We consider the problem of stability of anti-de Sitter spacetime in five dimensions under small purely gravitational perturbations satisfying the cohomogeneity-two biaxial Bianchi IX Ansatz. In analogy to spherically symmetric scalar perturbations, we observe numerically a black hole formation on the time-scale \(\mathcal {O}(\varepsilon ^{-2})\), where \(\varepsilon \) is the size of the perturbation.

In this paper, we derive the mass exclusion limits for the hypothetical vector resonances of a strongly interacting extension of the Standard Model using the most recent upper bounds on the cross sections for various resonance production processes. The SU\((2)_{\rm L+R}\) triplet of the vector resonances under consideration is embedded into the effective Lagrangian based on the non-linear sigma model with the \(125\)-GeV SU\((2)_{\rm L+R}\) scalar singlet. No direct interactions of the vector resonance to the SM fermions are assumed. We find that among eleven processes considered in this paper, only those where the vector resonances decay to \(WW\) and \(WZ\) provide the mass exclusion limit. Depending on the values of other parameters of the model, the mass limit can be as low as 1 TeV.

In this research work, thick target yields for gamma-ray emission from the \(^{32}\)S\((d,p\gamma _{1})^{32}\)S \((E_\gamma =841\) keV) nuclear reaction were measured by bombarding pure-element sulfur target with deuterons in the energy range of 1300–2000 keV. Gamma rays were detected with a high purity germanium detector (HPGe) placed at an angle of \(90^{\circ } \) with respect to the beam direction. The obtained thick target gamma-ray yields were compared with the previously published data. The overall systematic uncertainty of the thick target yield values was estimated to be better than \(\pm 9\)%. The measurements were conducted in a reaction chamber optimized for Particle Induced Gamma-ray Emission (PIGE) spectrometry. The main advantage of this reaction chamber is that the employed charged particle detector can be readily approached to or retracted from the target — along the preferred direction of RBS measurement — during the experiments to perform PIGE measurements with the least possible uncertainty in beam charge collection at a wide range of beam currents.

We study the survival probability of moving relativistic unstable particles with definite momentum \(\vec {p} \neq 0\). The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time \(t\) by \(t/\gamma \) (where \(\gamma \) is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as \(t\rightarrow \infty \) much slower than one would expect using classical time dilation relation. Here, we show also that for some physically admissible models of unstable states, the computed decay curves of the moving particles have a fluctuating form at relatively short times including times of the order of the lifetime.

A wide variety of real random composites can be studied by means of prototypes of multiphase microstructures with a controllable spatial inhomogeneity. To create them, we propose a versatile model of randomly overlapping super-spheres of a given radius and deformed in their shape by the parameter \(p\). With the help of the so-called decomposable entropic measure, a clear dependence of the phase inhomogeneity degree on the values of the parameter \(p\) is found. Thus, a leading trend in changes of the phase inhomogeneity can be forecast. It makes searching for possible structure/property relations easier. For the chosen values of \(p\), examples of two- and three-phase prototypical microstructures show how the phase inhomogeneity degree evolves at different length scales. The approach can also be applied to preparing the optimal starting configurations in reconstructing real materials.

Our primary goal of this work is to exhibit and examine a novel kind of complex synchronization. We may call it a complex phase synchronization (CPHS). There are bizarre properties of the CPHS and do not exist in the writing, for example, (i) this sort of synchronization can be investigated just for complex nonlinear systems; (ii) the CPHS contains or includes two sorts of synchronizations (anti-phase synchronization APS and phase synchronization PHS); (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A description of the CPHS is presented for two identical chaotic or hyperchaotic complex nonlinear models. In view of the stability theorem, a scheme is intended to fulfill CPHS of chaotic or hyperchaotic attractors of these systems. The effectiveness of the acquired outcomes is shown by a reproduction illustration on the hyperchaotic complex Chen system. Numerical outcomes are plotted to show state variables, modulus errors, phase errors and the development of the attractors of these hyperchaotic models after synchronization to demonstrate that CPHS is achieved.