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This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The detonation process is simulated using a combination of a thermochemical code to determine the Chapman–Jouguet (C-J) conditions, coupled with an approximate spatially homogeneous model that describes the radial expansion of the detonation matrix. The conditions at the C-J point serve as initial conditions for the detonation dynamic model. The Mie–Grüneisen Equation of State (EoS) is used, with the "cold curve" represented by the Jones–Wilkins–Lee Equation of State. The particulate phenomena, representing the formation of metallic oxide nanoparticles from liquid droplets, are described by a Population Balance Equation (PBE) that accounts for the coalescence and coagulation mechanisms. The variables associated with detonation dynamics interact with the kernels of both phenomena. The numerical approach employed to handle the PBE relies on spatial discretization based on a fixed-pivot scheme. The dynamic solution of the models representing both processes is evolved with time using a Differential-Algebraic Equation (DAE) implicit solver. The strategy is applied to simulate the production of alumina nanoparticles from Ammonium Nitrate Fuel Oil aluminized emulsions. The results show good agreement with the literature and experience-based knowledge, demonstrating the tool's potential in advancing understanding of the detonation route. [ABSTRACT FROM AUTHOR]

We consider optimal designs for clinical trials when response variance depends on treatment and covariates are included in the response model. These designs are generalizations of Neyman allocation, and commonly employed in personalized medicine where external covariates linearly affect the response. Very often, these designs aim at maximizing the amount of information gathered but fail to assure ethical requirements. We analyze compound optimal designs that maximize a criterion weighting the amount of information and the reward of allocating the patients to the most effective/least risky treatment. We develop a general representation for static (a priori) allocation and propose a semidefinite programming (SDP) formulation to support their numerical computation. This setup is extended assuming the variance and the parameters of the response of all treatments are unknown and an adaptive sequential optimal design scheme is implemented and used for demonstration. Purely information theoretic designs for the same allocation have been addressed elsewhere, and we use them to support the techniques applied to compound designs. [ABSTRACT FROM AUTHOR]

We study optimal designs for clinical trials when the value of the response and its variance depend on treatment and covariates are included in the response model. Such designs are generalizations of Neyman allocation, commonly used in personalized medicine when external factors may have differing effects on the response depending on subgroups of patients. We develop theoretical results for D-, A-, E- and D$_{\rm{A}}$ A-optimal designs and construct semidefinite programming (SDP) formulations that support their numerical computation. D-, A-, and E-optimal designs are appropriate for efficient estimation of distinct properties of the parameters of the response models. Our formulation allows finding optimal allocation schemes for a general number of treatments and of covariates. Finally, we study frequentist sequential clinical trial allocation within contexts where response parameters and their respective variances remain unknown. We illustrate, with a simulated example and with a redesigned clinical trial on the treatment of neuro-degenerative disease, that both theoretical and SDP results, derived under the assumption of known variances, converge asymptotically to allocations obtained through the sequential scheme. Procedures to use static and sequential allocation are proposed. [ABSTRACT FROM AUTHOR]

The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions. [ABSTRACT FROM AUTHOR]

Companies regularly face market pressure to develop products faster but they also need to simultaneously incorporate technological constraints, sustainability trends, and customer requirements into their designs, which requires the use of systematic procedures. Firms that exploit natural resources and convert them into high-value products are among them. However, the literature on the application of such systematic approaches to products of this type remains scarce, as they often requrire extensive experimental plans involving the testing and optimization of multiple formulations. Here, we propose a systematic approach to the design of pine-resin-in-water emulsions, which can be used to fabricate pressure-sensitive adhesives. The strategy is customer-centric in the sense that the customers' specifications are integrated into the decision-making tool used to assess the quality of the formulations obtained through experiments. This tool uses loss functions to assess satisfaction with individual quality characteristics and multi-attribute decision-making methods to integrate them into an overall quality metric. Our framework is aligned with industrial practices and consists of three sequential stages: (i) screening of primary factors; (ii) optimization of secondary factors; and (iii) assessment of the experimental repeatability of the formulations. In each of these stages, the decision-making tool is used to "drive" the process of finding the optimal formulation. [ABSTRACT FROM AUTHOR]

