ORCID Profile
0000-0001-9885-3287
Current Organisation
The University of Newcastle
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Civil Geotechnical Engineering | Civil Engineering | Theoretical and Applied Mechanics | Applied Mathematics | Nanotechnology | Nanotechnology | Applied Mathematics not elsewhere classified | Materials Engineering Not Elsewhere Classified | Biomedical Engineering Not Elsewhere Classified |
Construction Design not elsewhere classified | Environmentally Sustainable Construction not elsewhere classified | Clinical health not specific to particular organs, diseases and conditions | Management of Solid Waste from Transport Activities | Cancer and related disorders | Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in Technology | Rail Infrastructure and Networks | Other
Publisher: Royal Society of Chemistry (RSC)
Date: 2013
DOI: 10.1039/C3RA43991G
Publisher: MDPI AG
Date: 21-02-2020
DOI: 10.3390/E22020248
Abstract: Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells. Under linear diffusion and recombination, this paper provides analytical solutions to the diffusion equation. Further, Lie symmetry analysis is adopted in order to explore analytical solutions to physically relevant special cases of the nonlinear diffusion equations. While analytical solutions may not be possible, we provide numerical solutions, which are in good agreement with the results given in the literature.
Publisher: Springer Science and Business Media LLC
Date: 04-2011
Publisher: Elsevier BV
Date: 02-2019
Publisher: American Physical Society (APS)
Date: 19-04-2013
Publisher: IOP Publishing
Date: 17-05-2011
DOI: 10.1088/0953-8984/23/22/225302
Abstract: Polyacetylene is a well-known conductive polymer and when doped its conductivity can be altered by up to 12 orders of magnitude. However, due to entropy effects a polyacetylene chain usually suffers from distortions and interchain couplings which lead to unpredictable changes in its conducting property. Encapsulating a polyacetylene chain into a carbon nanotube can resolve these issues. Furthermore, since the carbon nanotube itself possesses excellent electrical conductivity, the combination of the carbon nanotube and polyacetylene may give rise to a new material with superior transport behavior. In this paper, we model mathematically the molecular interaction between an acetylene molecule and a carbon nanotube in order to determine conditions at which configurations of the acetylene molecule are accepted into the carbon nanotube as well as its equilibrium configurations inside various sizes of carbon nanotubes. For special cases of the acetylene molecule lying on the tube axis, standing vertically with its center on the tube axis and staying far inside the tube, explicit analytical expressions for the interaction energy are obtained.
Publisher: AIP Publishing
Date: 04-2020
DOI: 10.1063/5.0006017
Abstract: Ceramic membranes have great potential for water treatment and filtering applications. However, one of the drawbacks of ceramic membrane filtration is its low permeability due to small functioning nanometer pore size. Increasing the membrane permeability without impairing its filtration function is, therefore, a crucial and practical problem. From hydrodynamical perspectives, keeping the inlet radius of membrane pores unchanged but only re-defining the pore geometry also could help to improve the permeate flow rate. In this paper, the membrane permeability with corrugated pores is investigated via hydrodynamical simulations using smoothed particle hydrodynamics. For a given corrugation length, it is found that there exists a range of values of the corrugation litude in which the membrane permeability is enhanced and a peak value is also achieved. On expanding the corrugation length, the range of the corrugation litude for permeability enhancement is larger and its permeability is further improved. The ratio of the corrugation litude to the corrugation length is found to be the key factor for permeability enhancement.
Publisher: ASME International
Date: 07-10-2008
DOI: 10.1115/1.2987874
Abstract: One approach to modeling fully developed shear flow of frictional granular materials is to use a yield condition and a flow rule, in an analogous way to that commonly employed in the fields of metal plasticity and soil mechanics. Typically, the yield condition of choice for granular materials is the Coulomb–Mohr criterion, as this constraint is relatively simple to apply but at the same time is also known to predict stresses that are in good agreement with experimental observations. On the other hand, there is no strong agreement within the engineering and applied mechanics community as to which flow rule is most appropriate, and this subject is still very much open to debate. This paper provides a review of the governing equations used to describe the flow of granular materials subject to the Coulomb–Mohr yield condition, concentrating on the coaxial and double-shearing flow rules in both plane strain and axially symmetric geometries. Emphasis is given to highly frictional materials, which are defined as those granular materials that possess angles of internal friction whose trigonometric sine is close in value to unity. Furthermore, a discussion is provided on the practical problems of determining the stress and velocity distributions in a gravity flow hopper, as well as the stress fields beneath a standing stockpile and within a stable rat-hole.
Publisher: Public Library of Science (PLoS)
Date: 07-07-2021
DOI: 10.1371/JOURNAL.PCBI.1008353
Abstract: Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the aggregation of juvenile wingless locust nymphs. In this paper we attempt to understand how the distribution of food resources affect the group formation process. We do this by introducing a multi-population partial differential equation model that includes non-local locust interactions, local locust and food interactions, and gregarisation. Our results suggest that, food acts to increase the maximum density of locust groups, lowers the percentage of the population that needs to be gregarious for group formation, and decreases both the required density of locusts and time for group formation around an optimal food width. Finally, by looking at foraging efficiency within the numerical experiments we find that there exists a foraging advantage to being gregarious.
