Academic literature on the topic 'Mean field optimal transport'
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Journal articles on the topic "Mean field optimal transport"
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Baudelet, Sebastian, Brieuc Frénais, Mathieu Laurière, Amal Machtalay, and Yuchen Zhu. "Deep learning for mean field optimal transport." ESAIM: Proceedings and Surveys 77 (2024): 145–75. http://dx.doi.org/10.1051/proc/202477145.
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Mean field control (MFC) problems have been introduced to study social optima in very large populations of strategic agents. The main idea is to consider an infinite population and to simplify the analysis by using a mean field approximation. These problems can also be viewed as optimal control problems for McKean-Vlasov dynamics. They have found applications in a wide range of fields, from economics and finance to social sciences and engineering. Usually, the goal for the agents is to minimize a total cost which consists in the integral of a running cost plus a terminal cost. In this work, we consider MFC problems in which there is no terminal cost but, instead, the terminal distribution is prescribed as in optimal transport problem. By analogy with MFC, we call such problems mean field optimal transport problems (or MFOT for short) since they can be viewed as a generalization of classical optimal transport problems when mean field interactions occur in the dynamics or the running cost function. We propose three numerical methods based on neural networks. The first one is based on directly learning an optimal control. The second one amounts to solve a forward-backward PDE system characterizing the solution. The third one relies on a primal-dual approach. We illustrate these methods with numerical experiments conducted on two families of examples.
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Cao, Haoyang, Xin Guo, and Mathieu Laurière. "Connecting GANs, Mean-Field Games, and Optimal Transport." SIAM Journal on Applied Mathematics 84, no. 4 (July 1, 2024): 1255–87. http://dx.doi.org/10.1137/22m1499534.
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Liu, Jiakun, and Grégoire Loeper. "Optimal transport with discrete long-range mean-field interactions." Bulletin of Mathematical Sciences 10, no. 02 (May 12, 2020): 2050011. http://dx.doi.org/10.1142/s1664360720500113.
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We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma–Trudinger–Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151–183.].
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Di Persio, Luca, and Matteo Garbelli. "From Optimal Control to Mean Field Optimal Transport via Stochastic Neural Networks." Symmetry 15, no. 9 (September 8, 2023): 1724. http://dx.doi.org/10.3390/sym15091724.
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In this paper, we derive a unified perspective for Optimal Transport (OT) and Mean Field Control (MFC) theories to analyse the learning process for Neural Network algorithms in a high-dimensional framework. We consider a Mean Field Neural Network in the context of MFC theory referring to the mean field formulation of OT theory that may allow the development of efficient algorithms in a high-dimensional framework while providing a powerful tool in the context of explainable Artificial Intelligence.
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Ruthotto, Lars, Stanley J. Osher, Wuchen Li, Levon Nurbekyan, and Samy Wu Fung. "A machine learning framework for solving high-dimensional mean field game and mean field control problems." Proceedings of the National Academy of Sciences 117, no. 17 (April 9, 2020): 9183–93. http://dx.doi.org/10.1073/pnas.1922204117.
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Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexible machine learning framework for the numerical solution of potential MFG and MFC models. State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse of dimensionality. We approximately solve high-dimensional problems by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning. More precisely, we work with a Lagrangian formulation of the problem and enforce the underlying Hamilton–Jacobi–Bellman (HJB) equation that is derived from the Eulerian formulation. Finally, a tailored neural network parameterization of the MFG/MFC solution helps us avoid any spatial discretization. Our numerical results include the approximate solution of 100-dimensional instances of optimal transport and crowd motion problems on a standard work station and a validation using a Eulerian solver in two dimensions. These results open the door to much-anticipated applications of MFG and MFC models that are beyond reach with existing numerical methods.
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Sivilevičius, Henrikas, and Mindaugas Martišius. "FIELD INVESTIGATION AND ASSESSMENT ON THE WEAR OF ASPHALT PAVEMENT MILLING MACHINE PICKS." Transport 36, no. 6 (February 9, 2022): 499–509. http://dx.doi.org/10.3846/transport.2021.16443.
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Deteriorated asphalt pavement material is recycled applying proved technologies based on scientific principles and practical experience. The asphalt pavement layer during rehabilitation process is loosened by a mobile transport machine fracturing into the required material grading and called Reclaimed Asphalt Pavement (RAP). RAP is extracted while cutting asphalt chip in required depth at optimal speed by mean of changeable picks installed in a toolholder of milling machine rotating drum. During interaction with the asphalt pavement to be demolished, the wear of picks appears, and the dimensions of their elements decrease. Methodology and results of a field experimental research allowed statistically to determine and evaluate the wear dynamics of picks from 2 manufacturers are provided in this paper. The results provide that length of pick, diameter of carbide tip and diameter of steel body of picks from these manufacturers were decreasing proportionally to milled asphalt pavement surface. Applying the Fisher’s criterion it was found that the variances of the reduction of these geometrical parameters are the same and they satisfy the normal distribution according to the Kolmogorov’s criterion. All values of Student’s criterion calculated statistics were higher than the critical values, which indicated that the wear intensiveness of the picks of the 2 manufacturers differed significantly. These data can be used to select suitable picks for the milling machine according to their wear intensity.
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BARTON, ALISTAIR, and NASSIF GHOUSSOUB. "Dynamic and stochastic propagation of the Brenier optimal mass transport." European Journal of Applied Mathematics 30, no. 6 (March 20, 2019): 1264–99. http://dx.doi.org/10.1017/s0956792519000032.
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Similar to how Hopf–Lax–Oleinik-type formula yield variational solutions for Hamilton–Jacobi equations on Euclidean space, optimal mass transportations can sometimes provide variational formulations for solutions of certain mean-field games. We investigate here the particular case of transports that maximize and minimize the following ‘ballistic’ cost functional on phase space TM, which propagates Brenier’s transport along a Lagrangian L, $$b_T(v, x):=\inf\left\{\langle v, \gamma (0)\rangle +\int_0^TL(t, \gamma (t), {\dot \gamma}(t))\, dt; \gamma \in C^1([0, T], M); \gamma(T)=x\right\}\!,$$ where $M = \mathbb{R}^d$, and T >0. We also consider the stochastic counterpart: \begin{align*} \underline{B}_T^s(\mu,\nu):=\inf\left\{\mathbb{E}\left[\langle V,X_0\rangle +\int_0^T L(t, X,\beta(t,X))\,dt\right]\!; X\in \mathcal{A}, V\sim\mu,X_T\sim \nu\right\}\!, \end{align*} where $\mathcal{A}$ is the set of stochastic processes satisfying dX = βX (t, X) dt + dWt, for some drift βX (t, X), and where Wt is σ(Xs: 0 ≤ s ≤ t)-Brownian motion. Both cases lead to Lax–Oleinik-type formulas on Wasserstein space that relate optimal ballistic transports to those associated with dynamic fixed-end transports studied by Bernard–Buffoni and Fathi–Figalli in the deterministic case, and by Mikami–Thieullen in the stochastic setting. While inf-convolution easily covers cost minimizing transports, this is not the case for total cost maximizing transports, which actually are sup-inf problems. However, in the case where the Lagrangian L is jointly convex on phase space, Bolza-type dualities – well known in the deterministic case but novel in the stochastic case – transform sup-inf problems to sup–sup settings. We also write Eulerian formulations and point to links with the theory of mean-field games.
