Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers.

The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis-Landel decomposition have been recently explained. From that insight, a new micro-macro chain stretch connection using the stretch tensor (instead of the right Cauchy-Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney-Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns.

Enhancement of solid-liquid mixing state quality in a mechanical stirred reactor with serial-chaotic rotation generated by basic speed method.

In this work, a novel controllable chaotic stirring strategy that basic speed with chaotic mappings is proposed to enhance the solid-liquid mixing state quality. Specially, the modern statistical image analysis technique is introduced to explore the intensification mechanism of the mixing process. Results show that the best experimental conditions are obtained by studying the influence of factors such as the type of chaotic mapping, the speed change time, and the basic speed on the mixing state quality. Moreover, the case in which the basic speed is set to 150 r/min generated by the cascaded Logistic-Cubic chaotic mapping is the best while the speed change time is set to 5 s and the fluctuation threshold is 30. The mixing time of this case is 50 s and the shortest, energy consumption is 1.64 × 104 W/m3 and appropriate, the solid particle suspension quality is 83 and the best.

The logical structure of experiments lays the foundation for a theory of reproducibility.

The scientific reform movement has proposed openness as a potential remedy to the putative reproducibility or replication crisis. However, the conceptual relationship among openness, replication experiments and results reproducibility has been obscure. We analyse the logical structure of experiments, define the mathematical notion of idealized experiment and use this notion to advance a theory of reproducibility. Idealized experiments clearly delineate the concepts of replication and results reproducibility, and capture key differences with precision, allowing us to study the relationship among them. We show how results reproducibility varies as a function of the elements of an idealized experiment, the true data-generating mechanism, and the closeness of the replication experiment to an original experiment. We clarify how openness of experiments is related to designing informative replication experiments and to obtaining reproducible results. With formal backing and evidence, we argue that the current 'crisis' reflects inadequate attention to a theoretical understanding of results reproducibility.

A stochastic model of edge-localized modes in magnetically confined plasmas.

Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated with instabilities in the low-to-high confinement transition and the H-mode. Specifically, we present a stochastic Langevin model of edge-localized modes (ELMs) by including stochastic noise terms in a previous ODE ELM model. We calculate exact time-dependent PDFs by numerically solving the Fokker-Planck equation and characterize time-varying statistical properties of ELMs for different energy fluxes and noise amplitudes. The stochastic noise is shown to introduce phase-mixing and plays a significant role in mitigating extreme bursts of large ELMs. Furthermore, based on time-dependent PDFs, we provide a path-dependent information geometric theory of the ELM dynamics and demonstrate its utility in capturing self-regulatory relaxation oscillations, bursts and a sudden change in the system. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Energetics and mechanisms for decomposition of cationized amino acids and peptides explored using guided ion beam tandem mass spectrometry.

Fragmentation studies of cationized amino acids and small peptides as studied using guided ion beam tandem mass spectrometry (GIBMS) are reviewed. After a brief examination of the key attributes of the GIBMS approach, results for a variety of systems are examined, compared, and contrasted. Cationization of amino acids, diglycine, and triglycine with alkali cations generally leads to dissociations in which the intact biomolecule is lost. Exceptions include most lithiated species as well as a few examples for sodiated and one example for potassiated species. Like the lithiated species, cationization by protons leads to numerous dissociation channels. Results for protonated glycine, cysteine, asparagine, diglycine, and a series of tripeptides are reviewed, along with the thermodynamic consequences that can be gleaned. Finally, the important physiological process of the deamidation of asparagine (Asn) residues is explored by the comparison of five dipeptides in which the C-terminal partner (AsnXxx) is altered. The GIBMS thermochemistry is shown to correlate well with kinetic results from solution phase studies.

Variations on Ogden's model: close and distant relatives.

