Indiana University-Purdue University Indianapolis (IUPUI) / Laser cutting is a manufacturing technology that uses a focused laser beam to melt, burn and vaporize materials, resulting in a high-quality cut edge. Although previous efforts are primarily based on a trial-and-error approach, there is insufficient understanding of the laser cutting process, thus hindering further development of the technology. Therefore, the motivation of this thesis is to address this research need by developing a series of models to understand the thermal and microstructure evolution in the process. The goal of the thesis is to design a tool for optimizing the steel laser cutting process through a modeling approach. The goal will be achieved through three interrelated objectives: (1) understand the thermal field in the laser cutting process of ASTM A36 steel using the finite element (FE) method coupled with the user-defined Moving Heat Source package; (2) apply machine learning method to predict heat-affected zone (HAZ) and kerf, the key features in the laser cutting process; and (3) employ kinetic Monte Carlo (kMC) simulation to simulate the resultant microstructures in the laser cutting process. Specifically, in the finite element model, a laser beam was applied to the model with the parameters of the laser’s power, cut speed, and focal diameter being tested. After receiving results generated by the finite element model, they were then used by two machine learning algorithms to predict the HAZ distance and kerf width that is produced due to the laser cutting process. The two machine learning algorithms tested were a neural network and a support vector machine. Finally, the thermal field was imported into the kMC model as the boundary conditions to predict grain evolution’s in the metals. The results of the research showed that by increasing the focal diameter of a laser, the kerf width can be decreased and the HAZ distance experienced a large decrease. Additionally, a pulse-like pattern was observed in the kerf width through modeling and can be minimized into more of a uniform cut through the increase of the focal diameter. By increasing the power of a laser, the HAZ distance, kerf width, and region of the material above its original temperature increase. Additionally, through the increase of the cut speed, the HAZ distance, kerf width, kerf pulse-like pattern, and region of the material above its original temperature decrease. Through the incorporation of machine learning algorithms, it was found that they can be used to effectively predict the HAZ distance to a certain degree. The Neural Network and Support Vector Machine models both show that the experimental HAZ distance data lines up with the results derived from ANSYS. The Gaussian Process Regression HAZ model shows that the algorithm is not powerful enough to create an accurate prediction. Additionally, all of the kerf width models show that the experimental data is being overfit by the ANSYS results. As such, the kerf width results from ANSYS need additional validation to prove their accuracy. Using the kMC model to examine the microstructure change due to the laser cutting process, three observations were made. First, the largest grain growth occurs at the edge of the laser where the material was not hot enough to be cut. Then, grain growth decays as the distance from the edge increases. Finally, at the edge of the HAZ boundary, grain growth does not occur.

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Alloys used in fission and in future fusion reactors are subjected to extreme conditions including high temperatures, corrosive and intense radiation environments. Understanding the processes occurring at the microscopic level during radiation events is essential for the further development of them. As a prospective candidate material for new reactors, oxide dispersion strengthened (ODS) steels have shown good radiation resistance and the ability to trap He into fine scale bubbles, thus preventing swelling and preserving high-temperature strength. This thesis represents the findings obtained by performing computational studies of radiation effects in pure iron, Y-Ti-O systems and a simplified model of ODS using Molecular Dynamics (MD) and on-the-fly Kinetic Monte Carlo (otf-KMC) techniques. MD studies of radiation damage were carried out in a perfect body-centred cubic (bcc) iron matrix (alpha-Fe) in which yttria nanoparticles are embedded as a simplified model of an ODS steel. The results have shown how the nanoparticles interact with nearby initiated collision cascades, through cascade blocking and energy absorption. Fe defects accumulate at the interface both directly from the ballistic collisions and also by attraction of defects generated close by. The nanoparticles generally remain intact during a radiation event and release absorbed energy over times longer than the ballistic phase of the collision cascade. Also the nanoparticles have shown ability to attract He atoms as a product of fission and fusion reactions. Moreover, studies showed that He clusters containing up to 4 He atoms are very mobile and clusters containing 5 He or more become stable by pushing an Fe atom out of its lattice position. The radiation damage study in the Y-Ti-O materials showed two types of residual damage behaviour: when the damage is localized in a region, usually close to the initial primary knock-on atom (PKA) position and when PKA is directed in the channelling direction and creates less defects compared to the localised damage case, but with a wider spread. The Y2TiO5 and Y2Ti2O7 systems showed increased recombination of defects with increased temperature, suggesting that the Y-Ti-O systems could have a higher radiation resistance at higher temperatures. The otf-KMC technique was used to estimate the influence of the prefactor in the Arrhenius equation for the long time scale motion of defects in alpha-Fe. It is shown that calculated prefactors vary widely between different defect types and it is thus important to determine these accurately when implementing KMC simulations. The technique was also used to study the recombination and clustering processes of post-cascade defects that occur on the longer time scales.

