A statistical theory incorporating temperature, angular momentum and deformation degrees of freedom for complex nuclear system has been developed. An investigation for nuclear specific heat as a function of temperature and angular momentum is provided. The occurrence of a peak structure in the specific heat at temperatures of the order of 2.0–3.0 MeV confirms the phase transitions for seven even–even 2\(s\)–1\(d\) shell nuclei.

In this paper, we investigate the speed of gravitational waves in the context of brane-world theory without mirror symmetry or any form of junction conditions. Using the geometric dark energy, we show that the speed of the propagation of such waves is greater in the bulk than that on the brane. So, we expect the 4D Lorentz violation effects manifest themselves in the gravitational sectors. Finally, we study the effect of the geometric dark energy on the red shift of gravitational waves.

The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in the two-dimensional Ising model. Here, the electromagnetic wave is linearly polarised in such a way that the direction of magnetic field is parallel to that of the magnetic spins. The coherent spin-cluster propagating mode is observed. The time average magnetisation over the full cycle (time) of the field defines the order parameter of the dynamic phase transition. Depending on the value of the temperature and the amplitude of the propagating magnetic field wave, a dynamical phase transition is observed. The transition is detected by studying the temperature dependences of the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The phase boundary of the dynamic transitions are drawn for two different values of the wave length of the propagating magnetic field wave. The phase boundary is observed to shrink (inward) for shorter wavelength of the EM wave. The signature of the divergence of the relevant length scale is observed at the transition point.

The subdiffusive systems are characterized by the diverging mean residence time. The escape of a subdiffusive particle from finite intervals cannot be characterized by the mean exit time. The situation significantly changes when instead of a single subdiffusive particle there is an ensemble of subdiffusive particles. In such a case, if the ensemble of particles is large enough, the mean minimal first escape time (first exit time of the fastest particle) is well defined quantity and the minimal first exit time distribution has fast decaying power-law asymptotics. Consequently, the increase in the number of particles facilitates escape kinetics and shortenes the system’s lifetime.

We investigate local and global properties of timelike geodesics in three static, spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical ‘twin paradox’ problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation, we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular geodesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti–Robinson spacetimes, the radial geodesics which infinitely many times oscillate between antipodal points in the space contain infinite number of equally separated conjugate points and there are no other cut points. Yet in these two spacetimes each outgoing or ingoing radial geodesic which does not cross the centre is globally of maximal length. Circular geodesics exist only in CAdS spacetime and contain an infinite sequence of equally separated conjugate points. The geodesic curves which intersect the circular ones at these points may either belong to the two-surface \(\theta =\pi /2\) or lie outside it.

We measure the strong coupling constant at NNLO corrections. We do this analysis with moments of event shape variables: thrust, \(C\) parameter, heavy hemisphere mass, wide and total jet broadening, by fitting the L3 and DELPHI data with NNLO model. Our real data are consistent with NNLO calculations, because the analysis involves higher order terms in QCD calculations.

The energy dependence of the source size of jets are studied in detail by the HBT correlation method using Monte Carlo Simulation generator Jetset7.4 to produce 40,000,000 events of \(e^+e^-\) collisions at \(\sqrt s = 30\), 50, 70, 91.2, 110, 130, 150 and 170 GeV, respectively. The source size of jets are measured using the HBT correlation method with the indistinguishability of identical final state pions. The average source radii of quark-jets and gluon-jets in \(e^+e^-\) collisions are obtained at the end of parton evolvement. It is found that the average source radii of quark-jets are obviously larger than those of gluon-jets and the average source radii measured with \(\pi ^0\) meson are smaller than those with \(\pi ^+\) or \(\pi ^-\) meson.

A simple system of coupled kinetic equations for quark and gluon anisotropic systems is solved numerically. The solutions are compared with the predictions of the anisotropic hydrodynamics describing a mixture of anisotropic fluids. We find that the solutions of the kinetic equations can be well reproduced by anisotropic hydrodynamics if the initial distribution are oblate for both quarks and gluons. On the other hand, the solutions of the kinetic equations have a different qualitative behavior from those obtained in anisotropic hydrodynamics if the initial configurations are oblate–prolate or prolate–prolate. This suggests that an extension of the anisotropic hydrodynamics scheme for the mixture of anisotropic fluids is needed, where higher moments of the kinetic equations are used and present simplifications are avoided.

This paper is devoted to the presentation of the lateral Casimir force between two sinusoidally corrugated eccentric cylinders. Despite that applying path integral formulation explains the problem exactly, procedure of applying this method is somehow complicated specially at non-zero temperature. Using the proximity force approximation (PFA) helps to achieve the lateral Casimir force in a truly explicit manner. We assume the cylinders to be slightly eccentric with similar radiuses and separations much smaller than corrugations’ wave length for the validity of PFA. For such short distances the effect of finite conductivity would be non negligible. In addition to the effect of finite conductivity, we investigate thermal corrections of the lateral Casimir force to reduce the inaccuracy of the result obtained by PFA. Assuming the Casimir force density between two parallel plates, the normal Casimir force between two cylinders is obtained. With the aid of additive summation of the Casimir energy between cylinders without corrugation, we obtain the lateral Casimir force between corrugated cylinders.