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Anwar MN, Hickson RI, Mehra S, Price DJ, McCaw JM, Flegg MB, Flegg JA. Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration. Bull Math Biol 2023; 85:43. [PMID: 37076740 PMCID: PMC10115738 DOI: 10.1007/s11538-023-01153-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 03/30/2023] [Indexed: 04/21/2023]
Abstract
Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as 'hypnozoites', they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as 'relapses'. As around 79-96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels.
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Affiliation(s)
- Md Nurul Anwar
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
- Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh
| | - Roslyn I Hickson
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
- Australian Institute of Tropical Health and Medicine, and College of Public Health, Medical and Veterinary Sciences, James Cook University, Townsville, Australia
- CSIRO, Townsville, Australia
| | - Somya Mehra
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
| | - David J Price
- Department of Infectious Diseases, The Peter Doherty Institute for Infection and Immunity, The University of Melbourne, Melbourne, Australia
- Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
| | - James M McCaw
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
- Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
| | - Mark B Flegg
- School of Mathematics, Monash University, Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia.
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Cavallo JC, Scholpp S, Flegg MB. Delay-driven oscillations via Axin2 feedback in the Wnt/β-catenin signalling pathway. J Theor Biol 2020; 507:110458. [DOI: 10.1016/j.jtbi.2020.110458] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Revised: 08/11/2020] [Accepted: 08/19/2020] [Indexed: 12/19/2022]
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Mehra S, McCaw JM, Flegg MB, Taylor PG, Flegg JA. An Activation-Clearance Model for Plasmodium vivax Malaria. Bull Math Biol 2020; 82:32. [DOI: 10.1007/s11538-020-00706-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Accepted: 01/27/2020] [Indexed: 11/24/2022]
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Gunaratne RS, Wilson DB, Flegg MB, Erban R. Multi-resolution dimer models in heat baths with short-range and long-range interactions. Interface Focus 2019; 9:20180070. [PMID: 31065341 PMCID: PMC6501348 DOI: 10.1098/rsfs.2018.0070] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/11/2019] [Indexed: 11/16/2022] Open
Abstract
This work investigates multi-resolution methodologies for simulating dimer models. The solvent particles which make up the heat bath interact with the monomers of the dimer either through direct collisions (short-range) or through harmonic springs (long-range). Two types of multi-resolution methodologies are considered in detail: (a) describing parts of the solvent far away from the dimer by a coarser approach; (b) describing each monomer of the dimer by using a model with different level of resolution. These methodologies are then used to investigate the effect of a shared heat bath versus two uncoupled heat baths, one for each monomer. Furthermore, the validity of the multi-resolution methods is discussed by comparison to dynamics of macroscopic Langevin equations.
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Affiliation(s)
- Ravinda S. Gunaratne
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Daniel B. Wilson
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Mark B. Flegg
- School of Mathematical Sciences, Monash University, 9 Rainforest walk, Clayton campus, Victoria 3168, Australia
| | - Radek Erban
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
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Jayathilake C, Maini PK, Hopf HW, Sean McElwain DL, Byrne HM, Flegg MB, Flegg JA. A mathematical model of the use of supplemental oxygen to combat surgical site infection. J Theor Biol 2019; 466:11-23. [PMID: 30659823 DOI: 10.1016/j.jtbi.2019.01.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2018] [Revised: 12/13/2018] [Accepted: 01/11/2019] [Indexed: 11/26/2022]
Abstract
Infections are a common complication of any surgery, often requiring a recovery period in hospital. Supplemental oxygen therapy administered during and immediately after surgery is thought to enhance the immune response to bacterial contamination. However, aerobic bacteria thrive in oxygen-rich environments, and so it is unclear whether oxygen has a net positive effect on recovery. Here, we develop a mathematical model of post-surgery infection to investigate the efficacy of supplemental oxygen therapy on surgical-site infections. A 4-species, coupled, set of non-linear partial differential equations that describes the space-time dependence of neutrophils, bacteria, chemoattractant and oxygen is developed and analysed to determine its underlying properties. Through numerical solutions, we quantify the efficacy of different supplemental oxygen regimes on the treatment of surgical site infections in wounds of different initial bacterial load. A sensitivity analysis is performed to investigate the robustness of the predictions to changes in the model parameters. The numerical results are in good agreement with analyses of the associated well-mixed model. Our model findings provide insight into how the nature of the contaminant and its initial density influence bacterial infection dynamics in the surgical wound.
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Affiliation(s)
| | - Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | | | - D L Sean McElwain
- School of Mathematical Sciences and Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia.
| | - Helen M Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Mark B Flegg
- School of Mathematical Sciences, Monash University, Australia.
| | - Jennifer A Flegg
- School of Mathematics and Statistics, University of Melbourne, Australia.
