After years of trying to get a Labor in the Pulpit presentation at St .Mary's, pastor Fr. Brian Clary scheduled a meeting with me and agreed to give it the green light by handing off the entire logistics to the parish social director, Mr. Albert L'Etoile. I want to stress that Mr. L'Etoile is a Eucharistic administer and is the social director for after-mass meetings. However, he is in no way affiliated with the Social Justice organization for St. Mary's. I was mum when he suggested I contact them. Indirectly, I asked Fr. Clary if they might be interested in any of the Mass Interfaith Worker Justice campaigns. Fr. Clary informed me that they were not interested and instead requested that I communicate directly with Mr. L'Etoile in establishing an initial venue.
Mr. L'Etoile published information on the Labor in the Pulpit presentation in the bulletin for approximately five weeks prior to the event, which was held after the Sunday Service on April 8th at 11:30 AM in the adjoining school cafeteria. It coincided with the after service social, but he set aside a seating area in the cafeteria for Mass IWJ. There were maybe five total parishioners, and thank you Joyce Harvey for attending and padding the audience to a whopping six. Although this was not a typical presentation from the pulpit, there were some nice advantages to this venue. Firstly, it gave a more personal feel to the presentation. Also, it provided a nice opportunity to later talk with a couple of attendees who were very much interested in Mass IWJ and its campaigns.
Because of the extemporaneous and impersonal venue, we met a professional lawyer who is very interested in Mass IWJ and plans on attending our meetings. She can potentially be quite the ally, as she is an immigration lawyer. We also met another woman who is a marketing professional.
The presentation by the Airport Workers was greatly appreciated. Supervisor Damian Oquendo and his co-worker Dayail Gethers were compelling in detailing the plight of our airport workers and their struggles while working for the subcontractor of some of the major airlines, such as Jet Blue.
I cannot thank Jeb Mays enough and everyone at Mass IWJ for their support and responsiveness. I never gave up faith that this was possible at my parish. It just took some perseverance and eventually finding the right contact. Perhaps now there can be the beginnings of establishing a strong Mass IWJ presence at St. Mary's of the Assumption.
This Monday, 7/9 Stand with SEIU 509 CLASS Inc Workers!


