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Science News' Articles
- Letters to the Editor
Letters to the editor
- Letters to the Editor
Letters to the editor
- Science Future
Upcoming events
- Letters to the Editor
Letters to the editor
- SN Online
SN Online
See good news for birds in "So far, the great tit has coped with climate change."
Fossils show how birds shifted their weight as they evolved. Read "Birds may have had to crouch before they could fly."
Flowerlike corals pulsate to boost photosynthesis by algae harbored inside. See "Why corals do calisthenics."
Tom Siegfried examines theories of generosity in "Greed may breed financial fitness, but evolution allows unselfishness to survive."
- Reviews & Previews
A Palette of Particles by Jeremy Bernstein
A guide to the subatomic realm uses the metaphor of a painter's palette, with protons, neutrons and electrons as primary colors and more exotic particles adding new shades.
Belknap, 2013, 212 p., $18.95
- Reviews & Previews
Between Man and Beast
Victorian explorer Paul Du Chaillu heads into African forests in 1856 to find a mysterious creature then just a rumor in the Western world: the gorilla.
Doubleday, 2013, 331 p., $26.95
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A Renaissance Globemaker's Toolbox
Meet Johannes Schöner, a 16th century mathematician and scientist who collected and corrected the star charts and maps of his day.
Library of Congress, 2013, 176 p., $29.95
- Reviews & Previews
Pieces of Light
A psychologist outlines a new understanding of how the brain forms memories, not by taking snapshots but by re-creating them each time.
Harper, 2013, 305 p., $26.99
- Science Future
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Nb: infants must be under the age of 2 and
children must be under the age of 12 at the time of
Best central position (3 minutes walk to the First cable car) beautiful, comfortable small apartment house "Smaragd", built in 2008. In the district of Gydisdorf, 100 m from the centre, in a sunny position, south facing position. Private: terrace, garden furniture. In the house: storage room for skis, washing machine, tumble dryer (for shared use, extra). Linen change weekly (suppl. charge extra). Room cleaning on request (extra). Communal covered parking. Shopping centre 150 m, restaurant, bar, bus stop 100 m, railway station "500", indoor swimming pool 400 m. Golf course 1.5 km, tennis 1 km, sports centre 400 m, gondola lift 100 m, ski bus stop 120 m. Please note: ski bus (free of charge). There are more similar properties for rent in this same residence. By the terrace there is an alpine garden and a small Bergseeli. 2-room apartment 70 m2, south facing position, very beautiful and cosy furnishings: living/dining room with cable TV. Exit to the terrace. 1 double bedroom with 2 beds (90 cm, length 200 cm). Open kitchen (4 hot plates, oven, dishwasher, microwave, electric coffee machine). Bath/shower/WC. Floor heating. Terrace 45 m2, south facing position, south facing position. Terrace furniture, box-room. Marvellous panoramic view of the mountains. Facilities: Internet (WiFi, free). Reserved parking space n 5. Please note: non-smokers only. Pretty apartment.
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subset: commoncrawl


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Canterbury Cathedral, St Augustine's Abbey, and St Martin's Church
Canterbury Cathedral, St Augustine's Abbey, and St Martin's Church
Canterbury, in Kent, has been the seat of the spiritual head of the Church of England for nearly five centuries. Canterbury's other important monuments are the modest Church of St Martin, the oldest church in England; the ruins of the Abbey of St Augustine, a reminder of the saint's evangelizing role in the Heptarchy from 597; and Christ Church Cathedral, a breathtaking mixture of Romanesque and Perpendicular Gothic, where Archbishop Thomas Becket was murdered in 1170.
Cathédrale, abbaye Saint-Augustin et église Saint-Martin à Cantorbéry
Siège presque cinq fois centenaire du chef spirituel de l'Église d'Angleterre, Cantorbéry, dans le Kent, abrite la modeste église Saint-Martin, la plus ancienne d'Angleterre, les ruines de l'abbaye Saint-Augustin, qui rappellent la mission évangélisatrice du saint dans l'Heptarchie à partir de 597, et la superbe cathédrale de Christ Church, saisissant mélange des styles roman et gothique perpendiculaire, où l'archevêque Thomas Becket fut assassiné en 1170.
