An official website of the United States government
We study in this work the so-called "instantaneous time mirrors" in the context of surface plasmons. The latter are associated with high frequency waves at the surface of a conducting sheet. Instantaneous time mirrors were introduced in [3], with the idea that singular perturbations in the time variable in a wave-type equation create a time-reversed focusing wave. We consider the time-dependent three-dimensional Maxwell's equations, coupled to Drude's model for the description of the surface current. The time mirror is modeled by a sudden, strong, change in the Drude weight of the electrons on the sheet. Our goal is to characterize the time-reversed wave, in particular to quantify the quality of refocusing. We establish that the latter depends on the distance of the source to the sheet, and on some physical parameters such as the relaxation time of the electrons. We also show that, in addition to the plasmonic wave, the time mirror generates a free propagating wave that offers, contrary to the surface wave, some resolution in the direction orthogonal to the sheet. Blurring effects due to non-instantaneous mirrors are finally investigated.
more »
« less
Fifty years of Schallamach waves: from rubber friction to nanoscale fracture
The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such systems commonly show interesting stick–slip dynamics, wherein the interface moves intermittently despite uniform remote loading. The year 2021 marked the 50th anniversary of the publication of a seminal paper by Adolf Schallamach ( Wear , 1971), which first revealed an intimate link between stick–slip and moving detachment waves, now called Schallamach waves. We place Schallamach’s results in a broader context and review subsequent investigations of stick–slip, before discussing recent observations of solitary Schallamach waves. This variant is not observable in standard contacts so that a special cylindrical contact must be used to quantify its properties. The latter configuration also reveals the occurrence of a dual wave—the so-called separation pulse—that propagates in a direction opposite to Schallamach waves. We show how the dual wave and other, more general, Schallamach-type waves can be described using continuum theory and provide pointers for future research. In the process, fundamental analogues of Schallamach-type waves emerge in nanoscale mechanics and interface fracture. The result is an ongoing application of lessons learnt from Schallamach-type waves to better understand these latter phenomena. This article is part of the theme issue ‘Nanocracks in nature and industry’.
more »
« less
- Award ID(s):
- 2100568
- PAR ID:
- 10397682
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 380
- Issue:
- 2232
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
ABSTRACTDrilling vibrations can cause inefficient drilling and accelerated damage to system components. Therefore, reducing or eliminating such vibrations is a major focus area for natural gas and geothermal drilling applications. One particularly important vibration mode is stick-slip. Stick-slip occurs when the bottom-hole angular velocity starts oscillating while the top hole angular velocity remains relatively constant. This not only causes poor drilling, it is also difficult to detect using surface sensors. In this work, we describe the development and testing of a benchtop drilling system for studying stick-slip dynamics and mitigation. We show how this system can produce stick-slip oscillations. Next, we use this data to formulate a data-driven rock-bit interaction model. This model can be combined with linear systems analysis to predict stick-slip and understand mitigation methods. We describe out instrumentation that enables closed-loop control under simulated communications constraints. We conclude by providing preliminary experimental data on bench-level stick-slip. INTRODUCTIONExploration via autonomous drilling processes for geothermal resources is an important focus area for drilling research. However, to fully realize the clean-energy promise of geothermal energy, key challenges still need to be resolved.Issues arising in the drilling process often originate from a drillstring's increased susceptibility to vibrational oscillations as depths increase. Some examples of drilling vibrations include stick-slip (Navarro-Lopez and Suarez, 2004), bit-bounce (Spanos et al., 1995), and whirl (Jansen, 1991). Torsional oscillations are the focus of this work.Torsional vibrations result in a destructive phenomenon known as stick-slip. Initiated at the bit-rock surface, the drillstring bit experiences large angular velocity oscillations not seen at the surface (Pavone and Desplans, 1994; Besselink et al., 2011; Kessai et al., 2020). Stick-slip results in premature bit wear and drillstring fracture.Stick-slip is a fundamentally nonlinear and unpredictable phenomena. Stick-slip results from the combination of bit-rock interactions and drillstring compliance. As a result, there is a key need for experimental studies of stick-slip dynamics and mitigation.more » « less
-
Abstract Faults can release energy via a variety of different slip mechanisms ranging from steady creep to fast and destructive earthquakes. Tying the rheology of the crust to various slip dynamics is important for our understanding of plate tectonics and earthquake generation. Here we propose that the interplay of fractures and viscous flow leads to a spectrum between stick‐slip and creep. We use an elasto‐visco‐plastic rock analog (Carbopol U‐21) where we vary the yield stress to investigate its impact on slip dynamics in shear experiments. The experiments are performed using a simple shear apparatus, which provides distributed shear across the entire width of the experiment and allows in situ observations of deformation. We record force and displacement during deformation and use time lapse photography to document fracture development. A low yield stress (25 Pa) leads to creep dynamics in the absence of fractures. An intermediate yield stress (144 Pa) leads to the development and interaction of opening (mode I) and shear (mode II) fractures. This interaction leads to a spectrum in slip dynamics ranging from creep to stick‐slip. A high yield stress (357 Pa) results in the development of many mode I fractures and a deformation signal dominated by stick‐slip. These results show that bulk yield stress, fracture formation, and slip dynamics are closely linked and can lead to a continuum between creep and stick‐slip. We suggest that rheology should be considered as an additional mechanism to explain the broad range of slip dynamics in natural faults.more » « less
-
Abstract Many natural faults are believed to consist of velocity weakening (VW) patches surrounded by velocity strengthening (VS) sections. Numerical studies routinely employ this framework to study earthquake sequences including repeating earthquakes. In this laboratory study, we made a VW asperity, of lengthL, from a bare Poly(methyl methacrylate) PMMA frictional interface and coated the surrounding interface with Teflon to make VS fault sections. Behavior of this isolated asperity was studied as a function ofL(ranging from 100 to 400 mm) and the critical nucleation length, , which is inversely proportional to the applied normal stress (2–16 MPa). Consistent with recent numerical simulations, we observed aseismic slip for < 2, periodic slip for 2 < < 6, and non‐periodic slip for 10 < . Furthermore, we compared the experiments whereLwas contained by VS material to standard stick‐slip events whereLwas bounded by free surfaces (i.e.,L = the total sample length). The free surface case produced ∼10 times larger slip during stick‐slip events compared to the contained fault ruptures, even with identical . This disparity highlights how standard, complete‐rupture stick‐slip events differ from contained events expected in nature, due to both the free surface conditions and the heterogeneous normal stress along the fault near the free ends, as confirmed by Digital Image Correlation analysis. This study not only introduces the Teflon coating experimental technique for containing laboratory earthquake ruptures, but also highlights the utility of as a predictive parameter for earthquake behavior.more » « less
-
A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. ( Phys. Rev. Lett. , vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsta.2021.0339