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Igbida, Noureddine, and Van Thanh Nguyen. "Optimal partial transport problem with Lagrangian costs." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 2109–32. http://dx.doi.org/10.1051/m2an/2018001.
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We introduce a dual dynamical formulation for the optimal partial transport problem with Lagrangian costs cL(x,y) := ξ∈Lip([0,1];ℝN)inf {∫01 L(ξ(t), ξ˙(t))dt : ξ(0) = x, ξ(1) = y} based on a constrained Hamilton–Jacobi equation. Optimality condition is given that takes the form of a system of PDEs in some way similar to constrained mean field games. The equivalent formulations are then used to give numerical approximations to the optimal partial transport problem via augmented Lagrangian methods. One of advantages is that the approach requires only values of L and does not need to evaluate cL(x, y), for each pair of endpoints x and y, which comes from a variational problem. This method also provides at the same time active submeasures and the associated optimal transportation.
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Miatselskaya, N. S., A. I. Bril, A. P. Chaikovsky, Yu Yu Yukhymchuk, G. P. Milinevski, and A. A. Simon. "OPTIMAL INTERPOLATION OF AERONET RADIOMETRIC NETWORK OBSERVATIONS FOR THE EVALUATION OF THE AEROSOL OPTICAL DEPTH DISTRIBUTION IN THE EASTERN EUROPEAN REGION." Journal of Applied Spectroscopy 89, no. 2 (March 18, 2022): 246–53. http://dx.doi.org/10.47612/0514-7506-2022-89-2-246-253.
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The application of the optimal interpolation method for the assimilation of the observational data of aerosol optical thickness (AOT), which are sparse in space and time, in the chemical transport model is herein validated. Assuming the negligible error of AOT observations in the AERONET ground-based radiometric network, spatial and temporal correlation functions of the errors in the results of the AOT simulated by the GEOS-Chem chemical transport model are obtained. The optimal interpolation method is applied to the AERONET data using the GEOS-Chem results as a background field for the Eastern European region for 2015–2016. It is shown that the use of the optimal interpolation method permits to reduce the root-mean-square error of the AOT estimation by more than a third in places where there are no AERONET stations in comparison with the model results.
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Hassanzadeh, Pedram, Gregory P. Chini, and Charles R. Doering. "Wall to wall optimal transport." Journal of Fluid Mechanics 751 (June 24, 2014): 627–62. http://dx.doi.org/10.1017/jfm.2014.306.
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AbstractThe calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy (mean square velocity) or a fixed value of the enstrophy (mean square vorticity). The optimizing flows consist of an array of (convection) cells of a particular aspect ratio $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\varGamma $. We solve the nonlinear Euler–Lagrange equations analytically for weak flows and numerically – as well as via matched asymptotic analysis in the fixed energy case – for strong flows. We report the results in terms of the Nusselt number ${\mathit{Nu}}$, a dimensionless measure of the tracer transport, as a function of the Péclet number ${\mathit{Pe}}$, a dimensionless measure of the strength of the flow. For both constraints, the maximum transport ${\mathit{Nu}}_{\mathit{MAX}}({\mathit{Pe}})$ is realized in cells of decreasing aspect ratio $\varGamma _{\mathit{opt}}({\mathit{Pe}})$ as ${\mathit{Pe}}$ increases. For the fixed energy problem, ${\mathit{Nu}}_{\mathit{MAX}} \sim {\mathit{Pe}}$ and $\varGamma _{\mathit{opt}} \sim {\mathit{Pe}}^{-1/2}$, while for the fixed enstrophy scenario, ${\mathit{Nu}}_{\mathit{MAX}} \sim {\mathit{Pe}}^{10/17}$ and $\varGamma _{\mathit{opt}} \sim {\mathit{Pe}}^{-0.36}$. We interpret our results in the context of buoyancy-driven Rayleigh–Bénard convection problems that satisfy the flow intensity constraints, enabling us to investigate how the transport scalings compare with upper bounds on ${\mathit{Nu}}$ expressed as a function of the Rayleigh number ${\mathit{Ra}}$. For steady convection in porous media, corresponding to the fixed energy problem, we find ${\mathit{Nu}}_{\mathit{MAX}} \sim {\mathit{Ra}}$ and $\varGamma _{\mathit{opt}} \sim {\mathit{Ra}}^{-1/2}$, while for steady convection in a pure fluid layer between stress-free isothermal walls, corresponding to fixed enstrophy transport, ${\mathit{Nu}}_{\mathit{MAX}} \sim {\mathit{Ra}}^{5/12}$ and $\varGamma _{\mathit{opt}} \sim {\mathit{Ra}}^{-1/4}$.
Dissertations / Theses on the topic "Mean field optimal transport"
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Mészáros, Alpár Richárd. "Density constraints in optimal transport, PDEs and mean field games." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112155/document.
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Movité par des questions posées par F. Santambrogio, cette thèse est dédiée à l'étude de jeux à champ moyen et des modèles impliquant le transport optimal avec contraintes de densité. A fin d'étudier des modèles de MFG d'ordre deux dans l'esprit des travaux de F. Santambrogio, on introduit en tant que brique élementaire un modèle diffusif de mouvement de foule avec contraintes de densité (en généralisant dans une sense les travaux de Maury et al.). Le modèle est décrit par l'évolutions de la densité de la foule, qui peut être vu comme une courbe dans l'espace de Wasserstein. Du point de vu EDP, ça correspond à une équation de Fokker-Planck modifiée, avec un terme supplémentaire, le gradient d'une pression (seulement dans la zone saturée) dans le drift. En passant par l'équation duale et en utilisant des estimations paraboliques bien connues, on démontre l'unicité du pair densité et pression. Motivé initialement par l'algorithm de splitting (utilisé dans le résultat d'existence ci-dessus), on étudie des propriétés fines de la projection de Wasserstein en dessous d'un seuil donné. Intégrant cette question dans une classe plus grande de problèmes impliquant le transport optimal, on démontre des estimations BV pour les optimiseurs. D'autres applications possibles (en transport partiel, optimisation de forme et problèmes paraboliques dégénérés) de ces estimations BV sont également discutées.En changeant le point de vu, on étudie également des modèles de MFG variationnels avec contraintes de densité. Dans ce sens, les systèmes de MFG sont obtenus comme conditions d'optimalité de premier ordre pour deux problèmes convexes en dualité. Dans ces systèmes un terme additionnel apparaît, interpreté comme un prix à payer quand les agents passent dans des zones saturées. Premièrement, en profitant des résultats de régularité elliptique, on montre l'existence et la caractérisation de solutions des MFG de deuxième ordre stationnaires avec contraintes de densité. Comme résultat additionnel, on caractérise le sous-différentiel d'une fonctionnelle introduite par Benamou-Brenier pour donner une formulation dynamique du problème de transport optimal. Deuxièmement, (basé sur une technique de pénalisation) on montre qu'une classe de systèmes de MFG de premier ordre avec contraintes de densité est bien posée. Une connexion inattendu avec les équations d'Euler incompressible à la Brenier est égalment donnéeMotivated by some questions raised by F. Santambrogio, this thesis is devoted to the study of Mean Field Games and models involving optimal transport with density constraints. To study second order MFG models in the spirit of the work of F. Santambrogio, as a possible first step we introduce and show the well-posedness of a diffusive crowd motion model with density constraints (generalizing in some sense the works by B. Maury et al.). The model is described by the evolution of the people's density, that can be seen as a curve in the Wasserstein space. From the PDE point of view, this corresponds to a modified Fokker-Planck equation, with an additional gradient of a pressure (only living in the saturated zone) in the drift. We provide a uniqueness result for the pair density and pressure by passing through the dual equation and using some well-known parabolic estimates. Initially motivated by the splitting algorithm (used for the above existence result), we study some fine properties of the Wasserstein projection below a given threshold. Embedding this question into a larger class of variational problems involving optimal transport, we show BV estimates for the optimizers. Other possible applications (for partial optimal transport, shape optimization and degenerate parabolic problems) of these BV estimates are also discussed.Changing the point of view, we also study variational Mean Field Game models with density constraints. In this sense, the MFG systems are obtained as first order optimality conditions of two convex problems in duality. In these systems an additional term appears, interpreted as a price to be paid when agents pass through saturated zones. Firstly, profiting from the regularity results of elliptic PDEs, we give the existence and characterization of the solutions of stationary second order MFGs with density constraints. As a byproduct we characterize the subdifferential of a convex functional introduced initially by Benamou-Brenier to give a dynamic formulation of the optimal transport problem. Secondly, (based on a penalization technique) we prove the well-posedness of a class of first order evolutive MFG systems with density constraints. An unexpected connection with the incompressible Euler's equations à la Brenier is also given
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Marzufero, Luciano. "Some optimal visiting problems: from a single player to a mean-field type model." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/350780.
