Science Topics

Look at the Rainbow in a Soap Film: A simple STEM Project

/ Danilo Roccatano / Leave a comment

My heart leaps up when I behold 
   A rainbow in the sky:
So was it when my life began; 
So is it now I am a man; 
So be it when I shall grow old, 
   Or let me die!
The Child is father of the Man;
And I could wish my days to be
Bound each to each by natural piety.

William Wordsworth, March 26, 1802


I couldn’t resist citing the beautiful poetry by Wordsworth about the rainbow to introduce my new Instructable, ‘Explore the Physics of Soap Films with the SoapFilmScope.’ I got the idea for this project by reading an article by Gaulon et al. [1]. The authors describe in detail the use of soap film as an educational aid to explore interesting effects in the fluid dynamics of this system. In particular, they examine the impact of acoustic waves on the unique optical properties of the film. In this Instructable, we have designed a device called the SoapFilmScope to perform these experiments. This tutorial will guide you through the process of creating this device, showcasing the mesmerizing interaction between sound waves and liquid membranes. The SoapFilmScope offers an engaging way to explore the physics of acoustics, light interference, and fluid dynamics.

When a sound wave travels through the tube and vibrates the soap film, it creates dynamic patterns through several fascinating mechanisms:

The device consists of a vertical soap film delicately suspended at the end of a tube obtained from a PVC T-shaped fitting that you can get from any DIY store. By attaching a small inexpensive speaker to it, you can let the film dance to the rhythm of the music.

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Retro Programming Nostalgia VI: Exploring the Hyperspace

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Henk Rogers: Um, I like Pascal. Assembler is my go-to. But never underestimate…
Alexey Pajitnov: …the power of BASIC.

From the movie Tetris (2023).

It has been a long while that I wanted to write this article. The usual motivation is to propose another of my BASIC programming explorations performed in the 80s on my Philips MSX VG-8010 and Amiga 500 microcomputer. The exploration was encouraged by the reading of another of the brilliant articles by A. K. Dewdney in his column “Ricreazioni al Calcolatore” (Computer Recreation) of Le Scienze, the edition in Italian of Scientific American [1]. Dewdney’s article was inspired by the beautiful book by Thomas F. Banchoff [2] who pioneered in the early 1990s the study using computer graphics of hyperdimensional objects.

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Exploring Disordered Proteins: A Study on Flexible Peptides

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Proteins are not always rigid structures. Many of their most important parts — linkers, loops, and disordered regions — are highly flexible, constantly changing shape in solution. To understand how these regions behave, scientists often study short model peptides that capture the essential physics of flexibility. In a new article [1], I have explored the behavior of glycine- and serine-rich octapeptides using molecular dynamics simulations combined with concepts from FRET (Förster Resonance Energy Transfer) spectroscopy (see also my previous post).

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Easter 2024: Dinosaur Eggs, Kinder Surprise, Drug Capsules, Jumping Beans Toy and Retro programming

/ Danilo Roccatano / 1 Comment

Oh my God. Do you know what this is? This is a dinosaur egg. The dinosaurs are breeding.

Dr. Alan Grant, Jurassic Park movie (1993)

We are again approaching Easter time and, as tradition, I would like to celebrate with an article dedicated to the most perfect thing in nature: the egg. I came across interesting books about the discovery of dinosaur eggs last year. Dinosaurs are the ancestors of birds and modern reptiles, so we will take a little detour from the traditional Easter egg, and with the spirit of equal opportunity justice, we will look at the shape of these.

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El cálculo de la constante de Madelung

/ Danilo Roccatano / Leave a comment

To all the Spanish-speaking readers, this is an AI-assisted translation experiment using WordPress. Please bear with me as my knowledge of the Spanish language is limited, so I cannot detect possible incorrect translations of the original test in Italiano. If you appreciate my efforts, please let me know. If you notice any errors in the translation, please send me a message to correct them. You can find my original versions in English, Italian, and German  language of this text by clicking the links.

Estimados lectores de habla hispana, este es un experimento de traducción asistida por IA utilizando WordPress. Les pido paciencia ya que mi conocimiento del idioma español es limitado, por lo que no puedo detectar posibles traducciones incorrectas del texto original en italiano. Si aprecian mis esfuerzos, por favor háganmelo saber. Si notan algún error en la traducción, por favor envíenme un mensaje para corregirlo. Pueden encontrar las versiones originales en inglés, italiano y alemán de este texto haciendo clic en los enlaces.

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Methods of Calculating Atomic Charges based on Electronegativity. Part I.

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The electronegativity of a chemical element measures the tendency of an atom to attract electrons around it. This definition was formalized for the first time, in a semi-empirical form, by the chemist Linus Pauling in the early 1930s, but it had already been proposed in the late 1800s by the Swedish chemist Berzelius. In molecules, this tendency determines the molecular electronic distribution and therefore influences molecular properties such as the distribution of partial charges and chemical reactivity. Pauling provided an electronegativity scale by comparing bond dissociation energies of pairs of atoms (A, B) using the equation

\chi_P=E_{AB}-\left(\frac{E_{AA}-E_{BB}}{2}\right)

With $E_{AB}$, $E_{AA}$, and $E_{BB}$ being the dissociation energies of the molecules AB, AA, and BB, respectively.

A few years later, in 1934, Mulliken proposed an expanded definition of electronegativity based on spectroscopically measurable atomic properties such as ionization potential (I) and electron affinity (E):

\chi_M=\left(\frac{I-A}{2}\right)

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I Metodi di Calcolo delle Cariche Atomiche basati sull’Elettronegatività. Parte I.

