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Z. C. Tu

Publications and source records attributed to Z. C. Tu.

At least 55 records · Page 3Linked to original sources
arXiv2010

First-principles study on physical properties of a single ZnO monolayer with graphene-like structure

The elastic, piezoelectric, electronic, and optical properties of a single ZnO monolayer (SZOML) with graphene-like structure are investigated from the first-principles calculations. The phonon dispersion curves contain three acoustic and three optical branches. At $Γ$ point, the out-of-plane acoustic mode has an asymptotic behavior $ω(q)=Bq^2$ with $B=1.385 \times 10^{-7}$ m$^2$/s, while two in-plane acoustic modes have sound velocities $2.801$ km/s and $8.095$ km/s; the other three optical modes have frequencies 250 cm$^{-1}$, 566 cm$^{-1}$, and 631 cm$^{-1}$. The elastic and piezoelectric constants are obtained from the relaxed ion model. It is found that the SZOML is much softer than graphene, while it is a piezoelectric material. The electronic band gap is 3.576 eV, which implies that the SZOML is a wide band gap semiconductor. Many peaks exist in the linear optical spectra, where the first peak at 3.58 eV corresponds to the band gap of SZOML.

cond-mat.mtrl-sci↗
arXiv2010

Compatibility between shape equation and boundary conditions of lipid membranes with free edges

Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) There is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh \emph{et al.}, Proc. Natl. Acad. Sci. USA \textbf{95}, 1026 (1998)].

cond-mat.soft↗
arXiv2009

Extend Special Relativity to the Superluminal Case

First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal inertial frame, and that the coordinate transformations from any superluminal inertial frame to the rest frame (here rest just says in a relative sense) are the same as the Lorentz transformations from some normal inertial frame to the rest frame. Consequently, the causality can not be violated. Secondly, we investigate the superluminal theory of dynamics and find that the total energy of any object moving at a speed of $v$ (faster than the speed of light in vacuum $c$) is equal to the total energy of that object moving at a speed of $u (u<c)$ provided that the product of two speeds satisfy $uv=c^{2}$. Lastly, we conjecture that this superluminal theory can give a novel interpretation to the essence of matter waves put forward by de Broglie.

physics.gen-ph↗
arXiv2008

Theoretical and numerical investigations on shapes of planar lipid monolayer domains

Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains which consist of the surface energy, line tension energy, and dipole electrostatic energy. The shape equation which describes boundary curves of the domains at equilibrium state is derived from the first order variation of the formation energy. A relaxation method is proposed to find the numerical solutions of the shape equation. The theoretical and numerical results are in good agreement with previous experimental observation. Some new shapes not observed in previous experiments are also obtained, which awaits experimental confirmation in the future.

cond-mat.soft↗
arXiv2008

Efficiency at maximum power of Feynman's ratchet as a heat engine

The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency ($η_\ast$) are investigated by optimizing both the internal parameter and the external load. When a perfect ratchet device (no heat exchange between the ratchet and the paw via kinetic energy) works between two thermal baths at temperatures $T_1> T_2$, its efficiency at maximum power is found to be $η_\ast =η_C^2 /[η_C-(1-η_C)\ln(1-η_C)]$, where $η_C\equiv 1-T_2/T_1$. This efficiency is slightly higher than the value $1-\sqrt{T_2/T_1}$ obtained by Curzon and Ahlborn [\textit{Am. J. Phys.} \textbf{43} (1975) 22] for macroscopic heat engines. It is also slightly larger than the result $η_{SS}\equiv 2η_C/(4-η_C)$ obtained by Schmiedl and Seifert [\textit{EPL} \textbf{81} (2008) 20003] for stochastic heat engines working at small temperature difference, while the evident deviation between $η_\ast$ and $η_{SS}$ appears at large temperature difference. For an imperfect ratchet device in which the heat exchange between the ratchet and the paw via kinetic energy is non-vanishing, the efficiency at maximum power decreases with increasing the heat conductivity.

cond-mat.stat-mech↗
arXiv2008

Elastic theory of low-dimensional continua and its applications in bio- and nano-structures