Publisher: Elsevier BV
Date: 2014
Publisher: Informa UK Limited
Date: 07-05-2010
Publisher: Elsevier BV
Date: 07-2011
Publisher: IOP Publishing
Date: 07-2008
Publisher: Cold Spring Harbor Laboratory
Date: 21-09-2020
DOI: 10.1101/2020.09.21.305896
Abstract: Locust swarms are a major threat to agriculture, affecting every continent except Antarctica and impacting the lives of 1 in 10 people. Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the formation of hopper bands by the juvenile wingless locust nymphs. It is thus important to understand the hopper band formation process to control locust outbreaks. On longer time-scales, environmental conditions such as rain events synchronize locust lifecycles and can lead to repeated outbreaks. On shorter time-scales, changes in resource distributions at both small and large spatial scales have an effect on locust gregarisation. It is these short time-scale locust-resource relationships and their effect on hopper band formation that are of interest. In this paper we investigate not only the effect of food on both the formation and characteristics of locust hopper bands but also a possible evolutionary explanation for gregarisation in this context. We do this by deriving a multi-population aggregation equation that includes non-local inter-in idual interactions and local inter-in idual and food interactions. By performing a series of numerical experiments we find that there exists an optimal food width for locust hopper band formation, and by looking at foraging efficiency within the model framework we uncover a possible evolutionary reason for gregarisation. Locusts are short horned grass hoppers that live in two diametrically opposed behavioural states. In the first, solitarious, they will actively avoid other locusts, whereas the second, gregarious, they will actively seek them out. It is in this gregarious state that locusts form the recognisable and destructive flying adult swarms. However, prior to swarm formation juvenile flightless locusts will form marching hopper bands and make their way from food source to food source. Predicting where these hopper bands might form is key to controlling locust outbreaks. Research has shown that changes in food distributions can affect the transition from solitarious to gregarious. In this paper we construct a mathematical model of locust-locust and locust-food interactions to investigate how and why isolated food distributions affect hopper band formation. Our findings suggest that there is an optimal food width for hopper band formation and that being gregarious increases a locusts ability to forage when food width decreases.
Publisher: SAGE Publications
Date: 26-07-2010
Abstract: Modelling molecular interactions in a benzene dimer is a typical ex le of a class of problems involving aromatic molecules. Although many studies on the benzene dimer have been carried out both theoretically and experimentally and energetically favorable structures of a benzene dimer have been found, an investigation of all equilibrium structures of a benzene dimer has not so far been done. Previously, the present authors investigated the interaction energy and geometries of a benzene dimer for the special case in which only one rotational angle is used to describe the relative position between two benzene molecules. In general, two rotational angles are necessary to describe the most general relative orientation. Here, we apply the same approach in which the discrete atomic structure of a benzene molecule is replaced by two continuous rings of atoms, namely an inner carbon ring and an outer hydrogen ring with average constant atomic densities and the molecular interaction forces are calculated from the Lennard-Jones potential function. An analytical expression for the interaction energy is obtained which we use to determine all equilibrium structures of a benzene dimer as well as to determine those domains in which certain configurations are more favorable than others. Our results show that parallel, T-shaped, parallel displaced and tilted structures are all possible configurations of a benzene dimer and they exist at different regions of vertical and offset distances at different energy levels.
Publisher: SAGE Publications
Date: 09-2010
Publisher: SAGE Publications
Date: 26-07-2010
Abstract: Nanotechnology is currently an area of intense research activity. To date there is some limited experimental data, and considerably more computational data arising from molecular dynamics simulations, but there is very little applied mathematical modelling from the disciplines associated with modelling, namely mathematics and mechanics. This paper reviews some of the mathematical and mechanical modelling contributions for interacting molecular structures. Modelling can indicate to the experimentalist materials and geometry where a certain outcome may be anticipated. A combined modelling—computational approach can make efficient a computational procedure that alone is not practical. The present review aims to provide an overview of contributions to date, but is necessarily focussed on the work of the present authors, since the number of mathematically orientated workers in the field is limited.
Publisher: MDPI AG
Date: 30-11-2020
DOI: 10.3390/W12123354
Abstract: The motion of a flexible elastic plate under wave action is simulated, and the well–known phenomena of overwash is investigated. The fluid motion is modelled by smoothed particle hydrodynamics, a mesh-free solution method which, while computationally demanding, is flexible and able to simulate complex fluid flows. The freely floating plate is modelled using linear thin plate elasticity plus the nonlinear rigid body motions. This assumption limits the elastic plate motion to be small but is valid for many cases both in geophysics and in the laboratory. The principal conclusion is that the inclusion of flexural motion causes significantly less overwash than that which occurs for a rigid plate.
Publisher: The Royal Society
Date: 08-01-2008
Abstract: Carbon nanotubes are nanostructures that promise much in the area of constructing nanoscale devices due to their enhanced mechanical, electrical and thermal properties. In this paper, we examine a gigahertz oscillator that comprises a carbon nanotube oscillating in a uniform concentric ring or bundle of carbon nanotubes. A number of existing results for nanotube oscillators are employed to analyse the design considerations of optimizing such a device, and significant new results are also derived. These include a new analytical expression for the interaction per unit length of two parallel carbon nanotubes involving the Appell hypergeometric functions. This expression is employed to precisely determine the relationship between the bundle radius and the radii of the nanotubes forming the bundle. Furthermore, several pragmatic approximations are also given, including the relationships between the bundle radius and the constituent nanotube radius and the oscillating tube radius and the bundle nanotube radius. We also present a simplified analysis of the force and energy for a nanotube oscillating in a nanotube bundle leading to an expression for the oscillating frequency and the maximum oscillating frequency, including constraints on configurations under which this maximum is possible.
Publisher: Informa UK Limited
Date: 04-03-2018
Publisher: Elsevier BV
Date: 11-2003
Publisher: American Physical Society (APS)
Date: 29-07-2008
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-03-2022
DOI: 10.21914/ANZIAMJ.V62.16056
Abstract: Aggregations abound in nature, from cell formations to locust swarms. One method of modelling these aggregations is the non-local aggregation equation with the addition of degenerate diffusion. In this article we develop a finite volume based numerical scheme for this style of equation and perform an error, computation time, and convergence analysis. In addition we investigate two methods for approximating the non-local component. References A. J. Bernoff and C. M. Topaz. Nonlocal aggregation models: A primer of swarm equilibria. SIAM Rev. 55.4 (2013), pp. 709–747. doi: 10.1137/130925669 R. Bürger, D. Inzunza, P. Mulet, and L. M. Villada. Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour. Appl. Numer. Math. 144 (2019), pp. 234–252. doi: 10.1016/j.apnum.2019.04.018 J. A. Carrillo, A. Chertock, and Y. Huang. A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. In: Commun. Comput. Phys. 17.1 (2015), pp. 233–258. doi: 10.4208/cicp.160214.010814a J. R. Dormand and P. J. Prince. A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math. 6.1 (1980), pp. 19–26. doi: 10.1016/0771-050X(80)90013-3 J. von zur Gathen and J. Gerhard. Modern computer algebra. 3rd ed. Cambridge University Press, 2013. doi: 10.1017/CBO9781139856065 F. Georgiou, J. Buhl, J. E. F. Green, B. Lamichhane, and N. Thamwattana. Modelling locust foraging: How and why food affects group formation. PLOS Comput. Biol. 17.7 (2021), e1008353. doi: 10.1371/journal.pcbi.1008353 F. Georgiou, B. P. Lamichhane, and N. Thamwattana. An adaptive numerical scheme for a partial integro-differential equation. Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018. Ed. by B. Lamichhane, T. Tran, and J. Bunder. Vol. 60. ANZIAM J. 2019, pp. C187–C200. doi: 10.21914/anziamj.v60i0.14066 F. Georgiou, N. Thamwattana, and B. P. Lamichhane. Modelling cell aggregation using a modified swarm model. Proceedings of the 23rd International Congress on Modelling and Simulation, MODSIM2019. Vol. 6. 2019, pp. 22–27. doi: 10.36334/modsim.2019.a1.georgiou J. E. F. Green, S. L. Waters, J. P. Whiteley, L. Edelstein-Keshet, K. M. Shakesheff, and H. M. Byrne. Non-local models for the formation of hepatocyte–stellate cell aggregates. J. Theor. Bio. 267.1 (2010), pp. 106–120. doi: 10.1016/j.jtbi.2010.08.013 R. J. LeVeque. Finite-volume methods for hyperbolic Pproblems. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2002. doi: 10.1017/CBO9780511791253 C. F. Van Loan. Introduction to Scientific Computing: A Matrix Vector Approach Using MATLAB. 1997. url: s/higher-education rogram/Van- Loan-Introduction-to-Scientific-Computing-A-Matrix-Vector- Approach-Using-MATLAB-2nd-Edition/PGM215520.html A. Mogilner and L. Edelstein-Keshet. A non-local model for a swarm. J. Math. Bio. 38.6 (1999), pp. 534–570. doi: 10.1007/s002850050158 C. M. Topaz, A. L. Bertozzi, and M. A. Lewis. A nonlocal continuum model for biological aggregation. Bull. Math. Biol. 68 (2006), p. 1601. doi: 10.1007/s11538-006-9088-6 C. M. Topaz, M. R. D’Orsogna, L. Edelstein-Keshet, and A. J. Bernoff. Locust dynamics: Behavioral phase change and swarming. PLOS Comput. Bio. 8.8 (2012), e1002642. doi: 10.1371/journal.pcbi.1002642
Publisher: Elsevier BV
Date: 09-2023
Publisher: IOP Publishing
Date: 16-10-2007
Publisher: American Chemical Society (ACS)
Date: 18-08-2022
Publisher: IOP Publishing
Date: 07-10-2011
DOI: 10.1088/0957-4484/22/44/445707
Abstract: We investigate the van der Waals interaction of D,L-Ala cyclopeptide nanotubes and various ions, ion-water clusters and C(60) fullerenes, using the Lennard-Jones potential and a continuum approach which assumes that the atoms are smeared over the peptide nanotube providing an average atomic density. Our results predict that Li(+), Na(+), Rb(+) and Cl(-) ions and ion-water clusters are accepted into peptide nanotubes of 8.5 Å internal diameter whereas the C(60) molecule is rejected. The model indicates that the C(60) molecule is accepted into peptide nanotubes of 13 Å internal diameter, suggesting that the interaction energy depends on the size of the molecule and the internal diameter of the peptide nanotube. This result may be useful for the design of peptide nanotubes for drug delivery applications. Further, we also find that the ions prefer a position inside the peptide ring where the energy is minimum. In contrast, Li(+)-water clusters prefer to be in the space between each peptide ring.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 18-09-2023
Publisher: Elsevier BV
Date: 02-2014
Publisher: MDPI AG
Date: 31-03-2021
DOI: 10.3390/MATH9070749
Abstract: Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initial-boundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose solution is known. These arbitrary functions are determined by imposing that the solution of the initial value problem satisfies the given boundary conditions. Exact analytical solutions of some moving boundary problems that have not been previously obtained are provided. Moreover, ex les of fixed boundary problems over semi-infinite and bounded intervals are given, thus providing an alternative approach to the usual methods of solution.
Publisher: Elsevier BV
Date: 05-2020
Publisher: IOP Publishing
Date: 19-06-2007
Publisher: Springer Science and Business Media LLC
Date: 24-12-2012
Publisher: Springer Science and Business Media LLC
Date: 06-01-2009
Publisher: Wiley
Date: 12-03-2023
Abstract: Carbon nanostructures are of particular interest as platforms for molecular storage and adsorption. In this paper, the adsorption of a single stranded DNA molecule onto a graphene sheet is considered. Even though DNA molecules are complicated heterogeneous structures comprising several types of atoms, it is found that the repeated patterns within the DNA molecules enable the use of a continuum approach to model the DNA‐graphene sheet interaction. Here, a model is proposed such that the heterogeneity across the DNA molecule is captured by interaction functions, which are used to replace the attractive and repulsive constants in the Lennard‐Jones potential. Result from this new model shows better agreement to molecular dynamics simulations compared to the traditional continuum approach where atoms on the DNA are averaged evenly across the molecule. Finally, the paper comments on the model, its parameters, and suggests ways for improvement.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 16-02-2023
DOI: 10.21914/ANZIAMJ.V63.17984
Abstract: This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2021 Mathematics in Industry Study Group (MISG-2021) held at the University of Newcastle from 27 to 30 January 2021. This report provides the equation-free outcomes.
