Simulation of sheet-titanium forming of welded blanks

The increase in demand for the light and tough drawn-parts causes the growing interest in sheet metal forming of Tailor-Welded Blanks (TWB). Application of such blanks allows for achieving in one operation the drawn-parts characterized by diverse strength and functional properties. It also allows for reduction of material waste and decrease in number of parts needed to produce component. Weight reduction is especially important for the car and aircraft industry. Forming welded blanks requires solving many problems such as different plasticity of the joined materials, presence of the weld and its dislocation. In order to evaluate suitability of welded blanks for the forming processes, it is necessary to carry out several studies, including numerical simulations of the process, that will allow for prediction of sheet behaviour in consecutive forming stages. Although to date aluminium and steel TWBs are mainly used, the aircraft industry is also interested in application of titanium TWBs. Generally sheet-titanium forming is more difficult than steel or aluminium sheets. The weld presence complicates the forming process additionally. In the paper some numerical simulation results of sheet-titanium forming of welded blanks will be presented. Forming the spherical caps from the uniform and welded blanks will be analysed. Grade 2 and Grade 5 (Ti6Al4V) titanium sheets with thickness of 0.8 mm will be examined. A three-dimensional model of the forming process and numerical simulation will be performed using the ADINA System v.8.6, based on the finite element method (FEM). An analysis of the mechanical properties and geometrical parameters of the weld and heat affected zone (HAZ) are based on the experimental studies. Drawability and possibilities of plastic deformation will be assessed basing on the comparative analysis of the determined plastic strain distributions in the drawn-parts material and thickness changes of the drawn-part wall. The results obtained in the numerical simulations will provide important information about the process course. They will be useful in design and optimization of the forming process

Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid

In this work we revisit collapse and revival oscillations in superfluids suddenly quenched by strong local interactions for the case of a one-dimensional Bose-Hubbard model. As the main result we identify the inherent nonequilibrium quantum many-body character of these oscillations by revealing that they are controlled by a sequence of underlying dynamical quantum phase transitions in the real-time evolution after the quench, which manifest as temporal nonanalyticities in return probabilities or Loschmidt echos. Specifically, we find that the time scale of the collapse and revival oscillations is, firstly, set by the frequency at which dynamical quantum phase transitions appear, and is, secondly, of emergent nonequilibrium nature, since it is not only determined by the final Hamiltonian but also depends on the initial condition.Comment: 5 pages, 4 figure

Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in O~(mn^(4/3) log{W}/epsilon) total time (where the edge weights are from [1,W]) and explicitly maintains a (1+epsilon)-approximate distance matrix. For a fixed epsilon>0, this is the first deterministic partially dynamic algorithm for all-pairs shortest paths in directed graphs, whose update time is o(n^2) regardless of the number of edges. Furthermore, we also show how to improve the state-of-the-art partially dynamic randomized algorithms for all-pairs shortest paths [Baswana et al. STOC\u2702, Bernstein STOC\u2713] from Monte Carlo randomized to Las Vegas randomized without increasing the running time bounds (with respect to the O~(*) notation). Our results are obtained by giving new algorithms for the problem of dynamically maintaining hubs, that is a set of O~(n/d) vertices which hit a shortest path between each pair of vertices, provided it has hop-length Omega(d). We give new subquadratic deterministic and Las Vegas algorithms for maintenance of hubs under either edge insertions or deletions

Fast dynamics for atoms in optical lattices

Cold atoms in optical lattices allow for accurate studies of many body dynamics. Rapid time-dependent modifications of optical lattice potentials may result in significant excitations in atomic systems. The dynamics in such a case is frequently quite incompletely described by standard applications of tight-binding models (such as e.g. Bose-Hubbard model or its extensions) that typically neglect the effect of the dynamics on the transformation between the real space and the tight-binding basis. We illustrate the importance of a proper quantum mechanical description using a multi-band extended Bose-Hubbard model with time-dependent Wannier functions. We apply it to situations, directly related to experiments.Comment: 4pp+supplement, final version accepted in Phys. Rev. Let

Partition Function Zeros of an Ising Spin Glass

We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched averages. This study is motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization flows in such models with frustration, and by the possible connection of the latter with spin glass behaviour. In any finite volume, the simultaneous distribution of the zeros of all partition functions can be viewed as part of the more general problem of finding the location of all the zeros of a certain class of random polynomials with positive integer coefficients. Some aspects of this problem have been studied in various branches of mathematics, and we show how polynomial mappings which are used in graph theory to classify graphs, may help in characterizing the distribution of zeros. We finally discuss the possible limiting set as the volume is sent to infinity.Comment: LaTeX, 18 pages, hardcopies of 15 figures by request to [email protected], CERN--TH-7383/94 (a note and a reference added