الكاتدرائية ودير القديس أغسطين وكنيسة سان مارتان في كانتربيري
بعد أن شكلت مقراً للزعيم الروحي لكنيسة انكلترا طيلة خمسة قرون تقريباً، تحتضن كانتربيري في مقاطعة كنت كنيسة سان مارتان الصغيرة والأولى من حيث القدم في انكلترا، الى جانب آثار دير القديس أغسطين التي تعيد الى الذاكرة بعثة التبشير بالإنجيل التي تولاها القديس المذكور في الممالك السبع منذ عام 597 وكاتدرائية كنيسة السيد المسيح الرائعة بمزيجها الأخاذ بين الطراز الروماني والقوطي العمودي الخطوط والتي شهدت اغتيال المطران طوماس بيكيت عام 1170.
source: UNESCO/ERI
source: UNESCO/ERI
Кафедральный собор, монастырь Сент-Огастин и церковь Сент-Мартин в городе Кентербери
Город Кентербери в Кенте является местопребыванием духовного главы Англиканской церкви в течение почти пяти веков. Важными памятниками Кентербери являются: скромная церковь Сент-Мартин – старейшая церковь Англии; руины монастыря Сент-Огастин – напоминание о роли Св. Августина в крещении «Хептархии» (семи королевств англо-саксов), начиная с 597 г.; и кафедральный собор – захватывающее дух соединение романского стиля и перпендикулярной готики, где в 1170 г. был убит архиепископ Томас Бекет.
source: UNESCO/ERI
Catedral, abadía de San Agustín e iglesia de San Martín en Canterbury
Situada en el condado de Kent, la pequeña ciudad de Canterbury es la sede del primado de la Iglesia Anglicana. Sus monumentos más importantes son: la humilde iglesia de San Martín, que es la más antigua de Inglaterra; las ruinas de la abadía de San Agustín de Canterbury, que traen a la memoria la misión evangelizadora emprendida el año 597 por este santo en los reinos de la Heptarquía; y la soberbia Iglesia Catedral de Cristo, escenario del asesinato del arzobispo Thomas Becket en el año 1170, en cuya arquitectura se funden con increíble acierto el estilo románico y el gótico perpendicular.
source: UNESCO/ERI
source: NFUAJ
Kathedraal van Canterbury, Sint Augustinus abdij en kerk van Sint Martin
Canterbury ligt in Kent en is sinds bijna vijf eeuwen de zetel van de geestelijk leider van de Kerk van Engeland. Aartsbisschop Thomas Becket werd in 1170 vermoord in de kathedraal van Canterbury, mede hierdoor is Canterbury van belang als pelgrimsoord. Na de moord en de heiligverklaring van Becket transformeerde de kathedraal en trok pelgrims uit heel Europa. Andere belangrijke Canterbury-monumenten zijn de bescheiden kerk van Sint Martin (de oudste kerk in Engeland) en de ruïnes van de Sint Augustinus abdij (een herinnering aan de evangeliserende rol van deze heilige in de Heptarchie vanaf 597).
Source: unesco.nl
Outstanding Universal Value
Brief synthesis
Christ Church Cathedral Canterbury in Kent, South East England, a breath-taking mixture of Romanesque and Gothic architecture, has been the seat of the spiritual head of the Church of England for nearly five centuries. Following the murder of Archbishop Thomas Becket in 1170 AD and his subsequent canonisation it became a place of pilgrimage. St Martin's church and the ruins of St Augustine's Abbey form the other main elements of the Property.
St Martin's Church, the ruins of St Augustine's Abbey and Christ Church Cathedral together reflect milestones in the history of Christianity in Britain. They reflect in tangible form the reintroduction of Christianity to southern Britain by St Augustine, commencing at St Martin's Church where Queen Bertha already worshipped, and leading to the conversion of King Ethelbert. They also reflect the successive architectural responses to Canterbury's developing role as focus of the Church in England – adaptation of Roman buildings, the development of Anglo-Saxon building in mortared brick and stone, and the flowering of Romanesque and Gothic styles in addition to the development under St Augustine and the monks from Rome, of early Benedictine monasticism, which spread from its cradle in Canterbury throughout Britain, had a profound impact on English society. The Abbey scriptorium was one of the great centres of insular book production, and its influence extended far beyond the boundaries of Kent and Northumbria. The development of literacy, education and scholarship at the Abbey meant that Canterbury became the most important centre of learning in the country and Canterbury's importance as a pilgrimage centre, based on Augustine and its other early saints, was transformed by the murder and canonisation of Archbishop Thomas Becket, whose Cathedral shrine attracted pilgrims from all over Europe and Canterbury became the seat of the spiritual leader of the Church of England. The wealth and power of the Cathedral in the 12th century resulting from the offerings of large numbers of pilgrims helped the building of the magnificent enlargement of the east end, with its exceptional stained glass windows and the rebuilding of the choir and transepts following the fire of 1174. These features form one of the finest examples of Early Gothic art and the Cathedral's rich panorama of Romanesque, early Gothic and late Gothic art and architecture is exceptional.
