Search results for "Linear Algebra."
showing 10 items of 552 documents
Mohr-cyclides, a 3D representation of geological tensors: The examples of stress and flow
2008
Mohr-circles are commonly used to represent second-rank tensors in two dimensions. In geology, this mainly applies to stress, flow, strain and deformation. Three-dimensional second rank tensors have been represented by sets of three Mohr-circles, mainly in the application of stress. This paper demonstrates that three-dimensional second rank tensors can in fact be represented in a three-dimensional reference frame by Mohr surfaces, which are members of the cyclide family. Such Mohr-cyclides can be used to represent any second rank tensor and are exemplified with the stress and flow tensors.
The Neural Basis of Idea Density During Natural Spoken Language
2019
Idea density (ID) evolved as a quantification of propositional base structure. Besides its function as a measure of linguistic complexity, ID has also been used as an index of general linguistic ability. In order to find the neural basis for the processing of high or low ID during spontaneous speech, a sample of healthy adults was assessed using the functional resonance imaging (fMRI) technique; participants described pictures presented to them while in the scanner. Differential patterns of activation were observed for the low- and high-ID conditions, providing new insights into the processing correlates of ID.
Special interpretation of formal measurement scales for the case of multiple heterogeneous properties
2001
A formal model of measurement is constructed and its components are outlined in this paper. An integrated hierarchical formal four-level structure which allows description of the multiple heterogeneous properties of a complex object under measurement is developed in order to have a uniform tool for the selection of specific scales for the measurement of these properties. A special treatment of a measurement scale defined on the space of the object states is offered, and corresponding structures of basic types of scales are explained permitting to take into consideration distances between relations on these states. Our approach can serve as the uniform formalised basis for development of mea…
Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering
2020
We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.
Efficient Analysis of Arbitrarily Shaped Inductive Obstacles in Rectangular Waveguides Using a Surface Integral Equation Formulation
2007
In this paper we propose to use the Surface Integral Equation technique for the analysis of arbitrarily shaped Hplane obstacles in rectangular waveguides, which can contain both metallic and/or dielectric objects. The Green functions are formulated using both spectral and spatial images series, whose convergence behavior has been improved through several acceleration techniques. Proceeding in this way, the convergence of the series is not attached to the employment of any particular basis or test function, thus consequently increasing the flexibility of the implemented technique. In order to test the accuracy and numerical efficiency of the proposed method, results for practical microwave c…
Numerical-Experimental Study Regarding the Single Point Incremental Forming Process
2021
The present paper proposes a numerical-experimental comparative study on the single point incremental forming process. A DC04 steel sheet with a thickness of 0.6 mm was used for both the numerical simulation using the finite element method and the experimental research. The type of trajectory used was a spiral trajectory and the finished part obtained was a truncated cone-shaped part. The analysis program used for simulation was Ls-Dyna. The simulations were performed in several variants: with a fixed mesh and with an adaptive mesh, using two different element formulations: 25 (Belytschko-Tsay formulation with thickness stretch) and -16 (fully integrated shell element modified for higher ac…
Deviations from equilibrium at the interface of a charged membrane
1989
The local equilibrium assumption commonly employed for the transport through the interface of a charged membrane has been analysed from a simplified electric double layer model. This layer is characterized on the basis of a surface potential arising from a non-zero surface charge density placed on the membrane surface. The dependence of deviations from local equilibrium on the characteristic parameters of the problem is shown. Connection with the classical treatment by Donnan is discussed. Although the complexity of the problem calls for a number of simplifications, the results obtained appears to be significative. Thus, the analysis carried out displays not only that deviations from equili…
Thermodynamics of Nanoparticles: Experimental Protocol Based on a Comprehensive Ginzburg-Landau Interpretation
2014
MATERIAUX+SMR:SDA; The effects of surface and interface on the thermodynamics of small particles require a deeper understanding. This step is crucial for the development of models that can be used for decision-making support to design nanomaterials with original properties. On the basis of experimental results for phase transitions in compressed ZnO nanoparticles, we show the limitations of classical thermodynamics approaches (Gibbs and Landau). We develop a new model based on the Ginzburg-Landau theory that requires the consideration of several terms, such as the interaction between nanoparticles, pressure gradients, defect density, and so on. This phenomenological approach sheds light on …
Bridging scales with thermodynamics: from nano to macro
2014
We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to curre…
Deep Gaussian Processes for Geophysical Parameter Retrieval
2018
This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well to large datasets, and improves prediction accuracy over standard full and sparse GP models. We give empirical evidence of performance for estimation of surface dew point temperature from infrared sounding data.