What is the length of a knot in a polymer?

We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).Comment: 9 pages, 5 Postscript figure

A scale-free network hidden in the collapsing polymer

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $\gamma = 1/(2-c)$ up to a cut-off degree $d_c \propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.Comment: 4 pages, 3 figures, address correcte

Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl

Diffusion of a ring polymer in good solution via the Brownian dynamics

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.Comment: 11 pages, 4 figure

Knot localization in adsorbing polymer rings

We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\phi$ and the metric exponent $\nu$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.

Impedance measurements and simulations on the TCT and TDI LHC collimators

The LHC collimation system is a critical element for the safe operation of the LHC machine and it is subject to continuous performance monitoring, hardware upgrade and optimization. In this work we will address the impact on impedance of the upgrades performed on the injection protection target dump (TDI), where the absorber material has been changed to mitigate the device heating observed in machine operation, and on selected secondary (TCS) and tertiary (TCT) collimators, where beam position monitors (BPM) have been embedded for faster jaw alignment. Con- cerning the TDI, we will present the RF measurements per- formed before and after the upgrade, comparing the result to heating and tune shift beam measurements. For the TCTs, we will study how the higher order modes (HOM) intro- duced by the BPM addition have been cured by means of ferrite placement in the device. The impedance mitigation campaign has been supported by RF measurements whose results are in good agreement with GdfidL and CST simula- tions. The presence of undamped low frequency modes is proved not to be detrimental to the safe LHC operation

Diffusion mechanisms of localised knots along a polymer

We consider the diffusive motion of a localized knot along a linear polymer chain. In particular, we derive the mean diffusion time of the knot before it escapes from the chain once it gets close to one of the chain ends. Self-reptation of the entire chain between either end and the knot position, during which the knot is provided with free volume, leads to an L^3 scaling of diffusion time; for sufficiently long chains, subdiffusion will enhance this time even more. Conversely, we propose local ``breathing'', i.e., local conformational rearrangement inside the knot region (KR) and its immediate neighbourhood, as additional mechanism. The contribution of KR-breathing to the diffusion time scales only quadratically, L^2, speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.Comment: 7 pages, 2 figures. Accepted to Europhys. Let

The geometrical nature of optical resonances : from a sphere to fused dimer nanoparticles

We study the electromagnetic response of smooth gold nanoparticles with shapes varying from a single sphere to two ellipsoids joined smoothly at their vertices. We show that the plasmonic resonance visible in the extinction and absorption cross sections shifts to longer wavelengths and eventually disappears as the mid-plane waist of the composite particle becomes narrower. This process corresponds to an increase of the numbers of internal and scattering modes that are mainly confined to the surface and coupled to the incident field. These modes strongly affect the near field, and therefore are of great importance in surface spectroscopy, but are almost undetectable in the far field

Design of a high power production target for the Beam Dump Facility at CERN

The Beam Dump Facility (BDF) project is a proposed general-purpose facility at CERN, dedicated to beam dump and fixed target experiments. In its initial phase, the facility is foreseen to be exploited by the Search for Hidden Particles (SHiP) experiment. Physics requirements call for a pulsed 400 GeV/c proton beam as well as the highest possible number of protons on target (POT) each year of operation, in order to search for feebly interacting particles. The target/dump assembly lies at the heart of the facility, with the aim of safely absorbing the full high intensity Super Proton Synchrotron (SPS) beam, while maximizing the production of charmed and beauty mesons. High-Z materials are required for the target/dump, in order to have the shortest possible absorber and reduce muon background for the downstream experiment. The high average power deposited on target (305 kW) creates a challenge for heat removal. During the BDF facility Comprehensive Design Study (CDS), launched by CERN in 2016, extensive studies have been carried out in order to define and assess the target assembly design. These studies are described in the present contribution, which details the proposed design of the BDF production target, as well as the material selection process and the optimization of the target configuration and beam dilution. One of the specific challenges and novelty of this work is the need to consider new target materials, such as a molybdenum alloy (TZM) as core absorbing material and Ta2.5W as cladding. Thermo-structural and fluid dynamics calculations have been performed to evaluate the reliability of the target and its cooling system under beam operation. In the framework of the target comprehensive design, a preliminary mechanical design of the full target assembly has also been carried out, assessing the feasibility of the whole target system.Comment: 17 pages, 18 figure

On the size of knots in ring polymers

We give two different, statistically consistent definitions of the length l of a prime knot tied into a polymer ring. In the good solvent regime the polymer is modelled by a self avoiding polygon of N steps on cubic lattice and l is the number of steps over which the knot ``spreads'' in a given configuration. An analysis of extensive Monte Carlo data in equilibrium shows that the probability distribution of l as a function of N obeys a scaling of the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could be independent of knot type. As a consequence, the knot is weakly localized, i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak localization implies the existence of a peculiar characteristic length l^(nu) ~ N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the whole ring, this length determines a leading power law correction which is much stronger than that found in the case of unrestricted topology. The existence of such correction is confirmed by an analysis of extensive Monte Carlo data for the radius of gyration. The collapsed regime is studied by introducing in the model sufficiently strong attractive interactions for nearest neighbor sites visited by the self-avoiding polygon. In this regime knot length determinations can be based on the entropic competition between two knotted loops separated by a slip link. These measurements enable us to conclude that each knot is delocalized (t ~ 1).Comment: 29 pages, 14 figure