arXiv subjects

Shantanu Chakraborty

Publications and source records attributed to Shantanu Chakraborty.

12 recordsLinked to original sources

arXiv2026

How Well Do AI Systems Solve AP Physics? A Comparative Evaluation of Large Language Models on Algebra-Based Free Response Questions

The rapid advancement of LLMs has generated growing interest in their potential role in physics education and assessment, yet a focused evaluation of their performance on multi-faceted, free-response physics problems remains underexplored. In this study, we systematically evaluate the performance of four widely accessible AI systems-ChatGPT 4.1 mini, Gemini 2.5 Flash, Claude 4.0 Sonnet, and DeepSeek R1-on AP Physics 1 and 2 free-response questions administered between 2015 and 2025. Model-generated solutions were produced under standardized exam-style prompting and evaluated by three independent physics experts using official College Board scoring guidelines. All models achieved relatively high mean scores (82-92%), indicating strong capability in structured algebraic problem solving. However, substantial year-to-year variability was observed, particularly for AP Physics 1, where statistical testing revealed no consistent performance hierarchy among models. In contrast, AP Physics 2 results showed statistically significant differences, with Gemini and DeepSeek demonstrating more consistent performance than Claude. A qualitative analysis revealed recurring error patterns across all models, including misinterpretation of diagrams and graphs, incorrect graph construction, incorrect reasoning about vector direction, circuit topology errors, partial and misleading qualitative explanations, and difficulties applying three-dimensional concepts such as the right-hand rule. These findings suggest that while contemporary AI systems can effectively support routine physics problem solving, they remain limited in tasks requiring spatial reasoning, visual interpretation, and conceptual integration. The results highlight both the instructional potential and current pedagogical limitations of AI-assisted learning tools in physics education.

physics.ed-ph↗

arXiv2025

Breaking Barriers: Investigating Gender Dynamics in Introductory Physics Lab Classes

The persistent underrepresentation of women and other gender minorities in physical science fields has been an ongoing concern. This study investigates gender dynamics in introductory physics laboratory courses, focusing on whether students of different gender identities exhibit equal inclination and confidence in conducting lab experiments, and whether they face barriers that impact their participation. Conducted across three institutions and involving non-physics STEM students enrolled in algebra-based and calculus-based physics courses, the study found mixed results, with two institutions showing no significant gender-based differences in participation levels during lab activities, while one institution demonstrated significant differences. Chi-square tests revealed no significant association between gender and task preference or comfortability, though the small dataset suggests the need for further investigation. While quantitative analysis provided limited evidence of systematic barriers, qualitative feedback revealed that some female students experienced challenges related to gender dynamics, such as perceived assumptions about competence, being overlooked during discussions, and hesitation to voice opinions in male-dominated groups. These findings highlight the complex influence of gender and institutional factors on laboratory experiences and underscore the need for creating inclusive environments that promote equitable engagement and participation for all gender identities in STEM education.

physics.ed-ph↗

arXiv2024

Teaching Physics to Life Sciences Students in the SCALE-UP Style

Physics has a reputation among majority of life sciences students for being very complicated and tough. If we leave students with this impression, it is likely that students see physics class as useless and irrelevant to life sciences. Concepts of physics are vital in oder to understand physics based technological tools and biophysical topics essential and relevant for life sciences. This review summarizes approaches for improving teaching and learning in introductory physics courses to life science students in the SCALE- UP style. We also discuss our experiences in adapting IPLS Courses to better meet the needs of life sciences students. to better meet the needs of life sciences students.

physics.ed-ph↗

arXiv2021

Freeway network design with exclusive lanes for automated vehicles under endogenous mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions. Additional resource allocation at the network level, such as AV-exclusive lanes, can further foster the usage of AVs rendering this mode of travel more attractive than legacy vehicles (LV). However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters' demand split among AVs and LVs via a logit model incorporating class-based utilities. We incorporate the link transmission model (LTM) as the underlying traffic flow model due to its computational efficiency for system optimum dynamic traffic assignment. The LTM is modified to integrate two vehicle classes namely, LVs and AVs with a lane-based approach. The presence of binary variables to represent lane design and the logit model for endogenous demand estimation results in a nonconvex mixed-integer nonlinear program (MINLP) formulation. We propose a Benders' decomposition approach to tackle this challenging optimization problem. Our approach iteratively explores possible lane designs in the Benders' master problem and, at each iteration, solves a sequence of system-optimum dynamic traffic assignment (SODTA) problems which is shown to converge to fixed-points representative of logit-compatible demand splits. Further, we prove that the proposed solution method converges to a local optima of the nonconvex problem and identify under which conditions this local optima is a global solution. The proposed approach is implemented on three hypothetical freeway networks with single and multiple origins and destinations.

