Diffusion and Random Walks

Imagine you've just added a packet of dry flavored drink powder to a bottle of water without doing anything else to mix it together. How long will it take to fully dissolve so that you can no longer sense any of the texture of the powder on your tongue whenever you take a drink?

How long that might takes depends on the mechanics of diffusion, which is described as the net movement of particles from an area of higher concentration to an area of lower concentration. It doesn't matter whether those particles are atoms, molecules, aromas, viruses, drink mixes, foraging animals, et cetera, the process of diffusion ensures that eventually, the particles will go from being concentrated to being uniformly spread out in the medium to which they have been added.

The following video starts with an experiment the differences in how drops of colored dye become diffused in liquid water held at different temperatures, before introducing the math of random walks and how they lead to the equations that define the process of diffusion. The presenter also manages to throw in a biblical reference to explain what diffusion is, all in less than 13 minutes.

If you want to graduate to modeling random walks in diffusion, we'll point you to another video that provides both an introduction into two-dimensional random walks without any biblical references, but with its own special kind of goofy fun, before getting into how to program a random walk using Monte Carlo simulations in the Python programming language.

Solving diffusion problems represents a big challenge, because traditionally, their solution through modeling random walks requires lots of computing resources to approximate solutions using iterative numerical analysis. Or did, until this year, when Luca Giuggioli worked out how to more easily frame these kinds of problems for direct solution using mathematical tools originally developed to solve other problems, such as Chebyshev polynomials and the method of images (video).

The diffusion equation models random movement and is one of the fundamental equations of physics. To compare model predictions with empirical observations, the diffusion equation needs to be studied in finite space. When space and time are continuous, the analytic solution of the diffusion equation in finite domains has been known for a long time. But finding an exact solution when space and time are discrete has remained an outstanding problem for over a century—until now. I find the analytic solution of the discrete diffusion equation in confined domains and use it to predict how the probability for various reaction diffusion processes changes over time.

I make 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 allows me to construct hierarchically the solution to the discrete diffusion equation in higher dimensions from the one in lower dimensions.

The exact solution allows me to calculate transport quantities that, until now, could be derived only via time-consuming computer simulations or not at all because of prohibitive computational costs. In the context of random search processes, it is now possible to calculate accurately the probability for a “searcher” to reach a target for the first time, to return to its initial starting position, and to remain trapped at special defective locations.

These findings are directly relevant to a vast number of applications such as molecules moving inside a cell, animals foraging for resources in their home ranges, robots searching in a disaster area, and humans passing information or a disease.

That last bit explains the focus of the press release that accompanied Giuggioli's paper's publication, coming as it did during the global coronavirus pandemic of 2020, but which we think actually diminishes the accomplishment. In crafting a framework that allows direct solution of the equations describing diffusion processes, Giuggioli's approach has the potential to greatly reduce the amount of time and computing resources required to reach useful solutions across a wide range of applications. It's a leading contender to become one of the biggest math stories of the year.

References

Giuggioli, Luca. Exact Spatiotemporal Dynamics of Confined Lattice Random Walks in Arbitrary Dimensions: A Century after Smoluchowski and Pólya. Physical Review X. Vol. 10, Iss. 2 — April - June 2020 – Published 28 May 2020. DOI: 10.1103/PhysRevX.10.021045.

Johnston, Derek. An Introduction to Random Walks. [PDF Document]. 5 August 2011.

Bazant, Martin. 18.366 Random Walks and Diffusion. Fall 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA. [Course Home | Study Materials]. Fall 2006.

Australian Politics 2020-07-30 15:37:00

Uncategorized

African women lived it up at a cocktail bar, Thai restaurant and NINE other venues after lying about flying into Queensland from Melbourne - and they may have sparked a major COVID-19 cluster

A coronavirus-infected teenager enjoyed trips to a cocktail bar and a Thai restaurant after returning to Queensland from Melbourne and lying about where she had been.

There are fears Olivia Winnie Muranga and Diana Lasu's extraordinary disregard for COVID-19 rules could spark a Victoria-style outbreak in Queensland, which recorded its first community transmission in two months on Wednesday.

The pair, both 19, arrived together in Brisbane from Melbourne via Sydney on July 21 and made false declarations on their border paperwork. They are expected to be fined \$4,000 each.

A third woman who travelled with the women from the Victorian capital has already been fined and is awaiting her test results for coronavirus.