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In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field game framework, that is when a huge population of agents plays the optimal visiting problem with a controlled dynamics and with costs also depending on the distribution of the population. In particular, we investigate a single continuity equation with possible sinks and sources and the field possibly depending on the mass of the agents. The same problem is also studied on a network framework. More precisely, we study a mean-field game model by proving the existence of a suitable definition of an approximated mean-field equilibrium and then we address the passage to the limit.
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Frénais, Brieuc. "Modèles stochastiques de branchement-sélection." Electronic Thesis or Diss., Strasbourg, 2024. http://www.theses.fr/2024STRAD033.
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L'objet central de cette thèse est un système de particules se déplaçant sur la droite réelle et soumises à des règles de branchement et de sélection, appelé N-processus de Markov branchant, qui généralise le N-mouvement brownien branchant étudié par Maillard en autorisant des trajectoires plus générales pour les particules. Nos principaux résultats établissent sous certaines hypothèses de régularité l'existence d'une limite hydrodynamique pour ce système de particule, qui est la fonction de répartition de la loi du processus sous-jacent conditionné à ne pas avoir franchi une certaine frontière, caractérisée comme solution d'un problème inverse du premier temps de passage. La démonstration repose sur un couplage avec des processus auxiliaires, construit en exploitant une hypothèse de monotonie stochastique du processus sous-jacent. En parallèle, nous abordons un problème de transport optimal en champ moyen sous un angle numérique. Nous développons trois méthodes d'apprentissage profond pour obtenir des solutions approchées, mises en œuvre sur divers cas tests, illustrant l'efficacité des approches proposéesThe central object of this thesis is a system of particles moving on the real line and subject to branching and selection rules, called N-branching Markov process, which generalizes the N-branching Brownian motion studied by Maillard, by allowing more general trajectories for the particles. Our main results establish under certain regularity assumptions the existence of a hydrodynamic limit for this particle system, which is the c.d.f. of the distribution of the underlying process conditioned on not having crossed a certain boundary, characterized as the solution of an inverse first-passage time problem. The proof relies on a coupling with auxiliary processes, constructed by exploiting an assumption of stochastic monotonicity on the underlying process. In parallel, we consider the mean field optimal transport problem with a numerical point of view. We develop three deep learning methods to obtain approximate solutions, implemented on various test cases, illustrating the effectiveness of the proposed approaches
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Bonnet, Benoît. "Optimal control in Wasserstein spaces." Electronic Thesis or Diss., Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0442.
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Une vaste quantité d'outils mathématiques permettant la modélisation et l'analyse des problèmes multi-agents ont récemment été développés dans le cadre de la théorie du transport optimal. Dans cette thèse, nous étendons pour la première fois plusieurs de ces concepts à des problématiques issues de la théorie du contrôle. Nous démontrons plusieurs résultats sur ce sujet, notamment des conditions nécessaires d'optimalité de type Pontryagin dans les espaces de Wasserstein, des conditions assurant la régularité intrinsèque de solutions optimales, des conditions suffisantes pour l'émergence de différents motifs, ainsi qu'un résultat auxiliaire à propos des arrangements de certaines singularités en géométrie sous-RiemannienneA wealth of mathematical tools allowing to model and analyse multi-agent systems has been brought forth as a consequence of recent developments in optimal transport theory. In this thesis, we extend for the first time several of these concepts to the framework of control theory. We prove several results on this topic, including Pontryagin optimality necessary conditions in Wasserstein spaces, intrinsic regularity properties of optimal solutions, sufficient conditions for different kinds of pattern formation, and an auxiliary result pertaining to singularity arrangements in Sub-Riemannian geometry
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Capuani, Rossana. "Mean Field Games with State Constraints." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED006.
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L’objet de cette thèse est l’étude des jeux champs moyen déterministes avec contrainte sur l’état. La théorie des jeux à champ moyen (mean field games (MFG)), initiée par Lasry et Lions en 2006, étudie des problèmes d’optimisation pour grandes populations d'agents dans un milieu dynamique. L'analyse mathématique de tels problèmes s'est jusqu'à présent concentrée sur des situations dans lequel les agents évoluent dans tout l’espace. En pratique, cependant, les agents ont des contraintes sur l'état. Le but de la thèse est celle d'étudier l'impact de ces contraintes sur l'analyse des systèmes de jeux à champ moyen. Nous montrons que les équilibres de Nash peuvent être décrits en termes de point fixe sur un espace de mesure sur des courbes contraintes (notion d’équilibre généralisé). Afin d’obtenir des résultats plus fins sur de tels équilibres, nous montrons un principe d’optimalité lisse pour les courbes optimales avec contraintes sur l’état. Nous en déduisons que les équilibres généralisés satisfont un système MFG, où les équations de Hamiton-Jacobi et les équations de transport doivent être entendues dans un sens spécifiqueThe aim of this Thesis is to study deterministic mean field games with state constraints. Mean field games (MFG) is a recent theory invented by Lasry and Lions which studies optimization problems with large populations of agents in a dynamical framework. The mathematical analysis of such problems has so far focused on situations where the agents can evolve in the whole space. In practice, however, the agents often have constraints on their state. The aim of this Thesis is to understand the consequence of such constraints on the analysis of mean field games. We first show that the Nash MFG equilibria can be described as fixed points on the space of measures on constrained trajectories (generalized MFG equilibria). In order to obtain more precise results on these equilibria, we show a smooth optimality principle for the optimal trajectories of control problem with state constraints. We derive from this that the generalized equilibria satisfy a MFG system in which the Hamilton-Jacobi equation and the continuity equation have to be understand in a specific sense
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Monson, Peter A. "Dynamic mean field theory for fluids in mesoporous materials." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184643.
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Monson, Peter A. "Dynamic mean field theory for fluids in mesoporous materials." Diffusion fundamentals 16 (2011) 13, S. 1-2, 2011. https://ul.qucosa.de/id/qucosa%3A13742.