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Lawson BA, Flegg MB. A mathematical model for the induction of the mammalian ureteric bud. J Theor Biol 2016; 394:43-56. [DOI: 10.1016/j.jtbi.2015.12.025] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Revised: 12/22/2015] [Accepted: 12/24/2015] [Indexed: 01/18/2023]
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Yates CA, Flegg MB. The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion. J R Soc Interface 2015; 12:20150141. [PMID: 25904527 PMCID: PMC4424691 DOI: 10.1098/rsif.2015.0141] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2015] [Accepted: 03/30/2015] [Indexed: 12/27/2022] Open
Abstract
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of the first, it is derived in the continuum limit over the PDE region alone. We test our hybrid methods for functionality and accuracy in a variety of different scenarios by comparing the averaged simulations with analytical solutions of PDEs for mean concentrations.
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Affiliation(s)
- Christian A Yates
- Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
| | - Mark B Flegg
- School of Mathematical Sciences, Monash University, Wellington Road, Clayton, Victoria 3800, Australia
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Langton CM, Wille ML, Flegg MB. A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models. Proc Inst Mech Eng H 2014; 228:321-9. [DOI: 10.1177/0954411914523582] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The acceptance of broadband ultrasound attenuation for the assessment of osteoporosis suffers from a limited understanding of ultrasound wave propagation through cancellous bone. It has recently been proposed that the ultrasound wave propagation can be described by a concept of parallel sonic rays. This concept approximates the detected transmission signal to be the superposition of all sonic rays that travel directly from transmitting to receiving transducer. The transit time of each ray is defined by the proportion of bone and marrow propagated. An ultrasound transit time spectrum describes the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit times over the surface of the receiving ultrasound transducer. The aim of this study was to provide a proof of concept that a transit time spectrum may be derived from digital deconvolution of input and output ultrasound signals. We have applied the active-set method deconvolution algorithm to determine the ultrasound transit time spectra in the three orthogonal directions of four cancellous bone replica samples and have compared experimental data with the prediction from the computer simulation. The agreement between experimental and predicted ultrasound transit time spectrum analyses derived from Bland–Altman analysis ranged from 92% to 99%, thereby supporting the concept of parallel sonic rays for ultrasound propagation in cancellous bone. In addition to further validation of the parallel sonic ray concept, this technique offers the opportunity to consider quantitative characterisation of the material and structural properties of cancellous bone, not previously available utilising ultrasound.
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Affiliation(s)
- Christian M Langton
- Biomedical Engineering & Medical Physics Discipline, Science & Engineering Faculty and Institute of Health & Biomedical Innovation, Queensland University of Technology, Brisbane, QLD, Australia
| | - Marie-Luise Wille
- Biomedical Engineering & Medical Physics Discipline, Science & Engineering Faculty and Institute of Health & Biomedical Innovation, Queensland University of Technology, Brisbane, QLD, Australia
| | - Mark B Flegg
- Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Oxford, UK
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Erban R, Flegg MB, Papoian GA. Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia. Bull Math Biol 2013; 76:799-818. [DOI: 10.1007/s11538-013-9844-3] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Accepted: 04/12/2013] [Indexed: 10/26/2022]
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Flegg MB, Rüdiger S, Erban R. Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release. J Chem Phys 2013; 138:154103. [DOI: 10.1063/1.4796417] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
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Flegg JA, Byrne HM, Flegg MB, McElwain DLS. Wound healing angiogenesis: the clinical implications of a simple mathematical model. J Theor Biol 2012; 300:309-16. [PMID: 22326476 DOI: 10.1016/j.jtbi.2012.01.043] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2011] [Revised: 01/25/2012] [Accepted: 01/27/2012] [Indexed: 10/14/2022]
Abstract
Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.
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Affiliation(s)
- Jennifer A Flegg
- School of Mathematical Sciences and Institute of Health and Biomedical Innovation, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Australia.
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Abstract
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
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Affiliation(s)
- Mark B Flegg
- Mathematical Institute, University of Oxford, Oxford, UK.
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Burchill MJ, Gramotnev DK, Gramotnev G, Davison BM, Flegg MB. Monitoring and analysis of combustion aerosol emissions from fast moving diesel trains. Sci Total Environ 2011; 409:985-993. [PMID: 21193225 DOI: 10.1016/j.scitotenv.2010.11.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2010] [Revised: 11/16/2010] [Accepted: 11/22/2010] [Indexed: 05/30/2023]
Abstract
In this paper we report the results of the detailed monitoring and analysis of combustion emissions from fast moving diesel trains. A new highly efficient monitoring methodology is proposed based on the measurements of the total number concentration (TNC) of combustion aerosols at a fixed point (on a bridge overpassing the railway) inside the violently mixing zone created by a fast moving train. Applicability conditions for the proposed methodology are presented, discussed and linked to the formation of the stable and uniform mixing zone. In particular, it is demonstrated that if such a mixing zone is formed, the monitoring results are highly consistent, repeatable (with typically negligible statistical errors and dispersion), stable with respect to the external atmospheric turbulence and result in an unusual pattern of the aerosol evolution with two or three distinct TNC maximums. It is also shown that the stability and uniformity of the created mixing zone (as well as the repeatability of the monitoring results) increase with increasing length of the train (with an estimated critical train length of ~10 carriages, at the speed of ~150km/h). The analysis of the obtained evolutionary dependencies of aerosol TNC suggests that the major possible mechanisms responsible for the formation of the distinct concentration maximums are condensation (the second maximum) and thermal fragmentation of solid nanoparticle aggregates (third maximum). The obtained results and the new methodology will be important for monitoring and analysis of combustion emissions from fast moving trains, and for the determination of the impact of rail networks on the atmospheric environment and human exposure to combustion emissions.