text:
ITV 1963 – from Transdiffusion
The ITA's guide to Independent Television in 1963
Tag: Channel 11
South and South-East England
CHILLERTON DOWN
Population within measured contours: Primary 1.91 mn, Secondary 0.53 mn, Fringe 0.52 mn. Total 2.96 mn.
Channel: Band III Channel 11 (vertically polarised)
Vision Carrier Frequency: Actual 204.75 Mc/s
Sound Carrier Frequency: Actual 201.25 Mc/s
Effective Radiated Power: Vision 100 kw maximum. Sound 25 kw maximum.
Power of Transmitters: Vision (peak white) 4 kW. Sound (carrier) 1 kW
Heights above sea level: Site 550 ft. Mean aerial 1,250 ft.
Location: 1° 19′ 40″ W, 50° 38′ 55″ N.
Vision Carrier Frequency: Nominal 199.75 Mc/s. Actual 199.7135 Mc/s
Sound Carrier Frequency: Nominal 196.25 Mc/s. Actual 196.1985 Mc/s
Location: 1° 14′ 58″ E, 51° 6′ 40″ N.
Chillerton Down (Channel 11) and Dover (Channel 10)
Company: Southern Television
Chillerton Down was the first of the two stations built to serve the south and south-east coastal areas of Britain. It was designed to cover central southern England, the important agricultural and holiday area along the coast from Weymouth in the west to Brighton in the east, together with the great ports of Southampton and Portsmouth and, inland, the county of Hampshire and adjoining parts of Dorset and Wiltshire. A BBC Band I station existed at Rowridge, on the Isle of Wight. In conformity with the Government's policy the Authority decided if possible to build its Band III station close to Rowridge. The site selected was on Chillerton Down, 550 ft. above sea level on the south side of the island. Opposition to a second television mast on the island was raised on grounds of amenity. However, the alternative of building at Rowridge a more massive and commanding tower to carry both the ITA and BBC television services and the BBC's VHF sound services proved even less welcome, and the Authority's proposal to use Chillerton Down for a slim 750 ft. mast was accepted.
The transmitting aerial has a semicircular power-radiation pattern, oriented to direct 100 kW in both directions along the coast as well as landwards, but radiating very low power across the English Channel to prevent interference with the services of Radiodiffusion-Télévision Francaise. Chillerton Down went into service on 30th August 1958 and serves the intended area well.
The sister station at Dover presented unusual problems. The general requirement was to serve the south-east corner of England not covered by Chillerton Down or Croydon. The site of the station was determined by the need to serve Folkestone and Dover, which lie at sea level under high cliffs. The solution was to build the station on the high cliff road linking the two towns. Church Hougham, 450 feet above sea level, was used and from a 750 ft. mast a signal could be directed into both towns. At the same time the station had to link up with the service area of Chillerton Down beyond Eastbourne, 5o miles west along the coast. 100 kW was sufficient to provide an adequate service for Eastbourne and the intermediate coastal towns, and there were no inhibiting power restrictions. Northward, to serve the towns on the Thames estuary not covered by Croydon, 10 kW to 20 kW e.r.p. was adequate. However, viewers in France had to be protected from interference to their reception of the signal from the Rouen station. Calculations showed that Dover must restrict its power to less than 1 kW over an arc of 90° towards the French Coast. It was no mean task to construct a transmitting aerial to do this, and at the same time to radiate 100 kW westward. Test transmissions were made for many weeks, during which the Authority's engineers developed a measuring technique, using a helicopter, to check the the radiation pattern of the transmitting aerial. This difficult operation accomplished, Dover went into service on full power on 31st January 1960.
Author Eric CrostonPosted on 1963 2016 Categories South and South-East EnglandTags Channel 10, Channel 11, Chillerton Down, Dover, South and South-East England, Southern TelevisionLeave a comment on South and South-East England
The Borders
CALDBECK
Population within measured contours: Primary 0.28 mn, Secondary 0.043 mn, Fringe 0.041 mn. Total 0.364 mn.
Channel: Band III Channel 11 (horizontally polarised)
Location: 3° 5′ 21″ W, 54° 46′ 24″ N.
Population within measured contours: Primary 0.071 mn, Secondary 0.026 mn, Fringe 0.019 mn. Total 0.116 mn.
Vision Carrier Frequency: Nominal 214.75 Mc/s. Actual 214.723 Mc/s
Sound Carrier Frequency: Nominal 211.25 Mc/s. Actual 211.223 Mc/s
Effective Radiated Power: Vision 25 kw maximum. Sound 6.25 kw maximum.
Power of Transmitters: Vision (peak white) 2 x 0.5 kW. Sound (carrier) 2 x 0.125 kW
Calbeck (Channel 11) and Selkirk (Channel 13)
Company: Border Television
The Border country has two well-populated areas separated by the high sparsely-populated Cheviot Hills. That in the west extends north and south of the Solway Firth and includes the towns of Carlisle, Penrith and Dumfries. The other, in the east, embraces the Valley of the Tweed, and includes Selkirk and the coastal town of Berwick-on-Tweed.
Planning studies indicated that the best way of serving the pupulated areas was to build two separate stations, one near Carlisle and one near Selkirk. The site chosen for the first station was at Caldbeck, 940 ft. above sea level and some 10 miles west of Carlisle, in the foothills of the Cumbrian Mountains. Caldbeck lies somewhat to the south of the area to be served and a directional transmitting aerial supported on a 1,000 ft. mast was provided to radiate the maximum power of 100 kW to the northeast and the south-west, about 7o kW to the north-west across the Solway Firth, but only 20 kW to the south-east. In this direction the useful signal would naturally be blocked by mountainous country, which would not, however, prevent an interfering signal from penetrating into the service area of Mendlesham (which uses the same channel) some 200 miles distant, unless power in that direction were appropriately restricted.
The second station was built on Lindean Moor, 944 feet above sea level and close to Selkirk. It has a 750 ft. mast and an aerial which radiates its effective power of 25 kW mainly eastwards towards the coast. This provides a good secondary service in Berwick-on-Tweed, whilst the numerous small towns of the Tweed Valley all receive a primary service.
The Selkirk station is a satellite of Caldbeck. It obtains its programmes by direct radio pick-up from Caldbeck and rebroadcasts them on a different channel. It is the first of a number of unattended remotely-controlled satellite stations of medium to low power to be constructed by the Authority.
Caldbeck began programme service on 1st September 1961 and Selkirk on 1st December in the same year, and both well fulfil the purpose for which they were designed.
Author Eric CrostonPosted on 1963 2016 Categories The BordersTags Border Television, Caldbeck, Channel 11, Channel 13, Selkirk, The BordersLeave a comment on The Borders
West and North Wales
PRESELY
Channel: Band III Channel 8 (horizontally polarised)
Vision Carrier Frequency: Nominal 189.75 Mc/s. Actual 189.75675 Mc/s
Sound Carrier Frequency: Nominal 186.25 Mc/s. Actual 186.27 Mc/s
Power of Transmitters: Vision (peak white) 5 kW. Sound (carrier) 1.25 kW
Heights above sea level: Site 1,100 ft. Mean aerial 1,835 ft.
ARFON
Effective Radiated Power: Vision 10 kw maximum. Sound 2.5 kw maximum.
Location: 4° 16′ 10″ W, 53° 1′ 10″ N.
MOEL-Y-PARC
Presely (Channel 8), Arfon (Channel 10), and Moel-y-Parc (Channel 11)
Company: Wales (West and North) Television
This group of stations was planned to bring Independent Television programmes to the Welsh-speaking populations of West and North Wales, including the area bordering on Cheshire which contains the towns of Denbigh, Mold and Wrexham. The populated areas are mainly along the west coast from Pembroke to Anglesey, and on the north coast from Conway and Llandudno to Prestatyn.
The technical problem was unusually complicated. It has been solved by the establishment of three stations, one on the Prescelly mountains in Pembrokeshire, one on the Lleyn Peninsula, and one on the Clwydian Range of mountains in the Flint-Denbigh area. This plan departed considerably from an earlier one based on sites previously selected for BBC Band I stations.
A site for the Presely station was found at Foel Drych 1,100 ft. above sea level, where a 770 ft. mast was sufficient to give the required coverage, although the radiation pattern of the transmitting aerial had to be extremely complicated. A narrow beam radiating 8o kW to the north was required to ensure a reliable programme link to the Arfon relay station. A beam of 100 kW to the south-east, in the direction of Carmarthen and Llanelly, was necessary to ensure that the service area of Presely joined that of St. Hilary; and a broad lobe of 5o kW to the south-west was needed to serve Pembrokeshire. At the same time severe power restrictions had to be incorporated in several directions to avoid co-channel interference in the service areas of the ITA's transmitters at Strabane, Burnhope and Lichfield, the Kilkenny station of the Irish Republic, and the French stations serving the coast of Brittany. Intensive development was necessary to construct an aerial with this complicated radiation pattern.
The unattended Arfon station, which rebroadcasts the Presely transmissions, is at Bryn-ychain, ten miles south of Caernarvon, 950 ft. above sea level. A 1,ooo ft. mast was used to "see" over the mountains of Portmadoc to the coast of Cardigan Bay from Harlech to Barmouth, and to ensure the link with the service area of Presely. A directional aerial was again necessary. 10 kW is radiated to the north and south-west, 5 kW to the east and south-east, and 2.5 kW to the west.
The third station is at Moel-y-Parc, a peak in the Clwydian Range 1,100 ft. above sea level, and serves the North Wales area. A 750 ft. mast was found adequate to reach the coastal resins from Conway to Prestatyn, which are shielded by mountains close to the coast. The radiation pattern of the transmitting aerial is approximately semicircular, 25 kW being radiated from south-east to north-west with reduced power to the north and east. This was necessary to cover the Welsh areas but to avoid overlap with English areas already served by Winter Hill. Moel-y-Parc rebroadcasts the transmissions from the Arfon station, conveyed to it by an off the air pick-up at Nebo, in Anglesey, followed by a microwave link.
All three stations for the west and north of the Principality were in programme service by early 1963.
Author Eric CrostonPosted on 1963 2016 Categories West and North WalesTags Arfon, Channel 10, Channel 11, Channel 8, Moel-y-Parc, Presely, Wales (West and North) Television, West and North WalesLeave a comment on West and North Wales
Power of Transmitters: Vision (peak white) 2 x 5 kW. Sound (carrier) 2 x 1.25 kW
Location: 1° 6′ 32″ E, 52° 14′ 3″ N.
Mendlesham (Channel 11)
Company: Anglia Television
The geographically large but not densely populated area of East Anglia which this station is designed to serve is of unusual interest to the technical planner. It is largely flat and circular in shape, with a diameter of about eighty miles. At first sight it seems to present an almost ideal case for service by an uncomplicated high-power station located at the geographical centre, radiating its power omnidirectionally. As so often happens, the simple approach could not be applied. The possibility of causing interference to West German viewers in the established service area of the Langenberg station and to French viewers of the Amiens station demanded that the power radiated over a prescribed south-easterly arc must not exceed about 15 kW. Other complications included the need to prevent interference in the service area of Chillerton Down, which uses the same channel, and the need to observe the principle that ITA and BBC stations should be adjacently sited.
Thus, to secure adequate service to the coastal areas of Suffolk and Essex, the site for the station had to be displaced well to the south-east of the geographical centre of the required service area and, incidentally, far from the BBC Norwich Band I station which serves much of the same general area. The Television Advisory Committee confirmed the Authority's conclusion that adjacent siting could not be followed in this instance and that the best site for the ITA station was at Mendlesham, about fifteen miles north-west of Ipswich. The towns of Ipswich, Colchester, Felixstowe and Harwich would then be close enough to the station to be well served, despite the relatively low power radiated in their direction.
