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Conversion of nuclear to 2-flavour quark matter in rotating compact stars A general relativ

Conversion of nuclear to 2-flavour quark matter in rotating compact stars A general relativ
Conversion of nuclear to 2-flavour quark matter in rotating compact stars A general relativ

a r X i v :0806.1800v 1 [a s t r o -p h ] 11 J u n 2008

Conversion of nuclear to 2-?avour quark matter in rotating compact

stars:A general relativistic perspective

Ritam Mallick ?

Department of Physics,Bose Institute,Kolkata -700009,India

Abhijit Bhattachryya

Department of Physics,Calcutta University,Kolkata -700009,India

Sanjay K.Ghosh,Sibaji Raha

Centre for Astroparticle Physics and Space Science &Department of Physics,Bose Institute,Kolkata -700009,India

The conversion of neutron star to strange star is argued to be a two step process.The ?rst process involves the decon?nement of nuclear to two-?avour quark matter.The GR results shows that the propagating front breaks up into fragments which propagate with di?erent velocities along di?erent directions.The time taken for this conversion to happen is of the order of few ms .This calculation indicates the inadequacy of non-relativistic (NR)or even Special Relativistic (SR)treatments for these cases.

PACS numbers:

I.INTRODUCTION

Strange Quark Matter (SQM),consisting of approximately equal numbers of up (u ),down (d )and strange (s )quarks,is conjectured to be the true ground state of strong interaction [1,2].SQM could naturally occur in the cores of compact stars,where central densities of about an order of magnitude higher than the nuclear matter saturation density.The transition from nuclear (hadronic)to quark matter should proceed through a conversion to an initial stage of (metastable)two ?avour quark matter,which should decay to the stable SQM.Thus,neutron stars with su?ciently high central densities ought to get converted to strange,or at least hybrid,stars.These transitions could have observable signatures in the form of a jump in the breaking index and gamma ray bursts [3,4].

There are several plausible scenarios where neutron stars could convert to quark stars,through a ”seed”of external SQM [5],or triggered by the rise in the central density due to a sudden spin-down in older neutron stars [6].Several authors have studied the conversion of nuclear matter to strange matter under di?erent assumptions [7,8,9].

In our recent work [10],we have argued that the conversion process is a two step process.The ?rst process involves the decon?nement of nuclear to two-?avour quark matter and the conversion process takes some milliseconds to occur.GR e?ects in such processes is studied by us [11].In this article,we make a detailed study of this process.

II.

THEORY

We use the Nonlinear Walecka model for the nuclear matter euqation of state (EOS).We consider the conversion of nuclear matter,consisting of only nucleons (i.e.without hyperons)to a two-?avour quark matter.The ?nal compo-sition of the quark matter is determined from the nuclear matter EOS by enforcing the baryon number conservation during the conversion process.

The metric describing the structure of the star,is given by [12]

ds 2=?e γ+ρdt 2+e 2α(dr 2+r 2dθ2)+

e γ?ρr 2sin 2θ(dφ?ωdt )2

(1)

The four gravitational potentials α,γ,ρand ωare functions of θand r only.The solution of the star is obtained from the ’rns’code [13].

We heuristically assume the existence of a combustive phase transition front of in?nitesimal thickness,and study the outward propagation of the front.Let us assume that the conversion front is generated at the center of the star,

FIG.1:Variation of velocity of the front along the radial direction of the star for three di?erent cases,namely SR,non-rotating GR and rotating GR.

FIG.2:Variation of velocity of the front along the radial direction for di?erent rotational velocity of the star.

and it propagates outwards through the star with a certain velocity.Employing the conservation conditions[14]and further employing the entropy condition[15],we determine the?ow velocity of matter in the two phases v1and v2. It is possible to classify the various conversion mechanisms by comparing the velocities of the respective phases with the corresponding velocities of sound in these phases.For the conversion to be physically possible,velocities should satisfy an additional condition,namely,0≤v2i≤1.If we plot di?erent velocities against baryon number,we get curves from which we could calculate the initial velocity of the front at the centre of the star[10].The results [10]also show that the range of values of baryon density,for which the?ow velocities are physical,increases with temperature.Starting with this initial velocity,we investigate the evolution of the front with time.Treating both nuclear and strange matters as ideal?uids,the system is governed,together with the metric and the EOS,by the Einstein’s equation R i k?1

?r =

W2v[K+K1]

FIG.3:Variation of velocity of the front along the radial direction for di?erentχ.

