Relevant bibliographies by topics / Calcule time-Scales

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Academic literature on the topic 'Calcule time-Scales'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Calcule time-Scales"

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Sahir, M. J. S. "Объединение классических и динамических неравенств, возникающих при анализе временных масштабов." Вестник КРАУНЦ. Физико-математические науки, no. 4 (December 29, 2020): 26–36. http://dx.doi.org/10.26117/2079-6641-2020-33-4-26-36.

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In this paper, we present an extension of dynamic Renyi’s inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov’s inequality and Radon’s inequality on time scales by using the time scale Riemann–Liouville type fractional integrals. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. В этой статье мы представляем расширение динамического неравенства Реньи на шкалы времени с помощью дробного интеграла типа Римана-Лиувилля. Кроме того, мы находим обобщения хорошо известного неравенства Ляпунова и неравенства Радона на шкалах времени с помощью дробных интегралов типа Римана-Лиувилля на шкале. Наши исследования объединяют и расширяют некоторые непрерывные неравенства и соответствующие им дискретные аналоги.
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Le-Anh, Duy, Ashit Rao, Amy Stetten, Subhash Ayirala, Mohammed Alotaibi, Michel Duits, Han Gardeniers, Ali AlYousef, and Frieder Mugele. "Oil Displacement in Calcite-Coated Microfluidic Chips via Waterflooding at Elevated Temperatures and Long Times." Micromachines 13, no. 8 (August 14, 2022): 1316. http://dx.doi.org/10.3390/mi13081316.

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In microfluidic studies of improved oil recovery, mostly pore networks with uniform depth and surface chemistry are used. To better mimic the multiple porosity length scales and surface heterogeneity of carbonate reservoirs, we coated a 2.5D glass microchannel with calcite particles. After aging with formation water and crude oil (CRO), high-salinity Water (HSW) was flooded at varying temperatures and durations. Time-resolved microscopy revealed the CRO displacements. Precise quantification of residual oil presented some challenges due to calcite-induced optical heterogeneity and brine–oil coexistence at (sub)micron length scales. Both issues were addressed using pixel-wise intensity calibration. During waterflooding, most of the ultimately produced oil gets liberated within the first pore volume (similar to glass micromodels). Increasing temperature from 22 °C to 60 °C and 90 °C produced some more oil. Waterflooding initiated directly at 90 °C produced significantly more oil than at 22 °C. Continuing HSW exposure at 90 °C for 8 days does not release additional oil; although, a spectacular growth of aqueous droplets is observed. The effect of calcite particles on CRO retention is weak on flat surfaces, where the coverage is ~20%. The calcite-rich pore edges retain significantly more oil suggesting that, in our micromodel wall roughness is a stronger determinant for oil retention than surface chemistry.
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Van Rampelbergh, M., S. Verheyden, M. Allan, Y. Quinif, E. Keppens, and P. Claeys. "Seasonal variations recorded in cave monitoring results and a 10 year monthly resolved speleothem δ<sup>18</sup>O and δ<sup>13</sup>C record from the Han-sur-Lesse cave, Belgium." Climate of the Past Discussions 10, no. 2 (April 22, 2014): 1821–56. http://dx.doi.org/10.5194/cpd-10-1821-2014.

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Abstract. Speleothems provide paleoclimate information on multi-millennial to decadal scales in the Holocene. However seasonal or even monthly resolved records remain scarce. They require fast growing stalagmites and a good understanding of the proxy transfer function on very short time scales. The Proserpine stalagmite from the Han-sur-Less cave (Belgium) displays seasonal layers of 0.5 to 2 mm thickness that reconstruct paleoclimates at a monthly scale. Through a regular cave monitoring, we acquired a good understanding of how δ18O and δ13C signals in modern calcite reflect climate variations on sub-seasonal scale. Cave parameters vary seasonally in response to the activity of the vegetation cover and outside air temperature. From December to June, the cave remains in "winter-mode". Outside temperatures are cold inducing low cave air and water temperatures. Bio-productivity in the soil is limited leading to low pCO2, higher δ13C composition of the CO2 in the cave air and high discharge due to the inactivity of the plant coverage. From June to December, the cave switches to "summer-mode" and the measured factors display an opposite behavior. The δ18O and δ13C signals of fresh calcite precipitated on glass slabs vary seasonally. Lowest δ18O values occur during the summer-mode when the δ13C values are high. The δ18O composition of the calcite is in equilibrium with the drip water δ18O and display seasonal variations due to changes in the cave air and water temperature. In contrast to the δ18O signal, δ13C values of the calcite precipitated on the glass slabs do not reflect equilibrium conditions. Highest δ13C values occur during summer, when discharge rates are low increasing the evaporation effect on the thin water film covering the stalagmite. This same antithetical behavior of the δ18O vs. the δ13C signals is seen in the monthly resolved speleothem record that covers the period between 1976 and 1985 AD. Dark layers are formed during summer, while light layers are formed during winter when calcite deposition occurs fast. The darker the color of a layer, the more compact its calcite structure, the more negative its δ18O signal and the more positive its δ13C signal.
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Putranto, W. A., Y. Umardhani, Sulistyo, Yurianto, and A. P. Bayuseno. "Analysis of calcium carbonate polymorphs deposited in water piping system and the effect of tartaric acid additive." MATEC Web of Conferences 159 (2018): 01054. http://dx.doi.org/10.1051/matecconf/201815901054.

