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A simple analytic expression for the first cumulant of the dynamic structure factor of a polymer coil in the Rouse model is derived. The obtained formula is exact within the usual assumption of the continuum distribution of beads along the chain. It reflects the contributions to the scattering of light or neutrons from both the internal motion of the polymer and its diffusion, and is valid in the whole region of the wave-vector change at the scattering.
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood fr
The Derjaguin approximation (DA) relates the force between curved surfaces to the interaction free energy between parallel planes. It is typically derived by considering the direct interaction between the bodies involved, thus treating the effect of
Let $R=K[X_1,dots, X_n]$ be a polynomial ring in $n$ variables over a field $K$ of charactersitic zero and $d$ a $K$-derivation of $R$. Consider the isotropy group if $d$: $ text{Aut}(R)_d :={rho in text{Aut}_K(R)|; rho d rho^{-1}=d}$. In his doctora
We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect
We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset of structural heterogeneities.