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Häggbom, Marcus, and Shayan Nafar. "Mean-Variance Portfolio Selection Accounting for Financial Bubbles: A Mean-Field Type Approach." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252299.
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The phenomenon of financial bubbles is known to have impacted various markets since the seventeenth century. Such bubbles are known to form when the market drastically overvalues the price of an asset, causing its market value to increase hyperbolically, only to suddenly collapse once the untenable perceived future prospects of the asset are realized. Hence, it remains crucial for investors to be able to sell off assets residing within a bubble before they burst and their value is significantly diminished. Thus, portfolio optimization methods capable of accounting for financial bubbles in stock dynamics is a field of great value and interest for market participants. Portfolio optimization with respect to the mean-field is a relatively novel approach to accounting for the bubble-phenomenon. Hence, this paper investigates a previously unattempted method of portfolio optimization, providing a mean-field solution to the mean-variance trade-off problem, as well as providing new definitions of stock dynamics capable of diverting investors from bubbles.Finansiella bubblor är ett fenomen som har påverkat marknader sedan 1600-talet. Bubblor tenderar att skapas när marknaden kraftigt övervärderar en tillgång vilket orsakar en hyperbolisk tillväxt i marknadspriset. Detta följs av en plötslig kollaps. Därför är det viktigt för investerare att kunna minska sin exponering mot aktier som befinner sig i en bubbla, så att risken för stora plötsliga förluster reduceras. Således är portföljoptimering där aktiedynamiken tar hänsyn till bubblor av högt intresse för marknadsdeltagare. Portföljoptimering med avseende på medelfältet är ett relativt nytt tillvägagångssätt för att behandla bubbelfenomen. Av denna anledning undersöks i detta arbete en hittills oprövad lösningsmetod som möjliggör en medelfältslösning till avvägningen mellan förväntad avkastning och risk. Där-utöver presenteras även ett antal nya modeller för aktier som kan bortleda investerare från bubblor.
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Basna, Rani. "Mean Field Games for Jump Non-Linear Markov Process." Doctoral thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-55852.
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The mean-field game theory is the study of strategic decision making in very large populations of weakly interacting individuals. Mean-field games have been an active area of research in the last decade due to its increased significance in many scientific fields. The foundations of mean-field theory go back to the theory of statistical and quantum physics. One may describe mean-field games as a type of stochastic differential game for which the interaction between the players is of mean-field type, i.e the players are coupled via their empirical measure. It was proposed by Larsy and Lions and independently by Huang, Malhame, and Caines. Since then, the mean-field games have become a rapidly growing area of research and has been studied by many researchers. However, most of these studies were dedicated to diffusion-type games. The main purpose of this thesis is to extend the theory of mean-field games to jump case in both discrete and continuous state space. Jump processes are a very important tool in many areas of applications. Specifically, when modeling abrupt events appearing in real life. For instance, financial modeling (option pricing and risk management), networks (electricity and Banks) and statistics (for modeling and analyzing spatial data). The thesis consists of two papers and one technical report which will be submitted soon: In the first publication, we study the mean-field game in a finite state space where the dynamics of the indistinguishable agents is governed by a controlled continuous time Markov chain. We have studied the control problem for a representative agent in the linear quadratic setting. A dynamic programming approach has been used to drive the Hamilton Jacobi Bellman equation, consequently, the optimal strategy has been achieved. The main result is to show that the individual optimal strategies for the mean-field game system represent 1/N-Nash equilibrium for the approximating system of N agents. As a second article, we generalize the previous results to agents driven by a non-linear pure jump Markov processes in Euclidean space. Mathematically, this means working with linear operators in Banach spaces adapted to the integro-differential operators of jump type and with non-linear partial differential equations instead of working with linear transformations in Euclidean spaces as in the first work. As a by-product, a generalization for the Koopman operator has been presented. In this setting, we studied the control problem in a more general sense, i.e. the cost function is not necessarily of linear quadratic form. We showed that the resulting unique optimal control is of Lipschitz type. Furthermore, a fixed point argument is presented in order to construct the approximate Nash Equilibrium. In addition, we show that the rate of convergence will be of special order as a result of utilizing a non-linear pure jump Markov process. In a third paper, we develop our approach to treat a more realistic case from a modelling perspective. In this step, we assume that all players are subject to an additional common noise of Brownian type. We especially study the well-posedness and the regularity for a jump version of the stochastic kinetic equation. Finally, we show that the solution of the master equation, which is a type of second order partial differential equation in the space of probability measures, provides an approximate Nash Equilibrium. This paper, unfortunately, has not been completely finished and it is still in preprint form. Hence, we have decided not to enclose it in the thesis. However, an outlook about the paper will be included.
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Chen, Rui. "Dynamic optimal control for distress large financial networks and Mean field systems with jumps Optimal connectivity for a large financial network Mean Field BSDEs and Global Dynamic Risk Measures." Thesis, Paris Sciences et Lettres (ComUE), 2019. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2019PSLED042.
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Cette thèse propose des modèles et des méthodes pour étudier le contrôle du risque dans de larges systèmes financiers. Nous proposons dans une première partie une approche structurelle : nous considérons un système financier représenté comme un réseau d’institutions connectées entre elles par des interactions stratégiques sources de financement mais également par des interactions qui les exposent à un risque de contagion de défaut. La nouveauté de notre approche réside dans le fait que ces deux types d’interaction interfèrent. Nous proposons des nouvelles notions d’équilibre pour ces systèmes et étudions la connectivité optimale du réseau et le risque systémique associé. Dans une deuxième partie, nous introduisons des mesures de risque systémique définies par des équations différentielles stochastiques rétrogrades dirigées par des opérateurs à champ moyen et étudions des problèmes d’arrêt optimal associés. La dernière partie aborde des questions de liquidation optimale de portefeuillesThis thesis presents models and methodologies to understand the control of systemic risk in large systems. We propose two approaches. The first one is structural : a financial system is represented as a network of institutions. They have strategic interactions as well as direct interactions through linkages in a contagion process. The novelty of our approach is that these two types of interactions are intertwined themselves and we propose new notions of equilibria for such games and analyze the systemic risk emerging in equilibrium. The second approach is a reduced form.We model the dynamics of regulatory capital using a mean field operator : required capital depends on the standalone risk but also on the evolution of the capital of all other banks in the system. In this model, required capital is a dynamic risk measure and is represented as a the solution of a mean-field BDSE with jumps. We show a novel dual representation theorem. In the context of meanfield BSDEs the representation gives yield to a stochastic discount factor and a worst-case probability measure that encompasses the overall interactions in the system. We also solve the optimal stopping problem of dynamic risk measure by connecting it to the solution of reflected meanfield BSDE with jumps. Finally, We provide a comprehensive model for the order book dynamics and optimal Market making strategy appeared in liquidity risk problems
Books on the topic "Mean field optimal transport"
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Sun, Jingrui, and Jiongmin Yong. Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48306-7.
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Cardaliaguet, Pierre, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions. The Master Equation and the Convergence Problem in Mean Field Games. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691190716.001.0001.
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This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. The book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. The book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
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Mean Field Games: AMS Short Course, Mean Field Games, Agent Based Models to Nash Equilibria, January 13--14, 2020, Denver, Colorado. American Mathematical Society, 2021.
