The Optimal Sight Angle Problem

We introduce the following problem in this paper. There are n points on the plane that are to be observed from some point on a circle of given radius that encloses all of the points. We wish to find the observation point that has the best possible view of the n points in the sense that if we draw lines of sight from the observation point to the given points, the smallest angle between the lines is maximized. Applications could include the planning of photographs or displays. This is a “maximin problem” in which the function to be maximized has many local optima. We present two methods for solving the problem, one more efficient in computer time, and the other in storage. We also present a simplified procedure for the case where the observation point is “infinitely” distant from the given points.     

Photoinduced changes in the optical constants of Ge–Se–AgI thin films

The photoinduced changes in the complex refractive index n=n − ik of thin films from the Ge–Se–AgI system with constant ratio Ge/Se=1/4 and concentrations of AgI of 0, 5 and 10 mol% are studied by real time measurements of reflectance (R) and transmittance (T) of the films. The phase delay (δ) between the components of the transmitted wave, which is proportional to the birefringence of the film, is measured in real time as well. The changes in the average value of the refractive index (Δn), and in the average value of the absorption index (Δk) in the imaginary part of n as well as the induced optical anisotropy are estimated by solving the inverse optical problem. It is found that involving small quantities of AgI into a Ge–Se matrix increases the sensitivity of the films, but the anisotropic effects are comparatively weakly in them. The maximum values of changes in the average refractive index (Δn=0.025) and in the average absorption index (Δk=−0.03) are obtained in the films, containing 5 and 10 mol% AgI, respectively. Considerable values of the photoinduced anisotropy – birefringence (Δn_a≈−0.002) and dichroism (ΔD≈0.05, which corresponds to Δk_a≈0.035) are observed in films without addition of AgI (“pure” Ge–Se film).     

Comparison of sensing characteristics of ChemFEC devices based on spin-coated thin films of calix[n]arenes

ChemFECs (chemical field effect capacitors) or EIS (Electrolyte-Insulator-Semiconductor) devices were coated with calix[n]arene macrocycles for cation sensors development. Silicon nitride surface electrodes were spin-coated with p-tert-butylcalix[n]arene molecules for n = 8, 9 and 11. Electrochemical capacitance measurements were carried out to evaluate the sensitivity of the calix[n]arene layers towards specific cations as calcium and copper ions. Sensor responses were due to the “host-guest” specific interaction between the rigid cavity of calix[n]arene receptors (ligand) and chemical ion species. The developed chemical sensors have demonstrated good analytical characteristic in terms of: stability, selectivity and lifetime. In addition, experimental results were fitted using the site binding model in order to determine complex association constants, pK (1.9 ≤ pK ≤ 6.39) and surface density of ligands, N_L (9.10¹⁴ ≤ N_L ≤ 2.10¹⁶). All results obtained in this work were compared with those obtained using silicon dioxide EIS electrodes coated with the same calix[n]arene receptors using both spin-coating and thermal evaporation deposit processes.     

A Maximin Location Problem with Maximum Distance Constraints

This paper deal with the problem where a facility must be placed among n points so that the shortest weighted distance to a point is as large as possible. At the same time the facility must be within a pre-specified distance from each point; the facility is to be located on a plane and Euclidean distances are used. Applications include the location of facilities that are obnoxious in the sense that they should be placed as far away from certain points as possible but still be within a pre-specified “reach” of these points.     

System Effectiveness Simulation Model with Nonparametric Dependability

The simulation model presented here is a useful extension of WSEIAC's system's effectiveness methodology. This model accepts information regarding uncertainty with the parametric estimates of the system's attributes. One of the system's attributes, defined as “dependability,” requires Markovian State Transition Process. Time-dependent queueing process and renewal theory application for this dependability matrix are avoided by resorting to a simulation technique. This dependability matrix requires reliability and repairability estimates, which are obtained based on a non-parametric approach. This approach is based on a test program with a very realistic environment where n identical units are placed on test for a mission duration T. At the end, the number of failed units r is noted. Units failed are not replaced. Times of failed units before failure are unknown. Based on these, the dependability matrix is generated, which results ultimately in generating a sampling distribution of system effectiveness of each subsystem and the overall system. This process is coded in FORTRAN IV.     