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Calcium carbonate (CaCO3) formed in a water piping system was investigated in the presence of chemical additives tartaric acid (0.00 and 10.00 ppm) and various temperatures ((27 and 50ºC). The flow rate inside pipe (35 ml/min) were selected. Solutions of CaCl2 and Na2CO3 were prepared in water with equimolar to Ca2+ concentration of 3000 ppm. The induction time of scale nucleation varied from 24 min to 44 min. An increasing temperature of the solution resulted in more CaCO3 scale, mass, while the higher tartaric acid made the reduced mass of scales by 90%. SEM/EDS analysis verified CaCO3 with a plate like morphology. Also the XRPD Rietveld method provided the confirmation of a major phase of calcite and vaterite minerals followed by the minor of aragonite in the absence of tartaric acid and at room temperature. However, the presence of 10 ppm tartaric acid yielded the increasing result of calcite, while aragonite precipitation was hampered under the influence of tartaric acid. The presence of tartaric acid at increasing temperature of 50ºC could delay formation of calcite, whereas aragonite could be formed significantly. Thus the study showed the capacity of the tartaric acid in influencing CaCO3 crystallization.
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Khan, Hares, Alo Laas, Rafael Marcé, Margot Sepp, and Biel Obrador. "Eutrophication and Geochemistry Drive Pelagic Calcite Precipitation in Lakes." Water 13, no. 5 (February 25, 2021): 597. http://dx.doi.org/10.3390/w13050597.

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Pelagic calcification shapes the carbon budget of lakes and the sensitivity of dissolved inorganic carbon (DIC) responses to lake metabolism. This process, being tightly linked to primary production, needs to be understood within the context of summer eutrophication which is increasing due to human stressors and global change. Most lake carbon budget models do not account for calcification because the conditions necessary for its occurrence are not well constrained. This study aims at identifying ratios between calcification and primary production and the drivers that control these ratios in freshwater. Using in situ incubations in several European freshwater lakes, we identify a strong relationship between calcite saturation and the ratio between calcification and net ecosystem production (NEP) (p-value < 0.001, R2 = 0.95). NEP-induced calcification is a short-term process that is potentiated by the increase in calcite saturation occurring at longer time scales, usually reaching the highest levels in summer. The resulting summer calcification event has effects on the DIC equilibria, causing deviations from the metabolic 1:1 stoichiometry between DIC and dissolved oxygen (DO). The strong dependency of the ratio between NEP and calcification on calcite saturation can be used to develop a suitable parameterization to account for calcification in lake carbon budgets.
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Blain, Gabriel C., and Monica C. Meschiatti. "Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index." Revista Brasileira de Engenharia Agrícola e Ambiental 19, no. 12 (December 2015): 1129–35. http://dx.doi.org/10.1590/1807-1929/agriambi.v19n12p1129-1135.

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ABSTRACT The Standardized Precipitation Index was developed as a probability-based index able to monitor rainfall deficit in a standardized or normalized way. Thus, the performance of this drought index is affected by the use of a distribution that does not provide an appropriate fit for the rainfall data. The goal of this study was to evaluate the adjustment of the gamma distribution for the rainfall amounts summed over several time scales (Pelotas, Rio Grande do Sul, Brazil), to assess the goodness-of-fit of alternative distributions to these rainfall series and to evaluate the normality assumption of the Standardized Precipitation Index series calculated from several distributions. Based on the Lilliefors test and on a normality test, it is verified that the gamma distribution is not suitable for calculating this Index in several timescales. The generalized normal distribution presented the best performance among all analysed distributions. It was also concluded that the drought early warning systems and the academic studies should re-evaluate the use of the gamma distribution in the Standardized Precipitation Index calculation algorithm. A computational code that allows calculating this drought index based on the generalized normal distribution has also been provided.
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Caley, T., and D. M. Roche. "δ<sup>18</sup>O water isotope in the <i>i</i>LOVECLIM model (version 1.0) – Part 3: A palaeo-perspective based on present-day data–model comparison for oxygen stable isotopes in carbonates." Geoscientific Model Development 6, no. 5 (September 12, 2013): 1505–16. http://dx.doi.org/10.5194/gmd-6-1505-2013.

