arXiv subjects

Jiaxin Hou

Publications and source records attributed to Jiaxin Hou.

4 recordsLinked to original sources

arXiv2026

A Coupled V2G Equilibrium Model of Electric Vehicle and Power System Interactions

Vehicle-to-grid (V2G) technology empowers electric vehicles (EVs) to act as mobile energy resources, providing critical support to power systems, especially under stressed conditions. To understand the economic mechanism driving V2G participation and its benefits to power grid, this paper proposes a multi-player coupled equilibrium framework that models the bidirectional interactions between power grid operations and EV routing, incorporating charging and discharging choice in a preprocessed feasible path generation procedure. Energy prices are endogenously determined by market clearance conditions. We formulate the overall problem as a Variational Inequality that unite the decision-making of Distribution System Operator, Charging Network Operator, Load Serving Entities, and EV drivers. Numerical studies validate the framework under two stress scenarios: increased household load and power line outages. Results show that when EVs are incentivized by reduced generalized path costs, V2G is particularly effective in eliminating load shedding and reducing distribution locational marginal electricity prices. On the transportation side, V2G can lead to divergence in EV behavior between normal and scarcity conditions, and alter route choices yet improve overall trip economic.

eess.SY↗

arXiv2026

The Lovász Theta Function for Recovering Planted Clique Covers and Graph Colorings

The problems of computing graph colorings and clique covers are central challenges in combinatorial optimization. Both of these are known to be NP-hard, and thus computationally intractable in the worst-case instance. A prominent approach for computing approximate solutions to these problems is the celebrated Lovász theta function $\vartheta(G)$, which is specified as the solution of a semidefinite program (SDP), and hence tractable to compute. In this work, we move beyond the worst-case analysis and set out to understand whether the Lovász theta function recovers clique covers for random instances that have a latent clique cover structure, possibly obscured by noise. We answer this question in the affirmative and show that for graphs generated from the planted clique model we introduce in this work, the SDP formulation of $\vartheta(G)$ has a unique solution that reveals the underlying clique-cover structure with high-probability. The main technical step is an intermediate result where we prove a deterministic condition of recovery based on an appropriate notion of sparsity.

math.OC↗

arXiv2025

Traffic Equilibrium in Mixed-Autonomy Network with Capped Customer Waiting

This paper develops a unified modeling framework to capture the equilibrium-state interactions among ride-hailing companies, travelers, and traffic of mixed-autonomy transportation networks. Our framework integrates four interrelated sub-modules: (i) the operational behavior of representative ride-hailing Mixed-Fleet Traffic Network Companies (MiFleet TNCs) managing autonomous vehicle (AV) and human-driven vehicle (HV) fleets, (ii) traveler mode-choice decisions taking into account travel costs and waiting time, (iii) capped customer waiting times to reflect the option available to travelers not to wait for TNCs' service beyond his/her patience and to resort to existing travel modes, and (iv) a flow-dependent traffic congestion model for travel times. A key modeling feature distinguishes AVs and HVs across the pickup and service (customer-on-board) stages: AVs follow Wardrop pickup routes but may deviate during service under company coordination, whereas HVs operate in the reverse manner. The overall framework is formulated as a Nonlinear Complementarity Problem (NCP), which is equivalent to a Variational Inequality(VI) formulation based on which the existence of a variational equilibrium solution to the traffic model is established. Numerical experiments examine how AV penetration and Wardrop relaxation factors, which bound route deviation, affect company, traveler, and system performance to various degrees. The results provide actionable insights for policymakers on regulating AV adoption and company vehicle deviation behavior in modern-day traffic systems that are fast changing due to the advances in technology and information accessibility.

eess.SY↗

arXiv2024

Macromolecular crowding in chiral assembly of ellipsoidal nanoparticles

Anisotropic colloidal particles have the ability to self-assemble into cholesteric structures. We used molecular dynamics to simulate the self-assembly of ellipsoidal particles with the objective to establish a general framework to reveal the primary factors driving chiral interactions. To characterize these interactions, we introduce a characteristic parameter following the crowding factor (CF) theory. Our simulations and statistical analysis showed good agreement with the CF theory; at the early stages of the assembly process, the ellipsoidal particles go through a critical aggregation point followed by further clustering towards nematic order. Further, we demonstrate that in high CF conditions, small initial clusters may induce a chiral twist which subsequently forms a cholesteric structure with no directional preference in higher organization states.

cond-mat.soft↗