Specific heat of classical disordered elastic systems
荷尔德林与希腊
荷尔德林与希腊硕士学位论文THESIS OF MASTER DEGREE 论文题目: 荷尔德林与希腊(英文): H?lderlinand Greece 作者: 葛体标指导教师: 张法教授 2008 年 5 月 10 日论文题目: (中文) 荷尔德林与希腊(外文)H?lderlin and Greece 所在院、系、所 : 哲学院专专业、名、称 : 美学指专导专教专师姓专名、职专称 :张法教授论文主题词 :荷尔德林;希腊;回返; 悲剧性时间转向;正在到来的神学专习专期专限 :2006年 9月至 2008年 7月论文提交时间:2008年 5月10日独创性声明本人郑重声明:所呈交的论文是我个人在导师指导下进行的研究工作及取得的研究成果。
尽我所知,除了文中特别加以标注和致谢的地方外,论文中不包含其他人已经发表或撰写的研究成果,也不包含为获得中国人民大学或其他教育机构的学位或证书所使用过的材料。
与我一同工作的同志对本研究所做的任何贡献已在论文中作了明确地说明并表示了谢意。
签名: 葛体标日期: 2008-05-10关于论文使用授权的说明本人完全了解中国人民大学有关保留、使用学位论文的规定,即:学校有权保留送交论文的复印件,允许论文被查阅和借阅;学校可以公布论文的全部或部分内容,可以采用影印、缩印或其他复制手段保存论文。
签名:葛体标导师签名: 张法日期:2008-05-101摘要论文共五个部分,力求从时间性角度出发,从荷尔德林作品的三种形式和三个阶段历时性地论述荷尔德林与希腊的关系。
引言:概述荷尔德林版本,介绍国外尤其是德语和法语学界荷尔德林研究,分析国内荷尔德林研究现状和欠缺之处。
第一章讨论荷尔德林书信体小说《许佩里翁或希腊的流亡者》中的希腊。
第一节分析法国大革命和德国启蒙思想对荷尔德林的影响,着重指出荷尔德林在古今之争中对启蒙思想继承和批判的交错结构。
第二节指出“从这儿过去有多远?”是小说的核心句,荷尔德林困扰于“回返”和“模仿”的可能性本身。
高中英语文化差异对比单选题50题
高中英语文化差异对比单选题50题1. In Japan, it's common to eat sushi with ___.A. forksB. chopsticksC. spoonsD. knives答案：B。
在日本，人们通常用筷子吃寿司。
选项A 叉子在日本吃寿司时不常用；选项 C 勺子一般不用来吃寿司；选项 D 刀子也不是吃寿司的主要工具。
2. When having a meal in India, people often use their ___ to eat.A. left handsB. right handsC. both handsD. no hands答案：B。
在印度用餐时，人们通常用右手进食。
因为在印度的文化中，左手被认为是不洁的。
选项A 左手被认为不洁，不用来进食；选项C 双手不符合印度的习惯；选项D 不用手无法进食。
3. In Italy, pasta is usually served with ___.A. soy sauceB. ketchupC. cheeseD. honey答案：C。
在意大利，意大利面通常搭配奶酪。
选项A 酱油不是意大利面的常见搭配；选项 B 番茄酱也不是意大利面的传统搭配；选项D 蜂蜜一般不会和意大利面一起食用。
4. In the UK, fish and chips are often eaten with ___.A. forks and knivesB. chopsticksC. handsD. spoons答案：A。
在英国，炸鱼薯条通常用刀叉食用。
英国的饮食文化中，这种食物更适合用刀叉。
选项 B 筷子不符合英国的饮食习惯；选项 C 用手不符合英国的用餐礼仪；选项 D 勺子不太适合吃炸鱼薯条。
5. In France, a typical breakfast may include ___.A. hamburgersB. sandwichesC. croissantsD. dumplings答案：C。
四世纪城市翻译
The Roman city: from the third into the fourth centuryA number of texts from the late third and early fourth centuries provide us with insights into topography of cities, especially Hermopolis Magna and Oxyrhynchus. This is, therefore, a convenient point at which to obtain something of a snapshot( with an exposure time of fifty years) of the developed cities of the Roman period.Hermopolis magnaRoeder’s (1959) Hermopolis ( excavated between 1929 and 1939) was a vast and ruinous site and even the huge resources that had at his disposal were only sufficient to clear small areas in the centre. He uncovered a series of substantial brick buildings which he associated with the water supply system. Roeder excavated numerous ‘public’buildings and identified these with structures known from the papyrological record, though the accuracy of these identifications is rather difficult to assess and many of the remains were inevitably inidentified.Wace, Megaw and Skeat concentrated on a building to the south of the Great Tetrasty in a prime site in the city. Its location was known as Kom el-Kenissa ( the Kom of the church) and, unsurprisingly, they identified the remains of a fifth-century basilical church, the cathedral of the city. The building that pre-dated thechurch was an enclosure of possibly religious function dedicated by the settlers and cavalry of Ptolemy iii. Surprisingly, it remained largely unaltered perhaps until the church was built. Similar continuities were found to the north of the Great Tetrastylon with the building known as the Bastion, excavated by the British Museum team. This plain hall of uncertain function is dated to the Ptolemaic period.The most significant element of continuity, however, was the temple of Hermes-Thoth. The British Museum team excavated the courtyard of the temple, partly to date the end of occupancy. There, they discovered a wall which closed off access to the temple and a rubbish dump on the temple side of the wall. The latest sherds in this dump were Islamic, but most were of fifth-or sixth-century date. The earliest dated form was African red Slip Form 67 dating from 360-470. although the bottom of the dump was not reached because of high ground-water levels, Bailey saw a connection between the formation of the dump and a closure of the temples by Theodosius in 391. the other closely datable material is lamps. Bailey observed that there were no frog lamps ( a very common type from the second century onwards) at the fourth-century monastic site of Kellis in the Nile Delta, which suggested to him that frog lamps ceased to be used by 390 or even 360. there was asingle frog lamp, of a crude type, in the temple forecourt excavations which Bailey dismissed as a residual. The other lamps mainly date from the early fifth century. Since the bottom of the dump was not excavated and pottery forms and the frog lamp which could date before 