To compensate for the displacement of the station from the natural geographical centre it was necessary for the power radiated towards the west and north to approach 200 kW. Again, because of the very low height of the Mendlesham site, 210 ft. above sea level, a 1,ooo ft. mast was considered technically appropriate. This was the highest television mast to be constructed in Europe and the first of five of the same height subsequently used at other ITA stations. The building of the station began early in 1959, and after some corrective adjustments to the aerial power-feeding networks the station began programme service on 27th October 1959.
Author Eric CrostonPosted on 1963 2016 Categories East AngliaTags Anglia Television, Channel 11, East Anglia, MendleshamLeave a comment on East Anglia
Advertising Control
Children and Television
Light Entertainment
News and News Magazines
Programme Policy
Rhaglenni Cymreig
Staff and Organisation
Talks, Discussions, Documentaries
Technical Achievements
Hints for Better Reception
Running an ITA Station
Transmitting Stations and Coverage Maps
North-East England
North-East Scotland
South Wales and West of England
South-West England
Television Act 1954, Sections 3, 4, 5 and 6
The Independent Television Authority
The ITV Audience
The ITV System
The Programme Companies
ABC Television
Associated TeleVision
Associated-Rediffusion
Border Television
Channel Television
Grampian Television
Granada TV Network
Independent Television Companies Association
Independent Television News
Scottish Television
Ulster Television
Wales (West and North) Television – Teledu Cymru
Westward Television
Wikipedia: {{cite book |last=Croston |first=Eric |date=March 1963 |title=ITV 1963 |url=http://itv1963.retropia.co.uk/ |location=London |publisher=Independent Broadcasting Authority}}
Print: Croston, Eric. "ITV 1963". 1963. Web. http://itv1963.retropia.co.uk/
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Transdiffusion Broadcasting System
Rediffusion, London
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text:
Football's dark secret
January 29, 2012 / benjaminjevans	/ Leave a comment
I've just been listening to a bit of football on the radio. Quite an exciting bit of football as it happens: Arsenal football club have just scored 3 times in 15 minutes at the start of the second half and now lead Aston Villa 3-2 in a highly entertaining cup tie. This is just one of many football stories this week, though as ever with the beautiful game, what happens on the pitch only makes up a fraction of what ends up written in the papers and discussed in pubs across the land.
This week we have Luis Suarez's continued ban for racially abusing Patrice Evra, John Terry's court 'appearance' for racially abusing Anton Ferdinand. Ferdinand himself received a spent shotgun cartridge in the post this week, which seems rather more than harsh; whether he was racially abused or not, he has surely done nothing to deserve this threat of death?
Football has been blighted by accusations of racism for many years, though thankfully we seem destined never to return to the peak of the 1970s and 80s when it was common for black players to receive monkey chants and have bananas thrown onto the pitch. The 'Kick Racism Out' campaign appears to have been successful, though it's probably more a case simply that times have changed, along with the notion of what is acceptable and the values of a more enlightened population in general have been reflected in the behaviour of the average football supporter.
So far so good, but as Alan Hansen said recently on Match of the Day whilst talking about the issue of racism in football: 'there's still a long way to go'. He's right of course, and until racism is 'kicked out' completely, we must continue to campaign and to educate. Unfortunately, in talking about racism, he also used the term 'coloured people', which meant that his sane message was lost in a tumult of calls to the BBC demanding his resignation for using such a derogatory term. OK, so the word coloured isn't exactly fashionable these days; it's a term more closely linked to 70s sitcom 'Mind your Language' and it does tend to imply that there are only two races in the world: 'Whites' and 'Coloureds'. But we all knew what Hansen was trying to say, and if his terminology was perhaps less than sound, at least his logic was fine. In any case, the National Association for the Advancement of Coloured People (NAACP) surely couldn't have had a problem, given that the word coloured makes up a pretty key part of their message to the world.
Maybe Hansen should have used the word 'Black'? I was under the impression that this was more offensive than 'coloured', but I have been informed by several of my friends that this is not so, and actually this term is far less controversial and far less likely to offend. However, returning to John Terry's court appearance, we find that he has been investigated and subsequently charged with the offence of calling Anton Ferdinand a 'black c*nt' during a recent West London Derby. Thank God he didn't call Ferdinand a 'coloured c*nt', then the shit would really have hit the fan. Actually, now I reflect further, isn't the word c*nt actually rather more offensive than either 'black' or 'coloured'? Admittedly it has no racial connotations, but I reckon it's about the most offensive individual word than one can utter in conversation.
Racial abuse is simply a sub-section of abuse, but due to the behaviour of past generations, it's a sub-section that lies far higher up the 'likely to cause public outrage' scale. There are undeniably some ignorant cromagnon football supporters that genuinely do believe that black people are genetically inferior to whites, but these are few and far between and are loathed unanimously within the football community. Most racist abuse is not indicative of an ideology that is unsound; it is simply a clutching at straws way of insulting another member of the human race. If John Terry called Anton Ferdinand a 'black c*nt', it shows him up to be an unpleasant man, not necessarily to be an institutional racist. Much of the debate around Luis Suarez's ban concerned the question of whether using a racist term necessarily meant that he himself was a racist. Surely this is just a case of labeling and semantics? If I laugh at a sexist joke am I necessarily displaying a serious tendency towards misogynism? Probably not, though it doesn't rule it out either. I would in either case not like to think that my entire belief system and ideological 'soundness' could be summarised by one outburst or reaction to a joke.
The problem with football, and more precisely with the fans that follow the sport, is that their own beliefs seem to take a back seat whenever it comes to issues regarding their club, the manager and the players. Do all Liverpool fans believe that Suarez is not a racist? Do all Manchester United fans believe that he is? Do all Chelsea fans really believe that John Terry is not a racist? Do they even have enough evidence? Loyalty to a club is one thing, but these issues go far beyond mere support from the terraces. It is perfectly possible for me to hope that my team will win, whilst also being disappointed in the behaviour of an individual that happens to play for the side I follow. Football supporters tend to lose their ability to think for themselves on issues involving their club, instead choosing to agree with any sentiments uttered by their players and manager. It's so much better to be told what to think by people that you admire rather then actually taking the time to have an opinion yourself.
But maybe they are the sensible ones, bearing in mind how difficult it is to engage anyone on the subject of racism without either being labelled as a woolly liberal or as a racist oneself. After all, several of my best friends are coloured, or should that be black?
All rather depressing
January 21, 2012 / benjaminjevans	/ 1 Comment
So the roving eye of the British public moves on. Bored of 'occupy', bored of bankers and bored of arguments over who's being racist on twitter (for the moment), it settles on the issue of depression, and depression in sport in particular.
Gary Speed kicked it all off when he went and hung himself. It was as shocking as it was surprising. That day, twitter was full of the standard 'RIP Gary', but was also inundated with messages urging people to spread the awareness about depression. This seemed odd; no valid reason has ever been suggested as to why Gary Speed would take his own life, and yet the twitter-ati clearly decided that it was an open and shut case, and the D word needed to get out. This made no more sense than the average man in the street, who upon hearing about a plane crash, immediately campaigns for greater public awareness of testicular cancer.
Depression does seem to affect a large number of sportsmen, and the incidences of suicide (especially in cricket) are certainly higher than most other professions. Marcus Trescothick's well publicised battle with the disease is a case in point, and it's clear that many sportsmen struggle to cope with life once their playing careers are finished. Ex-Hull City striker Dean Windass spoke to the Guardian this week, keen to admit (possibly as catharsis) that he was 'close to ending it all' this week.
I'm not an expert, but the link between sportsmen and depression seems to make sense. The weight of public expectation, the mighty highs and cavernous lows and the 'back to earth with a bump' that accompanies the end of one's playing career would indeed cause some of the less robust personalities to struggle to deal with the harsh realities of 'real' life. I was amazed that a colleague of mine chose to rail against this phenomena, expressing utter contempt for these sufferers and an amazement that they could be afflicted in this manner, given that they were performing in a role that many ordinary folk would give their eye-teeth to take on. 'Let them go and meet the maimed soldiers from Afghanistan' she wailed, 'then they'd know how lucky they are'. I'm pretty sure this is not how depression works. It would be easy to snap out of things if all one had to do was to be introduced to someone more worthy and/or more unlucky. I'm sure that the bi-polar Stephen Fry is aware that he is a clever, successful man, and very much the nation's favourite uncle. This doesn't seem to make him snap out of the medical condition with which he is afflicted.
As if to satisfy the public's curiosity with all things depressive, and hot on the heels of Gary Speed, came Andrew Flintoff, who opened his heart on his depressive past. Less convincing this one: his depression apparently co-incided with his only tour as England captain. As England slumped to only their second ever 5-0 Ashes defeat, and their first for 85 years, Flintoff admitted that he had felt down and had struggled to get out of bed in the morning. He had even started to drink too much. None of this seemed all that surprising. Legendary boozer Flintoff had carried on boozing. He had also felt pretty low and gutted that his team were being comprehensively thrashed. This isn't a depressive episode, it's just a bad day (or few weeks) at the office. Miraculously, this depressive episode seemed to pass once England started playing a little better.
Fintoff's mate Steve Harmison has now chipped in, blaming his lack of form on foreign pitches on depression. 'I didn't realise it at the time, but that's what it must have been'. Give it a label Steve, just to make yourself feel better.
The saddest thing of all is that many people do need to change their opinion of his disease, which is misunderstood and brushed under the carpet all too often. However, the more that celebrities trivialise depression and use it merely as a catch-all label to magic away the natural lows of their profession, the more that it will remain misunderstood. Ironically, by bringing it into the public eye in this manner, it is likely to provide just a few minutes of pub chat, and less likely to kick-start any worthwhile debate on the issue.
It's all just so depressing.


