Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branched Polymers with Excluded Volume Effects/ Relationship between
  Polymer Dimensions and Generation Number   We discuss the extension of the empirical equation: $\left\langle
s_{N}^{2}\right\rangle_{0}\propto g\,l^{2}$, where the subscript 0 denotes the
ideal value with no excluded volume and $g$ the generation number from the root
to the youngest (outermost) generation. By analogy with the linear chain
problem, we introduce the assumption that the scaling relation, $\left\langle
s_{N}^{2}\right\rangle_{0}\propto g^{2\lambda}\,l^{2}$, exists for arbitrary
polymeric architectures, where $\lambda$ is an exponent for the backbone
structure. Then, making use of the relationship between $g$ and $N$ (monomer
number), we can deduce the exponent, $\nu$, for polymers with various
architectures. The theory of the excluded volume effects impose the severe
restriction on the quantities: $\nu_{0}$, $\nu$, and $\lambda$; for instance,
the inequality, $\nu_{0}\ge\frac{1}{d+1}$, must be satisfied for isolated
polymers in good solvents. An intriguing question is whether or not there
exists an actual molecule that violates this inequality. We take up two
examples having $\nu_{0}=1/4$ for $d=2$ and $\nu_{0}=1/6$ for $d=3$, and
discuss this question.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org