Publisher: Cambridge University Press (CUP)
Date: 07-2015
DOI: 10.1017/S1446181115000164
Abstract: Recently, organic nanostructures have attracted much attention, and amongst them peptide nanotubes are of interest in many fields of application including medicine and nanobiotechnology. Peptide nanotubes are formed by self-assembly of cyclic peptides with alternating L- and D-amino acids. Due to their biodegradability, flexible design and easy synthesis, many applications have been proposed such as artificial transmembrane ion channels, templates for nanoparticles, mimicking pore structures, nanoscale testing tubes, biosensors and carriers for targeted drug delivery. The mechanisms of an ion, a water molecule and an ion–water cluster entering into a peptide nanotube of structure cyclo[(-D-Ala-L-Ala-) $_{4}$ ] are explored here. In particular, the Lennard-Jones potential and a continuum approach are employed to determine three entering mechanisms: (i) through the tube open end, (ii) through a region between each cyclic peptide ring and (iii) around the edge of the tube open end. The results show that while entering the nanotube by method (i) is possible, an ion or a molecule requires initial energy to overcome an energetic barrier to be able to enter the nanotube through positions (ii) and (iii). Due to its simple structure, the D-, L-Ala cyclopeptide nanotube is chosen in this model however, it can be easily extended to include more complicated nanotubes.
Publisher: Elsevier BV
Date: 11-2022
DOI: 10.1016/J.JINSPHYS.2022.104443
Abstract: Density dependent phase polyphenism is the exhibiting of two or more distinct phenotypes from a single genotype depending on local population density. The most well known insect to exhibit this phenomenon is the locust, with whom the profound effect on behaviour leads to the classification of the two phases solitarious, where locusts actively avoid other locusts, and gregarious, where locusts are strongly attracted to other locusts. It has been shown that food distributions at both small and large scales have an effect on the process of gregarisation. While gregarisation offers advantages, such as greater predator avoidance, the relationship between phase polyphenism and potential foraging benefits is still not fully understood. In this paper, we explore the effect of gregarisation on foraging within increasingly heterogeneous environments using a partial differential equation model. We first consider a single two dimensional simulation of a spatially heterogeneous environment to understand the mechanics of gregarious/solitarious foraging. We then look at the steady state foraging advantage (measured as the ratio of per-capita contact with food) in environments ranging from homogeneous to very spatially heterogeneous. Finally, we perform a parameter sensitivity analysis to find which model parameters have the greatest effect on foraging advantage. We find that during the aggregation stage, prior to the onset of marching (which we do not model here), in increasingly heterogeneous food environments it is better to be gregarious than solitarious. In addition, we find that this is intrinsic to the gregarious/solitarious behavioural dynamic as it occurs almost regardless of the model parameters. That is to say, it doesn't matter how fast the organisms disperse or how strong their long range interactions as long as there is the solitarious/gregarious behaviour the gregarious foraging advantage will exist.
Publisher: American Scientific Publishers
Date: 11-2013
Publisher: Springer Netherlands
Date: 2009
Publisher: Springer Science and Business Media LLC
Date: 03-2004
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 06-12-2022
DOI: 10.21914/ANZIAMJ.V62.17406
Abstract: MISG 2020 University of Newcastle, Australia 28 January -- 1 February, 2020 This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2020 Mathematics and Statistics in Industry Study Group (MISG 2020) held at the University of Newcastle from 28 January -- 1 February 2020. The MISG is a special interest meeting of ANZIAM, the Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) ision of the Australian Mathematics Society. The MISG meetings take place annually and provide a forum where projects proposed by industry can be worked on intensively, by high profile scientists in the fields of Applied Mathematics, Statistics and Operations Research, from Australia, New Zealand and the world beyond, along with representatives from the industries proposing the projects. The writing of these papers was coordinated by the project moderators in consultation with the coauthors and company representatives. The manuscripts were submitted to the editors, Associate Professor Mike Meylan, Professor Ngamta Thamwattana and Professor Tony Roberts, and were subsequently refereed by two expert referees. On the advice of the referees, manuscripts were accepted for publication, subject to the recommended revisions, and formally approved by the editorial committee. At MISG 2020, six projects were presented from erse industries, with 78 delegates participating. Industry Partners We gratefully acknowledge the support of our industry partners: Lovells Springs Safearth Concrush Hyper Q Aerospace. Acknowledgements In addition to our industry partners, we gratefully acknowledge support from the following organisations: ANZIAM Office of the NSW Chief Scientist \\& Engineer, Department of Industry, NSW Government Priority Research Centre: Computer Assisted Research Mathematics and its Applications, The University of Newcastle Faculty of Science, The University of Newcastle. We are also grateful to Professor Ryan Loxton from the Centre for Optimisation and Decision Science, Curtin University, for giving a public lecture on power of optimisation research in mining, energy, and agriculture industries, as part of the MISG's outreach event and acknowledge the support from the Hunter Branch of the Royal Society of NSW in promoting the public lecture. We are also grateful to Professor Mark McGuinness (Victoria University of Wellington), Professor Troy Farrell (Queensland University of Technology), Associate Professor Amie Albrecht (University of South Australia) and Dr Neville Fowkes (University of Western Australia) for their helpful advice and comments in organising the MISG 2020. MISG2020 Organising Committee Professor Ngamta Thamwattana (Co-Director) Associate Professor Mike Meylan (Co-Director) Mrs Juliane Turner (Administrative Support) Dr David Allingham (Technical Support)
Publisher: American Scientific Publishers
Date: 07-2017
Publisher: Elsevier BV
Date: 11-2011
Publisher: American Society of Civil Engineers (ASCE)
Date: 05-2020
Publisher: Oxford University Press (OUP)
Date: 07-03-2007
DOI: 10.1093/QJMAM/HBM005
Publisher: IOP Publishing
Date: 11-09-2007
DOI: 10.1088/0953-8984/19/40/406209
Abstract: Continuum based models are presented here for certain boron nitride and carbon nanostructures. In particular, certain fullerene interactions, C(60)-C(60), B(36)N(36)-B(36)N(36) and C(60)-B(36)N(36), and fullerene-nanotube oscillator interactions, C(60)-boron nitride nanotube, C(60)-carbon nanotube, B(36)N(36)-boron nitride nanotube and B(36)N(36)-carbon nanotube, are studied using the Lennard-Jones potential and the continuum approach, which assumes a uniform distribution of atoms on the surface of each molecule. Issues regarding the encapsulation of a fullerene into a nanotube are also addressed, including acceptance and suction energies of the fullerenes, preferred position of the fullerenes inside the nanotube and the gigahertz frequency oscillation of the inner molecule inside the outer nanotube. Our primary purpose here is to extend a number of established results for carbon to the boron nitride nanostructures.
