
via University of Bristol
A Bristol academic has achieved a milestone in statistical/mathematical physics by solving a 100-year-old physics problem – the discrete diffusion equation in finite space.
The long-sought-after solution could be used to accurately predict encounter and transmission probability between individuals in a closed environment, without the need for time-consuming computer simulations.
In his paper, published in Physical Review X, Dr Luca Giuggioli from the Department of Engineering Mathematics at the University of Bristol describes how to analytically calculate the probability of occupation (in discrete time and discrete space) of a diffusing particle or entity in a confined space – something that until now was only possible computationally.
Dr Giuggioli said: “The diffusion equation models random movement and is one of the fundamental equations of physics. The analytic solution of the diffusion equation in finite domains, when time and space is continuous, has been known for a long time.
“However, to compare model predictions with empirical observations, one needs to study the diffusion equation in finite space. Despite the work of illustrious scientists such as Smoluchowski, Pólya, and other investigators of yore, this has remained an outstanding problem for over a century—until now.
“Excitingly, the discovery of this exact analytic solution allows us to tackle problems that were almost impossible in the past because of the prohibitive computational costs.”
The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells, bacteria roaming in a petri dish, animals foraging within their home ranges, or robots searching in a disaster area.
It could even be used to predict how a pathogen is transmitted in a crowd between individuals.
Solving the conundrum involved the joint use of two techniques: special mathematical functions known as Chebyshev polynomials, and a technique invented to tackle electrostatic problems, the so-called method of images.
This approach allowed Dr Giuggioli to construct hierarchically the solution to the discrete diffusion equation in higher dimension from the one in lower dimensions.
The Latest Updates from Bing News & Google News
Go deeper with Bing News on:
Transmission probability
- Tidying Up Nigeria’s Power Transmission System
Emmanuel Addeh writes that transmission, which is one of the tripod on which Nigeria’s electricity supply system rests, could be up for good news soon with the federal government’s renewed ...
- Rabies in Goats
Episode 93For the Love of Goats Although rabies in goats is not common, it is possible. In today’s episode we are talking to Dr. Kevin Pelzer, a Professor of Large Animal Clinical Science, ...
- Is your fleet using the right fluids?
Fluids run from the front at the radiator to the rear in the differential of the vehicle. Is your fleet getting it all right?
- Long-Term Triangle Breakdown; F&O Stock Shows ‘Massive Downside’!
The Nifty 50 index is witnessing increased selling pressure going into the session’s close, currently trading 0.66% down at 16,963, by 3:02 PM IST. All sectors are trading with a cut with Nifty Media ...
- Risk Analysis: Beyond Probability and Severity
9 This article addresses another aspect of risk evaluation: the consideration of factors other than the probability of harm occurrence and the severity of that harm if it were to occur. While the ...
Go deeper with Google Headlines on:
Transmission probability
[google_news title=”” keyword=”transmission probability” num_posts=”5″ blurb_length=”0″ show_thumb=”left”]
Go deeper with Bing News on:
Covid-19 transmission
- Amid spike in Covid-19, influenza cases, Health Ministry issues fresh guidelines: ‘Avoid overcrowding, wear masks’
Re-emphasising the need for robust testing, the statement noted that in the past several weeks, in some states, Covid-19 testing has declined and the current testing levels are insufficient as ...
- 2023-2029 Transmission Electronics Market: Understanding Growth Opportunities
Mar 25, 2023 (The Expresswire) -- "Final Report will add the analysis of the impact of COVID-19 on this industry." Latest [102 Pages] “Transmission Electronics Market” forecast report for the period ...
- Advocate Health Moves to Relax COVID-19 Protocols
Masking will continue to be required for visitors of patients in “transmission-based isolation,” including patients who are COVID-19 positive. Get Chicago local news, weather forecasts, sports and ...
- Covid-19 watch: Centre plans nationwide mock drill at hospitals, issues fresh advisory
Amid rising cases of COVID-19 and seasonal influenza, the government is planning a nationwide mock drill on April 10 and 11 to take stock of hospital preparedness. According to a joint advisory issued ...
- Advocate Health Care shifting to optional masking policies as COVID-19 cases remain low in Illinois
The shift marks the first easing of masking requirements at the health system since the pandemic hit more than three years ago ...
Go deeper with Google Headlines on:
Covid-19 transmission
[google_news title=”” keyword=”Covid-19 transmission” num_posts=”5″ blurb_length=”0″ show_thumb=”left”]