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Affiliation(s)
- Michael J Burchill
- Applied Optics and Nanotechnology Program, Faculty of Science and Technology, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
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Flegg MB, Poole CM, Whittaker AK, Keen I, Langton CM. Rayleigh theory of ultrasound scattering applied to liquid-filled contrast nanoparticles. Phys Med Biol 2010; 55:3061-76. [PMID: 20463372 DOI: 10.1088/0031-9155/55/11/005] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
We present a novel modified theory based upon Rayleigh scattering of ultrasound from composite nanoparticles with a liquid core and solid shell. We derive closed form solutions to the scattering cross-section and have applied this model to an ultrasound contrast agent consisting of a liquid-filled core (perfluorooctyl bromide, PFOB) encapsulated by a polymer shell (poly-caprolactone, PCL). Sensitivity analysis was performed to predict the dependence of the scattering cross-section upon material and dimensional parameters. A rapid increase in the scattering cross-section was achieved by increasing the compressibility of the core, validating the incorporation of high compressibility PFOB; the compressibility of the shell had little impact on the overall scattering cross-section although a more compressible shell is desirable. Changes in the density of the shell and the core result in predicted local minima in the scattering cross-section, approximately corresponding to the PFOB-PCL contrast agent considered; hence, incorporation of a lower shell density could potentially significantly improve the scattering cross-section. A 50% reduction in shell thickness relative to external radius increased the predicted scattering cross-section by 50%. Although it has often been considered that the shell has a negative effect on the echogeneity due to its low compressibility, we have shown that it can potentially play an important role in the echogeneity of the contrast agent. The challenge for the future is to identify suitable shell and core materials that meet the predicted characteristics in order to achieve optimal echogenity.
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Affiliation(s)
- M B Flegg
- Faculty of Science & Technology, Queensland University of Technology, Brisbane, Australia
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Flegg MB, Pollett PK, Gramotnev DK. Ehrenfest model for condensation and evaporation processes in degrading aggregates with multiple bonds. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 78:031117. [PMID: 18851003 DOI: 10.1103/physreve.78.031117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Indexed: 05/26/2023]
Abstract
We present an explicit theory of the degradation and thermal fragmentation kinetics of polymerlike systems and aggregates with multiple bonds in the presence of stochastic evaporation and condensation (restoration) of bonds. The analysis is conducted on the basis of the determination of the first passage time to state zero (fragmented state) in the Ehrenfest diffusion model in continuous time. The main approximations of the developed theory include the assumption that multiple bonds in any link between the primary elements in the aggregate do not interact with each other and that the coagulation rate after thermal fragmentation of the aggregates is negligible (which gives the absorbing zero state in the Ehrenfest model). In particular, it is demonstrated that even small condensation rates (of approximately 10 times smaller than the rates of bond evaporation) may have a significant effect on typical evolution times for the degrading aggregates and can result in a strong accumulation of nanoaggregates in the intermediate fragmentation modes. The simple asymptotic (predominantly exponential) behavior of the obtained solution at large evolution times is analyzed and discussed. The results will be important for the investigation of the degradation kinetics of a variety of polymerlike systems with multiple bonds, including self-arranged structures, polymer networks, different types of nanoclusters and their thermal fragmentation, etc.
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Affiliation(s)
- M B Flegg
- Applied Optics and Nanotechnology Program, School of Physical and Chemical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
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Flegg MB, Gramotnev DK. Exact solution for stochastic degradation and fragmentation processes in arbitrary chain and ring aggregates with multiple bonds. Phys Rev E 2008; 77:021105. [PMID: 18351985 DOI: 10.1103/physreve.77.021105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2007] [Indexed: 11/07/2022]
Abstract
This paper presents a statistical theory of stochastic evaporation and degradation processes in complex polymerlike ring and chain aggregates with multiple degrading bonds between the primary particles (monomers). The exact kinetic solution fully describing fragmentation processes is obtained for such aggregates with arbitrary number of primary particles (monomers) and bonds between them. The effects of additional interaction of multiple bonds with each other is shown to have a drastic impact on the predicted kinetic processes and time-dependent particle size distributions during aggregate degradation. Structural effects associated with different distributions of multiple bonds and bonding configurations in the aggregates are also investigated and shown to have a significant impact on typical fragmentation time and accumulation of fragmenting aggregates in intermediate modes. The developed theory and its results will be important for degradation of multistranded polymers, polymer networks, self-assembling structures, surface nanoclusters and nanotechnology, and formation and evolution of aerosol aggregates resulting from transport and industry emissions.
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Affiliation(s)
- Mark B Flegg
- Applied Optics Program, School of Physical and Chemical Science, Queensland University of Technology, Brisbane, QLD, Australia
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