Publisher: Elsevier BV
Date: 05-2008
Publisher: Springer Science and Business Media LLC
Date: 18-06-2013
Publisher: Springer Science and Business Media LLC
Date: 2015
DOI: 10.1007/S11538-014-0056-2
Abstract: Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C[Formula: see text] antiviral compounds and the HIV. In particular, this paper predicts the energy and force arising from the interaction between HIV active region and the antiviral molecule which is attached to the external surface of a fullerene C[Formula: see text]. These interactions are calculated based on the structure of the antiviral molecules. Our results show that the binding of fullerene C[Formula: see text] to the antiviral molecules increases the efficiency of the compound to prohibit the activity of HIV.
Publisher: American Scientific Publishers
Date: 2014
Publisher: Elsevier BV
Date: 2021
Publisher: Elsevier BV
Date: 11-2009
Publisher: Springer Science and Business Media LLC
Date: 07-2005
Publisher: Springer Science and Business Media LLC
Date: 06-10-2008
Publisher: Springer Science and Business Media LLC
Date: 30-03-2006
Publisher: Springer Science and Business Media LLC
Date: 29-07-2011
Publisher: IOP Publishing
Date: 21-05-2008
Publisher: IOP Publishing
Date: 18-03-2009
DOI: 10.1088/0953-8984/21/14/144214
Abstract: In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques, which provides considerable insight into the underlying mechanisms of the nanoscaled oscillators. The paper presents a synopsis of the major results derived in detail by the present authors (Cox et al 2007 Proc. R. Soc. A 464 691-710 and Cox et al 2007 J. Phys. A: Math. Theor. 40 13197-208).
Publisher: AIP Publishing
Date: 04-2023
DOI: 10.1063/5.0138858
Abstract: In this paper, ice melting under the impacts of water waves was studied numerically via smoothed particle hydrodynamics simulations. Effects due to the ice elasticity were also included. Accordingly, the melting of an ice plate, modeled as an elastic object and interacting with transitional water waves with wave height and wave steepness up to 0.32 m and 0.093, respectively, was simulated and analyzed. The simulations showed that water waves' effects on the ice melting are seen via overflow over the top surface and local fluid circulations in the submerged region due to water–ice interactions and wave motions. Those effects result in a melting amount of the ice plate up to 1.78 times higher than the ice in still water. The overflow contributes up to 25% of the total amount of the melted ice. In comparison, fluid convection in the submerged region also leads to an increase in about 43% in the ice-melting amount over the submerged region. The melting rate is seen highest at the early stage of the simulation period and then is constantly reducing. The melting rate of the ice is seen linearly varying with the initial water temperature.
Publisher: MDPI AG
Date: 21-12-2020
DOI: 10.3390/COMPUTATION8040107
Abstract: The Lennard–Jones potential and a continuum approach can be used to successfully model interactions between various regular shaped molecules and nanostructures. For single atomic species molecules, the interaction can be approximated by assuming a uniform distribution of atoms over surfaces or volumes, which gives rise to a constant atomic density either over or throughout the molecule. However, for heterogeneous molecules, which comprise more than one type of atoms, the situation is more complicated. Thus far, two extended modeling approaches have been considered for heterogeneous molecules, namely a multi-surface semi-continuous model and a fully continuous model with average smearing of atomic contribution. In this paper, we propose yet another modeling approach using a single continuous surface, but replacing the atomic density and attractive and repulsive constants in the Lennard–Jones potential with functions, which depend on the heterogeneity across the molecules, and the new model is applied to study the adsorption of coronene onto a graphene sheet. Comparison of results is made between the new model and two other existing approaches as well as molecular dynamics simulations performed using the LAMMPS molecular dynamics simulator. We find that the new approach is superior to the other continuum models and provides excellent agreement with molecular dynamics simulations.
Publisher: Elsevier BV
Date: 09-2008
Publisher: American Institute of Physics
Date: 2009
DOI: 10.1063/1.3203231
Publisher: Elsevier BV
Date: 08-2013
Publisher: AIP Publishing
Date: 10-04-2006
DOI: 10.1063/1.2185607
Abstract: The problem of electric field-induced force between spheres is fundamental to electrorheological fluids. Previously published experimental results indicate that the interaction force between two spheres under an external field is not adequately explained by the existing approximate and numerical methods. The specific models compared were dipole, dipole with local field corrections and a finite-element analysis. This letter employs an exact solution (via the equivalent multipole-moment method) to the electrostatic problem which accurately predicts the low-frequency experimental results at all measured interstices. The solution presented later is self-contained and addresses specifically the geometry of the previously mentioned experimental results. While more general solutions have been published previously, they are more complex than is required by this problem. The solution presented here is accurate for all sphere spacings, but in particular could apply to nano-spheres in close proximity.