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Transport in Multilayered Nanostructures: The Dynamical Mean-Field Theory Approach. World Scientific Publishing Co Pte Ltd, 2006.
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Transport in Multilayered Nanostructures: The Dynamical Mean-field Theory Approach. Imperial College Press, 2006.
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Transport in Multilayered Nanostructures: The Dynamical Mean-field Theory Approach. World Scientific Publishing Co Pte Ltd, 2006.
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Yong, Jiongmin, and Jingrui Sun. Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems. Springer, 2020.
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Bezsudnov, Igor V., Joseph Malinsky, Alexander Morozovskiy, Vladimir A. Sevryukov, and Andrei A. Snarskii. Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation. Springer London, Limited, 2016.
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Snarskii, Andrei A. Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation. Springer, 2018.
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Tiwari, Sandip. Phase transitions and their devices. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0004.
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Phase transitions as a collective response of an ensemble, with appearance of unique stable properties spontaneously, is critical to a variety of devices: electronic, magnetic, optical, and their coupled forms. This chapter starts with a discussion of broken symmetry and its manifestation in the property changes in thermodynamic phase transition and the Landau mean-field articulation. It then follows it with an exploration of different phenomena and their use in devices. The first is ferroelectricity—spontaneous electric polarization—and its use in ferroelectric memories. Electron correlation effects are explored, and then conductivity transition from electron-electron and electron-phonon coupling and its use in novel memory and device forms. This is followed by development of an understanding of spin correlations and interactions and magnetism—spontaneous magnetic polarization. The use and manipulation of the magnetic phase transition in disk drives, magnetic and spin-torque memory as well as their stability is explored. Finally, as a fourth example, amorphous-crystalline structural transition in optical, electronic, and optoelectronic form are analyzed. This latter’s application include disk drives and resistive memories in the form of phase-change as well as those with electochemical transport.
Book chapters on the topic "Mean field optimal transport"
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Liu, Jiakun, and Grégoire Loeper. "Optimal Transport with Discrete Mean Field Interaction." In 2017 MATRIX Annals, 207–12. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04161-8_15.
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Sun, Jingrui, and Jiongmin Yong. "Mean-Field Linear-Quadratic Optimal Controls." In Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems, 69–123. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48306-7_3.
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Mailoud Sekkouri, Samy, and Sandro Wimberger. "Mean-Field Transport of a Bose-Einstein Condensate." In Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, 49–58. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47810-4_5.
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Liu, Huageng, and Donghua Shi. "An Euler-Poincaré Approach to Mean-Field Optimal Control." In Proceedings of 2021 International Conference on Autonomous Unmanned Systems (ICAUS 2021), 2066–72. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9492-9_204.
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Carmona, René, and François Delarue. "Optimal Control of SDEs of McKean-Vlasov Type." In Probabilistic Theory of Mean Field Games with Applications I, 513–617. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-58920-6_6.
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Øksendal, Bernt, and Agnès Sulem. "Optimal Control of Predictive Mean-Field Equations and Applications to Finance." In Stochastics of Environmental and Financial Economics, 301–20. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23425-0_12.
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Sun, Jingrui, and Jiongmin Yong. "Some Elements of Linear-Quadratic Optimal Controls." In Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems, 1–13. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48306-7_1.
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Gomez, Arnold D., Maureen L. Stone, Philip V. Bayly, and Jerry L. Prince. "Quantifying Tensor Field Similarity with Global Distributions and Optimal Transport." In Medical Image Computing and Computer Assisted Intervention – MICCAI 2018, 428–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00934-2_48.
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Sun, Jingrui, and Jiongmin Yong. "Linear-Quadratic Two-Person Differential Games." In Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems, 15–67. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48306-7_2.
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Takabe, Hideaki. "Non-local Transport of Electrons in Plasmas." In Springer Series in Plasma Science and Technology, 285–323. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-45473-8_6.
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AbstractSince plasma is high temperature and the charge particles are running with high temperature, for example, at 1 keV, about the velocity of 109 (electron) and 2 × 107 (ion) [cm/s]. Since Coulomb mean-free-path is proportional to (velocity)4, higher velocity component transfers its energy over a long distance without Coulomb collision. This is usually called as “non-local transport” and the traditional diffusion model in neutral gas cannot be applicable. In laser plasma, the locally heated electron thermal energy is transported into cold over-dense region non-locally. The best way to solve such problem is to solve Fokker-Planck equation, while it is time consuming and some theoretical models have been proposed and studied over the last four decades. The physics of such models are explained here and most recent model SNB is shown and compared to experiments. The difficulty of transport of charges particles such as electrons is how to include the effect of electrostatic field and magnetic field self-consistently.
Conference papers on the topic "Mean field optimal transport"
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Ringh, Axel, Isabel Haasler, Yongxin Chen, and Johan Karlsson. "Efficient computations of multi-species mean field games via graph-structured optimal transport." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9682861.
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Mukamel, Shaul, and Jasper Knoester. "Nonlinear Optical Susceptibilities; Beyond the Local Field Approximation." In Nonlinear Optical Properties of Materials. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/nlopm.1988.mb3.
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The Bloch-Maxwell equations are usually derived for isolated molecules interacting with an external electromagnetic field. This is justified in the limit of low molecular density, where intermolecular forces may be neglected. The problem which we address in this work is how to extend these equations in a systematic way to incorporate properly intermolecular forces. We thus develop a systematic microscopic basis for the calculation of nonlinear response functions and susceptibilities. Such a theory is essential for relating microscopic, single-molecule, polarizabilities to the macroscopic susceptibilities of optical materials. The local field approximation [1,2] is a mean-field procedure which is widely used in the calculation of molecular susceptibilities at finite densities, when intermolecular forces are important. The local field model provides a simple way to relate the polarizabilities of isolated molecules to the macroscopic susceptibilities. It is clear, however, that this procedure is not rigorous. It fails to take properly into account the correlated dynamics of the interacting many-body system, i.e., correlations among the molecules, as well as correlations between the molecules and the radiation field. Short-range forces (e.g., exchange) are totally neglected in this procedure. Moreover, even the dipoledipole forces are not fully taken into account. The resulting susceptibilities do not depend at all on the wavevectors (apart from the local field contribution) but just on the frequencies. This indicates that processes such as exciton migration and energy transfer and transport (e.g., the Forster transfer) are neglected in this procedure. Such processes are often added phenomelogically in order to interpret transient grating spectroscopy[3], which is a four-wave mixing technique that measures transport processes by following the wavevector dependence of the susceptibilities. The common derivation of the local field approximation cannot be extended to include these processes, since it is intrinsically a mean-field single molecule theory.
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Watson, George H., Paul M. Saulnier, I. Inane Tarhan, and Martin P. Zinkin. "Photon transport measurements in dense random media." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.tuff3.
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Recent results of photon transport measurements in highly multiple-scattering random media will be presented. Time-resolved transmission of picosecond laser pulses, coherent backscattering, and laser speckle statistics are several of the experimental probes being used to examine factors that influence photon transport and localization. The effects of spatial correlations among scatterers on the transport mean-free-path lengths obtained from time-resolved transmission and extinction compare favorably with corrections introduced into the Mie formalism via a static structure factor. Transport parameters determined from coherent back-scattering have been significantly improved by current theoretical models for samples with high surface reflectivity. Finally, new applications of laser speckle to the study of dense random media will be discussed. The recent advances in this field, including improved understanding of photon transport probes, should facilitate the search for localization of light in disordered optical superlattices.
