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Dynamical structure factor and a new method to measure the pairing gap in two-dimensional attractive Fermi-Hubbard model
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作者 Huaisong Zhao Feng Yuan +1 位作者 Tianxing Ma Peng Zou 《Chinese Physics B》 2025年第11期195-203,共9页
The measurement of the pairing gap is crucial for investigating the physical properties of superconductors or superfluids.We propose a strategy to measure the pairing gap through the dynamical excitations.With the ran... The measurement of the pairing gap is crucial for investigating the physical properties of superconductors or superfluids.We propose a strategy to measure the pairing gap through the dynamical excitations.With the random phase approximation(RPA),we study the dynamical excitations of a two-dimensional attractive Fermi-Hubbard model by calculating its dynamical structure factor.Two distinct collective modes emerge:a Goldstone phonon mode at transferred momentum q=[0,0]and a roton mode at q=[p,p].The roton mode exhibits a sharp molecular peak in the low-energy regime.Notably,the area under the roton molecular peak scales with the square of the pairing gap,which holds even in three-dimensional and spin-orbit coupled(SOC)optical lattices.This finding suggests an experimental approach to measure the pairing gap in lattice systems by analyzing the dynamical structure factor at q=[p,p]. 展开更多
关键词 attractive Fermi-Hubbard model SUPERFLUID dynamical excitations roton mode pairing gap measurement
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Loop-Current Fluctuations Mediated Chiral d-Wave Pairing in Kagome Lattice
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作者 Qi-Fang Li Gaopei Pan +4 位作者 Xu Zhang Satoru Nakatsuji Weilun Jiang Xiao Yan Xu Xianxin Wu 《Chinese Physics Letters》 2025年第5期123-139,共17页
Recent various experiments have provided evidence supporting the emergence of loop-current order in kagome metals. Particularly superconductivity in AV_(3)Sb_(5) is significantly enhanced when this charge order is sup... Recent various experiments have provided evidence supporting the emergence of loop-current order in kagome metals. Particularly superconductivity in AV_(3)Sb_(5) is significantly enhanced when this charge order is suppressed by pressure or doping. Distinct from magnetic order, loop-current order does not couple directly to spin and thus whether such fluctuations can enhance superconductivity remains elusive. We design a sign problem-free bilayer kagome model coupled to quantum Ising spins through bond currents and perform determinant quantum Monte Carlo simulations to explore single-particle properties and superconductivity arising from 2 × 2 loopcurrent fluctuations. We find that this loop-current order induces intriguing band folding, band broadening,and gap opening around saddle points. Remarkably, our pairing susceptibility analysis identifies a dominant enhancement of superconductivity due to loop-current fluctuations, with the dominant pairing being the chiral d-wave channel. This pairing primarily occurs within the intra-sublattice channel and involves third nearestneighbor sites, attributed to the unique sublattice texture associated with van Hove singularities. We also discuss potential experimental implications for kagome superconductors. 展开更多
关键词 kagome metals quantum ising spins quantum monte carlo simulations bond current enhance superconductivity chiral d wave pairing loop current fluctuations kagome lattice
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Comparison of “Exterior-interior Pairing of the Lung and Large Intestine” and “Gut-lung Crosstalk” Based on COVID-19
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作者 WANG Yunliang ZHANG Yan 《Chinese Medicine and Culture》 2025年第1期40-49,共10页
The infection of SARS-CoV-2 has triggered the COVID-19 pandemic. In addition to the fever and respiratory symptoms in the process of coronavirus infections, gastrointestinal symptoms, especially diarrhea, are prominen... The infection of SARS-CoV-2 has triggered the COVID-19 pandemic. In addition to the fever and respiratory symptoms in the process of coronavirus infections, gastrointestinal symptoms, especially diarrhea, are prominent features of its acute infection and long COVID. The associations between the lung and large intestine have been demonstrated by Western medicine in aspects such as tissue origin, microflora homeostasis, mucosal immunity, renin-angiotensin system(RAS) and autonomic nervous system as well, which are considered as the evidence of material basis and potential regulatory mechanisms for “gutlung crosstalk(肺肠串扰)” in COVID-19. We