390 were present, a slightly lower date for the dump seems possible, though it appears very unlikely that the dump could substantially pre-date 390, which is thus an effective terminus ante quem for the closure of the temple. This would seem to be contemporary with the build-up of rubbish on the dromos of Hermes outside the temple where, although some stray fragments are much earlier (third-fourth century), most fragments of African red slip and Egyptian red slip are form 67 (AD 360-450) or later. It is difficult to push the effective end of the temple any earlier.Hermes-Thoth was an important god in the Roman and late Roman period and was associated with a body of mystical and magical texts that became popular in the Greek and Roman world. Such interest should have meant that the cult was well placed to withstand the threats to paganism in the fourth century. The fourth-century archive of Theophanes emanates from a circle closely involved with the temple and tells us something of cult activity, though the archive cannot be closely dated. We can, I think, assume that the temple continued to operate into the final third ofthe fourth century, though the cult had a long afterlife, as the continued circulation of Hermetic texts attests.South of the temple, by the Great Tetrastylon, the brithsh Museum team excavated an Antonine temple. The temple appears to have been robbed out in the mid-or late fourth century and demolished in the early fifth century when a new pavement was laid over the podium of the temple and wells cut in front of the podium. One of the wells contained a coin of AD 390 and some fifth-century pottery. It looks as if the temple may not have functioned beyond the mid-fourth century.The papyri attest several elements of the topography of the city. The most famous text is the repair papyrus, attesting a sequence of buildings across the centre of Hermopolis. The text costs repairs to the stoai along Antinoe street and sometimes deviates to consider other areas in need of refurbishment. I cannot produce a convincing plan of the site. It lists the Gate of the Moon, the Tetrastylon of Athena, at least two private houses, the Antinoeion, the Hadrianeion, the Sarapeion, the Nilaion, the komasterion, the Nymphaion West and East, the Tuchaion, the Gate of the Sun, the first tetrastylon, the north and south stoai, the Apse, the Aphrodiseion, the Great Tetrastylon, the stoa of Athena and the Gate of the Moon, the city had several other major roads, includingDomitian Street just to the south of Antinoe Street. P. Vind. Sal 11 of AD 142 attests a number of avenues within the city, but the text is lacunose. There was also a Kaisareion by 192, a Sebasteion, a gymnasium, Baths of Hadrian, a city treasury and a mysterious covered area known as the kamara. A women’s baths is attested for the fifth century, though it is plausibly a much earlier construction. A temple of Thotoperios had some connection with the oil-workers’ guild. There was also a temple of Boubastis. In the (late？) fourth century, Bishop Plousianos arbitrated disputes at the gates of the Catholic church. The basic topographical framework of the city was enhanced by colonnades along the main paved road. Any visitor entering the city would have found his or her line sight directed along Antinoe Street towards the three tetrastyla whose columns must have risen considerably above the surrounding buildings, acting as ‘spatial punctuation’, marking the main intersections of the city. Proceeding further into the city, the visitor encountered various Classical-style public buildings and avenues, presumably also decked with stoai running north-south. This elongated civic centre culminated in the Great Tetrastylon, with the mysterious Ptolemaic structure to the south, the Roman komasterion to the north, the Bastion and the Antonine temple. Further to the north lay the temple area dominated by the temple ofHermes Trismegistos. The architecture appears to have been mainly Classical, though there were certainly Egyptian elements.Considerable effort was expended in laying out a city that had elements of Classical urban morphology, driving long straight avenues through a possibly more disordered traditional Egyptian Hermopolis give a rather different impression. The letter-carrier was to enter the city through the Gate of the Moon and walk towards the granaries. He was then to take the first street on the left behind the baths and head to the west, go down and up some steps ( presumably crossing a low-level road), turn right and pass the temple enclosure, before coming to a seven-story house with a statue of Tyche (possibly) on the gatehouse, opposite a