The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.

$$\boxed{{\displaystyle \boxed{{\displaystyle \hat{f}(\xi )={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(x)e^{-i2\pi \xi x}\mathrm{d}x,\mathrm{\forall }\xi \in \mathbb{R}.}}}}$$

Inverse Fourier Transform:
$$\boxed{{\displaystyle \boxed{{\displaystyle f(x)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\hat{f}(\xi )e^{i2\pi \xi x}\mathrm{d}\xi ,\mathrm{\forall }x\in \mathbb{R}.}}}}$$

The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: http://bit.ly/22kbNfi

King Most livestream on #kalw from 111 Minna for #DFT #sanfrancisco #dj

Just delivered a talk on algorithmic differentiation in our #dftk density-functional theory code at the #cecam workshop on #dft and #ai

Slides: https://michael-herbst.com/talks/2025.03.04_DFT_AI_Learning_each_other.pdf
#julialang demo: https://michael-herbst.com/talks/2025.03.04_DFT_AI_Learning_each_other_design.html

@schmitz (left) explaining his recent work on making #dftk algorithmically #differentiable at the #cecam workshop on #dft and #ai (https://www.cecam.org/workshop-details/1281). With his work derivatives of key density-functional theory quantities like forces or band structures wrt. model parameters can now be easily computed.

https://www.dsprelated.com/freebooks.php

I am shamefully copying this post from Linkedin but if you happen to know any candidate, do not hesitate to reach:

It's on. To my #ComputationalChemistry network, I am calling on you.

The PM2E team in the CIMAP laboratory (www.cimap.ensicaen.fr) is looking for a #PhD hashtag#candidate. The goal of the project is to understand key parameters in #semiconductor defects stability and physics (both vacancies and color centers, see for example: https://doi.org/10.1016/j.nimb.2022.12.025) through the use of
#DFT and #MolecularModeling. The end goals of the project is concerned with application for #QuantumComputing through the making of stable #qubit. Collaboration and communication with experimentalists will be part of the project.

If you're interested in #MolecularDynamics, #MonteCarlo simulations, or DFT and quantum calculations, we are waiting for you. We are using codes such as #Lammps and #QuantumEspresso. We are looking for a candidate finishing or already having a master degree (or equivalent diploma) with training in #physics/ #MaterialsScience / #TheoreticalChemistry. Any experience in programming using #Python, #C and the #Linux environment would be considered a plus.

The position is located in Alençon (Orne) between Caen and Le Mans. Founding is assured for relevant candidates.

Link to the offer (in french, you can ask for an english version): https://www.abg.asso.fr/en/candidatOffres/show/id_offre/127985/job/simulation-atomistique-de-defauts-crees-par-irradiation-dans-les-semiconducteurs

Finally, completely published in Carbon. New paper investigating the effect of strain on the ZPL of GeV color centers in (using #DFT )...as usual we learned a few things we didn't really want to learn: supercell size matters, you should extrapolate for exp. ppm %.
Had interesting discussions with our experimental partners of the WBGM group. For those interested: free access until Feb 28 via
https://authors.elsevier.com/a/1kPZ91zUAZr7H

#Transport and #TransportPlanning people, follow @DfTAnswers and you should see #DfT’s answers to parliamentary questions.

https://www.newcivilengineer.com/latest/lord-hendy-forced-systra-to-sack-engineer-for-raising-concerns-about-crowd-crush-at-euston-station-29-08-2024/

Probably the best article yet about the mess at the #DfT when the rail minister starts to make problems go away by forcing companies to fire the people raising the issues!

"There is not one density functional that performs equally well for all of these properties, not even within one class of density functionals." https://doi.org/10.21468/SciPostChem.3.1.001 #chemistry #dft

#PhDposition at UHasselt (BE) #QuATOMs group.

Are you a MSc. #chemistry , #physics , or #materiomics with an interest in #QM modelling? Up for a challenge? You love #HPC & #DFT ? Want to learn more about Lignin ?

Apply https://tinyurl.com/3jhdwnsw before 21/08/24.

(NL version: https://lnkd.in/gjWSrfuC
)

'Traffic levels in England and Wales are projected to grow by as much as 54% by 2060, predicts the U.K. government’s Department for Transport (DfT).'

https://www.forbes.com/sites/carltonreid/2022/12/13/uks-transport-ministry-predicts-54-traffic-rise-over-next-35-years-building-more-roads-will-make-this-worse/

'In a projections report issued December 12, the DfT also said road delays could rise by 85% to 2060.'

It's wild that we might be on the brink of WWIII, in no small part because of Donald Fucking Trump, and some people think the best President at this time would be... Donald Fucking Trump. #DFT

Lots of changes to #TAG Transport Appraisal Guidance announced recently by #DfT, going live in November.

Details at https://www.gov.uk/government/publications/tag-forthcoming-changes.
Tag-at-a-Glance on my website has a unit-by-unit summary of what's new: https://grahamjames.co.uk/tag-at-a-glance/

#transportplanning #bedtimereading @transport

My week at work (HS2 news edition): what the PM's announcement means for clients and communities, and what they will need to do next. Plus dependent development appraisal, rail connectivity and capacity planning, and new guidance on valuing and presenting carbon impacts.

Looking forward to the #DfT #TAG conference starting on Monday.

Photo is nothing to do with transport, just a nice thing near the office.

UK's Department for Transport #DfT thinks England needs a database of #ActiveTravel & #CyclingInfrastructure, to know what exists where, whether it complies with standards such as #LTN120, what's being built where etc.

"Active travel geospatial report " (2022) https://www.gov.uk/government/publications/walking-and-cycling-statistics-notes-and-definitions with PDF https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1101004/active-travel-discovery-report.pdf

Possible platforms include #OpenStreetMap, #ArcGIS, #OrdnanceSurvey etc.

Overall, paper asks lots of questions, offers options, doesn't make specific recommendations.