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Abstract. Oxygen stable isotopes (δ18O) are among the most useful tools in palaeoclimatology/palaeoceanography. Simulation of oxygen stable isotopes allows testing how the past variability of these isotopes in water can be interpreted. By modelling the proxy directly in the model, the results can also be directly compared with the data. Water isotopes have been implemented in the global three-dimensional model of intermediate complexity iLOVECLIM, allowing fully coupled atmosphere–ocean simulations. In this study, we present the validation of the model results for present-day climate against the global database for oxygen stable isotopes in carbonates. The limitation of the model together with the processes operating in the natural environment reveal the complexity of use the continental calcite-δ18O signal of speleothems for a global quantitative data–model comparison exercise. On the contrary, the reconstructed surface ocean calcite-δ18O signal in iLOVECLIM does show a very good agreement with the late Holocene database (foraminifers) at the global and regional scales. Our results indicate that temperature and the isotopic composition of the seawater are the main control on the fossil-δ18O signal recorded in foraminifer shells when all species are grouped together. Depth habitat, seasonality and other ecological effects play a more significant role when individual species are considered. We argue that a data–model comparison for surface ocean calcite δ18O in past climates, such as the Last Glacial Maximum (≈ 21 000 yr), could constitute an interesting tool for mapping the potential shifts of the frontal systems and circulation changes throughout time. Similarly, the potential changes in intermediate oceanic circulation systems in the past could be documented by a data (benthic foraminifers)-model comparison exercise whereas future investigations are necessary in order to quantitatively compare the results with data for the deep ocean.
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Caley, T., and D. M. Roche. "δ<sup>18</sup>O water isotope in the <i>i</i>LOVECLIM model (version 1.0) – Part 3: A paleoperspective based on present-day data-model comparison for oxygen stable isotopes in carbonates." Geoscientific Model Development Discussions 6, no. 1 (March 4, 2013): 1527–58. http://dx.doi.org/10.5194/gmdd-6-1527-2013.

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Abstract. Oxygen stable isotopes (18O) are among the most usual tools in paleoclimatology/paleoceanography. Simulation of oxygen stable isotopes allows testing how the past variability of these isotopes in water can be interpreted. By modelling the proxy directly in the model, the results can also be directly compared with the data. Water isotopes have been implemented in the global three-dimensional model of intermediate complexity iLOVECLIM allowing fully coupled atmosphere-ocean simulations. In this study, we present the validation of the model results for present day climate against global database for oxygen stable isotopes in carbonates. The limitation of the model together with the processes operating in the natural environment reveal the complexity of use the continental calcite 18O signal of speleothems for a data-model comparison exercise. On the contrary, the reconstructed surface ocean calcite δ18O signal in iLOVECLIM does show a very good agreement with late Holocene database (foraminifers) at the global and regional scales. Our results indicate that temperature and the isotopic composition of the seawater are the main control on the fossil δ18O signal recorded in foraminifer shells and that depth habitat and seasonality play a role but have secondary importance. We argue that a data-model comparison for surface ocean calcite δ18O in past climate, such as the last glacial maximum (&amp;approx;21 000 yr), could constitute an interesting tool for mapping the potential shifts of the frontal systems and circulation changes throughout time. Similarly, the potential changes in intermediate oceanic circulation systems in the past could be documented by a data (benthic foraminifers)-model comparison exercise whereas future investigations are necessary in order to quantitatively compare the results with data for the deep ocean.
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Claes, Steven, Fadi H. Nader, and Souhail Youssef. "Coupled experimental/numerical workflow for assessing quantitative diagenesis and dynamic porosity/permeability evolution in calcite-cemented sandstone reservoir rocks." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 (2018): 36. http://dx.doi.org/10.2516/ogst/2018027.

