耦合雙粒子在不對(duì)稱體系中的輸運(yùn)現(xiàn)象研究
發(fā)布時(shí)間：2019-01-20 11:17
【摘要】：輸運(yùn)現(xiàn)象廣泛存在于自然界之中,對(duì)這些現(xiàn)象的研究具有重要的理論與現(xiàn)實(shí)意義。作為一種獨(dú)特的類型,周期性不對(duì)稱體系中產(chǎn)生輸運(yùn)現(xiàn)象并不要求凈外力或者相應(yīng)物理量梯度的存在,空間對(duì)稱性的破缺結(jié)合具有一定自相關(guān)時(shí)間的無(wú)偏外擾動(dòng)即足以使體系中產(chǎn)生定向輸運(yùn),這類現(xiàn)象被稱為棘輪效應(yīng),或者布朗馬達(dá)。通常宏觀情況下粒子被當(dāng)作單質(zhì)點(diǎn)模型處理,因而忽略了粒子本身的結(jié)構(gòu)對(duì)運(yùn)動(dòng)的影響。然而有些時(shí)候這樣的忽略是不適宜的,尤其是當(dāng)粒子本身的尺寸與體系的空間結(jié)構(gòu)可相比擬時(shí),此時(shí)粒子的內(nèi)部相互作用以及本身結(jié)構(gòu)的不對(duì)稱性等因素都會(huì)對(duì)體系的輸運(yùn)性質(zhì)產(chǎn)生很大的影響,甚至可以造成輸運(yùn)方向的反轉(zhuǎn)變化。為了研究?jī)?nèi)部相互作用對(duì)體系輸運(yùn)性質(zhì)的影響,我們考慮了兩個(gè)彈性耦合在一起的相同粒子,它們被置于同一個(gè)熱環(huán)境與不對(duì)稱鋸齒勢(shì)之下,并且都受到了外加隨機(jī)色擾動(dòng)的作用。我們重點(diǎn)研究耦合雙粒子體系的輸運(yùn)性質(zhì)與彈性耦合作用之間的關(guān)系,發(fā)現(xiàn)體系的流對(duì)耦合參數(shù)具有依賴性,尤其是當(dāng)粒子間平衡距離的長(zhǎng)度位于鋸齒勢(shì)的兩個(gè)坡長(zhǎng)之間時(shí),流向可以在特定的彈性系數(shù)值處產(chǎn)生反轉(zhuǎn)。為了解釋這樣的流向反轉(zhuǎn)現(xiàn)象,我們對(duì)比了無(wú)耦合與剛性耦合兩種極限情況。在無(wú)耦合情況下,兩個(gè)粒子在原始鋸齒勢(shì)中獨(dú)立運(yùn)動(dòng);而在剛性耦合情況下,兩個(gè)粒子可以看作一個(gè)在等效勢(shì)下運(yùn)動(dòng)的等效單粒子。通過(guò)對(duì)照等效勢(shì)與原始勢(shì),我們發(fā)現(xiàn)當(dāng)粒子間平衡距離位于原始勢(shì)兩個(gè)坡長(zhǎng)之間時(shí),等效勢(shì)的不對(duì)性相對(duì)于原始勢(shì)會(huì)產(chǎn)生反轉(zhuǎn),而勢(shì)的不對(duì)稱反轉(zhuǎn)則會(huì)導(dǎo)致流向的反轉(zhuǎn)。在宏觀尺度下,熱噪聲一般被當(dāng)作高斯白噪聲處理,然而很多研究顯示分子尺度下熱噪聲的時(shí)間關(guān)聯(lián)性已不可忽略,因此已不適合繼續(xù)將其處理為白噪聲形式。由于分子本身的結(jié)構(gòu)特點(diǎn),它也不適合被處理為單質(zhì)點(diǎn)模型,分子的指向也會(huì)對(duì)其運(yùn)動(dòng)行為產(chǎn)生影響。為了研究分子尺度熱噪聲以及分子結(jié)構(gòu)的不對(duì)稱性對(duì)體系輸運(yùn)性質(zhì)的影響,我們考慮了一個(gè)簡(jiǎn)單的不對(duì)稱模型分子,它由兩個(gè)不同的部分剛性組合而成,并維持它的指向。我們將分子沿不同方向運(yùn)動(dòng)的不同表現(xiàn)為阻尼的不同,然后選取合適的模型以模擬熱噪聲,通過(guò)計(jì)算發(fā)現(xiàn)不對(duì)稱分子可以朝阻尼較小的方向產(chǎn)生定向運(yùn)動(dòng),這說(shuō)明分子本身結(jié)構(gòu)所提供的不對(duì)稱性結(jié)合熱噪聲的時(shí)間關(guān)聯(lián)性可以使得分子產(chǎn)生定向運(yùn)動(dòng)。然而如果分子的指向不被維持,那么這種定向運(yùn)動(dòng)則會(huì)很快消失,因此這種現(xiàn)象并不違反熱力學(xué)第二定律。
[Abstract]:Transport phenomena exist widely in nature, and the study of these phenomena has important theoretical and practical significance. As a unique type, transport in periodic asymmetric systems does not require the existence of net external forces or the corresponding physical gradient. The breaking and breaking of space symmetry and the unbiased external disturbance with a certain autocorrelation time are sufficient to produce directional transport in the system. This phenomenon is called ratchet effect or Brownian motor. In general, the particle is treated as a single mass point model under macroscopic conditions, thus neglecting the effect of the structure of the particle itself on the motion. Sometimes, however, such neglect is inappropriate, especially when the size of the particle itself is comparable to the spatial structure of the system. At this time, the internal interaction of particles and the asymmetry of their own structure will have a great impact on the transport properties of the system, and even lead to the reversal of the transport direction. In order to study the effect of internal interaction on the transport properties of the system, we consider two identical particles that are elastically coupled together, which are placed under the same thermal environment and asymmetric sawtooth potential. All of them are affected by random color perturbation. We focus on the relationship between the transport properties of the coupled two-particle system and the elastic coupling. It is found that the flow of the system is dependent on the coupling parameters, especially when the length of the equilibrium distance between particles lies between the two sloping lengths of the sawtooth potential. The flow direction can be reversed at a particular value of elasticity. In order to explain the flow reversal phenomenon, we compare the two limit cases of uncoupled and rigid coupling. In the case of no coupling, two particles move independently in the original sawtooth potential, while in the case of rigid coupling, the two particles can be regarded as an equivalent single particle moving under the equivalent potential. By comparing the equivalence potential with the original potential, we find that when the equilibrium distance between the particles lies between the two slope lengths of the original potential, the asymmetry reversal of the equivalent potential will lead to the reversal of the flow direction. At macro scale, thermal noise is generally treated as Gao Si white noise. However, many studies show that the temporal correlation of thermal noise at molecular scale can not be ignored, so it is not suitable to continue to treat thermal noise as white noise. Because of the structural characteristics of the molecule itself, it is not suitable to be treated as a single particle model, and the direction of the molecule will have an effect on its motion behavior. In order to study the effect of molecular scale thermal noise and the asymmetry of molecular structure on the transport properties of the system, we consider a simple asymmetric model molecule, which is composed of two different partial rigidities, and maintains its direction. In this paper, we show that the molecules moving in different directions are different in damping, and then we select the appropriate model to simulate the thermal noise, and we find that the asymmetrical molecules can produce directional motion in the direction of less damping. It is suggested that the time correlation of asymmetric and thermal noise can lead to directional motion of the molecule. However, if the direction of the molecule is not maintained, the directional motion will soon disappear, so this phenomenon does not violate the second law of thermodynamics.