Criterion (i): Christ Church Cathedral, especially the east sections, is a unique artistic creation. The beauty of its architecture is enhanced by a set of exceptional early stained glass windows which constitute the richest collection in the United Kingdom.
Criterion (ii): The influence of the Benedictine abbey of St Augustine was decisive throughout the Middle Ages in England. The influence of this monastic centre, and its scriptorium, extended far beyond the boundaries of Kent and Northumbria.
Criterion (vi): St Martin's Church, St Augustine's Abbey and the Cathedral are directly and tangibly associated with the history of the introduction of Christianity to the Anglo-Saxon kingdoms.
The three parts of this property, St Martin's Church, St Augustine's Abbey and Christ Church Cathedral, are linked by its buffer zone. The St Martin's Church component of the property is aligned with the boundaries of the Church and Churchyard. The main part of St Augustine's Abbey, including most of its outer precinct, is included within its boundary, although the areas of the precinct now occupied by the Sessions House and gaol that linked the Abbey with St Martin's Church, the Almonry buildings located on Lady Wootton's Green, and the detached 13th century Conduit House are excluded. The Cathedral section of the site is delineated by the ancient boundary of its precinct. The 12th century Conduit House, providing the Cathedral's water supply, located on Military Road is not included in the property.
Although the key attributes of the property are included in the boundaries in terms of the main structures, the visual and ceremonial links between them are only within the buffer zone as are a few ancillary buildings that relate to their functions. The overall integrity of the property thus relies to a degree on its buffer zone. The presence of a busy road through the buffer zone does affect the relationship between the three parts of the property. Development pressures in, or adjoining, the buffer zone are present and require ongoing careful management.
Individual ruins within the property suffer from weather and erosion and require regular inspection, maintenance and repair.
The structure of the Cathedral was said in 2006 to be under threat and a major fundraising campaign was launched to fund ongoing maintenance. This campaign is ongoing and the South East transept is undergoing extensive repair. However, the ruins remaining from Christ Church Priory are still considered to be in need of repair work.
In 1988, at the time of inscription, it was noted that the condition of preservation of the three parts of the property did not meet the same standards. The separateness of the three parts is still reflected by different conservation regimes. Work is ongoing to regularise this and a Conservation Plan has been prepared for the Cathedral. At the time of inscription the Bureau recommended that the Cathedral, St. Augustine's Abbey and St. Martin's Church should be included in one and the same protection area. This has been largely achieved by the designation of scheduled monuments and conservation areas.
St Martin's Church has been in continuous use as a place of worship since the 6th century and the present buildings of the Cathedral above ground since the 11th century. The Cathedral also thrives as a place of learning and pilgrimage including the site of the shrine of St Thomas Becket. The majority of the property therefore maintains its historic use and function.
The Cathedral is the mother church of the Diocese of Canterbury and is also known throughout the world as the seat of the Archbishop of Canterbury and the church which welcomes the ten yearly Lambeth conferences of the bishops of the Anglican Communion.
St Martin's Church has been altered and extended in the 6th, 7th and 14th centuries but the southern wall retains its Roman fabric. The Abbey was largely destroyed during the Reformation and is partially in ruins. The Cathedral and its precinct make up a diversified but coherent assembly of medieval architecture.
The vast Cathedral, and particularly its Bell Harry Tower, still dominates the city as it has done for five hundred years. The tower is the highest building in the city and its location in the valley floor means that it can be seen from surrounding higher land and extensively along the valley. Maintaining views to and from the Cathedral is crucial to sustain this visual dominance.
Inside the Cathedral are magnificent displays of medieval architecture, stained glass and furnishings. The coherence and almost perfect homogeneity of its choir, east transept, unfinished eastern tower, and Romanesque side chapels are still evident and these were seen at the time of inscription as one of the most beautiful architectural spaces of Early Gothic art.
The ruins of St Augustine's Abbey convey its value in a more low key way and the links between it and the Cathedral and St Martin's church need strengthening so that they can be seen as a single property and to convey more readily how they each contribute to the Outstanding Universal Value.
Protection and management requirements
The UK Government protects World Heritage properties in England in two ways. Firstly, individual buildings, monuments and landscapes are designated under the Planning (Listed Buildings and Conservation Areas) Act 1990 and the 1979 Ancient Monuments and Archaeological Areas Act, and secondly through the UK Spatial Planning system under the provisions of the Town and Country Planning Acts.