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Some of the world best hydrocarbon reservoirs (carbonates and siliciclastics) are also believed to be valuable for subsurface storage of CO2 and other fluids. Yet, these reservoirs are heterogeneous in terms of their mineralogy and flow properties, at varying spatial-temporal scales. Therefore, predicting the porosity and permeability (flow properties) evolution of carbonates and sandstones remains a tedious task. Diagenesis refers to the alteration of sedimentary rocks through geologic time, mainly due to rock-fluid interactions. It affects primarily the flow properties (porosity and permeability) of already heterogeneous reservoir rocks. In this project a new approach is proposed to calculate/quantify the influence of diagenetic phases (e.g. dissolution, cement plugging) on flow properties of typical sandstone reservoir rocks (Early Jurassic Luxembourg Formation). A series of laboratory experiments are performed in which diagenetic phases (e.g. pore blocking calcite cement in sandstone) are selectively leached from pre-studied samples, with the quantification of the petrophysical characteristics with and without cement to especially infer permeability evolution. Poorly and heavily calcite-cemented sandstone samples, as well as some intermediate cemented samples were used. The results show a distinctive dissolution pattern for different cementation grades and varying Representative Elementary Volumes (REVs). These conclusions have important consequences for upscaling diagenesis effects on reservoirs, and the interpretation of geochemical modelling results of diagenetic processes. The same approach can be applied on other type of cements and host-rocks, and could be improved by integrating other petrophysical analyses (e.g. petroacoustic, NMR).
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de Wet, Carol B., Andrew P. de Wet, Linda Godfrey, Elizabeth Driscoll, Samuel Patzkowsky, Chi Xu, Sophia Gigliotti, and Melina Feitl. "Pliocene short-term climate changes preserved in continental shallow lacustrine-palustrine carbonates: Western Opache Formation, Atacama Desert, Chile." GSA Bulletin 132, no. 9-10 (December 23, 2019): 1795–816. http://dx.doi.org/10.1130/b35227.1.

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Abstract Multiple climate proxies indicate episodic changes in moisture levels within an ∼1 Ma duration (early–mid Pliocene) interval. Limestones within the Opache Formation, Calama Basin, Atacama Desert region, Chile, contain evidence for wetter and drier periods on short time scales. Proxies include carbonate lithological changes, paleontology (stromatolites, oncolites, gastropods, ostracods and diatoms), O and C stable isotopes, geochemistry, and mineralogical changes (aragonite, calcite, Mg-calcite, dolomite and gypsum) throughout a 30 m stratigraphic section. Stromatolite fossil cyanobacteria dark and light laminations and mesohaline to hypersaline diatom species suggest Pliocene annual seasonality. Short-term changes between wetter and drier conditions indicate that at least this part of the Atacama region was experiencing relatively rapid early–mid Pliocene climate instability. The predominance of limestone in the Opache Formation, in contrast to the 1500 m of Oligocene-Miocene siliciclastic conglomerates and sandstones, interpreted as arid climate alluvium, that underlie it, indicates a shift from arid or hyperarid climate to a semi-arid climate. Semi-arid conditions promoted limestone deposition in a shallow lacustrine-palustrine environment. In this setting, events such as storms with associated surface water flow, erosion, siliciclastic sand, gravel, and intraclast deposition, coupled with significant biological activity, represent sedimentation during more humid periods in a shallow lacustrine depositional environment. In contrast, limestone characterized by mudcracks, Navicula diatoms, and vadose syndepositional cementation, reflect periods of enhanced evaporation, water shallowing, and episodic desiccation, characteristic of a palustrine depositional system. These facies shifts, in conjunction with geochemical and isotopic proxy evidence, yield a sedimentary record of wetter and drier climate shifts.
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Dissertations / Theses on the topic "Calcule time-Scales"

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Hariz, Belgacem Khader. "Higher-order Embedding Formalism, Noether’s Theorem on Time Scales and Eringen’s Nonlocal Elastica." Electronic Thesis or Diss., Pau, 2022. https://theses.hal.science/tel-03981833.

