23,996 research outputs found
Spiral symmetry and general Bloch's theorem
In this paper, spiral symmetry in cylindrical coordinate and general Bloch's
theorem induced from it are discussed. This general Bloch's theorem is useful
for considering the properties related to single-walled carbon nanotubes.Comment: 4 page
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)].Comment: 6 journal pages, 4 figure
Challenges in theoretical investigations on configurations of lipid membranes
This review reports some key results in theoretical investigations on
configurations of lipid membranes and presents several challenges in this field
which involve (i) exact solutions to the shape equation of lipid vesicles; (ii)
exact solutions to the governing equations of open lipid membranes; (iii) neck
condition of two-phase vesicles in the budding state; (iv) nonlocal theory of
membrane elasticity; (v) relationship between symmetry and the magnitude of
free energy.Comment: Chin. Phys. B 22, 028701 (2013
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 , \AA, TPa, respectively, while the
Young's moduli of multi-walled carbon nanotubes (MWNTs) are apparent functions
of the number of layers, , varying from 4.70TPa to 1.04TPa for N=1 to
. 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).Comment: 18 pages+5 figure; will appear as a Chapter in "Nanotubes: New
Research" (Nova Science Publishers, 2005
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)].Comment: 15 pages, 6 figure
Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model
Recent theoretical advances in elasticity of membranes following Helfrich's
famous spontaneous curvature model are summarized in this review. The governing
equations describing equilibrium configurations of lipid vesicles, lipid
membranes with free edges, and chiral lipid membranes are presented. Several
analytic solutions to these equations and their corresponding configurations
are demonstrated.Comment: 10 pages, 8 figure
Comment on "Highly Extended Image States around Nanotubes"
A Comment on the Letter by Granger et.al., Phys. Rev. Lett. 89, 135506
(2002).Comment: 2 page
Double-walled carbon nanotubes as hundred gigahertz oscillators
Based on the van der Waals interaction, the periodically nonlinear potential
of a singe-walled carbon nanotube (SWNT) with finite length in an infinite
length SWNT is analytically obtained. It is found that the inner SWNT can
oscillate in the outer SWNT with frequency beyond ten Gigahertz, even up to a
hundred Gigahertz.Comment: 9 pages, 8 figures, to PR
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.Comment: 12 pages + 3 figures. For the Seventh International Conference on
Geometry, Integrability and Quantization, Varna, 200
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.Comment: Review article for J. Comput. Theor. Nanosci., 27 pages, 15 figure
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