Darboux integrability of the stretch-twist-fold flow

The stretch-twist-fold (STF) flow, as a special case of Stokes flows, arises naturally in dynamo theory. The paper studies the integrability of the STF flow. The paper provides a complete classification of the irreducible Darboux polynomials for the system with all values of the parameter alpha. When the parameter is zero, the STF flow is integrable. When the parameter is more than zero, it is proved not to be Darboux integrable. The paper also proves the system has neither exponential factors nor polynomial first integrals at the parameter alpha more than zero.     

Chaotic behavior of modified stretch-twist-fold (STF) flow with fractal property

This study proposes a new lattice hydrodynamic model considering the effects of bilateral gaps on a road without lane discipline. In particular, a lattice hydrodynamic model is proposed to capture the impacts from the lateral gaps of the right-side and left-side sites of the considered lattice sites. Linear stability analysis of the proposed model is performed using the perturbation method to obtain the stability condition. Nonlinear analysis of the proposed model is performed using the reductive perturbation method to derive the modified Korteweg–de Vries (mKdV) equation to characterize the density wave propagation. Results from numerical experiments illustrate that the smoothness and stability of the proposed model are improved compared with the model that considers the effect of unilateral gap. Also, the proposed model is able to more quickly dissipate the effect of perturbation occurring in the vehicular traffic flow.     

Complex dynamics in double-diffusive convection

The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens–Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1. PACS 44.25.+f, 47.20.Bp, 05.45.-a     

Complex dynamics of financial indices

This paper presents a novel method for the analysis of nonlinear financial and economic systems. The modeling approach integrates the classical concepts of state space representation and time series regression. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the dynamical behavior. The results reveal that business cycles can be clearly revealed, while the noise effects common in financial indices can elegantly be filtered out of the results.     

Complex backflow dynamics in nematic liquid crystals

Received December 31, 2001 / Published online May 21, 2002     

Thermo-fluid dynamics of the unsteady channel flow

We present an exact analytical representation of the unsteady thermo-fluid dynamic field arising in a two-dimensional channel with parallel walls for a fluid with constant properties. We assume that the axial pressure gradient is an arbitrary function of time that can be expanded in Taylor series; a particular case is the impulsive motion generated by a sudden jump to a constant value; for large time values the flow reaches the well-known steady Poiseuille solution. As boundary conditions for the dynamic field we consider fixed and moving walls (unsteady Couette flow). The assigned temperature on the walls can be an arbitrary function of time. We also consider the coupling of the energy and momentum equations (i.e. Eckert number different from zero). The solution is obtained by series with simple expressions of the coefficients in terms of the error functions. The fundamental physical parameters, such as shear stress, mass flow and heat flux at the wall are obtained in explicit analytical form and discussed by means of their diagrams.     

Complex dynamics of multi-regional economic interactions

Nonlinear Dynamics - Dynamical systems are being employed over the last decades to investigate complex behaviors in traditional fields as engineering and physics, but also in biology, medicine,...     

Particle dynamics in dense shear granular flow

The particle dynamics in an annular shear granular flow is studied using the discrete element method, and the influences of packing fraction, shear rate and friction coefficient are analyzed. We demonstrate the existence of a critical packing fraction exists in the shear granular flow. When the packing fraction is lower than this critical value, the mean tangential velocity profile exhibits a rate-independent feature. However, when the packing fraction exceeds this critical value, the tangential velocity profile becomes rate-dependent and varies gradually from linear to nonlinear with increasing shear rate. Furthermore, we find a continuous transition from the unjammed state to the jammed state in a shear granular flow as the packing fraction increases. In this transforming process, the force distribution varies distinctly and the contact force network also exhibits different features.     

Particle and bubble dynamics in a creeping flow

Dynamics of a solid particle and non-deformable gaseous bubble in viscous fluid are studied analytically and numerically within the framework of creeping flow regime (flow at vanishingly small Reynolds numbers). Equations of motion for the particle and bubble include the consideration of the buoyancy force, Stokes drag force and memory-integral drag force. Exact analytical solutions are obtained and categorised in terms of inclusion (particle or bubble) density with respect to the density of a surrounding fluid. Through the analytical and numerical solutions, the dynamics of solid particle and air bubble in water have been found to behave differently especially at the early stages of motion, whereas some qualitative similarities exist in the long-term asymptotic.     

Two-dimensional reactive flow dynamics in cellular detonation waves

This investigation deals with the two-dimensional unsteady detonation characterized by the cellular structure resulting from trajectories of triple-shock configurations formed by the transverse waves and the leading shock front. The time-dependent reactive shock problem considered here is governed by a system of nonlinear hyperbolic conservation laws coupled to a polytropic equation of state and a one-step Arrhenius chemical reaction rate with heat release. The numerical solution obtained allowed us to follow the dynamics of the cellular detonation front involving the triple points, transverse waves and unreacted pockets. The calculations show that the weak tracks observed inside the detonation cells around the points of collision of the triple-shock configurations arise from interactions between the transverse shocks and compression waves generated by the collision. The unreacted pockets of gas formed during the collisions of triple points change form when the activation energy increases. For the self-sustained detonation considered here, the unreacted pockets burn inside the region independent of the downstream rarefaction, and thus the energy released supports the detonation propagation. The length of the region independent of the downstream is approximately the size of one or two detonation cell. Received 13 February 1998 / Accepted 13 August 1998     

Modeling the dynamics of colliding particles in a turbulent shear flow

A kinetic model for the probability density function (PDF) of the particle velocity in a turbulent flow with account for particle collisions is presented. The model is tested by comparison with the results of a numerical experiment for a nonstationary homogeneous shear layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1998. The study received financial support from the International Science Foundation INTAS (project No. 94-4348) and the Russian Foundation for Basic Research (project No. 97-01-00398).     