The power law in terms of stretch, the truncated series representation and the Valanis-Landel hypothesis are distinguished features of Ogden's strain-energy density function. While they represent a set of special constitutive choices, they have also been shown recently to allow a particular molecular statistical interpretation of the model, where each of these ingredients can be associated with a step in the development of the strain-energy density of the polymer network from the statistical mechanics of long-chain molecules. The schematic of this perspective brings us into a position to vary these steps individually. By this means, Ogden's theory can be embedded in a certain family of models within the large class of isotropic hyperelastic materials, whose members can be identified as close and distant 'relatives'. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Bimolecular Chemistry in the Ultracold Regime.

Advances in atomic, molecular, and optical physics techniques allowed the cooling of simple molecules down to the ultracold regime ([Formula: see text]1 mK) and opened opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques such as mass spectrometry and ion imaging significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short range. We discuss a series of studies on the reaction KRb + KRb → K2 + Rb2 initiated below 1 µK, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products.

Quantitative evaluation of the results of digital forensic investigations: a review of progress.

Unlike conventional forensics, digital forensics does not at present generally quantify the results of its investigations. It is suggested that digital forensics should aim to catch up with other forensic disciplines by using Bayesian and other numerical methodologies to quantify its investigations' results. Assessing the plausibility of alternative hypotheses (or propositions, or claims) which explain how recovered digital evidence came to exist on a device could assist both the prosecution and the defence sides in criminal proceedings: helping the prosecution to decide whether to proceed to trial and helping defence lawyers to advise a defendant how to plead. This paper reviews some numerical approaches to the goal of quantifying the relative weights of individual items of digital evidence and the plausibility of hypotheses based on that evidence. The potential advantages enabling the construction of cost-effective digital forensic triage schemas are also outlined.Key pointsThe absence of quantified results from digital forensic investigations, unlike those of conventional forensics, is highlighted.A number of approaches towards quantitative evaluation of the results of digital forensic investigations are reviewed.The significant potential benefits accruing from such approaches are discussed.

Application of a Statistical and Linear Response Theory to Multi-Ion Na+ Conduction in NaChBac.

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

The CREATE Method for Expressing Continuous Outcome Data in Absolute Terms for Use in Patient Treatment Decision Aids: A Validation Study.

BACKGROUND: Patient decision aids (PtDAs) supplement advice from health care professionals by communicating the absolute risk or benefit of treatment options (i.e., X/100). As such, PtDAs have been amenable to binary outcomes only. We aimed to develop and test the validity of the Conversion to Risk Estimates through Application of Normal Theory (CREATE) method for estimating absolute risk based on continuous outcome data. METHODS: CREATE is designed to derive an estimate of the proportion of those who experience a clinically relevant degree of change (CRDoC). We used a 2-stage validation process using real and simulated change score data, respectively. First, using raw data from published intervention trials, we calculated the proportion of patients with a CRDoC and compared that with our CREATE-derived estimate using chi-square tests of association. Second, 200,000 simulated distributions of change scores were generated with widely varying distribution characteristics. Actual and CREATE-derived estimates were compared for each simulated distribution, and relative differences were summarized graphically. RESULTS: The absolute difference between the estimated and actual CRDoC did not exceed 5% for any of the samples based on real data. Applying the CREATE method to 200,000 simulated scenarios demonstrated that the CREATE method should be avoided for outcomes where the underlying distribution can be reasonably assumed to have high levels of skew or kurtosis. CONCLUSION: Our results suggest that standard statistical theory can be used to estimate continuous outcomes in absolute terms with reasonable accuracy for use in PtDAs; caution is advised if outcome summary statistics are assumed to have been derived from highly skewed distributions.

On statistical inference in time series analysis of the evolution of road safety.

Data collected for building a road safety observatory usually include observations made sequentially through time. Examples of such data, called time series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of time series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate time series analysis techniques of varying complexity are employed to describe the development over time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in time series data. Dedicated time series analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural time series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of time series models in road safety research.

Variational transition-state theory study of the rate constant of the DMS·OH scavenging reaction by O2.