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Salt Lick are the Permanent Records house band and if you've been to Permanent—or picked up any of those Brown Acid comps—then you'll understand this sound instantly. It comes from a time after Sabbath and before punk, when band after isolated band arose determined to make their own noise from nowhere with guitar, bass, drums and a dedication to rock in its hardest-edged form. (Although they definitely made room for sludge and tar, too.) Salt Lick's coming self-titled full-length is in the proud tradition of those DIY shredders that time forgot, and opener "Midnight Oil" is half caveman rage and half Stooge-y wreck 'n' roll, like the band that could've/should've opened the show recorded for Metallic K.O. It's an ode to internal alienation, says Salt Lick's (and Jesus Sons' and Mind Meld's) Erik Lake: "'Midnight Oil' is a track about living within our own heads to the point of mental exhaustion." Salt Lick is out on 4/20 because fate demands it, and you can pre-order here—and they'll be doing a few dates in Spain and a double-hitter in Texas next month. Full dates below!


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While our guests may participate in various activities like water slides, animations and sport tournaments during daytimes, every moment of you nights in holiday becomes adorable entertainment with contented shows of animation team, live performances, special Parties, activities.


I recently discovered one of my favourite skin care brands uses mineral oil in its products. Despite never doing any personal research, I'd automatically assumed mineral oil was the equivalent of the skin care devil because well, Caroline Hirons said so. More fool me, turns out mineral oil isn't so bad after all.
Mineral oil is not, by default, bad for you or your skin. It's true mineral oil is a cheap ingredient, often used as a "filler" in place of more expensive ingredients. It's also fragrance free, colourless, doesn't oxidize and can easily be kept for a long time. For those reasons it frequently appears in many cosmetic products, however, is vilified under the assumption that it is man-made therefore toxic and cheap therefore poor quality.
Mineral oil is derived from crude oil, which originates from biological material (algae and plankton) buried underground and transformed by pressure over millions of years into carbon-containing compounds to make crude oil. It's then refined into different products including paraffin wax, gasoline, asphalt, and mineral oil, which are all vastly different from each other; while crude oil may contain carcinogenic properties, careful refining makes cosmetic grade mineral oil perfectly fine for human use.
There is a widespread misconception that "natural = good" and "man-made = toxic" which is simply wrong (and rather dangerous). Every chemical whether it's man-made or natural should be assessed based on its own merits.
Mineral oil has been accused of causing spots and aggravating acne, it's been blamed for stopping the skin from "breathing" and vilified for being a made-made "toxic" substance. These opinions were formed by studies in the 1970s, often spread by "natural" based cosmetic companies, internet consumer sites, and environmental groups who claim petrolatum and mineral oil cause harm to the skin by forming an occlusive oil film that "suffocates" it.
In 2005 a study discovered mineral oil does not cause breakouts on the face as was previously thought. This research debunked the myth derived from studies in the 1970s that put mineral oil on the comedogenic substances list. This research was carried out on the ears of rabbits who, unsurprisingly, react very differently to substances than we do and are much more prone to comedogenicity than humans. More recent studies have found products containing between 0 and 30% mineral oil are not comedogenic on human skin and even applying 100% mineral oil onto skin won't cause acne.
In regards to mineral oil "suffocating" the skin and preventing it from "breathing," this claim defies human biology. Mineral oil reduces transepidermal water loss by 40% and is equally as occlusive as coconut oil (preventing water loss and retaining moisture), yet does not induce acne. It also inhibits excessive inflammatory activity and has been documented to have anticarcinogenic and mild antibacterial effects.
For those who react negatively to mineral oil, it's important to remember it's possible for even the safest known ingredients to cause a negative reaction - even purified water. It's more likely a combination of ingredients causing your breakout than mineral oil alone, and most likely has nothing to do with mineral oil at all. There are much more likely culprits causing aggravation and acne in your beauty products than mineral oil. If you're concerned about mineral oil clogging pores (which, by the way, it can't since it cannot penetrate the skin far enough), only use products that are meant to be washed off after use and avoid moisturisers with a high content of mineral oil.
Assuming plant-based products are intrinsically better simply because they are "natural" is dangerous. Plant oils often have poorer safety profiles than mineral oils making them toxic and even harmful, they may also contain carcinogenic substances in unprocessed oils.
I think there are very few of us who can identify every item on a product's ingredients list so why do we automatically blame mineral oil when we break out? What we all need to realise is it's the combination and quantities of a product's ingredients that is most important. It could be any one of the many ingredients in a formula, or even a particular combination causing problems. There is significant evidence to show mineral oil is harmless and can even play a beneficial role in skin care routines, so quit freaking out about it.
Really informative post, thanks for clearing that up!
I agree that people automatically assume mineral oil is horrible and that it's the ingredient that's breaking them out when it's not!!! Like you said it's a combination or quantities of product's ingredients. I think Caroline is an amazing knowledge blogger who really knows her stuff but I think people take things and run with it till it's a ridiculous mess! Even Caroline posted recently and said don't freak out so much if you are using it..
The reason I avoid mineral oil is for the reasons you pointed out, its 'cheap' and a 'filler' ingredient offering me, a person with very troubled skin, no benefits at all.
I think if you have perfect skin and can look in the mirror without hating your complexion then go ahead and slap that mineral oil on there but for me (and many other people) it's a little more complicated than that and we have to actually think about what we're putting on our face and take care of if or else it all just gets a lot worse. I'm not talking a few spots once a month, I'm talking confidence sucking skin issues that make you hate the person you see in the mirror.
I don't think you can preach that mineral oil is okay when there is a lot more to consider than that, but for now I don't want to use something that in another form is PETROL. nope. no thank you. stay away from my face.
Because I have very sensitive skin I am always weary of products with a huge, un-pronouncable ingredient list. Countless times have I broken into a rash from skincare that includes too much perfume! For this, the Cosmetic Database is my best friend. Do you ever use it?
This was so interesting to read! I really enjoyed your post - to be honest, I've never paid that much attention to the mineral oil content in my skincare, and I'm just fine!
THIS. This was the reason I wrote this post. Not to tell people to use or not use mineral oil, but to explain that everybody should do their own research, to stop freaking out about specific ingredients because someone else told them to.
I have heard and briefly looked at the website.. I do like to look at a whole range of sources before I make my mind up about any product.
Also I think skin naturally tells you when it likes/dislikes something. I think mixing products on a daily or even weekly basis (like A LOT of people do) has far worse consequences than occasionally using ingredients such as mineral oil.
I don't think mineral oil is for everyone.. just like plant based products aren't for everyone either. I can't go near plant based facial oils because my skin breaks out SO BAD, but if I use mineral oil I have absolutely no reaction.. because it's non comedogenic!
I think it's important we all read (and understand) the labels on our beauty products (just like we should with the food we eat), but I think it's dangerous to vilify certain ingredients just because one person told us to.
And obviously yes, what works for one person may or may not work for another. Try it out, research it, make your own decision!
Hi Sophie, this is a great post and a much needed conversation. I'm from Oqibo Professional Skincare and one of the recent enquiring comments on our Skin Refining Exfoliator is that it contains mineral oil. Skincare companies take very different approaches to their research and development so I can't comment in the wider sense but the reason we chose to include mineral oil in this particular product echoes many of your thoughts and findings. For us it provides a low skin reactivity rate, provides a silky glide and protects the skin from any scratchy effects that exfoliation generally has. It's also excellent and picking up excess sebum, dirt and grime and helps us get the actives where they need to be. This is also a wash off product so the mineral oil is only in contact with the skin whilst in use.
Much of the confusion comes from the fact that there is so much conflicting information, your "do your research" mantra is the key point. Looking at fact based information, seeking out the latest research from reliable and knowledgable sources and taking a common sense approach ensures that you are choosing a product that's right for you. Context is vital and everything can be toxic at certain levels. Knowing your skin, and relying on your own investigative nous is really important.
Thanks again for a fab discussion!
I agree with this. If it works for you, then don't stop using it just because someone else doesn't like it. I constantly hear people raving about the wonders of certain oils, but lavender, rosehip and sweet almond oil all break me out terribly.
I could NOT agree with you more. Um, just cos Caroline Hirons says it, it is already ZE EVIL. Ive been using the Shu Uemura cleansing oils for years now and its #2 ingredient is mineral oil. If it were clogging, imagine my face now.
Excellent post - you did a great job in concisely explaining the issues concerning mineral oil and skincare products.
Thank you for doing some research!
Hello, I stumbled upon your blog and I really love your style! Personally I've not really thought hard about mineral oils but I do care about things like parabens, fragrance, SLS, etc. Thanks for posting this, I think in a nutshell people can make a decision for themselves about what they think are okay for their skin/bodies.
You make a lovely argument, and while the academic in me would like a list of references at the end of the post as well, I enjoyed your post. One of my fave products are Dr.Lucas' Pawpaw ointment.
If you follow the links within the post you'll find references to academic articles and reports supporting my statements :)) Like you I think it's important to have proper references when writing about subjects especially those surrounded with such controversy as this one.
I'm not arguing that everyone should use mineral oil because, of course, it won't work for some people BUT I am arguing that people should stop breathing life into this notion that mineral oil is bad.
I get your point, and I can relate. I have the rather dubious pleasure of being asked every day if a product contains parabens, with references to research done at the local uni. People are more afraid of the parabens that can't penetrate the skin - unless used in conjunction with certain other ingredients that has nothing whatsoever to do in skincare products - than of the bacteria that would rapidly multiply without it.
I think media carries a lot of the blame - as reports are translated to layman's terms with emphasis on the "revolutionizing" or "shocking" parts.
You also point out one very strong point for abolishing animal testing in cosmetics entirely, that the industry ofttimes seem to forget - animal skins react different to human. But I digress.
I completely agree with everything you wrote here. Best post ever. I always take what I read with a grain of salt and do my own research to make up my own mind. I hate the argument that "natural" is better. It makes no sense. Natural ingredients are essentially chemical components! Everything is a chemical. CH is a great blogger but it always irks me that many of her readers completely follow her advice like sheep with blind faith without thinking about their own needs and doing their own research. I personally have never had strong negative feelings towards mineral oil. It is in a lot of products I use and I don't think it ever has negatively impacted me so it never is a deal breaker for me.
Interesting, thanks for the post! It was well-written and clear, backed up with sources, which I always love. I follow the OCM and use mineral oil to cleanse; it hasn't done my skin any harm at all. While I respect Caroline Hirons and enjoy reading her blog, I do find some of her sources tend to be more anecdote than scientific.


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What can I expect for the afternoon?
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text:
Q: How common are single quotes (apostrophes) in Windows usernames? What about in Ireland? today we discovered our developer-focused GUI app doesn't work on systems where the username contains an apostrophe. Because although it's multi-platform, part of it runs in a linux VM where shell scripts are generated on the fly. We did the quoting needed to handle names and paths containing spaces, but didn't figure on single quotes.
It looks like scoop doesn't work in such environments either, but I need to do more investigation there. If that's the case, I can't imagine many developers insisting that their Windows name be their actual name.
Looking for feedback to figure out how I should prioritize this bug, which should be fixable, just not in a few hours.

A:
How common are single quotes (apostrophes) in Windows usernames?

That is a bit irrelevant. (Nor is it something that can be answered.)
You found that it is not only an allowed character in a Windows user name, but that people actually do assign usernames with that character.
So, if you can, please fix your broken code.
And then take into account that from AD and for modern Windows versions/applications/libraries there are surprisingly few restrictions with regards to for example the sAMAccountName attribute:
https://social.technet.microsoft.com/wiki/contents/articles/11216.active-directory-requirements-for-creating-objects.aspx#Objects_with_sAMAccountName_Attribute
As a counter point:
Regardless of what is technically allowed and possible in Windows/AD usually  organisations have implemented a much stricter naming policy for accounts.  Such policies restrict usernames to provide as much (backward) compatibility as possible, because in heterogenous environments yours is not the only application that breaks on usernames that don't meet "old" conventions.
In practice that means one indeed sees mostly relatively short POSIX compliant usernames with only characters from the portable character set a-Z , 0-9 and sometimes a hyphen -, underscore _ or dot  . somewhere in the middle. In turn such a naming convention provides little incentive to fix/modernise those applications.

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

The contact area between solid bodies is in general only a tiny fraction of the apparent (or nominal) macroscopic contact area, and is essentially proportional to the normal force between the bodies\cite{persson,bt}. This fact is at the core of many important characteristics of friction phenomena. In particular, it gives a natural explanation of the independence of the friction force with the nominal contact area, and the linear increase of friction force with normal load.
However, contact area, even under static external condition is a time dependent quantity, and this produces  time dependent effects in friction. For instance, the logarithmic time increase of static friction coefficient with the contact time, that is well described in many materials\cite{mudet,marone0}, is mostly related to a corresponding logarithmic increase in time of the contact area\cite{caroli}. Direct evidence of this geometric
aging effect was provided by Dieterich and Kilgore\cite{dk}. The
time increase of contact area is also related with the phenomenon of velocity weakening during sliding, namely the fact that the friction force between sliding surfaces can decrease when the relative velocity is increased.
The velocity weakening effect is extremely important in relation with the dynamics of the friction process. In fact, it can be shown that this effect is at the base of the process of earthquake generation during the relative motion of tectonic plates\cite{scholz}, and also plays an important role in the stick-slip dynamics of many sliding systems\cite{persson}.
These examples highlight the central role that the time increase of contact area has
in the description of many frictional phenomena. An understanding of the time dependence of contact area is thus
a very basic aim of any friction theory.