have noticed that probiotics and other preparations can regulate the intestines, and further treat COVID-19 with effective and gratifying results. In the system of traditional Chinese medicine(TCM), there's a term of “exterior-interior pairing of the lung and large intestine(肺与大肠相表里)”, showing an interconnection of the lung and the bowels. “Exterior-interior pairing of the lung and large intestine” is an important part of the theory of visceral activities proposed by ancient physicians through a long-term observation and practice. It's considered that “lung” and “large intestine” are interconnected and mutually exterior-interior in the normal physical activities and the disease development, providing a theoretical basis for treating lung diseases and bowel diseases from the perspective of overall concept. The study aims to compare the term of “exterior-interior pairing of the lung and large intestine” in TCM and “gut-lung crosstalk” in Western medicine regarding the development of COVID-19 and its intestinal symptoms, and provide more ideas for diagnosing and treating lung and bowel related diseases. 展开更多
关键词 Exterior-interior pairing of the lung and large intestine(肺与大肠相表里) Gut-lung crosstalk Connotation COVID-19 Traditional Chinese medicine
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Combination of Homoeologous Pairing Gene phKL and Ph2-deficiency in Common Wheat and Its Meiotic Behaviors in Hybrids with Alien Species 被引量:1
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作者 刘登才 郑有良 +3 位作者 颜泽洪 周永红 魏育明 兰秀锦 《Acta Botanica Sinica》 CSCD 2003年第9期1121-1128,共8页
The combined lines having both phKL and Ph2-deficiency were obtained in the genetic background of common wheat (Triticum aestivum L.) landrace. These lines had normal fertility. In the wheat combined lines X Aegilops ... The combined lines having both phKL and Ph2-deficiency were obtained in the genetic background of common wheat (Triticum aestivum L.) landrace. These lines had normal fertility. In the wheat combined lines X Aegilops variabilis Eig. (or rye), a significant increase in the chiasmata of homoeologous pairing was shown by the phKL+Ph2(-) plants with respect to their phKL+Ph2 sibs, which indicates that Ph2-deficiency and phKL showed an additive effect on promoting pairing. The effects were shown in the increment of rod bivalents, ring bivalents and trivalents and reduction of univalents, of which, reduction of univalents was mainly due to the increment of rod bivalents. The combined lines are probably more desirable materials for alien gene transferring than phKL or Ph2(-) lines alone. In comparison with that of ph1b X Ae. variabilis (or rye), phKL+Ph2(-) X Ae. variabilis (or rye) show higher (or similar) numbers of rod bivalents, while the total chromosome pairing level significantly reduced that ascribed to the decrement in ring bivalents and multivalents. These results probably indicate the different genetic mechanisms for Ph1 and Ph2 or phKL on controlling homoeologous pairing. 展开更多
关键词 Triticum aestivum homoeologous pairing Ph gene metaphase- I pairing interspecific hybrid
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Pairing transitions in a binary Bose gas
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作者 Zesheng Shen Lan Yin 《Chinese Physics B》 2025年第10期496-502,共7页
The stable Bardeen-Schrieffer-Cooper(BCS)pairing state of a bosonic system has long been sought theoretically and experimentally.Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas w... The stable Bardeen-Schrieffer-Cooper(BCS)pairing state of a bosonic system has long been sought theoretically and experimentally.Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas with s-wave intra-species repulsion and an inter-species attraction in the mean-field-stable region.We find that above the Bose-Einstein condensation(BEC)transition temperature,there is a phase transition from the normal state to a BCS state driven by interspecies pairing.When the temperature decreases,another phase transition from the BCS state to a mixed state featuring both atomic BEC and inter-species pairing occurs.As the temperature is further lowered,the mixed state is eventually taken over by the pure BEC state.We present the phase diagram of this system and discuss its experimental implications. 展开更多
关键词 pairing states Bose-Einstein condensates
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基于Tate Pairings的群组密钥协商方案 被引量:2
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作者 王勇 李明 曹元大 《计算机工程与应用》 CSCD 北大核心 2004年第36期1-3,86,共4页
该文提出了一种利用超奇异椭圆曲线上的TatePairing进行密钥协商的分布式群组密钥管理机制。该机制的通信开销随成员数目的增加而增长的幅度可忽略,3阶B-树的使用使得其计算开销为O(log3n)。它提供的安全属性包括群组密钥保密性、前向... 该文提出了一种利用超奇异椭圆曲线上的TatePairing进行密钥协商的分布式群组密钥管理机制。该机制的通信开销随成员数目的增加而增长的幅度可忽略,3阶B-树的使用使得其计算开销为O(log3n)。它提供的安全属性包括群组密钥保密性、前向保密和后向保密。从性能和安全性两方面来看,该机制适用于高延迟网络中的大型群组。 展开更多