The chemical tropospheric dimethyl sulfide (DMS, CH3SCH3) degradation involves several steps highly dependent on the environmental conditions. So, intensive efforts have been devoted during the last years to enhance the understanding of the DMS oxidation mechanism under different conditions. The reaction of DMS with OH is considered to be the most relevant process that initiates the whole oxidation process. The experimental observations have been explained by a two-channel mechanism consisting of a H-abstraction process leading to CH3S(O)CH3 and HO2 and an addition reaction leading to the DMS·OH adduct. In the presence of O2, the DMS·OH adduct is competitively scavenged increasing the contribution of the addition channel to the overall DMS oxidation. Recent experimental measurements have determined from a global fit that the rate constant of this scavenging process is independent of pressure and temperature but this rate constant cannot be directly measured. In this article, a variational transition-state theory calculation of the low- and high-pressure rate constants for the reaction between DMS·OH and O2 has been carried out as a function of temperature. Our proposal is that the slight temperature dependence of the scavenging rate constant can only be explained if the H-abstraction bottleneck is preceded by a dynamical bottleneck corresponding to the association process between the DMS·OH adduct and the O2 molecule. The agreement between the low-pressure and high-pressure rate constants confirms the experimental observations.

Modulus of Natural Rubber Cross-Linked by Dicumyl Peroxide III. Some Molecular Interpretations, Possible Refinements of Theory, and Conclusions.

The shear modulus G = 5.925 × 10 - 3(fp - 0.45)T+G* (Part I), its energy component G* = 0.0684 (fp - 0.45)+ 2.70 (Part II), and the number of effective suh-chains per unit volume ve = (G - G*)/RT are given detailed molecular consideration. G is given in Mdyn cm-2 for rubber cross-linked by adding p parts of dicumyl peroxide per hundred of rubber, and heating until a fraction f of the peroxide is decomposed. ve is found to be approximately twice the density of cross-links, after a correction for impurities and chain ends is made. It can not be computed as G/RT since only the entropy component of modulus is related to ve. The sub-chains for the most highly cross-linked rubbers studied had a molecular weight of about 575 g mol-1, corresponding to about 8 isoprene units. The modulus corresponding to no added cross-links is not zero. It is determined chiefiy by the energy component of the modulus; it does not arise from entanglements. The "front factor" is found to be unity. An extensive literature survey yields values of the quantity RTΨ(v 2), where Ψ (v 2) is the Flory- Rehner equation function of v 2, the equilibrium volume fraction obtained by swelling the cross-linked rubber. RTψ (v 2) is found to be greater than G - G* but not as large as G itself.

Modulus of Natural Rubber Cross-Linked by Dicumyl Peroxide II. Comparison With Theory.

Thermodynamics and molecular considerations are applied to an examination of the equation G = S(fp + B)T + H(fp + B) + A = 5.925 × 10-3(fp - 0.45)T + 0.0684(fp - 0.45) + 2.70, found experimentally in Part I. G is the shear modulus in Mdyn cm-2 at a temperature T for natural rubber cross-linked by adding p parts of dicumyl peroxide per hundred of rubber (phr) and heating until a fraction f of the peroxide is decomposed. G*, the energy component of the modulus, is H(fp + B) + A. The ratio G*/G decreases from 1.00 at the gel point (fp = 0.45 phr) to 0.5 near 2 phr and to 0.09 at 23.8 phr. The modulus G is related to ν e , the number of moles of effective sub-chains per cm3, by the equation G - G* = v e RT where R is the gas constant. If each molecule of decomposed dicumyl peroxide of molecular weight M d produces one cross-link in the rubber of specific volume υ ¯ r , then it is predicted that S = 2 R ( 100 M d υ ¯ r ) - 1 = 5.5535 × 10 - 3 Mdyn cm-2 phr-1 K-1, as compared with the experimental value 5.925 × 10-3. Theory gives no prediction of the values of A, or of H. The gel point may be located experimentally as the point where the slope of the modulus-temperature relation is zero. The value of G at the gel point is the energy component G*. The experimental value of fp at the gel point permits a calculation of the molecular weight of the rubber before cross-linking as 193,000. The results afford a very satisfactory confirmation of the essential validity of the statistical theory of rubber elasticity in its simplest form, if due regard is paid to G*, the energy component of the modulus.