It is generally accepted that the physical mechanisms by which contact area increases in time are associated with
plastic
phenomena occurring in the materials.
For our purposes, plastic processes can roughly be classified into two qualitatively different groups\cite{plasticity,lakes}. Rapid plastic effects occur when the
imposed deformation conditions produce the overpassing of the yield stress of the material. This behavior is typically
referred to as plastic flow. For lower applied stresses, in cases in which the yield stress is not
overpassed, there still exists the possibility of thermally activated reacommodations in the system that
tend to reduce gradually its free energy. These processes are much slower than those of plastic flow, and are strongly temperature dependent. They are refereed to as creep phenomena.
When two solid bodies are pressed together, the real contact occurs only in a tiny part of the surface, and the local stresses
are correspondingly very high. This may produce local plastic flows that increase the contact area until the local stresses decay below the material yield stress. After this initial stage, the contact area typically increases slowly in time due to creep processes. The time increase of contact area in this stage is seen to be logarithmic in time.

Creep processes (that in other contexts are referred to as aging effects) produce in the contacting bodies a tendency  to reach progressively more stable configurations. The meaning of ``more stable" here, is that the atomic rearrangements implied by a creep process must produce on average a decrease in the total free energy of the system.
This stabilizing tendency originates in the fact that  energy barriers to jump onto a lower energy state are in general lower than those to go to higher energy states, so on average creep produces always an energy reduction in the system. Along these lines, the phenomenon of contact area increase has been qualitatively described in some idealized geometries\cite{brechet,caroli}, and the experimental logarithmic increase law has been justified for these cases. Crucial in this analysis is the assumption of a phenomenological creep law in which some generic strain rate $\dot s$ is exponentially related to an appropriate stress $\sigma$, i.e., $\dot s\sim \exp(\sigma/S)$, where $S$ is called the strain rate sensitivity and is temperature dependent \cite{caroli}.
The modeling of the phenomenon in more realistic cases is prevented by the complication
to describe creep in the materials in a sensible and analytically (or even numerically) tractable way.
As far as I know there is no statistical model that, based on well defined microscopic evolution laws, is able to predict
the logarithmic increase of contact area with time.

Recently, a way to incorporate creep effects in the dynamics of sliding friction has been proposed in \cite{uno,dos}. In particular this has been applied to models (the Burridge-Knopoff\cite{bk} and Olami-Feder-Christensen\cite{ofc} models) used to describe seismic phenomena.
This kind of models describe the friction phenomena occurring at the flat (on average) contact surface between two solid bodies that are sheared against each other.
The kind of modeling proposed in \cite{uno,dos} consists in defining some ``plastic" degrees of freedom, and arguing that they evolve with a tendency to minimize the total energy of the system, which is a generic realization of creep processes as  described in the previous paragraph.
It was shown that the proposed relaxation mechanism is able to generate realistic sequences of earthquakes, a goal that had not been obtained previously without this kind of modification. Also, realistic frictional properties
are well reproduced using this relaxation mechanism. In particular, a logarithmic increase of the static friction coefficient with contact time, and an approximately logarithmic decrease of the average friction force as a function of relative velocity has been obtained.

In view of the standard interpretation of macroscopic friction features in terms of contact area, and since the structural relaxation mechanism in \cite{uno,dos} is consistent with macroscopic friction properties, the question arises if there is
a way to use that relaxation mechanism to model the time increase of contact area of solid bodies under static contact. Such a modeling, if successful, would give further support to the structural relaxation mechanism, and would provide an appropriate framework to study the phenomenon of time increase of contact area in greater detail than the rather qualitative descriptions available up to now.
I attempt this particular goal here.
In order to do this I explain a variation of the models presented in \cite{uno,dos} that allows to define the contact area, and at the same time incorporates the structural relaxation mechanism. I show that the main phenomenology associated to the contact area is re-obtained, particularly, its logarithmic time increase.

\section{The Model}

Typically, the surfaces of solid bodies in contact are at the same time rough and elastic (or elasto-plastic), and this is important when studying sliding friction. In the context of static contact however, some simplifying assumption can be made. I will consider the case of an elastic surface that is perfectly flat down to atomic scale in the absence of external forces, and an opposing surface that is atomically rough, but strictly rigid.
The two surfaces are oriented horizontally. The underlying rigid rough surface is described by a random variable defined over the plane $\xi({\bf r})$. In the numerical simulations the values of ${\bf r}$ will be restricted to lie on a two dimensional square mesh.
Two cases will be considered separately: one in which the $\xi({\bf r})$ are drawn from a unique Gaussian distribution
independently for each value of ${\bf r}$, and a second case in which the $\xi({\bf r})$ is spatially correlated in order to model a self-affine surface (see below).

A realistic modeling of the upper elastic surface should consist in principle in determining the equilibrium values of a three dimensional vector displacement field ${\bf u}$ depending upon the two horizontal coordinates, under the action of the surface forces, taking into account the elastic response of the surface, measured by an appropriate response function. This is what a full contact mechanics calculation aims to. In the present case, and already foreseeing the further inclusion of creep effect, some drastic simplifications have to be made.

The simplified description of the elastic surface (sketched in Fig. 1)
consists of a collection of scalar coordinates $u({\bf r})$, representing the vertical positions of the elastic surface at point ${\bf r}$, which are coupled via elastic springs connecting nearest neighbor mesh points, and elastic interactions with the bulk of the material, defined by a set of coordinates $u^0({\bf r})$. Note that the only degrees of freedom I allow are vertical displacements, and along this direction all the springs act.
This modeling of the elastic surface is highly simplistic, but at this point this is necessary in order to have a solvable model. Note in particular that the consideration of only vertical displacements means that we are dealing with a material with ``zero Poisson ratio".
Also, it can be seen that a localized force onto this surface generates a distortion that decays exponentially with distance, whereas the true response of a semi-infinite elastic body is known to decay as $\sim r^{-1}$.
The limitations and some unrealistic features of the elastic model I am using are described in more detail in the last section of the paper.

The restriction imposed by the contact geometry is that $u({\bf r})\geq \xi({\bf r})$.
Given a set of values $u^0({\bf r})$, the elastic energy of the system
is
\begin{equation}
E=\frac{k_0}{2}\sum_{({\bf r},{\bf r}')} [u({\bf r})-u({\bf r}')]^2 +\frac{k_1}{2}\sum_{{\bf r}}[u^0({\bf r})-u({\bf r})]^2
\label{e}
\end{equation}
where $({\bf r},{\bf r}')$ stands for pairs of neighbor sites on the numerical mesh. In all cases periodic boundary conditions will be used.
The equilibrium values of $u$'s are thus found by solving the set of equations obtained by minimizing Equation (\ref{e}), namely
\begin{equation}
k_0(\nabla^2 u)({\bf r})+k_1[u^0({\bf r})-u({\bf r})]=0
\label{us}
\end{equation}
(where $\nabla^2$ is the discrete Laplacian operator on the square lattice, lattice parameter is taken as unit of length) with
the constraint imposed by the contact condition $u({\bf r})\geq \xi({\bf r})$.
The number of points for which $u({\bf r})= \xi({\bf r})$ is the number of contact points, and I will take this number as a measure of the contact area $A$ in the model.
The global vertical position of the elastic surface can be measured by the mean value $\overline {u^0}$ of the $u^0$'s.
Note also that $\overline {u^0}$ can be interpreted as a measure of the nominal distance between the two bodies and that the normal force $F_N$ is the sum of the forces of all vertical springs, i.e, $F_N=k_1\sum_{\bf r} (u({\bf r})-u^0({\bf r}))$.

Conceptually in the same manner as in previous work\cite{uno,dos}, plastic relaxation is incorporated through a time dependence of the values of $u^0({\bf r})$. The form of the evolution will be obtained from the prescription that the energy of the system $E$ tends to be reduced during relaxation. Concretely, I use
\begin{equation}
\frac{du^0({\bf r})}{dt}=R\nabla^2\frac{\delta E}{\delta u^0({\bf r})}=k_1 R\nabla^2 (u^0({\bf r})-u({\bf r}))
\label{u0s}
\end{equation}
i.e, a standard relaxation equation that tends to reduce the value of $E$ over time as much as possible. The time scale for relaxation (controlled by $R^{-1}$) will be assumed to be much larger than the elastic time scale in which the elastic variables $u$ accommodate to satisfy Eq. (\ref{us}).
Note that the meaning of Eq. (\ref{u0s}) is that relaxation makes the force exerted by the vertical springs tend to an uniform value when $t\to\infty$.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f1.eps}}
\caption{One dimensional sketch of the model. (a) A flat and elastic surface (defined by the black dots) on top of a rigid rough one (defined by the top of the vertical segments), before contact.(b) The situation after contact.
Dots [with vertical coordinates $u({\bf r})$] are in equilibrium under the action of vertical and horizontal springs, and eventually the force exerted by the rigid rough surface defined by $\xi({\bf r})$. The coordinates $u^0({\bf r})$ evolve in time according to the relaxation equation (\ref{u0s}). The external control parameter is the mean value $\overline{u^0}$.
}
\label{f1}
\end{figure}

The variable that is assumed we can control is $\overline {u^0}$. In this respect, note that this variable is not modified by the time evolution [Eq. (\ref{u0s})]. Actually, this is one of the reasons to use a conserving dynamics, in which the Laplacian operator is introduced in Eq. (\ref{u0s}), instead of a non-conserving one, in which the Laplacian is absent\cite{chl} (in connection with this choice, see also the final Section of the paper).
To describe a possible experimental situation, I first assume (Fig. \ref{f1}(a)) that $\overline {u^0}$ is very large, in such a way that there is no contact between the two surfaces at any point. Allowing infinite time to relax under this condition, the system reaches the uniform state in which $u^0({\bf r})=\overline{u^0}$ and $u({\bf r})=\overline{u^0}$ everywhere. This is in fact the most relaxed configuration since the elastic energy of every spring is zero. I then place $\overline {u^0}$ at some value in which contact occurs at some positions (Fig. \ref{f1}(b)), and solve Equations (\ref{us}) and (\ref{u0s}) as a function of time.
Numerically, the procedure consists in advancing the solution of Eq. (\ref{u0s}) for $u^0$ by one time step, solve Eq. (\ref{us}) using a standard relaxation algorithm\cite{numrec} for the new values of $u$, and iterate the process.