Government guidance on protecting the Historic Environment and World Heritage is set out in the National Planning Policy Framework and Circular 07/09. Policies to protect, promote, conserve and enhance World Heritage properties, their settings and buffer zones, are also found in statutory planning documents.
Canterbury City Council, the local authority, is concerned with the management, promotion and interpretation of the three property components. Particular objectives are to improve the links between the three components and to preserve and enhance the 'buffer zone' and setting of the three components. The Canterbury District Local Plan includes policies to ensure that the setting of the World Heritage property is protected. The City Council adopted the Canterbury Conservation Area Appraisal. This appraisal includes the three parts of the World Heritage property and an analysis of strategic views into and within the city. The importance of preserving views of the Cathedral is recognised in the document and will be taken into account when assessing applications.
The majority of the Cathedral precincts is subject to the 'Care of Cathedrals Measure 1990' as amended in 2005, which has similar status to an Act of Parliament. The Cathedral itself has a corresponding exemption from listed building consent, as provided for in the 'Ecclesiastical Exemption (Listed Buildings and Conservation Areas) Order 2010.
The whole of the Cathedral precincts, the main parts of St Augustine's Abbey and St Martin's Church and Churchyard are included in Conservation Areas. The World Heritage Site Management Plan Committee is represented on the Canterbury Conservation Advisory Committee (CCAC), together with representatives of local historical, civic and amenity societies, local residential and business interests and local representatives of national professional and amenity organisations. The CCAC looks at all planning applications which affect the conservation areas within the City of Canterbury. This committee gives advice to the Planning Committee of the City Council and gives an opportunity for plans which affect the World Heritage Property itself and the buffer zone to be examined.
The whole of the World Heritage property lies within the Area of Archaeological Importance. Most of the area within the precincts of the Cathedral, together with the remains of St. Augustine's Abbey and part of its medieval precinct are Scheduled Ancient Monuments and many of the buildings within the World Heritage property are statutorily listed.
A Management Plan exists and is being reviewed regularly. The implementation of the Plan is overseen by the World Heritage Site Management Plan Committee that includes representatives of all the key stakeholders. Proposals for a buffer zone are under consideration.
The Dean and Chapter regularly carry out quinquennial inspections of the Cathedral building. A programme of major repairs is being carried out and the Trustees of Canterbury Cathedral Trust Fund are conducting an Appeal to fund this work.
Some of the ruins of the monastic buildings of the former Christ Church Priory are included in category B on the English Heritage 'Buildings at Risk' register. This category states that there is immediate risk of further rapid deterioration or loss of fabric. A solution has been agreed but not yet fully implemented although work is progressing slowly with the assistance of an English Heritage grant.
The three main parts of the World Heritage property have individual tourism management plans for the management of visitors and hold coordination liaison meetings. Canterbury City Council also has a tourist management scheme which is regularly reviewed, and there is frequent contact between the local authority and the constituent parts of the World Heritage property.
Long Description
Canterbury, in Kent, has been the seat of the spiritual head of the Church of England for almost five centuries. St Martin's Church, St Augustine's Abbey and the cathedral are directly and tangibly associated with the history of the introduction of Christianity to the Anglo-Saxon kingdoms. The influence of the Benedictine abbey of St Augustine was decisive throughout the high Middle Ages in England. The influence of this monastic centre and its scriptorium extended far beyond the boundaries of Kent and Northumbria. Christ Church Cathedral, especially the east sections, is a unique artistic creation. The beauty of its architecture is enhanced by a set of exceptional stained glass windows which constitute the richest collection in the United Kingdom.
Within the urban perimeter of Canterbury, three distinct cultural properties are on the World Heritage List: the modest St Martin's Church; the ruins of St Augustine's Abbey; and the superb Christ Church Cathedral, a breathtaking mixture of Romanesque and Perpendicular Gothic, where Archbishop Thomas Becket was murdered in 1170. These three monuments are milestones in the religious history of the regions of Great Britain before the Reformation.
St Martin's Church, to the east, located outside the walls of Roman Durovernum, existed in 597 when the monk Augustine was sent from Rome by Gregory the Great to bring Christianity to the Saxon kingdom of Kent. The church was built for the most part before the 8th century. It undoubtedly includes a Roman structure from the 4th century. Of the church located within the city walls, which St Augustine made his cathedral (probably at the very spot where Christ Church now stands) nothing has been conserved. However, ruins of the abbey are still visible, halfway between St Martin's Church and the cathedral. The abbey was dedicated to the Apostles Peter and Paul. In 978 the primitive institution, veritable cradle of Benedictine monasticism in England, was restored following the Scandinavian invasions. The abbey buildings virtually disappeared in their entirety following the dissolution of the Community by Henry VIII in 1538. The Royal Palace that stood in their place was located against the northern side aisle of the nave. It included the gutter wall and a few old portions, but this structure, too, has disappeared.
