A Clear Example of Artificial Satellites Ruining the Sky

Here there is a brief overview of how are massive satellite networks (such as Starlink) interfering with astronomy. The article shows an attempt to capture Neowise, only to be surrounded with several dashes of orbiting satellites.

Free Books, Courtesy of Springer

Springer, has announced some days ago, that they are making available plenty of their books (aimed at higher education) for free during the coronavirus pandemic. "These books will be available via SpringerLink until at least the end of July." Take a look at the announcement and at the list of the texts available in english and german.

If you are going to download some of them, I encourage you to obtain them as .epub, since it is more space efficient than pdf.

Disclaimer: the source of the books is completely legal, given away by the publisher itself.

Contribute Towards a Treatment Against Covid-19 (Folding@Home)

Folding@Home, which is a distributed computing project aimed at simulating protein folding in order to combat diseases, has now released a project to model the interaction between the proteins in the virus surface and its receptors. By processing this data, progress could be achieved towards a therapeutic antibody, which can block viral proteins from binding its receptors This results in turn could help to develop treatments against the novel illness.

By joining the project, you donate some spare computing power to perform certain tasks. I’ve previously donated some computing power myself.

Tackling Chemical Equations with Multiple Balancing Solutions

In rare cases the reader may find chemical equations that can be balanced in multiple ways, providing several possibilities for the coefficients, without considering multiples of other solutions.

For instance, take the following equation.

$$a*CrC{l}_3+b*KI+c*C{l}_2+d*KOH\to e*K_{2}Cr{O}_4+f*KI{O}_4+g*KC{l}_3+h*H_{2}O$$

With some iterations, the following solutions might be found.

$$2*CrC{l}_3+2*KI+11*C{l}_2+32*KOH\to 2*K_{2}Cr{O}_4+2*KI{O}_4+28*KC{l}_3+16*H_{2}O$$ $$8*CrC{l}_3+3*KI+24*C{l}_2+88*KOH\to 8*K_{2}Cr{O}_4+3*KI{O}_4+72*KC{l}_3+44*H_{2}O$$

Both are mathematically correct. Are they chemically correct? First, we will explore why there are two possible answers. By transforming the chemical equation into a linear system, one equation is obtained per each chemical element and the coefficients a ,b...h  defined as variables.

$$$$$$\mathrm{Cr:\; a}=e$$
$$\mathrm{Cl:\; 3}a+2c=g$$
$$\mathrm{K:\; b}+d=2e+f+g$$
$$\mathrm{I:\; b}=f$$
$$\mathrm{O:\; d}=4e+4f+h$$
$$\mathrm{H:\; d}=2h$$
$$\mathrm{<br>}$$

Be noticed that the amount  of equations is directly linked to the number of chemical elements, while the variables are linked to the quantity of compounds. Therefore, the system is underdetermined, thus that either there are no solutions or there are infinite ones. In the previous case we already mentioned possible solutions hence there are infinite solutions that balance the chemical equation.

What would make the reaction proceed with different proportions in real life conditions? A given solution would be favored by the physicochemical conditions in which the reaction takes place. In more complex situations, some solutions will be "more correct" because they may describe correctly the true reaction by taking into account its mechanism.

$$$$

To avoid these chaotic situations, many chemical processes shan't be combined into a single equation. They must hold their independence to avoid ambiguities. Such simplifications may lead to quantitative errors. Similar expositions on the topic may be seen here or there. Not every chemical equation follows stoichiometry in real life reactions, be referenced to Cotton's Advanced Organic Chemistry where it talks about non molecular solids.

Enfrentando ecuaciones químicas con múltiples soluciones de balanceo

En extrañas ocasiones quizás se encontrará con alguna ecuación química que se podría balancear de más de una manera distinta. Donde hay distintas posibilidades para los coeficientes, obviando aquellos casos que son múltiplos de otras soluciones.

Obsérvese para efectos de estudio, el caso de la siguiente ecuación.

$$a*CrC{l}_3+b*KI+c*C{l}_2+d*KOH\to e*K_{2}Cr{O}_4+f*KI{O}_4+g*KC{l}_3+h*H_{2}O$$
$$\mathrm{<br>}$$ $$$$

Con un ligero muestreo, se podrían encontrar las siguientes maneras de balancearla.

$$2*CrC{l}_3+2*KI+11*C{l}_2+32*KOH\to 2*K_{2}Cr{O}_4+2*KI{O}_4+28*KC{l}_3+16*H_{2}O$$ $$8*CrC{l}_3+3*KI+24*C{l}_2+88*KOH\to 8*K_{2}Cr{O}_4+3*KI{O}_4+72*KC{l}_3+44*H_{2}O$$
$$\mathrm{<br>}$$

Ambas son matemáticamente correctas. ¿Serán químicamente correctas? Para ahondar en el tema, primero se explorará porqué es que se encontraron dos soluciones posibles. Se procede a expresar la ecuación química de manera algebraica, obteniendo una ecuación para cada elemento en la ecuación química, y tomando como variables los coeficientes a, b…h.

