arXiv subjects

Julia Lange

Publications and source records attributed to Julia Lange.

3 recordsLinked to original sources

arXiv2026

CLInstGen: An Instance Generation Framework for Two-Tier City Logistics

City logistics addresses the design and management of efficient freight transportation in urban areas. Two-tier networks, where goods are moved by different vehicle fleets from distribution centers to customers using intermediate consolidation facilities, are particularly effective. Although studied from routing, location, and network design perspectives, the research progress is slowed by the lack of standardized, state-of-the-art benchmark data. Many studies rely on outdated and artificial or case-specific instances, limiting reproducibility, comparability, and generality of results. To address this gap, we identify general problem characteristics for two-tier city logistics, provide an instance generation framework CLInstGen that is applicable to a wide range of problem settings, and propose the first benchmark library CLLIB. The library and the CLInstGen code are open-source, allowing researchers to easily use, adapt, and generate instances for their specific applications. CLLIB is based on real-world geographies of urban regions and provides a curated collection of standardized instances for direct benchmarking of models and methods as well as statistical evaluation. A computational study with two different problem settings, namely tactical service network design on two tiers and vehicle routing with simultaneous pickups and deliveries on a single tier, confirms the versatility of both the generator and the library, and provides first numerical and managerial insights on the CLLIB benchmark instances.

math.OC↗

arXiv2026

Hamilton--Jacobi theory for non-conservative field theories in the $k$-contact framework

This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-contact geometry. We introduce evolution k-contact k-vector fields, extending the contact evolution formalism to field theories, and analyse the corresponding Hamilton--De Donder--Weyl equations. Moreover, we develop two distinct families of Hamilton--Jacobi theories: a z-independent approach, based on the reconstruction of the dynamics from an integrable k-vector field defined on the base manifold of $(\bigoplus^kT^*Q)\times\mathbb{R}^k\to Q$, and a z-dependent approach, where the integrable k-vector field is defined on the base manifold of $(\bigoplus^kT^*Q)\times\mathbb{R}^k\to Q\times\mathbb{R}^k$. We develop in detail the important case of Hamiltonian functions with affine dependence on the dissipative variables, show how quadratic dependence on these variables can be used structurally to enlarge the range of applications, and recover the ordinary contact Hamilton--Jacobi theory as the particular case k=1, while removing some technical assumptions appearing in previous formulations. Our theory is illustrated through several representative examples, including the telegrapher/Klein--Gordon equation, a dissipative Hunter--Saxton equation, a simple dissipative non-regular first-order field model, and a relativistic thermodynamic model.

math-ph↗

arXiv2023

A symplectic approach to Schr\"odinger equations in the infinite-dimensional unbounded setting

By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to $t$-dependent Schr\"odinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by unbounded $t$-dependent self-adjoint Hamiltonians satisfying a technical condition. As an application, the Marsden--Weinstein reduction procedure is employed to map above-mentioned $t$-dependent Schr\"odinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed.

math-ph↗