Numerical Study of Entropy Generation in Fully Developed Turbulent Circular Tube Flow Using an Elliptic Blending Turbulence Model

As computational fluid dynamics (CFD) advances, entropy generation minimization based on CFD becomes attractive for optimizing complex heat-transfer systems. This optimization depends on the accuracy of CFD results, such that accurate turbulence models, such as elliptic relaxation or elliptic blending turbulence models, become important. The performance of a previously developed elliptic blending turbulence model (the SST k–ω–φ–α model) to predict the rate of entropy generation in the fully developed turbulent circular tube flow with constant heat flux was studied to provide some guidelines for using this class of turbulence model to calculate entropy generation in complex systems. The flow and temperature fields were simulated by using a CFD package, and then the rate of entropy generation was calculated in post-processing. The analytical correlations and results of two popular turbulence models (the realizable k–ε and the shear stress transport (SST) k–ω models) were used as references to demonstrate the accuracy of the SST k–ω–φ–α model. The findings indicate that the turbulent Prandtl number (Pr_t) influences the entropy generation rate due to heat-transfer irreversibility. Pr_t = 0.85 produces the best results for the SST k–ω–φ–α model. For the realizable k–ε and SST k–ω models, Pr_t = 0.85 and Pr_t = 0.92 produce the best results, respectively. For the realizable k–ε and the SST k–ω models, the two methods used to predict the rate of entropy generation due to friction irreversibility produce the same results. However, for the SST k–ω–φ–α model, the rates of entropy generation due to friction irreversibility predicted by the two methods are different. The difference at a Reynolds number of 100,000 is about 14%. The method that incorporates the effective turbulent viscosity should be used to predict the rate of entropy generation due to friction irreversibility for the SST k–ω–φ–α model. Furthermore, when the temperature in the flow field changes dramatically, the temperature-dependent fluid properties must be considered.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

Two-Dimensional EspEn: A New Approach to Analyze Image Texture by Irregularity

Image processing has played a relevant role in various industries, where the main challenge is to extract specific features from images. Specifically, texture characterizes the phenomenon of the occurrence of a pattern along the spatial distribution, taking into account the intensities of the pixels for which it has been applied in classification and segmentation tasks. Therefore, several feature extraction methods have been proposed in recent decades, but few of them rely on entropy, which is a measure of uncertainty. Moreover, entropy algorithms have been little explored in bidimensional data. Nevertheless, there is a growing interest in developing algorithms to solve current limits, since Shannon Entropy does not consider spatial information, and SampEn2D generates unreliable values in small sizes. We introduce a proposed algorithm, EspEn (Espinosa Entropy), to measure the irregularity present in two-dimensional data, where the calculation requires setting the parameters as follows: m (length of square window), r (tolerance threshold), and ρ (percentage of similarity). Three experiments were performed; the first two were on simulated images contaminated with different noise levels. The last experiment was with grayscale images from the Normalized Brodatz Texture database (NBT). First, we compared the performance of EspEn against the entropy of Shannon and SampEn2D. Second, we evaluated the dependence of EspEn on variations of the values of the parameters m, r, and ρ. Third, we evaluated the EspEn algorithm on NBT images. The results revealed that EspEn could discriminate images with different size and degrees of noise. Finally, EspEn provides an alternative algorithm to quantify the irregularity in 2D data; the recommended parameters for better performance are m = 3, r = 20, and ρ = 0.7.     

Statistical Inference for Ergodic Algorithmic Model (EAM), Applied to Hydrophobic Hydration Processes

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnK_dual = (−ΔG°_dual/T) ={f(1/T)*g(T)} and β) RTlnK_dual = (−ΔG°_dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξ_w, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δh_for>_A = −22.7 ± 0.7 kJ·mol⁻¹ ·ξ_w⁻¹ sets with standard deviation σ = ±3.1% and <Δs_for>_A = −445 ± 3J·K⁻¹·mol⁻¹·ξ_w⁻¹J·K⁻¹·mol⁻¹·ξ_w⁻¹ with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated.     

