Arbitrary Function Of Time Research Articles

General kinematics of winding processes

Processes which trace, scan, or otherwise generate an Archimedian spiral are referred to as winding processes. A general theory of the kinematics of these processes is presented, in which the linear velocity with which the spiral is generated is assumed to be an arbitrary function of time, controlled by external mechanisms. Explicit formulas for radius, angular velocity, arc length, angular displacement, and angular acceleration are obtained. These quantities all exhibit a nonlinear time dependence, with the magnitude of the nonlinearity critically dependent upon certain physical parameters, which are identified and discussed. The results are directly applicable to many problems in metals, textiles, and paper processing, and also to the technology of audio and video recording processes.

A programmableUo=f(Ui) analogue-function generator using a microprocessor

The note describes a programmable analogue-function generator. Its main advantage over other schemes lies in its ability to generate not only time functions U o = f(t), but also input voltage functions U o = f(U i), whereU i, is an arbitrary time function: U i = g(t). It s then ideally suited for applications in analogue computation.

Stochastic behaviour and profit function of a system with precautionary measures under abnormal weather

A repairable system under normal and abnormal weather conditions is analysed. The system can be in one of the three modes—normal, partial and total failure. Failure rates of system and rates of change of weather conditions are constant while the repair rates are arbitrary functions of time. The repair time distributions depend upon the state from which the repair starts and are invariant with the change of weather. Using regenerative point technique various reliability characteristics such as mean time to system failure, steady state availability, the probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system are obtained.

A further generalization of Vaidya's star metric

In this paper, a metric containing five arbitrary functions of time is obtained which describes the gravitational field of an arbitrary accelerated and charged point-mass (star). It is a further generalization of Vaidya's star metric, [1]. In particular cases, it reduces to the Reissner-Nortström metric and the Kinnersley metric [2]. Since the various parameters of the source can vary arbitrarily in time, this metric is of wide applicability and may prove to be useful for various specific astronomical objects.

Constraints on generalized inflationary cosmologies

We consider cosmologies having an inflationary period during which the Robertson-Walker scale factor is an arbitrary function of time satisfying R ̈ > 0 (not necessarily an exponential). We show that any such inflationary period will produce long-wavelength gravitational waves which can affect present observations of the microwave background. Using present bounds on the quadrupole anisotropy we derive constraints on general background. Using present bounds on the power law inflation ( R ∼ t p ) are considered in detail and the maximum reheating temperature is given as a function of p. Finally, predictions for the anisotropy of the microwave background produced by gravitational waves generated by ordinary exponential inflation are presented.

A distribution-free upper confidence bound for PR ( [formula omitted]): an application to stress-strength models : N. Singh. IEEE Trans. Reliab.R-32 (2), 214 (June 1983)

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.

Theory of solute transport in soils from the method of characteristics

A general theory of vertical solute movement in a soil is presented, which takes into account uptake of water and solute by roots, irrigation or rainfall, and solute application and adsorption by the soil. Irrigation, rainfall, and the surface application of fertilizers are arbitrary functions of time. The main limitation of the theory is the neglect of the variability of soil-water conductivity with position. The theory is illustrated by comparing predictions and experimental observations of solute leaching losses measured in a lysimeter.

A new interior solution of Einstein's field equations for a spherically symmetric perfect fluid in shear-free motion

Although spherically symmetric expanding (or contracting) stars are a very important class of objects for the application of general relativity theory, only very few perfect fluid solutions of Einstein's equations have been found so far. A new class of exact solutions is presented which contains two arbitrary functions of time and one additional parameter.

A time-dependent Schrödinger equation

We reduce the solution of the Schrödinger equation with the potential U(r, t)=α1(t) r2+α2(t) x+α3(t) y +α4(t) z+α5(t) to the solution of the Schrödinger equation for a free particle. The αi(t) are arbitrary functions of time. A generalization of this is also considered.

Group properties and new solutions of Navier-Stokes equations

Using the machinery of Lie theory (groups and algebras) applied to the Navier-Stokes equations a number of exact solutions for the steady state are derived in (two) three dimensions. It is then shown how each of these generates an infinite number of time-dependent solutions via (three) four arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

Fog dispersal by CO_2 laser pulses: an exact solution including prevaporization heating

The coupled nonlinear equations governing the transmission of a collimated high-energy laser beam through a fog are solved analytically. The incident radiation is assumed to be of sufficient intensity to vaporize the droplets in the path of the beams, thus enabling a greater percentage than without vaporization of the incident energy to be transmitted. Prevaporization heating is included in the treatment, and the vaporization front provides a moving boundary condition for the solution. The initial laser intensity and aerosol density are taken to be arbitrary functions of time and position, respectively; Effects of scattering, molecular absorption, and heat conduction are ignored.

A non-autonomous Langevin equation

Abstract A Langevin differential equation which has a damping term and a control force both varying periodically at the same frequency, the equation being forced by an arbitrary function of time, is considered in this paper. The solution of the equation is reduced to that of a second-order linear differential equation in either the real or the complex domain ; no approximation is involved in this reduction, for it is exact. In particular, for the autonomous equation the exact solution shows that no limit cycles exist, contrary to the approximate results obtained by Ottoy for the equation whoso damping term fluctuates at twice the frequency of the control force. Next, a Langevin equation which is forced by a periodically fluctuating function of time (having arbitrary amplitude and frequency) is solved exactly when some of the parameters are interrelated in four distinct ways.