math.OC↗

arXiv2020

Reducing the Unfairness of Coordinated Inverter Dispatch in PV-Rich Distribution Networks

The integration of a high share of solar photovoltaics (PV) in distribution networks requires advanced voltage control technologies or network augmentation, both associated with significant investment costs. An alternative is to prevent new customers from installing solar PV systems, but this is against the common goal of increasing renewable energy generation. This paper demonstrates that solar PV curtailment in low voltage areas can be reduced and fairly distributed among PV owners by centrally coordinating the operation of PV inverters. The optimal inverter active and reactive power operation points are computed by solving a multi-objective optimization problem with a fairness objective. The main results show that fair optimal inverter dispatch (FOID) results in less power curtailment than passive voltage regulation based on Volt/VAr droop control, especially at high solar PV to load ratios. The effectiveness of the model is demonstrated on a residential low voltage network.

math.OC↗

arXiv2019

Automated Peer-to-peer Negotiation for Energy Contract Settlements in Residential Cooperatives

This paper presents an automated peer-to-peer negotiation strategy for settling energy contracts among prosumers in a Residential Energy Cooperative considering heterogeneity prosumer preferences. The heterogeneity arises from prosumers' evaluation of energy contracts through multiple societal and environmental criteria and the prosumers' private preferences over those criteria. The prosumers engage in bilateral negotiations with peers to mutually agree on periodical energy contracts/loans consisting of the energy volume to be exchanged at that period and the return time of the exchanged energy. The negotiating prosumers navigate through a common negotiation domain consisting of potential energy contracts and evaluate those contracts from their valuations on the entailed criteria against a utility function that is robust against generation and demand uncertainty. From the repeated interactions, a prosumer gradually learns about the compatibility of its peers in reaching energy contracts that are closer to Nash solutions. Empirical evaluation on real demand, generation and storage profiles -- in multiple system scales -- illustrates that the proposed negotiation based strategy can increase the system efficiency (measured by utilitarian social welfare) and fairness (measured by Nash social welfare) over a baseline strategy and an individual flexibility control strategy representing the status quo strategy. We thus elicit system benefits from peer-to-peer flexibility exchange already without any central coordination and market operator, providing a simple yet flexible and effective paradigm that complements existing markets.

cs.AI↗

arXiv2019

An Exchange Mechanism to Coordinate Flexibility in Residential Energy Cooperatives

Energy cooperatives (ECs) such as residential and industrial microgrids have the potential to mitigate increasing fluctuations in renewable electricity generation, but only if their joint response is coordinated. However, the coordination and control of independently operated flexible resources (e.g., storage, demand response) imposes critical challenges arising from the heterogeneity of the resources, conflict of interests, and impact on the grid. Correspondingly, overcoming these challenges with a general and fair yet efficient exchange mechanism that coordinates these distributed resources will accommodate renewable fluctuations on a local level, thereby supporting the energy transition. In this paper, we introduce such an exchange mechanism. It incorporates a payment structure that encourages prosumers to participate in the exchange by increasing their utility above baseline alternatives. The allocation from the proposed mechanism increases the system efficiency (utilitarian social welfare) and distributes profits more fairly (measured by Nash social welfare) than individual flexibility activation. A case study analyzing the mechanism performance and resulting payments in numerical experiments over real demand and generation profiles of the Pecan Street dataset elucidates the efficacy to promote cooperation between co-located flexibilities in residential cooperatives through local exchange.

cs.MA↗

arXiv2018

Directly Constraining Marginal Prices in Distribution Grids Using Demand-Side Flexibility

Recently, the volatility associated with marginal prices has increased due to large scale integration of renewable generation. Price volatility is undesirable from a consumer perspective. To address this issue, we present a framework for hedging that uses duality theory for quantifying the amount of demand-side flexibility required for constraining marginal prices to the consumers maximum willingness to pay for electricity. Using our formulation, we investigate the ability of an Energy Storage System (ESS), as a demand-side flexibility source, to hedge against electricity price volatility across a multi-time period horizon while accounting for its inter-temporal constraints. Additionally, we analyze the economical benefit that operating the ESS under information forecasts brings to the consumers.

math.OC↗

arXiv2018

The Role of Demand-Side Flexibility in Hedging Electricity Price Volatility in Distribution Grids