How to Utilize my App Reviews? A Novel Topics Extraction Machine Learning Schema for Strategic Business Purposes

Acquiring knowledge about users’ opinion and what they say regarding specific features within an app, constitutes a solid steppingstone for understanding their needs and concerns. App review utilization helps project management teams to identify threads and opportunities for app software maintenance, optimization and strategic marketing purposes. Nevertheless, app user review classification for identifying valuable gems of information for app software improvement, is a complex and multidimensional issue. It requires foresight and multiple combinations of sophisticated text pre-processing, feature extraction and machine learning methods to efficiently classify app reviews into specific topics. Against this backdrop, we propose a novel feature engineering classification schema that is capable to identify more efficiently and earlier terms-words within reviews that could be classified into specific topics. For this reason, we present a novel feature extraction method, the DEVMAX.DF combined with different machine learning algorithms to propose a solution in app review classification problems. One step further, a simulation of a real case scenario takes place to validate the effectiveness of the proposed classification schema into different apps. After multiple experiments, results indicate that the proposed schema outperforms other term extraction methods such as TF.IDF and χ² to classify app reviews into topics. To this end, the paper contributes to the knowledge expansion of research and practitioners with the purpose to reinforce their decision-making process within the realm of app reviews utilization.     

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr²ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr²ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.     

Effects of Match Location,Quality of Opposition and Match Outcome on Match Running Performance in a Portuguese Professional Football Team

The aim of this study was to analyze the effects of match location, quality of opposition and match outcome on match running performance according to playing position in a Portuguese professional football team. Twenty-three male professional football players were monitored from eighteen Portuguese Football League matches during the 2019–2020 season. Global positioning system technology (GPS) was used to collect time-motion data. The match running performance was obtained from five playing positions: central defenders (CD), fullbacks (FB), central midfielders (CM), wide midfielders (WM) and forwards (FW). Match running performance was analyzed within specific position and contextual factors using one-way analysis of variance (ANOVA) for repeated measures, standardized (Cohen) differences and smallest worthwhile change. CM and WM players covered significantly greater total distance (F = 15.45, p = 0.000, η² = 0.334) and average speed (F = 12.79, p < 0.001, η² = 0.294). WM and FB players covered higher distances at high-speed running (F = 16.93, p = 0.000, η² = 0.355) and sprinting (F = 13.49; p < 0.001, η² = 0.305). WM players covered the highest number of accelerations (F = 4.69, p < 0.001, η² = 0.132) and decelerations (F = 12.21, p < 0.001, η² = 0.284). The match running performance was influenced by match location (d = 0.06–2.04; CI: −0.42–2.31; SWC = 0.01–1.10), quality of opposition (d = 0.13–2.14; CI: –0.02–2.60; SWC = 0.01–1.55) and match outcome (d = 0.01–2.49; CI: −0.01–2.31; SWC = 0.01–0.35). Contextual factors influenced the match running performance with differential effects between playing positions. This study provides the first report about the contextual influence on match running performance in a Portuguese professional football team. Future research should also integrate tactical and technical key indicators when analyzing the match-related contextual influence on match running performance.     

Chemistry of a novel zerovalent ruthenium π-acidic alkene complex,Ru (η6-1,3,5-cyclooctatriene)(η2-dimethyl fumarate)2

A novel zerovalent ruthenium complex with a π-acidic ligand, Ru(η⁶-cyclooctatriene)(η²-dimethyl fumarate)₂ (1), was prepared from Ru(η⁴-cyclooctadiene)(η⁶-cyclooctatriene) [Ru(cod)(cot)]. Complex 1 or Ru(cod)(cot) catalyzes various new carbon-carbon bond-forming reactions that include the [2 + 2] cycloaddition of alkenes and alkynes via ruthenacycles, the creation of a new hydrocarbon, pentacyclo[6.6.0.0^2,6.0^3,13.0^10,14]tetradeca-4,11-diene [PCTD], by dimerization of 2,5-norbornadiene via C-C bond cleavage, and the codimerization of alkynes and/or alkenes. Complex 1 was shown to be an excellent mother complex for various zerovalent ruthenium complexes. Complex 1 reacts with amines, phosphines or water to give new zerovalent ruthenium complexes with the ligands. The resulting aqua complexes have a water ligand with an oxygen atom that is a chiral center, i.e., ruthenium complexes with a ‘chiral water’ ligand were prepared and fully characterized.     

Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Tipping the Balance: A Criticality Perspective

Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP). Under steady state conditions, the model has similarities with a well-known model of population genetics which exhibits a purely noise-induced transition from unimodality to bimodality at a critical value of the noise intensity σ2. The noise is associated with the parameter λ representing the system-environment coupling. In the case of the tumour model, λ has a natural interpretation in terms of the tissue microenvironment which has considerable influence on the phenotypic composition of the tumour. Oncogenic transformations give rise to considerable fluctuations in the parameter. We compute the λ−σ2 phase diagram in a stochastic setting, drawing analogies between bifurcations and phase transitions. In the region of bimodality, a transition from a state of balance to a state of dominance, in terms of the competing subpopulations, occurs at λ = 0. Away from this point, the NCP (CP) subpopulation becomes dominant as λ changes towards positive (negative) values. The variance of the steady state probability density function as well as two entropic measures provide characteristic signatures at the transition point.     

Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe

Pressure drop, heat transfer, and energy performance of ZnO/water nanofluid with rodlike particles flowing through a curved pipe are studied in the range of Reynolds number 5000 ≤ Re ≤ 30,000, particle volume concentration 0.1% ≤ Φ ≤ 5%, Schmidt number 10⁴ ≤ Sc ≤ 3 × 10⁵, particle aspect ratio 2 ≤ λ ≤ 14, and Dean number 5 × 10³ ≤ De ≤ 1.5 × 10⁴. The momentum and energy equations of nanofluid, together with the equation of particle number density for particles, are solved numerically. Some results are validated by comparing with the experimental results. The effect of Re, Φ, Sc, λ, and De on the friction factor f and Nusselt number Nu is analyzed. The results showed that the values of f are increased with increases in Φ, Sc, and De, and with decreases in Re and λ. The heat transfer performance is enhanced with increases in Re, Φ, λ, and De, and with decreases in Sc. The ratio of energy PEC for nanofluid to base fluid is increased with increases in Re, Φ, λ, and De, and with decreases in Sc. Finally, the formula of ratio of energy PEC for nanofluid to base fluid as a function of Re, Φ, Sc, λ, and De is derived based on the numerical data.     

Effects of Tau and Sampling Frequency on the Regularity Analysis of ECG and EEG Signals Using ApEn and SampEn Entropy Estimators

Electrocardiography (ECG) and electroencephalography (EEG) signals provide clinical information relevant to determine a patient’s health status. The nonlinear analysis of ECG and EEG signals allows for discovering characteristics that could not be found with traditional methods based on amplitude and frequency. Approximate entropy (ApEn) and sampling entropy (SampEn) are nonlinear data analysis algorithms that measure the data’s regularity, and these are used to classify different electrophysiological signals as normal or pathological. Entropy calculation requires setting the parameters r (tolerance threshold), m (immersion dimension), and τ (time delay), with the last one being related to how the time series is downsampled. In this study, we showed the dependence of ApEn and SampEn on different values of τ, for ECG and EEG signals with different sampling frequencies (F_s), extracted from a digital repository. We considered four values of F_s (128, 256, 384, and 512 Hz for the ECG signals, and 160, 320, 480, and 640 Hz for the EEG signals) and five values of τ (from 1 to 5). We performed parametric and nonparametric statistical tests to confirm that the groups of normal and pathological ECG and EEG signals were significantly different (p < 0.05) for each F and τ value. The separation between the entropy values of regular and irregular signals was variable, demonstrating the dependence of ApEn and SampEn with F_s and τ. For ECG signals, the separation between the conditions was more robust when using SampEn, the lowest value of F_s, and τ larger than 1. For EEG signals, the separation between the conditions was more robust when using SampEn with large values of F_s and τ larger than 1. Therefore, adjusting τ may be convenient for signals that were acquired with different F_s to ensure a reliable clinical classification. Furthermore, it is useful to set τ to values larger than 1 to reduce the computational cost.     