The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming, when the covariates are categorical variables, is still scarce. We propose mixed-integer semidefinite programming formulations, to find exact D-, A- and I-optimal designs for linear models, and locally optimal designs for nonlinear models when the design domain is a finite set of points. The strategy requires: (i) the generation of a set of candidate treatments; (ii) the formulation of the optimal design problem as a mixed-integer semidefinite program; and (iii) its solution, employing appropriate solvers. For comparison, we use semidefinite programming-based formulations to find equivalent approximate optimal designs. We demonstrate the application of the algorithm with various models, considering both unconstrained and constrained setups. Equivalent approximate optimal designs are used for comparison. [ABSTRACT FROM AUTHOR]

Quality-control via acceptance sampling is a technique well established for monitoring the quality of production by lots. The design of acceptance sampling plans for univariate characteristics that follow the Gaussian distribution is reported in various references. Formulations for finding statistically and economically optimal acceptance sampling plans have been consistently proposed. Contrarily, the extension of acceptance sampling to multivariate characteristics has limited applications and the methods available to design plans are still elusive as they involve complex numerical computation procedures. We propose optimization-based formulations to design acceptance sampling plans by variables for multivariate characteristics. First, we consider the independence of characteristics and address plans that satisfy all the controlled quality levels of each one. A Mixed Integer Nonlinear Programming formulation is introduced for such a purpose. Then, we extend the analysis to dependent characteristics and use Surrogate-based optimization to handle the problem. The formulations are demonstrated with simulated scenarios and an industrial case of practical interest. [ABSTRACT FROM AUTHOR]

Explicit models representing the response variables as functions of the control variables are standard in virtually all scientific fields. For these models, there is a vast literature on the optimal design of experiments (ODoE) to provide good estimates of the parameters with the use of minimal resources. Contrarily, the ODoE for implicit models is more complex and has not been systematically addressed. Nevertheless, there are practical examples where the models relating the response variables, the parameters and the factors are implicit or hardly convertible into an explicit form. We propose a general formulation for developing the theory of the ODoE for implicit algebraic models to specifically find continuous local designs. The treatment relies on converting the ODoE problem into an optimization problem of the nonlinear programming (NLP) class which includes the construction of the parameter sensitivities and the Cholesky decomposition of the Fisher information matrix. The NLP problem generated has multiple local optima, and we use global solvers, combined with an equivalence theorem from the theory of ODoE, to ensure the global optimality of our continuous optimal designs. We consider D- and A-optimality criteria and apply the approach to five examples of practical interest in chemistry and thermodynamics. for this article are available online. [ABSTRACT FROM AUTHOR]

Concept design is an early and crucial phase in product development where the general concept of a product is created. In this stage, various aspects of the product are considered, such as usability and technical performance, among others. Product design and development are currently a well-established area of knowledge, and academia is increasingly including its fundamentals in regular curricula, especially in the areas of engineering, design, and marketing. At the same time, industrial players recognize the potential of the method for i. responding successfully to market uncertainty and speed; ii. improving the knowledge available and the systematization of creative processes; and iii. ensuring that the decision process is explicit and well documented. Nevertheless, only a few studies demonstrating the concept design procedure in detail are available in the literature. In this paper, we thus present a detailed case study concerning the design of portable thermal slippers, so as to demonstrate the application of structured procedures and systematic approaches to concept design, and providing a pedagogical review of methods and tools to support the analysis and decisions along the several steps of the concept design procedure. The particular case study here addressed resulted from the collaboration between an academic institution and a company operating in the home footwear industry, with the design team including elements from both sides. [ABSTRACT FROM AUTHOR]