Locational Marginal Price (LMP) is a dual variable associated with supply-demand matching and represents the cost of delivering power to a particular location if the load at that location increases. In recent times it become more volatile due to increased integration of renewables that are intermittent. The issue of price volatility is further heightened during periods of grid congestion. Motivated by these problems, we propose a market design where, by constraining dual variables, we determine the amount of demand-side flexibility required to limit the rise of LMP. Through our proposed approach a price requesting load can specify its maximum willingness to pay for electricity and through demand-side flexibility hedge against price volatility. For achieving this, an organizational structure for flexibility management is proposed that exhibits the coordination required between the Distribution System Operator (DSO), an aggregator and the price requesting load. To demonstrate the viability of our proposed formulation, we run an illustrative simulation under infinite and finite line capacities.

math.OC↗

arXiv2018

Energy Contract Settlements through Automated Negotiation in Residential Cooperatives

This paper presents an automated peer-to-peer (P2P) negotiation strategy for settling energy contracts among prosumers in a Residential Energy Cooperative (REC) considering heterogeneous prosumer preferences. The heterogeneity arises from prosumers' evaluation of energy contracts through multiple societal and environmental criteria and the prosumers' private preferences over those criteria. The prosumers engage in bilateral negotiations with peers to mutually agree on periodical energy contracts/loans that consist of an energy volume to be exchanged at that period and the return time of the exchanged energy. The prosumers keep an ordered preference profile of possible energy contracts by evaluating the contracts from their own valuations on the entailed criteria, and iteratively offer the peers contracts until an agreement is formed. A prosumer embeds the valuations into a utility function that further considers uncertainties imposed by demand and generation profiles. Empirical evaluation on real demand, generation and storage profiles illustrates that the proposed negotiation based strategy is able to increase the system efficiency (measured by utilitarian social welfare) and fairness (measured by Nash social welfare) over a baseline strategy and an individual flexibility control strategy. We thus elicit system benefits from P2P flexibility exchange already with few agents and without central coordination, providing a simple yet flexible and effective paradigm that may complement existing markets.

cs.MA↗

arXiv2016

Robust Energy Storage Scheduling for Imbalance Reduction of Strategically Formed Energy Balancing Groups

Imbalance (on-line energy gap between contracted supply and actual demand, and associated cost) reduction is going to be a crucial service for a Power Producer and Supplier (PPS) in the deregulated energy market. PPS requires forward market interactions to procure energy as precisely as possible in order to reduce imbalance energy. This paper presents, 1) (off-line) an effective demand aggregation based strategy for creating a number of balancing groups that leads to higher predictability of group-wise aggregated demand, 2) (on-line) a robust energy storage scheduling that minimizes the imbalance for a particular balancing group considering the demand prediction uncertainty. The group formation is performed by a Probabilistic Programming approach using Bayesian Markov Chain Monte Carlo (MCMC) method after applied on the historical demand statistics. Apart from the group formation, the aggregation strategy (with the help of Bayesian Inference) also clears out the upper-limit of the required storage capacity for a formed group, fraction of which is to be utilized in on-line operation. For on-line operation, a robust energy storage scheduling method is proposed that minimizes expected imbalance energy and cost (a non-linear function of imbalance energy) while incorporating the demand uncertainty of a particular group. The proposed methods are applied on the real apartment buildings' demand data in Tokyo, Japan. Simulation results are presented to verify the effectiveness of the proposed methods.

eess.SY↗

arXiv2016

Optimal Demand Side Management by Distributed and Secured Energy Commitment Framework

This paper introduces a demand-side distributed and secured energy commitment framework and operations for a Power Producer and Supplier (PPS) in deregulated environment. Due to the diversity of geographical location as well as customers' energy profile coupled with high number of customers, managing energy transactions and resulting energy exchanges are challenging for a PPS. The envisioned PPS maintains several aggregators (e.g. Microgrids), named as Sub Service Provider (SSP) that manage customers/subscribers under their domains. The SSPs act as agents that perform local energy matching (inside their domains) and distributed energy matching within SSPs to determine the energy commitment. The goal of the distributed energy matching is to reduce the involvement of External Energy Supplier (e.g. Utility) while providing a platform to demand side players to be a part of energy transaction. A distributed assignment problem is designed that requires minimum and aggregated information exchange (hence, secured) and solved by Linear Programming (LP) that provides the distributed matching decision. The communicative burden among SSPs due to the exchange of energy information is reduced by applying an adaptive coalition formation method. The simulations are conducted by implementing a synchronous distributed matching algorithm while showing the effectiveness of the proposed framework.

cs.MA↗