Theory of Gelation: Post-Gelation Behavior

Within the framework of the random distribution assumption of cyclic bonds, the preceding theory of gelation is extended to mixing systems with various functionalities. To examine the validity of the assumption, the theory is applied to experimental data in polyurethane network formation, the result showing the soundness of the theory for the prediction of gel points and gel fraction.Comment: 14 pages, 7 figure

Analogy and Difference between Gelation and Percolation Process

It has been verified that the theory of gelation with cyclization effects is in good accord with experimental observations of gel points and gel fractions. Encouraged by this success we scrutinize the prediction limit of the theory through the rigor of the bond percolation theory. Significant disparity is found between the prediction of the gelation theory and that of the percolation theory. To find the reason of the disparity, we re-examine the distribution function of bond animals; the analysis showing that the percolation process differs from real gelations in two points: (i) whereas the real gelation obeys the principle of equireactivity of functional units, the percolation process does not; (ii) the substantial reduction of functionality occurs through the percolation process. These make the lattice model intrinsically different from real chemical processes. As a result, one can not make use of the percolation theory for the purpose of examining the validity of the gelation theory.Comment: 10 pages, 2 figure

N=4 SYM on K3 and the AdS(3)/CFT(2) Correspondence

We study the Fareytail expansion of the topological partition function of N=4 SU(N) super Yang-Mills theory on K3. We argue that this expansion corresponds to a sum over geometries in asymptotically AdS_3 spacetime, which is holographically dual to a large number of coincident fundamental heterotic strings.Comment: 10 pages; v5: typos correcte

Volume Expansion of Branched Polymers

The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the same method as employed for linear molecules. By simulating a model-polymer system, it is found that the excluded volume effects of branched polymers are manifested pronouncedly under any conditions from the dilution limit to the melt, including the $\Theta$ state; every result satisfies the restraining condition: $\langle s^2\rangle^{1/2} \ge N^{1/d}$ in accord with our experiences. As a result the Gaussian approximation extracts the essential features of the excluded volume effects of branched molecules.Comment: 14 pages, 6 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1606.0392

Concentration Dependence of Excluded Volume Effects

The concentration dependence of the excluded volume effects in polymer solutions is investigated. Through thermodynamic arguments for the interpenetration of polymer segments and the free energy change, we show that the disappearance of the excluded volume effects should occur at medium concentration. The result is in accord with the recent experimental observations.Comment: 12 pages, 6figures, 1 tabl

Coil Dimensions as a Function of Concentration

The preceding theory of excluded volume effects is applied to the Daud and coworkers' observations. Based on various researchers' experimental data, it is suggested that the Daud and coworkers' value in the bulk state may be revised from 82 \AA to 93\AA. Then agreement between the theory and the revised data is excellent, giving a support to the preceding result that the excluded volume effects should vanish at medium concentration.Comment: 5 pages, 2 figures, 3 Table

N=4 SYM on R times S^3 and PP-Wave

We consider the radial quantization of N=4 super Yang-Mills (SYM) in 4 dimensions, i.e., N=4 SYM on a cylinder R times S^3. We construct the generators of superconformal symmetry in the case of U(N) gauge group, generalizing the earlier work by Nicolai et al. for U(1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.Comment: 18 pages, lanlmac; v3: added a comment on Weyl anomal

Radius of Gyration of Randomly Branched Molecules

The mathematical derivation of the mean square radius of gyration, , of branched polymers is reinvestigated from a kinetic-equation-point of view. In particular we derive the corresponding quantity of the A-R-Bf-1 model; the result showing that the mean square radius of gyration is precisely identical with that of the R-Af model.Comment: 4 pages, 2 figure

Aging Concept in Population Dynamics

Author's early work on aging is developed to yield a relationship between life spans and the velocity of aging. The mathematical analysis shows that the mean extent of the advancement of aging throughout one's life is conserved, or equivalently, the product of the mean life span, and the mean rate of aging is constant. The result is in harmony with our experiences: It accounts for the unlimited replicability of tumor cells, and predicts the prolonged life spans of hibernating hamsters, in accordance with the Lyman and coworkers experiment. Comparing the present result and the empirical relationship between life spans of various mammals and basal metabolic rates, it is suggested that the mean rate of aging is intimately connected with the mean basal metabolic rate. With the help of this information, we inquire the reason of the difference in mean life spans between women and men, the result showing that the relative mean life span of women to men is 1 08, for various nations, which is close to the corresponding relative value of the basal metabolic rate. The present theory suggests, however, that this relationship between life spans and basal metabolic rates must be treated with caution.Comment: 19 Pages, 7 Figure

1/2 BPS Correlator and Free Fermion

We propose that in the BMN limit the effective interaction vertex in the 1/2 BPS sector of N=4 SYM is given by the Das-Jevicki-Sakita Hamiltonian. We check for some examples that it reproduces the 1/N correction to the correlation functions of 1/2 BPS operators.Comment: 10 pages, 2 figures, lanlmac; v4: references adde