The timescale of chemical reactions in solid-state systems greatly exceeds what may be modeled by direct integration of Newton's equation of motion. This limitation spawned the development of many different methods such as (adaptive) kinetic Monte Carlo (A)KMC, (harmonic) transition state theory (H)TST, parallel replica dynamics (PRD), hyperdynamics (HD), and temperature accelerated dynamics. The focus of this thesis was to (1) implement many of these methods in a single open-source software package (2) develop standard benchmarks to compare their accuracy and computational cost and (3) develop new long timescale methods. The lack of a open-source package that implements long timescale methods makes it difficult to directly evaluate the quality of different approaches. It also impedes the development of new techniques. Due to these concerns we developed Eon, a program that implements several long timescale methods including PRD, HD, and AKMC as well as global optimization algorithms basin hopping, and minima hopping. Standard benchmarks to evaluate the performance of local geometry optimization; global optimization; and single-ended and double-ended saddle point searches were created. Using Eon and several other well known programs, the accuracy and performance of different algorithms was compared. Important to this work is a website where anyone may download the code to repeat any of the numerical experiments. A new method for long timescale simulations is also introduced: molecular dynamics saddle search adaptive kinetic Monte Carlo (AKMC-MDSS). AKMC-MDSS improves upon AKMC by using short high-temperature MD trajectories to locate the important low-temperature reaction mechanisms of interest. Most importantly, the use of MD enables the development of a proper stopping criterion for the AKMC simulation that ensures that the relevant reaction mechanisms at the low temperature have been found. Important to the simulation of any material is knowledge of the experimental structure. Extended x-ray absorption fine structure (EXAFS) is a technique often used to determine local atomic structure. We propose a technique to quantitatively measure the accuracy of the commonly used fitting models. This technique reveals that the fitting models interpreted nanoparticles as being significantly more ordered and of much shorter bond length than they really are. / text

Growth mechanism of electroplated copper columns has been systematically studied by simulations and characterizations. A two-dimensional cross-sectional kinetic Monte Carlo (2DCS-KMC) model has been developed to simulate the electrodeposition of single crystal copper. The evolution of the microstructure has been visualized. The cluster density, average cluster size, variance of the cluster size and average aspect ratio were obtained from the simulations. The growth history of the deposition from the first atom to an equivalent of 100 monolayers was reconstructed. Following the single-lattice 2DCS-KMC model for a single crystal, a two-dimensional cross-sectional poly-lattice kinetic Monte Carlo (2DCSP-KMC) model has been developed for simulation of the electrodeposition of polycrystalline copper on both a copper and a gold substrate. With this model, the early-stage nucleation and the grain growth after impingement of nuclei can be simulated; as such the entire growth history is reconstructed in terms of the evolution of microstructure, grain statistics and grain boundary misorientation. The model is capable of capturing some key aspects of nucleation and growth mechanisms including the nucleation type (e.g. homogeneous or heterogeneous), texture development, the growth of grains and higher energetic state of grain boundaries. The model has also proven capable of capturing the effects of deposition parameters including applied electrode potential, concentration of cupric ions and temperature. Their effects are largely dependent on the substrates. The early-stage electrocrystallization of Cu on polycrystalline Au has been studied by ex-situ AFM observations. The evolution of surface morphology of the electrodeposited copper on a sputtered Au seed layer from 16ms to 1000s was observed and their formation mechanism discussed. The heterogeneous nucleation phenomenon, the competitive growth both longitudinally and laterally, and the dominant growth of some nuclei were experimentally observed, which are also visualized by the relevant KMC simulation results at a smaller size scale and a shorter time scale. A heuristic model is therefore proposed to describe the mechanism of the early-stage electrocrystallization of Cu on a polycrystalline Au seed layer. Electroplated copper columns plated for different times have been characterized in terms of the evolution of their external morphology, cross-sectional microstructure and crystal structure. The microstructure of electroplated copper columns is characteristic of bi-modal or tri-modal grain size distribution. The results indicate that recrystallization has occurred during or after the plating, top-down and laterally. Slight changes of the crystal structure were observed by in-situ XRD and it was found that the changes of the (111) and (200) planes occurred at different stages of self-annealing. Finally, the results indicate the presence of organic additives is not essential for self-annealing of a copper column to occur.