\section{Results for uncorrelated roughness}

I first show results in the case in which the variables $\xi({\bf r})$ that describe the roughness of the underlying surface are taken independently at each site, from a Gaussian distribution of zero mean and unitary variance. Although this case is not very realistic, we will see that in addition to the possibility of accurate numerical simulation, it allows for very insightful analytical treatment.
Results corresponding to $R=0$ are presented in Fig. 2, where the contact area $A$ (i.e., the number of points in contact) is plotted against $F_N$. Curves for different values of the ratio $k_1/k_0$ are shown.
Two main regimes are observed. For low normal load the contact area is essentially proportional to the load, whereas if load is too high, we reach a regime of full contact.
The crossover between partial contact and full contact occurs at a value of $F_N$ that depends on the elastic constants of the model. If one of the spring constant dominates over the other the crossover value of $F_N$ is proportional to the dominating spring constant. For instance, if $k_0$ is negligible compared to $k_1$, the elastic surface becomes a collection of independent springs (in other contexts this kind of description of an elastic surface is described as the Winkler model\cite{winkler}), and the crossover to full contact occurs for a normal load per spring of order $k_1\sigma$, where $\sigma$ is the typical roughness of the surface, that is taken as 1 in the present simulations.

Given the equilibrium configuration for some value of $F_N$, we can set a finite value of $R$ and follow the evolution of the contact area in time. In this process it has to be taken into account that if we keep $\overline {u^0}$ fixed, the value of $F_N$ will change in time. Since experiments are usually done at constant normal force instead of constant relative distance, I implemented a feedback loop in the simulation that allows to keep the value of $F_N$ as constant by changing $\overline{u^0}$.

The asymptotic ($t\to \infty$) value of the contact area is determined (according to Eq. \ref{u0s}) by the condition that forces on all springs $k_1$ are equal\cite{notita}. In this situation the actual value of $k_1$ is irrelevant, and the fully relaxed contact area becomes a function of $F_N/k_0$ (Fig. 1, open symbols).
Note that this asymptotic value of the contact area is not in general equal to the nominal area, i.e., the system does not reach full contact unless $F_N$ overpasses a crossover value that is proportional to $k_0$. In particular this means that if we consider the simplest case $k_0=0$ we obtain the unrealistic result that the contact area tends to the
nominal value as $t\to\infty$. This is the reason that makes mandatory the use of a lateral spring $k_0$ in the model.
In view of standard experimental conditions, below I will concentrate in cases in which $F_N$ is such that the contact area is only a small fraction of the nominal one.
I found that the dependence of the asymptotic contact area with normal force at low loads follows a power law  $A(t\to \infty)\sim F_N^p$, with an exponent $p\sim 0.8$.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f2.eps}}
\caption{
Contact area as a function of normal load, for different values of $k_1/k_0$ without relaxation (full symbols), and the fully relaxed state (open symbols), in which all the forces on the $k_1$ springs are equal, in a system of 200 $\times$ 200 elements. Note that the relaxed state has always a contact area larger than unrelaxed states with the same normal force. For reference, a dotted line with a slope of 1 is also plotted.}
\label{f2}
\end{figure}

The curves in Fig. \ref{f2} correspond either to ``instantaneous" or to ``fully relaxed" values of the contact area.
As a function of the contact time, the values of the contact area must evolve between these two limits.
First of all, note from Fig. \ref{f2} that the fully relaxed contact area is always larger than the unrelaxed configuration with the same normal force. This means that contact area will increase in time when relaxation is acting, which is the expected result.
The full temporal evolution of the contact area obtained by solving Eqs. (\ref{us}) and (\ref{u0s}) is shown in Fig. 3 for different values of the normal force $F_N$. I have found that all curves of Fig. 3 are very well described by expressions of the form
\begin{equation}
A(t)/A(0)=a-\frac{a-1}{(t/t_0+1)^q},
\label{a}
\end{equation}
i.e., they indicate a saturation towards the asymptotic value with the form of a power law.
The values of $a$, $q$, and $t_0$ depend on $F_N$. In particular, the dependence of the exponent $q$ on $F_N$ is seen in an inset in Fig. \ref{f3}. It is remarkable that $q$ has a dependence on $F_N$ of the form $q\sim F_N^{\beta}$ with $\beta$ being close to $0.5$. This means in particular that for $F_N\to 0$, we can approximate Eq. (\ref{a}) by
\begin{equation}
A(t)/A(0)=1+C\ln(t/t_0+1) ~~~~~{\mbox {for}}~~ F_N\to 0
\label{log}
\end{equation}
with $C=(a-1)q$. It is numerically found that the value of $C$ is not singular in this limit.
Since experimentally the values of $F_N$ are typically tiny compared to those necessary to reach full contact, we can say that
Eq. (\ref{log}) shows that in general we must expect a logarithmic increase of the contact area in time.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f3.eps}}
\caption{Time evolution of the contact area, for different values of $F_N$, and two values of the ratio $k_1/k_0$, for a system of 200$\times$200 sites. The corresponding fitting with the expression given in the text (Eq. \ref{a}) is shown by thin continuous lines. The exponent $q$ in the fitting function is plotted as a function of $F_N$ in the inset, where it is seen that $q$ goes to zero with $F_N$ as a power law (dotted line in the inset has a slope of 0.5).
}
\label{f3}
\end{figure}

\section{Results for Self-Affine Surfaces}

The results of the previous section were obtained using uncorrelated asperities. Numerically, there is no additional complication in trying more realistic distribution of surface roughness (although this will preclude analytic treatments as that of the next Section).
Real surfaces are in fact better described as self affine fractals\cite{fract}, and are characterized in terms of its Hurst exponent $H$. This exponent measures the decaying in wave vector of the spectral distribution of surface roughness. In this section I present numerical results using a self affine surface, and show that the results are qualitatively similar to those of the previous section.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f5.eps}}
\caption{(a) Topography of one realization of a self affine surface ($H=1/2$) in a a system of size 256 $\times$ 256 sites and $k_1/k_0=10$. Surface height goes form -0.3 to 0.3 from back to white. (b) Contact surface as a function of load, in the absence of relaxation.
}
\label{f51}
\end{figure}

I construct the self affine rough surface using the successive random mean point algorithm of Voss \cite{voss,robbins}.
The surface is characterized by its Hurst exponent $H$ and its small scale rms roughness $\Delta$.
The algorithm for the definition of the self-affine rough surface proceeds as follows\cite{robbins}: given a mesh of size $L\times L$ (for convenience $L$ is chosen to be a power of 2) the central point of the mesh is given a value of $\xi$ chosen at random from a Gaussian distribution with zero mean and width ${\ell}^H\Delta$, where ${\ell}=L/\sqrt{2}$ is the distance from the center to the corners. This center now becomes a corner of four new squares rotated by 45 $^\circ$ and with a new center-to-corner distance ${\ell}$ smaller by a factor $\sqrt{2}$. The value of $\xi$ at the center of each new square is obtained as the average of $\xi$ at the four corners plus a random value chosen from a Gaussian of width ${\ell}^H\Delta$. The process is iterated down to ${\ell}=1$. This algorithm produces a surface that is self-affine in the spatial scale between the mesh size and the full system size.
A Hurst exponent $H=0.5$ will be used (tests using other values of $H$ show no qualitative differences). I also use the value $\Delta=0.01$.
An example of the kind of surface obtained by this method is presented in Fig. \ref{f51}(a).
Once the underlying rough surface $\xi({\bf r})$ is defined in this way, the contact with the elastic surface is numerically evaluated exactly by the same methods used in the previous Section.
The actual contact area in the absence of relaxation and for different values of $F_N$ can be seen in \ref{f51}(b).
This looks qualitatively similar to the results obtained using more realistic elastic surfaces, as that made in Ref.
\cite{robbins}.
In Fig. \ref{f4} I present results for the dependence of the contact area on $F_N$ in the present model.
In the absence of relaxation, the dependence can be fitted by an expression of the form $A \sim F_N^q$, with $q\simeq 0.8$, i.e, is a slightly sub-linear dependence. Other numerical analysis of this problem, like those in Ref. \cite{robbins}
have obtained a linear dependence.
I attribute this slight discrepancy to the somewhat artificial description of the elastic surface in the present approach, compared with the more precise, truly three dimensional description in Ref. \cite{robbins}.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f4.eps}}
\caption{Contact area for a self affine surface with Hurst exponent $H=1/2$, using $k_1/k_0=10$. Solid symbols: Contact area as a function of normal load without relaxation, for two system sizes. A power law with exponent 0.8 is plotted as a reference. Note the independence of the contact area on system size in the region away from full contact.
Open symbols: corresponding fully relaxed states for the two system sizes analyzed.}
\label{f4}
\end{figure}

