Papers by Gemunu Gunaratne
Journal of the Optical Society of America, Jul 11, 2023
Computing locations and extent of images, except in the most trivial configurations or special ca... more Computing locations and extent of images, except in the most trivial configurations or special cases, is a complex task. Even rays emanating from a point source and passing through an optical system generally fail to converge at a single image point, highlighting the care needed to establish image locations. We use three approaches to study image formation in a simple configuration, that of a point source following reflection from a spherical concave mirror. We calculate the caustic surfaces and compute cross sections of flux densities on image surfaces, and compare the results with experimentally generated light intensity fields. One of the two caustic surfaces is linear while the other forms a surface. The latter, undergoes a metamorphosis from a distorted cone to an open surface as the source is moved away from the axis. Cross sections of the caustic surfaces with an image plane are found to coincide with peaks in the flux density. Experimental studies validate these conclusions.
MPRA Paper, 2006
There is much confusion in the literature over Hurst exponents. Recently, we took a step in the d... more There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H≠1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two-and one-point densities of fBm are constructed explicitly. The two-point density doesn't scale. The one-point density for a semi-infinite time interval is identical to that for a scaling Gaussian Markov process with H≠1/2 over a finite time interval. We conclude that both Hurst exponents and one point densities are inadequate for deducing the underlying dynamics from empirical data. We apply these conclusions in the end to make a focused statement about 'nonlinear diffusion'.
We study the formation of images in a reflective sphere in three configurations using caustics of... more We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system is, in general, a Gaussian surface with partial focus along the two principal directions of the Gaussian surface; i.e., there are two images of the source point, each with partial focus. As the source point moves, the images move on two surfaces, referred to as viewable surfaces. In our systems, one viewable surface consists of points with radial focus and the other consists of points with azimuthal focus. The problems we study are (1) imaging of a parallel beam of light, (2) imaging of the infinite viewed from a location outside the sphere, and (3) imaging of a planar object viewed through the point of its intersection with the radial line normal to the plane. We verify the existence of two images experimentally and show that the distance between them agrees with the computations.
Current Biology, Jun 1, 2022
Proceedings of SPIE, Jul 2, 1994
ABSTRACT A superconducting quantum interference grating (SQUIG), consisting of many Josephson jun... more ABSTRACT A superconducting quantum interference grating (SQUIG), consisting of many Josephson junctions in parallel, exhibits quantum interference analogous to the optical interference pattern produced by a diffraction grating, just as the dc SQUID is the magnetic analog of the double slit in optics. The field- dependent critical current of a SQUIG with sufficiently low inductance exhibits a series of sharp peaks, similar to the position-dependent intensity of a multiple-slit interference pattern. Such a device has the potential for improved sensitivity as a magnetic sensor because of its enhanced flux-to-voltage transfer coefficient. The behavior is quite different, however, when the inductance is large. In this limit, the field-dependent critical current becomes extremely hysteretic and exhibits self- organized phase coherence, in which a peak in the critical current (indicating coherence of the junction phases) is observed after each reversal of the field sweep. We have observed this phenomenon in large inductance arrays with up to ten YBa2Cu3O7 (YBCO) bi-crystal grain boundary junctions in parallel. We have modeled the behavior using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance. According to our model calculations, self-organized phase coherence occurs when the system relaxes from its critical state, causing the phases to simultaneously relax to minima in the periodic potential representing the Josephson coupling energy, and thus to become coherent modulo 2(pi) .
Computing locations and extent of images, except in the most trivial configurations or special ca... more Computing locations and extent of images, except in the most trivial configurations or special cases, is a complex task. Even rays emanating from a point source and passing through an optical system generally fail to converge at a single image point, highlighting the care needed to establish image locations. We use three approaches to study image formation in a simple configuration, that of a point source following reflection from a spherical concave mirror. We calculate the caustic surfaces and compute cross sections of flux densities on image surfaces, and compare the results with experimentally generated light intensity fields. One of the two caustic surfaces is linear while the other forms a surface. The latter, undergoes a metamorphosis from a distorted cone to an open surface as the source is moved away from the axis. Cross sections of the caustic surfaces with an image plane are found to coincide with peaks in the flux density. Experimental studies validate these conclusions.
