arXiv subjects

Dwaipayan Mukherjee

Publications and source records attributed to Dwaipayan Mukherjee.

11 recordsLinked to original sources

arXiv2026

Stability of Collective Neutrino Oscillations -- A Distributional Approach

We study the stability of collective neutrino oscillations using a distributional approach motivated by the statistical mechanics of Kuramoto synchronization. Treating the ensemble of neutrino flavor polarization vectors in the thermodynamic limit $N\to\infty$, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution $F(\vec{\mathbf{S}},\omega,t)$ on the flavor sphere. This equation admits a two-parameter family of azimuthally symmetric stationary solutions, whose stability we analyze by linearizing around them. The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes. In special limits the condition reproduces known synchronization thresholds in the two-beam model, providing a non-trivial check of the framework. We present analytical results for the eigenvalue equation and explore stability phase diagrams for physically relevant frequency distributions.

hep-ph↗

arXiv2026

Parameterizing the Standing Accretion Shock Instability for Inference with Galactic Supernova Neutrino Signals at IceCube

Simulations of core-collapse supernovae have revealed an epoch of hydrodynamic instability in which the matter of the collapsing star undergoes quasi-periodic oscillations, known as the standing accretion shock instability (SASI). Neutrinos produced in the core of the star travel through this oscillating matter, and information about this epoch is encoded in their high-statistics event rate observable at neutrino observatories. We propose a parametrization of the SASI-modulation to study its broad features, enabling statistical inference of SASI parameters. For the benchmark Galactic supernovae considered, we show that IceCube can identify this epoch of instability and reconstruct its parameters with precision at the sub-percent level for the SASI frequency, percent level for the peak time, and a few to ten percent level for the amplitude and duration.

astro-ph.SR↗

arXiv2025

Consensus-based formation of a swarm of quadrotors interacting over ring digraphs

This work proposes a cooperative strategy for a group of quadrotors interacting over ring digraphs with macro-vertices of size two. Consensus for a group of general double integrators has been initially investigated, and it has been proved that through a suitable choice of a single controller parameter, consensus and stability of the resulting networked dynamical system can be ensured. This further opens up the possibility of achieving a desired formation and to move a swarm of quadrotors, interacting over ring digraphs, at a desired flight velocity, using a single controller gain. An analysis of achievable velocities is performed. Examples have been provided to offer deeper insights into the obtained analytical results. Simulation studies clearly demonstrate that a desired formation is achieved, starting from arbitrary initial positions, while also ensuring convergence to a final desired flight velocity.

eess.SY↗

arXiv2025

On Robustness of Consensus over Pseudo-Undirected Path Graphs

Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed graphs permit asymmetry but make consensus dependent on root nodes and their influence. Both paradigms impose inherent restrictions on achievable consensus values and network robustness. This paper introduces a theoretical framework for achieving consensus over a class of network topologies, termed pseudo-undirected graphs, which retains bidirectional connectivity between node pairs but allows the corresponding edge weights to differ, including the possibility of negative values under bounded conditions. The resulting Laplacian is generally non-symmetric, yet it guarantees consensus under connectivity assumptions, to expand the solution space, which enables the system to achieve a stable consensus value that can lie outside the convex hull of the initial state set. We derive admissibility bounds for negative weights for a pseudo-undirected path graph, and show an application in the simultaneous interception of a moving target.

eess.SY↗

arXiv2025

Field-of-View and Input Constrained Impact Time Guidance Against Stationary Targets

This paper proposes a guidance strategy to achieve time-constrained interception of stationary targets, taking into account both the bounded field-of-view (FOV) of seeker-equipped interceptors and the actuator's physical constraints. Actuator saturation presents a significant challenge in real-world systems, often resulting in degraded performance. However, since these limitations are typically known in advance, incorporating them into the guidance design can enhance overall performance. To address the FOV constraint, a time-to-go error-based approach is adopted. Furthermore, to incorporate the lateral acceleration constraints, the engagement kinematics are augmented with an input saturation model. Subsequently, the guidance strategy that constrains the lateral acceleration and the time-to-go values within their respective bounds is derived using Lyapunov stability concepts and the backstepping technique. Furthermore, a multi-stage approach is suggested to expand the achievable range of impact time. Numerical simulations are performed to validate the efficacy of the proposed scheme for different initial engagement geometries.

eess.SY↗

arXiv2025

Sufficient and Necessary Conditions for Collective Neutrino Instability: Fast, Slow, and Mixed

Collective neutrino oscillations exhibit instabilities that induce appreciable flavor conversion, with crucial astrophysical implications. While the importance of initial phase-space distributions is well-established, a general instability criterion for distributions dependent on both energy and emission angle has been lacking. We identify and analyze the sufficient (and necessary) conditions for a generic collective neutrino flavor instability.