Two distinct structures seem to appear in Christ Church Cathedral, a major building of medieval architecture. To the east, partially covering a huge Romanesque crypt with admirably carved capitals, is some of the most beautiful architectural space of early Gothic art: the choir, the east transept, an unfinished apse, on either side of which stand Romanesque chapels dedicated to St Andrew and St Anselm, Trinity Chapel and the circular Corona Chapel. The two architects, William of Sens, a Frenchman, and William the Englishman, worked at the site from 1174 to 1184.
To the west the nave and the facade, with their very pure Perpendicular style, provide balance to the constructions on the eastern side. The architecture and remarkable stained glass and furnishings of Canterbury Cathedral thus provide a complete panorama of Gothic art, from its earliest beginnings to its culmination and decline.Source: UNESCO/CLT/WHC


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Don't miss any of Jack Reacher's adventures.
©2004 Lee Child; (P)2004 Brilliance Audio
"Not Lee Child At His Best..."
There's little new in this Jack Reacher novel...and much that Child has done before again and again -- usually with more interesting results.
The plot's flat and there is precious little to keep you listening. I felt it was "okay." Certainly NOT outstanding.
"Love that Reacher"
This was a new read for me. I find the character fun and mysterious. The story moves and twists and make the time fly. My kind of guy.
disenchanted citizen
"My "Burning" Question Answered"
Yes, at some future point. I often reread books, and there's no reason not to relisten to an audible, especially when it is something I have enjoyed.I have been a fan of the Jack Reacher novels for several years. While I don't recall which one I read first, I know I'd read several of the most recent ones before I decided to go back and read them all in chronological order. This particular one—Echo Burning—provided the answer to my "burning" question: why Did MP Jack Reacher end his military career? I won't give that away in this review—I don't want to spoil it for another who hasn't had that question answered as yet. I'll just say that as always, the plot is complex, the characters, though somewhat predictable, are interesting and believable. To sum it up, I find these novels to be "good reads," and that's what I look for in my leisure reading experience. By the way, this novel is my first experience with Audible/Kindle listening—the reader did a superb job in translating the written word into oral mode—voice, speech rhythm, diction, expression—all contributed to a very satisfactory experience. I've used recorded books for years as accompaniment to my exercise program, and as an antidote to insomnia—I enjoy the Audible experience more than dealing with a tape or CD player, especially during the night. I've learned that it is possible to attach a small speaker to the Kindle in place of my headphones when the volume isn't quite as high as I'd like, and this will remedy my only, very slight, problem.
As you might expect, it was when I finally understood the reason behind Jack Reacher's resignation from the military, and his choice to live as a vagabond.
No, this was my first Dick Hill performance as a reader on a recorded book. I thoroughly enjoyed his contribution and would look forward to hearing him read some book in the future.
I don't think so--it is a very long book, for one thing, and that would be beyond my ability to stay involved, to say nothing of awake. But I enjoy
I wish there way a way to download to 3G Kindle other than via my computer. Takes at least two hours this way, and I'm a bit spoiled by the speed with which the written version is downloaded to my Kindle. I plan to acquire a Kindle Fire at some point and hope that the download process is speedier.
"Not his best"
This was my third Jack Reacher book. The first two were great especially Killing Floor. It really got me into the Jack Reacher series. I didn't finish this one. If I was supposed to feel sorry for Carmen, I couldn't do it. Jack is a smart guy but he fell her story hook, line and sinker. Not like him in other the other books. He questions every thing. The book should have been over in the first two hours. Jack Reacher I've come to know in other books would have walked away.
Dick Hill is a great narrator of these stories and I'm glad Lee Child continues to use him. Love him as Reacher, but please never again have a grown man do a six year old girl's voice.
"Decent modern western"
This is basically one of those Clint Eastwood or Lone Ranger style stories, where a wandering hero meets a damsel in impossible distress. The hero is unbeatable, the damsel is pitiable, and the distress is distressing, so the elements are all there. Beyond that, it will probably depend on whether you like the writer's style or not.