This review presents the elastic theory of low-dimensional (one- and two-dimensional) continua and its applications in bio- and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua, is briefly described through Cartan moving frame method. The elastic theory of Kirchhoff rod, Helfrich rod, bending-soften rod, fluid membrane, and solid shell is revisited. Secondly, the application and availability of the elastic theory of low-dimensional continua in bio-structures, including short DNA rings, lipid membranes, and cell membranes, are discussed. The kink stability of short DNA rings is addressed by using the theory of Kirchhoff rod, Helfrich rod, and bending-soften rod. The lipid membranes obey the theory of fluid membrane. A cell membrane is simplified as a composite shell of lipid bilayer and membrane skeleton, which is a little similar to the solid shell. It is found that the membrane skeleton enhances highly the mechanical stability of cell membranes. Thirdly, the application and availability of the elastic theory of low-dimensional continua in nano-structures, including graphene and carbon nanotubes, are discussed. A revised Lenosky lattice model is proposed based on the local density approximation. Its continuum form up to the second order terms of curvatures and strains is the same as the free energy of 2D solid shells. Several typical mechanical properties of carbon nanotubes are revisited and investigated based on this continuum form. It is possible to avoid introducing the controversial concepts, the Young's modulus and thickness of graphene and single-walled carbon nanotubes, with this continuum form.

cond-mat.soft↗
arXiv2007

Concise theory of chiral lipid membranes

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\circ$ and 35$^\circ$, which are close to the most frequent values 5$^\circ$ and 28$^\circ$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir \textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda \textit{et al.}, Nature (London) \textbf{399}, 566 (1999)].

cond-mat.soft↗
arXiv2006

A possible generalized form of Jarzynski equality

The crucial condition in the derivation of the Jarzynski equality (JE) from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three \textit{Gedanken} experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.

cond-mat.stat-mech↗
arXiv2006

Elasticity and piezoelectricity of zinc oxide crystals, single layers, and possible single-walled nanotubes

The elasticity and piezoelectricity of zinc oxide (ZnO) crystals and single layers are investigated from the first-principles calculations. It is found that a ZnO thin film less than three Zn-O layers prefers a planar graphite-like structure to the wurtzite structure. ZnO single layers are much more flexible than graphite single layers in the elasticity and stronger than boron nitride single layers in the piezoelectricity. Single-walled ZnO nanotubes (SWZONTs) can exist in principle because of their negative binding energy. The piezoelectricity of SWZONTs depends on their chirality. For most ZnO nanotubes except the zigzag type, twists around the tube axis will induce axial polarizations. A possible scheme is proposed to achieve the SWZONTs from the solid-vapor phase process with carbon nanotubes as templates.

cond-mat.mtrl-sci↗
arXiv2006

Variational Problems in Elastic Theory of Biomembranes, Smectic-a Liquid Crystals, and Carbon Related Structures

After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential forms. The morphological problems of lipid bilayers and stabilities of cell membranes are also discussed. The key point is that the first and the second order variations of the free energy determine equilibrium shapes and mechanical stabilities of structures.

math-ph↗
arXiv2006

Theoretical determination of the necessary conditions for the formation of ZnO nanorings and nanohelices

The formation of ZnO nanorings and nanohelices with large polar surfaces observed in experiments [Nano Lett. 3, 1625 (2003); J. Am. Chem. Soc. 126, 6703 (2004)] is shown to be a result of the competition between elastic energy, spontaneous polarization-induced surface energy, volume energy, and defect-induced energy. It is found that nanorings and nanohelices observed in experiments are stable and energetically favorable structures.

cond-mat.mtrl-sci↗
arXiv2005

Elasticity of polymer vesicles by osmotic pressure: an intermediate theory between fluid membranes and solid shells

The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane strain energy plus Helfrich's curvature energy [Z. Naturforsch. C \textbf{28}, 693 (1973)]. The elastic constants in the free energy are obtained by discussing two simplified models: one is the polymer membrane without in-plane strains and asymmetry between its two sides, which is the counterpart of quantum mechanics in curved surface [Jensen and Koppe, Ann. Phys. \textbf{63}, 586 (1971)]; another is the planar rubber membrane with homogeneous in-plane strains. The equations to describe equilibrium shape and in-plane strains of the polymer vesicles by osmotic pressure are derived by taking the first order variation of the total free energy containing the elastic free energy, the surface tension energy and the term induced by osmotic pressure. The critical pressure, above which spherical polymer vesicle will lose its stability, is obtained by taking the second order variation of the total free energy. It is found that the in-plane mode also plays important role in the critical pressure because it couples with the out-of-plane mode. Theoretical results reveal that polymer vesicles possess the mechanical properties intermediate between fluid membranes and solid shells.

