Linearized stability analysis of two-dimension Burnett equations

The linearized stability analyses of two-dimension Burnett equations were studied in present paper for the first time. The characteristic stability equation of two-dimension original Burnett equation was first derived and the characteristic curve was achieved. The material derivatives in original Burnett equations are then replaced with the Euler and Navier-Stokes equations. The stabilities of these two alternative Burnett equations are then analyzed. The linearized stability analyses show that the two-dimension original Burnett and Euler-based Burnett equations are not stable while the Navier-Stokes-based Burnett equations are stable. The critical Knudsen number for the original Burnett and Euler-based Burnett equations are 0.074 and 0.353, respectively. These critical Knudsen number are smaller than those of corresponding one-dimension equations. The two-dimension Burnett equations are more unstable than one-dimension equations.     

Solitary re-entrant superconductivity in asymmetrical FSF structures

Solving the boundary value problem for the Eilenberger function, the superconducting and magnetic states of asymmetric ferromagnet–superconductor–ferromagnet (F₁SF₂) nanostructures are investigated. The dependences of critical temperature on an exchange field of the F metal, electronic correlations in the S and F metals, and thicknesses of layers F and S are derived. It is shown that the possibility of the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) state observation is especially increased in the asymmetrical trilayers F₁SF₂ for which solitary re-entrant superconductivity is predicted. The possibility of solitary re-entrant superconductivity for asymmetrical trilayers F₁SF₂ in the dirty limit is also shown.     

Analogue surface gravity near the QCD chiral phase transition

Using the formalism of relativistic acoustic geometry we study the expanding chiral fluid in the regime of broken chiral symmetry near the QCD chiral phase transition temperature _Tc$T_{\mathrm{c}}$. The dynamics of pions below _Tc$T_{\mathrm{c}}$ is described by the equation of motion for a massless scalar field propagating in curved spacetime similar to an open FRW universe. The metric tensor depends locally on the soft pion dispersion relation and the four-velocity of the fluid. In the neighbourhood of the critical point an analogue trapped region forms with the analogue trapped horizon as its boundary. We show that the associated surface gravity diverges near the critical point as κ∼(_Tc−T)⁻¹$\kappa \sim {(T_{\mathrm{c}}-T)}^{-1}$. Hence, if the horizon forms close to the critical temperature the analogue Hawking temperature may be comparable with or even larger than the background fluid temperature.     

Long-range quantum discord in critical spin systems

We show that quantum correlations as quantified by quantum discord can characterize quantum phase transitions by exhibiting nontrivial long-range decay as a function of distance in spin systems. This is rather different from the behavior of pairwise entanglement, which is typically short-ranged even in critical systems. In particular, we find a clear change in the decay rate of quantum discord as the system crosses a quantum critical point. We illustrate this phenomenon for first-order, second-order, and infinite-order quantum phase transitions, indicating that pairwise quantum discord is an appealing quantum correlation function for condensed matter systems.     

Magnetic phase transition in Heisenberg antiferromagnetic films with easy-axis single-ion anisotropy

The staggered susceptibility of spin-1 and spin-3/2 Heisenberg antiferromagnet with easy-axis single-ion anisotropy on the cubic lattice films consisting of n=2, 3, 4, 5 and 6 interacting square lattice layers is studied by high-temperature series expansions. Sixth order series in J/k_BT have been obtained for free-surface boundary conditions. The dependence of the Néel temperature on film thickness n and easy-axis anisotropy D has been investigated. The shifts of the Néel temperature from the bulk value can be described by a power law n^−λ with a shift exponent λ, where λ is the inverse of the bulk correlation length exponent. The effect of easy-axis single-ion anisotropy on shift exponent of antiferromagnetic films has been studied. A comparison is made with related works. The results obtained are qualitatively consistent with the predictions of finite-size scaling theory.     

Critical temperature studies of the anisotropic bilayer and multilayer Heisenberg ferromagnets in Pair Approximation

The Pair Approximation method is applied to studies of the bilayer and multilayer magnetic systems with simple cubic structure. The method allows to take into account quantum effects related to non-Ising couplings. The paper adopts the anisotropic Heisenberg model for spin S=1/2 and considers phase transition temperatures as a function of the strength of exchange integrals in line with the role of intra- and interplanar anisotropic interactions in the onset of low-dimensional magnetism. The compensation effect for the Curie temperature is found for asymmetric interactions within the neighbouring planes of the bilayer system. The paper predicts the saturation of the Curie temperature for strong interplanar interactions. However, such an effect for the multilayer system occurs only when the interplanar interactions are purely of isotropic character.     

Kinetics of node splitting in evolving complex networks

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k$k$ into k$k$ nodes of degree 1$1$. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p$p$, or splitting with probability 1−p$1-p$. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.     

Mechanism of the jamming transition in the two-dimensional traffic networks

The mechanism of the jamming transition in two-dimensional traffic networks is discussed on the basis of several models, where the update rule is deterministic, though the initial car configuration is random. It has turned out that the introduced concept of the occupation probability, which depends upon time and the site, is useful. The fluctuation in the local   car density plays an important role to give rise to small initial clusters of the cars. To examine the growth of such clusters a time-dependent function C$C$ is introduced, which is the number of the neighboring car pairs, and C$C$ increases to a certain maximum value, correlated with the total jamming. The critical car density in the symmetric two-dimensional N×N/N×N$N\times N/N\times N$ system is found to be 0.22–0.23 for each of the east-bound (x)$\left(x\right)$ and the north-bound (y)$\left(y\right)$ cars.