Fluid Dynamics

Navier-Stokes Equation

\rho [kg/m^3] : fluid density

\mu  [Pa\cdot s] : dynamic viscosity

\nu [N/\rho=m^2/s] : kinematic viscosity

\vec{V}=(u,v,w) [m/s] : velocity

\forall : volume

Conservation of mass

  1. For a system:

        \[ \frac{d}{dt}M_{SYS}=0 \]

  2. For a C.V. (Reynolds transport theorem):\]

    \[\frac{\partial}{\partial t}\int_{CV}{\rho d\forall}+\int_{CS}{\rho \vec{V}\cdot \hat{n} dA}=0 \]

Differential form (\delta x\delta y\delta z):

    \[ \frac{\partial}{\partial t}\int_{CV}{\rho d\forall}=\frac{\rho}{\partial t} \delta x\delta y\delta z \]

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RNN, LSTM & GRU

Recurrent Neural Network (RNN), Long-Short Term Memory (LSTM) & Gated Recurrent Unit (GRU)

Is a type of artificial neural network where connections between nodes form a sequence. This allows temporal dynamic behavior for time sequence.
There are 3 types of vanilla recurrent neural network: the simple (RNN), gated recurrent unit (GRU) and long short term memory unit (LSTM).

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Convolutional Neural Network (CNN)

Convolutional neural network introduction and tutorial

Introduction

Convolutional neural network (CNN or ConvNet) is a type of neural network used in artificial intelligence that is commonly applied to analyzing images.

They can be considered a pre-processing compared to image classification algorithms. They have applications in image and video recognition, recommender systems, image classification, natural language processing, etc.

Notation

f^l : filter size.
p^l : padding.
s^l : stride.
n^{l-1}_H \times n^{l-1}_W \times n^{l-1}_C: input.
n^{l}_H \times n^{l}_W \times n^{l}_C: output.
n^l = \floor{\frac{n^{l-1}+2p^l-f^l}{s^l}+1}.
f^l \times f^l \times n_c^l : filter.
a^l : activation function.
n_c^l : bias.

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RSA Algorithm

RSA encryption and decryption algorithm and implementation in C++

RSA is an algorithm used by modern computers to encrypt and decrypt messages. Modern encryption is mostly based on this algorithm.

It is an asymmetric cryptographic algorithm.

Asymmetric means that there are two different keys. This is also called public key cryptography because one of the keys can be given to anyone. The other key must be kept private, Elliptic curve algorithm uses asymmetric cryptography also.

The algorithm is based on the fact that finding the factors of a large composite number is difficult: when the integers are prime numbers, the problem is called prime factorization. It is also a key pair (public and private key) generator.

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Modern Cryptography

Cryptography introduction and different fields

Ancestors had the necessity to transmit information that could not be shared with the rest of the people, although messages may be intercepted and that was the beginnings of cryptography.

Encryption: conversion of information from a readable state to apparent nonsense.

The cryptography literature often uses the names Alice and Bob, who want to transmit information that could not be translated even being intercepted by a third party, Eve.

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