Equilibrium states for the geodesic flow

We give in this paper new results of large deviation type for the geodesic flow on a closed Riemannian manifold, which describe the proportion of geodesic arcs supporting measures close to the equilibrium states. We introduce zeta functions in terms of geodesic arcs and show that they define holomorphic functions on a half plane given by the topological pressure.     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the first Hopf bifurcation point. With adequate initial conditions and temporary imposition of small wave-type perturbation, multiple periodic flow states with three different pair numbers of spiral Taylor-Görtler (TG) vortices have been simulated successfully for β=0.06, of which the 1-pair and 2-pair of spiral TG vortices are newly obtained. Three different periodic flow states with shear waves, Stuart vortices or wavy outflow boundary, have been obtained for β=0.18. Analysis of the numerical results reveals these higher flow modes in terms of fundamental frequency, wave number and spatial structure.     

Global well posedness of traffic flow models with phase transitions

This note is devoted to the study of traffic flow models that develop phase transitions. From the analytical point of view, this is a first example of a well posedness result for conservation laws developing phase transitions, which is independent from the number of phase boundaries in the initial data or in the solutions. We consider below the Cauchy problem as well as the problem with boundaries.     

Stability of non-isothermal phase transitions in a steady van der Waals flow

This paper is concerned with the multidimensional stability of non-isothermal subsonic phase transitions in a steady supersonic flow of van der Waals type. For the sake of seeking physical admissible planar waves, the viscosity–capillarity criterion (Slemrod in Arch Ration Mech Anal 81(4):301–315, 1983) is chosen to be the admissible criterion. By showing the Lopatinski determinant being non-zero, we prove that subsonic phase transitions are uniformly stable in the sense of Majda (Mem Am Math Soc 41(275):1–95, 1983) under both one-dimensional and multidimensional perturbations.     

Equilibrium states for factor maps between subshifts

Let π:X→Y be a factor map, where (X,σX) and (Y,σY) are subshifts over finite alphabets. Assume that X satisfies weak specification. Let a=(a₁,a₂)∈R² with a₁>0 and a₂?0. Let f be a continuous function on X with sufficient regularity (Hölder continuity, for instance). We show that there is a unique shift invariant measure μ on X that maximizes . In particular, taking f≡0 we see that there is a unique invariant measure μ on X that maximizes the weighted entropy a₁hμ(σX)+a₂hμ°π−1(σY), which answers an open question raised by Gatzouras and Peres (1996) in [15]. An extension is given to high dimensional cases. As an application, we show that for each compact invariant set K on the k-torus under a diagonal endomorphism, if the symbolic coding of K satisfies weak specification, then there is a unique invariant measure μ supported on K so that dimHμ=dimHK.     

Cardiorespiratory dynamics during transitions between mechanical and spontaneous ventilation in intensive care

Life support devices (e.g., heart pacemakers, ventilators, dialysis machines) are commonly thought to affect mainly their target organ system. This preliminary study attempts to determine the extent to which mechanical support of one organ system (lungs by mechanical ventilator) affects functions of other systems (heart and blood vessels). We studied changes in cardiorespiratory interactions and in dynamics of cardiovascular system during scheduled transitions (spontaneous breathing trials, SBT) between mechanical and spontaneous ventilation in critically ill patients. This initial study population consisted of 13 patients admitted to a surgical intensive care unit (ICU) following surgery, trauma, or complications who were judged candidates for liberation from the ventilator. We collected continuous respiratory, cardiac (ECG), and perfusion (blood pressure and pulse oximetry) signals of mechanically ventilated patients before, during, and after SBT. The data were analyzed using spectral analysis, phase dynamics, and entropy measures. We found that the mechanical ventilation not only drives lung dynamics but also affects the dynamics of cardiac and vascular systems. Spontaneous cardiovascular rhythms are entrained by the mechanical ventilator and are drawn into synchrony. Sudden interruption of mechanical ventilation typically leads to rapid desynchronization. This synchronization is restored upon reinstitution of mechanical ventilation. The initial data suggest that therapies intended to support one organ system may propagate unanticipated effects to other organ systems. Moreover, sustained therapies may disturb mechanisms that promote natural synchronization and variability and thereby adversely affect recovery of normal organ system interactions. We suggest that new measures and displays of synchronization not only could provide insight into the organ–organ coupling but also could yield information to optimize the function of devices used to support the critically ill patient. © 2008 Wiley Periodicals, Inc. Complexity, 2008     

Couette flow between corrugated cylinders

This note reports some analytic Stokes solutions to the flows outside a rotating corrugated cylinder and between two rotating corrugated cylinders of either epitrochoidal or hypotrochoidal cross-sections. The results are obtained by using conformal mappings and general biharmonic solutions inside and outside of a unit circle.     

Slow flow between concentric cones

This paper considers the low-Reynolds-number flow of an incompressiblefluid contained in the gap between two coaxial cones with coincidentapices and bounded by a spherical lid. The two cones and thelid are allowed to rotate independently about their common axis,generating a swirling motion. The swirl induces a secondary,meridional circulation through inertial effects. For specificconfigurations complex eigenmodes representing an infinite sequenceof eddies, analogous to those found in two-dimensional cornerflows and some three-dimensional geometries, form a componentof this secondary circulation. When the cones rotate these eigenmodes,arising from the geometry, compete with the forced modes todetermine the flow near the apex. This paper studies the relative dominance of these two effectsand maps out regions of parameter space, with attention to howshear and overall rotation can destroy the infinite sequenceof eddies that may be present when only the lid is rotated.A qualitative picture of the number of eddies visible in themeridional circulation is obtained as a function of the rotationrates of cones and lid, for various choices of angles. The resultsare discussed in the context of previous work, including theirsignificance for applications to the mixing of viscous fluidsin this geometry.     

Non-Newtonian flow between concentric cylinders

The nonlinear rheological effects of Oldroyd 6-constant fluid between concentric cylinders is addressed. Numerical solution of nonlinear differential equation is given. The nonlinear effects on the velocity is shown and discussed. This reveal that characteristics for shear thickening/shear thinning behavior of a fluid is dependent upon the rheological properties.     

Optimal switching between collective motion states for two agents

We show that steering control can be chosen to give bistability between parallel and anti-parallel collective motion states for a continuous-time kinetic model of two agents moving in the plane with unit speed. Variational methods are used to determine the optimal input to the steering control of one of the agents which leads to switching between these collective states. For any given time interval of switching, such an optimal input is shown to exist and to be unique. The properties of optimal inputs are interpreted by considering the phase space geometry of the Euler–Lagrange equations associated with the optimization.