arXiv subjects
Publications and source records attributed to Luke Baker.
We construct approximate traveling wave solutions for the $3d$ focusing cubic NLS perturbed by a rapidly decaying external potential. As an application, we demonstrate that there exists a forward-global, $H^1$ bounded, nonscattering solution at any mass-energy higher than the ground state threshold for the unperturbed equation.
The ORBIT (Operations Responses and Business Intelligence Toolkit) project was initiated to assess agentic AI for the upcoming ESnet 7 initiative and to address persistent operational pain points in the Network Operations Center (NOC) workflow. ESnet operators experience slow retrieval from siloed data sources, incidents described in lengthy and difficult-to-parse tickets, and context loss across shift handoffs. These challenges increase cognitive load and prolong incident resolution times. ORBIT therefore targets routine automation, cross-source synthesis, and actionable insights delivered directly within operators' existing tooling. ORBIT is an agentic AI system integrated into ServiceNow, ESnet's primary incident management platform. The design uses a modular, layered architecture comprising a centralized reasoning hub, tool access via MCPs for ESnet data sources, a semantic search layer, and an operator-facing chat interface. To manage the complexity and stochasticity of the AI toolchain, ORBIT follows industry best practices by structuring task logic as versioned, tested "skills" that guide the system in performing bounded responsibilities. This improves reliability and predictability compared to fully unconstrained agent behavior. Key results show that ORBIT successfully delivered all six initial tasks, and the architecture enabled rapid development of two additional tasks proposed by NOC engineers. We observed strong organic adoption of general-purpose infrastructure components, especially the chat interface and LiteLLM model gateway, including high request volumes from outside the project. Experiments with skills indicate that this approach can reduce task completion steps while eliminating observed error modes.
We classify the dynamics of radial $H^1$ solutions at the (radial) ground state threshold for the $3d$ cubic NLS in the presence of a repulsive inverse-square potential.
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in two space dimensions for all powers $p>0$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case $0<p\leq 2$. We use the method of concentration-compactness and contradiction. We preclude the existence of compact solutions using a Morawetz estimate in the style of Nakanishi.
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in one space dimension for powers $p>2$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case $2<p\leq 4$. We use the method of concentration-compactness and contradiction, utilizing a Morawetz estimate in the style of Nakanishi in order to preclude the existence of compact solutions.
We formulate a control system model for the distributed flow of mixtures of highly heterogeneous gases through large-scale pipeline networks with time-varying injections of constituents, withdrawals, and control actions of compressors. This study is motivated by the proposed blending of clean hydrogen into natural gas pipelines as an interim means to reducing end use carbon emissions while utilizing existing infrastructure for its planned lifetime. We reformulate the partial differential equations for gas dynamics on pipelines and balance conditions at junctions using lumped elements to a sparse nonlinear differential algebraic equation system. Our key advance is modeling the mixing of constituents in time throughout the network, which requires doubling the state space needed for a single gas and increases numerical ill-conditioning. The reduced model is shown to be a consistent approximation of the original system, which we use as the dynamic constraints in a model-predictive optimal control problem for minimizing the energy expended by applying time-varying compressor operating profiles to guarantee time-varying delivery profiles subject to system pressure limits. The optimal control problem is implemented after time discretization using a nonlinear program, with validation of the results done using a transient simulation. We demonstrate the methodology for a small test network, and discuss scalability and potential applications.