Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Segment Distribution around the Center of Gravity of a Triangular
  Polymer   The segment distribution around the center of gravity is investigated for a
special comb polymer (triangular polymer) having the side chains of the same
generation number, $g$, as the main backbone. Common to all the other polymers,
the radial mass distribution is expressed as the sum of the distribution
functions for the end-to-end vectors, $\{\vec{r}_{Gh}\}$, from the center of
gravity to the monomers on the $h$th generation; the result being, for a large
$g$, \begin{equation}
\varphi_{\text{triang}}(s)=\frac{1}{N}\left\{\sum_{h=1}^{g}\left(\frac{d}{2\pi\left\langle
r_{Gh}^{2}\right\rangle}\right)^{\frac{d}{2}}\text{Exp}\left(-\frac{d}{2\left\langle
r_{Gh}^{2}\right\rangle}s^2\right)+\sum_{h=2}^{g}\sum_{j=1}^{g-h}\left(\frac{d}{2\pi\left\langle
r_{Gh_{j}}^{2}\right\rangle}\right)^{\frac{d}{2}}\text{Exp}\left(-\frac{d}{2\left\langle
r_{Gh_{j}}^{2}\right\rangle}s^2\right)\right\}\notag \end{equation} It is found
that the mean square of the radius of gyration varies as $\left\langle
s_{N}^{2}\right\rangle_{0}\doteq\frac{7}{15}\,g\,l^{2}$, as
$g\rightarrow\infty$. Since $g\propto \sqrt{N}$ for the triangular polymer,
this leads to $\left\langle s_{N}^{2}\right\rangle_{0}^{1/2}\propto N^{1/4}$,
giving the same exponent as observed for the randomly branched polymer. On the
basis of the present result, we put forth that all the known polymers obey the
equality: $\left\langle s_{N}^{2}\right\rangle_{0}=A\, g\,l^{2}$, where $A$ is
a polymer-species-dependent coefficient and also depends on the choice of the
root monomer. We discuss the extension of this empirical equation.

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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci