Saurav Talukdar

Exact topology reconstruction of radial dynamical systems with applications to distribution system of the power grid

In this article we present a method to reconstruct the interconnectedness of dynamically related stochastic processes, where the interactions are bi-directional and the underlying topology is a tree. Our approach is based on multivariate Wiener filtering which recovers spurious edges apart from the true edges in the topology reconstruction. The main contribution of this work is to show that all spurious links obtained using Wiener filtering can be eliminated if the underlying topology is a tree based on which we present a three stage network reconstruction procedure for trees. We illustrate the effectiveness of the method developed by applying it on a typical distribution system of the electric grid.

Reconstruction of networks of cyclostationary processes

Many complex systems can be described by agents that can be modeled as a network of dynamically interacting cyclo-stationary processes. Such systems arise in areas like power systems and climate sciences. For many of these systems a key objective is to understand mutual influences between various subsystems without altering the natural behavior of the system. Such an objective translates to unveiling the interconnection of the topology of the network using only passive means. Most existing related works have emphasized correlation based methods where interdependencies over different time-instants can be missed. Recent work where dynamic influences are incorporated assuming stationary statistics cannot accommodate applications that arise in many areas such as power and climate sciences. In this article an algorithm based on Wiener filtering is devised for the reconstruction of interconnectivity of dynamically related cyclo-stationary processes. It is shown that all existing interdependencies are detected and spurious detection remains local. Application to a microgrid power network is shown to yield useful insights.

Memory erasure using time-multiplexed potentials

We study the thermodynamics of a Brownian particle under the influence of a time-multiplexed harmonic potential of finite width. The memory storage mechanism and the erasure protocol based on time-multiplexed potentials are utilized to experimentally realize erasure with work performed close to Landauers bound. We quantify the work performed on the system with respect to the duty ratio of time multiplexing, which also provides a handle for approaching reversible erasures. A Langevin dynamics based simulation model is developed for the proposed memory bit and the erasure protocol, which guides the experimental realization. The study also provides insight into transport on the microscale.

Learning Exact Topology of a Loopy Power Grid from Ambient Dynamics

Estimation of the operational topology of the power grid is necessary for optimal market settlement and reliable dynamic operation of the grid. This paper presents a novel framework for topology estimation for general power grids (loopy or radial) using time-series measurements of nodal voltage phase angles that arise from the swing dynamics. Our learning framework utilizes multivariate Wiener filtering to unravel the interaction between fluctuations in voltage angles at different nodes and identifies operational edges by considering the phase response of the elements of the multivariate Wiener filter. The performance of our learning framework is demonstrated through simulations on standard IEEE test cases.

Analysis of Heat Dissipation and Reliability in Information Erasure: A Gaussian Mixture Approach

This article analyzes the effect of imperfections in physically realizable memory. Motivated by the realization of a bit as a Brownian particle within a double well potential, we investigate the energetics of an erasure protocol under a Gaussian mixture model. We obtain sharp quantitative entropy bounds that not only give rigorous justification for heuristics utilized in prior works, but also provide a guide toward the minimal scale at which an erasure protocol can be performed. We also compare the results obtained with the mean escape times from double wells to ensure reliability of the memory. The article quantifies the effect of overlap of two Gaussians on the the loss of interpretability of the state of a one bit memory, the required heat dissipated in partially successful erasures and reliability of information stored in a memory bit.

Steady state dynamics of molecular motors reveals load dependent cooperativity

Intracellular transport of cargoes inside eukaryotic cells is primarily carried out by bio-mechanical machines called molecular motors. These motors facilitate the directed transfer of intracellular cargo to desired locations inside the cell. In vivo modes of transport often involve multiple agents, possibly of different types, teaming up to carry a common cargo. We analyze the stochastic dynamics of such cargos and prove that the probability distribution of various motor-motor configurations in an ensemble reaches a unique steady state. Existence of such a unique steady state indicates a degree of robustness of the system of multiple motors sharing a cargo. Analysis of the steady state distribution for an ensemble of two kinesin motors for varying load forces reveals a degree of cooperativity between the motors, where configurations that have the two motors clustered together are favored for moderate loads. We further show that when subjected to high forces, such as those encountered due to obstacles along the path of travel, motors preferably adopt a configuration that facilitates high probability of regaining motion once the obstacle is removed. Simulation results of the steady state distribution of a two motor ensemble for low, moderate and high load forces are presented, which corroborate analytical studies.

Noise induced transport at microscale enabled by optical fields

Transport at the micro scale is an essential aspect for many emerging areas including manufacturing systems at the nanoscale. Transfer of beads decorated with cargo under the influence of optical fields provide an attractive means of such transport. Physical models that describe beads in optical fields under the influence of thermal noise are available which yield a qualitative understanding of the bead motion; however, it is difficult to arrive at models that provide quantitative agreement. The first contribution of the article is the determination of a model of a bead under a static field realized by optical forces where the model can be used to predict the motion of the bead under a time-varying optical potential with high fidelity. Close agreement between model based Monte Carlo simulations and experimental observations is seen. The other contribution is a strategy for directed transport of micron-sized particles that utilizes the proposed models to arrive at conclusions which are experimentally verified and easy to implement. The effectiveness of this transport mechanism is justified based on splitting probability computations. Applications to transport of cargo across multiple locations and transport of multiple cargo are experimentally demonstrated.