Spanwise variations in membrane flutter dynamics C. Mavroyiakoumou and S. Alben,
J. Fluids Struct. 130 (2024) 104194
We study spanwise nonuniformity in the flutter of rectangular membranes in 3-D inviscid flows. With spanwise symmetric and asymmetric initial perturbations, the motions eventually reach the same steady state in most cases, typically with spanwise asymmetric oscillations. ‘‘Side-to-side’’ and other standing wave and traveling wave motions propagate along the span, particularly with free side-edges. A large Poisson ratio gives somewhat smoother spatial and temporal features. Increasing the aspect ratio makes the deflection more uniform along the span. (ArXiv)

Optimal wall shapes and flows for steady planar convection S. Alben, J. Fluid Mech. (984) A43, 2024
We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer (Nu) between hot and cold walls, for a given rate of viscous dissipation by the flow. We show theoretically that flat walls are optimal in the case of no flow, and up to a critical nonzero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a scaling of horizontal lengths as Pe^-1/3, where Pe is the Peclet number. The corresponding rate of heat transfer Nu scales as Pe^2/3. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large Pe. (ArXiv)

Transition to branching flows in optimal planar convection S. Alben, Phys. Rev. Fluids (8) 074502, 2023
Fluid flow structures that enhance heat transfer are important in many natural and technological settings. Here we compute the steady planar incompressible fluid flows that maximize the rate of heat transfer from a solid surface, for various rates of viscous energy dissipation. We find a transition from rectangular convection rolls to flows that branch near the boundary. These flows may be related to branching flows that have been predicted theoretically and computed in three dimensions. (ArXiv)

Membrane flutter in three-dimensional inviscid flow C. Mavroyiakoumou and S. Alben, J. Fluid Mech. (953) A32--1-38, 2022
We study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3-D) inviscid fluid flow. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension and stretching rigidity. We find that the 3-D dynamics in the 12 cases naturally forms four groups based on the conditions at the leading and trailing edges. The conditions at the side edges, although generally less important, may have small or large qualitative effects on the membrane dynamics – e.g. steady vs unsteady, periodic vs chaotic or the variety of spanwise curvature distributions – depending on the group and the physical parameter values. (ArXiv)

Efficient bending and lifting patterns in snake locomotion S. Alben, Proc. Roy. Soc. A (478) 20220312, 2022
We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10-100% higher. (ArXiv)

Efficient sliding locomotion of three-link bodies with inertia A. Earnst and S. Alben, Phys. Rev. E (106) 044404, 2022
Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the body inertia. The optimal inertia is nonnegligible when the coefficient of friction for sliding transverse to the body axis is small. Inertia is also significant in a few cases with relatively large coefficients of friction for transverse and backward sliding, and here the optimal motions are less sensitive to the inertia parameter. For some of the optimal motions with significant inertia we find dramatic reductions in efficiency when the inertia parameter is decreased to zero. For the motions that are optimal with zero inertia, the efficiency decreases more gradually when we raise the inertia to moderate and large values. (ArXiv)

Packing of elastic rings with friction S. Alben, Proc. Roy. Soc. A (478) 20210742, 2022
We study the deformations of elastic filaments confined within slowly shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiralling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the −3/2 and −2 powers, respectively. With non-zero friction, the elastic energy follows a similar scaling but with a prefactor up to eight times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall. (ArXiv)

Dynamics of flags over wide ranges of mass and bending stiffness S. Alben, Phys. Rev. Fluids (7) 013903, 2022
There have been many studies of the instability of a flexible plate or flag to flapping motions, and of large-amplitude flapping. Here we use inviscid simulations and a linearized model to more generally study how key quantities—mode number (or wave number), frequency, and amplitude—depend on the two dimensionless parameters: flag mass and bending stiffness. In the limit of small flag mass, flags perform traveling wave motions that move at nearly the speed of the oncoming flow. The flag mode number scales as the −1/4 power of bending stiffness. The flapping frequency has the same scaling, with an additional slight increase with flag mass in the small-mass regime. The flapping amplitude scales approximately as flag mass to the 1/2 power. In a linearized model, the fastest growing modes have somewhat different power law scalings for wave number and frequency. We discuss how the numerical scalings are consistent with a weakly nonlinear model. (ArXiv)

Inverse design of self-oscillatory gels through deep learning D. Aksoy, S. Alben, R.D. Deegan, and A.A. Gorodetsky, Neural Computing and Applications, 2022
We develop a deep learning architecture for inverse design of a self-oscillating sheet propelled by an embedded chemical reaction. The dynamics of our problems are nonlinear and exhibit chaotic behavior, a challenging setting for existing deep-learning-based inverse design approaches. The aim is to explore data-driven design of soft robots using a novel locomotion mechanism. We train the architecture using a forward model of the locomotion mechanism. The architecture is shown to successfully map a snapshot of target motions of the gel into geometric and reaction parameters. Our inverse design setting is unique in that it considers both discrete and continuous outputs, requiring an architecture capable of classification and regression. Because the motion has a chaotic quality, our demonstration is able to show quantitative agreement for a small time horizon and qualitative agreement over longer time horizons.