Materials in nuclear reactors and satellites experience continually damaging radiation which leads to their degradation over time. Currently, a materials safe working lifetime within these environments is estimated with a large, costly, safety margin. The work of this thesis aims to improve the usefulness of an optical technique known as reflection anisotropy spectroscopy (RAS), which once fully characterised could allow materials to be actively monitored in such environments. The intrinsic optical anisotropy of the Cu(110) surface has been exploited to study nanoscale kinetics of ion bombarded surfaces. Within the Cu(110) RA spectrum the 2.1eV peak is particularly sensitive to surface defects and largely unaffected by the bulk of the substrate. Using the Poelsema-Comsa model (which assumes defects scatter surface electronic states within a patch centred on the defect) it can be demonstrated that at finite temperatures the decay of the 2.1eV peak contains information relating to the diffusion of surface defects. A kinetic Monte Carlo simulation has been created to model the destruction of this peak and allows further understanding of the diffusion processes involved. The decay of the 2.1eV peak with ion bombardment has been successfully modelled for a range of temperatures using experimental RAS data for comparison. Through a novel way of analysing RAS data, it has been shown that the total scattering cross section per ion impact decreases with bombardment time, which it is believed to be due to surface diffusion. This could give a novel way of measuring surface diffusion directly from RAS measurements. Clustering of ion induced surface defects has been analysed and the results found are consistent with STM images of the same surface obtained 30 minutes after bombardment. While molecular dynamics calculations have previously attempted to predict the surface topology and defect clustering nanoseconds after impact, using a kinetic Monte Carlo simulation improves on this, demonstrating that diffusion on long time scales (currently inaccessible using molecular dynamics calculations) play an important role in predicting nano-surface topology. 2.1eV peak recovery after surface damage by ion bombardment was also investigated. The peak was found to recover at finite temperatures, which is also seen in experimental data. It was concluded that the surface diffusivity values in the literature are too high and a new value for diffusivity has been calculated by comparing simulation and experimental data.

The photopolymerization of multifunctional acrylates leads to the formation of a complex and insoluble network due to cross-linking. This characteristic is a useful property for stereolithography applications, where solid parts of the desired shape are cured using a pre-determined energy exposure profile. Traditionally, the required energy exposure is determined using a critical energy--depth of penetration, or Ec--Dp, model. The parameters Ec and Dp, are usually fit to experimental data at a specific resin composition and cure intensity. As a result, since the Ec--Dp model does not explicitly incorporate cure kinetics, it cannot be used for a different set of process conditions without first obtaining experimental data at the new conditions. Thus, the Ec--Dp model does not provide any insight when a new process needs to be developed, and the best processing conditions are unknown. The kinetic model for multifunctional acrylate photopolymerization presented here is based on a set of ordinary differential equations (ODE), which can be used to predict part height versus exposure condition across varying resin compositions. Kinetic parameter information used in the model is obtained by fitting the model to double bond conversion data from Fourier Transform Infrared Spectroscopy (FTIR) measurements. An additional parameter, the critical conversion value, is necessary for determining the formation of a solid part of the desired height. The initial rate of initiation, Ri, combines all the factors that impact part height, and therefore, it is an important quantity that is required in order to find the critical conversion value. The critical conversion value is estimated using the Ri and Tgel value from microrheology measurements. Information about network connectivity, which can be used to get properties such as molecular weight, cannot be derived from models using traditional mass-action kinetics for the cross-linking system. Therefore, in addition to modeling the reaction using the ODE based model, the results from a statistical model based on Kinetic Monte Carlo (KMC) principles are also shown here. The KMC model is applicable in situations where the impact of chain length on the kinetics or molecular weight evolution is of interest. For the present project, the detailed information from network connectivity was not required to make part height predictions, and the conversion information from the ODE model was sufficient. The final results show that the kinetic ODE model presented here, based on the critical conversion value, captures the impact of process parameters such as initiator concentration, light intensity, and exposure time, on the final part height of the object. In addition, for the case of blanket cure samples, the part height predictions from the ODE model make comparable predictions to the Ec--Dp model. Thus, the ODE model presented here is a versatile tool that can be used to determine optimum operating conditions during process development.