Cambridge University Press eBooks, Jul 20, 2011
Physica D: Nonlinear Phenomena, Jul 1, 2020
Abstract There is an abundance of instances when the state of a complex network needs to be alter... more Abstract There is an abundance of instances when the state of a complex network needs to be altered to a pre-specified target state, one potential example being the need to alter a disease-induced tissue to a healthy state. Unfortunately, in many such cases, accurate models of the underlying network are unavailable. Consequently, the algorithms for control need to be model-independent. We have previously introduced an approach that relies only on the knowledge (of a partial list) of relevant nodes and the system feedback to perturbation on a selected subset of nodes. This feedback can be used to construct ‘response manifolds,’ which, as we argue, are all that is needed to design the necessary control. Here, we demonstrate the feasibility of the approach by successfully moving nonlinearly-coupled electrical circuits to pre-specified target states.
MRS Proceedings, 1992
ABSTRACTWe have carried out finite-inductance calculations of the critical current vs, flux(Ic-φ)... more ABSTRACTWe have carried out finite-inductance calculations of the critical current vs, flux(Ic-φ) and voltage vs, flux (V-φ) characteristics of superconducting interferometers with many Josephson junctions (JJ&amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s) in parallel. At least two features of our calculations suggest that interferometers with many junctions, which we call Superconducting QUantum Interference Gratings, or SQUIG&amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s, might be advantageous for the detection of magnetic flux. First, the voltage noise can potentially be reduced significantly as compared to a dc SQUID with the same overall voltage-to-flux transfer coefficient - a feature which might reduce 1/f noise and enhance the magnetic flux sensitivity of both low and high Tc superconducting (HTS) devices. In addition, nonuniformity of the junction critical currents appears to have little adverse effect on the predicted diffraction-grating like enhancement and narrowing of the peaks in the Ic-φcharacteristic, suggesting that flux uniformity, rather that critical current uniformity, is of primary importance.
Physical review, Jun 1, 1994
We report on the hysteretic field-dependent critical currents of large inductance arrays with up ... more We report on the hysteretic field-dependent critical currents of large inductance arrays with up to ten YBa2Cu307 grain-boundary junctions in parallel. A peak in the critical current, roughly equal to its initial zero-field value, is observed after each reversal of the field sweep. This behavior indicates that the junction phases become equal modulo 2m (self-organized phase coherence) as the system relaxes away from the critical state. The primary features can be modeled using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance.
Superlattices and Microstructures, 1992
We have generalized the Aharanov-Bohm effect from a single loop to a twodimensional rectangular n... more We have generalized the Aharanov-Bohm effect from a single loop to a twodimensional rectangular network containing MxN loops. each of equal area. For a given geometry, as the total number of loops increases, the periodic principal maxima m the t'lux-dependent conductance exhihit a spacing ol h/e per loop while becoming increasingly narrow and pronounced, and we observe M-2 subsidiary maxima between consecutive principal maxima. We predict a similar enhancement and narrowing of the principal maxima in the flux-dependent crttical current of a multi-junction SQUID array, although in this case the llux periodicity is N2e.
Journal of Fluid Mechanics, Feb 1, 2016
Modal decompositions of unperturbed and acoustically driven injector flows from shear coaxial jet... more Modal decompositions of unperturbed and acoustically driven injector flows from shear coaxial jets are implemented using dynamic-mode decomposition, which is a natural approach in the search for collective oscillatory behaviour in nonlinear systems. Previous studies using proper orthogonal decomposition had revealed the most energetic pairs of coherent structures in injector flows. One of the difficulties in extracting lower-energy coherent structures follows from the need to differentiate robust flow constituents from noise and other irregular facets of a flow. The identification of robust features is critical for applications such as flow control as well, since only they can be used for the tasks. A dynamic-mode decomposition based algorithm for this differentiation is introduced and used to identify different classes of robust dynamic modes. They include (1) background modes located outside the injector flow that decay rapidly, (2) injector modes – including those presented in earlier studies – located in the vicinity of the flow, (3) modes that persist under acoustic driving, (4) modes responding linearly to the driving and, most interestingly, (5) a mode whose density exhibits antiphase oscillatory behaviour in the observation plane and that appears only when $J$, the outer-to-inner-jet momentum flux ratio, is sufficiently large; we infer that this is a projection of a mode rotating about the symmetry axis and born via a spontaneous symmetry breaking. Each of these classes of modes is analysed as $J$ is increased, and their consequences for the flow patterns are discussed.