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Barz, Dominik P. J., and Peter Ehrhard. "Simulation of Flow and Mass Transport in a Meander Microchannel Subject to Electroosmotic Pumping." In ASME 2003 1st International Conference on Microchannels and Minichannels. ASMEDC, 2003. http://dx.doi.org/10.1115/icmm2003-1043.
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We have investigated the flow and mass transport within an electroosmotically-pumped incompressible liquid through a meander microchannel system. We employ two-dimensional, time-dependent Finite Element simulations in conjunction with a matched asymptotic treatment of the electrical double layers. The electroosmotic pumping is realized for two idealized and two realistic electrical fields, while a pressure-driven flow is used for comparison. We focus on the aspects of the electroosmotic transport. We find for most of the electroosmotically-driven cases rather complex flow fields, involving recirculation regions. These recirculation regions in all cases increase dispersion. (i) The least dispersion is associated with a plug-type velocity profile, which is obtained for an idealized purely wall-tangential orientation of the electrical field. (ii, iii) We find that both, the idealized horizontal electrical field and the real electrical field between two vertical plates give considerably higher dispersion than the pressure-driven flow. Vertical plate electrodes, therefore, do not allow for a electrical field, which minimizes dispersion. (iv) The arrangement of two point electrodes at the in and out sections likewise proves to be no optimal means to reduce dispersion beyond the pressure-driven flow. Thus, meander geometries of channels, in general, cause severe problems if electroosmotic pumping needs to be achieved in combination with minimized dispersion.
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Toulouse, Michael M., Guislain Doljac, Van P. Carey, and Cullen Bash. "Exploration of a Potential-Flow-Based Compact Model of Air-Flow Transport in Data Centers." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10806.
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This paper summarizes an exploration of a compact model of air flow and transport in data centers developed from potential flow theory. Boundaries for the airflow in the data center are often complex due to the numerous rows of servers and other equipment in the facility, and there are generally multiple air inlets and outlets, which produce a fairly complex three-dimensional flow field in the air space in the data center. The general problem of airflow and convective transport in a data center requires accurate treatment of a turbulent flow in a complex flow passage with some buoyancy effects. As a result, full CFD thermofluidic models tend to be time-consuming and tedious to set up for such complex flow circumstances. In this initial study, we formulated an approximate model that retains only the most basic physical mechanisms of the flow. The resulting model of air flow in the data center is based on potential flow theory, which is exact for irrotational inviscid flow. The temperature field resulting from server heat input is determined by solving the convective energy transport equation along potential flow streamlines. This innovative approach, which takes advantage of the irrotational character of the modeled flow, provides a fast computational method for determining the temperature field and convective transport of thermal energy in the data center. Computations to predict the three-dimensional flow and temperature fields with the model typically require less than 60 seconds to complete on a laptop computer. Flow and temperature field results predicted by the model for typical data center flow circumstances are presented and limitations of the model are assessed. Features of an intuitive graphical user interface for the model that simplifies input of the data center design parameters are also described. Results for case studies indicate low sensitivity to mesh size and convergence criteria. Although the flow and temperature field models developed here are more approximate than full CFD methods, they are good first approximations that provide the means to rapidly explore the parameter space for the data center design. This model can be used to quickly identify the optimal region of the design space, whereupon a more detailed CFD modeling can be used to fine-tune an optimal design. The results of this investigation demonstrate that this type of fast compact model can be a very useful tool when used as a precursor to full CFD modeling in data center design optimization.
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de Jager, B., and J. B. W. Kok. "Modeling of Turbulent Combustion of Lean Premixed Prevaporized Propane Using the CFI Combustion Model." In ASME Turbo Expo 2006: Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90565.
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In this paper combustion of propane under gas turbine conditions is investigated with a focus on the chemistry and chemical kinetics in turbulent flames. The work is aimed at efficient and accurate modeling of the chemistry of heavy hydrocarbons, ie. hydrocarbons with more than one carbon atom, as occurring in liquid fuels for gas turbine application. On the basis of one dimensional laminar flame simulations with detailed chemistry, weight factors are determined for optimal projection of species concentrations on one or several composed concentrations, using the Computational Singular Perturbation (CSP) method. This way the species concentration space of the detailed mechanism is projected on a one dimensional space spanned by the reaction progress variable for use in a turbulent simulation. In the projection process a thermochemical database is used to relate with the detailed chemistry of the laminar flame simulations. Transport equations are formulated in a RaNS code for the mean and variance of the reaction progress variable. The turbulent chemical reaction source term is calculated by presumed shape probability density function averaging of the laminar source term in the thermochemical database. The combined model is demonstrated and validated in a simulation of a turbulent premixed prevaporized swirling propane/air flame at atmospheric pressure. Experimental data are available for the temperature field, the velocity field and the unburnt hydrocarbon concentrations. The trends produced by CFI compare reasonable to the experiments.
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Fornasier, Massimo, Benedetto Piccoli, Nastassia Pouradier Duteil, and Francesco Rossi. "Mean-field optimal control by leaders." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7040482.
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Alias, Cyril, Mandar Jawale, Alexander Goudz, and Bernd Noche. "Applying Novel Future-Internet-Based Supply Chain Control Towers to the Transport and Logistics Domain." In ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/esda2014-20422.
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Competing supply chain networks all around the globe are under scrutiny due to ever-growing demand for service improvement and cost reduction. A major field of action in this respect is the realization of real-time monitoring means for supply chain processes including a constant comparison of the respective progress status with the planning guidelines and the best possible management of deviations and exceptions. Control towers have been named as the future tool of supply chain monitoring for quite a while. They are defined as decision-support systems merging different data streams from various subordinate levels and displaying the consolidated information at a higher level for the purpose of monitoring and control of processes while pursuing the goal of optimal process operation. Contrary to the technological constraints of the past which prevented a continuous and fully transparent real-time monitoring of supply chain processes, innovative evolving so-called Future Internet technologies enable genuine transparency and the handling of exceptions in a timely and cost-efficient manner nowadays. With the help of such technologies, newly designed and built control towers are supposed to assist actors on the planning and execution levels of their respective supply chain networks in their decision-making in case of relevant deviations or exceptions. This again raises the market acceptance of such control towers. This paper presents a novel approach to the functional principle of Future-Internet-based control tower solutions and describes the different components therein. Especially, the incorporation of manifold information sources from the Future Internet technologies for the purpose of real-time monitoring and control of supply chain processes is highlighted in the paper.
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Huanle Zhang, Yu Fu, and Jian Liu. "Optimal transmission distance of mean progress and mean transport in device-to-device networks." In International Conference on Cyberspace Technology (CCT 2013). Institution of Engineering and Technology, 2013. http://dx.doi.org/10.1049/cp.2013.2147.
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Mobinipouya, Neda, and Omid Mobinipouya. "On the Heat Transfer Enhancement of Turbulent Gas Floes in Short Round Tubes Engaging a Light Gas Mixed With Selected Heavier Gases." In ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2011. http://dx.doi.org/10.1115/icnmm2011-58136.