basket-weaver’s, and there he is to ask. The instructions do not make obvious use of a grid-plan and suggest that even after such a tortuous journey, he had to rely on local knowledge. There is a contrast between the grandiose ‘front’ of the city with its Classical order and the rather freer ’back’ with more alleys and passageways than avenuees.OxyrhynchusThe best topographical information for Oxyrhynchus comes from the early fourth century. There are two major documents and a number of minor texts combine to produce a deeply confusingpicture of the city. P. oxy I 43 verso is undated, but the recto of the papyrus, a related text, is dated to 296, suggesting a date of c. 300 for the verso. The verso is a list of guards and their stations commencing from the north and moving anti-clockwise around the city, as detailed in table 5.3The last three entries have no guards written in, which shows that the text is incomplete. But it seems unlikely that the topographical register lacks many entries.The second text is a report to the logistes concerning areas of the city in need of restoration in AD 316, as in table 5.4 Reconstructing the city from these attestations is a matter of guesswork and very quickly any attempt makes one’s head spin. Nevertheless, various assumptions listed in n. 104 are used to create figure 5.11, a schematic plan, the inaccuracies and wishfulness of which are obvious(103), after extensive discussion, produced a schematic plan of Oxyrhynchus which did not take account of t he then unpublished P.Oxy. Lxiv 4441. I follow Kruger’s plan in most aspects but would stress the considerable doubt the exact location of buildings within the city.In table 5.3 25 entries cover the west of the city and one would expect that about 50 entries would cover the city. The Sarapeion is The Thoereion is reached at 38, about 75 per cent of the way roundthe city. It would be very attractive therefore to see the Thoereion and the Sarapeion at approximately the same latitude weithin the city. Yet, the gymnasium was In the south, with the Thoereion by and probably someway south of the Sarapeion. Figure 5.11 leaves the north-east short of public buildings and clusters buildings near the Sarapein and between the theatre, the gymnasium and the Thoereion in the central and southern sectors. The traditional temples of Sarapis and Thoeris still dominate the topography of the city, a continued importance reflected in the locating of multiple guards in the two temples. They were rivalled, though not equaled, by the gymnasium, the Sarapeion, with its cluster of associated religious buildings and market was a traditional focal point of the city, probably paralleled by the Thoereion. The new buildings of the Roman period appear to have been located with little account of this traditional bifocal topography, being dispersed, though the major development was towards the south of the city, around the gymnasium and the theatre. As in Hermopolis, it seems that wide avenues were cut through the topography of the city and one presumes that their colonnades drew visitors along the main streets and provided some unity to the urban plan.The archaeological record at Oxyrhynchus is extremely poor but provides some illustrative material. The first excavations werepapyrus hunts and Grenfell and Hunt’s archaeological publications were extremely brief. Grenfell’s 1897 account mentioned a large and completely ruined ‘temple’ discernible only from the mound of stone chippings. He portrays a site with a number of very high mounds of rubbish on which the excavation concentrated so as to rescue as many papyris as possible. The architectural remains were mostly destroyed. Subsequent reports (Grenfell and Hunt 1904; 1905; 1906b; 1907) trace the progress of the excavation across the site. Darbishire drew a sketch of the excavations, published in p.Oxy. L, but this, in fact, adds little of value. The photographs and notebooks of the excavations mention Byzantine coffins, a church uncovered in a clandersting dig conducted by locals, and various granite columns.Subsequent visitors found the architectural remains little more inspiring. Petrie (1925:12-14) paused only briefly at the site to clear part of the theatre(104). He uncovered columns lining the street leading from the thratre towards the centre of the city and other fragments of colonnaded streets, one of which culminated in a pillar dedicated to the emperor phokas (AD 602-10) and, further north, a fifth-century statue base. He also found a fragment of a second-century marble statue and some relief sculpture. He then abandoned the city itself and excavated in the necropolis areawhere he discovered a number of church-like tombs.