Inertial Forces as Viewed from the ADM Slicing and their behaviour for Particles in Non-Circular Geodesics

Considering the definition of inertial forces acting on a test particle, following non-circular geodesics, in static and stationary space times we show that the centrifugal force reversal occurs only in the case of particles following prograde orbits around black holes. We first rewrite the covariant expressions for the acceleration components in terms of the lapse function, shift vector and the 3-metric \gm_{ij}, using the ADM 3+1 splitting and use these, for different cases as given by pure radial motion, pure azimuthal motion and the general non-circular motion. It is found that the reversal occurs only when the azimuthal angular velocity of the particle supersedes the radial velocity, which indeed depends upon the physical parameters $E$, $l$ and the Kerr parameter $a$.Comment: 16 Latex pages, 1 Table and 3 Figure

Centrifugal force in Kerr geometry

We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller) and determine the radius at which the ellipticity is maximum.Comment: 6 pages, LateX macro

Worldline deviations of charged spinning particles

The geodesic deviation equation is generalized to worldline deviation equations describing the relative accelerations of charged spinning particles in the framework of Dixon-Souriau equations of motion

Maximum life spiral bevel reduction design

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ratio under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque, and power. Significant parameters in the design are: the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear, and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives

Speech Recognition Robot using Endpoint Detection Algorithm

Controlling the machines and environment with speech makes human life easier and comfortable. In this direction a robot has been designed which can easily be controlled through the speech commands given by an authorised person. This work consists of two phases: Speech recognition and Robot control. Voice commands are given as an input, which is processed using the LabVIEW software. Speech processing is done using two algorithms: Endpoint detection algorithm and Silence removal algorithm. These algorithms differentiate the voice signal from the background noise, detect the word boundary and extract only the voiced part of the input signal and removing the background noise associated with it. The extracted voice command signal is then matched with the stored templates and on match, the code corresponding to a particular movement of robot is encoded and then transmitted to the robot controlling module via RF transmitter. RF receiver in robot controlling module receives the transmitted signal, which is decoded and applied as an input to microcontroller. The microcontroller interprets the code and initiates the robot movement depending on the command given. By giving proper command, robot can be made to stop, move forward, backward, turn left, turn right etc., This robot can be deployed in hazardous environment and can be controlled by an authorised person. It may also assist disabled people to carry out their daily work with ease

What makes the lac-pathway switch: identifying the fluctuations that trigger phenotype switching in gene regulatory systems

Multistable gene regulatory systems sustain different levels of gene expression under identical external conditions. Such multistability is used to encode phenotypic states in processes including nutrient uptake and persistence in bacteria, fate selection in viral infection, cell cycle control, and development. Stochastic switching between different phenotypes can occur as the result of random fluctuations in molecular copy numbers of mRNA and proteins arising in transcription, translation, transport, and binding. However, which component of a pathway triggers such a transition is generally not known. By linking single-cell experiments on the lactose-uptake pathway in E. coli to molecular simulations, we devise a general method to pinpoint the particular fluctuation driving phenotype switching and apply this method to the transition between the uninduced and induced states of the lac genes. We find that the transition to the induced state is not caused only by the single event of lac-repressor unbinding, but depends crucially on the time period over which the repressor remains unbound from the lac-operon. We confirm this notion in strains with a high expression level of the repressor (leading to shorter periods over which the lac-operon remains unbound), which show a reduced switching rate. Our techniques apply to multi-stable gene regulatory systems in general and allow to identify the molecular mechanisms behind stochastic transitions in gene regulatory circuits.Comment: Version