Graphene, a sheet of carbon atoms organized in a honeycomb lattice, is a two dimensional crystal. Even though the material has been known for a long time, only recently has it stimulated considerable interest across different research areas. Graphene is interesting not only as a platform to study fundamental physics in two dimensions, but it also has great potential for post-silicon microelectronics owing to its exceptional electronic properties. Of the several methods known to produce graphene, epitaxial growth of graphene by sublimation of silicon carbide is probably the most promising for practical applications. This thesis is a theoretical study of the growth kinetics of epitaxial graphene on SiC(0001). We propose a step-flow growth model using coarse-grained kinetic Monte Carlo (KMC) simulations and mean-field rate equations to study graphene growth on both vicinal and nano-faceted SiC surfaces. Our models are consistent with experimental observations and provide quantitative results which will allow experimenters to interpret the growth morphology and extract energy barriers from experiments. Recently, it has been shown that graphene grown epitaxially on metal surfaces may lead to potential applications such as large area transparent electrodes. To study deposition-type epitaxial growth, we investigate a new theoretical approach to this problem called the phase field method. Compared to other methods this method could be less computationally intensive, and easier to implement at large spatial scales for complicated epitaxial growth situations.

The formation of Ge nanowires in V-grooves has been studied experimentally as well as theoretically. As substrate oxide covered Si V-grooves were used formed by anisotropic etching of (001)Si wafers and subsequent oxidation of their surface. Implantation of 1E17 Ge+ cm^-2 at 70 keV was carried out into the oxide layer covering the V-grooves. Ion irradiation induces shape changes of the V-grooves, which are captured in a novel continuum model of surface evolution. It describes theoretically the effects of sputtering, redeposition of sputtered atoms, and swelling. Thereby, the time evolution of the target surface is determined by a nonlinear integro-differential equation, which was solved numerically for the V-groove geometry. A very good agreement is achieved for the predicted surface shape and the shape observed in XTEM images. Surprisingly, the model predicts material (Si, O, Ge) transport into the V-groove bottom which also suggests an Ge accumulation there proven by STEM-EDX investigations. In this Ge rich bottom region, subsequent annealing in N2 atmosphere results in the formation of a nanowire by coalescence of Ge precipitates shown by XTEM images. The process of phase separation during the nanowire growth was studied by means of kinetic 3D lattice Monte-Carlo simulations. These simulations also indicate the disintegration of continuous wires into droplets mediated by thermal fluctuations. Energy considerations have identified a fragmentation threshold and a lower boundary for the droplet radii which were confirmed by the Monte Carlo simulation. The here given results indicate the possibility of achieving nanowires being several nanometers wide by further growth optimizations as well as chains of equally spaced clusters with nearly uniform diameter.

Membranes find extensive applications today in numerous processes ranging from gas purification techniques to the treatment of industrial wastewater and the production of clean water because of their potential for better energy utilization and reduced production and equipment costs. A typical example is seawater desalination, where the use of advanced membrane technologies based on nanoporous, semipermeable materials with well controlled pore architectures would be favored over reverse osmosis due to lower operating cost and minimal environmental impact. But for membranes to achieve the desired levels of purification efficiency and effectiveness (they are also often susceptible to