It is believed all three lived the high life around Brisbane for eight days, going to work, visiting restaurants and bars.

A third woman who tested positive to coronavirus yesterday is believed to be the 22-year-old sister of one of the teenagers.

Ms Muranga went to work for two days at Parklands Christian College in Park Ridge, south of the city. She called in sick and went to see a doctor on Saturday who told her to get tested immediately.

She didn't do so until Monday.  Instead she continued to attend venues in Ipswich and Brisbane, including going to a Thai restaurant in Springfield on Sunday and a Southbank cocktail bar on Monday.

On Thursday Queensland's Deputy Police Commissioner Steve Gollschewski said the women are now involved in an ongoing police investigation. Authorities will probe how the women were able to travel from Melbourne to Brisbane despite the border closure, and whether they used fake names and contact details on their declaration passes.

Investigators will also probe whether the women were at party during their stay in Melbourne which was attended by about 20 people. The gathering was broken up by police, who issued fines totalling \$30,000.

Ms Muranga is a cleaner at Parklands Christian College in Park Ridge. The school's principal Gary Cully confirmed a coronavirus-infected cleaner worked for three days last week.'The staff member was on site last week and then rang in sick and then that's when the trace program started,' Mr Cully told The Courier Mail.

'As far as I'm aware they were not symptomatic while they were onsite and then called in sick the following day and then the next week were tested.'

Shopping centres, restaurants, a school, and a church they visited will shut while authorities scramble to conduct contact tracing.

The pair took flight VA863 from Melbourne to Sydney and flight VA977 from Sydney to Brisbane, 21 July

Scores of the women's contacts will be forced to isolate, and aged care facilities in the Metro South Health region will re-enter lockdown.

The incident prompted Queensland Premier Annastacia Palaszczuk to announce all Sydneysiders will be banned from entering the state from Saturday. 'There will be a thorough police investigation here but now we have to act as a community and in the areas where the chief health officer says need to be closed, will be closed and I urge people in those areas when that list goes out later on today to please ensure that if you are feeling sick you must go and get tested,' she said.

Queensland residents returning will have to isolate in a hotel for 14 days at their own expense.

Queensland Chief Health Officer Dr Jeannette Young called the pair 'reckless' and said she was 'very disappointed'.

Health Minister Steven Miles said there was a large amount of contact tracing that needed to be done with the community as well. 'These young women have gone about their business within the communities that they live in and so there will be a large amount of contact tracing to be done, largely within it the Logan and Springfield areas, including shopping malls, restaurants and a church.'

The pair's entry into Queensland is the subject of a criminal investigation, with penalties for lying on your declaration form incurring fines of \$4,003 or six months in jail.

There are now eight actives cases left in Queensland following three new cases on Wednesday.

SOURCE

A report from more than 150 experts and affected community members has called on the government to punish climate change enablers

Climate skeptics would like to see this go to court.  The case would collapse like a house of cards when the full weight of scientific evidence about global warming was led

In a sobering study released this week, Australia was revealed to have lost nearly three billion animals due to the devastating Black Summer bushfires.

The fossil fuel industry has “pushed Australia into a new bushfire era” and should pay for the carnage inflicted from blazes and other disasters across the country, former emergency leaders, climate scientists and doctors have declared.

The Emergency Leaders for Climate Action (ELCA), a group of more than 150 experts and affected community members, have called on the Federal Government to impose a levy on those contributing to climate change.

As part of the 165 recommendations, the group wants a climate disaster fund set up to cover the massive costs associated with natural disasters.

The rising impact of global warming evidenced in the summer’s devastating and extensive bushfires has created the need to “fundamentally rethink how we prepare for and manage this growing threat”, former Fire and Rescue NSW Commissioner Greg Mullins said.

“This plan outlines practical steps that all levels of government can take right now to better protect communities,” he said, who is also a Climate Councillor.

“It’s important that the Federal Government takes these recommendations seriously and acts on them urgently. “First and foremost, the Federal Government must tackle the root cause of climate change by urgently phasing out fossil fuels to reach net zero emissions.”

The declaration comes ahead of the royal commission report into the destructive bushfire season which is due to be handed to government next month, which Mr Mullins hopes will include provisions for a climate response.

The cost of extreme weather events is growing towards a total annual bill of \$39 billion by 2050, Deloitte Access Economics partner Nicki Hutley said, who also contributed to the report.

