Relevance of percolation theory to the vulcanization transition

Connecting the vulcanization transition to percolation.

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wavelength behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it ...

surveying the relevance of proportions to the content of quran verses

چکیده : قرآن چشمه سار زلال هدایتی است که از سوی خداوند حکیم نازل شده تا بشر را به سر منزل کمال برساند. و در این راستا از شیوه های گوناگون بیانی خطابی و بلاغی استفاده کرده تا با فطرت زیبا طلب انسان درآمیزد و اورا مقهور خویش ساخته، به سوی کمالات سوق دهد.ازجمله جنبه های بارز اعجاز بیانی قرآن وجود فواصل در پایان آیات است که کار برد سجع و قافیه در کلام بشر شبیه آن است. برخی ازعلمای سلف تفاوت هایی ب...

Semimicroscopic theory of elasticity near the vulcanization transition

Randomly cross-linked macromolecules undergo a liquid to amorphous-solid phase transition at a critical cross-link concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this paper, a semimicroscopic statistical mechanical theory of the elastic properties of the amorphous solid state i...

Renormalization-group approach to the vulcanization transition

The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-fi...

Theory & Practice Of Vulcanization