A variational inequality reformulation of a congested transit assignment model by Cominetti, Correa, Cepeda, and Florian

In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit networks. Transportation Science 35 (3), pp 250-267], an extension to the common-lines problem for general multidestination networks under congestion is analyzed. Their transit equilibrium assignment model allows for a full representation of congestion effects caused by the variation of effective frequencies experienced by passengers at transit stops. This model is the first to address these characteristics consistently with the concept of strategies. In a subsequent paper by Cepeda et al. (2006) [Cepeda, M., Cominetti, and R. Florian, M. (2006) A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria. Trans. Res B 40, 437-459], the computation of equilibrium is performed heuristically by the minimization of a gap function, using the method of successive averages. In this paper, a reformulation of this congested transit equilibrium assignment model is performed, demonstrating that the problem can be expressed as an equivalent variational inequality. The case of strictly capacitated transit networks is explored under the scope of this new reformulation, and new, broader conditions for the existence of solutions to this congested transit assignment model are determined.Peer ReviewedPostprint (published version

Uniqueness of gradient Gibbs measures with disorder

We consider - in uniformly strictly convex potential regime - two versions of random gradient models with disorder. In model (A) the interface feels a bulk term of random fields while in model (B) the disorder enters though the potential acting on the gradients. We assume a general distribution on the disorder with uniformly-bounded finite second moments. It is well known that for gradient models without disorder there are no Gibbs measures in infinite-volume in dimension $d = 2$, while there are shift-invariant gradient Gibbs measures describing an infinite-volume distribution for the gradients of the field, as was shown by Funaki and Spohn. Van Enter and Kuelske proved in 2008 that adding a disorder term as in model (A) prohibits the existence of such gradient Gibbs measures for general interaction potentials in $d = 2$. In Cotar and Kuelske (2012) we proved the existence of shift-covariant random gradient Gibbs measures for model (A) when $d\geq 3$, the disorder is i.i.d and has mean zero, and for model (B) when $d\geq 1$ and the disorder has stationary distribution. In the present paper, we prove existence and uniqueness of shift-covariant random gradient Gibbs measures with a given expected tilt $u\in R^d$ and with the corresponding annealed measure being ergodic: for model (A) when $d\geq 3$ and the disordered random fields are i.i.d. and symmetrically-distributed, and for model (B) when $d\geq 1$ and for any stationary disorder dependence structure. We also compute for both models for any gradient Gibbs measure constructed as in Cotar and Kuelske (2012), when the disorder is i.i.d. and its distribution satisfies a Poincar\'e inequality assumption, the optimal decay of covariances with respect to the averaged-over-the-disorder gradient Gibbs measure.Comment: 39 pages. arXiv admin note: text overlap with arXiv:1012.437

'Musicking' Musicking: Revealing the musicality of apparently straightforward musical practices

This submission comprises my recent compositions and accompanying writings, which depict a compositional practice that redirects attention to the nuances of musical activities that generally remain unnoticed. My works explore the impact of miniature durations upon form, the musical decisions behind score cosmetics, and listening as a creative practice. The portfolio predominantly consists of compositions gathered in series, ranging from music that calls for microscopic care, to music for imagined sound, to alternative listening modes for concert situations. The associated writings contextualise and reflect upon this approach to music making by reviewing literature on auditory morphogenesis (J. Tenney, A. Bregman, B. Snyder), non-traditional notation (C. Cardew, C. Wolff, E. Tufte), and on music as a network of activities (H. Brün, T. Coffey, C. Small)

Encoder-Decoder Approach to Predict Airport Operational Runway Configuration A case study for Amsterdam Schiphol airport

The runway configuration of an airport is the com- bination of runways that are active for arrivals and departures at any time. The runway configuration has a major influence on the capacity of the airport, taxiing times, the occupation of parking stands and taxiways, as well as on the management of traffic in the airspace surrounding the airport. The runway configuration of a given airport may change several times during the day, depending on the weather, air traffic demand and noise abatement rules, among other factors. This paper proposes an encoder-decoder model that is able to predict the future runway configuration sequence of an airport several hours upfront. In contrast to typical rule-based approaches, the proposed model is generic enough to be applied to any airport, since it only requires the past runway configuration history and the forecast traffic demand and weather in the prediction horizon. The performance of the model is assessed for the Amsterdam Schiphol Airport using three years of traffic, weather and runway use data.Peer ReviewedPostprint (published version

