Traveling Traders' Exchange Problem: Stochastic Modeling Framework and Two-Layer Model Identification Strategy

The Travelling Traders’ Exchange Problem (TTEP) is formalised, aiming at studying the collision-exchange systems found in various research areas. As an example of the TTEP models, a 1-D model is developed and characterised in detail. The computational stochastic simulation of the 1-D TTEP model relies on a stochastic simulation algorithm implemented based on the Monte Carlo method. A model identification framework is proposed where the money distribution in the system obtained from the stochastic model is characterised in terms of (a) standard deviation of the money redistribution; (b) its probability density function. Results indicate that the expressions of the estimated functions for (a) and (b) are tightly related to the system input conditions. The example of curve fitting on the probability density function shows how the variation of money redistribution in the system in time is driven by different values of the parameters describing the interaction mechanism

A stochastic modelling approach for the characterisation of collision exchange processes

Collision-exchange process is a common physical process where system members interact with each other to exchange materials and these individual interactions cumulatively drive a macroscopic system evolution in time. In this paper, a compartment-based stochastic model is formulated to study the collision-exchange process between members in a system. The discrete Markov analysis on the stochastic model presents the analytical results that show the independence of the system equilibrium on its initial distribution, and the derived differential equations reveal the deterministic time evolution of material amount on system members. As a specific example of a physical system that can be described via this model, a seed coating process is presented where the inter-particle coating variability is expressed by the stochastic model parameters. The promising agreement between simulation predictions and experimental results demonstrates the feasibility of stochastic modelling on the collision-exchange process and facilitates further model identification and applications to industrial processes

Development of Predictive Models of the Kinetics of a Hydrogen Abstraction Reaction Combining Quantum-Mechanical Calculations and Experimental Data

The importance of developing accurate modeling tools for the prediction of reaction kinetics is well recognized. In this work, a thorough investigation of the suitability of quantum mechanical (QM) calculations to predict the effect of temperature on the rate constant of the reaction between ethane and the hydroxyl radical is presented. Further, hybrid models that combine a limited number of QM calculations and experimental data are developed in order to increase their reliability. The activation energy barrier of the reaction is computed using various computational methods, such as B3LYP, M05-2X, M06-2X, MP2 and PMP2, CBS-QB3, and W1BD, with a selection of basis sets. A broad range of values is obtained, including negative barriers for all of the calculations with B3LYP. The rate constants are also obtained for each method, using conventional transition state theory, and are compared with available experimental values at 298 K. The best agreement is achieved with the M05-2X functional with cc-pV5Z basis set. Rate constants calculated at this level of theory are also found to be in good agreement with experimental values at different temperatures, resulting in a mean absolute error of the logarithm (MAEln) of the calculated values of 0.213 over a temperature range of 200–1250 K and 0.108 over a temperature range of 300–499 K. Tunnelling and vibrational anharmonicities are identified as important sources of discrepancies at low and high temperatures, respectively. Hybrid models are proposed and found to provide good correlated rate-constant values and to be competitive with conventional kinetic models, i.e., the Arrhenius and the three-parameter Arrhenius models. The combination of QM-calculated and experimental data sources proves particularly beneficial when fitting to scarce experimental data. The parameters of the model built on the hybrid strategy have a significantly reduced uncertainty (reflected in the much narrower 95% confidence intervals) compared with the conventional kinetic models while also capturing well the experimental reaction rates with a MAEln of the rate constant of 0.118. This provides a useful strategy for kinetic model development

Analysis of seed processing by the distinct element method

The undesirable breakage of seeds during processing may result in quality degradation. Seeds experience a portfolio of shear and impact stresses as they flow through various machinery, and this may cause surface damage as well as integral damage. An in-depth study and understanding of the microscopic mechanisms of the various processes is needed to investigate and address the problem of breakage. The main aim of this work is to carry out a parametric study of the effect of sliding and rolling friction on the flow field of seeds in a seed coater device by modeling particles motion using Distinct Element Method (DEM). It was found that sliding friction plays an important role in changing the flow pattern and particles solid fraction in a specified measurement cell. However, study of particle rolling friction showed that flow pattern and solid fraction of particles will not be affected once the coefficient of rolling friction exceeds a value of 0.1