(105) Breccia led two visits to the site between 1928 and 1932 (Breccia 1932;1934). The mounds still stood several feet high in places and broken columns rose from the debris. Breccia’s team cleared a number of buildings, mostly private, and the photographs show houses(?) with paved courts and columns and bastions for supporting upper storeys. They also show barrel-vaulting (inact). Clearly, the extent of the remains overwhelmed the excavators and they were able to make little headway towards uncovering on obviously extremely confusing and late site. Breccia identified little public architecture but did rescue significant amounts of sculptural material including large numbers of funerary reliefs.(106) These are often of full-scale human figures. The style of these owes little to Egyptian traditions, though some of the figures carry items associated with traditional Egypaian religion(Kessler 1983). Clothing corresponds to Graeco-Roman norms. Such reliefs continued to appear on the antiquities market after 1945 and scholars tend to see parallels between them and Palmyrene sculpture of the second, third and fourth centuries AD (Schneider 1975; 1982; Kitzinger1938; Kessler1983; Parlasca 1978; Breccia 1934-7), which suggests that the elite displayed themselves using a sculptural language current throughout the eastern Mediterraneanbut into which they incorporated distinctive Egyptian elements.A large number of literary papyri have been found at Oxyrhynchus. Of these, over 75 per cent were from the second and third century, as shown in figure5.12 (Kruger 1990: 142-9). A more detailed breakdown of a sample of papyri from P.Oxy. shows that although Homer was by far the most popular single author, there was a tremendous diversity of second-century literary texts. The later literary material is less eclectic and Christian texts gradually achieve dominance.(107) Greek literature appears to have been widely disseminated in Roman Oxyrhynchus, which was, after all, a rather small and unimportant city, which suggests that a significant proportion of the population in pre-modern terms, invested heavily in acquiring a Classical Greek education(108). Greek culture was also disseminated through performance. Homericists were paid to perform in the theatre during festivals, but the number of dramatic texts preserved suggests that the theatre at Oxyrhynchus may have staged Greek tragedies, comedies and satyr plays.The literary papyri, the iconographic material, the archaeology and what can be gleaned from the topography of the city suggest a heavily Hellenized city which preserved some of the traditional aspects of Egyptian religion.Ptolemais EuergetisNo other Egyptian cities are so well attested as Hermopolis and Oxyrhynchus. The topography of Ptolemais Euergetis, for instance, is mysterious. Archaeological exploration of the site has been somewhat desultory. Although Schweinfurth’s map (published in Wicken 1997) points to the survival of a large enclosure to the north of the site, various mounds which one presumes are the remains of ancient structures, and a substantial district of housing immediately south of the large enclose, it was alrerady obvious in 1887 that our understanding of the site would rely very heavily on the papyri (Wilcken 1887)109. the best guide to the topography of the Roman city is a third-century papyrus which lists those paying craft taxes in various streets in the city. Many of the street names are difficult to understand and, unlike those in other tax lists, do not appear in topographical order, as can be seen in table 5.5. there is some relationship。
蒸汽饱和度 英文
蒸汽饱和度英文Steam saturation is the ratio of the mass of water vapor within a given volume to the mass needed for the volume to reach saturation, at a given temperature and pressure of steam. The saturation temperature and pressure of steam are related, as steam only becomes saturated at a specific pressure-temperature point. When the pressure and temperature of steam increase, the steam saturation becomes higher, meaning that there is more water vapor in the space relative to the amount that is needed for saturation.In steam engines, understanding steam saturation is critical for proper operation. When steam passes over the blades of a turbine, it loses part of its heat energy and condenses back into water. When this occurs, optimal steam saturation occurs at the turbine's exit stage. This prevents erosion and blade damage, improving efficiency and extending the life of the engine.One way to understand steam saturation within an engine is to observe the use of a steam trap. Asteam trap is a device that removes excess water from the