FIG.4:Variation of time of arrival of the front at certain radial distance for di?erent cases.

III.RESULTS AND DISCUSSION

Having constructed the density pro?le of the star for a?xed central density,the respective?ow velocities v1and v2of the nuclear and quark matter in the rest frame of the front,at a radius in?nitesimally close to the center of the star.This would give us the initial velocity of the front(?v1),at that radius,in the nuclear matter rest frame.With this,we integrate eqn.(2)outwards along the radius of the star.The solution gives the variation of the velocity with position as a function of the time of arrival of the https://www.sodocs.net/doc/31157073.html,ing this velocity pro?le,we can calculate the time required to convert the whole star using the relation dr

Therefore,at any particular instant of time,we may have a situation where the polar part of the star has been converted while along the equatorial direction,the front is still propagating.

From?g.(4)we can see that the time taken by the conversion front to convert the neutron star to two-?avour quark star is of the order of few ms.The static star takes the minimum time(3.3ms)whereas the rotating star takes the maximum time(5.1ms)due to the enlarged equatorial radius.The polar part of the star needs much lesser time for conversion(3.1ms),even less than static star,as its radius gets compressed.

To summarize,we have shown in this article that the conversion of nuclear matter to quark matter in compact stars, especially rotating stars which are more realistic than static stars,is strongly a?ected by GR e?ects.The emergence of di?erent conversion fronts,propagating with di?erent velocities along di?erent radial directions was not anticipated by Newtonian or SR calculations.It remains to be explored whether the incorporation of dissipative e?ects materially changes the results.Though the calculation is much involved,such an investigation is on our immediate agenda.

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[2]E.Farhi and R.L.Ja?e,Phys.Rev.D30,2379(1984)

[3]A.Bhattacharyya,S.K.Ghosh,M.Hanauske and S.Raha,Phys.Rev.C71,048801(2005)

[4]A.Bhattacharyya,S.K.Ghosh and S.Raha,Phys.Lett.B635,195(2006)

[5]C.Alcock,E.Farhi and A.Olinto,Astrophys.J.310,261(1986)

[6]N.K.Glendenning,Nucl.Phys.(Proc.Suppl.)B24,110(1991);Phys.Rev.D46,1274(1992)

[7]A.Olinto,Phys.Lett.B192,71(1987);Nucl.Phys.(Proc.Suppl.)B24,103(1991)

[8]O.G.Benvenuto,and J.E.Horvarth,Phys.Lett.B213,516(1988)

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New York(1967)

常用介词的用法

分考点1 表示时间的介词 Point 1 at, in, on 的用法 (1)at 的用法 At 表示时间点,用于具体的时刻(几点,正午,午夜,黎明,拂晓,日出,日落等),或把某一时间看作某一时刻的词之前以及某些节假日的词之前。 at 6:00 在6点钟 At noon 在中午 At daybreak 在拂晓 At down 在黎明 At Christmas 在圣诞节 【特别注意】在以下的时间短语中,at 表示时间段。 At dinner time 在(吃)晚饭时 At weekends/ the weekend 在周末 (2)in 的用法 ①表示时间段,与表示较长一段时间的词搭配,如年份,月份,季节,世纪,朝代,还可以用于泛指的上午、下午、傍晚等时间段的词前。 In 2009 在2009年 In April 在四月 In the 1990s 在20世纪90年代 In Tang Dynasty 在唐朝 In the morning在上午 ②后接时间段,用于将来时,表示“在一段时间之后”。 The film will begin in an hour. 电影将于一个小时之后开始。 【特别注意】当时间名词前有this,that,last,next,every,each,some等词修饰时,通常不用任何介词。 This morning 今天上午last year 去年 (3)on 的用法 ①表示在特定的日子、具体的日期、星期几、具体的某一天或某些日子。 On September the first 在9月1号 On National Day 在国庆节 We left the dock on a beautiful afternoon. 我们在一个明媚的下午离开了码头。 ②表示在具体的某一天的上午、下午或晚上(常有前置定语或后置定语修饰)。 On Sunday morning 在星期日的早上 On the night of October 1 在10月1号的晚上 【特别注意】“on +名词或动名词”表示“一...就...”. On my arrival home/ arriving home, I discovered they had gone. 我一到家就发现他们已经离开了。 Point 2 in,after 的用法 In 和after都可以接时间段,表示“在...之后”,但in 常与将来时连用,after 常与过去时连用。 We will meet again in two weeks.