Dynamics of tethered membranes in inviscid flow C. Mavroyiakoumou and S.Alben, J. Fluids Struct. (107) 103384-1--30, 2021
We investigate the dynamics of membranes that are held by freely-rotating rigid tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations in terms of deflection amplitudes, dominant periods, and numbers of local extrema of deflection along the membranes across the parameter space of membrane mass density, stretching modulus, pretension, and tether length. We determine the region of instability and the small-amplitude behavior by solving a nonlinear eigenvalue problem. We also consider an infinite periodic membrane model, which yields a regular eigenvalue problem, analytical results, and asymptotic scaling laws. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of membrane mass, pretension, and tether length/stiffness.(ArXiv)

Efficient sliding locomotion of three-link bodies S. Alben, Phys. Rev. E (103) 042414-1--18, 2021
We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into regions with distinct types of efficient kinematics: lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. A stochastic optimization algorithm finds that optimal kinematics are close to elliptical trajectories in most cases, except for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar, and relative efficiencies are much lower except with very large normal friction. (ArXiv)

Eigenmode analysis of membrane stability in inviscid flow
C. Mavroyiakoumou and S.Alben, Phys. Rev. Fluids (6) 043901-1--32, 2021
We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become ``wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.(ArXiv)

Collective locomotion of two-dimensional lattices of flapping plates. Part 2. Lattice flows and propulsive efficiency S. Alben, J. Fluid Mech. (915) A21-1--25, 2021
We study propulsion of rectangular and rhombic lattices of flapping plates at O(10–100) Reynolds numbers in incompressible flow. We classify the propulsive performances of the lattices and the periodicities of the flows with respect to flapping amplitude and frequency, horizontal and vertical spacings between plates, and oncoming flow velocity. Non-periodic states are most common at small streamwise spacing, large lateral spacing and large Reynolds number. Lattices that are closely spaced streamwise shed intense vortex dipoles. The flows transition sharply from drag- to thrust-producing at critical flow speeds, and pass through a variety of periodic and non-periodic states. Multiple stable self-propelled speeds can occur. As the streamwise spacing increases (and with large lateral spacing), the plates may shed vortex streets that impinge on downstream neighbors. With small lateral spacing, the rectangular lattices yield net drag, while the rhombic lattices may generate net thrust efficiently. As lateral spacing increases, the two types of flows converge. The lattices’ maximum Froude efficiencies exceed those of an isolated plate by a factor that grows with decreasing Re, exceeding two at Re = 70. (ArXiv)

Collective locomotion of two-dimensional lattices of flapping plates. Part 1. Numerical method, single-plate case and lattice input power S. Alben, J. Fluid Mech. (915) A20-1--28, 2021
We propose a model and numerical method for the propulsion of rectangular and rhombic lattices of flapping plates at O(10–100) Reynolds numbers in incompressible flow. We use an adaptive mesh to mitigate singularities at the plates’ edges, and find convergence rates in a test problem. We then establish benchmark results for a single flapping plate, including vortex wake characteristics and Froude efficiency over ranges of flapping amplitude, frequency and Strouhal number. As a prelude to a study of propulsive efficiency in Part 2, we study a key ingredient: the time-averaged input power in lattices of plates. Scaling laws for the mean input power are estimated in the limits of small and large streamwise spacings, using steady flow models with small-gap and Poiseuille-like flows between the plates respectively in the two limits. (ArXiv)

Intermittent sliding locomotion of a two-link body S. Alben and C. Puritz, Phys. Rev. E (101) 052613-1--20, 2020
We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. The anisotropy ratio of the sliding friction coefficients is a key parameter. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes. We find these motions in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively, and with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction. (ArXiv)

Large-amplitude membrane flutter in inviscid flow C. Mavroyiakoumou and S. Alben, J. Fluid Mech. (891) A23--1-24, 2020
We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional inviscid fluid flows. The dynamics depend on three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically or aperiodically (at larger mass density). With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow. (ArXiv) Movie

Semi-implicit methods for the dynamics of elastic sheets S. Alben, A. A. Gorodetsky, D. Kim, and R.D. Deegan, J. Comp. Phys. (399) 108952--1-17, 2019
Recent applications (e.g. active gels and the self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints of explicit methods. For a triangular lattice discretization, our semi-implicit approach is stable for all time steps in the case of overdamped dynamics. For a more general finite-difference formulation that can allow for general elastic constants, we use the analogous approach on a square grid, and find that the largest stable time step is two to three orders of magnitude greater than for an explicit scheme. For a model problem with a radial traveling wave form of the reference metric, we find transitions from quasi-periodic to chaotic dynamics as the sheet thickness is reduced, wave amplitude is increased, and damping constant is reduced. (ArXiv)

Efficient sliding locomotion with isotropic friction S. Alben, Phys. Rev. E (99) 062402--1-17, 2019
Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction.We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction. (ArXiv)