A Flow-Through Dissolution Approach to In Vivo/In Vitro Correlation of Adinazolam Release from Sustained Release Formulations

A Copley^TM fraction collector and a Disotest^TM flow-through system were coupled to provide an automatic discrete sampling flow-through dissolution system for use both in the “open-loop” and “closed-loop” mode. The system was used to investigate the release characteristics of adinazolam in sustained release formulations using a pH 1.2 simulated gastric fluid (without enzymes) dissolution medium (USP XXI). These experimental formulations are designed to provide relatively slow to rapid drug release. The dissolution effluent was analysed off-line by reverse phase HPLC to determine the adinazolam concentration at programmed timed intervals. The differential dissolution profiles produced when the system is used in the “open-loop” configuration are more discriminating in describing the release characteristics of the formulations according to the relative release rates than the “closed-loop” cumulative profiles. Using the characteristic dissolution time parameter from the Weibull function, a better correlation with in vivo bioavailability data was achieved for the data from the system in the “open-loop” mode than when it was used in the “closed-loop” mode. In the “open-loop” mode the Weibull function characteristic dissolution time parameter yielded the best quantitative correlation with a correlation coefficient of 0.92 compared to a value of 0.85 for the “closed-loop” configuration     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Rotation numbers for quasi-periodically forced monotone circle maps

Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form „ - 1/n ≤(1/n)(y_n - y₀) ≤„ + 1/n, where (1/n)(y_n - y₀) is an estimate of the rotation number obtained from an orbit of length n with initial condition y₀, and „ is the true rotation number. This allows rotation numbers to be computed reliably and efficiently. Although Herman has proved that quasi-periodically forced circle maps also possess a well-defined rotation number, independent of initial condition, the analogous bound does not appear to hold. In particular, two of the authors have recently given numerical evidence that there exist quasi-periodically forced circle maps for which y_n - y₀ - „n is not bounded. This renders the estimation of rotation numbers for quasi-periodically forced circle maps much more problematical. In this paper, a new characterization of the rotation number is derived for quasiperiodically forced circle maps based upon integrating iterates of an arbitrary smooth curve. This satisfies analogous bounds to above and permits us to develop improved numerical techniques for computing the rotation number. Additionally, the boundedness of y_n - y₀ - „n is considered. It is shown that if this quantity is bounded (both above and below) for one orbit, then it is bounded for all orbits. Conversely, if for any orbit y_n - y₀ - „n is unbounded either above or below, then there is a residual set of orbits for which y_n - y₀ - „n is unbounded both above and below. In proving these results a min-max characterization of the rotation number is also presented. The performance of an algorithm based on this is evaluated, and on the whole it is found to be inferior to the integral based method.     

A modified effective crack-length formulation in elastic-plastic fracture mechanics

In examining the performance of standard effective crack-length formulations, the authors noted quantitative accuracy up to “high” fractions of limit load under loading conditions for which the elastic T-stress was non-negative, while a pronounced deviation from the corresponding continuum elastic-plastic plane-strain finite-element solutions was seen in shallow-cracked geometries having negative T-stress. This trend can be rationalized by noting that, under modified boundary layer (K_I and T) loading, the maximum plastic zone radius strongly increases as the T-stress decreases from zero (J.R. Rice (1974), J. Mech. Phys. Solids 22, 17–26; S.G. Larsson and A.J. Carlsson (1973), J. Mech. Phys. Solids 21, 263–277; N.P. O'Dowd and C.F. Shih (1991), J. Mech. Phys. Solids 39(8), 989–1015.) Accordingly, we formulate a modified effective crack length to account for the effects of the elastic T-stress.

The new formulation consistently extends the load range for which accurate predictions of compliance, J-integral, and crack-tip constraint are obtained in several plane strain specimen geometries. The magnitude of influence of the T-stress varies with specimen type and relative crack depth. The greatest “improvement” to standard effective crack length approximations occurs in specimens of “moderately” negative T-stress.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

A dynamic measure of order in structural glasses

Although some patterns of physical behavior are common in the glass transition and in the properties of supercooled liquids and glasses (characteristic viscoelasticity, temperature dependence of viscosity and relaxation times, property evolution through “physical aging”, difficulties in performing equilibrium measurements or simulations, etc.), it is difficult to arrive at a definition of the glass transition which distinguishes it from other phenomena exhibiting similar features. The present paper addresses this problem by defining a dynamical measure of order involving the average “shape” of particle trajectories in supercooled liquids. This dynamic order parameter should provide a measure of “closeness” to the glass transition and some indirect insights into the physical nature of supercooled liquids and glasses. Arguments are given that the proposed dynamic measure of order [“generalized capacity”, C(T)] is related to the temperature-dependent “effective hydrodynamic radius” R_H(T) measured in supercooled liquids and model numerical calculations are given to support this view. Some consequences of the intermittent particle motion at low temperatures for stress relaxation are also discussed.     

Modifying the buckyball

Structural and electronic properties of carbon clusters, in particular the C₆₀ “buckyball” molecule as well as structurally and chemically modified fullerenes, are calculated using a combination of predictive ab initio techniques and parametrized total energy schemes. These calculations indicate that single- and multi-shell fullerenes are the most stable C_n isomers at T = 0 for n < 20. More open structures are favored by entropy at higher temperatures. Upon interaction with donor elements, C₆₀ molecules form stable M@C₆₀ endohedral complexes; analogous acceptor-based complexes are unstable. Solid C₆₀ reacts with alkali metals and forms a stable intercalation compound which shows superconducting behavior. The relatively high value of the critical temperature for superconductivity can be explained quantitatively within the Bardeen-Cooper-Schrieffer formalism.     