fouling and tend to exhibit low chemical resistance) they must possess an array of desired and novel properties such as high tensile strength and a well-defined nanoscale porous structure; the latter could allow the selective transport of (e.g.) water while simultaneously blocking undesired compounds (e.g., organic molecules). A typical such membrane operation is nanofiltration (NF), driven by applying a pressure difference between the two sides of the membrane. In the last decade, a large number of experimental studies have identified carbon nanotubes (CNTs) as a very attractive new class of nanoporous materials for designing nanostructured polymeric membranes characterized by exceptionally selective and permeable nanopores. Unfortunately, contradicting experimental results have often been reported as far as the magnitude of flow enhancement is concerned during water transport through nanometer-wide CNTs embedded in micrometer thick membranes. For example, Holt et al. [Nano Letters, 2004] reported an enhancement factor of 4 to 5 orders of magnitude higher while Majumder et al. [Nature, 2005] found water flows that are 2 to 4 orders of magnitude larger than the predicted ones by macroscopic continuum models. More recent experimental results [Qin et al., Nano Letters, 2011] on individual ultra-long (several micrometers) CNTs with diameter in the range 0.81-1.59 nm reported flow enhancement rates below 1000, thus contradicting for the same diameter the results of the two previous studies. A thorough review of the existing literature [Kannam et al., JCP, 2013] has shown that data for the slip length (which characterizes the flow rate of water in CNTs) are scattered over 5 orders of magnitude for nanotubes of diameter 0.81–10 nm. To help clarify some of the above observations, in this Master’s thesis, we have developed and implemented a coarse-grained method for simulating diffusion of a small molecule (water) within a glassy PMMA membrane containing CNTs which has allowed us to probe significantly longer times than what is possible today by atomistic molecular dynamics (MD) simulations. The method is known as kinetic Monte Carlo, is realized on a lattice, and uses as input data only the transition rates for a water molecule to hop from one lattice site to another. To take into account the nanostructure of the polymeric membrane and the fact that water diffuses much faster within a CNT than within a glassy polymer, lattice sites belonging to PMMA regions of the membrane have been assigned a different rate constant than lattice sites belonging to the interior of a CNT. The two constants have been computed by borrowing data for water diffusivity in the PMMA matrix and in a CNT either from experimental measurements or from independent simulation studies. At T=300K and for CNTs with a diameter D larger than about 2 nm, the rates are equal to 1.3x108 s-1 for PMMA and 2.3x1011 s-1 for CNT. That is, CNT sites correspond to “fast-diffusing” regions while PMMA ones to “slow-diffusing” regions, for a given water molecule. The simulations begin by distributing a large number of ghost water molecules on the sites of the lattice and letting them hop from site to site by using the above predetermined transition rates. In the simulations, hopping from a PMMA site towards a CNT interior site and backwards is forbidden; the only possible way for a walker to enter-exit a CNT is via the CNT entrance region. From the KMC method we compute the mean square displacement (msd) of all walkers as a function of time and then we apply Einstein’s equation to extract the corresponding effective diffusivity Deff quantifying water transport in the entire polymeric membrane given that the diffusive motion of the penetrants is Fickian. We conducted several such KMC runs both for randomly placed and perfectly aligned CNTs in the matrix, and we calculated the dependence of Deff on the size of CNTs (their diameter D and length L) and their concentration C (% vol.) in the PMMA matrix. Our simulation results indicate that CNT