Variational Average-Atom in Quantum Plasmas (VAAQP) – Application to radiative properties

We present an application of the Variational Average-Atom in Quantum Plasmas (VAAQP) model and numerical code to dense plasmas radiative properties. We propose an approximate Detailed Configuration Accounting (DCA) approach starting from the variational model of configurations in jellium. This leads to a simplified model which is qualitatively different from those which usually stem from the atom-in-cell approach. It is also shown that, with some additional approximations, the DCA calculation can be handled by use of the Gaussian approximation to perform a statistical approach to the spectrum. Our purpose here is to show that this model provides a simple way to calculate the radiative properties and is likely to give realistic results.     

Multi-mode solitons in a long-short range traffic lattice model with time delay

We consider a new form of solutions of a special lattice model for traffic system. By analyzing nearest sites’ interactions, time delay, and bumpy effects, we deduce the bifurcation lines and surfaces for stable and unstable regions and show how they vary as parameters vary. It shows that keeping other conditions unchanged, as the incoming flow increases, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable. Besides, considering delayed optimal flow, multiple sites effect or artificial parameters can also help stabilize the traffic road condition. Moreover, by putting it into the framework of mKdV equations, we obtain the kink–antikink solitons involving all parameters, which show the feature of the traffic congestion. The result is original, and our model in differential or difference form can be reduced into the previous ones by choosing appropriate parameters. Since the optimal velocity function we considered involves finitely or infinitely many sites, the density waves can be in multi-mode and high dimension forms and can also be quasi-periodic, we show a new feature of the traffic lattice system.

     

Interactions among different types of nonlinear waves described by the Kadomtsev–Petviashvili equation

In nonlinear science, the interactions among solitons are well studied because the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlevé waves. In this paper, taking the Kadomtsev–Petviashvili (KP) equation as an illustration model, a new method is established to find interactions among different types of nonlinear waves. The nonlocal symmetries related to the Darboux transformation (DT) of the KP equation is localized after embedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant solutions. It is shown that the essential and unique role of the DT is to add an additional soliton on a Boussinesq-type wave or a KdV-type wave, which are two basic reductions of the KP equation.     

Waves in microstructured solids and the Boussinesq paradigm

The emergence of soliton trains and interaction of solitons are analyzed by using a Boussinesq-type equation which describes the propagation of bi-directional deformation waves in microstructured solids. The governing equation in the one-dimensional setting is based on the Mindlin model. This model includes scale parameters which show explicitly the influence of the microstructure in wave motion. As a result the governing equation has a hierarchical structure. The analysis is based on numerical simulation using the pseudospectral method. It is shown how the number of solitons in emerging trains depends on the initial excitation. The head-on collision of emerged solitons is not fully elastic due to radiation but the solitons preserve their identity after collision and the speed of solitons is retained while the radiation keeps a certain mean value. That is why we have kept through this paper the notion of solitons.     

Experimental investigation of cylindrically diverging solitons in an electric lattice

The results of an experimental investigation of cylindrical solitons in a two-dimensional electric LC-lattice are given. It is shown that in the continuum limit, propagation of cylindrical waves far from the center of symmetry in such a lattice may be described for each ray tube by a known modification of the Korteweg-de Vries equation which takes account of the cylindrical divergence. The dispersion term in this equation depends on the direction of wave propagation relative to the direction of the main axes of the lattice. Formation of solitons from non-soliton-shaped pulses was observed. The variations of soliton amplitude and duration with distance have been determined. They agree well with the numerical calculations by Maxon & Viecelli [2] and Dorfman [9]. Comparison of the obtained experimental data with the known theoretical laws of amplitude attenuation for diverging solitons [2, 12, 14] seems to favor the validity of the law A r^−2/3 rather than A r^−1/2.     

Two-dimensional accessible solitons in PT-symmetric potentials

Two-dimensional parity-time (PT) symmetric potentials are introduced, which allow the existence of spatial solitons in the model of the strongly nonlocal nonlinear Schr?dinger equation. Two-dimensional accessible solitons are found in the form of solutions separating the radial amplitude, given in terms of Laguerre polynomials, a?phase function involving quadratic, linear, and constant phase shifts, and a specific azimuthal modulation function. Shape-preserving solitons are constructed from Laguerre?CGaussian functions containing the self-similar variable and an exponential form of the azimuthal modulation, containing sine and cosine functions, when a suitable PT-symmetric potential is chosen. Interesting soliton profiles and the corresponding PT-symmetric potentials are displayed for different values of the parameters.     

On the theory of three-dimensional multihump solitons in active-dissipative media

Stable localized nonlinear coherent structures, i.e. solitons, play a key role in the stochastization of the processes occurring in active-dissipative media. In this study, three-dimensional multi-hump solitons are investigated for a model equation which qualitatively describes the wave processes in some physical systems. The existence of 3D multihump solitons is demonstrated numerically and the soliton behavior is studied. The results are generalized to describe multihump solitons in descending viscous-fluid layers [1]. An unusual physical phenomenon observed in experiments [1], namely, stable two-hump coherent structures on the surface of a downflowing viscous-fluid layer, is explained qualitatively.     