Annealing Textures for Drawability: Influence of the Degree of Cold Rolling Reduction for Low-Carbon and Extra Low-Carbon Ferritic Steels

This work considers the optimization of deep drawing properties by studying the influence of hot rolling conditions, cold reduction rate, and final annealing on the evolution of steel sheet textures. Two steels have been selected: a low-C steel used for enameling applications, and an extra-low-C steel of the interstitial-free type. Results show that the intensity of {111} component—and, consequently, drawability—is considerably higher in the textures of cold-rolled and annealed sheets than in hot-rolled sheets. It is suggested that drawability of sheets annealed after cold rolling improves if greater than conventional reduction rates are used during rolling. Finally, it is shown that, contrary to what has sometimes been claimed, improvements of the “r” coefficient are not accompanied by a “pancake” morphology of the ferrite grains.     

A new method for reducing DNL in nuclear ADCs using an interpolation technique

The paper describes a new method for reducing the DNL associated with nuclear ADCs. The method named the “interpolation technique” is utilized to derive the quantisation steps corresponding to the last n bits of the digital code by dividing quantisation steps due to higher significant bits of the DAC, using a chain of resistors. Using comparators, these quantisation steps are compared with the analog voltage to be digitized, which is applied as a voltage shift at both ends of this chain. The output states of the comparators define the n bit code. The errors due to offset voltages and bias currents of the comparators are statistically neutralized by changing the polarity of quantisation steps as well as the polarity of analog voltage corresponding to last n bits) for alternate A/D conversion. The effect of averaging on the channel profile can be minimized. A 12 bit ADC was constructured using this technique which gives DNL of less than ±1% over most of the channels for conversion time of nearly 4.5 μs. Gatti's sliding scale technique can be implemented for further reduction of DNL. The interpolation technique has a promising potential of improving the resolution of existing 12 bit ADCs to 16 bit, without degrading the percentage DNL significantly.     

Cost optimal preventive maintenance and replacement scheduling

In this paper, we present a method for predicting a cost-optimal preventive maintenance policy for a repairable system with an increasing Rate of Occurrence Of Failure (ROCOF). We segment the maintenance planning horizon into n discrete and equally-sized periods. For each period, we predict which of three possible actions, (maintain the system, replace the system, or do nothing to the system) should be taken, such that the total net present worth of all future costs is minimized. Our model expands upon previous work by utilizing the concept that maintenance reduces the “effective age” of the system and hence the system ROCOF. We develop the model and evaluate three solution procedures, namely, a random search, a genetic algorithm, and a branch-and-bound approach. The entire approach is illustrated through the use of a numerical example.     

Experimental Design for a Granulation Process with “Priori” Criterias

Optimization techniques representr analytical tools available for the best solution to a particular problem.

Pharmaceutical product and process design problems were structured as constrained optimization problems and subsequently solved by the “a priori” optimality approach using an exchange algorithm.

The effect of the amount of added water plus granulation time and impeller speed on two properties of the granulates were investigated.

Experimental results obtained for the optimal formulation agreed well with the predictions.     

The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity

This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the “forward-pass” concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.     

Single and multiobjective structural optimization in discrete-continuous variables using simulated annealing

A multivariable optimization technique based on the Monte-Carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems. This procedure, known as simulated annealing, draws an analogy between energy minimization in physical systems and objective function minimization in structural systems. The search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. Numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete-continuous variables are presented. The influence of cooling schedule parameters on the optimum solutions obtained is discussed. Simulation results indicate that, in several instances, the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient-based and discrete optimization techniques. The results also indicate that simulated annealing has substantial potential for additional applications in optimization, especially for problems with mixed discrete-continuous variables.     

Monte Carlo study of thin magnetic Ising films

The average magnetization of thin simple cubic Ising films (with thicknesses n of 1, 2, 3, 5, 10 and 20 atomic layers, respectively) is calculated as a function of temperature using the Monte Carlo technique. The “magnetization profile” across the film is also obtained. To approximate the infinite extension in the plane parallel to the surfaces of the films, films with linear dimensions 55 × 55 and periodic boundary conditions are considered. The shift of the critical temperature is consistent with an n^-λ law where λ = 1/v₃ = 1.56 is the reciprocal exponent of the correlation length. This result is critically compared with previous estimates obtained by various authors using other techniques. By interpreting the results in terms of Fisher and Barber's scaling theory, the finite size scaling function for the magnetization is determined. It is pointed out that the spatial distribution of the magnetization can be reasonably interpreted in terms of surface properties.