Unperturbed Data Research Articles

WELL-CONDITIONED NUMERICAL APPROACH FOR THE SOLUTION OF THE INVERSE HEAT CONDUCTION PROBLEM

A numerical procedure is presented for the solution of the inverse heat conduction problem. The method finds the desired heat flux in either the frequency domain through the inverse discrete transfer function, or in the time domain through the two-sided convolution with the discrete inverse impulse response function. The method is shown to be well conditioned, in the sense that it never yields heat fluxes oscillating with increasing amplitudes; and for unperturbed data, it does not require stabilization or regularization as the time step is decreased or the spatial discretization is refined. This discretization is carried out using the finite-element method. However, the method is also suitable for finite differences or any other discretization procedure. A series of numerical examples illustrate the accuracy and efficiency of the proposed method.

Review article : Computer simulation of the progression of an acute myelocytic leukemia in the brown norway rat

Reduction and extrapolation of experimental data concerning both the perturbed and unperturbed growth characteristics of a malignant population was the reason for developing a simple descriptive mathematical model. Data were obtained by inoculating BN/Rij rats i.v. with 10 7 viable cells of a transplantable myelocytic leukemia (BNML). At various time points the tumor load in the bone marrow was determined by means of a clonogenic stemcell (LCFU-S) assay or by a dose–survival time bioassay (SVL). By fitting hypothetical growth curves to the LCFU-S datapoints, using a non-linear least squares computer algorithm, an optimal functional relationship between the BNML population size, N, and time after inoculation, t, was found. The unperturbed data are best explained by a curve that consists of an exponential part which, at a transition point, changes into a Gompertz curve to account for a steady state plateau phase. Chemotherapy applied for perturbation purposes consisted of a single dose (100 mg/kg) of cyclophosphamide (CY) given i.p. at day 13. The effect of the drug was modelled as either pulse-shaped or as a more gradual event. In the former case an instantaneous tumor load reduction occurs, after which regrowth can be modelled in a way similar to unperturbed growth. Different parameter values apply, resulting in slower population size increase and a lower level plateau phase. Statistical significance is rather poor though, owing to uncertainty in the observations. The tumor load reduction is somewhat larger than can be deduced from dose–response experiments (6.0 and 5.5 decades, respectively). Correction is possible, without changing the goodness of fit, by introducing a time delay in the early exponential phase. To model gradual drug influence various functions were tested, i.e. a constant level during some time, an exponentially decreasing level, parabolic increase and decrease, and a combination of the first two categories. This last one, when superimposed on the function for unperturbed growth, yielded the best fit to the observed LCFU-S datapoints. Taking the total correlation coefficient, TCC, as measure of goodness of fit (TCC tends to 1 with improving fit) it must be concluded that the instantaneous drug effect model is only slight better than the gradual model (TCC = 0.80253 and 0.84915, respectively). The SVL datapoints also indicate instaneous rather than gradual drug effect.

Computer simulation of the progression of an acute myelocytic leukemia in the brown Norway rat

Reduction and extrapolation of experimental data concerning both the perturbed and unperturbed growth characteristics of a malignant population was the reason for developing a simple descriptive mathematical model. Data were obtained by inoculating BN/Rij rats i.v. with 10 7 viable cells of a transplantable myelocytic leukemia (BNML). At various time points the tumor load in the bone marrow was determined by means of a clonogenic stemcell (LCFU-S) assay or by a dose-survival time bioassay (SVL). By fitting hypothetical growth curves to the LCFU-S datapoints, using a non-linear least squares computer algorithm, an optimal functional relationship between the BNML populations size, N, and time after inoculation, t, was found. The unperturbed data are best explained by a curve that consists of an exponential part which, at a transition point, changes into a Gompertz curve to account for a steady state plateau phase. Chemotheraphy applied for perturbation consisted of a single dose (100 mg/kg) of cyclophosphamide (CY) given i.p. at day 13. The effect of the drug was modelled as either pulse-shaped or as a more gradual event. In the former case an instantaneous tumor load reduction occurs, after whicregrowth can be modelled in a way similar to unperturbed growth. Different parameter values apply, resulting in slower population size increase and a lower level plateau phase. Statistical significance is rather poor though, owing to uncertainty in the observations. The tumor load reduction is somewhat larger than can be deduced from dose-response experiments (6.0 and 5.5 decades, respectively). Correction is possible, without changing the goodness of fit, by introducing a time delay in the early exponential phase. To model gradual drug influence various functions were tested, i.e. a constant level during some time, an exponentially decreasing level, parabolic increase and decrease, and a combination of the first two categories. This last one, when superimposed on the function for unperturbed growth, yielded the best fit to the observed LCFU-S datapoints. Taking the total correlation coefficient, TCC, as measure of goodness of fit (TCC tends to 1 with improving fit) it must be concluded that the instantaneous drug effect model is only slight better than the gradual model (TCC = 0.85023 and 0.84915, respectively). The SVL datapoints also indicate instantaneous rather than gradual drug effect.

