for a broadening of the color distribution at higher redshifts, consistent with our locally characterized trend of a broadening in the IR color distribution at the highest luminosities.

The automatic lung parameter estimator (ALPE) system: non-invasive estimation of pulmonary gas exchange parameters in 10-15 minutes.

Clinical measurements of pulmonary gas exchange abnormalities might help prevent hypoxaemia and be useful in monitoring the effects of therapy. In clinical practice single parameters are often used to describe the abnormality e.g., the "effective shunt." A single parameter description is often insufficient, lumping the effects of several abnormalities. A more detailed picture can be obtained from experiments where FiO2 is varied and two parameters estimated. These experiments have previously taken 30-40 minutes to complete, making them inappropriate for routine clinical use. However with automation of data collection and parameter estimation, the experimental time can be reduced to 10-15 minutes. A system has been built for non-invasive, Automatic, Lung Parameter Estimation (ALPE). This system consists of a ventilator, a gas analyser with pulse oximeter, and a computer. Computer programs control the experimental procedure, collect data from the ventilator and gas analyser, and estimate pulmonary gas exchange parameters. Use of the ALPE system, i.e. in estimating gas exchange parameters and reducing experimental time, has been tested on five normal subjects, two patients before and during diuretic therapy, and on 50 occasions in patients before and after surgical intervention. The ALPE system provides estimation of pulmonary gas exchange parameters from a simple, clinical, non-invasive procedure, automatically and quickly. For normal subjects and in patients receiving diuretic therapy, data collection by clinicians familiar with ALPE took (mean +/- SD) 13 min 40 sec +/- 1 min 23 sec. For studies on patients before and after surgery, data collection by an intensive care nurse took (mean +/- SD) 10 min 47 sec +/- 2 min 14 sec. Parameter estimates were: for normal subjects, shunt = 4.95% +/- 2.64% and fA2 = 0.89 +/- 0.01; for patients with heart failure prior to diuretic therapy, patient 1, shunt = 11.50% fA2 = 0.41, patient 2 shunt = 11.61% fA2 = 0.55; and during therapy: patient 1, shunt = 11.51% fA2 = 0.71, patient 2, shunt = 11.22% fA2 = 0.49. The ALPE system provides quick, non-invasive estimation of pulmonary gas exchange parameters and may have several clinical applications. These include, monitoring pulmonary gas exchange abnormalities in the ICU, assessing post-operative gas exchange abnormalities, and titrating diuretic therapy in patients with heart failure.

The crack driving force for fatigue crack propagation

Kinked, forked and twisted paths of a mode I crack cause a “local mixed” mode loading at the crack tip. The best known single parameter description of this problem is the local crack driving force K tip , based on the maximum strain energy release rate. For fatigue crack propagation near the threshold, the shear stress distribution may be more important than the strain energy release rate. Hence, for kinked and doubly kinked cracks the dependence of K tip is compared to the dependence of the shear stress distribution as a function of the angles of the kinks. It will be shown that K tip is more affected by the geometry than the shear stress field.

Velocity distribution and skin friction resistance in rectangular ducts

This paper summarizes analytical and experimental findings about the characteristics of fully-developed flow in smooth-walled rectangular conduits. Results are presented which support the equivalent diameter concept for the single-parameter description of friction effects in turbulent conduit flow, including ducts of large aspect ratio.

Application of the BET equation to heterogeneous surfaces

It is shown that a previously published procedure for obtaining site energy distributions can be applied to data which include multilayer adsorption, with the BET equation used as the local isotherm function. When applied to the adsorption of argon on rutile, the resulting distribution function is essentially the same as that obtained by Drain and Morrison using a nearly thermodynamic procedure. The BET model can thus be applied to adsorption on heterogeneous surfaces. On the other hand, the BET c value obtained from a simple fitting of the equation to the adsorption isotherm reflects only the average energy of those sites being filled in the region of the fit, and is low. A better single-parameter description of the adsorbent surface is given by the average site energy as obtained from the actual distribution function.