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f6.eps}}
\caption{Time evolution of the contact area in the presence of relaxation for a self affine surface with $H=1/2$ (a) Un-normalized values for different normal forces and system sizes. (b) Results in units of the initial area for two different values of $k_1/k_0$. The results in (b) are well approximated by a logarithmic time increase with a slope that is independent of normal force, and roughly proportional to the value of $k_1/k_0$.
}
\label{f6}
\end{figure}

Now I will consider the effect of relaxation.
The value of the limit contact area, i.e, the contact area at infinite time as a function of the normal force can be seen also in Fig. \ref{f4}. This curve, as in the uncorrelated case, was
obtained in a simulation in which a constant force on each of the vertical springs is imposed.
The results for the increase of contact area with time are presented in Fig. \ref{f6} (note that the values of $F_N/k_0$ correspond, according to Fig. \ref{f4} to cases in which the contact area is a small fraction of the nominal one).
We see that qualitatively the behavior is very similar to the previous case.
In particular, for the case of very light loads and except for very long times, a very good fitting is provided by an expression as that given by Eq. (\ref{log}), with $C$ being independent of the external load.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f7.eps}}
\caption{Time evolution of the contact surface for $F_N/k_0=10$, $k_1/k_0=10$. System size is 256 $\times$ 256. The final configuration in the last panel ($t\to \infty$)
is obtained from an independent simulation, as explained in the text.
}
\label{f52}
\end{figure}

We can see the actual contact surface
at different times in Fig. \ref{f52}. We observe how the increase of contact area involves both an increase of the area of individual contact spots, and the appearance of new ones. This trend is very similar to the experimental findings of Dieterich and Kilgore\cite{dk}. The asymptotic surface of contact (which cannot be typically accessed experimentally), shown in the last plot in Fig. \ref{f52}, displays a uniformly scattered distribution of contact points. In particular, points that were at contact in the first stages of the process may become detached at very long times, due to the stress redistribution that occurs due to relaxation.

\section{Analytical Results}

In the limit of very light loads, the contact between surface and substrate occurs only in very few points. If
we are considering the case of uncorrelated surface roughness, these contact point  will typically be well separated spatially.
This allows for an analytical solution of the model in this limit. We will confirm in this way the logarithmic increase of contact area in time. The analytical treatment I present turns out to be formally similar to that made in the
viscoelastic Greenwood-Williamson model \cite{caroli,hui,gauss-exp,ronsin}. In fact, the creep phenomena I am modeling through the relaxation mechanism is a kind of viscoelastic relaxation \cite{lakes,fischer-c1,fischer-c2}.
I will come back to this point by the end of the paper.

The strategy to find the solution in this limiting case is to calculate the response of the system in an ``indentation hardness test"\cite{fischer-c2}, and then exploit the linearity of Eqs. (\ref{us}-\ref{u0s}) to find the full solution.
In fact, due to their linearity, Eqs. (\ref{us}-\ref{u0s}) can be solved by Fourier decomposition.
In the case there is a single contact point between the two surfaces (supposed to be the coordinate origin) on which the force is zero for $t<0$, and takes some constant value $f_0$ for $t>0$, a direct calculation of the Fourier modes $\tilde u_q$ gives:

\begin{equation}
\tilde u_q=f_0 \left [ \frac{1}{k_0q^2}+\left (\frac{1}{k_1+k_0q^2}-\frac{1}{k_0q^2} \right)\exp[-z_qt]\right]
\label{uq}
\end{equation}
where
\begin{equation}
z_q=\frac{Rq^4k_0k_1}{k_1+q^2k_0},
\end{equation}
and the initial condition $u^0({\bf r})=0$ at $t=0$ (corresponding to a totally relaxed configuration {\em before}
contact) has been used.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f8.eps}}
\caption{The dimensionless $G(x_1,x_2)$ function (Eq. (\ref{u})) as a function of $x_2$, for different values of $x_1$. Note the logarithmic increase for large $x_2$, independent of the value of $x_1$. Dotted line is the function $a_0 \ln (x_2)+a_1$, with $a_0=0.04$, $a_1=0.3$.
}
\label{funciong}
\end{figure}

By Fourier inverting this expression we can obtain the time evolution of the surface under this indentation condition. Of particular importance will be the time evolution of the variable $u$ at the contact point, i.e, $u({\bf r}=0,t)$, and its velocity $v_0(t)\equiv du({\bf r}=0,t)/dt$.
The structure of Eq. (\ref{uq}) allows to write the solution in the form

\begin{equation}
u({\bf r}=0,t)=\frac{f_0}{k_0}G\left(\frac{k_1}{k_0},k_0Rt\right)
\label{u}
\end{equation}
and
\begin{equation}
v_0(t)=f_0RG'\left(\frac{k_1}{k_0},k_0Rt\right)
\label{v0}
\end{equation}
where $G(x_1,x_2)$ is a dimensionless function of two variables, and $G'(x_1,x_2)\equiv dG/dx_2$. In Fig. \ref{funciong} I show the values
of $G$ as a function of $x_2$, for a few different values of $x_1$. We see that for $x_2$ sufficiently large (this means according to Eq. (\ref{u}), for $t$ sufficiently large) the function has a logarithmic increase, with a slope that is independent of other parameters of the model.
The form of the function $G$ is all we need to get a full solution of the contact problem on the assumption of few well separated contacts.

In the contact geometry, the value of $u({\bf r}=0,t)$ must be constant and equal to $\xi({\bf r}=0)$. In order to maintain the contact force equal to $f_0$, we have to adapt $\overline {u^0}$ accordingly,  namely
we must have
\begin{equation}
\frac{d\overline {u^0}}{dt}=-v_0(t)
\label{du0}
\end{equation}
To solve the problem of many contact points (in the assumption  that the distance among them is large compared to the size of the distortion that any contact exerts onto the surface)
we first need to generalize the form of $v_0(t)$ for a constant force $f_0$, to a new function $v(t)$ for an arbitrary time dependent form of the contact force $f(t)$. This can be done from the previous solution because of the linearity of the equations. The result is

\begin{equation}
v(t)=\int_{-\infty}^{t} d\tau R\frac{df(\tau)}{d\tau}  G'\left(\frac{k_1}{k_0}, k_0R(t-\tau)\right)
\label{vt}
\end{equation}
To generalize Eq. (\ref{du0}) to the case of many contacts, under the action of a total normal force $F_N$,
I use the fact that this normal force has to be distributed among all contacts at any time.
We obtain

\begin{equation}
\frac{d\overline {u^0}}{dt}=\frac{\sum_{m} v_m(t)}{N(t)}
\end{equation}
where $N(t)$ is the number of points at contact at time $t$, $m$ labels the contact points, and $v_m(t)$ is expression (\ref{vt}) calculated with the particular (still unknown) form of $f_m(t)$ for the contact force at point $m$. Using Eq. (\ref{vt}) and the fact that all forces must sum up to $F_N$, we obtain the simple result
\begin{equation}
\frac{d\overline {u^0}}{dt}= \frac{v_0(t)}{N(t)}
\end{equation}
where $v_0(t)$ is given in Eq. (\ref{v0}).
Namely, the change of the control variable is equal to a prescribed function of time, divided by the actual number of contacts at that time.
From here, and assuming a generic distribution of asperities given by a probability distribution $P(\xi)$, the following equation for the time evolution of the number of contacts can be derived:

\begin{equation}
\frac{dN(t)}{dt}=N_0P(\overline {u^0}(t))\frac{d\overline {u^0}}{dt}=\frac{N_0P(\overline {u^0}(t))v_0(t)}{N(t)}
\end{equation}
where $N_0$ is the total number of mesh points in the system. Integrating, one obtains
\begin{equation}
\int_{N(t=0)}^{N(t)} \frac{N(t')}{P(\overline {u^0}(t'))}dN(t')=N_0\int_0^t v_0(t')dt'
\end{equation}
The integral on the left of this equation is explicit, but it is not analytic if the $P$ distribution is taken to be a Gaussian. We can replace the Gaussian form of $P$ by an exponential to obtain a closed form, i.e., assuming $P(\xi)=\gamma \exp(-\gamma \xi)$, we obtain
\begin{equation}
N(t)=N(t=0)\left (1+k_1\int_0^t v_0(t')dt' \right).
\label{ndet}
\end{equation}
where $N(t=0)$ is the number of contacts at $t=0$, and is given (for exponentially distributed asperities) by
$N(t=0)=\gamma f_0/k_1$.
Using the asymptotic form of $v_0$ (Eqs. (\ref{u}),(\ref{v0}), and Fig. \ref{funciong}), we obtain for large $t$
\begin{equation}
\frac{N(t)}{N(t=0)}\simeq\frac{a_0 k_1}{k_0}\ln \left(k_0Rt\right).
\label{ndet2}
\end{equation}
with $a_0\simeq 0.04$.
As numerically shown by Greenwood and Williamson\cite{gauss-exp} the consideration of a Gaussian distribution of asperities does not alter this result in the load range in which $1\ll N(t)\ll N_0$.
In this way, we obtain analytically a result that is nicely compatible with the numerical results: for small loads, the contact area increases logarithmically in time, and once scaled with the value of the area at $t=0$, the result is independent of the precise value of the applied force.
Note also that the numerical results (Figs. \ref{f3} and \ref{f6}) show an increase of the logarithm prefactor when $k_1/k_0$ is increased, compatible with Eq. (\ref{ndet2}).
The main
hypothesis to derive Eq. (\ref{ndet2}) have been the uncorrelated distribution of asperities, and the fact that elastic distortions of the surface at the contact points do not influence other contact points, and this means that the contact points have to be sufficiently away from each other. I will analyze this expression further in the last section of the paper.

