International Journal of Modern Physics B

One aim of synthetic biology is to construct increasingly complex genetic networks from interconnected simpler ones to address challenges in medicine and biotechnology. However, as systems increase in size and complexity, emergent properties lead to unexpected and complex dynamics due to nonlinear and nonequilibrium properties from component interactions. We focus on four different studies of biological systems which exhibit complex and unexpected dynamics. Using simple synthetic genetic networks, small and large populations of phase-coupled quorum sensing repressilators, Goodwin oscillators, and bistable switches, we review how coupled and stochastic components can result in clustering, chaos, noise-induced coherence and speed-dependent decision making. A system of repressilators exhibits oscillations, limit cycles, steady states or chaos depending on the nature and strength of the coupling mechanism. In large repressilator networks, rich dynamics can also be exhibited, such as clustering and chaos. In populations of Goodwin oscillators, noise can induce coherent oscillations. In bistable systems, the speed with which incoming external signals reach steady state can bias the network towards particular attractors. These studies showcase the range of dynamical behavior that simple synthetic genetic networks can exhibit. In addition, they demonstrate the ability of mathematical modeling to analyze nonlinearity and inhomogeneity within these systems.

The (1+1)-dimensional higher-order Broer–Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.

The elastic and electronic properties of cubic structure CeO₂ under pressure are investigated in the frame of density functional theory (DFT). By using the local-density approximation (LDA) plus U(LDA+U) method with U = 6 eV, the calculated lattice parameters, bulk modulus and elastic properties of the cubic CeO₂ at 0 GPa and 0 K are in good agreement with the available experimental data. The pressure dependences of lattice parameters, bulk and shear modulus, Debye temperature, Young's moduli, Poisson's ratio and the compressional and shear wave velocities of the cubic CeO₂ are obtained successfully. In addition, the total density of states (TDOS) and the band gaps of the cubic CeO₂ under pressures are also investigated. By comparing the results of LDA and LDA+U, both the conventional LDA and the LDA+U methods can be used to describe the structure of the cubic CeO₂ due to the electronic localization of 4f-electron in Ce which is not so strong. However, the LDA+U approach can obtain a proper shape of the density of electronic states that agrees well with the measured values.

The single-walled carbon nanotubes (SWCNTs) under high internal pressure are studied by the constant-pressure molecular dynamics method. The results show that SWCNTs are suitable candidates for high pressure nanocontainer, and they can resist 30 GPa to 110 GPa internal pressure. We find that the ultimate internal pressure that nanotubes can sustain is mainly determined by the radius of the tube, and it is not sensitive to the tube chirality. The breaking of the nanotube induced by high internal pressure is mainly due to bond stretching rather than bond angle changing. An elastic model is used to explain the size-dependent ultimate internal pressure behavior for SWCNTs.

A comprehensive study of structural, morphological, magnetic and hydrogen absorption properties of LaNi₅–H system was investigated. The X-ray diffraction patterns show that as-synthesized LaNi₅ alloy is single phase with CaCu₅-type structure while some weak peaks of elemental nickel also appeared after several hydrogenation/dehydrogenation (H/D) cycling. The presence of pure Ni was also followed using the room temperature magnetic measurements. After H/D cycling, the particle size decreases and particle size distribution was found nearly uniform compared to noncycled alloy. The pressure-composition isotherms (PCIs) of the hydrogen absorption reaction were determined in the temperature range 20–80°C using a homemade Sievert's type experimental apparatus, and then the enthalpy and entropy of hydride formation were calculated. The hydriding kinetic mechanism of LaNi₅ was evaluated using the different fitting models: Jander diffusion model (JDM), Johnson–Mehl–Avrami (JMA) and Chou models. All employed models confirm an increase in the hydriding reaction rate with temperature. However, the calculated results using JMA model show a better agreement with the experimental data and hence we believe that diffusion along with nucleation and growth is the rate-controlling step for the hydriding reaction. The values of activation energy for hydriding reaction were also obtained by JD and JMA models.

In this paper, we realize all kinds of 1 → 2 approximate quantum cloning, including optimal 1 → 2 symmetric (or asymmetric) universal quantum cloning (UQC) and phase-covariant cloning (PCC), symmetric economical phase-covariant cloning (EPCC) and real state quantum cloning, with the XY-type exchange interactions of the flux qubits which are coupled by dc superconducting quantum interference devices (SQUIDs). It is shown that our schemes can be realized with the current experimental technology.

From the viewpoint of the SU(2) coherent states (CS) and their path integrals (PI) labeled by a full set of Euler angles (ϕ, θ, ψ) which we developed in the previous paper, we study the relations between gauge symmetries of Lagrangians and allowed quantum states; We investigate permissible types of fiducial vectors (FV) in the full quantum dynamics in terms of SU(2) CS for typical Lagrangians. We propose a general framework for a Lagrangian having a certain gauge symmetry with respect to one of the Euler angles ψ. We find that for the case FV are so restricted that they belong to the eigenstates of Ŝ₃ or to the orbits of them under the action of the SU(2); And the strength of a fictitious monopole, which appears in the Lagrangian, is a multiple of ½. In this case Dirac strings are permitted. Our formulations and results deepen those of the preceding work by Stone that has piloted us; We illustrate the relation between the two methods. The reasoning here does not work for a Lagrangian without the gauge symmetry. This suggests a new possibility about monopole charge quantization. Besides analogies to field theory and entanglements in quantum information (QI) are briefly mentioned.

We investigate the BCS–BEC crossover in an ultracold atomic gas in the presence of disorder. The disorder is incorporated in the mean-field formalism through Gaussian fluctuations. We observe evolution to an asymmetric line-shape of fidelity susceptibility (FS) as a function of interaction coupling with increasing disorder strength which may point to an impending quantum phase transition (QPT). The asymmetric line-shape is further analyzed using the statistical tools of skewness and kurtosis. We extend our analysis to density of states (DOS) for a better understanding of the crossover in the disordered environment.

We have carried out the molecular dynamics (MD) simulation to study the structural properties and to estimate the diffusivity of molecular nitrogen (N₂) gas (solute) in extended simple point charge model (SPC/E) water (solvent) with N₂ mole fraction of 0.018 at different temperatures. For the structural properties of the system, we have determined radial distribution function (RDF). The solute–solute, solute–solvent and solvent–solvent RDF have been evaluated. Self-diffusion coefficient of N₂ was estimated by evaluating mean-squared displacement (MSD) and velocity autocorrelation function (VACF) separately. The diffusion coefficients obtained from the two methods agree within 3%. The results are in agreement with the experimentally determined values within 10%. The self-diffusion coefficient of water (H₂O) was also estimated by evaluating MSD. Mutual diffusion coefficient of the system have also been estimated invoking Darken's relation. The temperature dependance of the diffusion coefficients were found to follow Arrhenius relation.