Instability criteria for steady flows of a perfect fluid

An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.     

Instability of flat spacetime in semiclassical gravity

The semiclassical theory of gravity is considered in which an asymptotically flat background metric is coupled to quantized matter. We show that, in general, there are modes with spacelike wave vectors for small metric fluctuations around flat spacetime. Besides the usual axioms of quantum field theory in flat spacetime, the proof rests on the existence of a hard trace anomaly in the energy-momentum tensor due to matter self-couplings. Two possible interpretations of the result are discussed.     

Structural elements and collapse regimes in 3D flows on a slope

The mechanisms and structural elements of an instability whose development results in the collapse of flow fragments have been studied in the scope of the Hamilton version of the “shallow water” 3D model on a slope. The study indicated that the 3D model differs from its 2D analog in a more varied set of collapsing solutions. In particular, the solutions describing anisotropic collapse, during which the area of a collapsing fragment in contact with the slope contracts into a segment rather than a point, exist together with the solutions describing radially symmetric (isotropic) collapse.     

Bimetric renormalization group flows in quantum Einstein gravity

The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.     

Bubble splitting in oscillatory flows on ground and in reduced gravity

The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration a _cr . The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops subjected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view.     

Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid on slope in the shallow water approximation

Magnetohydrodynamic equations for a heavy fluid over an arbitrary surface are studied in the shallow water approximation. While solutions to the shallow water equations for a neutral fluid are well known, shallow water magnetohydrodynamic (SMHD) equations over a nonflat boundary have an additional dependence on the magnetic field, and the number of equations in the magnetic case exceeds that in the neutral case. As a consequence, the number of Riemann invariants defining SMHD equations is also greater. The classical simple wave solutions do not exist for hyperbolic SMHD equations over an arbitrary surface due to the appearance of a source term. In this paper, we suggest a more general definition of simple wave solutions that reduce to the classical ones in the case of zero source term. We show that simple wave solutions exist only for underlying surfaces that are slopes of constant inclination. All self-similar discontinuous and continuous solutions are found. Exact explicit solutions of the initial discontinuity decay problem over a slope are found. It is shown that the initial discontinuity decay solution is represented by one of four possible wave configurations. For each configuration, the necessary and sufficient conditions for its realization are found. The change of dependent and independent variables transforming the initial equations over a slope to those over a flat plane is found.     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

Dynamical flow arrest in confined gravity driven flows of soft jammed particles

Using numerical simulations, we study the gravity driven flow of jammed soft disks in confined channels. We demonstrate that confinement results in increasing the yield threshold for the Poiseuille flow, in contrast to the planar Couette flow. By solving a nonlocal flow model for such systems, we show that this effect is due to the correlated dynamics responsible for flow, coupled with the stress heterogeneity imposed for the Poiseuille flow. We also observe that with increasing confinement, the cooperative nature of the flow results in increasing intermittent behavior. Our studies indicate that such features are generic properties of a wide variety of jammed materials.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

Magnetoelectronic Instability of Graphene on a Ferromagnetic Substrate

JETP Letters - The shape of the coherent population trapping resonance in optically thin cells with antirelaxation coating of the walls has been determined by solving the quantum kinetic equation...     

Spiral flows on a potential plane

The Tollmien plane spiral potential flow in which, as is known, the isobars are logarithmic spirals, is considered. In this study, the principal feature is the use of a potential plane and possible exact solutions on this plane. As it turns out, one such solution results in a spiral flow, which makes it possible to carry out further considerations on the potential plane.     

Instability of a periodically moving plate

The parametric instability of the in-plane motion of a rectangular plate of periodically varying length is investigated. The boundaries of the instability regions are found and plotted.     

Thermosolutal Instability of a Rotating Plasma

The thermosolutal instability of a plasma is studied to include the effects of coriolis forces and the finiteness of ion Larmor Radius in the presence of transverse magnetic field. It is observed that the effect of rotation is destabilizing only in a typical case. However, the F. L. R. and stable solute gradient have stabilizing effects on stationary convection irrespective of the presence of coriolis forces.