abstract

Sine-Gordon model reduced from 3+1 to 1+1 curved dimensions is considered. In the framework of the Bogomolny arguments, the existence of kink solutions in curved space is studied. The relaxation method is used to produce kink profiles in a curved Josephson junction.

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Considering that time-delay is frequently encountered in a variety of practical chaotic systems, we investigate the complete synchronization (CS) of coupled multiple-time-delay complex chaotic systems and design the control law by error feedback, which is simple in principle and easy to implement in engineering. A communication scheme is further designed according to chaotic masking. We take coupled multiple-time-delay complex Lorenz system as an example, make simulations and verify the effect of the controllers. The error feedback is extended to complex chaotic systems with multiple-time-delay. The CS of real chaotic systems and complex chaotic systems without time-delay are its special cases.

abstract

Multipole matrix of the Green function of the Laplace equation defined by double convolution of two spherical harmonics with the Green function of the Laplace equation is calculated. The multipole matrix elements in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly overlapping) sphere of the same radius. We calculate the multipole matrix from its Fourier transform. An essential part of our considerations is simplification of the three-dimensional Fourier transformation of a multipole matrix by its rotational symmetry to the one-dimensional Hankel transformation.

abstract

The main parts of the LHC diffractive physics programme possible to be measured using a proton tagging technique are presented. The geometric acceptance of the ATLAS forward proton detectors: ALFA and AFP for various LHC optics settings is shown. The probabilities of observing a proton originating from a minimum-bias event in ALFA and AFP stations are given. The main properties of single diffractive and double Pomeron exchange production of dijets, photon+jet, jet–gap–jet and \(W/Z\) bosons are discussed. The possibility of measuring the jet production in exclusive (double proton tag) and semi-exclusive (single tag) mode is evaluated.

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We apply the flow analysis for multi-particle correlations used in heavy-ion collisions to multi-particle production from a Pomeron. We show that the \(n^{\rm th}\) order angular harmonic arising from an \(m\) particle correlation \(v_n[m]\) satisfies \(v_n[m] \approx v_n[p]\) for \(n\ge 1\). We discuss some implications of this for the Color Glass Condensate description of high energy hadronic collisions.

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We test several BFKL-like evolution equations for unintegrated gluon distributions against forward–central dijet production at the LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimuthal decorrelations for forward–central dijet production and compare with the existing data.

abstract

In this paper, multiplicity distributions of charged particles produced in 14.5 \(A\) GeV/\(c\) \(^{28}\)Si–AgBr interactions and the events generated by Monte Carlo models, FRITIOF and HIJING, are analysed using Scaled Factorial Moments (SFMs) approach in terms of the Ginzburg–Landau formalism. The reported power-law behaviour of the higher-order and second-order scaled factorial moments is searched for in the experimental and simulated data. The analysis of anomalous fractal dimensions does not favour occurrence of any exotic phenomenon. Further, the values of the slopes, \(\beta _q\), are used to determine a universal scaling exponent, \(\nu \), for both the experimental and simulated data in terms of Ginzburg–Landau approach in order to investigate the nature of phase transition from the de-confined quark–gluon medium to the confined hadronic state. The analysis indicates that the values of \(\nu \) for the experimental and FRITIOF data compare reasonably well with its critical value. Nevertheless, the value of \(\nu \) for the HIJING data is in marked disagreement. This may be attributed to the fact that local fluctuations are not addressed effectively by HIJING model; however, it successfully explains the phenomenon of flow. Finally, some evidences regarding second-order phase transition are found.

abstract

We present the analysis of a time-inhomogeneous Markov chain model based on the in vivo viral infection dynamics. The exact solution of a general in-host model with time-dependent rates is obtained by using the Lie-theoretic approach. The results provide both an improvement in numerical efficiency and the potential for analytical solution of other biological processes without clear symmetry.

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An agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger’s postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied. The model considered, while manageable, is significantly complex, however. It is already able to reveal phenomena that can be interpreted as an emergence and collapse of money as well as the related competition effects. In particular, it is shown that — as an extra emerging effect — the money lifetimes near the critical threshold value develop multiscaling, which allow one to set parallels to critical phenomena and, thus, to the real financial markets.

abstract

The field of a uniformly magnetized rotating sphere is studied with special attention to the surface, where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the rotating magnetized sphere, is obtained. Inside the light cylinder, this surface can be considered as a force-free surface, i.e. as a place where the particles with strong radiation damping can be trapped due to their energy loss. Outside the light cylinder, this surface makes just a geometric locus which moves with a superlight velocity around the axis of rotation. The 2- and 3-dimensional plots of the force-free surface are constructed. Estimation of influence of the centrifugal force on the particle dynamics is made. It is shown that in the case of strong magnetic field, the centrifugal force is negligible small everywhere except a narrow neighbourhood of the light cylinder.