International Journal of Modern Physics C

The Painlevé property of coupled, nonautonomous Korteweg–de Vries (KdV) type of systems is studied. The conditions under which the systems pass the Painlevé test for integrability are obtained. For some of the integrable cases, exact solutions are given.

In this paper, we investigate the lane expansion effect of the tollbooth system. To this end, two typical values of randomization probability p:p=0.5 and p=0.1 are chosen. It is shown that for p=0.5, the full capacity of the single lane highway can be restored. However, for p=0.1, our simulations show that the full capacity of the single lane highway cannot be restored due to the existence of the merge section in the lane expansion section. Moreover, we have investigated the dependence of road capacity on the length of lane expansion section as well as the effects of the positions of the tollbooths in the lane expansion section under different values of p.

Recently, synchronization in the Burridge–Knopoff model has been found to depend on the initial conditions. Here we report the existence of three modes of oscillations of the system of three blocks. In one of the modes, two lateral blocks are synchronized. In the second mode, the central block moves with almost constant velocity, i.e., it does not stick. Two lateral blocks do stick and they move in opposite phases. In the third mode, the blocks oscillate with aperiodic amplitude. The lateral blocks move in opposite phases and their frequency is lower than the one for the central block. The mode selected by the system depends on the initial conditions. Numerical results indicate that there is no modes in the phase space.

Surprisingly, still very little is known about the mathematical modeling of peaks in the binding affinities distribution function. In general, it is believed that the peaks represent antibodies directed towards single epitopes. In this paper, we refer to fluorescence flow cytometry experiments and show that even monoclonal antibodies can display multi-modal histograms of affinity distribution. This result take place when some obstacles appear in the paratope–epitope reaction such that the process of reaching the specific epitope ceases to be a point Poisson process. A typical example is the large area of cell surface, which could be unreachable by antibodies leading to the heterogeneity of the cell surface repletion. In this case the affinity of cells to bind the antibodies should be described by a more complex process than the pure-Poisson point process. We suggested to use a doubly stochastic Poisson process, where the points are replaced by a binomial point process resulting in the Neyman distribution. The distribution can have a strongly multinomial character, and with the number of modes depending on the concentration of antibodies and epitopes. All this means that there is a possibility to go beyond the simplified theory, one response towards one epitope. As a consequence, our description provides perspectives for describing antigen–antibody reactions, both qualitatively and quantitavely, even in the case when some peaks result from more than one binding mechanism.

By using the microcanonical molecular dynamics simulation, the melting processes of the clusters bound by Morse potential are investigated. It is found that these clusters show a multi-step melting process as long as the range of the Morse potential is a suitable value. The origins of this multi-step process are analyzed. I find that not only the repulsive core of the potential but also the attractive tail range of the potential influences the melting process. Moreover, the occurrence of the multi-step melting process is more sensitive to the tail region of the Morse potential.

Sznajd-Weron and Sznajd introduced a model investigating the democratic development in a closed community. This model is based on the USDF-principle ("united we stand, divided we fall"). However, it faces the problem that the system tends either to a dictatorship (i.e., 100% pro or 100% contra) or to a stalemate state (i.e., exactly 50% pro, 50% contra). Based on their model, I will show that a democratic system keeps alive due to the existence of both opportunists and persons in opposition.

This paper presents a simple numerical method to calculate the eutectic mixture composition and melting temperature. Using a Newton–Raphson method to solve the nonlinear problem, the calculation is possible for n-component eutectic. We tested this algorithm on inorganic and organic mixtures. A better correlation between experimental and numerical results has been found for organic compound.

Muon cycling dynamics for muon catalyzed fusion in heterogeneous solid layers are considered through decay of complex molecule . The suggested fusion system consists of three layers which are alternatively repeated. The first layer is D/T (deuterium, tritium) which provides molecules. The second layer is T₂ molecules which are used to slow down the muonic atoms and the third layer is D₂ molecules. The design is in a way in which dtμ, muonic deuterium and tritium molecules, are produced in resonance. It is shown, by considering muonic dynamics theoretically in a suggested heterogeneous system and determining its cycling rate by using a more advanced calculational method, that for equal deuterium, tritium concentration (C_d=C_t=0.5) in D/T layer and ϕ'=ϕ₀=ϕ=1 (relative density for each layer respectively and given in liquid hydrogen density LHD=4.25×10²²cm^-3), the muon cycling rate is optimum for the suggested heterogeneous system and has 15% enhancement with respect to the conventional D/T system. It is also shown that for ϕ₀<0.0003 the muon cycling rate in D₂ is almost stopped, and for ϕ₀≥1 muon cycling rate increases, but this is not recommended due to low and costly tritium availability.

In this paper, computations of transient, incompressible, turbulent, plane jets using the discrete lattice BGK Boltzmann equation are reported. Á priori derivation of the discrete lattice BGK Boltzmann equation with a spatially and temporally dependent relaxation time parameter, which is used to represent the averaged flow field, from its corresponding continuous form is given. The averaged behavior of the turbulence field is represented by the standard k–∊ turbulence model and computed using a finite-volume scheme on nonuniform grids. Computed results are compared with analytical solutions, experimental data and results of other computational methods. Satisfactory agreement is shown.

Considering the effects of different factors on the stochastic delay probability, the delay probability has been classified into three cases. The first case corresponding to the brake state has a large delay probability if the anticipant velocity is larger than the gap between the successive cars. The second one corresponding to the following-the-leader rule has intermediate delay probability if the anticipant velocity is equal to the gap. Finally, the third case is the acceleration, which has minimum delay probability. The fundamental diagram obtained by numerical simulation shows the different properties compared to that by the NaSch model, in which there exist two different regions, corresponding to the coexistence state, and jamming state respectively.

We present a variation of the N-fold way algorithm, which improves efficiency when one combines the Wang–Landau method with the N-fold way. It is shown that the new version of the N-fold way algorithm has good performance when used for importance sampling and compared with the usual N-fold version or the Metropolis algorithm. The new N-fold algorithm combined with the Wang–Landau method is applied to the square Ising model using a multi-range approach. A comparative study is presented for all these algorithms, Wang–Landau and the two combined versions with the N-fold way. The role of boundary effects is discussed.

The projective Riccati equations method is extended to find some novel exact solutions of a (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation. Applying the extended method and symbolic computation, six families of exact analytical solutions for this NLS equation are reported, which include some new and more general exact soliton-like solutions, trigonometric function forms solutions and rational forms solutions.