arXiv subjects

Anton Pershin

Publications and source records attributed to Anton Pershin.

22 records · Page 2Linked to original sources

arXiv2020

A probabilistic protocol for the assessment of transition and control

Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to turbulence is achieved via the broadening or narrowing of the basin of attraction of the laminar flow. In this paper, a novel methodology to assess the robustness of the laminar flow and the efficiency of control strategies is introduced. It relies on the statistical sampling of the phase space neighborhood around the laminar flow in order to assess the transition probability of perturbations as a function of their energy. This approach is applied to a canonical flow (plane Couette flow) and provides invaluable insight: in the presence of the chosen control, transition is significantly suppressed whereas plausible scalar indicators of the nonlinear stability of the flow, such as the edge state energy, do not provide conclusive predictions. The methodology presented here in the context of transition to turbulence is applicable to any nonlinear system displaying finite-amplitude instability.

physics.flu-dyn↗

arXiv2019

Dynamics of spatially localized states in transitional plane Couette flow

Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider $\textit{et al.}$ 2010a). These branches can be used to generate a number of spatially localized initial conditions whose transition can be investigated. From the low Reynolds numbers where homoclinic snaking is first observed ($Re < 175$) to transitional ones ($Re \approx 325$), these spatially localized states traverse various regimes where their relaminarisation time and dynamics are affected by the dynamical structure of phase space. These regimes are reported and characterised in this paper for a $4π$ periodic domain in the streamwise direction as a function of the two remaining variables: the Reynolds number and the width of the localized pattern. Close to the snaking, localized states are attracted by spatially localized periodic orbits before relaminarising. At larger values of the Reynolds number, the flow enters a chaotic transient of variable duration before relaminarising. Very long chaotic transients ($t > 10^4$) can be observed without difficulty for relatively low values of the Reynolds number ($Re \approx 250$).

physics.flu-dyn↗

arXiv2017

Bounds on heat transfer for Bénard-Marangoni convection at infinite Prandtl number

The vertical heat transfer in Bénard-Marangoni convection of a fluid layer with infinite Prandtl number is studied by means of upper bounds on the Nusselt number $Nu$ as a function of the Marangoni number $Ma$. Using the background method for the temperature field, it has recently been proven by Hagstrom & Doering that $ Nu\leq 0.838\,Ma^{2/7}$. In this work we extend previous background method analysis to include balance parameters and derive a variational principle for the bound on $Nu$, expressed in terms of a scaled background field, that yields a better bound than Hagstrom & Doering's formulation at a given $Ma$. Using a piecewise-linear, monotonically decreasing profile we then show that $Nu \leq 0.803\,Ma^{2/7}$, lowering the previous prefactor by 4.2%. However, we also demonstrate that optimisation of the balance parameters does not affect the asymptotic scaling of the optimal bound achievable with Hagstrom & Doering's original formulation. We subsequently utilise convex optimisation to optimise the bound on $Nu$ over all admissible background fields, as well as over two smaller families of profiles constrained by monotonicity and convexity. The results show that $Nu \leq O(Ma^{2/7}(\ln Ma)^{-1/2})$ when the background field has a non-monotonic boundary layer near the surface, while a power-law bound with exponent 2/7 is optimal within the class of monotonic background fields. Further analysis of our upper-bounding principle reveals the role of non-monotonicity, and how it may be exploited in a rigorous mathematical argument.

physics.flu-dyn↗

arXiv2017

Correlated electron-hole mechanism for molecular doping in organic semiconductors

The electronic and optical properties of the paradigmatic F4TCNQ-doped pentacene in the low-doping limit are investigated by a combination of state-of-the-art many-body \emph{ab initio} methods accounting for environmental screening effects, and a carefully parametrized model Hamiltonian. We demonstrate that while the acceptor level lies very deep in the gap, the inclusion of electron-hole interactions strongly stabilizes dopant-semiconductor charge transfer states and, together with spin statistics and structural relaxation effects, rationalize the possibility for room-temperature dopant ionization. Our findings reconcile available experimental data, shedding light on the partial vs. full charge transfer scenario discussed in the literature, and question the relevance of the standard classification in shallow or deep impurity levels prevailing for inorganic semiconductors.

cond-mat.mtrl-sci↗