orientation does not significantly affect the water effective diffusivity. We also found that Deff varies practically linearly with both the CNT aspect ratio and CNT concentration. This allowed us to come up with a simple linear expression for Deff as a function of C and L/D describing the mobility of water molecules in the membrane. The predictions of this analytical equation are in excellent agreement with the simulation findings. / Για την αποτελεσματική επεξεργασία βιομηχανικών λυμάτων συχνά χρησιμοποιούνται μεμβράνες. Με αυτόν τον τρόπο γίνεται η προσπάθεια απομάκρυνσης τοξικών καθώς και διαφόρων άλλων οργανικών λυμάτων. Οι συμβατικές πλαστικές μεμβράνες παρουσιάζουν χαμηλή διαπερατότητα στα μόρια του νερού με αποτέλεσμα, οι ρυθμοί καθαρισμού των λυμάτων να είναι πολύ χαμηλοί. Στόχος μας είναι να βελτιώσουμε τις μεμβράνες αυτές. Συνεπώς, η επιλογή των κατάλληλων υλικών και η βελτιστοποίηση των ιδιοτήτων διαπερατότητας τους, αποτελούν βασικά ζητήματα. Οι νανοσωλήνες άνθρακα αποτελούν μία πολύ ελκυστική επιλογή λόγω της ικανότητας απόρριψης οργανικών ρύπων χαμηλού μοριακού βάρους. Πρόκειται για ένα πολλά υποσχόμενο νάνο-υλικό το οποίο δύναται να κατασκευασθεί εύκολα και μάλιστα με αρκετά χαμηλό κόστος. Πλήθος ερευνητών έχουν παρατηρήσει ότι η διαχυτότητα του νερού διαμέσω των νανοσωλήνων, ειναι κάποιες τάξεις μεγέθους μεγαλύτερη από την αντίστοιχη διαχυτότητα στις πλαστικές μεμβράνες. Γι’ αυτό το λόγο, η διεξαγωγή μοριακών προσομοιώσεων είναι πολύ σημαντική, όσον αναφορά στη μελέτη της μεταφοράς των μορίων αυτών, έτσι ώστε να επιτευχθεί καλύτερος σχεδιασμός των υλικών. Στην παρούσα εργασία, το ενδιαφέρον μας στρέφεται γύρω από την κινητικότητα που αναπτύσουν τα μόρια του νερού μέσα σε νανοσύνθετες μεμβράνες πολυμερούς (PMMA) με νανοσωλήνες άνθρακα (CNTs). Τόσο από προσομοιώσεις μοριακής δυναμικής, όσο και από πειραματικά δεδομένα, γνωρίζουμε την τιμή του συντελεστή διάχυσης του νερόυ στους νανοσωλήνες, καθώς και στην πολυμερική μήτρα PMMA. Η αναλυτική μέθοδος της μοριακής δυναμικής αδυναμεί να εξετάσει παραμετρικά τέτοια μεγάλα συστήματα, μεγάλων χαρακτηριστικών χρόνων χαλάρωσης, λόγω πολύ υψηλού υπολογιστκού κόστους. Η τεχνική που χρησιμοποιήσαμε είναι μία στοχαστική μέθοδος προσομοίωσης Kinetic Monte Carlo. Πρόκειται για μία μέθοδο που από τη μία προσομοιώνει δυναμικά φαινόμενα, σαν αυτό της διάχυσης που μελετάμε, ενώ από την άλλη, λόγω έλλειψης δυναμικών αλληλεπίδρασης, είναι εκπληκτικά γρηγορότερη της μοριακής δυναμικής, ακόμα και σε μεγάλα συστήματα. Όλες οι προσομοιώσεις πραγματοποιήθηκαν σε κυβικά πλέγματα, οι ακμές των οποίων θεωρούνται είτε “γρήγορες” περιοχές νανοσωλήνων, είτε “αργές” περιοχές PMMA. Τα μόρια του νερού μπορούν να κινούνται μόνο στο διακριτό χώρο που ορίζουν οι ακμές αυτές, έτσι ώστε να εισέρχονται και να εξέρχονται από τους νανοσωλήνες. Υπολογίζεται έτσι η χρονική εξέλιξη της μέσης τετραγωνικής μετατόπισης των μορίων του νερού (περιπατητές) στη μεμβράνη, από την οποία εξάγεται η τιμή του συντελεστή της αποτελεσματικής διαχυτότητας Deff του νερού στο νανοσύνθετο. Μελετήθηκαν συστήματα με παράλληλους νανοσωλήνες, καθώς και με νανοσωλήνες τυχαίας διεύθυνσης. Η τιμή της Deff δε φάνηκε να εξαρτάται από την διευθέτηση των CNTs. Παρατηρήθηκε ότι η αύξηση της κατ’όγκο συγκέντρωσης (c %) της μεμβράνης σε νανοσωλήνες, αυξάνει την αποτελεσματική διαχυτότητα του νερού. Επιπλέον, σημαντική ήταν η αύξηση της Deff υπό την αύξηση του αδιάστατου χαρακτηριστικού λόγου “μήκους νανοσωλήνα / διάμετρο νανοσωλήνα” (L/D), υπό σταθερή συγκέντρωση. Προσομοιώθηκαν συνολικά 70 συστήματα. Η μέγιστη κατ’όγκο συγκέντρωση σε νανοσωλήνες είναι 30%, ενώ ο μέγιστος λόγος L/D εφθασε το 42. Η μέγιστη τιμή της Deff λαμβάνεται στα μέγιστα της συγκέντρωσης σε νανοσωλήνες και του χαρακτηριστικού λόγου L/D, και είναι περίπου 7 φορές μεγαλύτερη της διαχυτότητας του νερού στη μεμβράνη, απουσία νανοσωλήνων. Προτείνεται επίσης ένα μοντέλο, το οποίο προβλέπει με πολύ μεγάλη ακρίβεια τα αποτελέσματα των προσομοιώσεων, τόσο σε συστήματα παράλληλων, όσο και σε συστήματα τυχαιάς διεύθυνσης νανοσωλήνων.