pipeline while maintaining steamsaturation in the pipeline. When steam traps are functioning correctly, they help remove water and air from the pipeline, which can reduce the efficiency and durability of the engine.Steam saturation is also a crucial factor in steam boilers. The boiler must operate within a specific range of pressure and temperature to prevent steam saturation. The design of the boiling process should also enable the recovery of steam that has been condensed, reducing the amount of energy used and improving efficiency.In summary, steam saturation is the ratio of the mass of water vapor within a given volume to the mass required for the volume to attain saturation. It is critical for the proper operation of steam engines and boilers. By understanding steam saturation, engineers and operators can optimize the efficiency and longevity of their engines and boilers.。
Vitamin Is a Good Friend that We Cannot Afford to Lose 维他命,生命不能承受之轻
Vitamin Is a Good Friend that We Cannot Afford to LoseNowadays more and more people consider vitamins as one of necessities for life, because they have realized that vitamins are essential for the normal growth and development of a multicultural organism. As far as I am concerned, vitamins are essential to our body just like a good friend for one’s struggling long life.There is an old saying goes that, one who lives with cripples learns to limp. That is to say, to follow certain rules is needed when picking company around you. Otherwise, a disordered friends-making style has definitely side-effect. For instance, having a lots of dancing-loving friends who are enthusiastic and full of energy will makes you tend to positive and prefer to deal with challenges in an optimistic way facing difficulties, and this kind of feeling promote you to pursue a promising life. However, always hanging around with someone ferocious and aggressive, this sort of personalities, such as smoke, drug-addictive, or excessive drinking, may lead you easily get angered, pick a fight even make criminals.In a word, friends play an important role in our life, whether better or worse.So does the vitamins. A guide to the amount an average person needs each day to remain healthy has been determined for each vitamin. Consuming too little of certain vitamins may lead to a nutrient deficiency. Well-known human vitamin deficiencies involve thiamine (beriberi), niacin (pellagra), vitamin C (scurvy), and vitamin D (rickets). In much of the developed world, such deficiencies are rare; this is due to an adequate supply of food and the addition of vitamins and minerals to common foods, often called fortification. In addition to these classical vitamin deficiency diseases, some evidence has also suggested links between vitamin deficiency and a number of different disorders. On the other hand, consuming too much of certain vitamins may lead to nutrient toxicity. In large doses, some vitamins have documented side-effects that tend to be more severe with a larger dosage. The likelihood of consuming too much of any vitamin from food is remote, but overdosing (vitamin poisoning) from vitamin supplementation does occur. At high enough dosages, some vitamins cause side-effects such as nausea, diarrhea, and vomiting. When side-effects emerge,recovery is often accomplished by reducing the dosage.What’s more, Consumption of a wide variety of foods that have adequate vitamins and minerals is the basis of a healthy diet. Obtaining nutrients through food remains the best method for obtaining vitamins; however, requirements may be higher because of the tumor or cancer therapy. Therefore, supplements may be necessary. People who eat a varied diet are unlikely to develop a severe primary vitamin deficiency. In contrast, restrictive diets have the potential to cause prolonged vitamin deficits, which may result in often painful and potentially deadly diseases.Above all, vitamins are essential for our health, just like a good friend that we cannot afford to lose, and also we should treat and use them properly.。
中外文化的差异 诗歌篇 英文版 speech
By this point, poetry was being composed according to regulated tone patterns. Regulated and unregulated poetry were distinguished as "ancient-style" gushi poetry and regulated, "recentstyle" jintishi poetry.
Tang poetic forms include: lvshi, a type of regulated verse with an eight-line form having five, six, or seven characters per line; ci (verse following set rhythmic patterns); and jueju (truncated verse), a four-line poem with five, six, or seven characters per line.
1）.Blank verse （无韵诗体） Blank verse: unrhymed iambic pentameter, a line consisting of five feet of unstressed and stressed syllables.