“Climate change, which is fuelling more severe extreme weather events and worsening bushfire danger, has serious economic consequences,” she said.

“Reducing emissions, building community resilience, and boosting emergency resourcing can help us avoid huge economic impacts and damage in the future, while creating clean new jobs right now.”

The report comes as the government faces increasing pressure to invest in a major green energy plan, with groups from across the political spectrum declaring an investment is imminent to help propel the economy out of the virus crisis.

Once the iconic divide between conservative and progressive politicians, activists and lobby groups say the need for action on climate change has reached a boiling point with evidence of environmental damage now being undeniable.

“The pressure is growing and the larger picture is a lot of the Coalition members, Liberals and Nationals, do support this transition and understand it ultimately will happen,” Coalition for Conservation chair Cristina Talacko told news.com.au.

“It’s not a question of debating the ideology behind climate anymore, we’ve gone totally past that, now it’s about what’s good for Australia, what’s going to give us resilience because we don’t want the droughts and the bushfires.”

Climate Council chief executive Amanda McKenzie said calls for a green energy policy overhaul is coming from most segments of the community but insists there are still hurdles within the party led by Scott Morrison, who once famously brandished a lump of coal during Question Time.

“There are a few dinosaurs in federal parliament but the amount of support that’s now coming from state governments, from business, and from industry will be irrepressible,” she told news.com.au.

SOURCE

Firefighting tactics should change as climate warms, say fire chiefs

Blaming the fires on global warming is just propaganda.  Australia's biggest fires were many years ago. The important thing is to get a more effective response to the fires. And for that the measures called for below are a step in the right direction

Australian bushfire fighters should change tactics to focus on early detection and extinguishment of blazes rather than their containment as climate change has altered the nature of fires on the continent, an expert group has recommended.

Former Fire and Rescue NSW commissioner Greg Mullins said that in the hotter and drier conditions more common in Australia due to global warming, containment was more difficult or impossible at times – and on high-danger days, firefighters should seek to detect and put out fires as fast as possible.

The change in tactics would require increased funding by governments so bushfire authorities could use early-warning technologies including thermal-imaging drones and satellites and increase the number of highly trained airborne firefighting teams of the sort that defended the famous grove of ancient Wollemi Pines in the Blue Mountains.

Further, on such days, aircraft should be deployed as soon as fires are detected, said Mr Mullins.

A shortage of airborne firefighting equipment means they are often not deployed until firefighters on the ground have surveyed the fire, by which time it was often too late, Mr Mullins said.

He was commenting on the release of a report into the fires drafted after a summit of emergency, local government and community leaders, economists, academics and climate scientists earlier this year.

He called on the federal government to purchase new purpose-built firefighting aircraft such as the CL-415 Superscooper, an amphibious aircraft that can land on any large enough body of water and collect 6000 litres of water in 18 seconds. He noted that during the summer fires, many aircraft deployed on the NSW South Coast had to return to the RAAF base Richmond to refill.

The recommendations were among 165 developed during the summit hosted by the Emergency Leaders for Climate Action and the Climate Council earlier this year who gathered to develop plans for bushfire response, readiness and recovery in an era of increased fire danger.

Underscoring all the recommendations was a call for all governments, the private sector and community groups to work together to immediately reduce greenhouse gas emissions.

"We are rapidly moving to a climate outside the range of human experience," says the summit's report Australia Bushfire and Climate Plan.

"This is driving an increase in the frequency and severity of extreme events and disasters including out-of-scale bushfires. Addressing greenhouse gas emissions from the burning of coal, oil and gas must therefore be the highest priority because changes in our climate are increasing the bushfire threat and reducing the effectiveness of current hazard reduction strategies."

The report has also called for improved co-ordination between firefighting authorities and the Australian Defence Force.

"Often you'll have the military saying to fire services, 'what do you need', but fire services have no idea what Defence has to offer," said Mr Mullins. Better co-ordination will be critical in fighting future fires, he said.

"You don't want soldiers fighting fires, they are not trained to do it. But they have huge capacity in engineering, in logistics. They have air bases and infrastructure. Every person they put in the field releases a firefighter to do their job."

The group also called for reforms to insurance practices in the face of increased disaster risks, and recommended that the federal government map extreme weather risks street by street across the country and identify areas where under- and non-insurance was placing recovery at risk.