Soliton dynamics for a nonintegrable model of light-colloid interactive fluids

A nonintegrable model with the super-Kerr nonlinearity is investigated, which describes the light-matter interactions in a fluidic suspension of colloidal nanoparticles. Existence of the solitons with semi-analytic forms is shown for this model via the variational method. Numerical simulation is performed to demonstrate the good accordance with the variational analysis. Soliton interactions and soliton bound states are discussed in both the homogeneous and inhomogeneous media. In particular, inelastic interactions of two solitons are presented, and we find that there is an energy distribution \(P_\pm \), which has a dependence with the velocity of the high-energy solitons. Simulations also reveal that the maximum value of \(P_-\) relates with the soliton energy and the model parameter \(\beta \). Moreover, two different patterns of the three-soliton interactions are depicted as manifestation of the nonintegrability.     

An Optimization Approach to Kinetic Model Reduction for Combustion Chemistry

Model reduction methods are relevant when the computation time of a full convection–diffusion–reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we consider a model reduction approach based on optimization of trajectories and its applicability to realistic combustion models. As many model reduction methods, it identifies points on a slow invariant manifold based on time scale separation in the dynamics of the reaction system. The numerical approximation of points on the manifold is achieved by solving a semi-infinite optimization problem, where the dynamics enter the problem as constraints. The proof of existence of a solution for an arbitrarily chosen dimension of the reduced model (slow manifold) is extended to the case of realistic combustion models including thermochemistry by considering the properties of proper maps. The model reduction approach is finally applied to two models based on realistic reaction mechanisms: ozone decomposition as a small test case and syngas combustion as a test case including all features of a detailed combustion mechanism.     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Solitons and complexitons solutions of an integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain

In this paper, we consider an integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain. Using the ansatz method, bright and dark 1-soliton solutions are derived. Also, some conditions are given which guarantee the existence of solitons. In addition, some exact solutions also derived based on the sub-ODE method. At last, the explicit power series solutions also presented.     

On $$\varvec{}$$-mixed-type soliton propagation in dispersive nonautonomous long waves with waveguides

In this paper N-soliton propagations for the Calogero–Bogoyavlenskii–Schiff (CBS) equation in an inhomogeneous media which describes the long nonautonomous waves are obtained. Here attention is focused to study the effect of the dispersion coefficient on the propagation solitons waves. It is found that N-bright-dark solitons are produced by periodic or coupled periodic and pulses waves. Solitons waves are propagated for two and three pulses with periodic oscillating. Further, the double-periodic and solitary waves are dispersive to broken-solitons waves for the graded-index with oscillating reflection components. These results are useful for the application for long-distance telecommunication and optical fiber.     

Adiabatic decohesion in a thermoplastic craze thickening at constant or increasing rate

When a crack in a thermally non-diffusive material is impact loaded—or propagates at high speed—a cohesive process which resists slow crack extension may itself cause decohesion by adiabatic heating. By assuming that decohesion ultimately occurs by low-energy disentanglement within a melt layer of critical thickness, the fracture resistance of craze-forming crystalline polymers can be estimated quantitatively. Previous estimates used a simple, thermomechanically linear representation of craze fibril drawing. This paper presents a more physically realistic, numerical formulation, and demonstrates it for constant craze thickening rate (as imposed by an ideal full-notch tension test) and for linearly increasing thickening rate (as at the tip of an impact-loaded or rapidly propagating crack). For a linear material, the numerical formulation gives results which asymptotically approach those from analytical solutions, as craze density approaches zero. In more realistic model polymers, the enthalpy of fusion increasingly delays decohesion as impact speed increases, although the temperature distribution of an endotherm appears to have little effect. Increasing molecular weight, heuristically associated with decreasing craze density and increasing structural dimension, increases the predicted impact fracture resistance. In every case, fracture resistance passes through a minimum as impact speed increases. The conclusions encourage the use of impact fracture tests, and discourage the use of the full-notch tension test, to assess the dynamic fracture resistance of a craze-forming polymer.     

Fission of solitons in a symmetric triangular channel with variable cross section

In this paper, we study the disintegration of a soliton in a symmetric triangular channel when it propagates from one uniform cross section of the channel into another through a transition region. A criterion under which a soliton is split into n solitons is given. Numerical results for n = 3 are presented to confirm the analytical predictions.     

A consideration of curved interfaces in stress-assisted martensite formation

A purely mechanical, sharp interface model is developed to consider curved interfaces that have been observed between martensite phase variants. The approach is based on a theory of small strains as distinct from small displacement gradients. It admits a realistic characterization of each phase with standard elasticity tensors and allows for inhomogeneous states of strain within each phase including inhomogeneous, finite rotations. The model indicates that any signficant interface curvature must be due to material rotation because interfaces cannot be finitely curved with respect to the material lattice. It is also found that the interface driving traction is not influenced by local lattice rotations unless inertia affects the reaction.     

On solitons in media modelled by the hierarchical KdV equation

In the present paper, formation of solitons in microstructured continuum, modelled by a hierarchical Korteweg–de Vries equation, is studied. The model equation is integrated numerically making use of the discrete Fourier transform-based pseudospectral method under different initial conditions. Main attention is paid to the formation of hidden solitons and applicability of the discrete spectral analysis.