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news/2025/2/8 19:40:01 标签: constraints, shapes, structure, application, delay, forms


 


我英语不行,到家将就看吧.

我觉得一定要把自己做过的工作进行详细介绍.

My name is XX, a PH.D candidate of XXX.

I got your email address from WWW and I am very interested in your research
field. This message is to ask for the information of the PH.D and Postdoctoral program of
your group.

I have published 5 papers(see the attachment for my paper list written by Latex
convention) since 1996, including different topics: Controlling Chaos, Dynamics,
and Bio-membranes. The two papers of Bio-membrane were both finished in this
year, one is to discuss the pattern formation of periodic square
texture(egg-carton) in Lipid bilayers; the other is to discuss the Complex
vesicle under the framework of the spontaneous curvature energy model.


Iam also interested in Polymer dynamics, DNA structure transition and have read
many related papers. In fact, I have started to do some calculations in this
field.

Would you please to consider my application to join your group, especially
as a graduate student under your guidance? The reasons I want to obtain my PH.D
there are: 1). A PH.D obtained in such a famous University will be helpful to get a
good research position when I come back; 2). I want to be educated at a high
level since my dream is to be a successful researcher in the future.

Looking to your message.

Best regards!

Yours, XX.

BTW: The following is an introduction to my works:

1. XX, "Title" (accepted by Phy./ Rev./ E/ and
scheduled tentatively for the issue of: XXX ).

With numerical approach, we obtain a catalog of non-axisymmetric vesicle shapes
for the first time in the study of membrane configurations with the Spontaneous
Curvature (SC) model.
The software we used to search for the surfaces is the ``Surface Evolver"(SE)
package of computer programs (developed by Kenneth A. Brakke as one of the
main projects of the Geometry Center of the University of Minnesota) which initially
served to devote to minimal surfaces and constant mean curvature surfaces by
mathematicians and in principle is based on the discretization of the curvature
energy, the area, and the volume on a triangulated surface. The energy in the SE
can be a combination of surface tension, gravitational energy, squared mean
curvature, etc.. The constraints allowed for the software can be geometrical
constraints on vertex positions or constraints on integrated quantities such
as body volume, surface area, etc.. All such the constraints can also be
incorporated in the bending energy by which we then are able to generize th
e SE into the present study, searching for non-axisymmetric vesicle shapes. The
resulting total energy is minimized by a gradient descent procedure, and the
resulting shape is a local energy minimum with the result of a lenthy numerical
simulation.
We report a catalog of interesting shapes including a {/sl corniculate} shape
with six corns, a quadri-concave shape, a shape resembling {/sl sickle cells},
a shape resembling {/sl acanthocytes}, and two {/sl tube} like shapes. Most of
these shapes can be related to experimental observations in red blood cells
(RBCs) and other experiments in fluid membrane all of which have not been
treated in theory for a long time untill the present work. In addition, we
get a locally stable convex four-fold symmetric starfish with a convex core and four arms, which is
different from the reported starfishes with flat core by other
authors. The study shows there may exist a critical positive value of
spontanoeus curvarure below which the formation of starfish like vesicles is inhibited.

2. XX, "Title", Mod.Phys.Lett. B {/bf XX}, No.XX (1998).

The instability and periodic deformation of bilayer membranes during freezing
processes are studied as a function of the difference of the shape energy
between the high and the low temperature membrane states.
It is shown that there exists a threshold stability condition, bellow which
a planar configuration will be deformed. Among the deformed shapes,the periodic
curved square textures are shown being one kind of thesolutions of the
associated shape equation. The optimal ratioof period and amplitude for such a
texture is found to be approximatelyequal to $/sqrt{2}/pi$, which is good
in consistency with the recent experimental observations.

3. XX, "Title", Phys./ Lett./ A/ {/bf XX}, XX (1997).

For the purpose of controlling chaos, we describe a method to eliminate the deviations
of the trajectories from the desired orbit in the fastest way, independent of the orbit
being periodic or not. This is especially useful for cases where the OGY(Ott, Grebogi and
Yorke) method does not work, namely when the disired orbit has complex eigenvalues, the
eigenvalues in the stable eigendirections are near unity, and the unstable manifold is
multi-dimensional. Application for many aspects concerning chaos control are discussed.
We demonstrate the method by an application to the control of the kicked double rotor map
in the presence of noise.

4. XX, "Nonlinear differential
delay equations using the Poincare section technique ",
Phys./ Rev./ E/ {/bf XX}, XX (1996).

This paper shows that the Poincare section technique is a powerful tool for representing the
solutions of differential delay equations(DDEs). The tool enables us to conveniently
identify the periodicity of solutions of a DDE. With this tool we illustrated the fine
structure, including the Farey tree structure, of the bifurcation diagram with a DDE
related to optical bistability.

5. /bibitem{5} XX, "Title", Phys./ Rev./ E./ {/bf XX}, XX (1996).

We presented a mathematical framework for describing the allowable forms of perturbations
of a control parameter for the purpose of controlling chaos. The paper extends the idea
initially proposed by Ott, Grebogi, and Yorke in 1990. Among the allowable feedback
forms, those that don't include the coordinates of the desired control object explicitly
provide a natural way to go about tracking, especially when the parameter changes are
involuntary. Another benifit of the method is that the control can be implemented by using
of the earlier states of the system as the feedback information. The method can be
conveniently used to deal with an experimental system in the absence a priori mathematical
system model where the delay coordinates are used.

The paper list:

/begin{thebibliography}{17}
XX
XX

/end{thebibliography}

My CV:
 


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