The plot twists are wild and at times too convenient, at others too far-fetched. Lee Child tells the story with such an authority and such detail that you can believe the developments and actions if you let yourself. Jack Reacher, the hero, does things that stretch credulity, and probably break it if you look too closely, so if you are critical, you may want to walk past this one. If you like to be led through a good fantasy that you can sort of imagine happening, this is a good trip.
The story takes place in west Texas and follows a lot of stereotypes. I went back and forth on whether I thought Child had ever been to Pecos, and concluded he probably drove through it. He's got the big things right, but the little details seem rather generic, and the people not very convincing, for the most part. Stereotypical bigots without any nuance are good for an action story, but not for anything more complex.
The damsel is a mixed bag. The details of her history are intriguing, but other than that the character seems simplistic, not believable, even with the plot twists that emerge.
Overall, the story is well told, well written, and fun enough. Better than a lot of stuff in the serial action/detective genres, but not transcendent of the genre. I liked "The Killing Floor" better.
I agree with the concensus on the reader. Great with Reacher's voice, offensive on the female characters. He bleeds the depth out of female characters with too little to begin with, and with one in particular he makes her a joke. Weakest aspect of the story.
"Formulaic and not believable"
Child exaggerates this novel's characters to the point where they're not at all believable. The plot is the usual formula, and utterly predictable.
AUDIO: With the men, Hill isn't that bad, but he pulverizes the women. With the women whom Child portrays as strong, competent and smart, Hill makes them weak, whiney, and querulous. He thus destroys what little sense the plot might otherwise have made.
"Whining Women"
I am a big fan of Reacher, and Dick Hill as a narrator. But this book was very annoying. The two main women characters whined. Reacher would say something, and they would ignore what he said and just whine. The story was, as usual, compelling. I just wasn't crazy about the women characters and their inability to listen.
"Annoying characters and narration"
I usually don't have a problem with getting through a book but this was tough. The Carmen character was so annoying that it was difficult to just listen to her and the narration made things work. Dick Hill's impersonation of female characters really grates on you. Both Carmen and her daughter always come across as whining and weak. Within a few hours of listening to their voices you really just want to turn off the book to end the misery.
"Half and Half"
Well written story. Good production. Dick Hill is a great narrator but he should not agree to do women voices or children. You are too male to do women, I have listen to him on other books Mr. Hill narrated they had a woman do their part. It worked much better. Mr. Hill I really wish you wouldn't sigh in the mics so much. But maybe I will learn not to hear it. Lee Childs wrote an interesting intriguing story. I truly enjoyed. Listener if you can get passed the things critized you can enjoy a well written book. I am glad I bought this book. Lee Childs will be a writer I look for again.
"The Worst Jack Reacher Ever!"
This book started off good. The story was interesting and the narration was great, but about 2/3 of the way thru the book I became so annoyed as Jack Reacher slowly turned into a clarvoyant superman. It just became ridiculous! I had a very hard time finishing it. I'd recommend another book instead of this one.
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Buy Green Products
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Nonlinearity Ramping for Improving Convergence of Nonlinear Problems
Walter Frei | December 3, 2013
As we saw in "Load Ramping of Nonlinear Problems", we can use the continuation method to ramp the loads on a problem up from an unloaded case where we know the solution. This algorithm was also useful for understanding what happens near a failure load. However, load ramping will not work in all cases, or may be inefficient. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence.
Nonlinearity Ramping Example
Consider again the system shown below, of a force applied to a spring with nonlinear stiffness.
We've seen that we can solve this problem using the Newton method with damping or by using the continuation method and ramping the load to give the Newton method good starting points. Now we'll examine how to ramp the nonlinearity. First let's take another look at the function describing the force balance on our single node:
We can re-write this more generally as: f(u)=p-k(u)u where k(u) is the nonlinear spring stiffness. Now we can solve a different problem that uses a stiffness defined as:
In other words, we divide our spring stiffness function into two parts — a linear term, k(u_0), and a nonlinear term, \left[ k(u) - k(u_0) \right] — and then introduce an additional parameter, \beta, that interpolates between the linear and nonlinear case. We then use the same Newton method as before on a series of problems with the parameter \beta, getting ramped from zero to one. That is, we use the continuation method to ramp from a (simple to solve) linear problem to a (more difficult) nonlinear problem.