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A unique way for maximizing turbulent free convection from heated vertical plates to cold gases is studied in this paper. The central idea is to examine the attributes that binary gas mixtures having helium as the principal gas and xenon, nitrogen, oxygen, carbon dioxide, methane, tetrafluoromethane and sulfur hexafluoride as secondary gases may bring forward. From fluid physics, it is known that the thermo-physical properties affecting free convection with binary gas mixtures are viscosity ηmix, thermal conductivity λmix, density ρmix, and heat capacity at constant pressure. The quartet ηmix, λmix, ρmix, and Cp,mix is represented by triple-valued functions of the film temperature the pressure P, and the molar gas composition w. The viscosity is obtained from the Kinetic Theory of Gases conjoined with the Chapman-Enskog solution of the Boltzmann Transport Equation. The thermal conductivity is computed from the Kinetic Theory of Gases. The density is determined with a truncated virial equation of state. The heat capacity at constant pressure is calculated from Statistical Thermodynamics merged with the standard mixing rule. Using the similarity variable method, the descriptive Navier-Stokes and energy equations for turbulent Grashof numbers Grx > 109 are transformed into a system of two nonlinear ordinary differential equations, which is solved by the shooting method and the efficient fourth-order Runge-Kutta-Fehlberg algorithm. The numerical temperature fields T(x, y) for the five binary gas mixtures He-Xe, He-N2, He-O2, He-CO2, He-CH4, He-CF4 and He-SF6 are channeled through the allied mean convection coefficient hmix/B varying with the molar gas composition w in proper w-domain [0, 1]. For the seven binary gas mixtures utilized, the allied mean convection coefficient hmix/B versus the molar gas composition w is graphed in congruous diagrams. At a low film temperature Tf = 300 K, the global maximum allied mean convection coefficient hmix,max/B = 85 is furnished by the He-SF6 gas mixture at an optimal molar gas composition wopt = 0.93. The global maximum allied mean convection coefficient hmix,max/B = 57 is supplied by pure methane gas SF6 (w = 1) at a high film temperature Tf = 1000 K instead of the He-SF6 gas mixture.
Reports on the topic "Mean field optimal transport"
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Russo, David, Daniel M. Tartakovsky, and Shlomo P. Neuman. Development of Predictive Tools for Contaminant Transport through Variably-Saturated Heterogeneous Composite Porous Formations. United States Department of Agriculture, December 2012. http://dx.doi.org/10.32747/2012.7592658.bard.
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The vadose (unsaturated) zone forms a major hydrologic link between the ground surface and underlying aquifers. To understand properly its role in protecting groundwater from near surface sources of contamination, one must be able to analyze quantitatively water flow and contaminant transport in variably saturated subsurface environments that are highly heterogeneous, often consisting of multiple geologic units and/or high and/or low permeability inclusions. The specific objectives of this research were: (i) to develop efficient and accurate tools for probabilistic delineation of dominant geologic features comprising the vadose zone; (ii) to develop a complementary set of data analysis tools for discerning the fractal properties of hydraulic and transport parameters of highly heterogeneous vadose zone; (iii) to develop and test the associated computational methods for probabilistic analysis of flow and transport in highly heterogeneous subsurface environments; and (iv) to apply the computational framework to design an “optimal” observation network for monitoring and forecasting the fate and migration of contaminant plumes originating from agricultural activities. During the course of the project, we modified the third objective to include additional computational method, based on the notion that the heterogeneous formation can be considered as a mixture of populations of differing spatial structures. Regarding uncertainly analysis, going beyond approaches based on mean and variance of system states, we succeeded to develop probability density function (PDF) solutions enabling one to evaluate probabilities of rare events, required for probabilistic risk assessment. In addition, we developed reduced complexity models for the probabilistic forecasting of infiltration rates in heterogeneous soils during surface runoff and/or flooding events Regarding flow and transport in variably saturated, spatially heterogeneous formations associated with fine- and coarse-textured embedded soils (FTES- and CTES-formations, respectively).We succeeded to develop first-order and numerical frameworks for flow and transport in three-dimensional (3-D), variably saturated, bimodal, heterogeneous formations, with single and dual porosity, respectively. Regarding the sampling problem defined as, how many sampling points are needed, and where to locate them spatially in the horizontal x₂x₃ plane of the field. Based on our computational framework, we succeeded to develop and demonstrate a methdology that might improve considerably our ability to describe quntitaively the response of complicated 3-D flow systems. The results of the project are of theoretical and practical importance; they provided a rigorous framework to modeling water flow and solute transport in a realistic, highly heterogeneous, composite flow system with uncertain properties under-specified by data. Specifically, they: (i) enhanced fundamental understanding of the basic mechanisms of field-scale flow and transport in near-surface geological formations under realistic flow scenarios, (ii) provided a means to assess the ability of existing flow and transport models to handle realistic flow conditions, and (iii) provided a means to assess quantitatively the threats posed to groundwater by contamination from agricultural sources.
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Kong, Zhihao, and Na Lu. Field Implementation of Concrete Strength Sensor to Determine Optimal Traffic Opening Time. Purdue University, 2024. http://dx.doi.org/10.5703/1288284317724.
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In the fast-paced and time-sensitive fields of construction and concrete production, real-time monitoring of concrete strength is crucial. Traditional testing methods, such as hydraulic compression (ASTM C 39) and maturity methods (ASTM C 1074), are often laborious and challenging to implement on-site. Building on prior research (SPR 4210 and SPR 4513), we have advanced the electromechanical impedance (EMI) technique for in-situ concrete strength monitoring, crucial for determining safe traffic opening times. These projects have made significant strides in technology, including the development of an IoT-based hardware system for wireless data collection and a cloud-based platform for efficient data processing. A key innovation is the integration of machine learning tools, which not only enhance immediate strength predictions but also facilitate long-term projections vital for maintenance and asset management. To bring this technology to practical use, we collaborated with third-party manufacturers to set up a production line for the sensor and datalogger assembly. The system was extensively tested in various field scenarios, including pavements, patches, and bridge decks. Our refined signal processing algorithms, benchmarked against a mean absolute percentage error (MAPE) of 16%, which is comparable to the ASTM C39 interlaboratory variance of 14%, demonstrate reliable accuracy. Additionally, we have developed a comprehensive user manual to aid field engineers in deploying, connecting, and maintaining the sensing system, paving the way for broader implementation in real-world construction settings.
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Russo, David, and William A. Jury. Characterization of Preferential Flow in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, October 2001. http://dx.doi.org/10.32747/2001.7580681.bard.