关键词 群组密钥管理 Tate pairingS B-树
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Spatial channel pairing-based maximum ratio combining algorithm for cooperative relay networks
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作者 胡锦松 束锋 +4 位作者 许正文 阙非 黄晓晖 刘婷婷 陆锦辉 《Journal of Southeast University(English Edition)》 EI CAS 2016年第2期146-150,共5页
To improve the reliable performance of information transmission in cooperative relay networks, the scheme of the max-rate spatial channel pairing (SCP) based on maximum ratio combining (MRC) is proposed. The schem... To improve the reliable performance of information transmission in cooperative relay networks, the scheme of the max-rate spatial channel pairing (SCP) based on maximum ratio combining (MRC) is proposed. The scheme includes three steps: channel phase cancellation, MRC, and SCP. Eventually, the solution of the scheme is modeled as convex optimization. The objective function of the optimization problem is to maximize the transmission rate and the optimization variable is the strategy of pairing between the uplink spatial sub-channels of each user and the corresponding downlink spatial ones. The theorem of the arrangement inequalities is adopted to obtain the approximate closed-form solution of the optimal pairing for this convex optimization. Simulation results demonstrate that compared to the existing distributed space-time block coding and coherent combined schemes without SCP, the proposed max-rate SCP plus MRC algorithm achieves appreciable improvements in symbol error rate in medium and high signal-to-noise ratio regimes. The achievable performance gain is due to the use of maxrate SCP. 展开更多
关键词 RELAY maximum ratio combining coherentcombining spatial channel pairing distributed space-timeblock coding
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基于Pairing的可认证的群密钥协商协议
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作者 李明 王勇 +1 位作者 谷大武 白英彩 《上海交通大学学报》 EI CAS CSCD 北大核心 2004年第z1期200-203,共4页
基于Pairing计算和密钥树提出了一种高效的动态群密钥协商方案.通过引入群公钥证书并在群密钥中结合群以及成员的长期密钥和临时密钥,提供了隐含密钥认证,以有效地对抗中间人攻击.此外,该方案的设计思想可以作为一种通用方法,把可认证两... 基于Pairing计算和密钥树提出了一种高效的动态群密钥协商方案.通过引入群公钥证书并在群密钥中结合群以及成员的长期密钥和临时密钥,提供了隐含密钥认证,以有效地对抗中间人攻击.此外,该方案的设计思想可以作为一种通用方法,把可认证两方Diffile-Hellman协议扩展到群环境. 展开更多
关键词 pairing 群密钥协商 隐含密钥认证
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An Efficient Method of Generating Parameters for Pairing-Based Cryptosystems
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作者 WANG Maocai DAI Guangming PEN Lei ZHEN Chang QIN Ruijie 《China Communications》 SCIE CSCD 2010年第4期167-171,共5页
Efficient computation of Tate pairing is a crucial factor for practical applications of pairing-based cryptosystems(PBC).Recently,there have been many improvements for the computation of Tate pairing,which focuses on ... Efficient computation of Tate pairing is a crucial factor for practical applications of pairing-based cryptosystems(PBC).Recently,there have been many improvements for the computation of Tate pairing,which focuses on the arithmetical operations above the finite field.In this paper,we analyze the structure of Miller’s algorithm firstly,which is used to implement Tate pairing.Based on the characteristics that Miller’s algorithm will be improved tremendous if the order of the subgroup of elliptic curve group is low hamming prime,a new method for generating parameters for PBC is put forward,which enable it feasible that there is certain some subgroup of low hamming prime order in the elliptic curve group generated.Finally,we analyze the computation efficiency of Tate pairing using the new parameters for PBC and give the test result.It is clear that the computation of Tate pairing above the elliptic curve group generating by our method can be improved tremendously. 展开更多
关键词 pairing-based Cryptosystems Miller's Algorithm Tate pairing Low Hamming Elliptic Curve
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Efficient Certificateless Authenticated Key Agreement Protocol from Pairings 被引量:24
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作者 WANG Shengbao CAO Zhenfu WANG Licheng 《Wuhan University Journal of Natural Sciences》 CAS 2006年第5期1278-1282,共5页
In the area of secure Web information system, mutual authentication and key agreement are essential between Web clients and servers. An efficient certificateless authenticated key agreement protocol for Web client/ser... In the area of secure Web information system, mutual authentication and key agreement are essential between Web clients and servers. An efficient certificateless authenticated key agreement protocol for Web client/server setting is proposed, which uses pairings on certain elliptic curves. We show that the newly proposed key agreement protocol is practical and of great efficiency, meanwhile, it satisfies every desired security require ments for key agreement protocols. 展开更多
