A programmable low-profile array antenna based on nematic liquid crystals(NLCs)is proposed.Each antenna unit comprises a square patch radiating structure and a tunable NLC-based phase shifter capable of achieving a ph...A programmable low-profile array antenna based on nematic liquid crystals(NLCs)is proposed.Each antenna unit comprises a square patch radiating structure and a tunable NLC-based phase shifter capable of achieving a phase shift exceeding 360°with high linearity.First,the above 64 antenna units are periodically arranged into an 8×8 NLC-based antenna array,and the bias voltage of the NLC-based phase shifter loaded on the antenna unit is adjusted through the control of the field-programmable gate array(FPGA)programming sequences.This configuration enables precise phase changes for all 64 channels.Numerical simulation,sample processing,and experimental measurements of the antenna array are conducted to validate the performance of the antenna.The numerical and experimental results demonstrate that the proposed antenna performs well within the frequency range of 19.5-20.5 GHz,with a 3 dB relative bandwidth of 10%and a maximum main lobe gain of 14.1 dBi.A maximum scanning angle of±34°is achieved through the adjustment of the FPGA programming sequence.This NLC-based programmable array antenna shows promising potential for applications in satellite communication.展开更多
Active matter exhibits collective motions at various scales.Geometric confinement has been identified as an effective way to control and manipulate active fluids,with much attention given to external factors.However,t...Active matter exhibits collective motions at various scales.Geometric confinement has been identified as an effective way to control and manipulate active fluids,with much attention given to external factors.However,the impact of the inherent properties of active particles on collective motion under confined conditions remains elusive.Here,we use a highly tunable active nematics model to study active systems under confinement,focusing on the effect of the self-driven speed of active particles.We identify three distinct states characterized by unique particle and flow fields within confined active nematic systems,among which circular rotation emerges as a collective motion involving rotational movement in both particle and flow fields.The theoretical phase diagram shows that increasing the self-driven speed of active particles significantly enhances the region of the circular rotation state and improves its stability.Our results provide insights into the formation of high quality vortices in confined active nematic systems.展开更多
The modulation of dielectric anisotropy(△ε)is pivotal for elucidating molecular interactions and directing the alignment of liquid crystals.In this study,we combine liquid crystals with opposing dielectric anisotrop...The modulation of dielectric anisotropy(△ε)is pivotal for elucidating molecular interactions and directing the alignment of liquid crystals.In this study,we combine liquid crystals with opposing dielectric anisotropies to explore the impact of varying concentrations on their properties.We report the sign-reversal of△εin both the nematic and smectic A phases of these mixed liquid crystals,alongside a dual-frequency behaviour across a broad temperature spectrum.Our research further quantifies the influence of mixture ratios under various temperatures and electric field frequencies.This exploration may pave the way for the discovery of new physical phenomena.展开更多
In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in...In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.展开更多
The kinetics of I-->N transition of a side chain nematic polymethacrylate has been studied by small angle depolarized light scattering intensity measurements using a charge coupled device linear image sensor. The p...The kinetics of I-->N transition of a side chain nematic polymethacrylate has been studied by small angle depolarized light scattering intensity measurements using a charge coupled device linear image sensor. The polymer shows the transition temperatures K52N79I in degreesC, The H-v scattering intensity T(q,t) during the transition I (at 80.2degreesC)-->N (at 75.8degreesC) shows that T(q) is independent of q for all t, and during the initial stage (in 6 s) T(t) increases exponentially with t. In the later stage of the transition T(t) approaches a saturation value in 2 min. This experimental result indicates that the I-->N transition of a liquid crystalline polymer is a spinodal type of phase transition mediated by orientation fluctuation.展开更多
In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Land...In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.展开更多
A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybri...A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.展开更多
We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers （LCPs） governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simpl...We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers （LCPs） governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs： when the normalized polymer concentration b is below a critical value b＊ （6.T314863965）, the only equilibrium state is isotropic and it is stable; when b＊ 〈 b 〈 15/2, two anisotropic （prolate） equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b 〉 15/2, there are three equilibrium states： a stable prolate state, an unstable isotropie state and an unstable oblate state.展开更多
A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates.In this way,the problem is reduced to finding the steady st...A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates.In this way,the problem is reduced to finding the steady state of an overdamped evolution system according to a kinetic law,rather than directly solving the coupled nonlinear equations.This enables one to account for the complicated director distribution and obtain the precise wrinkling morphology of the film.Though the approach proposed here is for a twist nematic film,it can be extended to study glassy nematic films with other director distributions.展开更多
In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis an...In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1（R3） additionally.展开更多