The design of double acceptance sampling (AS) plans for attributes based on the operating characteristic curve paradigm is usually addressed by enumeration algorithms. These AS plans may be non optimal regarding the sample size to inspect as they were obtained without the requirement that the constraints at the OC curve controlled points are not violated for minimum Average Sample Number (ASN) scenarios. An approach based on mathematical programming is proposed to systematically design double AS plans for attributes, where the characteristics controlled are modelled by binomial or Poisson distributions. Specifically, Mixed Integer Nonlinear Programming (MINLP) formulations are developed and combined with an enumeration algorithm that allows finding ASN minimax optimal plans. A theoretical result is developed with the purpose of assuring the global optimum design is reached by iteration where a convenient solver is used to find local optima. To validate the algorithm, we compare our results with those of tables commonly used for practical purposes, consider different rates of risk, and setups commonly used in Lot Quality Assurance Plans (LQAS) for health monitoring programmes. Finally, we compare AS plans determined for processes described by binomial and Poisson distributions. [ABSTRACT FROM AUTHOR]

We consider the dependence on the measurement schedule of optimal experiments for kinetic parameters when the rates are temperature-dependent and follow the Arrhenius law. We compare three different approaches using the D-optimality criterion: (1) a locally optimal design based on a sequence of four batches where the process is observed at a single time; (2) two batches carried out at constant temperature where the process is observed at a pre-defined grid of times; and (3) a single batch where the temperature profile is optimal regarding the amount of information extracted and the process is observed at a pre-defined grid of times. An extension of the generalized equivalence theorem of optimal experimental design provides insight into the structure of the designs we find. The local D-optimality of the designs obtained is validated using the extended theorem for the latter two approaches. [ABSTRACT FROM AUTHOR]

This article discusses findings of a study which focused on the numerical solution of population balance equations (PBE) and on the transfer of finite elements method applied to the solution of partial differential equations (PDE). PBE is described as a form of integropartial-differential hyperbolic equation whose numerical solution is difficult to reach because of instability and numerical diffusion. The two categories of approaches for PBE solution include methods where global basis functions associated to time dependent coefficients are used to approximate the solution and methods which are based on the discretization of the spatial dimension into a given number of intervals.

The problem of finding optimal production and inventory policies is crucial for companies of the food industry, especially those processing multiple products. Since companies are required to adopt the most efficient solutions to prosper, the operation at these optimal conditions can have an extensive impact on profit, resource allocation and product quality. We address the problem of finding the optimal production and inventory policy in a multiproduct bakery unit for two contexts: (i) deterministic consumption without inventory control; and (ii) stochastic consumption combined with delayed inventory control. A formulation is proposed for each of these two setups. The restrictions considered in the model framework are related to workforce availability, and the cost structure includes four components: (i) production cost; (ii) inventory cost; (iii) setup cost; and (iv) the cost due to the degradation of perceived quality. The problem is formulated as a Mixed Integer Linear Programming one and solved with a branch and cut algorithm-based solver. The formulation is applied to a real bakery unit producing a mix of eight products. Distinct demand and inventory lower levels are used for building scenarios to test both models and characterize the economic performance of the multiproduct bakery unit. [ABSTRACT FROM AUTHOR]

The paper studies randomization rules for a sequential two-treatment, two-site clinical trial in Parkinson's disease. An important feature is that we have values of responses and five potential prognostic factors from a sample of 144 patients similar to those to be enrolled in the trial. Analysis of this sample provides a model for trial analysis. The comparison of allocation rules is made by simulation yielding measures of loss due to imbalance and of potential bias. A major novelty of the paper is the use of this sample, via a two-stage algorithm, to provide an empirical distribution of covariates for the simulation; sampling of a correlated multivariate normal distribution is followed by transformation to variables following the empirical marginal distributions. Six allocation rules are evaluated. The paper concludes with some comments on general aspects of the evaluation of such rules and provides a recommendation for two allocation rules, one for each site, depending on the target number of patients to be enrolled., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier Inc.)

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique., (© 2019 International Biometric Society.)

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D -, A - and E -optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D -optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.