abstract

We study a process of released substance from a medium in the shape of sphere. In both the sphere and a surrounding medium occurs subdiffusion. Using linear partial differential equations with a fractional time derivative, we obtain concentration profiles and a time evolution of an amount of substance which released from the sphere, both in the limit of large values of time. We also briefly discuss the obtained results.

abstract

We present an extension of the classical Kuramoto model, adjusted for analysis of sets of asymmetrically coupled units. Results of numerical simulations suggest that violating Newton’s Third Law by adding a strongly dominating unit can lead to synchronization in systems previously unable to synchronize.

abstract

The \(\tau \) lepton plays an important role in the physics program at the Large Hadron Collider. Spin of the \(\tau \) lepton represents an interesting phenomenological quantity which can be used for separation of signal from background in searches for New Physics processes or in measuring properties of New Particles decaying to \(\tau \) leptons. A proper treatment of \(\tau \) spin effects in the Monte Carlo simulations is important for understanding the detector acceptance and for measurements of \(\tau \) polarization and \(\tau \) spin correlations. The TauSpinner package is a software tool allowing to modify \(\tau \) spin effects in any event sample containing \(\tau \) leptons. By calculating spin weights, attributed on the event-by-event basis, it enables numerical evaluation and/or modification of the spin effects on experimentally measured distributions. We review a selection of simple distributions which can be used to monitor longitudinal spin effects in \(\tau \) decays. New methods, with respect to previous publications, for validation of spin content of the user-prepared event sample are provided.

abstract

We examine the possibility of constraining the anomalous \(WW\gamma \) and \(WWZ\) couplings by measuring total cross sections of the \(ep\to \nu _{e}q\gamma X\) and \(ep\to \nu _{e}qZX\) processes at the LHeC collider with the electron beam energy \(E_{e}=60\) GeV and \(E_{e}=140\) GeV. We consider the cases of unpolarized and polarized electron beams. The difference of the upper and lower bounds on the anomalous couplings, (\(\delta \Delta \kappa _{\gamma }\),\(\delta \lambda _{\gamma }\)) and (\(\delta \Delta \kappa _{Z}\),\(\delta \lambda _{Z}\)) are obtained as (\(0.990\), \(0.122\)) and (\(0.362\), \(0.012\)) without electron beam polarization at the beam energy of \(E_{e}=140\) GeV for an integrated luminosity of \(L_{\mathrm {int}}=100\) fb\(^{-1}\), respectively. With the possibility of \(e\)-beam polarization, we obtain more improved results as (\(0.975\), \(0.118\)) and (\(0.285\), \(0.009\)) for (\(\delta \Delta \kappa _{\gamma },\delta \lambda _{\gamma }\)) and (\(\delta \Delta \kappa _{Z},\delta \lambda _{Z}\)), respectively. The results are found to be comparable with the current experimental limits obtained from two-parameter fits to the data collected in the lepton and hadron colliders. It is found that the limits on the anomalous couplings (\(\Delta \kappa _{Z}\),\(\lambda _{Z}\)) through the process \(ep\to \nu _{e}qZX\) at the LHeC can further improve the current experimental limits.

abstract

Various observables measured at low beam energy of 180 MeV for proton induced reactions on \(^{27}\)Al targets have been compared with theoretical predictions of different spallation models. These models assume that the reactions proceed in two stages: the intranuclear cascade of nucleon–nucleon collisions followed by the de-excitation of equilibrated, excited remnants of the cascade. The calculations of the intranuclear cascade were performed by means of the INCL4.6 code, whereas the second stage of the reactions was realized using four different models: ABLA07, GEMINI++, GEM2, and SMM. It was found that the main properties of the experimental isobaric total production cross sections are reasonably well reproduced by all these spallation models. The shape of the energy averaged angular distributions of ejectiles with \(A=7\), 12, 16, 22, 24, and 25 was also well described by the models listed above, however the absolute magnitude of \(A=7\) and \(A=25\) data is strongly underestimated and overestimated, respectively. The theoretical energy spectra for \(A=7\), \(A=16\), and \(A=22\) are very similar for all the models and reproduce well the data for heavier ejectiles, whereas the \(A=7\) data deviate from the model cross sections for energies smaller than \(\approx 10\) MeV what may indicate the presence of a reaction mechanism not included in the spallation models. The following ranking of the four used models — all of them being coupled to the very same INCL4.6 INC model — was determined using the statistical \(H\)-test in a quantitative analysis: (1) GEMINI++, (2) SMM, (3) ABLA07, and (4) GEM2.

abstract

A detailed study of the accuracy of the description of nuclear mass by theoretical models is performed. Seven models of a different nature are taken for the study. The discrepancy between the theoretical masses and the recently evaluated experimental ones is calculated for each nucleus in the region of heavy nuclei (with the proton number \(Z \geq 82\)). Main results are presented in the form of maps (colored online), one for each model. It is found that for one of the very recent models (WS4+RBF), a very small discrepancy, \(\mid \delta m\mid \) \(\leq 250\) keV, is obtained for most of the considered nuclei.

abstract

The Large Hadron Collider has provided large amounts of data on collisions of small systems, such as proton–proton and proton–lead at unprecedented collision energies. Their space-time size and structure can be inferred from the measurement of the femtoscopic correlations for pairs of identical particles. The analysis is complicated by the presence of significant additional sources of two-particle correlations, which influence the correlation function in the region of the femtoscopic effect. In this work, we use \(p\)–Pb events generated in a model that includes such additional correlation sources to characterize them and propose a robust method of taking them into account in the extraction of the femtoscopic information.

abstract

The concept of fractals was used in the analysis of the fracture surfaces of two different polymeric materials. Polymer networks obtained from three popular dental dimethacrylate monomers: Bis-GMA, TEGDMA and UDMA as well as two copolymers of these monomers were analysed. Dense polymer membranes with dispersed magnetic powder (magnetic membranes) for air separation were also investigated. In both cases, profiles of fractures were described by a modified fractal dimension. It is based on scaling the length of a profile with the size of a measuring step. The modified fractal dimension is considered a diagnostic tool for structure-morphology analysis of fracture path and roughness parameter. A quantitative description of fracture surface is an important link in the investigation of the properties of materials and mechanisms of their decohesion.