Global dynamic modeling of a transmission system

The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system

Hartree-Fock calculations of a finite inhomogeneous quantum wire

We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We find that with the increase in the potential barrier, the low density electrons under it go from a non-magnetic state to an antiferromagnetic state, and then to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads. At this final stage, in response to a continuously increasing barrier potential, the system undergoes a series of abrupt density changes, corresponding to the successive expulsion of a single electron from the spin-aligned region under the barrier. Motivated by the recent momentum-resolved tunneling experiments in a parallel wire geometry, we also compute the momentum resolved tunneling matrix elements. Our calculations suggest that the eigenstates being expelled are spatially localized, consistent with the experimental observations. However, additional mechanisms are needed to account for the experimentally observed large spectral weight at near $k=0$ in the tunneling matrix elements.Comment: 10 pages, 14 figure

Single-cluster dynamics for the random-cluster model

We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the $q$-state Potts model to non-integer values $q>1$. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full cluster decomposition of random-cluster configurations. We explore the critical dynamics of this algorithm for several two-dimensional Potts and random-cluster models. For integer $q$, the single-cluster algorithm can be reduced to the Wolff algorithm, for which case we find that the autocorrelation functions decay almost purely exponentially, with dynamic exponents $z_{\rm exp} =0.07 (1), 0.521 (7)$, and $1.007 (9)$ for $q=2, 3$, and 4 respectively. For non-integer $q$, the dynamical behavior of the single-cluster algorithm appears to be very dissimilar to that of the SWCM algorithm. For large critical systems, the autocorrelation function displays a range of power-law behavior as a function of time. The dynamic exponents are relatively large. We provide an explanation for this peculiar dynamic behavior.Comment: 7 figures, 4 table

Current Dissipation in Thin Superconducting Wires: Accurate Numerical Evaluation Using the String Method

Current dissipation in thin superconducting wires is numerically evaluated by using the string method, within the framework of time-dependent Ginzburg-Landau equation with a Langevin noise term. The most probable transition pathway between two neighboring current-carrying metastable states, continuously linking the Langer-Ambegaokar saddle-point state to a state in which the order parameter vanishes somewhere, is found numerically. We also give a numerically accurate algorithm to evaluate the prefactors for the rate of current-reducing transitions.Comment: 25 pages, 5 figure

Analytical theory of dark nonlocal solitons

We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe the dark solitons, for the first time, in the whole range of degree of nonlocality.Comment: to be published in Optics Letter

The most plausible explanation of the cyclical period changes in close binaries: the case of the RS CVn-type binary WW Dra

We searched the orbital period changes in 182 EA-type (including the 101 Algol systems used by \cite{hal89}), 43 EB-type and 53 EW-type binaries with known both the mass ratio and the spectral type of their secondary components. We reproduced and improved the same diagram as Hall's (1989) according to the new collected data. Our plots do not support the conclusion derived by \cite{hal89} that all cases of cyclical period changes are restricted to binaries having the secondary component with spectral types later than F5. The presence of period changes also among stars with secondary component of early type indicates that the magnetic activity is one cause, but not the only one, for the period variation. It is discovered that cyclic period changes, likely due to the presence of a third body are more frequent in EW-type binaries among close binaries. Therefore, the most plausible explanation of the cyclical period changes is the LTTE via the presence of a third body. By using the century-long historical record of the times of light minimum, we analyzed the cyclical period change in the Algol binary WW Dra. It is found that the orbital period of the binary shows a $\sim112.2 \textbf{\textrm{yr}}$ cyclic variation with an amplitude of $\sim0.1977\textbf{\textrm{days}}$. The cyclic oscillation can be attributed to the LTTE via a third body with a mass no less than $6.43 M_{\odot}$. However, no spectral lines of the third body were discovered indicating that it may be a candidate black hole. The third body is orbiting the binary at a distance shorter than 14.4 AU and it may play an important role in the evolution of this system.Comment: 9 pages, 5 figures, published by MNRA