\section{Summary and discussion}

In this paper, a simplified model for the time evolution of the contact area between solid bodies in contact has been presented. The goals of the model are twofold. On one side, for very light loads and in the case of a totally uncorrelated surface roughness, the model can be worked out analytically, and it can be shown that a logarithmic dependence of the contact area with time emerges. This means that we are able to go all the way from a well defined statistical model to its solution, and obtain logarithmic aging. Secondly, numerical simulations can be done in cases where the applied load is not necessarily small, and systematic dependences of the contact area in time others than logarithmic have been found in this case. Also, the model allows to study more realistic cases in which the roughness of the surface is assumed to be correlated.
I now focus on a discussion of the process of logarithmic increase in time of contact area, that is the most directly comparable with available experimental results.

The analytical results of the previous Section provide the clearest understanding of the origin of such a logarithmic increase within the framework of the present model. In fact, this logarithmic increase is originated in the form of the surface response to a localized and constant applied load. This can be rephrased in the following form:
If we push the surface of (our model of) an elastic body with a constant force at a single point, and look for the deformation this force produces, the indentation increases logarithmically in time due to the relaxation processes considered by the model.
In this respect, I notice that the logarithmic increase is crucially dependent on the dimensionality of the surface. For instance, in the case of a line (i.e., the border of a half plane) the same relaxation mechanism would produce a displacement that grows with time as $t^{1/4}$ (this dependence appearing when summing up the $q$ modes of Eq. (\ref{uq}) in a one-dimensional geometry), which is (at least in principle) discernible from a logarithmic increase. It thus remains to be seen if there are experimental realizations on this confined geometry configuration that allows to test this prediction.

I now want to discuss in more detail the analytical expression in Eq. (\ref{ndet2}), that we saw is well verified in the simulations, and compare it with available experimental results.
One of the most detailed experimental studies of temporal effects in friction measurement have been provided by Baumberger and co-workers in a series of papers \cite{caroli,berthoud,baum1,baum2}.
One important parameter they consider, is the coefficient defined as the derivative of the static friction coefficient $\mu_s$ with respect to the logarithm of the hold time\cite{caroli,marone0}, namely $B\equiv \frac{d \mu_s}{d\ln(t)}$. This hold time is the time during which the two surfaces are left in rest contact, before the friction force necessary to start sliding is measured.
 This coefficient (that is independent of the time unit chosen) is typically found to have a conserved value for a variety of materials, in a range close to
$10^{-2}$.

Following Tabor\cite{bt}, the friction force $F_{fr}$ between two solids can be written as $F_{fr}=\sigma_S A$, where $\sigma_S$ is the so-called shear strength of the interface and $A$ the real area of contact. Using also the standard expression $F_{fr}=\mu_s F_N$, we can write $\mu_s=A\sigma_S/F_N$, where we see that the friction coefficient is directly related to the contact area. In particular, if we assume that $\sigma_S/F_N$ takes some constant value, we can write
\begin{equation}
\frac{1}{\mu_s}\frac{d\mu_s}{d\ln t}=\frac{1}{A}\frac{dA}{d\ln t}
\end{equation}
and since $\mu_s$ is typically of order one, we can roughly write
\begin{equation}
B\simeq \frac{1}{A}\frac{dA}{d\ln t}\simeq \frac{d(A/A(t=0))}{d\ln t}
\end{equation}
This form gives a direct access to the $B$ coefficient as predicted by the model presented in this paper.
We see first of all (from Eq. \ref{ndet2}) that $B$ does not depend on the relaxation coefficient $R$. This seems a bit surprising but is not contradictory: although the contact area increase in time is produced by a non-zero value of $R$, this coefficient enters directly in setting the time scale (as it is obvious from Eq. (\ref{u0s})) but the logarithmic derivative of contact area is independent of it. Once this fact is recognized, we may ask to what extent the value of $B$ in our model can be considered to be constant, independent of other parameters, and if this is the case, if this value is in the experimentally observed range $B\sim 10^{-2}$. In this respect, it seems that the answer is negative, since the coefficient is directly related to the ratio $k_1/k_0$ (Eq. (\ref{ndet2})), which can in principle be set arbitrarily. However, I already stressed the fact that the description of our elastic surface is not very accurate. In fact, the elastic properties of the surface of an elastic body, that I consider isotropic for simplicity, can be characterized by the values of one elastic constant (the Young modulus $Y$, for instance) and are only weakly
dependent of a second parameter, namely the Poisson ratio $\nu$.
The dependence of $B$ on the dimensionless ratio $k_1/k_0$ is an indication that in a hypothetical more accurate description of the elastic body, $B$ cannot depend explicitly on the value of $Y$. Only a dependence on $\nu$ can exist.
Then I expect in fact a rather weak dependence of $B$ on the elastic parameters of the body, and then a conserved value of $B$ for different materials. Whether this conserved value is compatible with the experimental value $\sim 10^{-2}$ has to be answered once a more realistic description of the elastic surface of the body is done.

Going a step further we must discuss the effect of temperature. The Brechet-Estrin analysis \cite{brechet} predicts that the $B$ coefficient must be temperature dependent, with values that increase with increasing temperature.
Berthoud {\it et al.}\cite{berthoud} were able to observe systematic variations of this coefficient with temperature in different experimental situations, that are roughly compatible with the predictions of Brechet and Estrin. Typically, an increase of $B$ (up to a factor of roughly ten) was observed when the glass temperature of the material was approached.
In the present model it is  not obvious where a temperature dependence can enter that alter the value of the $B$ coefficient. The only obvious temperature dependent parameter is the relaxation coefficient $R$, but we have already
seen that $B$ is independent of $R$.

\begin{figure}
\centerline{\includegraphics[width=.5\textwidth]{contact_f9.eps}}
\caption{Depth of an indentation experiment on the model, under a constant load $f_0$, as a function of time, for $k_1/k_0=3$, in the presence of creep relaxation and viscoelastic relaxation, measured respectively by the coefficients $R$ and $\tilde R$. (see Eq.  (\ref{dosrs})). Note the increase in the slope of the asymptotic logarithmic behavior, as $\tilde R/R$ is increased.
}
\label{indent}
\end{figure}

A possible way out to this situation may involve to consider the possibility of other mechanisms of relaxation, in addition to the one considered in Eq. (\ref{u0s}). For instance, in addition to the present mechanism that responds to the fluctuations of the forces on the $k_1$ springs, we can add a term that is directly dependent of the force itself.
This would generalize Eq. (\ref{u0s}) to an equation of the type

\begin{equation}
\frac{du^0({\bf r})}{dt}=R\nabla^2\frac{\delta E}{\delta u^0({\bf r})}-\tilde R\frac{\delta E}{\delta u^0({\bf r})}
\label{dosrs}
\end{equation}

One of the main qualitative difference caused by the inclusion of the last term is that under the action of a constant
value of $\overline {u^0}$, the value of $F_N$ goes to zero at very large times (contrary to the finite value reached in the presence of the first term alone). In this sense the last term represents a ``viscous" relaxation in the system, that may have a progressively larger effect as the temperature increases towards the glass temperature of the system.
This suggests that $\tilde R/R$ may be considered to be an increasing function of temperature.

The effect of this term can be seen in Fig. \ref{indent}. There I show the time dependence of the indentation depth for a point contact on the surface of the elastic body for increasing values of $\tilde R/R$. These results are obtained by solving analytically the system equations for $u_q$ as I did in Section V, using Eq. (\ref{dosrs}) instead of (\ref{u0s}), and Fourier inverting numerically the result. We see that the logarithmic increase of $u$ in time is conserved in the presence of the $\tilde R$ term, and the slope increases as $\tilde R$ increases. This slope measures directly the value of $B$ in the model. It can be easily shown that $B$ doubles its value as $\tilde R/R$ goes from zero to large values. This means that the consideration of alternative relaxation mechanisms can justify a variation of the $B$ coefficient with temperature. Whether the change of the $B$ coefficient observed by Berthoud {\em et al.}\cite{berthoud}
is related to a change of relaxation mechanism or not remains to be investigated
further, both theoretically and experimentally.

This research was financially supported by Consejo Nacional de Investigaciones Cient\'{\i}ficas y T\'ecnicas (CONICET), Argentina. Partial support from PICT 32859/2005 (ANPCyT, Argentina) is also acknowledged.\\

redpajama_set_name: RedPajamaArXiv


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