arXiv subjects

Sachin Goyal

Publications and source records attributed to Sachin Goyal.

32 records · Page 2Linked to original sources

arXiv2020

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Initially straight slender elastic rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is also known that beyond a critical value of the pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Recently, we showed that pre-stressed planar shapes when immersed in a dissipative fluid and animated by nonconservative follower forces exhibit stable large-amplitude flapping oscillations. Here, we use time-stepper methods to analyze the three-dimensional instabilities and dynamics of pre-stressed planar and non-planar filament configurations when subject to active follower forces and dissipative fluid drag. First, we find that type of boundary constraint determines the nature of the non-linear patterns following instability. When the filament is clamped at one end and pinned at the other with follower forces directed towards the clamped end, we observe only stable planar (flapping) oscillations termed flapping result. When both ends are clamped however, we observe a secondary instability wherein planar oscillations are destabilized by off-planar perturbations and result in fully three-dimensional swirling patterns characterized by two distinct time-scales. The first time scale characterizes continuous and unidirectional swirling rotation around the end-to-end axis. The second time scale captures the rate at which the direction of swirling reverses or flips. The overall time over which the direction of swirling flips is very short compared to the long times over which the filament swirls in the same direction. Computations indicate that the reversal of swirling oscillations resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations.

nlin.PS↗

arXiv2020

Indoor Distance Estimation using LSTMs over WLAN Network

The Global Navigation Satellite Systems (GNSS) like GPS suffer from accuracy degradation and are almost unavailable in indoor environments. Indoor positioning systems (IPS) based on WiFi signals have been gaining popularity. However, owing to the strong spatial and temporal variations of wireless communication channels in the indoor environment, the achieved accuracy of existing IPS is around several tens of centimeters. We present the detailed design and implementation of a self-adaptive WiFi-based indoor distance estimation system using LSTMs. The system is novel in its method of estimating with high accuracy the distance of an object by overcoming possible causes of channel variations and is self-adaptive to the changing environmental and surrounding conditions. The proposed design has been developed and physically realized over a WiFi network consisting of ESP8266 (NodeMCU) devices. The experiment were conducted in a real indoor environment while changing the surroundings in order to establish the adaptability of the system. We introduce and compare different architectures for this task based on LSTMs, CNNs, and fully connected networks (FCNs). We show that the LSTM based model performs better among all the above-mentioned architectures by achieving an accuracy of 5.85 cm with a confidence interval of 93% on the scale of (4.14 m * 2.86 m). To the best of our knowledge, the proposed method outperforms other methods reported in the literature by a significant margin.

eess.SP↗

arXiv2019

Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces

Elastically driven filaments subjected to animating compressive follower forces provide a synthetic way to mimic the oscillatory beating of active biological filaments such as eukaryotic cilia. The dynamics of such active filaments can, under favorable conditions, exhibit stable time-periodic responses that result due to the interplay of elastic buckling instabilities, geometric constraints, boundary conditions, and dissipation due to fluid drag. In this paper, we use a continuum elastic rod model to estimate the critical follower force required for the onset of the stable time-periodic flapping oscillations in pre-stressed rods subjected to fluid drag. The pre-stress is generated by imposing either clamped-clamped or clamped-pinned boundary constraints and the results are compared with those of clamped-free case, which is without pre-stress. We find that the critical value increases with the initial slack--that quantifies the pre-stress, and strongly depends on the type of the constraints at the boundaries. The frequency of oscillations far from the onset, however, depends primarily on the magnitude of the follower force, not on the boundary constraints. Interestingly, oscillations for the clamped-pinned case are observed only when the follower forces are directed towards the clamped end. This finding can be exploited to design a mechanical switch to initiate or quench the oscillations by reversing the direction of the follower force or altering the boundary conditions.

physics.bio-ph↗

arXiv2018

Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for prestressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.

physics.comp-ph↗

arXiv2017

Clinical Facts Along With a Feedback Control Perspective Suggest That Increased Response Time Might be the Cause of Parkinsonian Rest Tremor

Parkinson's disease (PD) is a neurodegenerative disorder characterized by increased response times leading to a variety of biomechanical symptoms such as tremors, stooping and gait instability. Although the deterioration in biomechanical control can intuitively be related to sluggish response times, how the delay leads to such biomechanical symptoms as tremor is not yet understood. Only recently has it been explained from the perspective of feedback control theory that delay beyond a threshold can be the cause of Parkinsonian tremor [1]. This paper correlates several observations from this perspective to clinical facts and reinforces them with simple numerical and experimental examples. This work provides a framework towards developing a deeper conceptual understanding of the mechanism behind PD symptoms. Furthermore, it lays a foundation for developing tools for diagnosis and progress tracking of the disease by identifying some key trends.

q-bio.QM↗

arXiv2010

Constitutive-law Modeling of Microfilaments from their Discrete-Structure Simulations - A Method based on an Inverse Approach Applied to a Static Rod Model

Twisting and bending deformations are crucial to the biological functions of microfilaments such as DNA molecules. Although continuum-rod models have emerged as efficient tools to describe the nonlinear dynamics of these deformations, a major roadblock in the continuum-mechanics-based description of microfilaments is the accurate modeling of the constitutive law, which follows from its atomistic structure and bond-stiffnesses. Since first-principle derivation of the constitutive law from atomistic structure is impractical and so are direct experimental measurements due to the small length-scales, a natural alternative is to estimate the constitutive law from discrete-structure simulations such as molecular-dynamics (MD) simulations. In this paper, we present a two-step inverse method for estimating the constitutive law using rod theory and data generated from discrete-structure simulations. We illustrate the method on a filament with an artificial and simplistic discrete-structure. We simulate its deformation in response to a prescribed loading using a multi-body dynamics (MBD) solver. Using data generated from the MBD solver, we first estimate the curvature of the filament and subsequently use it in the two-step method to estimate the effective constitutive-law relationship between the restoring moment and curvature. Finally, we also illustrate how the estimated constitutive law can be tested under independent loading conditions.

