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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
41

Electrostatic Interactions in Coarse-Grained Simulations : Implementations and Applications

Wang, Yong-Lei January 2013 (has links)
Electrostatic interactions between charged species play a prominent role in determining structures and states of physical system, leading to important technological and biological applications. In coarse-grained simulations, accurate description of electrostatic interactions is crucial in addressing physical phenomena at larger spatial and longer temporal scales. In this thesis, we implement ENUF method, an abbreviation for Ewald summation based on non-uniform fast Fourier transform technique, into dissipative particle dynamics (DPD) scheme. With determined suitable parameters, the computational complexity of ENUF-DPD method is approximately described as O(N logN). The ENUF-DPD method is further validated by investigating dependence of polyelectrolyte conformations on charge fraction of polyelectrolyte and counterion valency of added salts, and studying of specific binding structures of dendrimers on amphiphilic membranes. In coarse-grained simulations, electrostatic interactions are either explicitly calculated with suitable methods, or implicitly included in effective potentials. The effect of treatment fashion of electrostatic interactions on phase behavior of [BMIM][PF6] ionic liquid (IL) is systematically investigated. Our systematic analyses show that electrostatic interactions should be incorporated explicitly in development of effective potentials, as well as in coarse-grained simulations to improve reliability of simulation results. Detailed image of microscopic structures and orientations of [BMIM][PF6] at graphene and vacuum interfaces are investigated by using atomistic simulations. Imidazolium rings and alkyl side chains of [BMIM] lie preferentially flat on graphene surface. At IL-vacuum interface, ionic groups pack closely together to form polar domains, leaving alkyl side chains populated at interface and imparting hydrophobic character. With the increase of IL filmthickness, orientations of [BMIM] change gradually from dominant flat distributions along graphene surface to orientations where imidazolium rings are either parallel or perpendicular to IL-vacuum interface with tilted angles. The interfacial spatial ionic structural heterogeneity formed by ionic groups also contributes to heterogeneous dynamics in interfacial regions.
42

High efficiency coarse-grained customised dynamically reconfigurable architecture for digital image processing and compression technologies

Zhao, Xin January 2012 (has links)
Digital image processing and compression technologies have significant market potential, especially the JPEG2000 standard which offers outstanding codestream flexibility and high compression ratio. Strong demand for high performance digital image processing and compression system solutions is forcing designers to seek proper architectures that offer competitive advantages in terms of all performance metrics, such as speed and power. Traditional architectures such as ASIC, FPGA and DSPs have limitations in either low flexibility or high power consumption. On the other hand, through the provision of a degree of flexibility similar to that of a DSP and performance and power consumption advantages approaching that of an ASIC, coarse-grained dynamically reconfigurable architectures are proving to be strong candidates for future high performance digital image processing and compression systems. This thesis investigates dynamically reconfigurable architectures and especially the newly emerging RICA paradigm. Case studies such as Reed- Solomon decoder and WiMAX OFDM timing synchronisation engine are implemented in order to explore the potential of RICA-based architectures and the possible optimisation approaches such as eliminating conditional branches, reducing memory accesses and constructing kernels. Based on investigations in this thesis, a novel customised dynamically reconfigurable architecture targeting digital image processing and compression applications is devised, which can be tailored to adopt different applications. A demosaicing engine based on the Freeman algorithm is designed and implemented on the proposed architecture as the pre-processing module in a digital imaging system. An efficient data buffer rotating scheme is designed with the aim of reducing memory accesses. Meanwhile an investigation targeting mapping the demosaicing engine onto a dual-core RICA platform is performed. After optimisation, the performance of the proposed engine is carefully evaluated and compared in aspects of throughput and consumed computational resources. When targeting the JPEG2000 standard, the core tasks such as 2-D Discrete Wavelet Transform (DWT) and Embedded Block Coding with Optimal Truncation (EBCOT) are implemented and optimised on the proposed architecture. A novel 2-D DWT architecture based on vector operations associated with RICA paradigm is developed, and the complete DWT application is highly optimised for both throughput and area. For the EBCOT implementation, a novel Partial Parallel Architecture (PPA) for the most computationally intensive module in EBCOT, termed Context Modeling (CM), is devised. Based on the algorithm evaluation, an ARM core is integrated into the proposed architecture for performance enhancement. A Ping-Pong memory switching mode with carefully designed communication scheme between RICA based architecture and ARM is proposed. Simulation results demonstrate that the proposed architecture for JPEG2000 offers significant advantage in throughput.
43