Nematic liquid crystal system of interacting biaxial particles via dispersion forces is studied.The molecular orienting potential form in a magnetic field is given for the first time.Weakly ordered isotropic phase is ...Nematic liquid crystal system of interacting biaxial particles via dispersion forces is studied.The molecular orienting potential form in a magnetic field is given for the first time.Weakly ordered isotropic phase is treated in the two-particle cluster approximation.Taking account of the molecular biaxiality,it is found that the ratio of the lowest supercooling temperature T^(*)to the nematic-isotropic phase transition temperature TC approaches the observed value,and the validity of the mean field theory is clarified.展开更多
In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution o...In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].展开更多
In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematic...In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.展开更多
Flexoelectric-induced voltage shift in a weak anchoring hybrid aligned nematic fiquid crystai cell is investigated theoretically. Based on the elastic theory of liquid crystal and the variation method, the equations f...Flexoelectric-induced voltage shift in a weak anchoring hybrid aligned nematic fiquid crystai cell is investigated theoretically. Based on the elastic theory of liquid crystal and the variation method, the equations for the bulk and the boundary of the cell are derived. By computer simulation, the dependence of the shift voltage on the sum of the ttexoelectric coefficients and the anchoring energy strength is obtained. As a result, a novel method to determine the sum of the flexoelectric coefficients by measuring the shift voltage is put forward.展开更多
The electronic doping effect on both the superconductivity and the nematic order in the FeSe nanoflake are investigated by using the electric-double-layer transistor configuration. The superconductivity can be effecti...The electronic doping effect on both the superconductivity and the nematic order in the FeSe nanoflake are investigated by using the electric-double-layer transistor configuration. The superconductivity can be effectively controlled by electronic doping, and the onset superconducting transition temperature Tc reaches as high as 45 K at a gate voltage Of Vg = 4 V. Meanwhile, the nematic phase is gradually suppressed with the increase of electronic doping （or Vg）. The results provide an effective method with variable charge doping for investigation of the rich physics in the FeSe superconductor.展开更多
Nematic elastomers are new materials that have many remarkable properties.In this article,we study how nonlinear elasticity of semi-soft nematic elastomers can be described phenomenologically.We start with a theory ba...Nematic elastomers are new materials that have many remarkable properties.In this article,we study how nonlinear elasticity of semi-soft nematic elastomers can be described phenomenologically.We start with a theory based on strain tensor only,and then continue to develop a phenomenological description with the liquid crystal order tensor included explicitly.Such a description has the virtue of being able to treat the strain tensor and the liquid crystal order tensor equally and thus making the complicated symmetries of nematic elastomers easier to understand.展开更多
We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these...We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.展开更多
In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such s...In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if （u, d）is smooth up to time T provided that ∫T 0‖△×u（t, ·）‖BMO（R3） ＋‖△d（t, ·）‖8L4（R3）dt 〈∞.展开更多
We report comprehensive angle-resolved photoemission investigations on the electronic structures and nematicity of the parent compounds of the iron-based superconductors including CeFeAsO, BaFe2As2, NaFeAs, FeSe and u...We report comprehensive angle-resolved photoemission investigations on the electronic structures and nematicity of the parent compounds of the iron-based superconductors including CeFeAsO, BaFe2As2, NaFeAs, FeSe and undoped FeSe/SrTiO3 films with 1, 2 and 20 layers. While the electronic structure near tile Brillouin zone center F varies dramatically among different materials, the electronic structure near the Brillouin zone corners （M points）, as well as their temperature dependence, are rather similar. The electronic structure near the zone corners is dominated by the electronic nematicity that gives rise to a band splitting of the dxz and dyz bands below the nematie transition temperature. A clear relation is observed between the band splitting magnitude arid the onset temperature of nematicity. Our results may shed light on the origin of nematicity, its effect on the electronic structures, and its relation with superconductivity in the iron-based superconductors.展开更多
基金The National Natural Science Foundation of China(No.62401168,62401139,62401170)China Postdoctoral Science Foundation(No.2023MD744197)+2 种基金Postdoctoral Fellowship Program of CPSF(No.GZC20230631)Project for Enhancing Young and Middle-aged Teacher’s Research Basis Ability in Colleges of Guangxi(No.2023KY0218)Guangxi Key Laboratory Foundation of Optoelectronic Information Processing(No.GD23102)。
文摘A programmable low-profile array antenna based on nematic liquid crystals(NLCs)is proposed.Each antenna unit comprises a square patch radiating structure and a tunable NLC-based phase shifter capable of achieving a phase shift exceeding 360°with high linearity.First,the above 64 antenna units are periodically arranged into an 8×8 NLC-based antenna array,and the bias voltage of the NLC-based phase shifter loaded on the antenna unit is adjusted through the control of the field-programmable gate array(FPGA)programming sequences.This configuration enables precise phase changes for all 64 channels.Numerical simulation,sample processing,and experimental measurements of the antenna array are conducted to validate the performance of the antenna.The numerical and experimental results demonstrate that the proposed antenna performs well within the frequency range of 19.5-20.5 GHz,with a 3 dB relative bandwidth of 10%and a maximum main lobe gain of 14.1 dBi.A maximum scanning angle of±34°is achieved through the adjustment of the FPGA programming sequence.This NLC-based programmable array antenna shows promising potential for applications in satellite communication.
基金supported by the National Key Research and Development Program of China under Grant No.2022YFA1405000Innovation Program for Quantum Science and Technology under Grant No.2024ZD0300101the National Natural Science Foundation of China under Grant Nos.12274212,12174184,12347102。
文摘Active matter exhibits collective motions at various scales.Geometric confinement has been identified as an effective way to control and manipulate active fluids,with much attention given to external factors.However,the impact of the inherent properties of active particles on collective motion under confined conditions remains elusive.Here,we use a highly tunable active nematics model to study active systems under confinement,focusing on the effect of the self-driven speed of active particles.We identify three distinct states characterized by unique particle and flow fields within confined active nematic systems,among which circular rotation emerges as a collective motion involving rotational movement in both particle and flow fields.The theoretical phase diagram shows that increasing the self-driven speed of active particles significantly enhances the region of the circular rotation state and improves its stability.Our results provide insights into the formation of high quality vortices in confined active nematic systems.
基金Project supported by the National Key Research and Development Program of China (Grant No.2022YFA1405000)the National Natural Science Foundation of China (Grant No.62375141)+1 种基金the Natural Science Foundation of Jiangsu Province,Major Project (Grant No.BK20212004)the Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications (Grant Nos.NY222122 and NY222105)。
文摘The modulation of dielectric anisotropy(△ε)is pivotal for elucidating molecular interactions and directing the alignment of liquid crystals.In this study,we combine liquid crystals with opposing dielectric anisotropies to explore the impact of varying concentrations on their properties.We report the sign-reversal of△εin both the nematic and smectic A phases of these mixed liquid crystals,alongside a dual-frequency behaviour across a broad temperature spectrum.Our research further quantifies the influence of mixture ratios under various temperatures and electric field frequencies.This exploration may pave the way for the discovery of new physical phenomena.
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
基金support by the NSFC(12071391,12231016)the Guangdong Basic and Applied Basic Research Foundation(2022A1515010860)support by the China Postdoctoral Science Foundation(2023M742401)。
文摘In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.
基金This work was supported by the National Key Projects for Fundamental Research, "Macromolecular Condensed State" of Ministry of Science and Technology of China.
文摘The kinetics of I-->N transition of a side chain nematic polymethacrylate has been studied by small angle depolarized light scattering intensity measurements using a charge coupled device linear image sensor. The polymer shows the transition temperatures K52N79I in degreesC, The H-v scattering intensity T(q,t) during the transition I (at 80.2degreesC)-->N (at 75.8degreesC) shows that T(q) is independent of q for all t, and during the initial stage (in 6 s) T(t) increases exponentially with t. In the later stage of the transition T(t) approaches a saturation value in 2 min. This experimental result indicates that the I-->N transition of a liquid crystalline polymer is a spinodal type of phase transition mediated by orientation fluctuation.
基金Hong Kong RGC Earmarked Research Grants 14305315,CUHK4041/11P and CUHK4048/13PThe Chinese University of Hong Kong,a Croucher Foundation-CAS Joint Grant,and a NSFC/RGC Joint Research Scheme(N-CUHK443/14)
文摘In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.
基金supported by the National Natural Science Foundation of China(Grant Nos.11274088,11374087,and 11304074)the Natural Science Foundation of Hebei Province,China(Grant No.A2014202123)+2 种基金the Research Project of Hebei Education Department,China(Grant Nos.Z2012061 and QN2014130)the Science and Technology Plan Project of Hebei Province,China(Grant No.134576260)the Key Subject Construction Project of Hebei Province University,China
文摘A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.
基金supported by the National Science Foundation and by the Office of Naval Research
文摘We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers （LCPs） governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs： when the normalized polymer concentration b is below a critical value b＊ （6.T314863965）, the only equilibrium state is isotropic and it is stable; when b＊ 〈 b 〈 15/2, two anisotropic （prolate） equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b 〉 15/2, there are three equilibrium states： a stable prolate state, an unstable isotropie state and an unstable oblate state.
基金supported by the National Natural Science Foundation of China(Grant 11072231)Collaborative Innovation Center of Suzhou Nano Science and Technology
文摘A kinetics approach is developed for the geometrically nonlinear analysis of photo-induced wrinkling of glassy twist nematic films on soft elastic substrates.In this way,the problem is reduced to finding the steady state of an overdamped evolution system according to a kinetic law,rather than directly solving the coupled nonlinear equations.This enables one to account for the complicated director distribution and obtain the precise wrinkling morphology of the film.Though the approach proposed here is for a twist nematic film,it can be extended to study glassy nematic films with other director distributions.
