Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Boson gas in a periodic array of tubes

We report the thermodynamic properties of an ideal boson gas confined in an infinite periodic array of channels modeled by two, mutually perpendicular, Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y directions, allowing tunneling of particles through the walls, while no confinement along the z direction is considered. It is shown that there exists a finite Bose- Einstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the strength of confinement $P_{0}$ is increased while keeping the channel's cross section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the specific heat exhibits a set of maxima and minima. The minimum located at the highest temperature is a clear signal of the confinement effect which occurs when the boson wavelength is twice the cross-section side size. This confinement is amplified when the wall strength is increased until a dimensional crossover from 3D to 1D is produced. Some of these features in the specific heat obtained from this simple model can be related, qualitatively, to at least two different experimental situations: $^4$He adsorbed within the interstitial channels of a bundle of carbon nanotubes and superconductor-multistrand-wires Nb$_{3}$Sn.Comment: 9 pages, 10 figures, submitte

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure

Physical Links: Defining and detecting inter-chain entanglement

Fluctuating filaments, from densely-packed biopolymers to defect lines in structured fluids, are prone to become interlaced and form intricate architectures. Understanding the ensuing mechanical and relaxation properties depends critically on being able to capture such entanglement in quantitative terms. So far, this has been an elusive challenge. Here we introduce the first general characterization of non-ephemeral forms of entanglement in linear curves by introducing novel descriptors that extend topological measures of linking from close to open curves. We thus establish the concept of physical links. This general method is applied to diverse contexts: equilibrated ring polymers, mechanically-stretched links and concentrated solutions of linear chains. The abundance, complexity and space distribution of their physical links gives access to a whole new layer of understanding of such systems and open new perspectives for others, such as reconnection events and topological simplification in dissipative fields and defect lines

Knotted vs. Unknotted Proteins: Evidence of Knot-Promoting Loops

Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These "knot-promoting" loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational studies or excision experiments

The SHiP experiment at the proposed CERN SPS Beam Dump Facility

The Search for Hidden Particles (SHiP) Collaboration has proposed a general-purpose experimental facility operating in beam-dump mode at the CERN SPS accelerator to search for light, feebly interacting particles. In the baseline configuration, the SHiP experiment incorporates two complementary detectors. The upstream detector is designed for recoil signatures of light dark matter (LDM) scattering and for neutrino physics, in particular with tau neutrinos. It consists of a spectrometer magnet housing a layered detector system with high-density LDM/neutrino target plates, emulsion-film technology and electronic high-precision tracking. The total detector target mass amounts to about eight tonnes. The downstream detector system aims at measuring visible decays of feebly interacting particles to both fully reconstructed final states and to partially reconstructed final states with neutrinos, in a nearly background-free environment. The detector consists of a 50 m long decay volume under vacuum followed by a spectrometer and particle identification system with a rectangular acceptance of 5 m in width and 10 m in height. Using the high-intensity beam of 400 GeV protons, the experiment aims at profiting from the 4 x 10(19) protons per year that are currently unexploited at the SPS, over a period of 5-10 years. This allows probing dark photons, dark scalars and pseudo-scalars, and heavy neutral leptons with GeV-scale masses in the direct searches at sensitivities that largely exceed those of existing and projected experiments. The sensitivity to light dark matter through scattering reaches well below the dark matter relic density limits in the range from a few MeV/c(2) up to 100 MeV-scale masses, and it will be possible to study tau neutrino interactions with unprecedented statistics. This paper describes the SHiP experiment baseline setup and the detector systems, together with performance results from prototypes in test beams, as it was prepared for the 2020 Update of the European Strategy for Particle Physics. The expected detector performance from simulation is summarised at the end

Fast simulation of muons produced at the SHiP experiment using generative adversarial networks

This paper presents a fast approach to simulating muons produced in interactions of the SPS proton beams with the target of the SHiP experiment. The SHiP experiment will be able to search for new long-lived particles produced in a 400 GeV/c SPS proton beam dump and which travel distances between fifty metres and tens of kilometers. The SHiP detector needs to operate under ultra-low background conditions and requires large simulated samples of muon induced background processes. Through the use of Generative Adversarial Networks it is possible to emulate the simulation of the interaction of 400 GeV/c proton beams with the SHiP target, an otherwise computationally intensive process. For the simulation requirements of the SHiP experiment, generative networks are capable of approximating the full simulation of the dense fixed target, offering a speed increase by a factor of Script O(106). To evaluate the performance of such an approach, comparisons of the distributions of reconstructed muon momenta in SHiP's spectrometer between samples using the full simulation and samples produced through generative models are presented. The methods discussed in this paper can be generalised and applied to modelling any non-discrete multi-dimensional distribution

The experimental facility for the Search for Hidden Particles at the CERN SPS

The International School for Advanced Studies (SISSA) logo The International School for Advanced Studies (SISSA) logo The following article is OPEN ACCESS The experimental facility for the Search for Hidden Particles at the CERN SPS C. Ahdida44, R. Albanese14,a, A. Alexandrov14, A. Anokhina39, S. Aoki18, G. Arduini44, E. Atkin38, N. Azorskiy29, J.J. Back54, A. Bagulya32Show full author list Published 25 March 2019 • © 2019 CERN Journal of Instrumentation, Volume 14, March 2019 Download Article PDF References Download PDF 543 Total downloads 7 7 total citations on Dimensions. Article has an altmetric score of 1 Turn on MathJax Share this article Share this content via email Share on Facebook Share on Twitter Share on Google+ Share on Mendeley Article information Abstract The Search for Hidden Particles (SHiP) Collaboration has shown that the CERN SPS accelerator with its 400 GeV/c proton beam offers a unique opportunity to explore the Hidden Sector [1–3]. The proposed experiment is an intensity frontier experiment which is capable of searching for hidden particles through both visible decays and through scattering signatures from recoil of electrons or nuclei. The high-intensity experimental facility developed by the SHiP Collaboration is based on a number of key features and developments which provide the possibility of probing a large part of the parameter space for a wide range of models with light long-lived super-weakly interacting particles with masses up to Script O(10) GeV/c2 in an environment of extremely clean background conditions. This paper describes the proposal for the experimental facility together with the most important feasibility studies. The paper focuses on the challenging new ideas behind the beam extraction and beam delivery, the proton beam dump, and the suppression of beam-induced background