It called for the establishment of a permanent independent insurance price monitor either with the Australian Consumer and Competition Commission or as a stand-alone entity.

The group also called for the creation of a national climate disaster fund to help preparation and recovery efforts to be funded by a levy on fossil fuel producers.

SOURCE

Horticulture giants warn fruit and vegetable prices could rise due to labour shortage

Border closures really are a problem here

The horticulture industry has warned fruit and vegetable prices could rise up to 60 per cent and 127,900 jobs are at risk across the economy as the backpacker workforce faces being decimated due to the coronavirus pandemic.

In a new parliamentary submission, the industry says the loss of the foreign harvest workforce, which includes young people from Europe and South East Asia on working holiday maker visas, would cut Australia's GDP by \$13 billion while slashing the value of the horticulture industry by \$6.3 billion.

To address feared shortages in coming months the horticulture industry has called for a special one-off \$1200 payment funded by the federal government to lure Australians from the cities to work on farms at harvest time.

The workforce concerns are outlined in a submission from the Australian Fresh Produce Alliance (AFPA) to federal Parliament's Joint Standing Committee on Migration's "Inquiry into the Working Holiday Maker Program". The industry group consists of fresh food heavyweights including ASX-listed Costa Group and privately owned Perfection Fresh.

The working holiday maker program accounts for about 80 per cent of the harvest labour workforce, and the industry is concerned that COVID-19 border closures and restrictions could severely disrupt the number of backpackers able to work in Australia.

Tens of thousands of backpackers have left Australia this year and the industry fears this trend will continue.

Australian farmers need to continue to secure a workforce to harvest fruit and vegetables for Australian families.

Michael Rogers, CEO of Australian Fresh Produce Alliance
The Australian Fresh Produce Alliance has proposed the \$1200 payment to harvest workers only be paid after they complete three months of work. The group has also called for a \$1200 induction support payment for businesses who hire workers under this arrangement, also paid after three months.

"The AFPA has obtained data from member companies, other growers and labour hire companies that indicates from March 2020 to June 2020 these companies received 23,000 inquiries for work. Only 8 per cent of these inquiries were made by Australian citizens and permanent residents," the submission says.

The economic calculations about job losses and prices come from modelling by Deloitte Access Economics, commissioned by the Australian Fresh Produce Alliance. The 127,900 job loss estimate includes lost harvest worker roles, as well as the impact on other sectors from a dramatically smaller harvest including in transport, food manufacturing and retail.

The Australian Fresh Produce Alliance fears that without a backpacker labour force, fruit and vegetables would be left to wither and rot, or crops would not be planted because of labour force concerns.

Darren Gray explores how society sources its food, investigating how apples get from the orchard to your table.

It is also asking for the number of harvest workers coming to Australia via the Seasonal Worker Program and Pacific Labour Scheme increased from 12,000 to 15,000 per year.

"Australian farmers need to continue to secure a workforce to harvest fruit and vegetables for Australian families. And we have a current and very real challenge that we will have a shortage of workers," said the group's chief executive Michael Rogers.

Michael Simonetta, chief executive of fresh produce giant Perfection Fresh, said backpackers had been a vital horticulture industry workforce for years.

"Now it's absolutely critical to us and the horticulture industry to harvest the crops that we grow, to feed Australia and our neighbours to the north," he said.

Asked what would happen if working holiday maker harvest workers disappeared, Mr Simonetta said: "Our industry would be devastated. We wouldn't be able to pick all the crops that growers are labouring over and investing a lot of money in.

SOURCE

Posted by John J. Ray (M.A.; Ph.D.).    For a daily critique of Leftist activities,  see DISSECTING LEFTISM.  To keep up with attacks on free speech see Tongue Tied. Also, don't forget your daily roundup  of pro-environment but anti-Greenie  news and commentary at GREENIE WATCH .  Email me  here

Order, Disorder, Disruptive Events and a Bubble

If you've been paying attention, you might have noticed the stock market has entered some exciting new territory during the global coronavirus pandemic. To understand how exciting, let's revisit some basic concepts for what defines order, disorder, disruptive events, and bubbles as they apply to stock prices.

Order exists in a market whenever the change in the price of assets in the market are closely coupled with the change in the income that might be realized from owning or holding the assets, within a band of approximately normal variation about a central tendency.