Dynamics and locomotion of flexible foils in a frictional environment X. Wang and S. Alben, Proc. Roy. Soc. A (474) 2209:20170503--1-20, 2018
We study the dynamics of snake-like bodies (flexible foils) under frictional forces to understand the physics of locomotion by passive appendages in terrestrial environments. When a flexible foil is oscillated by heaving at one end but is not free to locomote, the dynamics change from periodic to non-periodic and chaotic as the heaving amplitude increases or the bending rigidity decreases. Resonant peaks and bistable states are observed. When the foil is free to locomote, the horizontal motion smoothes the resonant peaks. Locomotion is steady but slow at moderate frictional coefficients, and faster at larger transverse friction and small tangential friction corresponding to wheeled snake robots. Here travelling wave motions arise spontaneously, and move with horizontal speeds that scale as transverse friction coefficient to the power 1/4 and input power that scales as the transverse friction coefficient to the power 5/12. These scalings correspond to boundary layers near the foil’s leading edge. (ArXiv)

Intracellular localization of nanoparticle dimers by chirality reversal
M. Sun, L. Xu, J.H. Bahng, H. Kuang, S. Alben, N.A. Kotov, and C. Xu. Nature Communications (8), 1847--1-10, 2017
The intra- and extracellular positioning of plasmonic nanoparticles (NPs) can dramatically alter their curative/diagnostic abilities and medical outcomes. Here we show that the chiroptical activity of DNA-bridged NP dimers allows one to follow the process of internalization of the particles by mammalian cells and to distinguish their extra- vs intra-cellular localizations by real-time spectroscopy in ensemble. This finding opens the door for spectroscopic targeting of plasmonic nanodrugs and quantitative assessment of nanoscale interactions.

Improved convection cooling in steady channel flows
S. Alben, Phys. Rev. Fluids (2), 104501--1-26, 2017
Convective cooling of the heated walls of a 2D channel is a benchmark problem with recent applications. We find steady flows that maximize the heat removed from fixed-temperature walls for a given rate of energy used to drive the flow, Pe². These flows have a boundary layer structure, and heat transfer proportional to Pe^2/5, an improvement over the Pe^1/3 scaling of Poiseuille flow.

Optimal convection cooling flows in general 2D geometries S. Alben, J. Fluid Mech. (814) 484-509, 2017 We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with a hot interior and cold exterior.

Enhanced convection heat transfer using small-scale vorticity concentrations effected by flow-driven, aeroelastically vibrating reeds
A. Glezer, R. Mittal, and S. Alben, Air Force Research Laboratory Technical Report, 2016
We use experimental/modeling/numerical approaches to study the formation, shedding, and advection of small-scale vortical motions induced by autonomous, aeroelastic fluttering of a cantilevered thin-film reed at the centerplane of a rectangular air channel. The flow mechanisms and scaling of the interactions between the reeds and the channel flow were explored to develop the fundamental knowledge needed to overcome the limits of forced convection heat transport from air-side heat exchangers at low (laminar or transitional) Reynolds numbers.

Fluid–structure interactions with applications to biology W.-X. Huang and S. Alben, Acta Mechanica Sinica 32 (6): 977-979, 2016
Introduction to a thematic issue.

Stability and scalability of piezoelectric flags X.Wang, S. Alben, C. Li, and Y.L. Young. Phys. Fluids (28) 023601-1-19, 2016
We investigate the effect of piezoelectric material on the flutter speed, vibration mode and frequency, and energy harvesting power and efficiency of a flexible flag. We develop a fully coupled fluid-solid-electric model by combining the inviscid vortex sheet model with a linear electro-mechanical coupling model. A consistent optimal resistance is found that maximizes the flutter speed and the energy harvesting power. For a resonant RL circuit, by tuning the inductance to match the circuit frequency to the flag’s vibration frequency, the flutter speed can be greatly decreased, and a larger averaged power and efficiency are obtained. We find that the resistance only circuit is more effective when the flag is placed in a lighter fluid (e.g., air), while the RL circuit is able to reduce the flutter speed when the flag is placed in a heavier fluid (e.g., water).

The dynamics of vortex streets in channels
X.Wang and S. Alben, Phys. Fluids, (27) 073603-1-15, 2015
We study the dynamics of regular and reverse von Karman vortex streets in channels. Reverse streets maintain their structure while regular vortex streets undergo inversion. We find a transition to asymmetry when the vortices are strong, viscosity is low, or the street is compressed horizontally or extended vertically.

Passive Vibration Control of Flexible Hydrofoils using Piezoelectric Material
C. Li, E.J. Chae, Y.L. Young, X. Wang, and S. Alben. Fourth International Symposium on Marine Propulsors, 2015.
This work explores the use of a piezoelectric material for passive vibration control of a cantilevered, flexible hydrofoil. The integrated fluid-solid-electrical response is modeled by coupling a 2-D viscous unsteady Reynolds Averaged Navier Stokes (uRANS) solver for the fluid with a two-degrees-of-freedom (2-DOF) solid model, which is coupled with the circuit equation. The results show that activation of the PZT circuit increases the vibration frequencies, as the electromechanical coupling force adds an additional contribution to the system stiffness. The changes in system stiffness and response frequency depend on the resistance. A well-tuned resistor in parallel with a PZT circuit can be used to delay flutter and control flow-induced vibrations.