Conventional liquid crystal elastomer(LCE)-based robots are limited by the need for complex controllers and bulky power supplies,restricting their use in microrobots and soft robots.This paper introduces a novel light...Conventional liquid crystal elastomer(LCE)-based robots are limited by the need for complex controllers and bulky power supplies,restricting their use in microrobots and soft robots.This paper introduces a novel light-powered dicycle that uses an LCE rod,enabling self-rolling by harvesting energy from the environment.The LCE rod serves as the driving force,with energy being supplied by a line light source.Employing a dynamic LCE model,we calculate the transverse curvature of the LCE rod after deformation,as well as the driving moment generated by the shift in a rod’s center of gravity,which allows the dicycle to roll on its own.Through extensive numerical simulations,we identify the correlations between the angular velocity of the dicycle and the key system parameters,specifically the light intensity,LCE rod length,light penetration depth,overall mass of the dicycle,rolling friction coefficient,and wheel radius.Further,the experimental verification is the same as the theoretical result.This proposed light-powered self-rolling dicycle comes with the benefits of the simple structure,the convenient control,the stationary light source,and the small luminous area of the light source.It not only demonstrates self-sustaining oscillations based on active materials,but also highlights the great potential of light-responsive LCE rods in applications such as robotics,aerospace,healthcare,and automation.展开更多
Chiral tetraphenylethylene(TPE) dicycle tetraaldehyde and TPE dicycle tetraacids bearing optically pure groups on the cycles were designed and synthesized. Due to the propeller-like conformation immobilization of TPE ...Chiral tetraphenylethylene(TPE) dicycle tetraaldehyde and TPE dicycle tetraacids bearing optically pure groups on the cycles were designed and synthesized. Due to the propeller-like conformation immobilization of TPE unit, this new class of TPE dicycle was resolved into M-and P-enantiomers, which could emit strong circular polarized luminescence(CPL). Interestingly,these TPE helicates displayed exceptional ability of molecule recognition. While the TPE dicycle tetraaldehyde could detect the microscale water in anhydrous tetrahydrofuran, the chiral TPE dicycle tetraacid could display different fluorescent color after interacting with two enantiomers of a wide variety of chiral amines including monoamines, diamines, and aminols, which could be applied to chiral recognition of these chiral amines. Furthermore, the emission wavelength of TPE dicycle tetraacid was found to change linearly with the enantiomer purity of chiral amine from enantiomer excess(ee) percent-100% to +100%, for the first time showing the potential for quantitative chiral analysis of chiral amines based on emission wavelength change. The emission wavelength was affected less by environmental factors than fluorescence intensity, which would enable the chiral analysis based on wavelength change with higher accuracy and repeatability.展开更多
The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the ...The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.展开更多
For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)a...For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)ab=a^(−1)),the dicyclic group of order 4n(n≥3),which is also known as the generalized quaternion group.We mainly investigate the properties and metric dimension of the commuting graphs on the dicyclic group T4n.展开更多
基金supported by the National Natural Science Foundation of China(No.12172001)the University Natural Science Research Project of Anhui Province of China(No.2022AH020029)+1 种基金the Anhui Provincial Natural Science Foundation(Nos.2208085Y01 and 2008085QA23)the Housing and Urban-Rural Development Science and Technology Project of Anhui Province of China(No.2023-YF129)。
文摘Conventional liquid crystal elastomer(LCE)-based robots are limited by the need for complex controllers and bulky power supplies,restricting their use in microrobots and soft robots.This paper introduces a novel light-powered dicycle that uses an LCE rod,enabling self-rolling by harvesting energy from the environment.The LCE rod serves as the driving force,with energy being supplied by a line light source.Employing a dynamic LCE model,we calculate the transverse curvature of the LCE rod after deformation,as well as the driving moment generated by the shift in a rod’s center of gravity,which allows the dicycle to roll on its own.Through extensive numerical simulations,we identify the correlations between the angular velocity of the dicycle and the key system parameters,specifically the light intensity,LCE rod length,light penetration depth,overall mass of the dicycle,rolling friction coefficient,and wheel radius.Further,the experimental verification is the same as the theoretical result.This proposed light-powered self-rolling dicycle comes with the benefits of the simple structure,the convenient control,the stationary light source,and the small luminous area of the light source.It not only demonstrates self-sustaining oscillations based on active materials,but also highlights the great potential of light-responsive LCE rods in applications such as robotics,aerospace,healthcare,and automation.
基金the National Natural Science Foundation of China (22072050 and 22372066) for financial support。
文摘Chiral tetraphenylethylene(TPE) dicycle tetraaldehyde and TPE dicycle tetraacids bearing optically pure groups on the cycles were designed and synthesized. Due to the propeller-like conformation immobilization of TPE unit, this new class of TPE dicycle was resolved into M-and P-enantiomers, which could emit strong circular polarized luminescence(CPL). Interestingly,these TPE helicates displayed exceptional ability of molecule recognition. While the TPE dicycle tetraaldehyde could detect the microscale water in anhydrous tetrahydrofuran, the chiral TPE dicycle tetraacid could display different fluorescent color after interacting with two enantiomers of a wide variety of chiral amines including monoamines, diamines, and aminols, which could be applied to chiral recognition of these chiral amines. Furthermore, the emission wavelength of TPE dicycle tetraacid was found to change linearly with the enantiomer purity of chiral amine from enantiomer excess(ee) percent-100% to +100%, for the first time showing the potential for quantitative chiral analysis of chiral amines based on emission wavelength change. The emission wavelength was affected less by environmental factors than fluorescence intensity, which would enable the chiral analysis based on wavelength change with higher accuracy and repeatability.
基金supported by NSFC(No.12201202)NSF of Hunan Province(No.2023JJ30180)NSFC(No.12471022)。
文摘The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.
基金This work was supported by NSFC Grant 11871206Natural Science Foundation of Hunan Province(No.2020JJ4233,No.2020JJ5096).
文摘For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)ab=a^(−1)),the dicyclic group of order 4n(n≥3),which is also known as the generalized quaternion group.We mainly investigate the properties and metric dimension of the commuting graphs on the dicyclic group T4n.