【學(xué)位授予單位】：中國(guó)科學(xué)院研究生院(上海應(yīng)用物理研究所)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O572.2
本文編號(hào)：2411993
[Abstract]:Transport phenomena exist widely in nature, and the study of these phenomena has important theoretical and practical significance. As a unique type, transport in periodic asymmetric systems does not require the existence of net external forces or the corresponding physical gradient. The breaking and breaking of space symmetry and the unbiased external disturbance with a certain autocorrelation time are sufficient to produce directional transport in the system. This phenomenon is called ratchet effect or Brownian motor. In general, the particle is treated as a single mass point model under macroscopic conditions, thus neglecting the effect of the structure of the particle itself on the motion. Sometimes, however, such neglect is inappropriate, especially when the size of the particle itself is comparable to the spatial structure of the system. At this time, the internal interaction of particles and the asymmetry of their own structure will have a great impact on the transport properties of the system, and even lead to the reversal of the transport direction. In order to study the effect of internal interaction on the transport properties of the system, we consider two identical particles that are elastically coupled together, which are placed under the same thermal environment and asymmetric sawtooth potential. All of them are affected by random color perturbation. We focus on the relationship between the transport properties of the coupled two-particle system and the elastic coupling. It is found that the flow of the system is dependent on the coupling parameters, especially when the length of the equilibrium distance between particles lies between the two sloping lengths of the sawtooth potential. The flow direction can be reversed at a particular value of elasticity. In order to explain the flow reversal phenomenon, we compare the two limit cases of uncoupled and rigid coupling. In the case of no coupling, two particles move independently in the original sawtooth potential, while in the case of rigid coupling, the two particles can be regarded as an equivalent single particle moving under the equivalent potential. By comparing the equivalence potential with the original potential, we find that when the equilibrium distance between the particles lies between the two slope lengths of the original potential, the asymmetry reversal of the equivalent potential will lead to the reversal of the flow direction. At macro scale, thermal noise is generally treated as Gao Si white noise. However, many studies show that the temporal correlation of thermal noise at molecular scale can not be ignored, so it is not suitable to continue to treat thermal noise as white noise. Because of the structural characteristics of the molecule itself, it is not suitable to be treated as a single particle model, and the direction of the molecule will have an effect on its motion behavior. In order to study the effect of molecular scale thermal noise and the asymmetry of molecular structure on the transport properties of the system, we consider a simple asymmetric model molecule, which is composed of two different partial rigidities, and maintains its direction. In this paper, we show that the molecules moving in different directions are different in damping, and then we select the appropriate model to simulate the thermal noise, and we find that the asymmetrical molecules can produce directional motion in the direction of less damping. It is suggested that the time correlation of asymmetric and thermal noise can lead to directional motion of the molecule. However, if the direction of the molecule is not maintained, the directional motion will soon disappear, so this phenomenon does not violate the second law of thermodynamics.
【學(xué)位授予單位】：中國(guó)科學(xué)院研究生院(上海應(yīng)用物理研究所)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O572.2
【參考文獻(xiàn)】
相關(guān)期刊論文 前4條
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2 SHENG Nan;TU Yu-song;GUO Pan;WAN Rong-zheng;FANG Hai-ping;;DIFFUSING OF AN AMMONIA MOLECULE IN WATER IN A VERY SHORT TIME PERIOD[J];Journal of Hydrodynamics;2012年06期
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4 ;Biased transportations in a spatially asymmetric system at the nano-scale under thermal noise[J];Science China(Physics,Mechanics & Astronomy);2010年08期
，本文編號(hào)：2411993
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