Publications de Tobias Schneider

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One approach for describing spatiotemporal chaos is to study the unstable invariant sets embedded in the chaotic attractor of the system. While equilibria, periodic orbits, and invariant tori can be computed using existing methods, the numerical identifica ...

We combine theory, numerical simulation, and experiments to investigate the breakup of two identical droplets entering a Y-junction with controlled spatial offset by which the second droplet trails the first. Based on fully resolved 3D simulations, we desc ...

Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatiotemporal chaos and turbulence. Finding these UPOs is, however, notoriously difficult. Matrix-free loop convergence algorithms deform entire space-time fields (l ...

In a vertical channel driven by an imposed horizontal temperature gradient, numerical simulations (Gao et al., Phys. Rev. E, vol. 88, 2013, 023010; Phys. Rev. E, vol. 91, 2015, 013006; Phys. Rev. E, vol. 97, 2018, 053107) have previously shown steady, time ...

Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a mul ...

Spatiotemporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A recent dynamical syst ...

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...

The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a ch ...

Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise v ...

In linearly stable shear flows at moderate Reynolds number, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge, which separates decaying perturbations from those triggering turbulence. We statistically anal ...

Transitional turbulence in shear flows is supported by a network of unstable exact invariant solutions of the Navier-Stokes equations. The network is interconnected by heteroclinic connections along which the turbulent trajectories evolve between invariant ...

In this paper, we examine the fundamental processes that occur during femtosecond-laser hyperdoping of silicon with a gas-phase dopant precursor. We probe the dopant concentration profile as a function of the number of laser pulses and pressure of the dopa ...

Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. ...

At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistica ...

The high-throughput selection of individual droplets is an essential function in droplet-based microfluidics. Fluorescence-activated droplet sorting is achieved using electric fields triggered at rates up to 30 kHz, providing the ultra-high throughput rele ...

We numerically study wall-bounded convectively driven magneto-hydrodynamic (MHD) flows subject to rotation in a Cartesian periodic channel. For the accurate treatment of the rotating MHD equations, we develop a pseudo-spectral simulation code with accurate ...

Fluorescence-activated droplet sorting (FADS) is one of the most important features provided by droplet-based microfluidics. However, to date, it does not allow to compete with the high-throughput multiplexed sorting capabilities offered by flow cytometery ...

Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not ...

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields ...

It has recently been speculated that long-time average quantities of hyperchaotic dissipative systems may be approximated by weighted sums over unstable invariant tori embedded in the attractor, analogous to equivalent sums over periodic orbits, which are ...

Tobias Schneider

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Jacobian-free variational method for computing connecting orbits in nonlinear dynamical systems

Interaction and breakup of droplet pairs in a microchannel Y-junction

Data-driven Guessing and Gluing of Unstable Periodic Orbits

Natural convection in a vertical channel. Part 1. Wavenumber interaction and Eckhaus instability in a narrow domain

Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states

Periodic orbits exhibit oblique stripe patterns in plane Couette flow

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation

Turbulent-laminar patterns in plane Poiseuille flow

Studying edge geometry in transiently turbulent shear flows

Computing heteroclinic orbits using adjoint-based methods

Femtosecond-laser hyperdoping silicon in an SF6 atmosphere: Dopant incorporation mechanism

Buckling instabilities and spatio-temporal dynamics of active elastic filaments

Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Rational design of a high-throughput droplet sorter

Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method

High-throughput multiplexed fluorescence-activated droplet sorting

Superspreading events suggest aerosol transmission of SARS-CoV-2 by accumulation in enclosed spaces

Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions

Predicting chaotic statistics with unstable invariant tori