cond-mat.soft↗
arXiv2005

Molecular Motor Constructed from a Double-Walled Carbon Nanotube Driven by Axially Varying Voltage

A new molecular motor is conceptually constructed from a double-walled carbon nanotube (DWNT) consisting of a long inner single-walled carbon nanotube (SWNT) and a short outer SWNT with different chirality. The interaction between inner and outer tubes is the sum of the Lennard-Jones potentials between carbon atoms in inner tube and those in outer one. Within the framework of Smoluchowski-Feynman ratchet, it is theoretically shown that this system in an isothermal bath will exhibit a unidirectional rotation in the presence of a varying axial electrical voltage.

cond-mat.mtrl-sci↗
arXiv2005

Structures, Symmetries, Mechanics and Motors of carbon nanotubes

The structures and symmetries of single-walled carbon nanotubes (SWNTs) are introduced in detail. The physical properties of SWNTs induced by their symmetries can be described by tensors in mathematical point of view. It is found that there are 2, 4, and 5 different parameters in the second, third, and fourth rank tensors representing electronic conductivity (or static polarizability), the second order nonlinear polarizability, and elastic constants of SWNTs, respectively. The values of elastic constants obtained from tight-binding method imply that SWNTs might be very weakly anisotropic in mechanical properties. The further study on the mechanical properties shows that the elastic shell theory in the macroscopic scale can be applied to carbon nanotubes (CNTs) in the mesoscopic scale, as a result, SWNTs can be regarded as an isotropic material with Poisson ratio, effective thickness, and Young's modulus being $ν=0.34$, $h=0.75$Å, $Y=4.70$TPa, respectively, while the Young's moduli of multi-walled carbon nanotubes (MWNTs) are apparent functions of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$. Based on the chirality of CNTs, it is predicted that a new kind of molecular motor driven by alternating voltage can be constructed from double walled carbon nanotubes (DWNTs).

cond-mat.mes-hall↗
arXiv2005

Elasticities and stabilities: lipid membranes vs cell membranes

A cell membrane can be simply regarded as composite material consisting of lipid bilayer, membrane cytoskeleton beneath lipid bilayer, and proteins embedded in lipid bilayer and linked with membrane cytoskeleton if one only concerns its mechanical properties. In this Chapter, above all, the authors give a brief introduction to some important work on mechanical properties of lipid bilayers following Helfrich's seminal work on spontaneous curvature energy of lipid bilayers. Next, the entropy of a polymer confined in a curved surface and the free energy of membrane cytoskeleton are obtained by scaling analysis. It is found that the free energy of cell membranes has the form of the in-plane strain energy plus Helfrich's curvature energy. The equations to describe equilibrium shapes and in-plane strains of cell membranes by osmotic pressures are obtained by taking the first order variation of the total free energy containing the elastic free energy, the surface tension energy and the term induced by osmotic pressure. The stability of spherical cell membrane is discussed and the critical pressure is found to be much larger than that of spherical lipid bilayer without membrane cytoskeleton. Lastly, the authors try to extend the present static mechanical model of cell membranes to the cell structure dynamics by proposing a group of coupling equations involving tensegrity architecture of cytoskeleton, fluid dynamics of cytoplasm and elasticities of cell membranes.

q-bio.OT↗
arXiv2004

Geometric theory on the elasticity of bio-membranes

The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on the surfaces embedded in three-dimensional Euclidean space by using exterior differential forms.

cond-mat.soft↗
arXiv2004

Lipid membranes with free edges

Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrich's free energy and the surface and line tension energy. The equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy. These equations can also be applied to the membrane with several freely exposed edges. Analytical and numerical solutions to these equations are obtained under the axisymmetric condition. The numerical results can be used to explain recent experimental results obtained by Saitoh \emph{et al}. [Proc. Natl. Acad. Sci. \textbf{95}, 1026 (1998)].

cond-mat.soft↗