英语介词用法大全

英语介词用法大全 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】

介词(The Preposition)又叫做前置词,通常置于名词之前。它是一种虚词,不需要重读,在句中不单独作任何句子成分,只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时,往往会出现遗漏介词或误用介词的错误,因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词,按照不同的分类标准可分为以下几类: (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如: at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如: Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如: In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点(包括动向)的介词。如: About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如: About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如: beside , but, except等。 {4} 表比较的介词。如: As, like, above, over等。 {5} 表反对的介词。如: againt ,with 等。 {6} 表原因、目的的介词。如: for, with, from 等。 {7} 表结果的介词。如: to, with , without 等。 {8} 表手段、方式的介词。如: by, in ,with 等。 {9} 表所属的介词。如: of , with 等。 {10} 表条件的介词。如:

翻译研究中的概念混淆(翻译策略、方法与技巧)).

翻译研究中的概念混淆 ——以“翻译策略”、“翻译方法”和“翻译技巧”为例 熊兵华中师范大学 《中国翻译》2014(3)82-88 摘要:本文对学界在“翻译策略”、“翻译方法”和“翻译技巧”这三个基本概念上所存在的普遍的混淆进行了剖析,提出应对这三个概念进行明确区分。在此基础上论文对这三个概念的定义、特性、相互关系及其各自的分类体系进行了系统阐述。 关键词:翻译策略;翻译方法;翻译技巧;混淆;定义;分类 1.话题缘起 在翻译研究中,有一个问题一直以来都未引起学界足够的重视,并因此在一定程度上妨碍了翻译研究的进一步发展,这个问题即为翻译研究中的概念混淆,其中又尤以“翻译策略”、“翻译方法”和“翻译技巧”这三个概念的混淆为甚。一方面,学界对翻译“策略”、“方法”和“技巧”的讨论虽多如牛毛,但把它们作为一个方法论系统的关键要素进行综合研究,深入考察其各自的内涵、相互关系及分类体系的系统性研究还相当少见。另一方面,学界在对这三个术语的认识和使用上普遍存在着定义不明、分类不当、概念混淆不清的问题。例如,在一些翻译教材中中,“归化”与“异化”一方面被作为“翻译方法”加以讨论(如龚芬,2011:79—81),另一方面又被视为“翻译策略”进行阐述(同上:93—106)。一些翻译论文把本应属于翻译技巧层面的增补型翻译(类似于增译)、浓缩型翻译(类似于减译)划归为“翻译策略”的类别(如李克兴,2004:66—67)。在一些翻译方向的硕士研究生论文中,把翻译“策略”、“方法”、“技巧”混为一谈的更是比比皆是。甚至翻译专业的老师对此问题也存在一些模糊的、甚至是错误的看法(如把归化等同于意译,把异化等同于直译)。 国外学界对此也存在一些模糊或混淆(或未予严格区分。比如Shuttleworth & Cowie (2004:44,59)一方面把domestication/foreignization称作是“strategy”,另一方面却又把free/literal translation也视为“strategy”(同上:63,96 )。Vinay & Darbelnet (1958/2000:84—93) 把翻译方法(method)分为两类:直接翻译(direct translation)和间接翻译(oblique translation),前者包括三种处理方式(procedures),即借译,拟译,直译,后者包括四种处理方式,即词类转换,视点转换,等值翻译,顺应翻译。可在论述中却经常把其划分出来的“方法”(methods)和“处理方式”(procedures)混为一谈。另外,他们把“借译、拟译、直译、等值翻译、顺应翻译”和“词类转换、视角转换”划归为一类(同属procedures)也欠妥当,因为前者应属“翻译方法”的范畴,而后者则应属“翻译技巧”的范畴。实际上,这里Vinay &Darbelnet的分类涉及到三个层面:翻译策略、翻译方法和翻译技巧。其划分出来的两大“翻译方法”(直接翻译和间接翻译)其实应为“翻译策略”(所以Munday说,“The two general translation strategies identified by Vinay &Darbelnet are direct translation and oblique translation”,见Munday,2008:56),而在其划分出来的七类“处理方式”中,前三类和最后两类属于“翻译方法”,第四、第五类则属于“翻译技巧”。总之,Vinay &Darbelnet在其分类中把翻译“策略、方法、技巧”混淆在一起,这也导致后来很长时间学界在这几个概念上的混淆(Molina &Albir,2002:506 0 关于国外译学界在译学术语,特别是在“翻译策略、翻译方法、翻译技巧”三个术语上所存在的概念混淆、使用混乱的问题,Chesterman(2005)和Molina & Albir(2002)曾专门撰文予以讨论。如Chesterman指出,学界用于描述文本操作过程的术语除翻译“策略”外,其他还有“技巧、方法、转换、转化、变易”等等(2005:17)。他认为这种众多术语相互混用