关键词 Web security authenticated key agreement certificateless public key cryptography bilinear pairings
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Tailoring Variant Pairing to Enhance Impact Toughness in High-Strength Low-Alloy Steels via Trace Carbon Addition 被引量:4
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作者 Yi-Shuang Yu Zhi-Quan Wang +4 位作者 Bin-Bin Wu Jing-Xiao Zhao Xue-Lin Wang Hui Guo Cheng-Jia Shang 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 2021年第6期755-764,共10页
Alloying can make conventional metals reach ultra-high strength,but this usually comes at dramatic loss of toughness.In this work,a desirable strength–toughness combination in high-strength low-alloy steel achieved v... Alloying can make conventional metals reach ultra-high strength,but this usually comes at dramatic loss of toughness.In this work,a desirable strength–toughness combination in high-strength low-alloy steel achieved via trace carbon addition.The significance of carbon in tailoring variant pairing and tuning impact toughness was elucidated from the perspective of crystallography and thermodynamics.As the carbon content increases,the packets and blocks are refined,and the-40 impact toughness improves.The enhancement of impact toughness results from the higher density of block boundaries,and the fracture mode shifts from brittle fracture to ductile–brittle combined fractures,then to ductile fracture due to the increased carbon.Increasing the carbon content would lower the martensite start temperature(M_S)temperature and driving force for martensitic transformation,and increase the strength of austenite matrix,which in turn contributes to producing more V1/V2 variant pairs to accommodate the transformation strain. 展开更多
关键词 High-strength low-alloy steel Carbon Impact toughness Variant pairing Phase transformation
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A THRESHOLD BLIND SIGNATURE FROM WEIL PAIRING ON ELLIPTIC CURVES 被引量:6
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作者 Cheng Xiangguo Xu Weidong Wang Xinmei 《Journal of Electronics(China)》 2006年第1期76-80,共5页
The idea behind a (t, n) threshold blind signature is that a user can ask at least t out of n players of a group to cooperate to generate a signature for a message without revealing its content. This paper first prese... The idea behind a (t, n) threshold blind signature is that a user can ask at least t out of n players of a group to cooperate to generate a signature for a message without revealing its content. This paper first presents a new blind signature scheme from Weil pairing on elliptic curves. Based on this scheme, a threshold blind signature scheme is proposed. It is efficient and has the security properties of robustness and unforgeability. In the proposed scheme, the group manger is introduced to take the role of distributing the group secret key to each player. However, he cannot forge the players to generate partial blind signatures (Each partial blind signature depends on not only the secret key of the player, but also a random number the player picks). Compared with a threshold signature with a trusted third party, its advantage is obvious; Compared with a threshold signature without a trusted third party, it is more simple and efficient. 展开更多
关键词 Signature scheme Threshold blind signature scheme Well pairing Gap Diffie-Hellman group
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Efficient and Provably Secure Multi-Recipient Signcryption from Bilinear Pairings 被引量:5
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作者 LI Fagen HU Yupu LIU Shuanggen 《Wuhan University Journal of Natural Sciences》 CAS 2007年第1期17-20,共4页
Signcryption is a cryptographic primitive that performs signature and encryption simultaneously, at lower computational costs and communication overheads than the signature-then- encryption approach. In this paper, we... Signcryption is a cryptographic primitive that performs signature and encryption simultaneously, at lower computational costs and communication overheads than the signature-then- encryption approach. In this paper, we propose an efficient multi-recipient signcryption scheme based on the bilinear pairings, which broadcasts a message to multiple users in a secure and authenticated manner. We prove its semantic security and unforgeability under the Gap Diffie-Hellman problem assumption in the random oracle model. The proposed scheme is more efficient than re-signcrypting a message n times using a signcryption scheme in terms of computational costs and communication overheads. 展开更多
