In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macros...
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In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macros...
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In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic physical quantity, will be appropriately determined from molecular dynamics simulations on the microscale. This way, performance predictions become possible prior to material synthesis. However, standard methods produce in general wrong results for ensemble setups which correspond to battery or capacitor *** introduce a novel method to derive correct values also for such problems. These values are then used in a macroscopic system of partial differential equation (Poisson-Nernst-Planck system) for the numerical simulation of ion migration in a battery.
Crash simulation results show both deterministic and stochastic behavior. For optimization in automotive design it is very important to distinguish between effects caused by variation of simulation parameters and effe...
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The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a ...
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ISBN:
(数字)9783709112861
ISBN:
(纸本)3709112850
The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.
The ever increasing complexity of the physical phenomena studied in scientific and engineering disciplines , requires the development of new approaches and powerful technique for processing and analysis of complex dat...
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The ever increasing complexity of the physical phenomena studied in scientific and engineering disciplines , requires the development of new approaches and powerful technique for processing and analysis of complex data. scientific Visualization developing methods and tools for understanding the problems to be solved by bringing in a person's ability to see and perceive the image. The article deals with the preconditions of occurrence of this scientific field, the stages of its formation as a scientific discipline and major achievements. Shows the transition from technology to render virtual environment. Currently, scientific visualization is quite complete scientific discipline. Purpose of virtual environments is to provide users with a virtual workspace, in which they can observe and investigate create the virtual real-time data, models and the scenes. Presents selected results of the development of scientific visualization and virtual environment from the Moscow institute of Physics and Technology and the institute of computing for Physics and Technology in cooperation with research centers in Germany and Singapore. In conclusion ascertained advantages of visualization technologies and virtual environments to improve the efficiency of fundamental research, to meet the challenges of science, education and industry. Promising areas of research in this subject area are information visualization , visual analytics, a new man-machine interfaces based on haptic devices and tangible images.
In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensi...
ISBN:
(纸本)9783642317026
In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.
Interpreting the rapidly increasing amount of experimental data requires the availability and representation of biological knowledge in a computable form. The Biological expression language (BEL) encodes the data in f...
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Computer simulations of chemical systems can be used to reliably predict physical properties. Accurate molecular models, which are indispensable, are mathematically described by force fields, which have to be paramete...
Computer simulations of chemical systems can be used to reliably predict physical properties. Accurate molecular models, which are indispensable, are mathematically described by force fields, which have to be parameterized. Recently, an automated gradient-based parametrization procedure was published by the authors based on the minimization of a loss function between simulated and experimental physical properties. The applicability of the utilized algorithms is not trivial at all because of two reasons: First, simulation data is affected by statistical noise and second, the molecular simulations required for the loss function evaluations (involving finite differences approximations of gradients and Hessians) are extremely time-consuming. In this work, a more efficient approach to compute gradients and Hessians is presented. The method developed here is based on directional instead of partial derivatives. It is shown that up to 75% of the simulations can be avoided using this method.
In many applications, particularly in the engineering field, the need to consider uncertainties is recognized. To reduce the number of necessary simulations, metamodels can be used. We present a novel method on the ba...
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ISBN:
(纸本)9783950353709
In many applications, particularly in the engineering field, the need to consider uncertainties is recognized. To reduce the number of necessary simulations, metamodels can be used. We present a novel method on the basis of metamodels, that allows us to model not only the deterministic responses, but also the propagation of uncertainty in the entire design space. Our procedure makes it possible to determine the robust optimum quickly with common multi-criteria optimization algorithms. The novel approach offers the possibility to include the tolerance of the metamodel in the calculation. We introduce a new class of robustness measures that characterizes the propagation of uncertainty more accurately than usual: the median as measure of central tendency and the difference between median and a high quantile q as measure of dispersion. This allows the user to adjust the degree of robustness to his wishes via q. It can handle even extremely skewed distributions in an appropriate way. For the determination of the quantiles we use a novel combination of sampling scheme and nonparametric quantile estimation. This enables a fast computation on a local level. The suitability of the proposed proceeding is proved on several examples. The applicability is demonstrated on a real life example from automotive industry.
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