The Interaction of Growth Rates and Diffusion Coefficients in a Three-dimensional Mathematical Model of Gliomas

1997 ◽  
Vol 56 (6) ◽  
pp. 704-713 ◽  
Author(s):  
Patricia K. Burgess ◽  
Paul M. Kulesa ◽  
James D. Murray ◽  
Ellsworth C. Alvord
Author(s):  
Boris Gordeychik ◽  
Tatiana Churikova ◽  
Thomas Shea ◽  
Andreas Kronz ◽  
Alexander Simakin ◽  
...  

Abstract Nickel is a strongly compatible element in olivine, and thus fractional crystallization of olivine typically results in a concave-up trend on a Fo–Ni diagram. ‘Ni-enriched’ olivine compositions are considered those that fall above such a crystallization trend. To explain Ni-enriched olivine crystals, we develop a set of theoretical and computational models to describe how primitive olivine phenocrysts from a parent (high-Mg, high-Ni) basalt re-equilibrate with an evolved (low-Mg, low-Ni) melt through diffusion. These models describe the progressive loss of Fo and Ni in olivine cores during protracted diffusion for various crystal shapes and different relative diffusivities for Ni and Fe–Mg. In the case when the diffusivity of Ni is lower than that for Fe–Mg interdiffusion, then olivine phenocrysts affected by protracted diffusion form a concave-down trend that contrasts with the concave-up crystallization trend. Models for different simple geometries show that the concavity of the diffusion trend does not depend on the size of the crystals and only weakly depends on their shape. We also find that the effect of diffusion anisotropy on trend concavity is of the same magnitude as the effect of crystal shape. Thus, both diffusion anisotropy and crystal shape do not significantly change the concave-down diffusion trend. Three-dimensional numerical diffusion models using a range of more complex, realistic olivine morphologies with anisotropy corroborate this conclusion. Thus, the curvature of the concave-down diffusion trend is mainly determined by the ratio of Ni and Fe–Mg diffusion coefficients. The initial and final points of the diffusion trend are in turn determined by the compositional contrast between mafic and more evolved melts that have mixed to cause disequilibrium between olivine cores and surrounding melt. We present several examples of measurements on olivine from arc basalts from Kamchatka, and published olivine datasets from mafic magmas from non-subduction settings (lamproites and kimberlites) that are consistent with diffusion-controlled Fo–Ni behaviour. In each case the ratio of Ni and Fe–Mg diffusion coefficients is indicated to be <1. These examples show that crystallization and diffusion can be distinguished by concave-up and concave-down trends in Fo–Ni diagrams.


Author(s):  
Galiya Z. Lotova

AbstractSome problems of the theory of electron transfer in gases under the action of a strong external electric field is considered in the paper. Based on the three-dimensional ELSHOW algorithm, samples of states of particles in an electron avalanche are obtained for a given time moment in order to calculate the corresponding ‘diffusion radii’ and diffusion coefficients. Randomized projection estimators and kernel estimators (for test purpose) are constructed with the use of grouped samples for evaluation of the distribution density of particles in an avalanche. Test computations demonstrate a high efficiency of projection estimators for calculation of diffusive characteristics.


Author(s):  
Jihoon Seo ◽  
Akshay Gowda ◽  
Panart Khajornrungruang ◽  
Satomi Hamada ◽  
S.V. Babu

AbstractWe extend our recent 2D trajectory (x–y plane) and diffusion coefficient data of ceria particles near a glass surface obtained at pH 3, 5, and 7 using evanescent wave microscopy and video imaging to 3D trajectories by analyzing the separation distance between the particles and the glass surface in the vertical z‐direction. Mean squared displacement (MSD3D) of ceria particles was calculated to quantify 3D trajectories. Three‐dimensional diffusion coefficients were obtained from the MSD3D curves and were compared with two‐dimensional diffusion coefficients. By analyzing the MSD curves, we found that ceria particles exhibited only confined motion at pH 3 and 5, while both confined and Brownian motion were showed at pH 7. We also evaluated the cleaning ability of DI water adjusted to pH 10 and 12 to remove ceria particles from glass surfaces and related the results to the calculated trajectory, diffusion coefficient, and interaction potential data.


Author(s):  
Bogusław Bożek ◽  
Lucjan Sapa ◽  
Katarzyna Tkacz-Śmiech ◽  
Marek Zajusz ◽  
Marek Danielewski

AbstractInterdiffusion between dissimilar solids can change the properties of joined materials. Although much work has been done to study experimentally and theoretically interdiffusion in one-dimensional (1-D) diffusion couples, studying interdiffusion in two-dimensional (2-D) or three-dimensional (3-D) solids remains a challenge. In this article, we report an experiment and develop a model to study interdiffusion in a multicomponent system of 2-D geometry. The results (concentration maps and profiles) are compared with data obtained by modeling and numerical simulations. It is assumed that the system satisfies Vegard’s rule and diffusion coefficients are composition dependent. To model the multidimensional diffusion with a drift, we take benefit of the concept of the drift potential. A nonlinear parabolic-elliptic system of strongly coupled differential equations is formulated and the implicit difference method, preserving Vegard’s rule, is applied in the simulations.


1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.


1989 ◽  
Vol 54 (11) ◽  
pp. 2951-2961 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt

Measured growth and dissolution rates of single crystals and tablets were used to calculate the overall linear rates of growth and dissolution of CuSO4.5 H2O crystals. The growth rate for the tablet is by 20% higher than that calculated for the single crystal. It has been concluded that this difference is due to a preferred orientation of crystal faces on the tablet surface. Calculated diffusion coefficients and thicknesses of the diffusion and hydrodynamic layers in the vicinity of the growing or dissolving crystal are in good agreement with published values.


2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.


Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1770
Author(s):  
Xiaoqiang Zhang ◽  
Xuangang Yan

To prevent the leakage of image content, image encryption technology has received increasing attention. Most current algorithms are only suitable for the images of certain types and cannot update keys in a timely manner. To tackle such problems, we propose an adaptive chaotic image encryption algorithm based on RNA and pixel depth. Firstly, a novel chaotic system, two-dimensional improved Logistic-adjusted-Sine map is designed. Then, we propose a three-dimensional adaptive Arnold transform for scrambling. Secondly, keys are generated by the hash values of the plain image and current time to achieve one-image, one-key, and one-time pad simultaneously. Thirdly, we build a pre-permuted RNA cube for 3D adaptive scrambling by pixel depth, chaotic sequences, and adaptive RNA coding. Finally, selective diffusion combined with pixel depth and RNA operations is performed, in which the RNA operators are determined by the chemical structure and properties of amino acids. Pixel depth is integrated into the whole procedure of parameter generation, scrambling, and diffusion. Experiments and algorithm analyses show that our algorithm has strong security, desirable performance, and a broader scope of application.


2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.


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