La simulation mésoscopique par dynamique dissipative

Palato, Samuel January 2013 (has links)
La simulation des matériaux demande une compréhension de leur comportement à de nombreuses échelles de temps et d’espace. Ces différentes échelles requièrent des méthodes de simulations différentes, qui se basent sur des approximations différentes et donnent accès à différentes propriétés. La simulation multiéchelle est une approche qui regroupe l’utilisation de ces différentes méthodes, ainsi que des relations qui les unissent. Des développements plus récents ont permis la mise au point de méthodes mésoscopiques, comblant le trou entre les simulations atomistiques (< 10 nm) et les milieux continus (>mm). La dynamique de particules dissipatives (DPD) est une telle méthode, qui présente de nombreux avantages théoriques et pratiques en comparaison avec d’autres méthodes mésoscopiques. La DPD est une méthode modélisant la matière par des particules molles, s’inspirant de l’équation de Langevin. La dynamique des particules est gérée par trois forces : une force conservative, une force dissipative et une force aléatoire. La force conservative naît des interactions effectives moyennes à l’échelle méso, alors que la force dissipative et la force aléatoire sont d’origine statistique. Différentes formulations et contributions à la force conservative sont présentées, permettant notamment la simulation de polymères enchevêtrés et de systèmes chargés. Les contraintes auxquelles les forces statistiques sont soumises, ainsi que leurs impacts sur les dynamiques, sont ensuite discutés. La présentation de la DPD se termine par des considérations sur les effets numériques particuliers à la DPD. La puissance de la DPD est démontrée par la simulation de polymères arborescents. Les polymères arborescents sont des macromolécules hyperbranchées obtenues par une séquence de réactions de greffage de chaînes polymères. La structure qu’adoptent ces molécules n’est pas connue avec certitude. Des expériences ont permis aux chercheurs de proposer un modèle en loi de puissance pour le profil de densité radiale. Or, cette propriété n’est accessible qu’indirectement aux méthodes expérimentales, alors qu’elle peut être obtenue directement des travaux de simulation. La masse énorme de ces composés, ainsi que leur topologie complexe, impossible à réduire à un modèle plus simple, empêche toute simulation par des méthodes microscopiques traditionnelles. L’utilisation de méthodes mésoscopiques s’impose donc. Les polymères arborescents de génération 2 (d’une masse de l’ordre de 3,2×103 kDa) en solution (5 %) peuvent être simulés explicitement grâce à la DPD, et ce, en un temps acceptable. Les propriétés du solvant peuvent être ajustées, notamment leur qualité et leur masse moléculaire. Le profil de densité radiale moyen simulé correspond plutôt bien au modèle en loi de puissance proposé. L’analyse des données expérimentale suppose une symétrie sphérique des molécules individuelles qui s’avère être erronée. L’anisotropie des macromolécules est étudiée et s’avère être hautement variable. Des fonctions de distribution radiale ainsi que les patrons de diffusion de neutrons associés ont été obtenus. Ces derniers pourront être comparés directement aux résultats expérimentaux lorsque ces derniers seront disponibles. L’utilisation de la DPD est riche en possibilités. Elle est facilement étendue à diverses classes de matériaux. Par sa nature dynamique et ses propriétés, la DPD donne accès à certaines classes de phénomènes inaccessibles aux autres méthodes de simulation mésoscopique. Notamment, la DPD permet naturellement la simulation dans l’état stationnaire, tel que démontré par la simulation de la structure du Nafion c sous cisaillement. De plus, le comportement hydrodynamique devrait permettre la simulation à l’échelle mésoscopique de la transition vitreuse ou à tout le moins, d’une transition lui ressemblant. De plus, la DPD peut être étendue afin d’effectuer la simulation dans d’autres ensembles thermodynamiques, qui donnent accès à d’autres propriétés d’intérêt pour les matériaux (conductivité thermique, propriétés mécaniques). Les versions actuelles de la DPD, bien que versatiles, ne permettent pas encore de reproduire quantitativement les propriétés des matériaux. Différents succès, obstacles et pistes de réflexion sont présentés. Le perfectionnement de la DPD fournit à la fois un prétexte et un banc d’essai de choix pour tenter de comprendre les questions fondamentales suscitées par le coarse-graining et l’échelle méso en elle-même.
44