$$$$$$\mathrm{Cr:\; a}=e$$
$$\mathrm{Cl:\; 3}a+2c=g$$
$$\mathrm{K:\; b}+d=2e+f+g$$
$$\mathrm{I:\; b}=f$$
$$\mathrm{O:\; d}=4e+4f+h$$
$$\mathrm{H:\; d}=2h$$
$$\mathrm{<br>}$$

Obsérvese que la cantidad de ecuaciones está ligada a la cantidad de elementos químicos, y la de variables está relacionada con la cantidad de compuestos. Ante esta situación, se tiene un sistema infradeterminado, donde la cantidad de ecuaciones es menor a la cantidad de variables. En dichos sistemas, se puede dar que no haya ninguna solución, o bien que hayan infinitas soluciones. En el caso enunciado con anterioridad, ya se sabe de la existencia de soluciones, y por ende se concluye que hay soluciones infinitas para balancear la ecuación química.

¿Cuál es la justificación en el mundo real, para infinitas proporciones que pueden satisfacer la reacción? Una determinada solución se vería favorecida por las condiciones fisicoquímicas en las que se lleva a cabo la reacción. En casos más complejos, algunas soluciones serán “más correctas” por su afinidad describiendo el fenómeno real, si se tiene en cuenta el mecanismo de la reacción.

$$$$

Finalmente, para evitar casos tan caóticos como este, cabe resaltar que no se deberían combinar tantos procesos en una única ecuación química, sino mantener la independencia de cada una para evitar ambigüedades. Tales simplificaciones de procesos químicos pueden llevar a errores cuantitativos. Se pueden observar fenómenos similares aquí o allá… También vale la pena considerar que no toda ecuación química va a respetar la estequiometría en el mundo real, por ejemplo véase el capítulo de sólidos no moleculares en el libro Química Inorgánica Avanzada_Cotton.

Primer on the R Language

Disclaimer: This material is based on my notes during an R course. It also includes content I consider important for starting. The original material may be found in a GITLAB repository.

Introducction and Basic Interface Commands

Clean a session of R: Ctrl + L

Save a script,in Mac OS Command+S; Linux/Windows Ctrl+S

A command may be interrupted using Esc o Ctrl+C You may want to interrupt a command when there is a loop that just won’t finish

Define the workspace (In RStudio you can also use Session > Set Working Directory > Choose directory)

setwd("PATH")
#Insert the path of your workspace

To run a selected line: In Mac, Command+Enter. In Linux or Windows Ctrl+Enter.

Using R for arithmetical calculations

1+100

## [1] 101

The order of arithmetical operations is respected

(3+(5*(2^2)))

## [1] 23

3 + 5 * 2^2

## [1] 23

1/100000

## [1] 1e-05

Exponential notation may be used

3e2

## [1] 300

3e-2

## [1] 0.03

Trigonometrical functions

Trigonometrical functions are incorporated

•          cos(x)

•          sin(x)

•          tan(x)

•          acos(x)

•          asin(x)

•          atan(x)

For default you must use radians

sin(pi/2)

## [1] 1

Logarithms

The function log() is a natural logarithm Be noticed that the number e, is written as exp(1) in the R language

log(exp(1))

## [1] 1

For a logarithm of base ’n’, use logn()

log2(2)

## [1] 1

Rational Operators

•          ‘>’ More than

•          ‘<’ Less than

•          ‘<=’ Less or equal than

•          ‘>=’ More or equal than

•          ‘==’ Equal

•          ‘!=’ Different

4 != 4

## [1] FALSE

Logical Operators

•          ‘!’ Logical negation

•          ‘&’ Logical conjunction by element

•          ‘&&’ Logical conjunction

•          ‘||’ Logical disjunction

Variable Assignation

Use the operator ‘<- o:p="">

x <- span=""> 9 #Assigning 9 to the value of x

x #Check the value of x

## [1] 9

x <- span="">1/3
y <-x span="">+1

Basic rules for variable assignation

a.        They can’t start with numbers or ’_’

b.        There should not be blank spaces within the name

Vectorization

1:10 #Create a vector with all whole numbers from 1 up to 10

##  [1]  1  2  3  4  5  6  7  8  9 10

1+1:10 #Sum 1 to each member of the vector

##  [1]  2  3  4  5  6  7  8  9 10 11

var<- span="">1:10
var*2 #Multiply by 2 every member of the vector

##  [1]  2  4  6  8 10 12 14 16 18 20

Consult the variables created

ls()

Delete elements

rm()

Example:

t=1

rm(t)

Administrating packages

Check for installed packages

installed.packages()

Install package

install.packages()

Update packages

update.packages()

Delete package

remove.packages()

Download package

install.packages()

”Activate” a package

library()

Search for help in R

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help()