基金supported by NNSFC(11271381and 11501373)China 973 Program(2011CB808002)+5 种基金the Natural Science Foundation of Guangdong Province(2016A0300310019 and 2016A030307042)Guangdong Provincial culture of seedling of China(2013LYM0081)the Education research platform project of Guangdong Province(2014KQNCX208)the Education Reform Project of Guangdong Province(2015558)the Shaoguan Science and Technology Foundation(20157201)Education Reform Project of Shaoguan University(SYJY20121361 and SYJY20141576)
文摘In this paper,we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1（R3） additionally.
基金Supported by the Hebei Province Natural Science Foundation of China under Grant No.198002.
文摘Nematic liquid crystal system of interacting biaxial particles via dispersion forces is studied.The molecular orienting potential form in a magnetic field is given for the first time.Weakly ordered isotropic phase is treated in the two-particle cluster approximation.Taking account of the molecular biaxiality,it is found that the ratio of the lowest supercooling temperature T^(*)to the nematic-isotropic phase transition temperature TC approaches the observed value,and the validity of the mean field theory is clarified.
基金Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174)
文摘In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].
基金Project supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No07JKD140095)
文摘In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.
基金Supported by the Natural Science Foundation of Hebei Province under Grant No. A2010000004the National Natural Science Foundation of China under Grant No. 60736042+1 种基金the Key Subject Construction Project of Hebei Province Universitythe Research Project of Hebei Education Department under Grant No. Z2011133
文摘Flexoelectric-induced voltage shift in a weak anchoring hybrid aligned nematic fiquid crystai cell is investigated theoretically. Based on the elastic theory of liquid crystal and the variation method, the equations for the bulk and the boundary of the cell are derived. By computer simulation, the dependence of the shift voltage on the sum of the ttexoelectric coefficients and the anchoring energy strength is obtained. As a result, a novel method to determine the sum of the flexoelectric coefficients by measuring the shift voltage is put forward.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11174294,11174291,11374302,11304319,U1332209,U1432251 and U1532153the China Postdoctoral Science Foundation under Grant No 2015M582020+1 种基金the Program of Users with Excellence,the Hefei Science Center of Chinese Academy of Sciencesthe CAS/SAFEA International Partnership Program for Creative Research Teams of China
文摘The electronic doping effect on both the superconductivity and the nematic order in the FeSe nanoflake are investigated by using the electric-double-layer transistor configuration. The superconductivity can be effectively controlled by electronic doping, and the onset superconducting transition temperature Tc reaches as high as 45 K at a gate voltage Of Vg = 4 V. Meanwhile, the nematic phase is gradually suppressed with the increase of electronic doping （or Vg）. The results provide an effective method with variable charge doping for investigation of the rich physics in the FeSe superconductor.
文摘Nematic elastomers are new materials that have many remarkable properties.In this article,we study how nonlinear elasticity of semi-soft nematic elastomers can be described phenomenologically.We start with a theory based on strain tensor only,and then continue to develop a phenomenological description with the liquid crystal order tensor included explicitly.Such a description has the virtue of being able to treat the strain tensor and the liquid crystal order tensor equally and thus making the complicated symmetries of nematic elastomers easier to understand.
基金supported by National Natural Science Foundation of China under Grant No.2006CB921605the Science Research Foundation of Shunde College
文摘We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.
基金supported by the Natural Science Key Foundation of Universities of Fujian Province(JZ160406)Natural Science Foundation of Fujian Province(2015J01582)
文摘In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if （u, d）is smooth up to time T provided that ∫T 0‖△×u（t, ·）‖BMO（R3） ＋‖△d（t, ·）‖8L4（R3）dt 〈∞.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11190022,11334010 and 11534007the National Basic Research Program of China under Grant No 2015CB921000the Strategic Priority Research Program(B)of Chinese Academy of Sciences under Grant No XDB07020300
文摘We report comprehensive angle-resolved photoemission investigations on the electronic structures and nematicity of the parent compounds of the iron-based superconductors including CeFeAsO, BaFe2As2, NaFeAs, FeSe and undoped FeSe/SrTiO3 films with 1, 2 and 20 layers. While the electronic structure near tile Brillouin zone center F varies dramatically among different materials, the electronic structure near the Brillouin zone corners （M points）, as well as their temperature dependence, are rather similar. The electronic structure near the zone corners is dominated by the electronic nematicity that gives rise to a band splitting of the dxz and dyz bands below the nematie transition temperature. A clear relation is observed between the band splitting magnitude arid the onset temperature of nematicity. Our results may shed light on the origin of nematicity, its effect on the electronic structures, and its relation with superconductivity in the iron-based superconductors.
