Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

Finding three-dimensional layouts for crashworthiness load cases using the graph and heuristic based topology optimization

In this paper we present a new procedure using the graph and heuristic based topology optimization in order to find layouts for three-dimensional frame structures under crash loads. A three-dimensional graph describes the geometry and is used to derive a finite element shell model. The model of the frame structure consists of different profiles with continuous cross-sections. The ends of the profiles are currently rigidly connected. Each cross-section is defined by an individual two-dimensional graph. After performing a simulation its results are used by competing heuristics to propose new topologies for the frame structure. Most of these heuristics are derived from expert knowledge. Over several iterations, the goal is to improve the structures mechanical behavior. Typical objectives are the minimization of the structural intrusion in a crash scenario or the minimization of the maximal contact force between structural components. The presented method includes topology optimization by heuristics and shape optimization respectively sizing by mathematical optimization algorithms. The new flexible syntax for three- and two-dimensional graphs, the optimization process and the currently used heuristics are described. The performance is demonstrated for two examples, each optimized twice with opposing objectives.

A Design Method for Rail Profiles in Switch Panel of Turnout Based on the Contact Stress Analysis

Contact stress between wheel and rail is believed to cause damage to the rail. The relationship between the contact stress and the radius of the rail is initially based on the Hertz contact theory. By adjusting its radius, the rail profile is designed with an objective of reducing the maximal contact stress between wheel and rail. The rail profile of turnout is parameterized by defining several control cross sections along the switch. The experiment of dynamic vehicle-turnout interaction is also carried out to investigate the effect of the improved rail profile on the dynamical behavior of the vehicle. The method is then verified through examples using rail profile with a switch width of 20 mm and LM worn-type tread at the CN60-350-1:12 turnout. The results show that the designed rail has a higher matching degree with the wheel profile. It can reduce the contact stress, improve the wheel-rail contact state, and prolong the service life of the rail without deteriorating the dynamic performance of the vehicle passing through the turnout.

But Who’s Counting? Plotting Age in Trollope

Anthony Trollope is unusually concerned with numbers: consider both the famous obsession with productivity and the figures that organize his serial fictions, what Mary Hamer has called his “writing by numbers.” Yet while such numerals control his narrative flow, forming the remarkable torrents of his romans fleuve, this essay focuses on ones that appear as such within his novels: those used to designate his characters’ ages. Age has long been recognized as a central Trollopian concern, but exploring formally Trollope’s habitual use of age-related integers reveals Trollope’s practice of counting the years to be another kind of “writing by numbers.” “X was now Y years of age” is a favorite locution, and all Trollope’s novels measure the gap between adjacent nows by watching characters grow older. Trollope’s now is thus crucially a sign of age, dependent upon its adjacent number for its force, coloring it and alerting us to its relationship with other numbers as with previous and future selves. This now should be distinguished both from what Mikhail Bakhtin calls the novel’s foundation in “maximal contact with the present” and from Jonathan Culler’s lyric “now.” Instead, it is a paradoxically durational present—a special generic marker of the roman fleuve. Trollope’s figures thus bear heavily on his form of plotting. Narrative generally depends on keeping track of numbers, but not all genres of narrative count in the same ways. Trollope’s age-related numbers show what happens when plot is not only subordinated to but also embodied in character.

Monomial generators of complete planar ideals

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals.

A GENERALIZED METHOD FOR PREDICTING CONTACT STRENGTH, WEAR, AND THE LIFE OF INVOLUTE CONICAL SPUR AND HELICAL GEARS: PART 2. HELICAL GEARS

The paper presents the results of research undertaken to determine maximum contact pressures, wear, and the life of involute conical helical gear, taking account of gear height correction, tooth engagement, and weargenerated changes in the curvature of their involute profile. We have established the following: (a) initial maximal contact pressures will be almost the same at the engagement in external and internal segments; (b) their highest meanings occur in different points of engagement depending on the coefficients of displacement; (c) the maximal tooth wear of the rings in the internal section will be a little bit lower than in the external; (d) the coefficients of displacement have an optimum at which the highest gear life is possible; and, (e) the gear life in the frontal section will be 1.25 lower than in the internal section. The calculations were made for a reduced cylindrical gear using a method developed by the authors. The effect of applied conditions of tooth engagement in the frontal and internal sections of a cylindrical gear ring is shown graphically. In addition, optimal correction coefficients ensuring the longest possible gear life are determined.

Dynamic response for shock loadings and stress analysis of a trajectory correcting fuse based on fuse–projectile–barrel coupling

This paper creates a fuse–projectile–barrel coupling model and conducts an implicit–explicit sequential finite element dynamic simulation to analyze the response of the components in ammunition to shock loadings during the whole launch process accurately. The engraving process continues at 3.05 ms and leads to the acceleration fluctuation of the fuse bearings. The deflection of the gun barrel due to gravity at 52 degrees quadrant elevation (QE) is acquired. Then the displacement and velocity of the projectile are obtained to verify the gun tube deflection. The bearing axial and radial acceleration in the fuse are depicted. The results indicate that the axial acceleration imposed on the bearings during launch is a major loading, and base pressure and pressure dissipation result in shock loadings on the bearings. The accelerated spin and collision of the projectile with the barrel produce centrifugal inertia force and gyroscopic coupling, which influence the radial acceleration. In addition to this, a calculation method is proposed to work out the maximal contact stress of the bearing’s components. The method is combined with the bearings’ components maximal acceleration from simulation. The results of the research prove that the calculation method is correct and credible. The research conclusions provide some reference for the structural design of a trajectory correcting fuse.