Publisher: American Scientific Publishers
Date: 08-2015
Publisher: IOP Publishing
Date: 08-2020
Abstract: Originated in 1991 by O‘Regan and Grätzel, dye-sensitized solar cells (DSSCs) provide alternative solutions for renewable energy problems. Earlier mathematical models for DSSCs are based on junction solar cells, which was first studied by Chapin et al in 1954. These equations were derived from Shockley’s work on modelling semiconductors in the late 1940s. However, it was pointed out by Cao et al and Gregg that diffusion model is more suitable for modelling DSSCs. Since the study by Södergren in 1994, the diffusion model has become prevalent in literature and the development of this model by including additional equations to incorporate electrolyte concentrations, time dependence for charge carrier densities and nonlinear diffusivity has shown to capture more complex processes of charge transport within DSSCs. In this paper, we review the development of the diffusion model for the charge carrier densities in a conduction band of DSSCs.
Publisher: Springer Science and Business Media LLC
Date: 21-06-2004
Publisher: AIP Publishing
Date: 05-2022
DOI: 10.1063/5.0088536
Abstract: In this work, a newly developed Smoothed Particle Hydrodynamics (SPH) algorithm for nonlinear elasticity is combined with an incompressible SPH fluid solver to investigate the dynamics of a floating plate under impacts of regular water waves with a high steepness. Two scenarios of the plate's rigidity are investigated. The simulation results show that deformations of the stiffer plate mainly occur in a simple bending mode with small litudes, and the plate is almost submerged by a strong fluid flow over its surface. In the other scenario, the plate deforms more complexly with much higher deformation litudes but experiences a much weaker overwash. The more flexible plate is less resistant to wave motions and converts more wave energy into elastic deformations, and therefore, the overwash is less severe. A strong overflow exerts a pressure force onto the plate that alters the plate's dynamics and adds a viscous (d ing) effect on the plate's elastic vibrations, especially in high-frequency modes. A rigorous examination of the numerical convergence and validation using the linear thin plate theory is also carried out. The new SPH algorithm for nonlinear elasticity shows its stability and reliability in evaluating finite and large elastic deformations. Therefore, it is promising for simulating elastic structures in fluid–structure interaction problems.
Publisher: American Scientific Publishers
Date: 05-2009
Publisher: Elsevier BV
Date: 05-2022
Publisher: Springer Science and Business Media LLC
Date: 27-03-2015
Publisher: Springer Science and Business Media LLC
Date: 29-08-2009
Publisher: Cambridge University Press (CUP)
Date: 06-2005
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 19-03-2022
DOI: 10.21914/ANZIAMJ.V62.15964
Abstract: Innovative design of helicopters promises great benefitsover conventional aircraft but there are a number oftechnical challenges. Hyper Q Aerospace brought a project tothe 2020 Mathematics-in-Industry Study Group to consider ahelicopter design with a counter-rotating, coaxial, doublerotor. Specific considerations were the vibration andharmonic properties of the rotor blades, the noise from theaircraft and the aerodynamic characteristics.Euler--Bernoulli beam theory and classical airfoil theorywere implemented to consider the vibration and aerodynamicfeatures of the aircraft and the rotor system. Thefundamental lengthwise and lateral harmonics of the bladeswere obtained and compared with typical rotational forcingfrequencies. The modification to the lift generated by thecounter-rotating blades and noise mitigation strategies werediscussed. Improved design strategies were presented.
Publisher: American Scientific Publishers
Date: 05-2009
Publisher: IEEE
Date: 2006
Publisher: Elsevier BV
Date: 12-2003
Publisher: MDPI AG
Date: 28-06-2020
DOI: 10.3390/MOLECULES25132966
Abstract: Dye-sensitized solar cells have continued to receive much attention since their introduction by O’Regan and Grätzel in 1991. Modelling charge transfer during the sensitization process is one of several active research areas for the development of dye-sensitized solar cells in order to control and improve their performance and efficiency. Mathematical models for transport of electron density inside nanoporous semiconductors based on diffusion equations have been shown to give good agreement with results observed experimentally. However, the process of charge transfer in dye-sensitized solar cells is complicated and many issues are in need of further investigation, such as the effect of the porous structure of the semiconductor and the recombination of electrons at the interfaces between the semiconductor and electrolyte couple. This paper proposes a new model for electron transport inside the conduction band of a dye-sensitized solar cell comprising of TiO 2 as its nanoporous semiconductor. This model is based on fractional diffusion equations, taking into consideration the random walk network of TiO 2 . Finally, the paper presents numerical solutions of the fractional diffusion model to demonstrate the effect of the fractal geometry of TiO 2 on the fundamental performance parameters of dye-sensitized solar cells, such as the short-circuit current density, open-circuit voltage and efficiency.
Publisher: Elsevier BV
Date: 04-2011
Publisher: American Scientific Publishers
Date: 04-2013
Publisher: IEEE
Date: 2006
Publisher: American Scientific Publishers
Date: 10-2011
Publisher: MDPI AG
Date: 22-05-2020
DOI: 10.3390/MATH8050841
Abstract: Solar energy is an alternative source of energy that can be used to replace fossil fuels. Various types of solar cells have been developed to harvest this seemingly endless supply of energy, leading to the construction of solar cell devices, such as dye-sensitized solar cells. An important factor that affects energy conversion efficiency of dye-sensitized solar cells is the distribution of dye molecules within the porous semiconductor (TiO 2 ). In this paper, we formulate a continuum model for the interaction between the dye molecule Tris(2,2 ′ -bipyridyl)ruthenium(II) (Ru(bpy) 3 2 + ) and titanium dioxide (TiO 2 ) semiconductor. We obtain the equilibrium position at the minimum energy position between the dye molecules and between the dye and TiO 2 nanoporous structure. Our main outcome is an analytical expression for the energy of the two molecules as a function of their sizes. We also show that the interaction energy obtained using the continuum model is in close agreement with molecular dynamics simulations.