关键词 SIGNCRYPTION multi-recipient signcryption bilinear pairings provable security
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NEW ID-BASED GROUP SIGNATURE FROM PAIRINGS 被引量:8
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作者 Chen Xiaofeng Zhang Fangguo Kwangjo Kim 《Journal of Electronics(China)》 2006年第6期892-900,共9页
We argue that traditional identity-based systems from pairings seem unsuitable for designing group signature schemes due to the problem of key escrow. In this paper we first propose new ID-based public key systems wit... We argue that traditional identity-based systems from pairings seem unsuitable for designing group signature schemes due to the problem of key escrow. In this paper we first propose new ID-based public key systems without trusted PKG (Private Key Generator) from bilinear pairings. In our new ID-based systems, if the dishonest PKG impersonates an honest user to communicate with others, the user can provide a proof of treachery of the PKG afterwards, which is similar to certificate-based systems. Therefore, our systems reach the Girault’s trusted level 3. We then propose a group signature scheme under the new ID-based systems, the security and performance of which rely on the new systems. The size of the group public key and the length of the signature are independent on the numbers of the group. 展开更多
关键词 Group signature Bilinear pairings Identity-based cryptography
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Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory 被引量:2
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作者 Yang Su Ze-Yu Li +3 位作者 Li-Le Liu Guo-Xiang Dong Xiao-Bao Wang Yong-Jing Chen 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2024年第3期198-207,共10页
Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pair... Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data. 展开更多
关键词 Nuclear fission Density functional theory pairing force Potential energy surfaces Fission fragment distribution
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Resource Allocation Based on User Pairing and Subcarrier Matching for Downlink Non-Orthogonal Multiple Access Networks 被引量:2
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作者 Zhixin Liu Changjian Liang +2 位作者 Yazhou Yuan Kit Yan Chan Xinping Guan 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第3期679-689,共11页
The traditional orthogonal multiple access(OMA)is unable to satisfy the needs of large number of smart devices.To increase the transmission rate in the limited spectrum resource,implementation of both non-orthogonal m... The traditional orthogonal multiple access(OMA)is unable to satisfy the needs of large number of smart devices.To increase the transmission rate in the limited spectrum resource,implementation of both non-orthogonal multiple access(NOMA)and successive interference cancelation(SIC)is essential.In this paper,an optimal resource allocation algorithm in NOMA is proposed to maximize the total system rate in a multi-sector multi-subcarrier relay-assisted communication network.Since the original problem is a non-convex problem with mixed integer programming which is non-deterministic polynomial-time(NP)-hard,a three-step solution is proposed to solve the primal problem.Firstly,we determine the optimal power allocation of the outer users by using the approach of monotonic discrimination,and then the optimal user pairing is determined.Secondly,the successive convex approximation(SCA)method is introduced to transform the non-convex problem involving central users into convex one,and the Lagrangian dual method is used to determine the optimal solution.Finally,the standard Hungarian algorithm is utilized to determine the optimal subcarrier matching.The simulation results show that resource allocation algorithm is able to meet the user performance requirements with NOMA,and the total system rate is improved compared to the existing algorithms. 展开更多
关键词 Non-orthogonal multiple access(NOMA) power control rate maximization subcarrier matching user pairing
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Pairing effects on the fragment mass distribution of Th,U,Pu,and Cm isotopes 被引量:2
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作者 Xin Guan Jin‑Huan Zheng Mei‑Yan Zheng 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第11期128-139,共12页