physics.comp-ph↗

arXiv2010

Estimation of Nonlinear Three-dimensional Constitutive Law for DNA Molecules

Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of DNA molecules. The elastic rod model predictions are however very sensitive to the constitutive law (material properties) of the molecule, which in turn, vary along the molecules length according to its base-pair sequence. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we develop techniques to use elastic rod model equations in combination with limited experimental measurements or high-fidelity molecular dynamics simulation data to estimate the nonlinear constitutive law governing DNA molecules. We first cast the elastic rod model equations in state-space form and express the effect of the unknown constitutive law as an unknown input to the system. We then develop a two-step technique to estimate the unknown constitutive law. We discuss various generalizations and investigate the robustness of this technique through simulations.

physics.comp-ph↗

arXiv2009

An Estimation Method of a Constitutive-law for the Rod Model of DNA using Discrete-Structure Simulations

The continuum-rod model has emerged as an efficient tool to describe the long-length-scale structural-deformations of DNA which are critical to understanding the nature of many biological processes such as gene expression. However, a significant challenge in continuum-mechanics-based modeling of DNA is to estimate its constitutive law, which follows from its interatomic bond-stiffness. Experiments and all-atom molecular dynamics (MD) simulations have suggested that the constitutive law is nonlinear and non-homogeneous (sequence-dependent) along the length of DNA. In this paper, we present an estimation method and a validation study using discrete-structure simulations. We consider a simple cantilever-rod with an artificially constructed, discrete lattice-structure which gives rise to a constitutive law. Large deformations are then simulated. An effective constitutive-law is estimated from these deformations using inverse methods. Finally, we test the estimated law by employing it in the continuum rod-model and comparing the simulation results with those of discrete-structure simulations under a different cantilever loading-conditions.

physics.bio-ph↗

arXiv2007

Modeling of Cables with High and Low Tension Zones using a Hybrid Rod-Catenary Formulation

Cables under very low tension may become highly contorted and form loops, tangles, knots and kinks. These nonlinear deformations, which are dominated by flexure and torsion, pose serious concerns for cable deployment. Simulation of the three-dimensional nonlinear dynamics of loop and tangle formation requires a 12th order rod model and the computational effort increases rapidly with increasing cable length and integration time. However, marine cable applications which result in local zones of low-tension very frequently involve large zones of high-tension where the effects of flexure and torsion are insignificant. Simulation of the three-dimensional dynamics of high-tension cables requires only a 6th order catenary model which significantly reduces computational effort relative to a rod model. We propose herein a hybrid computational cable model that employs computationally efficient catenary elements in high-tension zones and rod elements in localized low-tension zones to capture flexure and torsion precisely where needed.

physics.comp-ph↗

arXiv2007

Cable dynamics applied to long-length scale mechanics of DNA

This paper introduces the use of cable dynamics models as a means to explore the mechanics of DNA on long-length scales. It is on these length scales that DNA forms twisted and curved three-dimensional shapes known as supercoils and loops. These long-length scale DNA structures have a pronounced influence on the functions of this molecule within the cell including the packing of DNA in the cell nucleus, transcription, replication and gene repair. We provide a short background to the mechanics of DNA and suggest the logical connection to the mechanics of a low tension cable. A computational model is then summarized and example results are presented for DNA supercoiling and looping.

physics.bio-ph↗

arXiv2007

Writhing Dynamics of Cables with Self-contact

Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is reviewed herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-alpha method for finite differencing in both space and time. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, through the dynamic collapse of this helix into a loop, and subsequent intertwining of the loop with multiple sites of self-contact.

physics.comp-ph↗

arXiv2007

Structural Modeling of DNA Loops in Lactose-Repressor

It is well known that the structural deformations (stressed states) of DNA molecule play a crucial role in its biological functions including gene expression. For instance, looping in DNA (often mediated by protein binding) is a crucial step in many gene regulatory mechanisms. We use the mechanical rod model of DNA molecules to simulate its structural interactions with proteins (enzymes) during gene expression. Our rod model can simulate the nonlinear dynamics of loop and supercoil formation in DNA on long length scales. The formulation accounts for the structural stiffness of the DNA strand, its intrinsic curvature, chiral (right-handed helical) construction and its physical interactions with the surrounding medium. The simulations of protein-mediated DNA looping illustrate how the mechanical properties of DNA may affect the chemical kinetics of DNA-protein interactions and thereby regulate gene expression.

physics.bio-ph↗

arXiv2007

Nonlinear dynamic strand model with coupled tension and torsion

We simulate the nonlinear dynamic responses in Kirchhoff rod by including the important effects due to inertia and kinematic coupling of tension and torsion. We begin by reviewing a dynamic rod model of a strand (length of cable or DNA) in the form of a 12th order partial differential equation system. Numerical solutions reveal the effects of dynamics on clamped strands due to slow movements of their ends. We note that inertia plays a critical role in this process, particularly under loading conditions that pass through an instability. For example, we simulated a dynamic trasition path between two possible equilibria of a clamped rod subject to very slow compression.

physics.comp-ph↗

arXiv2007

Nonlinear dynamic intertwining of rods with self-contact

Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or hockles are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively by the dynamic conversion of twist (Tw) to writhe (Wr). KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable Hockling

math-ph↗