Coarse Geometry for Noncommutative Spaces

Banerjee, Tathagata 25 November 2015 (has links)
No description available.
45

Charakteristika hrubého atmosférického aerosolu v městském prostředí / Characterization of coarse atmospheric aerol in urban environment

Granici, Olga January 2015 (has links)
(EN) This Diploma Thesis is concerned with statistical analysis of coarse aerosol at the area of the capital city Prague with focus on its time and space variability. The data covers time period from year 2005 up to year 2010 included. The concentrations of coarse aerosol were originally calculated from recorded values of PM10 a PM2,5. The assessment used in this thesis is based on concentrations of coarse aerosol recorded on four pollutant stations which are localized in the capital city. Three out of four those air pollution monitoring stations are characterized as traffic stations kind of purse, where we can assume the traffic's impact over the coarse aerosol concentration. The last station is distinguished to be background to report the data of region less loaded by pollution. The analysis is executed within particular parameters supposing that main source of coarse aerosol is traffic in urban environment. For time period examination variability the year, season, week and day running was carried out. The spatial variability was researched by the air pollution monitoring stations localization. To determine a rate of dependency among particular parameters the correlation analysis according to Spearman was used within the calculation of correlation coefficients. Beside the analysis this thesis...
46

Lateralidade e curso temporal do processamento de frequências espaciais na codificação de faces / Laterality and processing time-course of spatial frequencies on face encoding