arXiv (Cornell University), Oct 9, 2013
Control of complex processes is a major goal of network analyses. Most approaches to control nonl... more Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor the network topology is known for many important systems. On the other hand, system responses to perturbations are often easily measured. We show how the collection of such responses-a response surface-can be used for network control. Analyses of model systems show that response surfaces are smooth and hence can be approximated using low order polynomials. Importantly, these approximations are largely insensitive to stochastic fluctuations in data or measurement errors. They can be used to compute how a small set of nodes need to be altered in order to direct the network close to a pre-specified target state. These ideas, illustrated on a nonlinear electrical circuit, can prove useful in many contexts including in reprogramming cellular states. N atural and artificial systems such as those underlying biological processes 1,2 and the internet 3 consist of collections of interacting elements, and can be modeled as networks of coupled nodes 1,4. Feedback within such networks is believed to buffer their response under external changes and minor alterations in the systems 5. The feedback-induced moderation lies at the heart of robustness, for example, of biological processes. Unfortunately, the robustness also makes it difficult to implement controlled alterations of the underlying system. Thus, modifying one or a few nodes may be countered by feedback or may initiate uncontrolled, and possibly damaging, consequences. The surprising lack of efficacy of many drugs designed to act on single molecular targets 6,7 and harmful side-effect from medications (e.g., Vioxx 8) are a testament to these difficulties. Such problems can be addressed if techniques to direct nonlinearly coupled networks to target states were available. Precise controllability, one of the major goals of network analyses, has inspired several recent studies. Controllability of a system is defined as the ability to steer the system from any initial state to an arbitrary final state in finite time 9,10. In networks, the number of control nodes depends primarily on the degree distribution but not on the clustering coefficient or the community structure of the network 11,12. Furthermore, contrary to expectations, it was found that the driver nodes are typically not the high-degree nodes of a network 11. However, scale-free networks can be driven to a pre-specified state 13 or steered to a desired evolution 14 by pinning or targeting their most highly-connected nodes. Ref. 15 analyzes graph structures of controllable linear systems 16 , and shows that nodes required for network control include source nodes (i.e., those with only outgoing links), internal dilations (due to branching points), and external dilations (due to surplus nodes with only incoming links). The application of these algorithms requires knowledge of the network topology. In contrast, the approach introduced in Ref. 17 (which applies to linearly or nonlinearly coupled networks) relies on perturbation of control nodes and following the evolution of the system to search for passage from an undesirable initial state to the basin boundary of a desirable target state. It was used to identify possible therapeutic targets for T-LGL leukemia and to drive an associative memory network to a target state 17. Unfortunately, the network topology of many real systems is not known 18 , and it is difficult to follow the time evolution of other systems (e.g., gene regulatory networks) experimentally. Here, we propose a methodology to address a more restricted issue on partially-known systems, namely how to move such a system close to a prespecified target state. Although the methodology applies for a broad class of systems, we introduce terminology from gene regulatory networks for ease of presentation. The state of the system is the collection of values taken by the nodes. The state is to be changed by altering the values of a small set n of nodes, defined as the master nodes; the remaining nodes are slave nodes. States obtained by externally setting the values of the master nodes are referred to
American Institute of Aeronautics and Astronautics, Inc. eBooks, 2023
Abstract and Applied Analysis, 2012
We present the application of the sn-ns method to solve nonlinear partial differential equations.... more We present the application of the sn-ns method to solve nonlinear partial differential equations. We show that the well-known tanh-coth method is a particular case of the sn-ns method.
Contributions to statistics, 2018
We propose a novel methodology to predict high-dimensional time series with exogenous variables u... more We propose a novel methodology to predict high-dimensional time series with exogenous variables using Koopman operator framework, by assuming that the time series are generated by some underlying unknown dynamical system with input as exogenous variables. In order to do that, we first generalize the definition of the original Koopman operator to allow for input to the underlying dynamical system. We then obtain a formulation of the generalized Koopman operator in reproducing kernel Hilbert space (RKHS) and a new derivation of its numerical approximation methods, namely, Extended Dynamic Mode Decomposition (EDMD) and its kernel-based version. We also obtain a statistical interpretation of kernel-based EDMD developed for deterministic Koopman operator by utilizing the connection between RKHS and Gaussian processes regression, and relate it to the stochastic Koopman and Perron-Frobenius operator. In applications, we found that the prediction performance of this methodology is promising in forecasting real world high-dimensional time series with exogenous variables, including financial markets data. We believe that this methodology will be of interest to the community of scientists and engineers working on quantitative finance, econometrics, system biology, neurosciences, meteorology, oceanography, system identification and control, data mining, machine learning, computational intelligence, and many other fields involving high-dimensional time series and spatio-temporal data.
Journal of Statistical Physics, Mar 22, 2017
First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specifie... more First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically-often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time-and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221-233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra-and inter-day behavior similar to those of empirical first-passage-time distributions.
Mathematics, May 8, 2021
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
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Papers by Gemunu Gunaratne