arXiv subjects

Michael Gomez

Publications and source records attributed to Michael Gomez.

15 recordsLinked to original sources

arXiv2025

Self-locking and Stability of the Bowline Knot

We investigate the self-locking of the bowline knot through numerical simulations, experiments, and theoretical analysis. Specifically, we perform two complementary types of simulations using the 3D finite-element method (FEM) and a reduced-order model based on the discrete-element method (DEM). For the FEM simulations, we develop a novel mapping technique that automatically transforms the centerline of the rod into the required knot topology prior to loading. In parallel, we conduct experiments using a nearly inextensible elastic rod tied into a bowline around a rigid cylinder. One end of the rod is pulled to load the knot while the other is left free. The measured force-displacement response serves to validate both the FEM and DEM simulations. Leveraging these validated computational frameworks, we analyze the internal tension profile along the rod's centerline, revealing that a sharp drop in tension concentrates around a strategic locking region, whose geometry resembles that observed in other knot types. By considering the coupling of tension, bending, and friction, we formulate a theoretical model inspired by the classic capstan problem to predict the stability conditions of the bowline, finding excellent agreement with our FEM and DEM simulations. Our methodology and findings offer new tools and insights for future studies on the performance and reliability of other complex knots.

cond-mat.soft↗

arXiv2024

Effective extensional-torsional elasticity and dynamics of helical filaments under distributed loads

We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an 'equivalent-rod' theory from the Kirchhoff rod equations: the helical filament is described as a naturally-straight rod (aligned with the helix axis) for which the extensional and torsional deformations are coupled. Importantly, our analysis is asymptotically exact in the limit of a 'highly-coiled' filament (when the helical wavelength is much smaller than the characteristic lengthscale over which the filament bends due to external loading) and is able to account for large, unsteady displacements. In addition, our analysis yields explicit conditions on the external loading that must be satisfied for a straight helix axis. In the small-deformation limit, we exactly recover the coupled wave equations used to describe the free vibrations of helical coil springs, thereby justifying previous equivalent-rod approximations in which linearised stiffness coefficients are assumed to apply locally and dynamically. We then illustrate our theory with two loading scenarios: (I) a heavy helical rod deforming under its own weight; and (II) the dynamics of axial rotation (twirling) in viscous fluid, which may be considered as a simple model for a bacteria flagellar filament. In both scenarios, we demonstrate excellent agreement with solutions of the full Kirchhoff rod equations, even beyond the formal limit of validity of the highly-coiled assumption. More broadly, our analysis provides a framework to develop reduced models of helical rods in a wide variety of physical and biological settings, and yields analytical insight into their elastic instabilities. In particular, our analysis indicates that tensile instabilities are a generic phenomenon when both distributed forces and moments are present.

cond-mat.soft↗

arXiv2023

The Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space

In this paper we study the Gauss map of hypersurfaces with constant weighted mean curvature in the Gaussian space. We show that if the image of the Gauss map is in a closed hemisphere, then the hypersurface is a hyperplane or a generalized cylinder. We also show that if the image of the Gauss map is in $S^{n}\setminus\bar{S}_{+}^{n-1}$, then the hypersurface is a hyperplane. This generalizes previous results for self-shrinkers obtained by Ding-Xin-Yang.

math.DG↗

arXiv2023

Gyrophilia: Harnessing Centrifugal and Euler Forces for Tunable Buckling of a Rotating Elastica

We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent `fictitious' (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an angular acceleration around a fixed axis, we demonstrate that centrifugal and Euler forces can be combined to produce tunable structural deformation. Specifically, using an imposed acceleration ramp, the buckling onset of a cantilevered beam can be precisely tuned and its deformation direction selected. In a second configuration, a pre-arched beam can be made to snap, on demand, between its two stable states. We also formulate a theoretical model rooted in Euler's elastica that rationalizes the problem and provides predictions in excellent quantitative agreement with the experimental data. Our findings demonstrate an innovative approach to programmable actuation of slender rotating structures.

cond-mat.soft↗

arXiv2023

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.

cond-mat.soft↗

arXiv2022

Integration of discrete-event dynamics and machining dynamics for machine tool: modeling, analysis and algorithms

Machining dynamics research lays a solid foundation for machining operations by providing stable combinations of spindle speed and depth of cut. Furthermore, machine learning has been applied to predict tool life as a function of cutting speed. However, the existing research does not consider the discrete-event dynamics in machine shop, i.e., the machine tool needs to process a series of parts in queue under various practical production requirements. This paper addresses the integration of discrete-event dynamics and machining dynamics to achieve cost savings in machining. We first propose a learning-based cost function for the studied integrated optimization problem of machine tool. The proposed cost function utilizes the predicted tool life under different stable cutting speeds for further optimizing speed selection of machine tool to deal with the discrete-event dynamics in machine shop. Then, according to the practical production requirements, we develop several mathematical optimization models for the related integrated optimization problems with the consideration of cost, makespan and due date. Numerical results show the effectiveness of our proposed methods and also the potential to be used in practice.