Moraes Júnior, Rui de 01 February 2016 (has links)
O sinal de entrada na retina é decomposto em termos de frequência espacial (FE), variações periódicas de luminância ao longo do espaço. Existe vasta literatura sobre o processamento de FE no córtex visual primário. No entanto, não se sabe ao certo como esta informação sensorial básica é processada e integrada numa visão de alto nível. Esta tese aborda este tema ao investigar lateralidade cerebral, tempo de processamento e contexto cognitivo em três diferentes seções com objetivos específicos. Estas seções investigaram comportamentalmente visão de alto nível tendo a face humana como estímulo, dado sua relevância biológica e social. Na primeira seção (Theoretical Review), uma revisão apresenta estudos clínicos e neuropsicológicos que mostram áreas cerebrais envolvidas na percepção de faces e como os hemisférios esquerdo e direito realizam um processamento holístico e analítico baseado em informações de FEs. A especialização hemisférica de FE no reconhecimento de faces é então revisada e discutida. Concluiu-se que assimetrias sensoriais podem ser a base para assimetrias cognitivas de alta ordem. Ademais, foi destacado a influência do tempo de processamento. Na segunda seção (Study 1), foi investigado por método psicofísico a lateralidade de baixas e altas FEs no reconhecimento de faces em diferentes tempos de exposição. Faces com filtragem de FE foram apresentadas em campo visual dividido em alta e baixa restrição temporal em duas tarefas: reconhecimento facial (Experimento 1) e reconhecimento do sexo facial (Experimento 2). No Experimento 1, informações faciais de baixas e altas FEs foram mais eficientemente processadas no hemisfério direito e esquerdo, respectivamente, sem efeito do tempo de exposição das faces. Os resultados do Experimento 2 mostraram uma assimetria do hemisfério direito para baixas FEs em baixa restrição temporal. Conclui-se que o processamento de altas e baixas FEs é lateralizado nos hemisférios cerebrais no reconhecimento de faces. No entanto, a contribuição de altas e baixas FEs é dependente da tarefa e do tempo de exposição. Na terceira seção (Study 2) foi investigado qual estratégia temporal, coarse-to-fine (de baixas para altas FEs) ou fine-to-coarse, cada hemisfério cerebral utiliza para integrar informação de FE de faces humanas numa tarefa de categorização facial homem-mulher. Sequências dinâmicas breves coarse-to-fine e fine-to-coarse de faces foram apresentadas no campo visual esquerdo, direito e central. Os resultados do tempo de resposta e do score de eficiência invertida mostraram uma prevalência geral de um processamento coarse-to-fine, independente do campo visual de apresentação. Ainda, os dados da taxa de erro ressaltam o processamento coarse-to-fine realizado pelo hemisfério direito. No geral, esta tese fornece insights sobre assimetria cerebral funcional, integração de alto nível e curso temporal do processamento de FEs, principalmente para aqueles interessados na percepção de faces. Também foi mostrado que operações lateralizadas, tarefa-dependente e coarse-to-fine podem coexistir e interagir no cérebro para processar informação de FE. / Retinal input is decomposed in terms of spatial frequency (SF), i.e., periodic variations of luminance through space. There is extensive literature on the processing of SF in the primary visual cortex. However, it is still unclear how SF information is processed and integrated in high-level vision. This thesis addressed this issue in terms of laterality effects, processing time-course, and the cognitive context in three different sections with specific purposes. These sections behaviorally tackle high-level vision using human faces as stimuli due to their biological and social relevance. In the first section (Theoretical Review) a literature review presented clinical and neurophysiological studies that show brain areas that are involved in face perception and how the right and left hemispheres perform holistic and analytic processing, depending on SF information. The SF hemispheric specialization in face recognition is then reviewed and discussed. Our conclusion is that functional sensorial asymmetries may be the basis for high-level cognitive asymmetries. In addition, we highlighted the role of the processing time. In the second section (Study 1), we psychophysically investigated laterality of low and high SF in face recognition at different exposure times. The SF filtered faces were presented in a divided visual field at high and low temporal constraint in two tasks: face recognition (Experiment 1) and face gender recognition (Experiment 2). In Experiment 1, low and high SF facial information were more efficiently processed in the right and in the left hemisphere, respectively, with no effect of exposure time. In Experiment 2, results showed a right hemisphere asymmetry for low SF faces at low temporal constraint. We concluded that the processing of low and high SF is lateralized in the brain hemispheres for face recognition. However, low and high SF contribution is dependent on the task and the exposure time. In the third section (Study 2), we aimed to investigate which temporal strategy, i.e., coarse-to-fine (from low to high SF) or fine-to-course, each brain hemisphere performs to integrate SF information of human faces in a male-female categorization task. Coarse-to-fine and fine-to-course brief dynamic sequences of faces were presented in the left, right and central visual field. Results of the correct response time and the inverse efficiency score showed an overall advantage of coarse-to-fine processing, irrespective of the visual field of presentation. Data of the error rate also highlights the role of the right hemisphere in the coarse-to-fine processing. All in all, this thesis provided some insights on functional brain asymmetry, high-level integration, and processing time-course of SF information, mainly for those interested in face perception. It was also shown that lateralized, diagnostic-oriented, and coarse-to-fine operations may coexist and interact in the human brain to process SF information.
47

Coarse grained potential functions for proteins derived from all-atom explicit-solvent molecular dynamics simulations