Energetics of nanoparticle oxides: interplay between surface energy and polymorphism†

Many oxides tend to form different structures (polymorphs) for small particles. High temperature oxide melt solution calorimetry has been used to measure the enthalpy as a function of polymorphism and surface area for oxides of Al, Ti, and Zr. The results confirm crossovers in polymorph stability at the nanoscale. The energies of internal and external surfaces of zeolitic silicas with open framework structures are an order of magnitude smaller than those of oxides of normal density

A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems

We revisit a K-theoretical invariant that was invented by the first author some years ago for studying multiparameter bifurcation of branches of critical points of functionals. Our main aim is to apply this invariant to investigate bifurcation of homoclinic solutions of families of Hamiltonian systems which are parametrised by tori

Novel diagnostic DNA methylation episignatures expand and refine the epigenetic landscapes of Mendelian disorders.

Overlapping clinical phenotypes and an expanding breadth and complexity of genomic associations are a growing challenge in the diagnosis and clinical management of Mendelian disorders. The functional consequences and clinical impacts of genomic variation may involve unique, disorder-specific, genomic DNA methylation episignatures. In this study, we describe 19 novel episignature disorders and compare the findings alongside 38 previously established episignatures for a total of 57 episignatures associated with 65 genetic syndromes. We demonstrate increasing resolution and specificity ranging from protein complex, gene, sub-gene, protein domain, and even single nucleotide-level Mendelian episignatures. We show the power of multiclass modeling to develop highly accurate and disease-specific diagnostic classifiers. This study significantly expands the number and spectrum of disorders with detectable DNA methylation episignatures, improves the clinical diagnostic capabilities through the resolution of unsolved cases and the reclassification of variants of unknown clinical significance, and provides further insight into the molecular etiology of Mendelian conditions

A two-layer identification strategy for the development of stochastic models of the travelling traders' exchange problem

The travelling traders’ exchange problem (TTEP) is a general mathematical problem arising in a number of applications where the purpose is to characterise the distribution of money over time related to a population of traders which can move in space and interact with each other. Results from stochastic simulations of TTEP models can be analysed over time in terms of i) standard deviation (STD); ii) probability density function (PDF) of the observations in time. A two-layer model identification strategy is proposed in this paper for the development of time-dependent nonlinear regression models from the results of TTEP computational stochastic simulations. The models are capable of representing the money distribution as a function of the TTEP operating parameters, paving the way to a new framework for model identification

Effect of particle shape on flow in discrete element method simulation of a rotary batch seed coater

In the seed processing industry, rotary batch seed coaters are widely used for providing a protective coating layer (consisting of various ingredients including fertilisers and crop protection chemicals) on the seeds. Seed motion and mixing are important in ensuring uniform coating. In the batch seed coater, the base of a cylindrical vessel rotates, whilst the cylindrical wall is stationary and two baffles turn the bed over for mixing. In the present study, the Discrete Element Method (DEM) is used to simulate the effect of particle shape on motion and mixing in this device. Corn seed is used as a model material and the effect of its shape on motion is analysed by considering two approaches: (1) manipulation of rolling friction to account for shape as it is commonly used in the field; (2) approximation of the actual shape by a number of overlapping spheres of various sizes. The geometry of corn seeds is captured using X-Ray micro tomography and then the ASG2013 software (Cogency, South Africa) is used to generate and optimise the arrangement of the overlapping spheres. A comparison is made of the predicted tangential and radial velocity distributions of the particles from DEM and those measured experimentally. It is concluded that for rapid shearing systems with short collisional contacts a small number of clumped spheres suffices to provide a reasonable agreement with experimental results. Equally well, manipulating the rolling friction coefficient can provide results that match experiments but its most suitable value is unknown a priori, hence the approach is empirical rather than predictive