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Abstract We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from e + e − → f 1(1285)π + π − that imply stringent limits on the high-energy behavior and, for the first time, allow us to provide an unambiguous determination of the couplings corresponding to the two antisymmetric TFFs. We discuss how these constraints can be implemented in a vector-meson-dominance picture, and, in combination with contributions from the light-cone expansion, construct TFFs as input for the evaluation of axial-vector contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

In this paper we first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating The most novel part of this paper is to use open-closed Gromov-Witten-Floer theory (operator We use this open-closed Gromov-Witten-Floer theory to produce new examples. Especially using the calculation of Lagrangian Floer cohomology with bulk deformation in Fukaya, et al. (2010, 2011, 2016), we produce examples of compact symplectic manifolds Many of these applications were announced in Fukaya, et al. (2010, 2011, 2012).

This study examines the structure of the Lofoten Anticyclone, located in the Lofoten Basin of the Norwegian Sea. The high-resolution ROMS model is used for hydrodynamic modeling of the Lofoten Basin circulation. The dynamics of the Lofoten Vortex are investigated using the Lagrangian methods, where trajectories of passive tracers advected by the model velocity field are calculated, and Lagrangian indicators are computed for the studied region. Lagrangian markers initially located both in the core and on the periphery of the Lofoten Vortex are considered, showing different behaviors. Lagrangian markers in the core move along closed trajectories with angular velocities depending on their distance from the eddy's center. Those initially on the periphery form a series of S-shaped folds and twists, entering and exiting the eddy. We refer to this process as “ventilation of the vortex periphery”. We demonstrated that particles leave the core and periphery of the eddy intermittently rather than uniformly over time, and the statistics of this process are analyzed. Additionally, it was found that the center of the Lofoten Vortex not only drifts cyclonically at an average speed of 3.8 cm/s but also oscillates in the horizontal plane, with the amplitude increasing in the eastern part of the Vortex’s movement area.

Lagrangian k -surgery modifies an immersed Lagrangian submanifold by topological k -surgery while removing a self-intersection. Associated to a k -surgery is a Lagrangian surgery trace cobordism. We prove that every Lagrangian cobordism is exactly homotopic to a concatenation of suspension cobordisms and Lagrangian surgery traces. This exact homotopy can be chosen with as small Hofer norm as desired. Furthermore, we show that each Lagrangian surgery trace bounds a holomorphic teardrop pairing the Morse cochain associated with the handle attachment to the Floer cochain generated by the self-intersection. We give a sample computation for how these decompositions can be used to algorithmically construct bounding cochains for Lagrangian submanifolds. In an appendix, we describe a 2-ended embedded monotone Lagrangian cobordism which is not the suspension of a Hamiltonian isotopy following a suggestion of Abouzaid and Auroux.

An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.

An efficient forward trajectory model is proposed, in which the property and position of the fluids advected from the Euler coordinates to the Lagrangian coordinates can be accurately evaluated. After sorting and aligning those fluid elements on the irregular Lagrangian curves, we apply the cubic or other high-degree polynomials to interpolate the properties of the elements from the irregular curves to the regular grids. There is no need to solve the cubic equations and the associated coefficients as proposed previously. The model is quite simple, accurate, and much more efficient than the previous models. It also allows higher-order polynomials to be employed in the interpolations. It is suitable for simulating the multi-dimensional fast-moving flows with large Courant Numbers, the transport of pollutants in the atmosphere and ocean, and movement of raindrops in atmospheric models.

The nuclear norm is widely used to induce low-rank solutions for many optimization problems with matrix variables. Recently, it has been shown that the augmented Lagrangian method (ALM) and the alternating direction method (ADM) are very efficient for many convex programming problems arising from various applications, provided that the resulting subproblems are sufficiently simple to have closed-form solutions. In this paper, we are interested in the application of the ALM and the ADM for some nuclear norm involved minimization problems. When the resulting subproblems do not have closed-form solutions, we propose to linearize these subproblems such that closed-form solutions of these linearized subproblems can be easily derived. Global convergence results of these linearized ALM and ADM are established under standard assumptions. Finally, we verify the effectiveness and efficiency of these new methods by some numerical experiments.

The Lagrangian formalism has provided a powerful and elegant framework for obtaining governing equations for classical and quantum systems. It is based on the concept of action, which involves Lagrangians, whose a priori knowledge is required. There are different methods to obtain Lagrangians for given equations of motion, and a brief review of these methods is presented. However, the main purpose of this review paper is to describe the so-called null Lagrangians and their gauge functions, and discuss their physical applications. The paper also reviews some recent results, which demonstrate that gauge functions play the most fundamental roles in classical dynamics as they can be used to predict the future states of dynamical systems, without solving the equations of motion, as well as to construct their Lagrangians.

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities. We obtain a series of convexity results, both positive and negative, for such singular integral affine base spaces. In particular, near a focus singular point, they are locally convex and the local-global convexity principle still applies. They are also globally convex under some natural additional conditions. However, when the monodromy is sufficiently large, the local-global convexity principle breaks down and the base spaces can be globally non-convex, even for compact manifolds. As a surprising example, we construct a 2-dimensional “integral affine black hole”, which is locally convex but for which a straight ray from the center can never escape.

Recent advances in modeling primary atomization in order to enable accurate practical-scale jet spray simulation are reviewed. Since the Eulerian–Lagrangian method is most widely used in academic studies and industrial applications, in which the continuous gas phase is treated in the Eulerian manner and droplets are calculated as Lagrangian point particles, the main focus is placed on improvement within this framework, especially focusing on primary atomization where modeling is the weakest. First, limitations of the conventional methods are described and then novel modeling proposals intended to tackle these issues are covered. These new modeling proposals include the Eulerian surface density approach, and the hybrid Eulerian surface/Lagrangian subgrid droplet generation approach. Compared to conventional simple yet sometimes non-physical models, recent models try to include more physical findings in primary atomization which have been obtained through experiments or direct numerical simulation (DNS). Model accuracy ranges from one that still needs some adjustment using experimental or DNS data to one which is totally self-closed so that no parameter tuning is necessary. These models have the potential to overcome the long-recognized bottleneck in primary atomization modeling and thus to improve the accuracy of whole spray simulation, and may greatly help to improve the spray design for higher combustion efficiency.