Andrews, Casey Tyler 01 December 2014 (has links)
The use of computational simulation to study the dynamics and interactions of macromolecules has become an important tool in the field of biochemistry. A common method to perform these simulations is to use all-atom explicit-solvent molecular dynamics (MD). However, due to the limitations in computational power currently available, this method is not practical for simulating large-scale biomolecular systems on long timescales. An alternative is to perform implicit-solvent Brownian dynamics (BD) simulations using a coarse grained (CG) model that allows for increased computational efficiency. However, if simulations using the CG model are not realistic, then the gain in computational efficiency from using a CG model is not worthwhile. This thesis describes the derivation of a set of bonded and nonbonded CG potential functions for use in implicit-solvent BD simulations of proteins derived from all-atom explicit-solvent MD simulations of amino acids. To determine which force field and water model to use in the MD simulations, Chapter II describes 1 Μs all-atom explicit-solvent MD simulations of glycine, asparagine, phenylalanine, and valine solutions at 50, 100, 200 and 300 mg/ml concentrations performed using eight different force field and water model combinations. To evaluate the accuracy of the force fields at high solute concentrations, the density, viscosity, and dielectric increments of the four amino acids were calculated from the simulations and compared to experimental results. Additionally, the change in the strength of hydrophobic and electrostatic interactions with increasing solute concentration was calculated for each force field and water model combination. As a result of this study, the Amber ff99SB-ILDN force field and TIP4P-Ew explicit-solvent water model were chosen for all subsequent MD simulations. Chapter III describes the derivation of CG bonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of each of the twenty amino acids, including a separate simulation for protonated histidine. The angle and dihedral probability distributions sampled during the MD simulations were used to optimize the bonded potential functions using the iterative Boltzmann inversion (IBI) method. Chapter IV describes the derivation of CG nonbonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of every possible pairing of the amino acids (231 different systems). The radial distribution functions calculated from these MD simulations were used to optimize a set of nonbonded CG potential functions using the IBI method. The optimized set of bonded and nonbonded potential functions, which is termed COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins), quantitatively reproduced all of the calculated MD distributions. To determine if COFFDROP would be useful for simulations of bimolecular systems, Chapter V describes the testing of the transferability of the force field. First, COFFDROP was used to simulate concentrated amino acid solutions. The clustering of the solutes in these simulations was directly compared with results from corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. Next, BD simulations of 9.2 mM solutions of the small protein villin headpiece were performed. The proteins aggregated during these simulations, which is in agreement with results from MD simulation but in disagreement with experiment. After scaling the strength of COFFDROP's nonbonded potential functions by a factor of 0.8 and rerunning the BD simulations, the amount of aggregation was comparable to experimental observations. Based on these results, COFFDROP is likely to be applicable in CG BD simulations of large, highly concentrated, biomolecular systems.
48

Pipeline Transport of Coarse Mineral Suspensions Displaying Shear Thickening

Andrew, Chryss, andrew.chryss@rmit.edu.au January 2008 (has links)
Transport properties of concentrated suspensions are of interest to many industries. Mineral slurries at higher solids concentrations have shown some rheologically interesting characteristics such as shear thickening, the increase of viscosity of a multi-phase mixture with increasing shear rate. The general literature on the rheology of suspensions records the presence of yield stresses, shear thinning and normal stress differences. Little is said specifically about shear thickening behaviour except for colloidal suspensions. The aim of this study is to examine the behaviour of coarse shear thickening suspensions and determine the causes of this phenomenon. The study intended to achieve the following objectives to; develop the appropriate techniques for rheometric studies of shear thickening suspensions; investigate the nature of particle-fluid interaction; develop a model of shear thickening behaviour as it occurs in non-colloidal suspensions and to develop a method of applying the rheology results to flows and flow geometries of practical relevance. The effects of wall slip dominate much of the literature of shear thickening materials. To investigate this aspect a significant portion of the experimental work examined the effect of shear thickening on torsional flow. The rheogram produced from parallel plate rheometry was reassessed as a non-controlled flow and a rheology model dependant analysis demonstrated that the effects of slip are considerably more problematic for shear thickening suspensions, particularly as wall slip is an increasing function of shear stress. As a consequence of the rheometric method described above it was observed that the rate of change of the first normal stress difference, N1, with shear rate changes as shear thickening commences for non-colloidal suspensions. N1 is initially negative and is increasingly negative at low shear rates. Additional rheometric analysis examined the transient effects in the behaviour of a non-colloidal shear thickening suspension. By employing large angle oscillating strain tests the strain required to initiate a shear thickening response was determined. Coherent back scattering of laser light experiments were able to show the change in orientation of the particles with respect to its rotation around the vorticity axis. After a viscosity minimum was reached the orientation became more random as particle rotation and lamina disruption occurred. This was considered to be the cause of the measured shear thickening. A model of shear thickening in concentrated, non-colloidal suspensions of non-spherical particles was developed. Based on hydrodynamic interaction in the Stokes flow regime, the flow of interstitial fluid subjected the adjacent particles to lubricating and Couette type forces, acting as a couple. When a series of force balances on a particle contained between two moving laminae are conducted as a time sequence, the particle orientation and motion can be observed. The model has qualitative agreement with several aspects of the experimentally observed behaviour of shear thickening suspensions, such as viscosity change with shear rate and concentration, and the first normal stress difference increasing with shear rate. Pipe line flow experiments were conducted on the model suspension. Particle settling produces unusual patterns in shear thickening suspensions, with an annulus of delayed settling near the wall.
49

