Indentation of a floating elastic sheet: Geometry versus applied tension

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force--indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations the force--indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.Comment: 24 pages, revised version submitted to Proc. R. Soc.

Wettability-independent droplet transport by \emph{Bendotaxis}

We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful means of transporting droplets in technological applications, for example in developing self-cleaning surfaces, and discuss the implications of our results for such applications.Comment: 5 pages, 4 figures. Supplementary Information available on reques

Dynamics of wrinkling in ultrathin elastic sheets

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic balance between the object's bending stiffness and an effective substrate stiffness, which may originate from a true substrate stiffness or from tension and curvature along the wrinkles. Here we investigate dynamic wrinkling, induced by the impact of a solid sphere onto an ultra-thin polymer sheet floating on water. The vertical deflection of the sheet's centre induced by impact draws material radially inwards, resulting in an azimuthal compression that is relieved by the wrinkling of the entire sheet. We show that this wrinkling is truly dynamic, exhibiting features that are qualitatively different to those seen in quasi-static wrinkling experiments. Moreover, we show that the wrinkles coarsen dynamically because of the inhibiting effect of the fluid inertia. This dynamic coarsening can be understood heuristically as the result of a dynamic stiffness, which dominates the static stiffnesses reported thus far, and allows new controls of wrinkle wavelength.Comment: 8 pages, 4 figures. Please see published version for supplementary movies and SI Appendi

The propagation of air fingers into an elastic branching network

We study experimentally the propagation of an air finger through the Y-bifurcation of an elastic, liquid-filled Hele-Shaw channel, as a benchtop model of airway reopening. With channel compliance provided by an elastic upper boundary, we can impose collapsed channel configurations into which we inject air with constant volume-flux. We typically observe steady finger propagation in the main channel, which is lost ahead of the Y-bifurcation but subsequently recovered in the daughter channels. At low levels of initial collapse, steady finger shapes and bubble pressure in the daughter channels map onto those in the main channel, despite small differences in initial collapse in different parts of the Y-channel. However, at higher levels of initial collapse where the elastic sheet almost touches the bottom boundary of the channel, experimentally indistinguishable fingers in the main channel can lead to multiple states of reopening of the daughter channels. The downstream distance at which steady propagation is recovered in the daughter channels also varies considerably with injection flow rate and initial collapse because of a transition in the mechanics regulating finger propagation. We find that the characteristic time and length-scales of this recovery are largest in the regime where viscous and surface tension forces dominate at low flow rate and/or low initial collapse, and that they decrease towards a constant plateau reached in the limit where elastic and surface tension forces balance at high flow rate and/or high initial collapse. Our findings suggest that practical networks are unlikely to comprise long enough channels for steady state propagation to remain established.Comment: 36 pages, 13 finger

Impact on floating thin elastic sheets: A mathematical model

We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time $t$ after impact, the transverse wave is located at a radial distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim t^{2/3}$ scaling observed for capillary--inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor, but subsequently addressing a finite-radius spherical impactor, contrasting this case with the classic Wagner theory of impact. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the geometrically-imposed compression without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments, and we compare our predictions with experimental data.Comment: 30 pages, 9 figures. Small edits toaccepted versio

Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.Comment: Submitted to the Astrophysical Journa

Granular segregation in a thin drum rotating with periodic modulation

We present the results of an experimental investigation into the effects of a sinusoidal modulation of the rotation rate on the segregation patterns formed in thin drum of granular material. The modulation transforms the base pattern formed under steady conditions by splitting or merging the initial streaks. Specifically, the relation between the frequency of modulation and the rotation rate determines the number of streaks which develop from the base state. The results are in accord with those of Fiedor and Ottino [J. Fluid. Mech. 533, 223 (2005)10.1017/S0022112005003952], and we show that their ideas apply over a wide range of parameter space. Furthermore, we provide evidence that the observed relationship is maintained for filling fractions far from 50% and generalize the result in terms of the geometry of the granular deposit

Is the combination of immunotherapy and radiotherapy in non-small cell lung cancer a feasible and effective approach?

For many years, conventional oncologic treatments such as surgery, chemotherapy, and radiotherapy (RT) have dominated the field of non-small-cell lung cancer (NSCLC). The recent introduction of immunotherapy (IT) in clinical practice, especially strategies targeting negative regulators of the immune system, so-called immune checkpoint inhibitors, has led to a paradigm shift in lung cancer as in many other solid tumors. Although antibodies against programmed death protein-1 (PD-1) and programmed death ligand-1 (PD-L1) are currently on the forefront of the immuno-oncology field, the first efforts to eradicate cancer by exploiting the host's immune system date back to several decades ago. Even then, researchers aimed to explore the addition of RT to IT strategies in NSCLC patients, attributing its potential benefit to local control of target lesions through direct and indirect DNA damage in cancer cells. However, recent pre-clinical and clinical data have shown RT may also modify antitumor immune responses through induction of immunogenic cell death and reprogramming of the tumor microenvironment. This has led many to reexamine RT as a partner therapy to immuno-oncology treatments and investigate their potential synergy in an exponentially growing number of clinical trials. Herein, the authors review the rationale of combining IT and RT across all NSCLC disease stages and summarize both historical and current clinical evidence surrounding these combination strategies. Furthermore, an overview is provided of active clinical trials exploring the IT-RT concept in different settings of NSCLC