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En mathématiques, le calcul des variations est un ensemble de méthodes permettant la détermination de solutions à des problèmes d'optimisation des quantités traduites en termes de fonctionnelle. De nombreuses applications existent, notamment dans la recherche de courbes ou de surfaces minimales. Les systèmes dynamiques considérés sont de natures diverses (équations différentielles, intégrales ou stochastiques) et modélisent des problèmes d'origines multiples : aérospatiale, automobile, biologie, économie, médecine, etc. Le théorème de Noether présente un fort intérêt puisqu'il propose une loi de conservation explicite (traduisant souvent une quantité physique comme l'énergie totale ou le moment angulaire en mécanique classique) qui permet de réduire ou d'intégrer l'équation différentielle associée par quadrature. L'objectif de ma thèse contient de nombreux thèmes, dans le premier but nous allons : *) donner le théorème de Noether discret dans le cadre ”time scale” (Le formalisme lagrangien et hamiltonien). Le passage de la nature discrète à la nature continue de la structure la morphologie est d'un intérêt primordial en physique pour comprendre comment la microstructure peut influencer les propriétés macroscopiques du matériau à plus grande échelle. Ce passage peut être modélisé par un système discret appelé 'Hencky's chain' et l'équation du mouvement est donnée par des équations aux différences non linéaires et cette équation ne possède pas de Lagrangien. Le deuxième but nous allons : *) donner les structures lagrangienne, hamiltonienne via le facteur intégrant et trouver la solution analytique de l'équation non locale au sens d'Eringen (nonlocalité différentielle d'Eringen, 1983). Le troisième but nous allons : *) étudier l'existence des formulations variationnelles via le principe de Brezis Ekeland-Nayroles (Gery de Saxce) - application sur la formulation 4D développée par E. Rouhaud pour l'étude des déformations des matériaux *) développer des schémas numériques qui respectent certaines particularités. En particulier, un schéma permettent de mettre en œuvre la théorie 4D développée par E. Rouhaud. *) applications numériques et théoriques sur le problème des déformations des matériaux
The aim of this thesis is to deal with the connection between continuous and discrete versions of a given object. This connection can be studied in two different directions: one going from a continuous setting to a discrete analogue, and in a symmetric way, from a discrete setting to a continuous one. The first procedure is typically used in numerical analysis in order to construct numerical integrators and the second one is typical of continuous modeling for the study of micro-structured materials.In this manuscript, we focus our attention on three distinct problems. In the first part, we propose a general framework precising different ways to derive a discrete version of a differential equation called discrete embedding formalism.More precisely, we exhibit three main discrete associate: the differential, integral or variational structure in both classical and high-order approximations.The second part focuses on the preservation of symmetries for discrete versions of Lagrangian and Hamiltonian systems, i.e., the discrete analogue of Noether's theorem.Finally, the third part applies these results in mechanics, i.e., the problem studied by N. Challamel, Kocsis and Wang called Eringen's nonlocal elastica equation which can beobtained by the continualization method. Precisely, we construct a discrete version of Eringen's nonlocal elastica then we study the difference with Challamel's proposal
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Ferreira, Rui Alexandre Cardoso. "Calculus of variations on time scales and discrete fractional calculus." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/2921.

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Doutoramento em Matemática
Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fraccionário em tempo discreto. Obtemos as correspondentes condições necessárias de Euler– Lagrange e Legendre, ilustrando depois a teoria com alguns exemplos.
We study problems of the calculus of variations and optimal control within the framework of time scales. Specifically, we obtain Euler–Lagrange type equations for both Lagrangians depending on higher order delta derivatives and isoperimetric problems. We also develop some direct methods to solve certain classes of variational problems via dynamic inequalities. In the last chapter we introduce fractional difference operators and propose a new discrete-time fractional calculus of variations. Corresponding Euler–Lagrange and Legendre necessary optimality conditions are derived and some illustrative examples provided.
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Dryl, Monika. "Calculus of variations on time scales and applications to economics." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12869.

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Doutoramento em Matemática
We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.
Consideramos alguns problemas do cálculo das variações em escalas temporais. Primeiramente, demonstramos equações do tipo de Euler-Lagrange e condições de transversalidade para problemas de horizonte infinito generalizados. De seguida, consideramos a composição de uma certa função escalar com os integrais delta e nabla de um campo vetorial. Presta-se atenção a problemas extremais inversos para funcionais variacionais em escalas de tempo arbitrárias. Começamos por demonstrar uma condição necessária para uma equação dinâmica integro-diferencial ser uma equação de Euler-Lagrange. Resultados novos e interessantes para o cálculo discreto e quantum são obtidos como casos particulares. Além disso, usando a equação de Euler-Lagrange e a condição de Legendre fortalecida, obtemos uma forma geral para uma funcional variacional atingir um mínimo local, num determinado ponto do espaço vetorial. No final, duas aplicações interessantes em termos económicos são apresentadas. No primeiro caso, consideramos uma empresa que quer programar as suas políticas de produção e de investimento para alcançar uma determinada taxa de produção e maximizar a sua competitividade no mercado futuro. O outro problema é mais complexo e relaciona a inflação e o desemprego, que inflige uma perda social. A perda social é escrita como uma função da taxa de inflação p e a taxa de desemprego u, com diferentes pesos. Em seguida, usando as relações conhecidas entre p, u, e a taxa de inflação esperada π, reescrevemos a função de perda social como uma função de π. A resposta é obtida através da aplicação do cálculo das variações, a fim de encontrar a curva ótima π que minimiza a perda social total ao longo de um determinado intervalo de tempo.
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Bastos, Nuno Rafael de Oliveira. "Fractional calculus on time scales - Cálculo fraccional em escalas temporais." Doctoral thesis, Universidade de Aveiro, 2012. http://hdl.handle.net/10773/8566.

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Doutoramento em Matemática
Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.
We introduce a discrete-time fractional calculus of variations on the time scales ℤ and (ℎℤ)!. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of the new Euler— Lagrange and Legendre type conditions are given. We also give new definitions of fractional derivatives and integrals on time scales via the inverse generalized Laplace transform.
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McMahon, Chris. "Calculus of Variations on Time Scales and Its Applications to Economics." TopSCHOLAR®, 2008. http://digitalcommons.wku.edu/theses/370.

