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Register a new userPath integrals for stiff polymers applied to membrane physics
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Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed, as well as the effective interaction between the two phases in the tensionless case where the two phases have differing bending rigidities.
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We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by a special three body interaction and impacts on the behaviour both locally and non-locally. When thick polymers undergo compaction due to an attractive self-interaction, we find a new type of phase transition between a compact phase and a swollen phase at zero temperature on increasing the thickness. In the vicinity of this transition, short tubes form space filling helices and sheets as observed in protein native state structures. Upon increasing the chain length, or the number of chains, we numerically find a crossover from secondary structure motifs to a quite distinct class of structures akin to the semi-crystalline phase of polymers or amyloid fibers in polypeptides.
We investigate the translocation of stiff polymers in the presence of binding particles through a nanopore by two-dimensional Langevin dynamics simulations. We find that the mean translocation time shows a minimum as a function of the binding energy $epsilon$ and the particle concentration $phi$, due to the interplay of the force from binding and the frictional force. Particularly, for the strong binding the translocation proceeds with a decreasing translocation velocity induced by a significant increase of the frictional force. In addition, both $epsilon$ and $phi$ have an notable impact on the distribution of the translocation time. With increasing $epsilon$ and $phi$, it undergoes a transition from an asymmetric and broad distribution under the weak binding to a nearly Gaussian one under the strong binding, and its width becomes gradually narrower.
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its invariance properties under variations of the action. These relations determine a dynamical algebra of bounded operators which encodes all properties of the corresponding quantum theory. This novel approach is applied to non-relativistic particles, where quantum mechanics emerges from it. The method works also in interacting quantum field theories and sheds new light on the foundations of quantum physics.
We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with bending rigidity as well as a number of models for electrolytes. The approach used is based on the relation between quadratic path integrals and Gaussian fields and we also show how it can be extended to the evaluation of even higher order path integrals.
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