International Journal of Modern Physics C

We review an event-based simulation approach which reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whole system but by generating detection events one-by-one according to an unknown distribution. We illustrate its applicability to various single photon and single neutron interferometry experiments and to two Bell-test experiments, a single-photon Einstein–Podolsky–Rosen experiment employing post-selection for photon pair identification and a single-neutron Bell test interferometry experiment with nearly 100% detection efficiency.

This research is aimed at investigating the leader–follower problem of third-order multi-agent with noise perturbation over fixed network under impulsive and switching control. Based on stochastic differential equation theory and hybrid control theory, effective impulsive and switching controllers are proposed, and the sufficient conditions for reaching multi-agent leader-following consensus are acquired. Numerical simulations verify the validity of the theoretical research results.

In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

The stochastic quasi-synchronization issue for uncertain chaotic delayed neural networks (DNNs) is investigated. Stochastic perturbation and three uncertain elements, including the discontinuous activation functions, mismatched connection weight parameters and unknown connection weight parameters, are considered in the chaotic DNNs. According to the Ito formula and the inequality techniques, the parameters update laws and the control laws are given to realize the synchronization. And a stochastic quasi-synchronization criterion is established. Furthermore, sufficient conditions are proposed for the control of the synchronization error bound by choosing appropriate control laws. Some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Several mathematical models of evolving systems assume that changes in the micro-states are constrained to the search of an optimal value in a local or global objective function. However, the concept of evolution requires a continuous change in the environment and species, making difficult the definition of absolute optimal values in objective functions. In this paper, we define constraints that are not absolute but relative to local micro-states, introducing a rupture in the invariance of the phase space of the system. This conceptual basis is useful to define alternative mathematical models for biological (or in general complex) evolving systems. We illustrate this concept with a modified Ising model, which can be useful to understand and model problems like the somatic evolution of cancer.

In this paper, numerical analysis aiming at simulating biological organisms immersed in a fluid are carried out. The fluid domain is modeled through the lattice Boltzmann (LB) method, while the immersed boundary method is used to account for the position of the organisms idealized as rigid bodies. The time discontinuous Galerkin method is employed to compute body motion. An explicit coupling strategy to combine the adopted numerical methods is proposed. The vertical take-off of a couple of butterflies is numerically simulated in different scenarios, showing the mutual interaction that a butterfly exerts on the other one. Moreover, the effect of lateral wind is investigated. A critical threshold value of the lateral wind is defined, thus corresponding to an increasing arduous take-off.

Employing an effective cellular automata model, we investigate and analyze the build-up and erosion of soil. Depending on the strategy employed for handling agricultural production, in many cases we find a critical dependence on the prescribed production target, with a sharp transition between stable production and complete breakdown of the system.

Strategies which are particularly well-suited for mimicking real-world management approaches can produce almost cyclic behavior, which can also either lead to sustainable production or to breakdown.

While designed to describe the dynamics of soil evolution, this model is quite general and may also be useful as a model for other renewable resources and may even be employed in other disciplines like psychology.

The Landau–Ginzburg (LG) model for membranes is numerically studied on triangulated spheres in R³. The LG model is in sharp contrast to the model of Helfrich–Polyakov (HP). The reason for this difference is that the curvature energy of the LG (HP) Hamiltonian is defined by means of the tangential (normal) vector of the surface. For this reason, the curvature energy of the LG model includes the in-plane bending or shear energy component, which is not included in the curvature energy of the HP model. From the simulation data, we find that the LG model undergoes a first-order collapse transition. The results of the LG model in the higher-dimensional spaces R^d(d > 3) and on the self-avoiding (SA) surfaces in R³ are presented and discussed. We also study the David–Guitter (DG) model, which is a variant of the LG model, and find that the DG model undergoes a first-order transition. It is also found that the transition can be observed only on the homogeneous surfaces, which are composed of almost uniform triangles according to the condition that the induced metric ∂_ar ⋅ ∂_br is close to δ_ab.

Large-scale molecular dynamics (MD) simulations of freely decaying turbulence in three-dimensional space are reported. Fluid components are defined from the microscopic states by eliminating thermal components from the coarse-grained fields. The energy spectrum of the fluid components is observed to scale reasonably well according to Kolmogorov scaling determined from the energy dissipation rate and the viscosity of the fluid, even though the Kolmogorov length is of the order of the molecular scale.