Bowen–York model solution redux

Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the “model” solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

Frequency-temporal characteristics of sleep spindles in IGE with variable phenotypes in adults

A Mathematical Wave Analysis was conducted to study the frequency-temporal characteristics of sleep spindles in idiopathic generalized epilepsy (IGE) with variable phenotypes in adults. In resistant generalized tonic-clonic seizures (GTCS), the maximum duration of the stationary part of the sleep spindle in the 10–12Hz frequency band in the frontal and parietal regions was greater with Juvenile Absence Epilepsy compared with Juvenile Myoclonic Epilepsy and IGE with isolated GTCS. In patients with GTCS remission who took antiepileptic drugs (AED’s) in the anamnesis, the frequency-time characteristics of the sleep spindle were not different. In the entire group, the maximum duration of the stationary part of the sleep spindles in patients with IGE with a variable phenotype receiving AED’s was significantly less than in patients who stopped receiving AED’s. The revealed differences in the duration of the stationary part of the sleep spindles are due to various pathogenetic mechanisms underlying the different types of generalized seizures in adults, and can be used to refine the subtype of the IGE and evaluate the efficacy of the AED’s.

Simulation of Collision Situations in RobotStudio

The article deals with the problem of the collision condition of robotic device, which is possible to be revealed by spatial simulation. In addressing the collision condition, RobotStudio program was used. It includes collision detection functions. Collision detection function automatically monitors objects and indicates the collision, which may arise during the operation of the robot. In my case, collision condition occurs between the stationary part, which is a component part and moving part, which is a burner.

Impact of the Pre-Swirl Nozzle Location on the Air Transfer System (ATS) Characteristic

In most industrial turbines the cooling air for rotating turbine blades, is extracted from the compressor and transferred via passageways in the stationary parts and the rotor to the blade roots. These passages form the stator-rotor air transfer system (ATS). In stationary part of the ATS the air is usually pre-swirled in the direction of rotation to reduce the temperature and to minimize the losses in the transition area. This paper presents the investigations of the impact of the pre-swirl nozzle location on the ATS characteristics. Two ATSs have been compared. Both have a similar design, with the main difference related to the position of a pre-swirl nozzle. In the first system the pre-swirl nozzle is located at the inlet, and in the second it is located at the outlet of the stationary part of the ATS. The detailed flow structure and characteristics of both systems have been calculated using commercial CFD code. The 3-D calculations provide better insight into the dominant physical mechanisms in complex, rotating, turbulent flow and allow the calculation of the performance of these systems under various conditions. The CFD calculations have been used for the calibration of the cooling system hydraulic model, and the latter was compared with the available measured data. The study showed that the two ATSs considered have very similar characteristics (i.e. similar reduction of cooling air temperature and similar losses) despite the fact that the flow structure is significantly different. Therefore, this design can be considered as neutral to the pre-swirl nozzle location, and this is a positive feature ensuring flexibility of the system.

A Stochastic Model for the Random Impact Series Method in Modal Testing

A novel stochastic model is developed to describe a random series of impacts in modal testing that can be performed manually or by using a specially designed random impact device. The number of the force pulses, representing the impacts, is modeled as a Poisson process with stationary increments. The force pulses are assumed to have an arbitrary, deterministic shape function, and random amplitudes and arrival times. The force signal in a finite time interval is shown to consist of a wide-sense stationary part and two nonstationary parts. The expectation of the force spectrum is obtained from two approaches. The expectations of the average power densities associated with the entire force signal and the stationary part of it are determined and compared. The analytical expressions are validated by numerical solutions for two different types of shape functions. A numerical example is given to illustrate the advantages of the random impact series over a single impact and an impact series with deterministic arrival times of the pulses in estimating the frequency response function. The model developed can be used to describe a random series of pulses in other applications.

An Improved Component-Mode Synthesis Method to Predict Vibration of Rotating Spindles and Its Application to Position Errors of Hard Disk Drives

This paper describes an accurate mathematical model that can predict forced vibration of a rotating spindle system with a flexible stationary part. In particular, we demonstrate this new formulation on a hard disk drive (HDD) spindle to predict its position error signal (PES). This improved method is a nontrivial extension of the mathematical model by Shen and his fellow researchers, as the improved method allows the flexible stationary part to comprise multiple substructures. When applied to HDD vibration, the improved model consists not only a rotating hub, multiple rotating disks, a stationary base, and bearings (as in Shen’s model) but also an independent flexible carriage part. Moreover, the carriage part is connected to the stationary base with pivot bearings and to the disks with air bearings at the head sliders mounted on the far end of the carriage. To build the improved mathematical model, we use finite element analysis (FEA) to model the complicated geometry of the rotating hub, the stationary base and the flexible carriage. With the mode shapes, natural frequencies, and modal damping ratios obtained from FEA, we use the principle of virtual work and component-mode synthesis to derive an equation of motion. Naturally, the stiffness and damping matrices of the equation of motion depend on properties of the pivot and air bearings as well as the natural frequencies and mode shapes of the flexible base, the flexible carriage, the hub, and the disks. Under this formulation, we define PES resulting from spindle vibration as the product of the relative displacement between the head element and the disk surface and the error rejection transfer function. To verify the improved model, we measured the frequency response functions using impact hammer tests for a real HDD that had a fluid-dynamic bearing spindle, two disks, and three heads. The experimental results agreed very well with the simulation results not only in natural frequencies but also in gain and phase.