Publisher: Royal Society of Chemistry (RSC)
Date: 2015
DOI: 10.1039/C5RA13353J
Abstract: The interaction between layers of graphene oxide is mathematically modelled and optimal interlayer distances are found and supported by MD simulation.
Publisher: Springer Netherlands
Date: 2005
Publisher: The Royal Society
Date: 08-01-2005
Abstract: In this paper, we deal with the materials possessing angles of internal friction ϕ for which 1 − sin ϕ is close to zero, and we use the solution for sin ϕ = 1 as the leading term in a regular perturbation series, where the correction terms are of order 1 − sin ϕ . In this way we obtain approximate analytical solutions which can be used to describe the behaviour of real granular materials. The solution procedure is illustrated with reference to quasi–static flow through wedge–shaped and conical hoppers. For these two problems, the obtained perturbation solutions are shown to be graphically indistinguishable from the numerical solutions for high angles of internal friction, and for moderately high angles of internal friction the perturbation solutions still provide excellent approximations.
Publisher: Elsevier BV
Date: 10-2007
Publisher: Springer Science and Business Media LLC
Date: 16-05-2007
Publisher: Oxford University Press (OUP)
Date: 08-2004
Publisher: Elsevier BV
Date: 10-2010
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 31-12-2021
DOI: 10.21914/ANZIAMJ.V63.15944
Abstract: Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement. doi:10.1017/S1446181121000353
Publisher: IOP Publishing
Date: 23-04-2019
Publisher: MDPI AG
Date: 15-01-2020
DOI: 10.3390/NANO10010152
Abstract: The production of single dimensional carbon structures has recently been made easier using carbon nanotubes. We consider here encapsulated coronene molecules, which are flat and circular-shaped polycyclic aromatic hydrocarbons, inside carbon nanotubes. Depending on the radius of the nanotube, certain specific configurations of the coronene molecules can be achieved that give rise to the formation of stacked columns or aid in forming nanoribbons. Due to their symmetrical structure, a coronene molecule may be modelled by three inner circular rings of carbon atoms and one outer circular ring of hydrogen atoms, while the carbon nanotube is modelled as a circular tube. Using the continuous model and the Lennard-Jones potential, we are able to analytically formulate an expression for the potential energy for a coronene dimer and coronene inside a carbon nanotube. Subsequently, stacking of coronene molecules inside a nanotube is investigated. We find that the minimum energy tilt angle of coronenes in a stack differs from that of a single coronene within the same nanotube. More specifically, for both (18, 0) and (19, 0) zigzag carbon nanotube, we find that the minimum energy tilt angles of the single coronene case (≈42 ° and ≈20 ° respectively) do not occur in the stack model.
Publisher: Elsevier BV
Date: 10-2016
Publisher: Springer Science and Business Media LLC
Date: 08-2003
Publisher: Cambridge University Press (CUP)
Date: 20-04-2023
DOI: 10.1017/S1446181123000160
Abstract: Three typical elastic problems, including beam bending, truss extension and compression, and two-rings collision are simulated with smoothed particle hydrodynamics (SPH) using Lagrangian and Eulerian algorithms. A contact-force model for elastic collisions and equation of state for pressure arising in colliding elastic bodies are also analytically derived. Numerical validations, on using the corresponding theoretical models, are carried out for the beam bending, truss extension and compression simulations. Numerical instabilities caused by largely deformed particle configurations in finite/large elastic deformations are analysed. The numerical experiments show that the algorithms handle small deformations well, but only the Lagrangian algorithm can handle large elastic deformations. The numerical results obtained from the Lagrangian algorithm also show a good agreement with the theoretical values.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 06-12-2022
DOI: 10.21914/ANZIAMJ.V64.17494
Abstract: This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2022 Mathematics in Industry Study Group (MISG2022) held at the University of Newcastle from 14--18 February 2022. This report provides the equation-free outcomes.
Publisher: Springer Science and Business Media LLC
Date: 22-03-2018
DOI: 10.1007/S00894-018-3630-Y
Abstract: The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds. We construct a model incorporating a single-walled carbon nanotube into a sheet of folded graphene. Variational calculus techniques are employed to determine the minimum energy structure and the resulting curves are shown to agree well with molecular dynamics study. Graphical Abstract Using calculus of variations, the elastic bending energy and van der Waals energy are minimised giving rise to Euler-Lagrange equation for which analytical solutions are derived to determine the optimal curved sturctures of graphene wrapped around carbon nanotubes . Overall agreement between the analytical solutions (with different values of bending rigidities) and results from molecular dynamics simulations (grey) is shown here for (6,6), (8,8) and (10,10) armchair nanotubes, respectively.
Publisher: American Physical Society (APS)
Date: 15-10-2007
Publisher: Royal Society of Chemistry (RSC)
Date: 2023
DOI: 10.1039/D3NA00349C
Abstract: The catalytic effect of graphene on the corannulene bowl-to-bowl inversion is confirmed in this paper using a pair-wise dispersion interaction model.
Publisher: American Scientific Publishers
Date: 05-2016
Publisher: IOP Publishing
Date: 16-09-2010
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 13-05-2023
DOI: 10.21914/ANZIAMJ.V63.16615
Abstract: Pneumatic conveying is the transportation of bulk solids in enclosed pipelines via a carrier gas, typically air. The local flow pattern in a pipeline is a function of the conditions, and slug flow can form under certain conditions. Slug flow is a naturally occurring, wave-like flow where the bulk material travels along the pipeline in distinct `slugs'. Establishing the environment for the formation of slugs within the conveying system is essential to maximise the overall system efficiency and minimise damage to the bulk material. MISG2021 considered a wide range of mathematical approaches to slug formation and travel. These two key problem areas have the most significant potential to impact the system design and efficiency. Critical interconnected facets of pneumatic conveying systems were investigated and an overview for future work was developed. Many of the avenues uncovered during the MISG2021 require more time for in-depth analysis. This analysis and framework will aid in optimising conveying system design and provide insight to construct more efficient pneumatic conveying systems.