Examples: Shakespeare's plays, Milton's Paradise Lost and Wordsworth's Prelude are written in blank verse. The following is from Shakespeare's As You Like It : All the world's a stage, And all the men and women merely players: They have their exits and their entrances.
fundamentals of thermoelectricity oxford 2015
fundamentals of thermoelectricityoxford 2015The fundamentals of thermoelectricity, as discussed in the Oxford 2015 book, are crucial for understanding the conversion of heat into electrical energy. This field combines principles from thermodynamics, solid-state physics, and materials science to explore the behavior and performance of thermoelectric devices. Thermoelectricity has gained significance in recent years due to its potential application in waste heat recovery, portable power generation, and energy-efficient cooling systems. Let's dive into some key concepts covered in this book.Thermoelectric phenomena arise from a temperature gradient across a material or device. The underlying principle is the Seebeck effect, which describes the generation of an electric voltage when there is a temperature difference between two points in a conductor or semiconductor. This voltage is proportional to the gradient in temperature and depends on the material properties.热电现象是在材料或器件中存在温度梯度时产生的。
中外文化的差异 诗歌篇 英文版 speech
By this point, poetry was being composed according to regulated tone patterns. Regulated and unregulated poetry were distinguished as "ancient-style" gushi poetry and regulated, "recentstyle" jintishi poetry.
6）. Epigram (讽刺短诗;警句;隽语 诗,)
• Epigram: a short poem ending in a witty turn of thought. Brief and rhymed, epigram is usually satiric, mercilessly playful and sometimes malicious. • Example: The following is from J.V. Cunningham (1911-1985) :
The various versions of Chinese poetry, as known historically and to the general knowledge of the modern world, include two ቤተ መጻሕፍቲ ባይዱrimary types, Classical Chinese poetry and Modern Chinese poetry
5）.Sonnet(十四行诗)
• Sonnet: a fourteen-line stanza of iambic pentameter. Coming originally from Italy and used often to write love poems, the English sonnet has different rhyme schemes. The Italian sonnet, or Petrarchan sonnet（ (意大 利诗人彼特拉克推广的) 彼特拉克体十四行 诗）, consists of an octave (8-line stanza) and sestet .The English sonnet, initiated by Edmund Spenser called Spenserian Stanza. • Shakespearean sonnet, consists of three quatrains and a couplet.
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a r X i v :c o n d -m a t /0301053v 3 20 J u n 2003Specific heat of classical disordered elastic systemsGregory Schehr,1Thierry Giamarchi,2and Pierre Le Doussal 11CNRS-Laboratoire de Physique Th´e orique de l’Ecole Normale Sup´e rieure,24Rue Lhomond 75231Paris,France2DPMC,University of Geneva,24Quai Ernest-Ansermet,CH-1211Geneva,Switzerland(Dated:February 2,2008)We study the thermodynamics of disordered elastic systems,applied to vortex lattices in the Bragg glass ing the replica variational method we compute the specific heat of pinned vortons in the classical limit.We find that the contribution of disorder is positive,linear at low temperature,and exhibits a maximum.It is found to be important compared to other contributions,e.g.core electrons,mean field and non linear elasticity that we evaluate.The contribution of droplets is subdominant at weak disorder in d =3.PACS numbers:Understanding the temperature dependence of the spe-cific heat in glasses remains puzzling,e.g.the linear low T behaviour observed in structural glasses [1]and spin glasses [2].In some systems the crossover tempera-ture from quantum to classical behaviour may be quite low.The phenomenological two levels system model [3]yields a linear behaviour both in the classical and quan-tum regime.Although the classical problem appears sim-pler there are only few,and mostly mean field,solvable models of glassy systems where one can actually compute the specific heat [2,4].Ordered systems with continous symmetry admit spin wave type excitations which yield a T -independent specific heat C v =C eq from the equipar-tition of the energy.Non linearities such as quenched disorder will cause a deviation which is interesting to characterize and compare with the linear contribution from the two level system arguments.A class of glassy systems recently much studied are disordered elastic systems,ranging from vortex lattices [5,6,7,8],electron crystals [9],charge and spin den-sity waves [10]to disordered liquid crystals [11].In all of these systems the competition between disorder and elasticity leads to pinning and glassy