The calculator as an instrument of validation of mathematical knowledge: a case study (extended version)

En este trabajo se describe detalladamente una experiencia llevada a cabo con profesores de matemáticas en formación, sobre el papel que pueden desarrollar las nuevas tecnologías para llevar a cabo procesos de demostración y prueba en el aula de secundaria

Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \nabla\phi systems with non-convex potential

We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for \nabla\phi-Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.Comment: 41 pages, 5 figure

Application of configurational mechanics to crack propagation

Crack initiation and propagation is an essential aspect in the mechanical behavior of a large variety of materials and structures in all fields of Engineering and, in particular, the prediction of crack trajectories is one of the major challenges of existing numerical methods. Classical procedures to fix crack direction have been based on local criteria such as maximum (tensile) hope stress. However, Fracture Mechanics principles suggest that global criteria should be used instead, such as maximizing structural energy release rates. An emerging trend along this way is based on Configurational Mechanics, which describes a dual version of the mechanical problem in terms of configurational pseudo-stresses, pseudo-forces, etc. all with a physical meaning related to the change in global structural elastic energy caused by changes in the structural geometry (configuration). In the FEM context, these concepts are applied to optimize the total energy of the mesh with respect to reference coordinates using the discrete configurational forces. Configurational stresses given by Eshelby’s energy-momentum tensor may be integrated using standard expressions to give configurational nodal forces. Adequate treatment of these forces in the context of iterative FE calculations, may lead to prediction of crack trajectories in terms of global structural energy

Assessment of the feasible CTA windows for efficient spacing with energy-neutral CDO

Continuous descent operations (CDO) with con- trolled times of arrival (CTA) at one or several metering fixes could enable environmentally friendly procedures at the same time that terminal airspace capacity is not compromised. This paper focuses on CTA updates once the descent has been already initiated, assessing the feasible CTA window (and associated fuel consumption) of CDO requiring neither thrust nor speed-brake usage along the whole descent (i.e. energy modulation through elevator control is used to achieve different times of arrival at the metering fixes). A multiphase optimal control problem is formulated and solved by means of numerical methods. The minimum and maximum times of arrival at the initial approach fix (IAF) and final approach point (FAP) of an hypothetical scenario are computed for an Airbus A320 descent and starting from a wide range of initial conditions. Results show CTA windows up to 4 minutes at the IAF and 70 seconds at the FAP. It has been also found that the feasible CTA window is affected by many factors, such as a previous CTA or the position of the top of descent. Moreover, minimum fuel trajectories almost correspond to those trajectories that minimise the time of arrival at the metering fix for the given initial conditionPeer ReviewedPostprint (published version

Infinite-body optimal transport with Coulomb Cost

We introduce and analyze symmetric infinite-body optimal transport (OT) problems with cost function of pair potential form. We show that for a natural class of such costs, the optimizer is given by the independent product measure all of whose factors are given by the one-body marginal. This is in striking contrast to standard finite-body OT problems, in which the optimizers are typically highly correlated, as well as to infinite-body OT problems with Gangbo-Swiech cost. Moreover, by adapting a construction from the study of exchangeable processes in probability theory, we prove that the corresponding $N$-body OT problem is well approximated by the infinite-body problem. To our class belongs the Coulomb cost which arises in many-electron quantum mechanics. The optimal cost of the Coulombic N-body OT problem as a function of the one-body marginal density is known in the physics and quantum chemistry literature under the name SCE functional, and arises naturally as the semiclassical limit of the celebrated Hohenberg-Kohn functional. Our results imply that in the inhomogeneous high-density limit (i.e. $N\to\infty$ with arbitrary fixed inhomogeneity profile $\rho/N$), the SCE functional converges to the mean field functional. We also present reformulations of the infinite-body and N-body OT problems as two-body OT problems with representability constraints and give a dual characterization of representable two-body measures which parallels an analogous result by Kummer on quantum representability of two-body density matrices.Comment: 22 pages, significant revision