Search results for "Mathematica"
showing 10 items of 7971 documents
Relations between multi-resolution analysis and quantum mechanics
2005
We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA. © 2005 American Institute of Physics.
Resolution of the ATLAS muon spectrometer monitored drift tubes in LHC Run 2
2019
The momentum measurement capability of the ATLAS muon spectrometer relies fundamentally on the intrinsic single-hit spatial resolution of the monitored drift tube precision tracking chambers. Optimal resolution is achieved with a dedicated calibration program that addresses the specific operating conditions of the 354 000 high-pressure drift tubes in the spectrometer. The calibrations consist of a set of timing offsets and drift time to drift distance transfer relations, and result in chamber resolution functions. This paper describes novel algorithms to obtain precision calibrations from data collected by ATLAS in LHC Run 2 and from a gas monitoring chamber, deployed in a dedicated gas fac…
Investigating the Affordances and Constraints of SimReal for Mathematical Learning : A Case Study in Teacher Education
2019
Visualizations tools are one of the most innovative technologies that emerged the last few years in educational settings. They provide new potentialities for mathematical learning by means of dynamic animations and representations, interactive simulations, and live streaming of lessons. Moreover, visualization tools have the potential to foster a visual, dynamic, distributed, and embodied mathematics rather than individual achievements and static representations. This paper uses the visualization tool SimReal in teacher education to explore the affordances of the tool for learning mathematics. It proposes a framework that captures the affordances of SimReal at a technological, pedagogical, …
On the Reception of Grassmann’s Work in Germany during the 1870’s
1996
It has often been remarked that Grassmann’s mathematics was not widely appreciated during his lifetime. Although awareness of the dimensions of his achievements began to spread in the early 1870’s, even in Germany relatively few mathematicians appear to have been well acquainted with either the original 1844 edition of Grassmann’s Ausdehnungslehre or the mathematically more accessible edition of 1862. The main reasons for this weak and rather delayed reception have been described often enough---Grassmann’s isolated working environment and his nearly impenetrable language---but there are a number of related aspects that still deserve closer consideration.1
A compliant visco-plastic particle contact model based on differential variational inequalities
2013
This work describes an approach to simulate contacts between threedimensional shapes with compliance and damping using the framework of the differential variational inequality theory. Within the context of nonsmooth dynamics, we introduce an extension to the classical set-valued model for frictional contacts between rigid bodies, allowing contacts to experience local compliance, viscosity, and plasticization. Different types of yield surfaces can be defined for various types of contact, a versatile approach that contains the classic dry Coulomb friction as a special case. The resulting problem is a differential variational inequality that can be solved, at each integration time step, as a v…
Singular points of electrochemical impedance function
2004
A model of EIS response for a system with two consecutive monoelectron transfers is developed in this work. Relevant information on the mechanism of these electrochemical systems is provided by the parametrical identification of the theoretical faradaic impedance function. The kinetic parameters of this model are easily calculated through the calculus of the characteristic points of this function. This calculus allows to interpret the metals anodic dissolution according to the reaction mechanism and, therefore, allows us to establish easily the kinetic and thermodynamic behaviour of these systems with respect to any experimental parameter.
Estimation of peak capacity based on peak simulation.
2018
Peak capacity (PC) is a key concept in chromatographic analysis, nowadays of great importance for characterising complex separations as a criterion to find the most promising conditions. A theoretical expression for PC estimation can be easily deduced in isocratic elution, provided that the column plate count is assumed constant for all analytes. In gradient elution, the complex dependence of peak width with the gradient program implies that an integral equation has to be solved, which is only possible in a limited number of situations. In 2005, Uwe Neue developed a comprehensive theory for the calculation of PC in gradient elution, which is only valid for certain situations: single linear …
Variances as order parameter and complexity measure for random Boolean networks
2005
Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.
2019
Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…
Answering Schrödinger's "What Is Life?"
2020
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