Publications by Tobias Schneider

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One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points ...

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle gamma and the Rayleigh number R. The present numerical i ...

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-d ...

Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many ...

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-d ...

A specific family of spanwise-localised invariant solutions of plane Couette flow exhibits homoclinic snaking, a process by which spatially localised invariant solutions of a nonlinear partial differential equation smoothly grow additional structure at the ...

Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of dra ...

Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet ...

In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is diff ...

The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry, and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of eig ...

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the nonbreaking base state is linearly stable, implying th ...

The Lugiato-Lefever equation (LLE) is a fundamental nonlinear model of pattern formation in damped-driven optical Kerr cavities with applications ranging from fiber to chip-integrated optical resonators. In standard dimensionless form the LLE describes dyn ...

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects ...

Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of ...

Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow exhibits homoclinic s ...

We present two spanwise-localized travelling-wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwi ...

Tobias Schneider

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Invariant tori in dissipative hyperchaos

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Spatio-temporal patterns in inclined layer convection

Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Ghost States Underlying Spatial and Temporal Patterns: How Nonexistent Invariant Solutions Control Nonlinear Dynamics

Modified snaking in plane Couette flow with wall-normal suction

Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids

Secondary instability and tertiary states in rotating plane Couette flow

Search for Unstable Relative Periodic Orbits in Channel Flow Using Symmetry-reduced Dynamic Mode Decomposition

Infinite geometric frustration in a cubic dipole cluster

Edge states control droplet breakup in subcritical extensional flows

Oscillating Turing Rolls as Periodic Orbits of the Lugiato-Lefever Equation

Nondestructive Prediction of the Buckling Load of Imperfect Shells

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Homoclinic snaking in plane Couette flow: bending, skewing and finite-size effects

Localized travelling waves in the asymptotic suction boundary layer

Origin of localized snakes-and-ladders solutions of plane Couette flow

Stability Landscape of Shell Buckling

Fully localized post-buckling states of cylindrical shells under axial compression