Publisher: Oxford University Press (OUP)
Date: 27-03-2008
DOI: 10.1093/QJMAM/HBN012
Publisher: AIP Publishing
Date: 24-11-2020
DOI: 10.1063/5.0025066
Abstract: Continuum modeling using the Lennard-Jones potential has been shown to provide a good estimation for the interaction energy between regular-shaped homogeneous molecules comprising the same type of atoms. However, this method may not be accurate for heterogeneous molecules, which are made up of more than one chemical element. The traditional method to deal with this involves approximating the molecule via multiple surfaces in a piecemeal fashion. While this approach works well for small sized molecules, calculations become intensive for large sized molecules as a large number of sums from multiple surface interactions are involved. To address this issue, we propose a new model that approximates a heterogeneous molecule with a single surface or volume, where attractive and repulsive constants (A and B) in the Lennard-Jones potential are replaced by functions A(r) and B(r), which depend on the parameterization of the surface r. We comment that this technique is suitable for regular-shaped nanostructures where their heterogeneity can be modeled by surface (or volume) parameterization. Validation of the new approach is carried out via two problems, namely, carbon nanotube–methane and carbon nanotube–coronene interactions. For coronene and methane, which are assumed to be radially symmetric, we propose A(r) and B(r) to be sigmoidal functions for which the interaction strength decreases from the inner region of the carbon atoms toward the outer region of the hydrogen atoms. Our results for both cases show that using the sigmoidal profiles for A(r) and B(r) gives rise to interaction energies that are in better agreement with those obtained from molecular dynamics studies compared to results using constant A and B. The new approach provides a significant improvement to the current continuum modeling using the Lennard-Jones potential.
Publisher: IOP Publishing
Date: 08-2020
Abstract: Chemical vapor deposition is a popular technique for producing high-quality graphene sheets on a substrate. However, the cooling process causes the graphene sheet to experience a strain-induced, out-of-plane buckling. These wrinkles structures can have undesirable effects on the properties of the graphene sheet. We construct a pair of models to analyse the conformation structure of these wrinkles. An arch-shaped wrinkle is first modelled then expanded to incorporate self-adhesion between the wrinkle edges. Variational techniques are employed on both models to determine the optimal conformation for graphene supported on Cu and Ni substrates. We find these models predict a similar structure to experimental analysis of graphene wrinkles on these solid metal substrates.
Publisher: Cambridge University Press (CUP)
Date: 10-2021
DOI: 10.1017/S1446181121000353
Abstract: Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.
Publisher: Springer Science and Business Media LLC
Date: 27-07-2013
Publisher: Public Library of Science (PLoS)
Date: 20-12-2021
Publisher: The Royal Society
Date: 11-10-2007
Abstract: The discovery of carbon nanotubes and C 60 fullerenes has created an enormous impact on possible new nanomechanical devices. Owing to their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, carbon nanotubes and C 60 fullerenes are of considerable interest to researchers from many scientific areas. One aspect that has attracted much attention is the creation of high-frequency nanoscale oscillators, or the so-called gigahertz oscillators, for applications such as ultrafast optical filters and nano-antennae. While there are difficulties for micromechanical oscillators, or resonators, to reach a frequency in the gigahertz range, it is possible for nanomechanical systems to achieve this. This study focuses on C 60 –single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C 60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C 60 molecule inside a carbon nanotube is determined, so as to predict its position with reference to the cross-section of the carbon nanotube. By considering the interaction force between the C 60 fullerene and the carbon nanotube, this paper provides a simple mathematical model, involving two Dirac delta functions, which can be used to capture the essential mechanisms underlying such gigahertz oscillators. As a preliminary to the calculation, the oscillatory behaviour of an isolated atom is examined. The new element of this study is the use of elementary mechanics and applied mathematical modelling in a scientific context previously dominated by molecular dynamical simulation.
Publisher: The Royal Society
Date: 11-10-2007
Abstract: Owing to their unusual properties, carbon nanostructures such as nanotubes and fullerenes have caused many new nanomechanical devices to be proposed. One such application is that of nanoscale oscillators which operate in the gigahertz range, the so-called gigahertz oscillators. Such devices have potential applications as ultrafast optical filters and nano-antennae. While there are difficulties in producing micromechanical oscillators which operate in the gigahertz range, molecular dynamical simulations indicate that nanoscale devices constructed of multi-walled carbon nanotubes or single-walled carbon nanotubes and C 60 fullerenes could feasibly operate at these high frequencies. This paper investigates the suction force experienced by either an atom or a C 60 fullerene molecule located in the vicinity of an open end of a single-walled carbon nanotube. The atom is modelled as a point mass, the fullerene as an averaged atomic mass distributed over the surface of a sphere. In both cases, the carbon nanotube is modelled as an averaged atomic mass distributed over the surface of an open semi-infinite cylinder. In both cases, the particle being introduced is assumed to be located on the axis of the cylinder. Using the Lennard-Jones potential, the van der Waals interaction force between the atom or C 60 fullerene and the carbon nanotube can be obtained analytically. Furthermore, by integrating the force, an explicit analytic expression for the work done by van der Waals forces is determined and used to derive an acceptance condition, that is whether the particle will be completely sucked into the carbon nanotube by virtue of van der Waals interactions alone, and a suction energy which is imparted to the introduced particle in the form of an increased velocity. The results of the acceptance condition and the calculated suction energy are shown to be in good agreement with the published molecular dynamical simulations. In part II of the paper, a new model is proposed to describe the oscillatory motion adopted by atoms and fullerenes that are sucked into carbon nanotubes.
Publisher: IEEE
Date: 02-2008
Start Date: 2017
End Date: 06-2022
Amount: $248,499.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2007
End Date: 12-2012
Amount: $795,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 02-2021
End Date: 03-2024
Amount: $570,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 07-2022
End Date: 07-2025
Amount: $540,000.00
Funder: Australian Research Council
View Funded Activity