Range Of Time Values Research Articles

Diffusion Penetration Time for Transient Heat Conduction

The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations because the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for six geometries, including one-dimensional cases for Cartesian, cylindrical, and spherical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in cylindrical coordinates. The sixth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a nonheated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case, showing the relationships between the temperature rise at the point of interest and the amount of time required to reach that temperature. It was found that a dimensionless parameter, defined herein as dimensionless penetration time, remains reasonably constant between the various geometries studied. The definition of this term is the dimensionless time required to bring about a desired temperature rise, with the characteristic length being the distance between the point of heating and the point of interest.

Guidance system for control periods under modelling threshold

This paper presents a new guidance system for process control that can improve the control performance of model-based advanced controllers or optimised adaptive controllers, when their control periods have to be selected within a lower range of time values that may increase the sensitivity of the predictive model parameters to identification errors. The guidance system generates at each control instant a future desired trajectory for the process output variable under control, from which it computes a set point for the derivative variable of the process output variable. A predictive or adaptive predictive controller drives the derivative variable to its set point and, as a consequence, the process output converges towards said desired trajectory. The new guidance system is illustrated by its application to the level control of a MIMO nonlinear process, in the presence of noises and disturbances. The results show how the control performance of the guidance system is not affected by 'small' control periods that would deteriorate the performance of an adaptive predictive controller for the same application.

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems

A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

An Implementation of Bouchouev's Method for a Short Time Calibration ofOption Pricing Models

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We are able to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.

The Laplace Transform Galerkin Technique: A time‐continuous finite element theory and application to mass transport in groundwater

A time‐continuous numerical technique, referred to as the Laplace Transform Galerkin (LTG) method, is developed and applied to the problem of solute transport in porous media. After application of Galerkin's procedure and subdivision of the domain into finite elements, the method involves a simple application of the Laplace transformation to eliminate the temporal derivatives appearing in the space‐discretized set of ordinary differential equations. Then, by solving the resulting transformed system of algebraic equations in Laplace p space, numerical inversion of the Laplace‐transformed nodal concentration is performed using the robust and accurate Crump (1976) algorithm. The Crump algorithm permits the concentration to be evaluated from a range of time values from a single set of Laplace p space solutions. Because each of the needed p space solutions are independent, the algorithm is well suited for execution on multiprocessor parallel computers. It is demonstrated by means of a series of examples that the LTG scheme is capable of providing highly accurate solutions essentially devoid of numerical dispersion for grid Peclet numbers in excess of 30. Examination of the complex‐valued, Laplace‐domain concentration profiles reveal that they are generally smooth, well‐behaved oscillatory functions compared to the profiles in the time domain, thus permitting the use of a coarse finite element grid. Because of the nature of the Laplace transformation, the LTG method is particularly well suited to the problem of transient groundwater flow and solute transport in fractured porous media or multiple aquifer‐aquitard systems based on the dual‐porosity integrodifferential equation approach.