介词from的语法特点与用法习惯

介词?f rom的语法特点与用法习惯 1.不要根据汉语意思在及物动词后误加介词?from。如: 他上个星期离开中国去日本了。 误:?H e left from China for Japan last week. 正:?H e left Chine for Japan last week. 另外,也不要根据汉语意思错用介词?from。如: 太阳从东方升起,从西方落下。 误:?T he sun rises from the east and sets from the west. 正:?T he sun rises in the east and sets in the west. 2.f rom虽然本身是介词,但它有时也可接介词短语作宾语。如: Choose a book from among these. 从这些书中选一本吧。 A man stepped out from behind the wall. 一个人从墙后走出来。 比较: I took it from the bed. 我从床那儿(或床上)拿的。 I took it from under the bed. 我从床下拿的。 注意,下面一句用了?from where(引导非限制性定语从句),而未用?f rom which,其中的where=i n the tree,即?from where=f rom in the tree。如: He hid himself in a tree, from where he could see the enemy in the distance. 他躲在一棵树上,从那儿他可以看到远处的敌人。 3.有时其后可接?w hen, where引导的宾语从句,此时可视为其前省略了?t he time, the place。如: He didn’t speak to me from when we moved in. 从我们迁入之时起,他没和我说过话。

英语介词用法详解

英语常用介词用法与辨析 ■表示方位的介词:in, to, on 1. in 表示在某地范围之内。如: Shanghai is/lies in the east of China. 上海在中国的东部。 2. to 表示在某地范围之外。如: Japan is/lies to the east of China. 日本位于中国的东面。 3. on 表示与某地相邻或接壤。如: Mongolia is/lies on the north of China. 蒙古国位于中国北边。 ■表示计量的介词:at, for, by 1. at表示“以……速度”“以……价格”。如: It flies at about 900 kilometers a hour. 它以每小时900公里的速度飞行。 I sold my car at a high price. 我以高价出售了我的汽车。 2. for表示“用……交换,以……为代价”。如: He sold his car for 500 dollars. 他以五百元把车卖了。 注意:at表示单价(price) ,for表示总钱数。 3. by表示“以……计”,后跟度量单位。如: They paid him by the month. 他们按月给他计酬。 Here eggs are sold by weight. 在这里鸡蛋是按重量卖的。 ■表示材料的介词:of, from, in 1. of成品仍可看出原料。如: This box is made of paper. 这个盒子是纸做的。 2. from成品已看不出原料。如: Wine is made from grapes. 葡萄酒是葡萄酿成的。 3. in表示用某种材料或语言。如: Please fill in the form in pencil first. 请先用铅笔填写这个表格。 They talk in English. 他们用英语交谈(from 。 注意:in指用材料,不用冠词;而with指用工具,要用冠词。请比较:draw in penc il/draw with a pencil。 ■表示工具或手段的介词:by, with, on 1. by用某种方式,多用于交通。如by bus乘公共汽车,by e-mail. 通过电子邮件。

with的用法大全

with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述,以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成,复合结构作介词with或without的复合宾语,复合宾语中第一部分宾语由名词或代词充当,第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当,分词可以是现在分词,也可以是过去分词。With结构构成方式如下: 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例:

1、 She came into the room,with her nose red because of cold.(with+名词+形容词,作伴随状语) 2、 With the meal over , we all went home.(with+名词+副词,作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语,作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house,with not a man ,woman or child to say he was kind to me.(with+名词+不定式,作伴随状语) He could not finish it without me to help him.(without+代词 +不定式,作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词,作伴随状语) 6、Without anything left in the cupboard, she went out to get something to eat.(without+代词+过去分词,作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语,表示行为方式,伴随情况、时间、原因或条件(详见上述例句)。

现代汉语连词意义及用法总结

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高中英语45个介词的基本用法

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with用法归纳

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and的用法及含义

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介词with的用法大全

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四种翻译方法,十种翻译技巧完整版本

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