Next we will look at solving the above example by using this technique. Our original spring stiffness, k(u)=\exp(u), gets re-written as:
We start by solving for \beta=0 and get a linear spring stiffness of k(u)=\exp(u_0), so now all we need to do is choose a linearization point, u_0. For this example, if we choose u_0=0, we see that f(u,\beta=0)=2-\exp(0)u = 2-u. Recall our discussion about solving linear static finite element problems, where we learned that you will always find the solution to a linear problem in a single Newton iteration. Now, ramp up the parameter \beta, as shown:
Clearly, only a few Newton iterations, starting from the solution to the \beta=0 case, are needed to solve \beta=0.25. So we can repeat with \beta=1 and thereby ramp from the fully linear to the fully nonlinear case.
This method is attractive because you can always find a solution to a linear problem, so you can always solve for \beta=0. You only need to consider which point u_0 to linearize about initially and what kind of nonlinearity ramping to use.
We can also use the concept of nonlinearity ramping to address the case where the nonlinear terms are not continuously differentiable. Recall the case from the blog post on Solving Nonlinear Static Finite Element Problems, the system with the piecewise constant spring stiffness, k=0.5 for u\le1.8, k=1 for 1.8<u<2.2, and k=1.5 for u\ge2.2, would result in a force balance function:
As we saw earlier, this problem cannot be solved by the Newton method, unless you happen to start within the (very small) radius of convergence of the solution. But now consider replacing the original spring stiffness with a smoothed stiffness that can be ramped up as shown in the figure below:
Clearly, this problem is solvable, and we can use this technique to get an approximate solution to the original problem. Using this method just requires that we find an appropriate smoothing function and nonlinearity ramping path.
Whenever you have a problem which has the kind of stepped behavior shown above, it is also worth trying out the Double Dogleg nonlinear solver instead of the Newton method. The Double-Dogleg is a Trust Region solver that works well when solving problems where the Newton method may oscillate between two different regions. A good physical example of this is a structural contact problem, where there is a sudden transfer of load as two objects come into physical contact.
Concluding Thoughts on Improving Convergence of Nonlinear Problems
We have now seen two methods for improving the convergence of nonlinear problems: load ramping and nonlinearity ramping. In practice, either or both methods can be used, and, through the careful design of your material properties and loads, it is possible to blend the two approaches. It can be difficult to say ahead of time which method will perform better, and each model you work on will require some experimentation in terms of the load ramping path, the nonlinearity ramping, and the choice of initial condition for linearization. Also, if you expect that the solution may oscillate between different cases, the Double-Dogleg solver can perform better than the Newton method. With experience, you will build up your engineering intuition about how best to solve the classes of problems that you are working on.
The techniques introduced here often work well for nonlinear static finite element problems where it may be difficult to find good initial conditions, or problems which have strong nonlinearities and discontinuities in the material properties. In practice, a very wide class of problems can be addressed using these approaches. However, you must also be aware that there are different meshing requirements when solving nonlinear problems. That is the next topic we will address, so stay tuned.
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Educator Effectiveness
Posted: Wed, 04/16/2014 - 2:28pm Updated: Fri, 07/31/2015 - 8:47am
The Office of Educator Effectiveness and Leadership (EEL) promotes high quality teachers and effective instruction in Indiana's P-12 schools to ensure that all students in the state are provided an excellent and competitive education. EEL provides guidance to school corporations on the implementation of evaluation legislation and locally developed annual evaluations based on multiple measures including student performance. This division works to ensure our future educators are attending high quality teacher preparation programs through the accreditation review process. EEL assists school corporations in the strategic use of Title IIA and related funding to support relevant and effective professional development opportunities.
Staff Directory
|Beatson, Caitlin
|Educator Effectiveness Specialist
|(317) 232-9173
|Mansfield, Tana
|Educator Effectiveness Specialist over Testing and Title II/HQT Specialist
|Pies, Sarah
|Educator Effectiveness Specialist
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Originally Posted by broccoli rob
You must be a big dude Dolphan because you don't look too small next to him..
Richie is 6'3"... dude is 5-6 inches shorter... not sure how that makes him a big dude
Originally Posted by Drfletcherdc
You guys talk about Richie's blocking - next time Garner gets into the game watch him become a turnstile - you will be begging for Incognito to return.
There would be little difference. Incognito is garbage.
Originally Posted by -=DolfanDave=-
Richie is 6'3"... dude is 5-6 inches shorter... not sure how that makes him a big dude
"Girth not length"
she said! (brudump/clash) thank you, try the veal
I didn't realize Chris Farley was still alive and a guard for the dolphins?
Originally Posted by dphins51
That is awesome Richie is my favorite player on the team. He has fight which some of the other players could learn from them...
I knew Richie had a fan out there somewhere. So, you're the one huh?
Originally Posted by Greyboy
small head with building size cement feet.
my granny moves better
Oh yes she does.