Resilience of a statistical sampling scheme

Most statistical sampling algorithms on hydrologic random fields assume that the new measurements will agree reasonably well with their predicted values. This in turn implies the stationarity of the estimated covariance function. In order to test the reliability of one such statistical algorithm (i.e., variance reduction analysis), noisy input data are generated, and results of sampling from these data are compared to the case of sampling with the unperturbed data. These comparisons and a related regret analysis reveal that the effects of the noisy data are primarily accommodated by adjustments to the covariance function parameters, while selected sets show a high degree of resilience. Variance reduction analysis seems to be a reliable method for maximizing information by sampling random fields with an unstable parameter space but a resilient action space.

Large-time behavior of solutions to a scalar conservation law in several space dimensions

We consider solutions of the Cauchy problem in R + n + 1 {\mathbf {R}}_ + ^{n + 1} for the equation u t + div x f ( u ) = 0 {u_t} + {\operatorname {div}_x}f(u) = 0 . The initial data is assumed to be a compact perturbation of a function of the form, φ ( x ) = a \varphi (x) = a for ⟨ x , μ ⟩ > 0 \left \langle {x,\,\mu } \right \rangle > 0 , φ ( x ) = b \varphi (x) = b for ⟨ x , μ ⟩ > 0 \left \langle {x,\,\mu } \right \rangle > 0 , where a a and b b are constants and μ \mu is a given unit vector. The Cauchy problem together with an entropy condition on u u is known to be well posed. The solution with unperturbed initial data, φ ( x ) \varphi (x) , is a traveling shock, φ ( x − k → t ) \varphi (x - \overrightarrow k t) , provided that φ ( x − k → t ) \varphi (x - \overrightarrow k t) satisfies the entropy condition (an inequality on a , b , μ a,\,b,\,\mu , and f f ). Assuming this type of condition on φ \varphi , we study the large-time behavior of u u . In particular, we show that u u converges to a traveling shock whose profile agrees with ⟨ x , μ ⟩ = 0 \left \langle {x,\,\mu } \right \rangle = 0 outside of a compact set.

Methodology for Predictive Testing of Fuel Cells

A perturbation testing method has been developed and tested for predictive testing of fuel cells. This method involves application of small changes to the operating conditions of the cell in a predetermined sequence. The resultant response of the cell is then measured and statistically correlated with the corresponding test conditions. This method has been applied to the phosphoric acid fuel cell, and the effect of operating and cell‐component variables on cell‐performance degradation has been studied. A strong effect of the cell temperature and cathode potential on fuel‐cell‐performance degradation has been observed. A cell‐performance degradation model has been formulated, and the unknown parameters in the model have been estimated by a regression analysis of the experimental data. A reasonable agreement between the fuel cell performance predicted by this model (derived from the perturbation experiments) and the unperturbed test data supports the applicability of the perturbation method.

Hydrogen permeation characteristics of some austenitic and nickel-base alloys

The hydrogen permeabilities of 321-SS, 316-SS, Inconel-625, and Inconel-718 have been measured for hydrogen driving pressures in the range from 10−3 to 104 Pa and for temperatures between 350 and 1050 K. It was found that the use of active hydrogen purity control measures, which included direct hydrogen supply by a temperature-controlled uranium hydride bed and the implementation of a throttled ion pump, greatly increased the capability to obtain unperturbed permeation data at low driving pressures, i.e., <10 Pa. For all four alloys studied, a half-power dependence of permeability on hydrogen driving pressure was obtained at the higher end of the pressure range studied. Also, the pressure at which deviations from a half-power dependence occurred was found to depend to a great extent on upstream hydrogen purity. In general, the Inconel alloys appeared slightly more sensitive to impurities (such as H2O and O2) than the austenitic alloys, quite possibly because of the presence of small amounts of aluminum in the Inconels.

Statistical evaluation and design of an evaporator control system

AbstractThe utility of a statistical procedure suggested by Box and Jenkins is assessed for the evaluation and modification of an industrial evaporator control system. Results, obtained from the analysis of routine unperturbed operating data, indicate that this approach is (i) readily adaptable to the analysis of the dynamic behaviour of a full scale chemical unit process, (ii) characterized by effective model form identification, and (iii) extremely useful in deriving conventional and more novel control functions to supplement existing control schemes.