Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European Physical Journal

Grad-GradaGrad? A Non-Monotone Adaptive Stochastic Gradient Method

The classical AdaGrad method adapts the learning rate by dividing by the square root of a sum of squared gradients. Because this sum on the denominator is increasing, the method can only decrease step sizes over time, and requires a learning rate scaling hyper-parameter to be carefully tuned. To overcome this restriction, we introduce GradaGrad, a method in the same family that naturally grows or shrinks the learning rate based on a different accumulation in the denominator, one that can both increase and decrease. We show that it obeys a similar convergence rate as AdaGrad and demonstrate its non-monotone adaptation capability with experiments

Modeling of austenitic grain growth of 25CrMo4 steel for the high-speed railway axle during hot working

371-378After hot deformation, the fine grains due to recrystallization are apt to grow up at high temperatures. The grain size affects directly the performance and quality of products, so it is of great significance to investigate the grain evolution. In this paper, 25CrMo4 steel samples are compressed until a strain of 0.6, under isothermal conditions using Gleeble-1500 at deformation temperatures in the range of 950-1100°C and at same strain rate 1.0 s-1, and then the samples are held at deformation temperatures for 0, 10, 20 and 30 min. Microstructure is retained by using water quench. The grain growth model is expressed by a differential function of both temperature and holding time. The material constants in grain growth model are determined using genetic algorithm (GA) optimization technology from experimental data. A good agreement between predicted results and experimental data is obtained, which shows that the developed grain growth model enables the grain size evolution at various high temperatures to be well predicted

The process parameters effect of ovality in cross wedge rolling for hollow valve without mandril

This paper presents the experimental and numerical results of the effect process parameters on ovality in cross wedge rolling (CWR) for hollow engine valve without mandrel. Numerical simulation model for ovality was established by means of the rigid-plastic finite element modeling (FEM) method for hollow engine valve. The experiments and numerical analyses suggest that the following parameters represent the best conditions for CWR of hollow engine valve: 30°-34° for the forming angle(α), 5°-7° for the stretching angle(β), 0.2-0.3mm for the mold void width(L), and 65%-70% for the area reduction(Ψ)

The process parameters effect of ovality in cross wedge rolling for hollow valve without mandril

This paper presents the experimental and numerical results of the effect process parameters on ovality in cross wedge rolling (CWR) for hollow engine valve without mandrel. Numerical simulation model for ovality was established by means of the rigid-plastic finite element modeling (FEM) method for hollow engine valve. The experiments and numerical analyses suggest that the following parameters represent the best conditions for CWR of hollow engine valve: 30°-34° for the forming angle(α), 5°-7° for the stretching angle(β), 0.2-0.3mm for the mold void width(L), and 65%-70% for the area reduction(Ψ)

Experimental Investigations of the In-Die Quenching Efficiency and Die Surface Temperature of Hot Stamping Aluminium Alloys

The in-die quenching is a key stage in the hot stamping volume production chain which determines the post-formed strength of lightweight alloy components, tool life, and hot stamping productivity. In this paper, the performance of in-die quenching, reflected by the quenching efficiency (the time of work-piece held within stamping dies) and die surface temperature during the simulated hot stamping process of AA6082, was experimentally and analytically investigated. A range of in-die quenching experiments were performed for different initial work-piece and die temperatures, quenching pressures, work-piece thickness, and die clearances, under hot stamping conditions. In addition, a one-dimensional (1D) closed-form heat transfer model was used to calculate the die surface temperature evolution that is difficult to obtain during practical manufacture situations. The results have shown that the in-die quenching efficiency can be significantly increased by decreasing the initial work-piece and die temperatures. Die clearances are required to be designed precisely to obtain sufficiently high quenching rates and satisfying post-formed strength for hot-stamped panel components. This study systematically considered an extensive variety of influencing factors on the in-die quenching performance, which can provide practical guides for stamping tool designers and manufacture systems for hot-stamping volume production

Hot compression deformation behavior and microstructure evolution rule of a high-speed railway axle steel

447-454The high performance of high-speed railway axle (HSRA) depends on the stress-strain state and microstructure formed in the hot processes, it is necessary to investigate the deformation behavior and microstructure evolution during hot uniaxial compression. Hot compression test was performed on specimen of a HSRA steel 25CrMo4 at a deformation temperature of 1040-1160oC at a strain rate of 1.0-10.0 /s using a Gleeble thermal mechanical simulator. During hot compression test, samples were compressed to different true strain: 0, 0.2, 0.4, 0.6 and 0.8. Hot compressive deformation behaviors and effects of processing parameters, including forming temperature, strain rate and deformation degree, on microstructure evolution of HSRA steel 25CrMo4 are investigated and studied by metallurgical analysis. Experiments results show that the peak value of flow stress increases about 30 MPa at a certain deformation temperature when the strain rate increases from 1.0 /s to 10.0 /s. At a certain strain rate, the peak value of flow stress increases about 20-30 MPa when the forming temperature decreases about 60oC. The average grain sizes increases with the increasing of forming temperature at a certain strain rate and a given strain. For a given forming temperature, grain size decreased before the critical strain of 0.4 and increased after strain of 0.4 due to grain growth, especially at lower strain rate. Therefore, grain size at lower strain rate is larger than that at higher strain rate when true strain reached 0.8

Modelling and experimental research in hot precision forging of shaft gear

In this paper, a hot forging die set is designed for a shaft gear. A finite element software DEFORM was employed to simulate the hot forging process. The forming parameter range was determined and the forging force was predicted. The metal flow law in hot forging processes was studied using metal flow analysis and point tracking analysis. The metal flow law was further analysed through finite element simulations and precision forging experiments. The accuracy of hot formed gears is analysed and the deviation of the tooth profile reaches the 8th grade, which meet the defined requirement. The pitch cumulative deviation of the forged part is low enough for practical applications

Modelling and experimental research in hot precision forging of shaft gear

In this paper, a hot forging die set is designed for a shaft gear. A finite element software DEFORM was employed to simulate the hot forging process. The forming parameter range was determined and the forging force was predicted. The metal flow law in hot forging processes was studied using metal flow analysis and point tracking analysis. The metal flow law was further analysed through finite element simulations and precision forging experiments. The accuracy of hot formed gears is analysed and the deviation of the tooth profile reaches the 8th grade, which meet the defined requirement. The pitch cumulative deviation of the forged part is low enough for practical applications