Knots, links, anyons and statistical mechanics of entangled polymer rings

The field theory approach to the statistical mechanics of a system of N polymer rings linked together is extended to the case of links whose paths in space are characterized by a fixed number 2s of maxima and minima. Such kind of links are called 2s-plats and appear for instance in the DNA of living organisms or in the wordlines of quasiparticles associated with vortices nucleated in a quasi-two-dimensional superfluid. The path integral theory describing the statistical mechanics of polymers subjected to topological constraints is mapped here into a field theory of quasiparticles (anyons). In the particular case of s=2, it is shown that this field theory admits vortex solutions with special self-dual points in which the interactions between the vortices vanish identically. The topological states of the link are distinguished using two topological invariants, namely the Gauss linking number and the so-called bridge number which is related to s. The Gauss linking number is a topological invariant that is relatively weak in distinguishing the different topological configurations of a general link. The addition of topological constraints based on the bridge number allows to get a glimpse into the non-abelian world of quasiparticles, which is relevant for important applications like topological quantum computing and high-TC superconductivity. At the end an useful connection with the cosh-Gordon equation is shown in the case s=2. © 201

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.Comment: 36 pages, 2 figures, LaTeX + REVTeX4 + graphicx, minor changes in the text, reference adde

Romantic Name for a Deadly Condition: Kissing Aneurysms of the Pericallosal Artery – A Case Report

Background: Kissing aneurysms are two independent but adjacent aneurysms protruding from two contralateral arterial locations. This report describes a successfully treated case of kissing aneurysms at the Department of Neurosurgery, Medical University of Gdansk. Case: A 45-year-old asymptomatic woman was diagnosed with unruptured bilateral aneurysms located in the pericallosal-callosomarginal division. Her medical history included a previous intracranial aneurysm and arterial hypertension. The patient underwent a successful treatment by surgical clipping and was discharged in good condition; neither disability nor neurologic deficit was noticed upon discharge. Surgical wound healing was complicated by an infection and resulted in a reoperation for the patient. Conclusion: The etiology of kissing aneurysms is still unknown and the best treatment method stills remains unclear. Thus, every case has to be carefully and individually assessed by an interdisciplinaryteam. As a result, patient transfer to an experienced neurosurgical center could be beneficial

On the connection of the generalized nonlinear sigma model with constrained stochastic dynamics

The dynamics of a freely jointed chain in the continuous limit is described by a field theory which closely resembles the nonlinear sigma model. The generating functional $\Psi[J]$ of this field theory contains nonholonomic constraints, which are imposed by inserting in the path integral expressing $\Psi[J]$ a suitable product of delta functions. The same procedure is commonly applied in statistical mechanics in order to enforce topological conditions on a system of linked polymers. The disadvantage of this method is that the contact with the stochastic process governing the diffusion of the chain is apparently lost. The main goal of this work is to reestablish this contact. To this purpose, it is shown here that the generating functional $\Psi[J]$ coincides with the generating functional of the correlation functions of the solutions of a constrained Langevin equation. In the discrete case, this Langevin equation describes as expected the Brownian motion of beads connected together by links of fixed length.Comment: LaTeX+RevTeX, 12 pages, no figure

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time declines with growing contour length $L$ as $\propto L^{-0.17}$, and with side chain length as $\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.Comment: 15 pages, 7 figure

Spinal Cord Stimulation in Failed Back Surgery Syndrome: Review of Clinical Use, Quality of Life and Cost-Effectiveness

Failed back surgery syndrome (FBSS) is complex and recurrent chronic pain after spinal surgery. Several important patient and surgery related risk factors play roles in development of FBSS. Inadequate selection of the candidates for the spinal surgeries is one of the most crucial causes. The guidelines suggest that conservative management featuring pharmacologic approaches and rehabilitation should be introduced first. For therapy-refractory FBSS, spinal cord stimulation (SCS) is recommended in selected patients. Treatment efficacy for FBSS has increased over the years with the majority of patients experiencing pain relief and reduced medicinal load. Improved quality of life can also be achieved using SCS. Cost-effectiveness of SCS still remains unclear. However evidence for SCS role in FBSS is controversial, SCS can be beneficial for carefully classified patients

Super-soft and super-elastic dry gels

Molecular combs and bottlebrushes are a new class of polymer architecture allowing for anomalously low density of entanglements in polymer melts. The conformations and rheological properties of melts of these branched macromolecule composed of a flexible backbone and side chains densely tethered to it are investigated theoretically, experimentally and by computer simulations.1,2 We develop the rule for dialing in the desired value of the melt plateau modulus of these molecules as low as 1000 times below the conventional values for linear polymer melts and experimentally verify the validity of our theory. The theory also predicts that elastomers made from these melts should be super-elastic and reversibly stretch up to ten times more than elastomers made from linear polymers. Hybrid networks with both permanent and reversible bonds made with this novel architecture are predicted to be super-tough and self-healing. References W.F.M. Daniel, J. Burdynska, M. Vatankhah-Varnoosfaderani, K. Matyjaszewski, J. Paturej, M. Rubinstein, A.V. Dobrynin and S.S. Sheiko, Nature Materials, 2016, 15, 183-190. L.H Cai, T.E. Kodger, R.E. Guerra, A.F. Pegoraro, M. Rubinstein, and D.A. Weitz, Advanced Materials 2015, 27, 5132–5140