behaviour.Spe-cific heat measurements in density waves gapped systems showed intermediate linear and sublinear regimes with non-equilibration effects [12,13].In superconductors in a field,the H and T dependence of C v relates both to the symmetry of the order parameter and to the thermo-dynamics of the vortex lattice.If the contribution of the normal electrons in the vortex cores dominate,the stan-dard expectation is that C v is linear in T with a linear in H dependence for s wave [14]and H 1/2for d -wave [15].A specific heat linear in temperature has indeed been measured in various materials.A H 1/2-dependence has been observed and argued for d -wave superconductivity in YbaCuO [16,17,18].However the nonlinear H depen-dence observed in other,a priori non d -wave materials,is a well known puzzle,as discussed in [19,20].On the other hand,the contribution of the phonons of the vortex lattice VL,the so-called ”vortons”,seems to be within ex-perimental resolution [21],and may lead,within the fulltemperature range below VL melting,to more complex behaviors.These were analyzed in absence of disorder,assuming a dissipative quantum dynamics with friction ηarising from interactions between vortons and vortex core electrons [22,23].It yields again C v ∝ηT withdifferent H dependence but only for T <T Dv ,the vor-ton Debye-like temperature which is poorly known (esti-mates in YBaCuO range from well below 1K up to 10Kin the superclean limit [22]).Above T Dv one recovers the equipartition value to which the specific heat anomaly was compared at melting [24,25,26,27].These analysis however neglect disorder and other non linearities whichfor T >T Dv can be treated classically.In this Letter we compute the specific heat of an elas-tic system in presence of pinning disorder in the classical regime.We show that disorder produces a substantial rise above equipartition,linear at low temperature and exhibiting a maximum at a characteristic depinning tem-perature.We show that in d >2the contribution from the two well droplet arguments is subdominant at weak disorder.We find that the disorder contribution is quite sizable compared to other contributions,e.g.of the non linear elasticity that we also evaluate.These results hold for a periodic object,i.e.a Bragg glass,or for interfaces with continuous degrees of freedom.In a companion pa-per [28]an analysis of the quantum regime revealed,in the absence of dissipation,a C v ∼T 3behaviour.An elastic system,such as the vortex lattice (VL)with external field aligned with z axis,is described by a N -component vector displacement field u α(R i ,z )(N =2for the VL in d =3).The equilibrium positions R i form a perfect N -dimensional lattice of spacing a .Interactions result in an elastic energy H el associated to the phonons of the vortex lattices H el [u ]=1(2π)2π/s −π/sdqz2 sion of elastic moduli is implicit whenever needed.Impu-rity disorder is modeled by a short range gaussian randompotential with in plane correlator∆(r)=δsǫ20e−r2/(4r2f)interacting with the local vortex density.Here2r f=ξthe superconducting coherence length,ǫ0=(Φ0/4πλ)2is the vortex energy scale per unit length along z andδa(small)dimensionless disorder parameter[35].Theequilibrium Bragg glass phase(absence of dislocations,a/R a≪1,R a being the translational correlation length)is described by the replicated partition function...denotes disorder average.Af-ter standard manipulations[29]the replicated Hamilto-nian becomes H eff[u]= a H el[u a]+H dis[u]with:H dis=−βW(u,x)W(u′,x)=δ(d)(x−x′)R(u−u′),R(u)=−NV(u2/N).We compute the specific heat perunit volume C v(T)=−T F F is the free energy,Ω=L d the volume.We present the method using anisotropic disorder and elasticity tensorΦαβ(q)=cq2δαβ,and generalize to the vortex lattice later.To obtain the low T behavior,afirst approach wouldbe to assume a single minimum of the energy H[u]andexpand around it.One thenfinds:C v(T)=C eq+AT+O(T2)(3)The exact expression for the linear term A=A1min,given in[30],involves cubic and quartic anharmonicity inH[u]in a given disorder realization.Disorder averaging isonly easy to perform perturbatively in disorder,yielding:A=A1min,pert=−1E c (R cE c lθ)where E c is the typicalpinning energy E c=cr2f R d−2c ,θthe free energy expo-nent.Approximating the contribution from scale l to the specific heat as:C l=L−d(L/l)di=1(E i(1+e−βE i)2≈π2E c l d(R c lC l is dominated by the smallest scales,yielding:A drop≈π2F(0)2 q G−1αβ,ab(q)u aα(q)u bβ(−q) which minimizes the variational free energy F var=F0+H eff−H0 H0,where F0denotes the free energy calcu-lated with H0.The specific heat C v=lim n→0−∂T∂βnΩcan be reexpressed as:C v=∂T limn→0131=−4γˆV ′′(B )J 2(Σ)(8)J n (z )=q1N ρ20K ∆K exp(−BK 2/2)and R cistheLarkin length[36].Eq.