A new lattice model of traffic flow with the consideration of the driver?s forecast effects

In this Letter, a new lattice model is presented with the consideration of the driver?s forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driver?s forecast intensity parameter, which is consistent with the theoretical analysis.     

The density wave in a new anisotropic continuum model

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.     

Analytical and numerical solutions of the Schrödinger–KdV equation

The Schrödinger–KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The G′/G method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are also given.     

Painlevé analysis and hamiltonian structure of a new space-dependent KdV equation

We deduce the Lax pair for a new space-dependent KdV equation, , via the technique of Painlevé analysis. From it, infinitely many conservation laws are deduced and the symplectic structure is obtained.     

Pattern formation in a predator–prey model with spatial effect

In this paper, spatial dynamics in the Beddington–DeAngelis predator–prey model with self-diffusion and cross-diffusion is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. Numerical simulations show that this system exhibits complex dynamical behaviors. In the Turing space, we find three types of typical patterns. One is the coexistence of hexagon patterns and stripe patterns. The other two are hexagon patterns of different types. The obtained results well enrich the finding in predator–prey models with Beddington–DeAngelis functional response.     

Numerical simulation of a solitonic gas in KdV and KdV–BBM equations

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes–Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term.     

Stability study of a model for the Klein–Gordon equation in Kerr space-time

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein–Gordon equation, describing the propagation of a scalar field of mass $\mu $ in the background of a rotating black hole. Rigorous results prove the stability of the reduced, by separation in the azimuth angle in Boyer–Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters $a$ extremely close to $1$ . Among others, the paper derives a model problem for the equation which supports the instability of the field down to $a/M \approx 0.97$ .     

Development of a numerical model for the electric current in burner-stabilised methane–air flames

This study presents a new model to simulate the electric behaviour of one-dimensional ionised flames and to predict the electric currents in these flames. The model utilises Poisson’s equation to compute the electric potential. A multi-component diffusion model, including the influence of an electric field, is used to model the diffusion of neutral and charged species. The model is incorporated into the existing CHEM1D flame simulation software. A comparison between the computed electric currents and experimental values from the literature shows good qualitative agreement for the voltage–current characteristic. Physical phenomena, such as saturation and the diodic effect, are captured by the model. The dependence of the saturation current on the equivalence ratio is also captured well for equivalence ratios between 0.6 and 1.2. Simulations show a clear relation between the saturation current and the total number of charged particles created. The model shows that the potential at which the electric field saturates is strongly dependent on the recombination rate and the diffusivity of the charged particles. The onset of saturation occurs because most created charged particles are withdrawn from the flame and because the electric field effects start dominating over mass based diffusion. It is shown that this knowledge can be used to optimise ionisation chemistry mechanisms. It is shown numerically that the so-called diodic effect is caused primarily by the distance the heavier cations have to travel to the cathode.     

The importance of OH radical–neutral low temperature tunnelling reactions in interstellar clouds using a new model

Recent laboratory experiments using a pulsed Laval nozzle apparatus have shown that reactions between a neutral molecule and the radical OH can occur efficiently at low temperatures despite activation energy barriers if there is a hydrogen-bonded complex in the entrance channel which allows the system to tunnel efficiently under the barrier. Since OH is a major radical in the interstellar medium, this class of reactions may well be important in the chemistry that occurs in the gas phase of interstellar clouds. Using a new gas-grain chemical network with both gas-phase reactions and reactions on the surfaces of dust particles, we studied the role of OH–neutral reactions in dense interstellar clouds at 10, 50, and 100 K. We determined that at least one of these reactions can be significant, especially at the lowest temperatures studied, where the rate constants are large. It was found in particular that the reaction between CH₃OH and OH provides an effective and unambiguous gas-phase route to the production of the gaseous methoxy radical (CH₃O), which has been recently detected in cold, dense interstsellar clouds. The role of other reactions in this class is explored.     

Focusing effect and modulation mechanism of the beam self-fields on the electronʼs Larmor rotation in a free-electron laser with an axial guide magnetic field

It is revealed that at anti-resonance in a free-electron laser with a reversed guide magnetic field, the beam self-fields can act to focus the beam transport and prevent the electrons from striking on the waveguide wall before the wiggler exit. It is found that the focusing function results from the modulation of the periodically-varying self-field tangential and normal components on the electron?s Larmor rotation. As a potential application, substantial improvement of the wave gain and output power at anti-resonance could be expected, since the beam current loss can be obviated by using this modulation mechanism.     

Neutrino mixing and masses in a left–right model with mirror fermions

In the framework of a left–right model containing mirror fermions with gauge group SU(3) _C ⊗SU(2) _L ⊗SU(2) _R ⊗U(1) _Y′, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes μ→eγ, τ→μγ and τ→eγ. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels N→W ^± l ^∓, N→Zν _l and N→Hν _l , which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to tri-bimaximal mixing matrix for light neutrinos.     

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, ...     

The Timoshenko–Reissner generalized model of a plate highly nonuniform in thickness

A thin plate fabricated of material that is transversally isotropic and nonuniform in thickness is considered. The model of the monolayer transversally homogeneous isotropic plate, which is approximately equivalent to a thickness-nonuniform plate in the deflection and in the lowest frequencies of free vibrations, is constructed. The range of applicability of the model constructed is very wide. The main result of this study is a formula for calculating the transverse-shear rigidity of an equivalent transversally isotropic plate.     

Solitons and conservation laws in magneto–optic waveguides with generalized Kudryashov’s equation

The modified sub–ODE approach secures optical soliton solutions in magneto–optic waveguides with generalized Kudryashov’s equation. The solutions are initially drafted in terms of Jacobi’s elliptic functions. The limiting process, when the modulus of ellipticity approaches zero or unity, the soliton solutions emerge. A few solutions in terms of Weierstrass’ elliptic functions are also revealed. Finally, the conservation laws are computed for the model using the multiplier approach.     

Painlevé integrability of a generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painlevé test for integrability only for three distinct cases. Moreover, the multisoliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.     

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.     

Products of distributions and collision of a δ-wave with a δ′-wave in a turbulent model

We study the possibility of collision of a δ-wave with a stationary δ′-wave in a model ruled by equation f (t)u _t+[u²?β(x?γ(t))u]_x = 0, where f, β and γ are given real functions and u = u(x, t) is the state variable. We adopt a solution concept which is a consistent extension of the classical solution concept. This concept is defined in the setting of a distributional product, which is not constructed by approximation processes. By a convenient choice of f, β and γ, we are able to distinguish three distinct dynamics for that collision, to which correspond phenomena of solitonic behaviour, scattering, and merging. Also, as a particular case, taking f = 2 and β = 0 we prove that the referred collision is impossible to arise in the setting of the inviscid Burgers equation. To show how this framework can be applied to other physical models, we included several results already obtained.