Numerical modeling the dynamics of flow in explosion above a surface

The hydrodynamics of processes occurring in explosion of condensed explosives in air is considered. The physical model, computation technique, and results of simulation of a two-dimensional hydrodynamic flow arising in explosion of cylindrical charges are discussed. In this case, the explosions are considered at some distance above the ground. To close the gas-dynamics equations, the Jones–Wilkins–Lee equation of state is used. The results of calculation allow one to obtain a detailed space–time pattern of the arising flow and to study the origination, propagation, and subsequent attenuation of shock waves. Cylindrical charges of the same mass but with different diameter-to-length ratios are considered. It is shown that the charge shape can render essential influence on dynamics of flow and the parameters of shock waves (in the near and medium fields of explosion).     

Particle and drop dynamics in the flow behind a shock wave

The results of an investigation of the dynamics of hard particles and liquid drops in the flow behind a transmitted shock wave are presented. From the equation of motion of a particle in the shock wave, relations for the displacement, velocity and acceleration as functions of time and certain velocity-relaxation parameters taking into account the properties of the gas and the aerodynamic drag of the particles are obtained for unsteady flow around the particles at an acceleration of 10³–10⁴ m/s². It is shown that the velocity-relaxation parameters are universal. Approaches to finding the aerodynamic drag of freely-accelerating bodies from the dynamics of their acceleration after being suddenly exposed to the flow are considered. It is established that under these conditions the drop dynamics observed can be well described in terms of the same velocity-relaxation parameters with account for linear growth of the transverse drop size. All the kinematic functions obtained are confirmed experimentally.     

Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES)

In this paper, a new fractional order stretch-twist-fold (STF) flow dynamical system is proposed. The stability analysis of the proposed system equilibria is accomplished and we establish that the system is exhibited chaos even for order less than 3. The active control method is applied to enquire the hybrid phase synchronization between two identical fractional order STF flow chaotic systems. These synchronized systems are applied to formulate an authenticated encryption scheme newly for message (text and image) recovery. It is widely applied in the field of secure communication. Numerical simulations are presented to validate the effectiveness of the proposed theory.     

Study of two-phase bubbly flow dynamics in binary mixtures

The results of an investigation of the bubble dynamics and wave phenomena in two-component vapor-liquid mixtures are presented. These mixtures are widely used in industrial systems as heat transfer media. The effects of various additives on the wave dynamics of vapor-liquid mixtures are of particular interest. A single-velocity two-pressure model was used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. The claim that mixture composition may have a peculiar effect on the bubble dynamics of a boiling non-ideal solution is substantiated. It is noted that the small free radial oscillation damping ratio for some binary systems lies outside the domain defined by the damping ratio of the constituents as a result of phase change diffusion effects. A criterion is proposed to identify cases of diffusion resistance responsible for the anomalous effect of component concentration on bubble behavior. The phase change delay due to diffusion results in observably higher mixture wave velocities and a smaller damping ratio than for respective single-component systems.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

Closed polymerization front dynamics in a plane radial flow

The behavior of perturbations of a steady cylindrical front of arbitrary amplitude is investigated numerically. A calculation algorithm is developed on the basis of the well-known boundary integral equation method [7]. The conclusion [5] concerning the stability of the front in the case of an internal supply of medium for perturbations of arbitrary amplitude is confirmed. In the case of an external supply of medium (in the direction of decreasing radial coordinate) the instability of the front and the formation of radial low-viscosity fingers is demonstrated. The method proposed can easily be modified to permit the calculation of the motion of free surfaces and interfaces in chemically inert high-viscosity media. In this connection, it can be used for numerically modeling the flow of plastic and glass melts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–10, September–October, 1991.     

Experimental investigation of the wall dynamics of the A-pillar vortex flow

The influence of the A-pillar vortex on the wall flow of the side window of a car is investigated experimentally using a 30° dihedron model. The measurement of the unsteady pressure at the wall provides a map of the pressure fluctuation intensity, and a spectral analysis is performed to track the dominant frequencies of the wall pressure fluctuations. The wall flow generated by the vortex structure that develops parallel to the side-wall is characterised by means of particle image velocimetry (PIV). Its structure is analysed and compared to cross-sections of the A-pillar vortex in order to identify the different separation and reattachment lines. A comparison of the field of turbulent kinetic energy obtained by PIV with the map of the pressure fluctuations shows a correlation between the structure of the A-pillar vortex and the pressure fluctuations. It is found that the dominant wall pressure fluctuations are located at the secondary separation line, whereas the primary reattachment line does not show any significant pressure variations, that the A-pillar vortex will not naturally break down and that discrete vortices may be associated with the pressure fluctuations.