(8)is the so called marginality condition (MC)which also holds for the one step solution in d =2.Starting from the expression:1 H =q 1T1du [ˆV(0)−ˆV (B (u ))](10)which,as B (w )=B (u )(setting w =u/T )and w c =u c /T [37],turns out to depend implicitly on T only through Σand B ,and using (7-9)and (6),one obtains for the specific heatC v (T )=C eq +N2B 2ˆV′′(B )where C eq =12q is the equipartition value,i.e.half the total number of modes per unit volume [38].Eq.(11)is valid for any T ,for periodic objects (Bragg glass)as well as manifolds,and independently of the replica structure of the solution (if broken,pro-vided MC holds).One thus finds that disorder increases the specific heat which has now a maximum and de-creases back to equipartition C eq at high T .Expand-ing (11)at low T one finds again (3)with an amplitude A var =896indeed larger by afactor (R c /a )3than (5).It also confirms the above dis-cussion:thanks to RSB (i.e.Σ=0),the problems (e.g.in d =2)of single minimum (i.e.replica symmetric)per-turbation theory are cured,the Larkin length being the natural scale.A plot of C v (T )is shown on Fig.1The generalization to the vortex lattice using (1)and N =2is straightforward.Eq.(11)still holds,but in theformulaes (7,8)which determine B and Σ=c 66R −2c onesets γ=1c 66c 44)where here andbelow we denote c 44=c 44(q ⊥=π/a )(below the dimen-sional crossover field,c 66/(c 44a 2)≪1/s 2,the integral0.0050.010.0150.020.0250.030.0350.0400.51 1.522.533.54c v (T ) - c e qT/T*FIG.1:Specific heat C v (T )−C eq in arbitrary units as afunction of T /T ∗.over q z can be extended up to infinity and the integral is dominated by q ⊥=π/a ).We can now discuss in details the behaviour of C v (T )for r f <a .In this limit ˆV(B )takes the dependence ˆV (B )≈−D/(2r 2f +B ),with D =δr 2f sǫ20/a 2,for B ≪a 2which holds up to melting.One finds:C v (T )=C eq +AT/(1+T/(2T ∗))3(12)A ≈δc 66c 44a 4)sa 2sa 3.At this value of the disorder oneobtains A ≈c 2L /(T m r 2f aǫ)and C ∗v−C eq ≈1/(a 3ǫ)(ǫ<1the anisotropy parameter [5]).C ∗v −C eq should be compared with the equipartition value,estimated as C eq =1/(sa 2).These become comparable around the dimensional crossover field B =B cr such that s ∼aǫ.The above classical contribution (12)will hold onlyabove the vorton Debye temperature T Dv ,below whichquantum effects become important.T Dv depends on the vortex mass,the Hall force and the friction force,which arise from the coupling of moving vortices with the nor-mal electrons bath in presence of scattering.Estimatesfor T Dv range [22]from 10−3T c in dirty (friction domi-nated)materials to 10−1T c in superclean limit (Hall dom-inated).There should thus exist a broad regime of tem-perature and field where the Bragg glass is stable and the result (12)holds.To assess whether this contribution (12)is observable,let us compare it with other terms linear in T in C v .First4 the normal electrons in the vortex core lead to[14]:C v core(T)≈TH c2)α(14)where T f is the Fermi temperature of the normal metal,α=1for s-wave superconductor[39]andα=1/2forlines of nodes in the gap[15].Given the large ratio T f/T m=O(102)for e.g.YBaCuO,onefinds,comparing A core and A dis that the contribution from the cores canbe comparable or smaller than the one from the disorder. There are other contributions from the vortex latticeas well.The meanfield specific heat[23]being C mf≈ǫ0T/(T2c a2),the ratio A dis/A mf≈(c2L aT c/(r f T m))2 can be large.We have also computed the contribu-tion from non linear elasticity of the VL.Performing,as in[34],an expansion of the vortex interaction energy dz ijǫ0K0((R i−R j+u i(z)−u j(z))/λ),we obtain:A nl=ρ0ǫ0a−4(c2L a2c44c66(c2L a2a)(15)up to O((a/λ)2)where the numerical prefactorsγ4andγ3are complicated lattice sums,given in[30].One can then estimate A nl/A dis∼r2f/a2and this contribution is likely to remain small until melting.None of thesecontributions[40]is expected to exhibit a maximum at scale distinct from T m.To conclude,we found by explicit calculation that thevortex lattice classical contribution to C v due to dis-order can be important at the very least in the range 10−1T c to T m,and possibly more.The coefficient A dis of the low T linear behavior is magneticfield dependent, A dis∝1/(T m a).It is convenient to express results us-ing the melting temperature T m,which is experimentally measured[24,25,27]and can also be estimated from the standard elastic expression of T m=4a3√B leads to T∗∝√。