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Preferential flow appears to be the rule rather than the exception in field soils and should be considered in the quantitative description of solute transport in the unsaturated zone of heterogeneous formations on the field scale. This study focused on both experimental monitoring and computer simulations to identify important features of preferential flow in the natural environment. The specific objectives of this research were: (1) To conduct dye tracing and multiple tracer experiments on undisturbed field plots to reveal information about the flow velocity, spatial prevalence, and time evolution of a preferential flow event; (2) To conduct numerical experiments to determine (i) whether preferential flow observations are consistent with the Richards flow equation; and (ii) whether volume averaging over a domain experiencing preferential flow is possible; (3) To develop a stochastic or a transfer function model that incorporates preferential flow. Regarding our field work, we succeeded to develop a new method for detecting flow patterns faithfully representing the movement of water flow paths in structured and non-structured soils. The method which is based on application of ammonium carbonate was tested in a laboratory study. Its use to detect preferential flow was also illustrated in a field experiment. It was shown that ammonium carbonate is a more conservative tracer of the water front than the popular Brilliant Blue. In our detailed field experiments we also succeeded to document the occurrence of preferential flow during soil water redistribution following the cessation of precipitation in several structureless field soils. Symptoms of the unstable flow observed included vertical fingers 20 - 60 cm wide, isolated patches, and highly concentrated areas of the tracers in the transmission zone. Soil moisture and tracer measurements revealed that the redistribution flow became fingered following a reversal of matric potential gradient within the wetted area. Regarding our simulation work, we succeeded to develop, implement and test a finite- difference, numerical scheme for solving the equations governing flow and transport in three-dimensional, heterogeneous, bimodal, flow domains with highly contrasting soil materials. Results of our simulations demonstrated that under steady-state flow conditions, the embedded clay lenses (with very low conductivity) in bimodal formations may induce preferential flow, and, consequently, may enhance considerably both the solute spreading and the skewing of the solute breakthrough curves. On the other hand, under transient flow conditions associated with substantial redistribution periods with diminishing water saturation, the effect of the embedded clay lenses on the flow and the transport might diminish substantially. Regarding our stochastic modeling effort, we succeeded to develop a theoretical framework for flow and transport in bimodal, heterogeneous, unsaturated formations, based on a stochastic continuum presentation of the flow and a general Lagrangian description of the transport. Results of our analysis show that, generally, a bimodal distribution of the formation properties, characterized by a relatively complex spatial correlation structure, contributes to the variability in water velocity and, consequently, may considerably enhance solute spreading. This applies especially in formations in which: (i) the correlation length scales and the variances of the soil properties associated with the embedded soil are much larger than those of the background soil; (ii) the contrast between mean properties of the two subdomains is large; (iii) mean water saturation is relatively small; and (iv) the volume fraction of the flow domain occupied by the embedded soil is relatively large.
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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.
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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.
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Wei, Fulu, Ce Wang, Xiangxi Tian, Shuo Li, and Jie Shan. Investigation of Durability and Performance of High Friction Surface Treatment. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317281.
Full textAbstract:
The Indiana Department of Transportation (INDOT) completed a total of 25 high friction surface treatment (HFST) projects across the state in 2018. This research study attempted to investigate the durability and performance of HFST in terms of its HFST-pavement system integrity and surface friction performance. Laboratory tests were conducted to determine the physical and mechanical properties of epoxy-bauxite mortar. Field inspections were carried out to identify site conditions and common early HFST distresses. Cyclic loading test and finite element method (FEM) analysis were performed to evaluate the bonding strength between HFST and existing pavement, in particular chip seal with different pretreatments such as vacuum sweeping, shotblasting, and scarification milling. Both surface friction and texture tests were undertaken periodically (generally once every 6 months) to evaluate the surface friction performance of HFST. Crash records over a 5-year period, i.e., 3 years before installation and 2 years after installation, were examined to determine the safety performance of HFST, crash modification factor (CMF) in particular. It was found that HFST epoxy-bauxite mortar has a coefficient of thermal expansion (CTE) significantly higher than those of hot mix asphalt (HMA) mixtures and Portland cement concrete (PCC), and good cracking resistance. The most common early HFST distresses in Indiana are reflective cracking, surface wrinkling, aggregate loss, and delamination. Vacuum sweeping is the optimal method for pretreating existing pavements, chip seal in particular. Chip seal in good condition is structurally capable of providing a sound base for HFST. On two-lane highway curves, HFST is capable of reducing the total vehicle crash by 30%, injury crash by 50%, and wet weather crash by 44%, and providing a CMF of 0.584 in Indiana. Great variability may arise in the results of friction tests on horizontal curves by the use of locked wheel skid tester (LWST) due both to the nature of vehicle dynamics and to the operation of test vehicle. Texture testing, however, is capable of providing continuous texture measurements that can be used to calculate a texture height parameter, i.e., mean profile depth (MPD), not only for evaluating friction performance but also implementing quality control (QC) and quality assurance (QA) plans for HFST.
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Haslam, Divna, Ben Mathews, Rosana Pacella, James Graham Scott, David Finkelhor, Daryl Higgins, Franziska Meinck, et al. The prevalence and impact of child maltreatment in Australia: Findings from the Australian Child Maltreatment Study: Brief Report. Queensland University of Technology, 2023. http://dx.doi.org/10.5204/rep.eprints.239397.
Full textAbstract:
The Australian Child Maltreatment Study (ACMS) is a landmark study for our nation. The ACMS research team has generated the first nationally representative data on the prevalence of each of the five types of child maltreatment in Australia, and their associated health impacts through life. We also identified information about the context of maltreatment experiences, including how old children are when it occurs, and who inflicts it. This knowledge about which children are most at risk of which types of abuse and neglect, at which ages, and by whom, is needed to develop evidencebased population approaches required to reduce child maltreatment in Australia. The concerning prevalence of maltreatment and its devastating associated outcomes present an urgent imperative for nation-building reform to better protect Australian children and reduce associated costs to individuals, families, communities and broader society. The ACMS collected data from 8500 randomly selected Australians aged 16-65 years and older. We included an oversample of 3500 young people 16-24 years of aged to generate particularly strong data about child maltreatment in contemporary Australian society, to assess its associated impacts in adolescence and early adulthood, and to allow future prevalence studies to detect reductions in prevalence rates over time. Our participants aged 25 and over enabled us to understand prevalence trends at different times in Australian history, and to measure associated health outcomes through life. Participants provided information on childhood experiences of each of the five types of child abuse and neglect, and other childhood adversities, mental health disorders, health risk behaviours, health services utilisation, and more. Our findings provide the first nationally representative data on the prevalence of child maltreatment in Australia. Moreover, the ACMS is the first national study globally to examine maltreatment experiences and associated health and social outcomes of all five forms of child maltreatment. Taken together, our findings provide a deep understanding of the prevalence, context and impact of child abuse and neglect in Australia and make an important contribution to the international field. This brief report presents the main findings from the ACMS for a general public audience. These main findings are further detailed in seven peer-reviewed scholarly articles, published in a special edition of the Medical Journal of Australia, Australia’s leading medical journal. Forthcoming work will examine other important questions about the impacts of specific maltreatment experiences to generate additional evidence to inform governments and stakeholders about optimal prevention policy and practice. There is cause for hope. In recent years, there have been reductions in physical abuse, and in some types of sexual abuse. These reductions are extremely important. They mean that fewer children are suffering, and they indicate that change is possible. Policies and programs to reduce these types of maltreatment are having an effect. Yet, there are other concerning trends, with some types of maltreatment becoming even more common, including emotional abuse, some types of sexual abuse, and exposure to domestic violence. And new types of sexual victimisation are also emerging. As a society, we have much work to do. We know that child maltreatment can be reduced if we work together as governments, service sectors, and communities. We need to invest more, and invest better. It is a moral, social and economic imperative for Australian governments to develop a coordinated long-term plan for generational reform. We have found that: 1. Child maltreatment is widespread. 2. Girls experience particularly high rates of sexual abuse and emotional abuse. 3. Child maltreatment is a major problem affecting today’s Australian children and youth – it is not just something that happened in the past. 4. Child maltreatment is associated with severe mental health problems and behavioural harms, both in childhood and adulthood. 5. Child maltreatment is associated with severe health risk behaviours, both in childhood and adulthood. 6. Emotional abuse is particularly harmful, and is much more damaging than society has understood.