The effects of moisture content and initial heterotrophic colonization on the decomposition of coarse woody debris

Barker, Jason Scot 10 June 2003 (has links)
Previous research on coarse woody debris (CWD) indicated that moisture content and initial heterotrophic colonization of decaying wood can affect the decomposition process. Six heterotrophic treatments were created to simulate the effects of physical penetration of the bark and wood and the transmission of ascomycetes versus basidiomycetes into CWD. In 1995, 360 Douglas-fir (Pseudotsuga menziesii) were randomly placed at five replicate sites in old-growth stands. Each site had 6 heterotrophic (HET) x 2 moisture combinations (TENT). One set of logs representing the treatment combinations was used for sampling respiration and another set was used to measure volume affected by insect gallery excavations and fungal rot and to determine decay rates. Respiration was sampled three times during the summer of 2001. The results indicated that the HET treatments were no longer affecting respiration rates. Analysis of the average of the three sampling periods revealed no TENT effect but examinations of the individual sampling dates suggests that tented logs might have higher respiration rates than non-tented logs as summer progresses. In the aggregate, the TENT treatment reduced moisture content from 45% to 36%, a 20 percent reduction in moisture levels. The HET and the TENT treatments did not affect decay rates. The mean density change for the logs was -0.072 g/cm�� �� 0.03 and the mean decay constant was 0.026 �� 0.011. The TENT treatment did affect heterotrophic activity. The mean volume of wood borer excavation and extent of brown rot was higher in the tented logs (256 cm��) than in the non-tented logs (59.9 cm��). There was also a statistically significant interaction between the HET and TENT treatments. The largest differences in volume affected by wood borers and fungal rot were found in treatments that injected ascomycetes into the experimental logs. In sum, there was limited evidence that the differences in moisture content caused by the TENT treatment affected the decomposition process but the HET treatments appear to not be directly influencing decomposition after six years. The findings suggest differences in the initial community composition of heterotrophs have a decreasing impact on the decomposition process as it progresses. / Graduation date: 2004
50

MULTI-SCALE MODELING OF POLYMERIC MATERIALS: AN ATOMISTIC AND COARSE-GRAINED MOLECULAR DYNAMICS STUDY

Wang, Qifei 01 August 2011 (has links)
Computational study of the structural, thermodynamic and transport properties of polymeric materials at equilibrium requires multi-scale modeling techniques due to processes occurring across a broad spectrum of time and length scales. Classical molecular-level simulation, such as Molecular Dynamics (MD), has proved very useful in the study of polymeric oligomers or short chains. However, there is a strong, nonlinear dependence of relaxation time with respect to chain length that requires the use of less computationally demanding techniques to describe the behavior of longer chains. As one of the mesoscale modeling techniques, Coarse-grained (CG) procedure has been developed recently to extend the molecular simulation to larger time and length scales. With a CG model, structural and dynamics of long chain polymeric systems can be directly studied though CG level simulation. In the CG simulations, the generation of the CG potential is an area of current research activity. The work in this dissertation focused on both the development of techniques for generating CG potentials as well as the application of CG potentials in Coarse-grained Molecular Dynamics (CGMD) simulations to describe structural, thermodynamic and transport properties of various polymer systems. First, an improved procedure for generated CG potentials from structural data obtained from atomistic simulation of short chains was developed. The Ornstein-Zernike integral equation with the Percus Yevick approximation was invoked to solve this inverse problem (OZPY-1). Then the OZPY-1 method was applied to CG modeling of polyethylene terephthalate (PET) and polyethylene glycol (PEG). Finally, CG procedure was applied to a model of sulfonated and cross-linked Poly (1, 3-cyclohexadiene) (sxPCHD) polymer that is designed for future application as a proton exchange membrane material used in fuel cell. Through above efforts, we developed an understanding of the strengths and limitations of various procedures for generating CG potentials. We were able to simulate entangled polymer chains for PET and study the structure and dynamics as a function of chain length. The work here also provides the first glimpses of the nanoscale morphology of the hydrated sxPCHD membrane. An understanding of this structure is important in the prediction of proton conductivity in the membrane.

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