Concept

Tableau périodique des éléments

Notebooks associés (12)

Illustrating Band Structures in Solids: Free Electrons and Atomic Orbitals

In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib widget The emergence of band structures[1]¶ If you have questions about this notebook, e-mail Oleg Malanyuk (oleg.malanyuk@epfl.ch) This jupyter notebook is intended to provide a illustration of the band structures in solides, starting from the points of v

Basic band structure calculation using the tight-binding approximation for a 1D periodic chain with two sites per unit cell

Ce notebook fournit un exemple de base du calcul de la structure de bande pour une chaîne périodique unidimensionnelle d'atomes avec deux sites par cellule unitaire, en utilisant l'approximation de la liaison serrée. Il construit l'hamiltonien en projetant les sauts intercellulaires et intracellulaires sur les sites A et B. Le notebook permet une exploration interactive de la façon dont différents paramètres, tels que les intégrales de saut et les énergies sur site, influencent la structure de bande.

Wavepacket construction and propagation in 1D tight-binding model

"# Wavepacket construction and propagation along the 1D chain \n", "\n", "## Introduction\n", "In this notebook, we demonstrate the wavepacket construction and propagation, which is at the heart of the semiclassical approximation. For simplicty, we will consider the familiar 1D chain described using the tight-binding Hamiltonian. We will have to take a sufficiently large number of sites

N

and impose periodic boundary conditions. For simplicity, in the code below we assume lattice constant $a =

Wave Interference

The plotted function is the superimposition of $n$ 2d-sine functions centered in $(0,Y_i)$: $$f(x,y)=\sin\big(p\cdot\sqrt{x^2+(y-Y_i)^2}\big)$$ The parameters that can be changed are: -- $n$ the number of sources (start with 2) -- $d$ the distance between sources -- $p$ the periodicity. Higher periodicity means shorter wavelength. $p =2\pi / \lambda$. Note that in electron microscopy the usual convention is to define the wave vector as $k=1/\lambda$. -- $f$ the field o

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

Real vs. Reciprocal Space in 2D[1]¶ Introduction[2]¶ In this short notebook, we will introduce the lattice with periodic(Born- von Karman) boundary condition. Following the boundary condition, there is a transformation from real lattice to the reciprocal lattice. In the code below, we define a1 and a2 through cartesian vectors. Hence, the reciprocal vectors will be the original rotated by 90 degrees multiplied by 2pi and divided by the area of the unit cell (|a1xa2|) In [1]: i

Understanding Hund s Rules

numbers

S

L

and

J

of an isolated atom or ion from its electronic configuration. Considering a partially filled electronic shell, the following three rules have to be applied in the order given below: 1. The total spin angular momentum

S=\Sigma|m_s|

takes its maximum possible value; 2. The total orbital angular momentum

L=\Sigma|m_l|

is maximized; 3. For more than half-filled shell, the total angular momentum number

J=L+S

, otherwise

J=\vert L-S \vert

. The sl

Adaptive Echo Cancellation using LMS Filter

Adaptive Echo Cancellation[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In this notebook we will use the adaptive LMS filter to estimate the impulse response of a reverberating room. A typical use case is handsfree telephony: since the received signal, amplified and played by the speaker, is picked up by the microphone, we need to eliminate it from the signal that is transmitted back in order to avoid a feedback loop. The signal picked up by the microph

Basic Example of Anderson Localization in a 1D System

Demonstration of Anderson localization[1]¶ This notebook is intended to show a very basic example of the Anderson localization in one-dimensional system. In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib inline To show the idea of Anderson localization, we can consider 1D chain of

N

atoms with perio

Estimation of Electron Density and Mean Free Time for Transparent Conductors

Chapter 1: Transparent Conductors[1]¶ Instruction: The purpose of this notebook is to try and find values of electron density and mean free time for a material suitable to be used as a transparent conductors. The final estimate should be the order of the two parameters to be used[2]¶ In [1]: import numpy as np from bokeh.io import push_notebook, output_notebook, show from bokeh.layouts import row, column from bokeh.plotting import figure output_notebook() from ipywidgets import interact from collect

Exploring the Karplus-Strong Algorithm for Sound Synthesis

The Karplus-Strong Algorithm[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

The Karplus-Strong algorithm is a simple method to generate synthetic sounds with arbitrary pitch. In this notebook we will explore a few variations of the method to illustrate some basic notions of discrete-time signal processing. In [1]: %matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython In [2]: plt.rcParams["figure.figsize"]

Understanding and Plotting the Discrete Fourier Transform (DFT)

Plotting the DFT[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In this notebook we will look at the practical issues associated to plotting the DFT and in particular the DFT of real-world signals. We will examine how to map the DFT coefficients to real-world frequencies and we will investigate the frequency resolution of the DFT and the effects of zero padding. In [1]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.p

Building a Dual-Tone Multi-Frequency (DTMF) Decoder using Short-Time Fourier Transform

Dual-tone multi-frequency (DTMF) signaling[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In this notebook we will build a dual-tone multi-frequency decoder based on the short-time Fourier transform. In [1]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython In [2]: plt.rcParams["figure.figsize"] = (14,4)

Introduction[4]¶ DTMF signaling is the way analog phones send the n

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Notebooks associés (12)

Illustrating Band Structures in Solids: Free Electrons and Atomic Orbitals

In [1]: import numpy as np from numpy import linalg as LA import matplotlib.pyplot as plt

from future import print_function

Basic band structure calculation using the tight-binding approximation for a 1D periodic chain with two sites per unit cell

Wavepacket construction and propagation in 1D tight-binding model

N

and impose periodic boundary conditions. For simplicity, in the code below we assume lattice constant $a =

Wave Interference

Introduction to Reciprocal Lattices with Periodic Boundary Conditions.

Understanding Hund s Rules

numbers

S

L

and

J

S=\Sigma|m_s|

takes its maximum possible value; 2. The total orbital angular momentum

L=\Sigma|m_l|

is maximized; 3. For more than half-filled shell, the total angular momentum number

J=L+S

, otherwise

J=\vert L-S \vert

. The sl

Adaptive Echo Cancellation using LMS Filter

Adaptive Echo Cancellation[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Basic Example of Anderson Localization in a 1D System

from future import print_function

from ipywidgets import interact, interactive, fixed, interact_manual import ipywidgets as widgets %matplotlib inline To show the idea of Anderson localization, we can consider 1D chain of

N

atoms with perio

Estimation of Electron Density and Mean Free Time for Transparent Conductors

Exploring the Karplus-Strong Algorithm for Sound Synthesis

The Karplus-Strong Algorithm[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

Understanding and Plotting the Discrete Fourier Transform (DFT)

Plotting the DFT[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.p

Building a Dual-Tone Multi-Frequency (DTMF) Decoder using Short-Time Fourier Transform

Dual-tone multi-frequency (DTMF) signaling[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In this notebook we will build a dual-tone multi-frequency decoder based on the short-time Fourier transform. In [1]:

first our usual bookkeeping

%matplotlib inline import matplotlib import matplotlib.pyplot as plt import numpy as np import IPython In [2]: plt.rcParams["figure.figsize"] = (14,4)

Introduction[4]¶ DTMF signaling is the way analog phones send the n