Dispersion in Three Dimensions: Approximate Analytic Solutions

Solutions to three-dimensional convection dispersion equation under different boundary conditions are obtained by integrating the appropriate Green's functions. Two approximations are used during the integration. First, error function differences are approximated by exponential functions through Taylor expansion. Second, the time integral is approximated by Laplace method. The error introduced due to these approximations is analysed and discussed. The pollution source is assumed to be an arbitrary function of time and of finite size in space. The boundary conditions considered are of a stream in a horizontal flow field and a water table in a vertical flow field. Such solutions have potential use in quick preliminary analysis of groundwater pollution problems.

Kinematic flow approximation of runoff on a plane: An exact analytical solution

A general analytical solution to the kinematic flow approximation is presented for an excess rainfall which is any arbitrary function of time. The present solution generalizes an earlier solution which applies when the excess rainfall is constant for a finite time interval. Application of the solution is illustrated by considering the runoff resulting from a variable rate of excess rainfall, and also a problem in border irrigation.

Unsteady Hydromagnetic Flow Near a Moving Porous Plate

Unsteady two-dimensional flow of a viscous incompressible and electrically conducting fluid near a moving porous plate of infinite extent in presence of a transverse magnetic field is investigated. Solution of the problem in closed form is obtained with the help of Laplace transform technique, when the plate is moving with a velocity which is an arbitrary function of time and the magnetic Prandtl number is unity. Three particular cases of physical interest are also discussed.

Chronopotentiometry on a rotating disk electrode with periodic current inputs

Duhamel's theorem can be used to solve chronopotentiometric problems on a rotating disk electrode when the current input is an arbitrary function of time. Periodic state surface concentrations for a two-step pulsed current are calculated by this method. The two-step pulse incorporates single step and periodically reversed pulses as special cases. A comparison of the exact convective diffusion results with the predictions of the Nernst model, and Filinovskii's analytical approximation shows good agreement for the values of the instantaneous limiting current density. A kinetic model is developed for the extraction of kinetic parameters of a first-order irreversible reaction occurring on a rotating disk electrode perturbed by a two-step cathodic current pulse.

Chronopotentiometry on a rotating disk electrode with periodic current inputs

Duhamel's theorem can be used to solve chronopotentiometric problems on a rotating disk electrode when the current input is an arbitrary function of time. Periodic state surface concentrations for a two-step pulsed current are calculated by this method. The two-step pulse incorporates single step and periodically reversed pulses as special cases. A comparison of the exact convective diffusion results with the predictions of the Nernst model, and Filinovskii's analytical approximation shows good agreement for the values of the instantaneous limiting current density. A kinetic model is developed for the extraction of kinetic parameters of a first-order irreversible reaction occurring on a rotating disk electrode perturbed by a two-step cathodic current pulse.

A practical closed form solution for systems with variable eigenvalues via bilinear system theory

AbstractThis paper treats systems in state variable formulation with non‐constant, parameter controlled system matrices. The synthesis of a system with controlled eigenvalues (ECS) is given. The synthesized system is a commutative bilinear system. Its solution has a closed form and is based on the solution of just one time invariant system although as many arbitrary time functions are involved as the system has independent states. The ECS is homologous to any system with a system matrix being an arbitrary, possibly time‐dependent function of a single constant system matrix.All results are deduced for multiple eigenvalues of the system matrix including single eigenvalues as a special case. They are fully analogous to the solution of time invariant systems by means of the Laplace transformation.

A general method of calculating stress redistribution due to differential creep in concrete structures

A method of calculating the variation with time of stress resultants in a loaded concrete structure whose members exhibit differential creep strains is presented. An arbitrary time function ϑ( t) is chosen to express the variation of creep deformations of structural concrete and a normalized new function F( t) is introduced. The solution of the problem at this stage is assumed to be carried out on a full section where compatibility of deformations is ensured. The proposed method leads to a compatibility system of linear differential equations the number of which depends on the degree of indeterminacy of the structure. The Runge-Kutta numerical procedure is employed for the solution of the differential system. The application of the method to the solution of some standard engineering structures is presented and the differential equations are developed. A numerical example of a reinforced concrete portal frame loaded for eight months, is carried out. The variation of the stress resultants with time are presented numerically and graphically. A listing of the computer programme developed is also presented.

Response function for transient heat conduction in semi-infinite media

The concept of response function is used to investigate the transient heat conduction in a semi-infinite medium, when the temperature of the surface is an arbitrary function of time. First, the response of the system to a unit step function of surface temperature T s ( t) is obtained. The temperature distribution in the medium corresponding to arbitrary surface temperature T s ( t) is then expressed in terms of the response function and convolution integral. The analytical solution of the convolution integral is obtained for a periodic variation of T s ( t). The resulting expression for T( x, t) is identical with that obtained by the usual periodic analysis. Numerical computations are carried out to investigate the dependence of the accuracy of numerical results on the upper limit of time ( t o ) in the convolution integral.