Effect Of Inertial Terms Research Articles

Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis.

The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction.

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.

Inertia flows of Bingham fluids through a planar channel: Hydroelastic instability analysis

In this paper, the effect of inertial terms on hydroelastic stability of a pressure-driven flow of a viscoplastic fluid flowing through a channel lined with a highly compliant polymeric gel is investigated. It is assumed that the fluid obeys the Bingham constuitive equation and the polymeric gel follows a two-constant Mooney–Rivlin material, which is used for modeling a nonviscous hyperelastic polymeric coating. A base-state solution is obtained for the fluid motion and solid deformation, simultaneously. Next, some infinitesimally small two-dimensional disturbances are imposed on the base-state solution. Dropping out all nonlinear perturbation terms, the modal linear stability analysis of the channel flow is conducted. The effects of the Bingham number and material constants are then examined on the critical Reynolds number. It is found that the yield stress has a stabilizing effect while the Mooney–Rivlin parameters have destabilizing effects on the pressure-driven flow of Bingham fluids.

Linear stability of shear-thinning fluids in deformable channels: Effect of inertial terms

In the present work, the effect of inertial terms is numerically investigated on the hydroelastic stability of shear-thinning fluids in pressure-driven flow between two parallel plates lined with a Mooney–Rivlin hyperelastic polymeric gel. Having obtained the basic flow for the fluid and the basic deformation for the solid, the vulnerability of the basic solutions are examined when subjected to infinitesimally-small, normal-mode perturbations. By dropping all nonlinear perturbation terms, an eigenvalue problem is obtained, in the form of two coupled fourth-order ODEs, which are solved using the shooting or spectral methods. Based on the numerical results obtained in this work, it is concluded that the Mooney–Rivlin gels having a negative first-normal-stress-difference are more stable than the neo-Hookean gels as far as hydroelastic instability in plane Poiseuille flow is concerned. While under creeping-flow conditions the effect of shear-thinning is predicted to be stabilizing, in inertial flows its effect is predicted to be stabilizing or destabilizing depending on the Reynolds number.

Kinetics of phase transitions in quark matter

We study the kinetics of chiral transitions in quark matter using a phenomenological framework (Ginzburg-Landau model). We focus on the effect of inertial terms on the coarsening dynamics subsequent to a quench from the massless quark phase to the massive quark phase. The domain growth process shows a crossover from a fast inertial regime (with ) to a diffusive Cahn-Allen regime (with ).

Wave-induced dynamic response and instability of seabed around caisson breakwater

In this study, standing wave-induced dynamic response and instability of seabed around a caisson breakwater are investigated. A seabed-rubble-caisson breakwater system is modeled using finite elements. The dynamic response of the porous seabed-rubble foundation is assumed to be governed by the Biot’s equations of coupled flow and deformation. Three possible formulations (fully dynamic, partly dynamic and quasi-static) are considered with respect to the inclusion of inertial terms associated with the motion of fluid and solids. The response is presented in terms of stress and pore pressure distributions at three locations underneath the breakwater. The instability of seabed and rubble mound due to instantaneous liquefaction is also studied. The effects of seabed and wave parameters and the effect of inertial terms on the standing wave-induced dynamic response and instability of the system are investigated through a set of parametric studies. Analyses show that quasi-static and partly dynamic formulations yield similar results while the fully dynamic formulation provides different response. The results from different formulations suggest the use of all inertial terms (fully dynamic formulation), providing the most complete solution and the least conservative response.

Inertial effects in butane stochastic dynamics

The range of validity of diffusive algorithms is studied by comparing the isomerization rates and rotational reorientation times from a series of Langevin dynamics trajectories of butane with the results of a Brownian dynamics (diffusive) trajectory, as well as with analytic approximations. It is found that inertial effects may be ignored for rotation at most liquid densities and contribute approximately 10% to the isomerization rate at water viscosities. For neat butane, or other short-chain alkane solvents at room temperature, the effect of inertial terms on isomerization rates is significant.

An Inertial Contribution to the Steady State Film Profiles of Viscous Drainage

Abstract The effect of inertial terms in the Navier-Stokes equation of viscous drainage on a flat plate is investigated. It is found that they give rise to a constant correction term to the Jeffreys' parabola which persists in the steady state.