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The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using the two separate theories of the calculus of variations on time scales. The next presentation will be of the solution of an adjustment model, for a specific form of a time scale, whose functional can only be optimized, using the existing theory, when written with the A operator. We will also develop certain elements of stochastic time scale calculus, in order to lay the groundwork necessary to develop the theory of stochastic calculus of variations on time scales.
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Arslan, Aykut. "Discrete Fractional Hermite-Hadamard Inequality." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1940.

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This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard inequality and characterize convexity in terms of this inequality. In the fifth chapter, we discuss convexity on n{dimensional discrete time scales T = T1 × T2 × ... × Tn where Ti ⊂ R , i = 1; 2,…,n are discrete time scales which are not necessarily periodic. We introduce the discrete analogues of the fundamental concepts of real convex optimization such as convexity of a function, subgradients, and the Karush-Kuhn-Tucker conditions. We close this thesis by two remarks for the future direction of the research in this area.
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Kisela, Tomáš. "Basics of Qualitative Theory of Linear Fractional Difference Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-234025.

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Tato doktorská práce se zabývá zlomkovým kalkulem na diskrétních množinách, přesněji v rámci takzvaného (q,h)-kalkulu a jeho speciálního případu h-kalkulu. Nejprve jsou položeny základy teorie lineárních zlomkových diferenčních rovnic v (q,h)-kalkulu. Jsou diskutovány některé jejich základní vlastnosti, jako např. existence, jednoznačnost a struktura řešení, a je zavedena diskrétní analogie Mittag-Lefflerovy funkce jako vlastní funkce operátoru zlomkové diference. Dále je v rámci h-kalkulu provedena kvalitativní analýza skalární a vektorové testovací zlomkové diferenční rovnice. Výsledky analýzy stability a asymptotických vlastností umožňují vymezit souvislosti s jinými matematickými disciplínami, např. spojitým zlomkovým kalkulem, Volterrovými diferenčními rovnicemi a numerickou analýzou. Nakonec je nastíněno možné rozšíření zlomkového kalkulu na obecnější časové škály.
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Books on the topic "Calcule time-Scales"

1

Variational Calculus on Time Scales. Nova Science Publishers, Incorporated, 2018.

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Georgiev, Svetlin G. Variational Calculus on Time Scales. Nova Science Publishers, Incorporated, 2018.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2017.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2017.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2018.

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Hardy Type Inequalities on Time Scales. Springer, 2016.

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O'Regan, Donal, Ravi P. Agarwal, and Samir H. Saker. Hardy Type Inequalities on Time Scales. Springer, 2016.

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O'Regan, Donal, Ravi P. Agarwal, and Samir H. Saker. Hardy Type Inequalities on Time Scales. Springer, 2018.

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R, Anderson Douglas, and Svetlin G. Georgiev. Conformable Dynamic Equations on Time Scales. Taylor & Francis Group, 2020.

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R, Anderson Douglas, and Svetlin G. Georgiev. Conformable Dynamic Equations on Time Scales. Taylor & Francis Group, 2020.

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Book chapters on the topic "Calcule time-Scales"

1

Bohner, Martin, and Svetlin G. Georgiev. "Time Scales." In Multivariable Dynamic Calculus on Time Scales, 1–22. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_1.

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Seiffertt, John, and Donald C. Wunsch. "The Time Scales Calculus." In Evolutionary Learning and Optimization, 49–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03180-9_4.

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Georgiev, Svetlin G. "Calculus on Time Scales." In Functional Dynamic Equations on Time Scales, 1–36. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15420-2_1.

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Bohner, Martin, and Allan Peterson. "The Time Scales Calculus." In Dynamic Equations on Time Scales, 1–50. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0201-1_1.

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Goodrich, Christopher, and Allan C. Peterson. "Calculus on Mixed Time Scales." In Discrete Fractional Calculus, 353–414. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25562-0_5.

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Georgiev, Svetlin G. "Elements of the Time Scale Calculus." In Integral Equations on Time Scales, 1–75. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1_1.

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Bohner, Martin, and Svetlin G. Georgiev. "Partial Differentiation on Time Scales." In Multivariable Dynamic Calculus on Time Scales, 303–447. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_6.

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Bohner, Martin, and Svetlin G. Georgiev. "Multiple Integration on Time Scales." In Multivariable Dynamic Calculus on Time Scales, 449–515. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_7.

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Georgiev, Svetlin G. "Convolution on Time Scales." In Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, 157–215. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73954-0_3.