I swear Richie looks so much like a human Barney Rubble.
Cool! He kind of looks like Chad Pennington who had one too many Twinkies!
Originally Posted by mrbunglez
Dudes got a small head.....
I think that's an illusion created by his gargantuan body.
Cool story!
Just win Phin baby!
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Practice Philosophy
I have been practicing Plastic Surgery for 20 years with 7 years of training, 10 years in group practice and 3 years in solo practice. I am passionate about both reconstructive and cosmetic surgery and helping patients overcome obstacles in their life and achieve their goals. I believe in patient safety, procedural efficacy and minimal recovery time with maximal results and use my expertice from reconstructive and cosmetic surgery to help all patients. I strive for patient satisfaction through compassionate care and skillful surgery learned throughout my surgery career, always looking towards new innovations as well as traditional methods. I am a member of the American Society of Aesthetic Surgeons as well as International Society of Aesthetic Surgeons and am dedicated to continued learning and education to fully help patients. I have been awarded the Certificate of Advanced Education in Cosmetic Surgery by the American Society of Aesthetic Plastic Surgery for the last 6 years.
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The consultation process is done to help educate patients to the various treatment options available to them, tailored to meet their needs and to help them reach their goals. It is an individualized process with specific recommendations and the opportunity to ask questions. Written materials and pamphlets are provided for the patient to take home with them to review and they will meet my office staff who may help them with teaching and any financial questions they may have.
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Tired of the same old routine?
Why not try something extraordinary—like walking from one end of the U.S. to the other?
This is precisely what James McKeighan is doing.
Pushing or pulling a wheeled cart that carries his belongings, McKeighan recently passed through the Kane area in his quest to walk across America.
[1] http://www.kanerepublican.com/sites/default/files/6.13.13 walker guy COLOR .jpg


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Link Ink: The Amazing Spider-Menace, Dazzler's Dismay and the Changing Faces of Hot Toys
Movies: Captain George Stacy takes aim at Spidey in some viral promo jazz for The Amazing Spider-Man movie.
Gaming: Preordering the PC and/or Mac version of Telltale's The Walking Dead game could score your undead likeness an in-game appearance.
Interviews: Steve Niles discusses Epitaph Records upcoming p


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Win Face Time With Stan Lee
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Bid NOW at http://cgi.ebay.com/ws/eBayISAPIdll?ViewItem&item=300129989278 to win the ultimate opportunity to hang with Stan Lee on a yacht on Friday, July 27, 2007 at this year's San Diego Comic Con International! Six winners will receive:
-Photo and face time with Stan aboard the Illusion TV Yacht, which is anchored in the beautiful San Diego Marina right behind the convention center.
-Two of your own personal comic books signed by Stan Lee and then certified by CGC with the prestigious Signature Series label


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Nathalie Millar
Movie Blog: 'Rust And Bone' Wrestles With Love, Human Nature
"Rust and Bone," a film by Jacques Audiard, explores how our various human natures interact in different relationships and shades of love. But don't expect something sentimental. Take it from the title: this is raw, a love story of wounds.


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Today's Wall Street Journal was riddled with examples of "smart" people in high places making age-old mistakes. And it's the oldest stuff in the book.
Yahoo's CEO misstated his college degree on his online biography. This would have been no big deal until Mr. Thompson decided to lie about how it got there by blaming a search firm. That is when the cover up got him fired. Does this remind anyone of the Martha Stewart lie that put her in jail?
Best Buy's new CEO was caught having an affair with a subordinate and resigned, but the Founder and Chairman didn't tell the ethics committee and is off the board.
Is this arrogance or ignorance? Do they believe they are too valuable to get fired or do they believe they won't get caught? Maybe it is simply lack of common sense. In the case of the CFO tweets, the comments were blatantly unprofessional.
We can spend our time wondering how this stuff still happens, or see the writing on your Facebook wall: it's hard to get away with bad behavior if you plan to publish it on line.
Good behavior is not just required of the ordinary employee. Executives are under closer scrutiny than ever, given that companies are judged by the hiring decisions they make. These executives put their boards in a difficult position, their brand in a bad light, and can put the company's stock price in peril. Best Buy is already struggling to compete with Amazon and Apple, Yahoo with Google. A blaring WSJ headline is certainly not going to help.
Ethics and social media policies are not just for the lowly, and they could be intertwined with an overall media policy. If these companys have them, did they share them with the executives who made these mistakes? I'd love to know how your company handles your code of conduct. Let us know. We won't tell.