Disorder exists in a market whenever the change in the price of assets in the market is not coupled with the change in the income that might be realized from owning or holding the assets within a band of approximately normal variation about a central tendency that would describe the relationship between the two when order exists in the market.

A disruptive event may be said to be taking place whenever a significant change in the price of assets in the market is not coupled with the change in the income that might be realized from owning or holding the assets over a limited period of time.

And finally, a bubble exists whenever the price of an asset that may be freely exchanged in a well-established market first soars then plummets over a sustained period of time at rates that are decoupled from the rate of growth of the income that might be realized from owning or holding the asset.

Now, let's look at the history of the S&P 500 (Index: SPX), as measured against its underlying dividends per share, or rather, the income that might be realized from owning or holding shares of an S&P 500 index fund or its component firms in your investing portfolio, from December 1991 through the nearly complete month of July 2020, which shows all of these things.

The action corresponding to the coronavirus pandemic is contained in the upper right hand corner of this chart. Following a period of relative order that ran from December 2018 through February 2020, the onset of the coronavirus pandemic in the U.S. in March 2020 represents both a disruptive event, which sent stock prices plunging into a new period of relative disorder.

That plunge reversed when the U.S. Federal Reserve initiated an unprecedented level of intervention to stabilize markets in late March 2020, flooding them with liquidity that succeeded in boosting stock prices in a bid to prevent the greater economic damage that would otherwise have resulted from a collapse in the value of these assets.

But far from stabilizing the situation in the market, by definition, the Fed has effectively blown a new bubble in stock prices, as seen by the rapid ascent of the S&P 500 that is decoupled from the index' underlying trailing year dividends per share, which have begun to fall after having stalled in the second quarter of 2020.

In nominal terms, the size of the bubble that has been inflated in the four months since March 2020 is a little smaller than the inflation phase of the Dot Com Bubble, which took far longer to inflate back in the period from April 1997 through August 2000.

It seems in this exciting new territory for the S&P 500, stock prices are reacting more to changes in the expected rate of growth of the Fed's balance sheet than they are to changes in the expected rate of growth of the S&P 500's underlying dividends per share.

How long that might last is anyone's guess. The only thing we know for certain is that eventually, all periods of relative order, disorder, disruptive events, or bubbles in the stock market come to an end. It's only ever a question of when.

29/07/20: Federal Deficit in COVID19 Era

Roger, we need a new scale for the chart.

Latest data for U.S. Federal deficit through June 2020 is shocking. Here is a visual:

June deficit was a whooping \$864.07 billion, the largest on record. This bring Trump 1 term cumulative deficits to a staggering \$5.105 trillion, far in excess to \$3.52 trillion average Obama term deficit.

Some historical comparatives:

The sheer scale of fiscal spending is frightening! No question, this is an emergency situation, but do observe that since 1980 through today, the U.S. has seen not a single decade of balanced fiscal policies. And within the next two months, the U.S. Federal deficit for 2020 alone will be in excess of the combined deficits accumulated in two decades between 1980 and 1999.

29/7/20: COVID19 Update: Russia and BRIICS

An infrequent update on Russia COVID19 stats:

Daily Cases and Deaths:

Russia is failing to arrest the new cases curve and the deaths curve, with both series running at elevated levels through July. Thee decline in new cases around the end of June was also associated with a drop in daily deaths. Since the opening up of the restrictions in advance of the July referendum vote, Russian COVID19 cases and deaths have shown disruption in the prior positive trends. Last 7-days average new cases are running at 5,741, which is statistically indistinguishable from the prior 7-days average of 6,197. Similarly, current 7-days average of 132 is materially indistinguishable from the prior 7-days average of 138.

I noted in late June that Russia is rushing into relaxation of restrictions and this is a mis-guided policy decision that seem to have nothing to do with the pandemic dynamics. It appears that my analysis was correct.

Mortality Rates:

Russian mortality rates are rising, and are now firmly close to the average of the BRIICS economies:

Amongst all countries with more than 25,000 cases (58 countries & EU27), currently, Russia ranks

• 22nd highest by the number of COVID19 cases per capita
• 32nd highest by the number of deaths per capita of population
• 44th highest by the mortality rate (deaths per 1,000 COVID19 cases)
• Cumulatively, across all three categories of metrics, Russia scores within the 95% confidence interval for the mean score for the group of 58 countries and the EU27.