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Bohner, Martin, Gusein Guseinov, and Allan Peterson. "Introduction to the Time Scales Calculus." In Advances in Dynamic Equations on Time Scales, 1–15. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-0-8176-8230-9_1.

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Conference papers on the topic "Calcule time-Scales"

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Kapcak, Sinan, and Ünal Ufuktepe. "Multivariable Calculus on Time Scales." In 2011 International Conference on Computational Science and Its Applications (ICCSA). IEEE, 2011. http://dx.doi.org/10.1109/iccsa.2011.28.

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Girejko, Ewa, Agnieszka B. Malinowska, and Delfim F. M. Torres. "A unified approach to the calculus of variations on time scales." In 2010 Chinese Control and Decision Conference (CCDC). IEEE, 2010. http://dx.doi.org/10.1109/ccdc.2010.5498972.

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Ligocka, Agnieszka, and Wojciech Bandurski. "Using Multiple Scales Method to calculate threshold crossing time for the ramp response for high inductance VLSI interconnects." In 2008 IEEE Workshop on Signal Propagation on Interconnects (SPI). IEEE, 2008. http://dx.doi.org/10.1109/spi.2008.4558391.

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Huang, Jianliang, Weidong Zhu, and Shuhui Chen. "An Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motion of Nonlinear Systems With Cubic Nonlinearity." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97582.

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Abstract A new incremental harmonic balance (IHB) method with two time scales procedure is used to analyze quasi-periodic motion of multiple degrees of freedom systems with cubic nonlinearity. An amplitude increment algorithm is adapted to deal with cases where the two frequencies are unknown a priori, in order to automatically trace frequency response of quasi-periodic motion of the system and accurately calculate all frequency components and their corresponding amplitudes. Results of application of the present IHB method to quasi-periodic free vibration of the nonlinear system are shown and compared with previously published results with Lau method and those from numerical integration. While differences are noted between results predicted by the present IHB method and Lau method, excellent agreement is achieved between results from the present IHB method and numerical integration even in cases of strongly nonlinear vibration.
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Dai, Chong, Zhaoyi Dai, Samiridhdi Paudyal, Saebom Ko, Yue Zhao, Xin Wang, Xuanzhu Yao, Amy Kan, and Mason Tomson. "New Kinetic Turbidity Test Method and Prediction Model for Calcite Inhibition." In SPE International Conference on Oilfield Chemistry. SPE, 2021. http://dx.doi.org/10.2118/204398-ms.

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Abstract Calcite, as one of the most common scales in oilfield can be inhibited by common scale inhibitors. The measurement of calcite nucleation and inhibition is a challenge, because of the difficulty to control pH as a result of CO2 partitioning in and out of the aqueous phase. A new kinetic turbidity test method was developed so that the partial pressure of CO2, pH, and SI can be precisely controlled. Calcite nucleation and inhibition batch tests were conducted under various conditions (SI = 0.24-2.41, T = 4-175 °C, and pH = 5.5-7.5) in the presence of common phosphonate and polymeric inhibitors. Based on experimental results, calcite nucleation and inhibition semi-empirical models are proposed, and the logarithm of the predicted induction time is in good agreement with the measured induction time. The models are also validated with laboratory and field observations. Furthermore, a new BCC CSTR Inhibition (BCIn) test method that applied the Continuous Stirred Tank Reactor (CSTR) theory has been developed, for the first time. This BCIn method was used for calcite inhibitor screening tests and minimum inhibitor concentration (MIC) estimation. By only running one experiment (&lt; 1 hour) for each inhibitor, BCIn method selected the effective inhibitors among 18 common inhibitors under the conditions of SI = 1.23 at 90 °C and pH = 6. It was also found that the critical concentration (Ccrit) from BCIn method has a correlation with the MIC from batch tests. This study provided a simple and reliable solution for conducting calcite scale inhibition tests in an efficient and low-cost way. Furthermore, the newly developed prediction models can be used as guidance for laboratory tests and field applications, potentially saving enormous amounts of time and money.
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Jalali, Ali, and C. Nataraj. "Prediction of Occurrence of Periventricular Leukomalacia in Neonates After Heart Surgery Using a Decision Tree Algorithm." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71301.