hep-ph↗

arXiv2024

Cooperative Salvo Guidance over Leader-Follower Network with Free-Will Arbitrary Time Convergence

A cooperative salvo strategy is proposed in this paper which achieves consensus among the interceptors within a pre-defined arbitrary settling time. Considering non-linear engagement kinematics and a system lag to capture the effect of interceptor autopilot as present in realistic interception scenarios, the guidance schemes use the time-to-go estimates of the interceptors in order to achieve simultaneous interception of a stationary target at a pre-determined impact time. The guidance scheme ensures that consensus among the time-to-go estimates of the interceptors is achieved within a settling time whose upper bound can be pre-specified arbitrarily independent of the initial conditions or design parameters. The efficacy of the proposed guidance strategy is demonstrated using numerical simulations with varied conditions of initial position, velocities and heading angle errors of the interceptors as well as different desired impact times.

eess.SY↗

arXiv2024

Consensus-driven Deviated Pursuit for Guaranteed Simultaneous Interception of Moving Targets

This work proposes a cooperative strategy that employs deviated pursuit guidance to simultaneously intercept a moving (but not manoeuvring) target. As opposed to many existing cooperative guidance strategies which use estimates of time-to-go, based on proportional-navigation guidance, the proposed strategy uses an exact expression for time-to-go to ensure simultaneous interception. The guidance design considers nonlinear engagement kinematics, allowing the proposed strategy to remain effective over a large operating regime. Unlike existing strategies on simultaneous interception that achieve interception at the average value of their initial time-to-go estimates, this work provides flexibility in the choice of impact time. By judiciously choosing the edge weights of the communication network, a weighted consensus in time-to-go can be achieved. It has been shown that by allowing an edge weight to be negative, consensus in time-to-go can even be achieved for an impact time that lies outside the convex hull of the set of initial time-to-go values of the individual interceptors. The bounds on such negative weights have been analysed for some special graphs, using Nyquist criterion. Simulations are provided to vindicate the efficacy of the proposed strategy.

eess.SY↗

arXiv2022

Three-agent Time-constrained Cooperative Pursuit-Evasion

This paper considers a pursuit-evasion scenario among three agents -- an evader, a pursuer, and a defender. We design cooperative guidance laws for the evader and the defender team to safeguard the evader from an attacking pursuer. Unlike differential games, optimal control formulations, and other heuristic methods, we propose a novel perspective on designing effective nonlinear feedback control laws for the evader-defender team using a time-constrained guidance approach. The evader lures the pursuer on the collision course by offering itself as bait. At the same time, the defender protects the evader from the pursuer by exercising control over the engagement duration. Depending on the nature of the mission, the defender may choose to take an aggressive or defensive stance. Such consideration widens the applicability of the proposed methods in various three-agent motion planning scenarios such as aircraft defense, asset guarding, search and rescue, surveillance, and secure transportation. We use a fixed-time sliding mode control strategy to design the control laws for the evader-defender team and a nonlinear finite-time disturbance observer to estimate the pursuer's maneuver. Finally, we present simulations to demonstrate favorable performance under various engagement geometries, thus vindicating the efficacy of the proposed designs.

eess.SY↗

arXiv2018

Finite-time Heterogeneous Cyclic Pursuit with Application to Target Interception

This paper presents a finite-time heterogeneous cyclic pursuit scheme that ensures consensus among agents modelled as integrators. It is shown that for the proposed sliding mode control, even when the gains corresponding to each agent are non-identical, consensus results within a finite-time provided all the gains are positive. An algorithm is presented to compute the consensus value and consensus time for a given set of gains and initial states of the agents. The set of values where consensus can occur, by varying the gains, has been derived and a second algorithm aids in determining the gains that enable consensus at any point in the aforementioned set, within a given finite-time. As an application, the finite-time consensus in line-of-sight (LOS) rates, over a cycle digraph, for a group of interceptors is shown to be effective in ensuring co-operative collision-free interception of a target, for both kinematic and realistic models of the interceptors. Simulations vindicate the theoretical results.

eess.SY↗

arXiv2016

Consensus over Weighted Directed Graphs: A Robustness Perspective

The present paper investigates the robustness of the consensus protocol over weighted directed graphs using the Nyquist criterion. The limit to which a single weight can vary, while consensus among the agents can be achieved, is explicitly derived. It is shown that even with a negative weight on one of the edges, consensus may be achieved. The result obtained in this paper is applied to a directed acyclic graph and to the directed cycle graph. Graph theoretic interpretations of the limits are provided for the two cases. Simulations support the theoretical results.

eess.SY↗