In this article,a comprehensive study of the fission process of Th,U,Pu,and Cm isotopes using a Yukawa-folded meanfield plus standard pairing model is presented.The study focused on analyzing the effects of the pairin... In this article,a comprehensive study of the fission process of Th,U,Pu,and Cm isotopes using a Yukawa-folded meanfield plus standard pairing model is presented.The study focused on analyzing the effects of the pairing interaction on the fragment mass distribution and its dependence on nuclear elongation.The significant role of pairing interactions in the fragment mass distributions of^(230)Th,^(234)U,^(240)Pu,and^(246)Cm was demonstrated.Numerical analysis revealed that increasing the pairing interaction strength decreased the asymmetric fragment mass distribution and increased the symmetric distribution.Furthermore,the odd-even mass differences at symmetric and asymmetric fission points were examined,highlighting their sensitivity to changes in the pairing interaction strength.Systematic analysis of the Th,U,Pu,and Cm isotope fragment mass distributions demonstrated the effectiveness of the model in reproducing the experimental data.In addition,the effects of the zero-point energy and half-width parameter on the fragment mass distribution for^(240)Pu were explored.Thus,this study provides valuable insights into the fission process by emphasizing the importance of pairing interactions and their relationship with nuclear elongation. 展开更多
关键词 Nuclear fission pairing interaction Fragment mass distribution Actinide nuclei
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Molecular Mechanisms of Homologous Chromosome Pairing and Segregation in Plants 被引量:2
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作者 Jing Zhang Bing Zhang +2 位作者 Handong Sua James A.Birchler Fangpu Han 《Journal of Genetics and Genomics》 SCIE CAS CSCD 2014年第3期117-123,共7页
In most eukaryotic species, three basic steps of pairing, recombination and synapsis occur during prophase of meiosis I. Homologous chromosomal pairing and recombination are essential for accurate segregation of chrom... In most eukaryotic species, three basic steps of pairing, recombination and synapsis occur during prophase of meiosis I. Homologous chromosomal pairing and recombination are essential for accurate segregation of chromosomes. In contrast to the well-studied processes such as recombination and synapsis, many aspects of chromosome pairing are still obscure. Recent progress in several species indicates that the telomere bouquet formation can facilitate homologous chromosome pairing by bringing chromosome ends into close proximity, but the sole presence of telomere clustering is not sufficient for recognizing homologous pairs. On the other hand, accurate segregation of the genetic material from parent to offspring during meiosis is dependent on the segregation of homologs in the reductional meiotic division (MI) with sister kinetochores exhibiting mono-orientation from the same pole, and the segregation of sister chromatids during the equational meiotic division (MII) with kinetochores showing bi-orientation from the two poles. The underlying mechanism of orientation and segregation is still unclear. Here we focus on recent studies in plants and other species that provide insight into how chromosomes find their partners and mechanisms mediating chromosomal segregation. 展开更多
关键词 Homologous chromosome pairing Orientation and segregation MEIOSIS
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Ion Pairing Kinetics Does not Necessarily Follow the Eigen-Tamm Mechanism 被引量:2
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作者 Qiang Zhang Bing-bing Zhang +1 位作者 Ling Jiang Wei Zhuang 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2013年第6期694-700,I0004,共8页
The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution: the completely solvat... The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution: the completely solvated state, 2SIP (double solvent separate ion pair), SIP (single solvent separate ion pair), and CIP (contact ion pair). Eigen and Tamm suggested that the transition from SIP to CIP is always the slowest step during the whole pairing process, due to a high free energy barrier between these two states. We carried out a series of potential of mean force calculations to study the pairing free energy profiles of two sets of model mono- atomic 1:1 ion pairs 2.0:x and x:2.0. For 2.0:x pairs the free energy barrier between the SIP and CIP states is largely reduced due to the salvation shell water structure. For these pairs the SIP to CIP transition is thus not the slowest step in the ion pair formation course. This is a deviation from the Eigen-Tamm model. 展开更多
关键词 Ion pairing Eigen-Tamm model Potential of mean force
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