Narrow Results

The reaction–diffusion systems represent various problems in the real world. For the Abrahams–Tsuneto reaction–diffusion system arising in superconductivity, we perform computerized symbolic computation and find its new exact analytic solutions, which are solitonic. We see the possibility that by way of the shock waves, the self–consistent superconducting interaction drives the Ginzburg–Landau order parameter, which might be observable.

In this work, we propose a car cellular automaton model that reproduces the experimental behavior of traffic flows in Bogotá. Our model includes three elements: hysteresis between the acceleration and brake gaps, a delay time in the acceleration, and an instantaneous brake. The parameters of our model were obtained from direct measurements inside a car on motorways in Bogotá. Next, we simulated this model with the flux-density fundamental diagram for a single-lane traffic road and compared it with experimental data. Our simulations are in very good agreement with the experimental measurements, not just in the shape of the fundamental diagram, but also in the numerical values for both the road capacity and the density of maximal flux. Our model reproduces, too, the qualitative behavior of shock waves. In addition, our work identifies the periodic boundary conditions as the source of false peaks in the fundamental diagram, when short roads are simulated, that have also been found in previous works. The phase transition between free and congested traffic is also investigated by computing both the relaxation time and the order parameter. Our work shows how different the traffic behavior from one city to another can be, and how important to determine the model parameters for each city.

This paper considers a set of shock physics experiments that investigate how materials respond to the extremes of deformation, pressure, and temperature when exposed to shock waves. Due to the complexity and the cost of these tests, the available experimental data set is often very sparse. A support vector machine (SVM) technique for regression is used for data estimation of velocity measurements from the underlying experiments. Because of good generalization performance, the SVM method successfully interpolates the experimental data. The analysis of the resulting velocity surface provides more information on the physical phenomena of the experiment. Additionally, the estimated data can be used to identify outlier data sets, as well as to increase the understanding of the other data from the experiment.

A new approach was recently proposed to construct equilibrium distribution functions of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct . In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.

The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.

This paper presents a detailed literature review on the studies carried out in the last three decades, for understanding the factors affecting the performance of the ejector. An ejector is one of the important components in many industrial applications in the field of refrigerant expansion, circulation of fluids, vacuum creation, etc. From the analysis of the reported works of the ejector, the CFD modeling has proved to be a convenient method for analyzing the complex phenomenon in the ejector like mixing process, turbulence characteristics, shock interactions, and condensation process. The first part of this paper discusses the operation of ejector, flow structure, parameters required for the computational modeling, governing equations, etc. The second part discusses the influence of geometrical parameters and various operating conditions on the ejector performance. The shape and position of shock waves in the ejector for various operating conditions are also narrated under the same section. Third part of this paper is devoted to discussions on advances in modeling to be considered for the performance improvement of ejectors. Finally, the paper concludes with clear guidelines for the effective ejector modeling. Future scope of ejector research, pathways to progress, etc., mentioned in the conclusion section should help researchers and designers in this field.

A"folding" transformation is used to reduce a two point boundary value problem to one point boundary values (with double the number of functions). A transformation to quasi-Lagrangian coordinates is used to transform discontinuities to rest. After these transformations the general purpose numerical package POST (partial and ordinary differential equations solver in time and one space coordinates) can be successfully applied to a system of hydrodynamical equations, whose solution exhibits jumps and cusp-type discontinuities. Numerical results are presented for the spherically-symmetric shock problem.

Large-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the adiabatic focusing term in the Fokker–Planck transport equation of cosmic rays. As a consequence of the adiabatic focusing term, the diffusion approximation to cosmic ray transport in the weak focusing limit gives rise to first-order Fermi acceleration of energetic particles if the product HL of the cross helicity state of Alfvenic turbulence H and the focusing length L is negative. The basic physical mechanisms for this new acceleration process are clarified and the astrophysical conditions for efficient acceleration are investigated. It is shown that in the interstellar medium this mechanism preferentially accelerates cosmic ray hadrons over 10 orders of magnitude in momentum. Due to heavy Coulomb and ionization losses at low momenta, injection or preacceleration of particles above the threshold momentum p_c≃0.17Z^2/3GeV/c is required.

We study the quantization of a free scalar field when the background metric satisfies Einstein's equations and develops gravitational shock waves.

The existence of time machines, understood as space–time constructions exhibiting physically realised closed timelike curves (CTC's), would raise fundamental problems with causality and challenge our current understanding of classical and quantum theories of gravity. In this paper, we investigate three proposals for time machines which share some common features: cosmic strings in relative motion, where the conical space–time appears to allow CTC's; colliding gravitational shock waves, which in Aichelburg–Sexl coordinates imply discontinuous geodesics; and the superluminal propagation of light in gravitational radiation metrics in a modified electrodynamics featuring violations of the strong equivalence principle. While we show that ultimately none of these constructions creates a working time machine, their study illustrates the subtle levels at which causal self-consistency imposes itself, and we consider what intuition can be drawn from these examples for future theories.

Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities.

Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited.

The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.

