Exponential sum approximations for t−βt^{-\beta}

Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in a compact interval $[\delta,T]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. One such an approximation, studied by Beylkin and Monz\'on, is obtained by applying the trapezoidal rule to an integral representation of $t^{-\beta}$, after which Prony's method is applied to reduce the number of terms in the sum with essentially no loss of accuracy. We review this method, and then describe a similar approach based on an alternative integral representation. The main difference is that the new approach achieves much better results before the application of Prony's method; after applying Prony's method the performance of both is much the same.Comment: 18 pages, 5 figures. I have completely rewritten this paper because after uploading the previous version I realised that there is a much better approach. Note the change to the title. Have included minor corrections following revie

Research on forging forming force in the composite technology of cross wedge rolling (CWR) and forging for universal joint fork

In this paper，the forging process of universal joint fork of automobile transmission shaft is simulated and the change of forming force of die forging is studied on the basis of the blank produced by cross wedge rolling (CWR). Temperature / T , friction factor / c and falling speed of upper die / V are the main process parameters affecting the forging forming force / F of universal joint fork. The effects of temperature, friction factor and speed on the forming force were studied respectively by single factor method. The results show that the lower the temperature, the greater the friction factor, the slower the speed, the greater the forming force, the more difficult for forming. The orthogonal test is designed and it obtained the order of process parameters affecting the forming force of die forging that is T > c > V and the best combination of process that the temperature is 1 100 °C the friction factor is 0,2 and speed of upper die is 150 mm/s

Influence of intrinsic decoherence on nonclassical properties of the output of a Bose-Einstein condensate

We investigate nonclassical properties of the output of a Bose-Einstein condensate in Milburn's model of intrinsic decoherence. It is shown that the squeezing property of the atom laser is suppressed due to decoherence. Nevertheless, if some very special conditions were satisfied, the squeezing properties of atom laser could be robust against the decoherence.Comment: 17 pages, 5 figures, Late

Reexamining the temperature and neutron density conditions for r-process nucleosynthesis with augmented nuclear mass models

We explore the effects of nuclear masses on the temperature and neutron density conditions required for r-process nucleosynthesis using four nuclear mass models augmented by the latest atomic mass evaluation. For each model we derive the conditions for producing the observed abundance peaks at mass numbers A ~ 80, 130, and 195 under the waiting-point approximation and further determine the sets of conditions that can best reproduce the r-process abundance patterns (r-patterns) inferred for the solar system and observed in metal-poor stars of the Milky Way halo. In broad agreement with previous studies, we find that (1) the conditions for producing abundance peaks at A ~ 80 and 195 tend to be very different, which suggests that, at least for some nuclear mass models, these two peaks are not produced simultaneously; (2) the typical conditions required by the critical waiting-point (CWP) nuclei with the N = 126 closed neutron shell overlap significantly with those required by the N=82 CWP nuclei, which enables coproduction of abundance peaks at A ~ 130 and 195 in accordance with observations of many metal-poor stars; and (3) the typical conditions required by the N = 82 CWP nuclei can reproduce the r-pattern observed in the metal-poor star HD 122563, which differs greatly from the solar r-pattern. We also examine how nuclear mass uncertainties affect the conditions required for the r-process and identify some key nuclei including76Ni to 78Ni, 82Zn, 131Cd, and 132Cd for precise mass measurements at rare-isotope beam facilities.Comment: 28 pages,9 figures,1 tabl

Anomalous microwave response of high-temperature superconducting thin-film microstrip resonator in weak dc magnetic fields

We have studied an anomalous microwave (mw) response of superconducting YBa_{2}Cu_{3}O_{7-delta} (YBCO) microstrip resonators in the presence of a weak dc magnetic field, H_{dc}. The surface resistance (R_{s}) and reactance (X_{s}) show a correlated non-monotonic behaviour as a function of H_{dc}. R_{s} and X_{s} were found to initially decrease with elevated H_{dc} and then increase after H_{dc} reaches a crossover field, H_{c}, which is independent of the amplitude and frequency of the input mw signal within the measurements. The frequency dependence of R_{s} is almost linear at fixed H_{dc} with different magnitudes (H_{c}). The impedance plane analysis demonstrates that r_{H}, which is defined as the ratio of the change in R_{s}(H_{dc}) and that in X_{s}(H_{dc}), is about 0.6 at H_{dc}<H_{c} and 0.1 at H_{dc}>H_{c}. The H_{dc} dependence of the surface impedance is qualitatively independent of the orientation of H_{dc}.Comment: REVTex 3.1, 5 pages, 6 EPS figures, submitted to Physica

Entanglement with phase decoherence

The system of an atom couples to two distinct optical cavities with phase decoherence is studied by making use of a dynamical algebraic method. We adopt the concurrence to characterize the entanglement between atom and cavities or between two optical cavities in the presence of the phase decoherence. It is found that the entanglement between atom and cavities can be controlled by adjusting the detuning parameter. Finally, we show that even if the atom is initially prepared in a maximally mixed state, it can also entangle the two mode cavity fields.Comment: 9 pages, 6 figures, lete

Finite element simulation of deformation behavior of prefabricated holes in ultra-heavy plates by gradient temperature rolling

Based on the Deform-3D finite element simulation software, the numerical analysis of prefabricated holes in the core of ultra-heavy plates is carried out in different rolling schemes. In this paper, the deformation of the hole in core under uniform temperature rolling (UTR) is compared by different gradient temperature rolling (GTR) processes. The results show that the GTR can improve the core deformation compared with the UTR. The increase of the number of water cooling can accelerate the welding of the core holes and the healing of the final gap, and multi-pass watercooled GTR should be used for ultra-heavy plate rolling

Finite element simulation of deformation behavior of prefabricated holes in ultra-heavy plates by gradient temperature rolling

Based on the Deform-3D finite element simulation software, the numerical analysis of prefabricated holes in the core of ultra-heavy plates is carried out in different rolling schemes. In this paper, the deformation of the hole in core under uniform temperature rolling (UTR) is compared by different gradient temperature rolling (GTR) processes. The results show that the GTR can improve the core deformation compared with the UTR. The increase of the number of water cooling can accelerate the welding of the core holes and the healing of the final gap, and multi-pass watercooled GTR should be used for ultra-heavy plate rolling

Differential flow in heavy-ion collisions at balance energies

A strong differential transverse collective flow is predicted for the first time to occur in heavy-ion collisions at balance energies. We also give a novel explanation for the disappearance of the total transverse collective flow at the balance energies. It is further shown that the differential flow especially at high transverse momenta is a useful microscope capable of resolving the balance energy's dual sensitivity to both the nuclear equation of state and in-medium nucleon-nucleon cross sections in the reaction dynamics.Comment: Phys. Rev. Lett. (1999) in pres