The influence of the group delay of digital filters on acoustic decay measurements

In this paper the error due to the phase response of digital filters on acoustic decay measurements is analyzed. There are two main sources of errors when an acoustic decay is filtered: the error due to the bandwidth of the filters related to their magnitude response, and the error due to their phase response. In this investigation the two components are separated and the phase error analyzed in terms of the group delay of the filters. Linear phase FIR filters and minimum phase IIR filters fulfilling the class 1 requirements of the IEC 61260 standard have been designed, and their errors compared. This makes it possible to explain the behavior of the phase error and develop recommendations for the use of each filtering technique. The paper is focused on the filtering techniques covered by current versions of the standards for measurement of acoustic decays and in the evaluation of the acoustic decay for narrow filters at low frequencies and low reverberation times (BT < 16).     

Fault Diagnosis of a Wind Turbine Gearbox Based on Improved Variational Mode Algorithm and Information Entropy

The working environment of wind turbine gearboxes is complex, complicating the effective monitoring of their running state. In this paper, a new gearbox fault diagnosis method based on improved variational mode decomposition (IVMD), combined with time-shift multi-scale sample entropy (TSMSE) and a sparrow search algorithm-based support vector machine (SSA-SVM), is proposed. Firstly, a novel algorithm, IVMD, is presented for solving the problem where VMD parameters (K and α) need to be selected in advance, which mainly contains two steps: the maximum kurtosis index is employed to preliminarily determine a series of local optimal decomposition parameters (K and α), then from the local parameters, the global optimum parameters are selected based on the minimum energy loss coefficient (ELC). After decomposition by IVMD, the raw signal is divided into K intrinsic mode functions (IMFs), the optimal IMF(s) with abundant fault information is (are) chosen based on the minimum envelopment entropy criterion. Secondly, the time-shift technique is introduced to information entropy, the time-shift multi-scale sample entropy algorithm is applied for the analysis of the complexity of the chosen optimal IMF and extract fault feature vectors. Finally, the sparrow search algorithm, which takes the classification error rate of SVM as the fitness function, is used to adaptively optimize the SVM parameters. Next, the extracted TSMSEs are input into the SSA-SVM model as the feature vector to identify the gear signal types under different conditions. The simulation and experimental results confirm that the proposed method is feasible and superior in gearbox fault diagnosis when compared with other methods.     

Heat Transfer and Fluid Flow Characteristics of Microchannel with Oval-Shaped Micro Pin Fins

A novel microchannel heat sink with oval-shaped micro pin fins (MOPF) is proposed and the characteristics of fluid flow and heat transfer are studied numerically for Reynolds number (Re) ranging from 157 to 668. In order to study the influence of geometry on flow and heat transfer characteristics, three non-dimensional variables are defined, such as the fin axial length ratio (α), width ratio (β), and height ratio (γ). The thermal enhancement factor (η) is adopted as an evaluation criterion to evaluate the best comprehensive thermal-hydraulic performance of MOPF. Results indicate that the oval-shaped pin fins in the microchannel can effectively prevent the rise of heat surface temperature along the flow direction, which improves the temperature distribution uniformity. In addition, results show that for the studied Reynolds number range and microchannel geometries in this paper, the thermal enhancement factor η increases firstly and then decreases with the increase of α and β. In addition, except for Re = 157, η decreases first and then increases with the increase of the fin height ratio γ. The thermal enhancement factor for MOPF with α = 4, β = 0.3, and γ = 0.5 achieves 1.56 at Re = 668. The results can provide a theoretical basis for the design of a microchannel heat exchanger.     