The phase composition and structure of a mixture of aluminum and quartz powders taken in a ratio of 1:1 have been studied after loading by spherical converging shock waves. A number of concentric layers (zones) have been observed in the sample after shock-wave loading. The presence of several zones in the sample reflects the specific features of the processes occurring in different pressure ranges. It has been established that pressures below ~45 GPa cause only additional compacting of the material and deformation of aluminum and quartz. In this case, the quartz grain size substantially decreases up to the transition into the X-ray amorphous state. The attainment of a pressure of ~45 GPa initiates the solid-state reaction of SiO₂ decomposition, which leads to the precipitation of pure silicon and the evolution of oxygen. The beginning of the silicon precipitation and the chemical reaction of Al₂O₃ formation are separated over the pressure scale. The critical pressure, which is necessary for the solid-state chemical reaction of the Al₂O₃ formation, is about 50 GPa.

Pressure wave refrigerators (PWR) refrigerate the gas through periodical expansion waves. Due to its simple structure and robustness, PWR may have many potential applications if the efficiency becomes competitive with existing alternative devices. In order to improve the efficiency, the characteristics of wave propagation in a PWR are studied by experiment, numerical simulation and theoretical analysis. Based on the experimental results and numerical simulation, a simplified model is suggested, which includes the assumptions of flux-equilibrium and conservation of the free energy. This allows the independent analysis of the operation parameters and design specifics. Furthermore, the optimum operation condition can be deduced. Some considerations to improve the PWR efficiency are also given.

In this paper, a compressible fluid model is proposed to investigate dynamics of the turbulent cavitating flow over a Clark-Y hydrofoil. The numerical simulation is based on the homogeneous mixture approach coupled with filter-based density correction model (FBDCM) turbulence model and Zwart cavitation model. Considering the compressibility effect, the equation of state of each phase is introduced into the numerical model. The results show that the predicted results agree well with experimental data concerning the time-averaged lift/drag coefficient and shedding frequency. The quasi-periodic evolution of sheet/cloud cavitation and the resulting lift and drag are discussed in detail. Especially, the present compressible-mixture numerical model is capable of simulating the shock waves in the final stage of cavity collapse. It is found that the shock waves may cause the transient significant increase and decrease in lift and drag if the cavity collapses near the foil surface.

The dispersion of particle rings or shells by a radially divergent shock front trailed by the pressurized gases takes the form of hierarchical particle jetting. Through a semi-two-dimensional configuration, we characterize the evolution of the jetting pattern using the boundary tracking technique. In contrast to the refined filamentary jetting spread induced by the dispersal of soft and ductile flour particles, the hard and brittle quartz sand particles are dispersed into a finger-like branched pattern with much fewer jets. The interplay between the primary and secondary jets suffices to reverse the flour jetting pattern, which by contrast is negligible in the quartz sand jetting. The distinct jetting patterns displayed by the flour and quartz sand particles are related with the distinguishable networks of force chains invoked in two particles which dictate the nucleation of jets.

In this work, weakly nonlinear wave equation in mono-dispersed, isothermal, bubbly, slightly compressible viscoelastic liquid is derived, using reduction perturbation method. The constitutive equation is based on the second-grade fluid model. Viscosity, relaxation, retardation and surface tension are considered under isothermal condition, which modifies the Rayleigh–Plesset equation for compressible liquid. A kink traveling wave solution is obtained using the tangent hyperbolic method combined with the Riccati equation. Graphical representation of the solution is given and analyzed with different parameter values.

In this work, two numerical schemes were developed to overcome the problem of shock waves that appear in the solutions of one/two-layer shallow water models. The proposed numerical schemes were based on the method of lines and artificial viscosity concept. The robustness and efficiency of the proposed schemes are validated on many applications such as dam-break problem and the problem of interface propagation of two-layer shallow water model. The von Neumann stability of proposed schemes is studied and hence, the sufficient condition for stability is deduced. The results were presented graphically. The verification of the obtained results is achieved by comparing them with exact solutions or another numerical solutions founded in literature. The results are satisfactory and in much have a close agreement with existing results.

In this work, we will try to find lump solutions, interaction between lump wave and solitary wave solutions, kink-solitary wave solutions and shock wave-type solutions to $(3+1)$-dimensional generalized nonlinear evolution equation arising in the shallow water waves. The lump solutions, the interaction between lump wave and solitary wave solutions and kink-solitary wave solutions are derived with symbolic computation based on a logarithmic derivative transform which is derived by the help of Hirota’s simple method. The shallow water waves in this equation are associated with some natural problems such as tides, storms, atmospheric currents and tsunamis. For the physical presentation of the solutions, we draw 3D and counter graphics by giving the suitable values to include the free parameters. We believe that disciplines such as mathematical physics, nonlinear dynamics, fluid mechanics and engineering sciences can benefit from this study.

Using similarity methods with general physical assumptions and sufficient mathematical relations, researchers can obtain approximate solutions ready for experimental confirmation. Singh et al. claimed to have analyzed the second-kind self-similar motion of converging cylindrical shock waves in magnetogasdynamics. However, we found the dominated equation (11) and relevant equations of Singh et al. [Chin. Phys. Lett. 28(9) (2011) 094701] as well as the dominated equation (12) and relevant equations of Singh et al. [AIAA J. 48(11) (2010) 2523] being not correct. We show the correct mathematical derivations in details. It seems to us corresponding equations as well as illustrations by Singh et al. are of doubt due to above-mentioned issues. Our results imply the similarity exponent $\alpha$ obtained by Singh et al. will be close to that for the converging spherical shock waves.

In this paper we will study the condition for the occurrence of flux spikes, such as momentum spikes for the Navier–Stokes equations. Flux spikes are observed in Computational Fluid Dynamics, but it is unknown what are the exact conditions at which they occur and whether they are physical or purely numerical. In the present paper we try to clarify these questions.