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L’elettronegatività di un elemento chimico misura la tendenza di un atomo ad attrarre intorno a sé elettroni. Questa definizione fu formalizzata per la prima volta, in forma semi-empirica, dal chimico Linus Pauling all’inizio del 1930, ma era già stata proposta nella seconda metà dell’1800 dal chimico svedese Berzelius. Nelle molecole, questa tendenza determina la distribuzione elettronica molecolare e quindi influenza le proprietà molecolari quali, per esempio, la distribuzione delle cariche parziali e la reattività chimica. Pauling ha fornito una scala di elettronegatività confrontando le energie di dissociazione di legame di coppie di atomi (A, B) usando la relazione

\chi_P=E_{AB}-\left(\frac{E_{AA}-E_{BB}}{2}\right)

con E_{AB}, E_{AA}, and E_{BB}, rispettivamente le energie di dissociazione delle molecole AB, AA, e BB.

Qualche anno dopo, nel 1934, Mulliken propose una definizione estesa di elettronegatività basata su proprietà atomiche misurabili spettroscopicamente, quali il potenziale di ionizzazione (I) e l’affinità elettronica (E):

\chi_M=\left(\frac{I-A}{2}\right)

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Retro Programming Nostalgia V: Phase Plane of Autonomous Planar System of DE

/ Danilo Roccatano / Leave a comment

What is the origin of the urge, the fascination that drives physicists, mathematicians, and presumably other scientists as well? Psychoanalysis suggests that it is sexual curiosity. You start by asking where little babies come from, one thing leads to another, and you find yourself preparing nitroglycerine or solving differential equations. This explanation is somewhat irritating, and therefore probably basically correct. David Ruelle, in Chance and Chaos

Here I am again for a new appointment with the Italian version of the column “Retro Programming Nostalgia“, my very own adventure in computer archaeology, rediscovering old programs written some time ago on microcomputers that have made their mark on an era.

This time, in my old floppy disks for the glorious Amiga 500, I found a program in Amiga Basic that I wrote during the early years of my university studies, when I was taking the course on differential equations II. Specifically, I was very fascinated by autonomous systems of differential equations due to their numerous applications in mathematical modeling of physical, chemical, and biological systems, as well as their importance in the theory of chaos. As in the series articles, I want to release an adapted version for the QB64 BASIC meta-compiler, but before presenting the program, I want to briefly explain what an autonomous system of differential equations is.

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Retro Programming Nostalgia V: Sistemi Autonomi di Equazioni differenziali

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“Qual è l’origine del desiderio, della fascinazione che spinge i fisici, i matematici e presumibilmente anche altri scienziati? La psicoanalisi suggerisce che si tratti di curiosità sessuale. Si comincia chiedendosi da dove vengano i bambini piccoli, una cosa porta all’altra e ci si ritrova a preparare il nitroglicerina o a risolvere equazioni differenziali. Questa spiegazione è un po’ irritante, e quindi probabilmente fondamentalmente corretta.” – David Ruelle, in “Chance and Chaos”

Eccomi di nuovo per un nuovo appuntamento con la versione in italiano della Rubrica “Retro Programming Nostalgia “, la mia personalissima avventura d’ archeologia informatica alla riscoperta di vecchi programmi scritti qualche tempo fa su microcomputers che hanno segnato un’epoca.

Questa volta, nei miei vecchi dischetti per il glorioso Amiga 500, ho trovato un programma in Amiga Basic che scrissi durante i primi anni dei miei studi universitari, quando studiavo nel corso di matematica II, i sistemi d’equazioni differenziali. In particolare, ero molto affascinato dai sistemi di equazioni differenziali autonomi per via delle molteplici applicazioni nella modellazione matematica di sistemi fisici, chimici e biologici, e per la loro importanza nella teoria del caos. Come negli articoli della serie, voglio rilasciare una versione riadattata per il meta compilatore QB64 BASIC, ma prima di presentare il programma, voglio brevemente spiegare cosa sia un sistema autonomo di equazioni differenziali.

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Madelung定数の計算

/ Danilo Roccatano / 1 Comment

To all Japanese-speaking readers, this text is part of an experiment using AI translation and WordPress. We kindly ask for your understanding and cooperation. If you find value in this initiative, please let us know. Additionally, if you notice any translation inaccuracies, we would greatly appreciate it if you could contact us. You can find the original text in English, Chinese, Italian, and German by clicking the links.

親愛なる日本語を話す読者の皆様へ、これはワードプレスを使用したAI翻訳の実験です。私の成長と改善にご協力いただければ幸いです。私の取り組みを評価していただける場合は、ぜひお知らせください。翻訳に誤りを見つけた場合は、修正するためにメッセージをお送りください。英語、中国語、イタリア語、ドイツ語のオリジナルテキストは、リンクをクリックすることで見つけることができます。

以前の記事で、結晶の格子エネルギーにおける静電エネルギー項の計算について説明しました。この記事では、この項を計算する方法について詳しく説明し、また単純なイオン系におけるこの項の値を提供します。

晶体の総クーロン相互作用エネルギーは、個々の相互作用項の合計として与えられます。

\displaystyle V_{AB} = \frac{e^2}{4\pi \epsilon_0} \frac{Z_AZ_B}{r_{AB}} \hfill (1)

固体の結晶構造では、電荷qAとqBを持つイオン対の間の距離rABによって生じるクーロン相互作用力で構成されます。この和は、固体中のすべてのイオン対にわたって計算されます。

最初の近傍は負の重要な寄与を提供するため、この和は非常に遅く収束します。2番目の近傍原子はわずかに弱い正の項を生成します。このプロセスは無限遠まで続き、交互の符号でますます小さい値を通じて行われます。このようにして、陽イオンと陰イオンの間の引力が主導し、固体のエネルギーに有益な負の寄与を提供します。

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