The 2-scope technique for rotator cuff surgery: are 2 scopes better than 1?

The arthroscopic treatment of rotator cuff tear involves 2 distinct phases: intra-articular and subacromial. We present the 2-scope technique with the aim to simultaneously perform these phases, entrusting them to 2 experienced surgeons, and to obtain possible benefits compared with the classic 1-scope technique. Better nosology of the lesion and a more accurate evaluation of suture passer action (equidistance of the sutures and avoidance of degenerated articular-side tendon areas) represent benefits of this technique. In contrast, the 2-scope technique needs an additional lateral portal and could give rise to an erroneous distribution of costs and surgeons

Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow

© 2016, Springer-Verlag Wien. Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in Rz as the mass flow moves from negative to positive for different internal heat sources

On the stability and uniqueness of the flow of a fluid through a porous medium

© 2016, The Author(s). In this short note, we study the stability of flows of a fluid through porous media that satisfies a generalization of Brinkman’s equation to include inertial effects. Such flows could have relevance to enhanced oil recovery and also to the flow of dense liquids through porous media. In any event, one cannot ignore the fact that flows through porous media are inherently unsteady, and thus, at least a part of the inertial term needs to be retained in many situations. We study the stability of the rest state and find it to be asymptotically stable. Next, we study the stability of a base flow and find that the flow is asymptotically stable, provided the base flow is sufficiently slow. Finally, we establish results concerning the uniqueness of the flow under appropriate conditions, and present some corresponding numerical results

Double-diffusive convection in an inclined porous layer with a concentration-based internal heat source

© 2017, The Author(s). The thermosolutal instability of double-diffusive convection in an inclined fluid-saturated porous layer with a concentration-based internal heat source is investigated. The linear instability of small-amplitude perturbations to the system is analyzed with respect to transverse and longitudinal rolls. The resultant eigenvalue problem is solved numerically utilizing the Chebyshev tau method. It is shown that an increasing inclination angle causes a strong stabilization in the transverse rolls irrespective of the internal heat source or vertical solutal Rayleigh number. Furthermore, substantial qualitative changes are demonstrated in the linear instability thresholds with variations in the inclination angle and concentration-based heat source

Hopf bifurcations and global nonlinear L2-energy stability in thermal MHD

The transfer of heat and mass by convection in a fluid horizontal layer L, heated from below – in the past as nowadays – has attracted the attention of many scientists since it can be driven by different factors and has a very relevant influence on the behaviour of many phenomena of the real world concerning meteorology, sun and stars physics, oceanography, heat insulation, air and water pollution, ... (see [1–12, 25–29] and references therein). When L is filled by a plasma and is embedded in a transverse constant magnetic field, in the non-relativistic scheme of magneto-hydrodynamic (MHD), in the early of 1950 ([1–2]), the Nobel Prize laureate (1983) S. Chandrasekhar – in linear thermal MHD – obtained a relevant inhibition of convection by a magnetic field, verified experimentally [9] and appeared in 1961 in the celebrated monograph [3]. Successively, during the years, many efforts have been done in order to recover this relevant stabilizing effect in the nonlinear thermal MHD theory (see [6, 10, 11, 13, 16]). This goal has been reached partially in 1988 in [13] and totally in [16] but only under very severe restrictions on the initial data (of the order <10−6). Recently in [17], via a non standard approach, assuming the verticality of the gradient pressure perturbations, it has been totally recovered in the nonlinear thermal MHD theory, the linear inhibition of convection by magnetic field for any admissible initial data (Linearization Principle). In the present paper, we return to the problem and show that, in thermal MHD, the linear asymptotic stability implies the global exponential nonlinear L2−energy stability, without requiring the verticality of the perturbations to the pressure gradient. As concerns the onset of instabilities in the free-free case, since Pr≥Pm (with Pr,Pm Prandtl and Prandlt magnetic numbers), implies the onset of steady bifurcation for any value of the Chandrasekhar number Q2, we analyze the case $P_rHopf bifurcation number the threshold Qc that the Chandrasekhar number has to cross for the occurring of Hopf bifurcations, we obtain that Qc=1+PrPm−Prπ2. This formula – new in the existing literature – removes the difficulties (mentioned in page 184 of [3]) on finding a "simpler formula which gives Qc as function of Pr, Pm"

Hopf bifurcations in dynamical systems

The onset of instability in autonomous dynamical systems (ADS) of ordinary differential equations is investigated. Binary, ternary and quaternary ADS are taken into account. The stability frontier of the spectrum is analyzed. Conditions necessary and sufficient for the occurring of Hopf, Hopf–Steady, Double-Hopf and unsteady aperiodic bifurcations—in closed form—and conditions guaranteeing the absence of unsteady bifurcations via symmetrizability, are obtained. The continuous triopoly Cournot game of mathematical economy is taken into account and it is shown that the ternary ADS governing the Nash equilibrium stability, is symmetrizable. The onset of Hopf bifurcations in rotatory thermal hydrodynamics is studied and the Hopf bifurcation number (threshold that the Taylor number crosses at the onset of Hopf bifurcations) is obtained