Development of β -keto ester and malonate chemistry: Palladium-catalyzed new reactions of their allylic esters

During extensive studies on π-allylpalladium chemistry, we have developed classical β-keto ester and malonate chemistry to a new generation by discovering a variety of palladium-catalyzed reactions of their allylic esters. Palladium enolates are generated from allyl β-keto esters after decarboxylation and undergo the following transformations; a) reductive elimination to provide α-allyl ketones, b) elimination of β-hydrogen to give α, β-unsaturated ketones, c) formation of α-methylene ketones, d) hydrogenolysis to give ketones, e) aldol condensation, and f) Michael addition. Allyl malonates and cyanoacetes undergo similar reactions. Results of these studies, including several applications carried out by other researchers are summarized.     

An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R<r<ρ. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.     

Filtering of stochastic optical radiation intensity

A formulation and solution of the recurrent filtering problem are proposed for correlated nonstationary optical radiation intensity fluctuations with single-electron discrete-time registration. The Bayes theory is used to find a quasi-optimal algorithm for filtering of a Markov sequence with a gamma distribution in the class of Y₂-minimax rules based on non-Gaussian approximations for a posteriori distributions.St. Petersburg State Telecommunications University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1587–1602, December, 1994.     

Magnetic field effect as a probe of distance-dependent electron transfer in systems undergoing free diffusion

A theoretical analysis is presented of the problem of how distance-dependent electron transfer in photoinduced forward electron transfer followed by geminate backward electron transfer in liquid solution is reflected in the viscosity dependence of the magnetic field effect (MFE) on the efficiency of free radical formation (φ_ce) in such reactions. The stochastic Liouville equation formalism is employed to model the reaction behaviour of distance-distributed, triplet-born radical pairs (RPs) undergoing free diffusion, distance- and spin-dependent backward electron transfer, coherent and incoherent spin evolution in the ps time domain. In comparison with real systems the spin situation is simplified by reducing it to a two state (S, T ₀) problem, yet it is parametrized in a way that allows sensible comparison of the results with those of recent experiments. It is predicted that the MFE on φ_ce exhibits characteristic minima in the MFE versus viscosity curves, and it is verified in detail that this feature is peculiar to the diffusional model with distance-dependent electron transfer, i.e. cannot be reproduced with the simpler (‘exponential’) RP model employing distance-independent rate constants. Thus, the MFE versus viscosity curves are established as a genuine fingerprint of distance-dependent electron transfer. The theoretical results compare favourably with recent experimental results obtained with Ru^III complex/methylviologen RPs.     

Random matrix theory filters in portfolio optimisation: A stability and risk assessment

Random matrix theory (RMT) filters, applied to covariance matrices of financial returns, have recently been shown to offer improvements to the optimisation of stock portfolios. This paper studies the effect of three RMT filters on the realised portfolio risk, and on the stability of the filtered covariance matrix, using bootstrap analysis and out-of-sample testing.We propose an extension to an existing RMT filter, (based on Krzanowski stability), which is observed to reduce risk and increase stability, when compared to other RMT filters tested. We also study a scheme for filtering the covariance matrix directly, as opposed to the standard method of filtering correlation, where the latter is found to lower the realised risk, on average, by up to 6.7%.We consider both equally and exponentially weighted covariance matrices in our analysis, and observe that the overall best method out-of-sample was that of the exponentially weighted covariance, with our Krzanowski stability-based filter applied to the correlation matrix. We also find that the optimal out-of-sample decay factors, for both filtered and unfiltered forecasts, were higher than those suggested by Riskmetrics [J.P. Morgan, Reuters, Riskmetrics technical document, Technical Report, 1996. http://www.riskmetrics.com/techdoc.html], with those for the latter approaching a value of α=1.In conclusion, RMT filtering reduced the realised risk, on average, and in the majority of cases when tested out-of-sample, but increased the realised risk on a marked number of individual days–in some cases more than doubling it.