math.DS↗

arXiv2020

Delayed bifurcation in elastic snap-through instabilities

We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. We study when and how the arch transitions between states and show that the end-shortening at which the fast 'snap' happens depends on the rate at which the end-shortening is reduced. This lag in snap-through is a consequence of delayed bifurcation and occurs even in the perfectly elastic case when viscous (and viscoelastic) effects are negligible. We present the results of numerical simulations to determine the magnitude of this lag as the loading rate and the importance of external viscous damping vary. We also present an asymptotic analysis of the geometrically-nonlinear problem that reduces the salient dynamics to that of an ordinary differential equation; the form of this reduced equation is generic for snap-through instabilities in which the relevant control parameter is ramped linearly in time. Moreover, this asymptotic reduction allows us to derive analytical results for the observed lag in snap-through that are in good agreement with the numerical results of our simulations. Finally, we discuss scaling laws for the lag that should be expected in other examples of delayed bifurcation in elastic instabilities.

cond-mat.soft↗

arXiv2020

Regional Flood Risk Projections under Climate Change

Flood-related risks to people and property are expected to increase in the future due to environmental and demographic changes. It is important to quantify and effectively communicate flood hazards and exposure to inform the design and implementation of flood risk management strategies. Here we develop an integrated modeling framework to assess projected changes in regional riverine flood inundation risks. The framework samples climate model outputs to force a hydrologic model and generate streamflow projections. Together with a statistical and hydraulic model, we use the projected streamflow to map the uncertainty of flood inundation projections for extreme flood events. We implement the framework for rivers across the state of Pennsylvania, United States. Our projections suggest that flood hazards and exposure across Pennsylvania are overall increasing with future climate change. Specific regions, including the main stem Susquehanna River, lower portion of the Allegheny basin and central portion of Delaware River basin, demonstrate higher flood inundation risks. In our analysis, the climate uncertainty dominates the overall uncertainty surrounding the flood inundation projection chain. The combined hydrologic and hydraulic uncertainties can account for as much as 37% of the total uncertainty. We discuss how this framework can provide regional and dynamic flood-risk assessments and help to inform the design of risk-management strategies.

stat.AP↗

arXiv2019

Phonon and Thermal Properties of Quasi-Two-Dimensional FePS3 and MnPS3 Antiferromagnetic Semiconductor Materials

We report results of investigation of the phonon and thermal properties of the exfoliated films of layered single crystals of antiferromagnetic FePS3 and MnPS3 semiconductors. The Raman spectroscopy was conducted using three different excitation lasers with the wavelengths of 325 nm (UV), 488 nm (blue), and 633 nm (red). The resonant UV-Raman spectroscopy reveals new spectral features, which are not detectable via visible Raman light scattering. The thermal conductivity of FePS3 and MnPS3 thin films was measured by two different techniques: the steady-state Raman optothermal and transient time-resolved magneto-optical Kerr effect. The Raman optothermal measurements provided the orientation-average thermal conductivity of FePS3 to be 1.35 W/mK at room temperature. The transient measurements revealed that the through-plane and in-plane thermal conductivity of FePS3 is 0.85 W/mK and 2.7 W/mK, respectively. The films of MnPS3 have higher thermal conductivity of 1.1 W/mK through-plane and 6.3 W/mK in-plane. The data obtained by both techniques reveal strong thermal anisotropy of the films and the dominant contribution of phonons to heat conduction. Our results are important for the proposed applications of the antiferromagnetic semiconductor thin films in spintronic devices.

cond-mat.mtrl-sci↗

arXiv2018

Dynamics of viscoelastic snap-through

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an `inverted' shape that snaps to a `natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays `pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.

cond-mat.soft↗

arXiv2018

Pull-in dynamics of overdamped microbeams

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations --- an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.

physics.app-ph↗

arXiv2017

The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling'

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by `mirror buckling' --- a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the shell to buckle azimuthally.

cond-mat.soft↗

arXiv2017

Delayed pull-in transitions in overdamped MEMS devices

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pull-in transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including state-of-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.

physics.app-ph↗

arXiv2017

Critical slowing down in purely elastic `snap-through' instabilities

Many elastic structures have two possible equilibrium states: from umbrellas that become inverted in a sudden gust of wind, to nano-electromechanical switches, origami patterns and the hopper popper, which jumps after being turned inside-out. These systems typically transition from one state to the other via a rapid `snap-through'. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions, as in the Venus flytrap. Similarly, the beak of the hummingbird snaps through to catch insects mid-flight, while technological applications are increasingly exploiting snap-through instabilities. In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. Here, we study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena, and provides a handheld demonstration of such phenomena, as well as a new tool for tuning dynamic responses in applications of elastic bistability.

cond-mat.soft↗

arXiv2017

Passive control of viscous flow via elastic snap-through

We demonstrate the passive control of viscous flow in a channel by using an elastic arch embedded in the flow. Depending on the fluid flux, the arch may `snap' between two states --- constricting and unconstricting --- that differ in hydraulic conductivity by up to an order of magnitude. We use a combination of experiments at a macroscopic scale and theory to study the constricting and unconstricting states, and determine the critical flux required to transition between them. We show that such a device may be precisely tuned for use in a range of applications, and in particular has potential as a passive microfluidic fuse to prevent excessive fluxes in rigid-walled channels.

cond-mat.soft↗