Regular Series


Vol. 50 (2019), No. 5, pp. 833 – 960


The Unexplored Landscape of Two-body Resonances

abstract

We propose a strategy for searching for theoretically-unanticipated new physics which avoids a large trials factor by focusing on experimental strengths. Searches for resonances decaying into pairs of visible particles are experimentally very powerful due to the localized mass peaks and have a rich history of discovery. Yet, due to a focus on subsets of theoretically-motivated models, the landscape of such resonances is far from thoroughly explored. We survey the existing set of searches, identify untapped experimental opportunities and discuss the theoretical constraints on models which would generate such resonances.


Dirac Shell Quark-core Model for the Study of Non-strange Baryonic Spectroscopy

abstract

A Dirac shell model is developed for the study of baryon spectroscopy, taking into account the most relevant results of the quark–diquark models. The lack of translational invariance of the shell model is avoided in the present work, by introducing a scalar–isoscalar fictitious particle that represents the origin of quark shell interaction; in this way, the states of the system are eigenstates of the total momentum of the baryon. Only one-particle excitations are considered. A two-quark core takes the place of the diquark, while the third quark is excited to reproduce the baryonic resonances. For the \(N(939)\) and \({\mit \Delta }(1232)\), that represent the ground states of the spectra, the three quarks are considered identical particles and the wave functions are completely antisymmetric. The model is used to calculate the spectra of the \(N\) and \({\mit \Delta }\) resonances and the nucleon magnetic moments. The results are compared to the present experimental data. Due to the presence of the core and to the one-particle excitations, the structure of the obtained spectra is analogous to that given by the quark–diquark models.


Globally Maximal Timelike Geodesics in Static Spherically Symmetric Spacetimes: Radial Geodesics in Static Spacetimes and Arbitrary Geodesic Curves in Ultrastatic Spacetimes

abstract

This work deals with intersection points — conjugate points and cut points — of timelike geodesics emanating from a common initial point in special spacetimes. The paper contains three results. First, it is shown that radial timelike geodesics in static spherically symmetric spacetimes are globally maximal (have no cut points) in adequate domains. Second, in two ultrastatic spherically symmetric spacetimes, Morris–Thorne wormhole and global Barriola–Vilenkin monopole, it is found which geodesics have cut points (and these must coincide with conjugate points) and which ones are globally maximal on their entire segments. This result, concerning all timelike geodesics of both the spacetimes, is the core of the work. The third outcome deals with the astonishing feature of all ultrastatic spacetimes: they provide a coordinate system which faithfully imitates the dynamical properties of the inertial reference frame. We precisely formulate these similarities.


Entropy Production and Collective Phenomena in Biological Channel Gating

abstract

We investigate gating kinetics of biological channels influenced by conformational changes within the membrane proteins forming the module, and subject to a coupling with other similar units. By introducing elements of stochastic thermodynamics, we analyze the information flow and associated entropy production during gating cycle of a single channel. In the second part of this paper, synchronized kinetics of multiple units of that type is analyzed in terms of Kuramoto’s theory.


Schramm–Loewner Evolution in the Random Scatterer Henon-percolation Landscapes

abstract

The Schramm–Loewner evolution (SLE) is a correlated exploration process, in which for the chordal setup, the tip of the trace evolves in a self-avoiding manner towards the infinity. The resulting curves are named SLE\(_{\kappa }\), emphasizing that the process is controlled by one parameter \(\kappa \) which classifies the conformal invariant random curves. This process when experiences some environmental imperfections or, equivalently, some scattering random points (which can be absorbing or repelling) results in some other effective scale-invariant curves, which are described by the other effective fractal dimensions and, equivalently, the other effective diffusivity parameters \(\kappa _{\mathrm {eff}}\). In this paper, we use the classical Henon map to generate scattering (absorbing/repelling) points over the lattice in a random way, that realizes the percolation lattice with which the SLE trace interacts. We find some meaningful power-law changes of the fractal dimension (and also the effective diffusivity parameter) in terms of the strength of the Henon coupling, namely, the \(z\) parameter. For this, we have tested the fractal dimension of the curves as well as the left passage probability. Our observations are in support of the fact that this deviation (or, equivalently, non-zero \(z\)s) breaks the conformal symmetry of the curves. Moreover, the effective fractal dimension of the curves vary with the second power of \(z\), i.e. \(D_{\mathrm {F}}(z)-D_{\mathrm {F}}(z=0)\sim z^2\).


Purposeful Random Attacks on Networks — Forecasting Node Ranking Not Based on Network Structure

abstract

We propose the conception of purposeful random attacks, which can greatly save attacking costs but achieve comparable effects to targeted attacks, based on the hidden degree centrality (HDC) defined according to node features in the one-dimensional circle model of network hidden metric spaces. The macro-matching degree is proposed to research attacking effects. Results show that when the optional node set for attacks is selected as nodes ranked in the top \(\beta \%\) according to HDC, the macro-matching degree will be \(\gt 80\%\) with \(\beta =0.5\). The smaller the value of \(\beta \), the higher the value of the matching degree, showing that random attacks on the optional node set would be performed at most of those really important nodes. Further, the effect of the purposeful random attack becomes better with the growth of parameter \(\alpha \) in the circle model. However, after \(\alpha \) grows to a fixed value, it would have no influence on the attack effectiveness. Jump phenomena presented by changing curves of the macro-matching degree with parameter \(\gamma \), another parameter in the circle model, show that networks should be divided into two groups for \(\gamma \gt 2.5\) or \(\gamma \lt 2.5\), and in any group, the effect of the purposeful random attack becomes worse with the growth of \(\gamma \).


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