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This paper is concerned with the prediction of the occurrence of Periventricular Leukomalacia (PVL), a form of white-matter brain injury, in neonates after heart surgery. The data which is collected over a period of 12 hours after the cardiac surgery contains measurements with different resolutions. The fact that data is collected at different time scales makes the modeling approach impractical, if not impossible. Hence, the decision tree classification technique has been selected for its capacity for discovering rules and novel associations in the data. It classifies groups based on reducing uncertainty in the classified data. From a physiological point of view we know that there are several regulatory mechanisms responsible for fluctuation of the hemodynamic variables at different time scales. To discover the most important active physiological components which might lead to the occurrence of PVL, we focus on the variation in the data in 1 min, 20 min and 2 hour periods. We calculate the energy of continuous wavelet transform coefficients of vital data at these time scales as a measure of variation in the different time frames. Results obtained from developing decision tree classifiers show that among all variations in all the variables, 2 hour and 20 minute variations in the heart rate and also 1 minute and 20 minute variation in Oxygen saturation are the most important parameters to predict PVL occurrence.
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Camp, T. R., and H. W. Shin. "Turbulence Intensity and Length Scale Measurements in Multistage Compressors." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-004.

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This paper describes the measurement and processing of turbulence data from multistage low-speed compressors. Measurements were made at the same relative positions in three four-stage compressors, each having different levels of the design stage loading coefficient. A new method of data processing to calculate turbulence intensities and integral length scales is outlined. Using this method, integral length scales have been measured in turbomachinery flows for the first time. It is shown how the turbulence intensity and integral length scale vary with position in the blade passage, with changing flow coefficient and with the value of the design stage loading coefficient. The results have been used to specify representative inlet conditions for experimental rigs and to improve the application of CFD turbulence models to turbomachinery modeling.
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Zheng, Yuan, and Jay P. Gore. "Time and Space Series Analysis of Spectral Radiation Intensities for a Partially Premixed Turbulent Flame." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47579.

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A recently developed technique called time and space series analysis was used to calculate the mean and fluctuating spectral radiation intensities leaving diametric and chord-like paths in turbulent partially premixed flames. A standard flame (Flame D) from Sandia Workshop on Turbulent Non-premixed Flames was selected to allow an evaluation of the radiation calculations at least at the single point statistics level. Measurements of spectral radiation intensities using a fast infrared array spectrometer provide an evaluation of the computations and also allow estimation of the length and time scales of scalar fluctuations, which appear as model parameters in the time and space series analysis modeling.
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Ross, Molly, John Matulis, and Hitesh Bindra. "A Statistical Approach to Quantify Taylor Microscale for Turbulent Flow Surrogate Model." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-91452.

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Abstract Non-equilibrium statistical mechanics models can be used to construct reduced order models from the time-dynamics data such as numerical or physical fluid mechanics experiments. One of the well-established statistical projection methods is the Kramers-Moyal expansion (KM) method. The first two terms of the KM expansion result can be used to construct a non-linear Langevin equation, which can serve as the statistically-trained reduced-order model. This non-linear Langevin equation can be approximated to the Fokker-Planck equation, which is similar to Advection-Diffusion equation, thereby preserving some characteristics of fluctuations associated with fluid mechanics. The KM method captures continuous-time dynamics, however, any data obtained through measurement is discrete. In order to accurately capture the time dynamics of the discrete data, the method for calculating the KM coefficients must be carefully chosen and implemented. To better represent the solution from discrete data, the drift and diffusion coefficients can be calculated at multiple time scales and then extrapolated to a time scale of zero, assuming a linear correlation. One challenge in using this method is that the calculated KM coefficients are only accurate for time scales greater than the Taylor microscale. This means that the extrapolation must use only the KM coefficients calculated for time scales greater than the Taylor microscale, however, this value is not always provided from the data nor simple to calculate. This work presents a method of approximating the Taylor microscale from the data through the relationship between the Markov property and the Taylor microscale and implementing this method to find the extrapolated KM coefficients. The KM method implementing the Taylor microscale estimation was applied to existing DNS turbulent channel flow data to model a time series. This generated time series was then compared to the DNS data using a statistical analysis including probability density function, autocorrelation, and power spectral density.
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Gopalan, Balaji, Edwin Malkiel, and Joseph Katz. "Diffusion of Slightly Buoyant Droplets in Isotropic Turbulence." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98530.

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We study the diffusion of slightly buoyant droplets in isotropic turbulence using High Speed Digital Holographic PIV. Droplets (Specific Gravity 0.85) are injected in the central portion of an isotropic turbulence facility with weak mean flow. Perpendicular digital inline holograms are recorded in a 37 × 37 × 37 mm3 region of interest using two high speed cameras. Data are recorded at 250 frames per second (2000 frames per second is the maximum possible frame rate). An automated program is developed to obtain two dimensional tracks of the droplets from two orthogonal images and match them to get three dimensional tracks. Cross correlation of droplet images are used for measuring their velocities. The time series are low pass filtered to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time history also enables us to calculate the three dimensional Lagrangian velocity autocorrelation function for different droplet radii. Integration of these functions gives us the diffusion coefficients. For shorter time scales, when the diffusion need not be Fickian we can use the three dimensional trajectories to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian.
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