Traditional Solution Procedures Research Articles

Rational Screening of Cocrystals using Thermal Analysis: Benchmarking on Energetic Materials

Cocrystal design is an important and well-developed approach in the pharmaceutical industry. Energetic materials can be thought of as unique and challenging objects for cocrystal engineering since abundant explosophoric functionalities prevent exploiting common supramolecular synthons. Screening of cocrystal formation using thermal analysis methods is investigated. A few approaches from the literature are combined in a single procedure that allows for automation, high-throughput screening, and the usage of milligrams of material. To estimate the accuracy of the screening procedure, we compiled available literature data on 213 cocrystals with energetic or very similar to energetic materials. The recommended procedure can detect cocrystal formation in 75% cases (with no false positives), according to a smaller sample data set of 28 cocrystal-forming systems. The procedure was then used to screen for novel cocrystals among several acidic energetic materials, ammonium and hydroxylammonium energetic salts, 3-nitro-1,2,4-triazole as a coformers, and 13 cocrystals were discovered. Then, using the traditional solution procedure, eight novel cocrystals were prepared, and their X-ray structures were reported. One of the cocrystals discovered, a complex of promising energetic material, dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate (also known as TKX-50) with 18-crown-6, is the first cocrystal of TKX-50 with a reported X-ray structure so far. Overall, we present a unified procedure of thermal screening for cocrystals and salts; benchmarking on challenging objects for cocrystal design (energetic materials) shows its high performance.

Mechanochemical ring-opening metathesis polymerization: development, scope, and mechano-exclusive polymer synthesis.

Ruthenium-alkylidene initiated ring-opening metathesis polymerization has been realized under solid-state conditions by employing a mechanochemical ball milling method. This method promotes greenness and broadens the scope to include mechano-exclusive products. The carbene- and pyridine-based Grubbs 3rd-generation complex outperformed other catalysts and maintained similar mechanistic features of solution-phase reactions. High-speed ball milling provides sufficient mixing and energy to the solid reaction mixture, which is composed of an initiator and monomers, to minimize or eliminate the use of solvents. Therefore, the solubility and miscibility of monomers and Ru-initiators are not limiting factors in solid-state ball milling. A wide variety of solid monomers, including ionomers, fluorous monomers, and macromonomers, were successfully polymerized under ball milling conditions. Importantly, direct copolymerization of immiscible (ionic/hydrophobic) monomers exemplifies the synthesis of mechano-exclusive polymers that are difficult to make using traditional solution procedures. Finally, the addition of a small amount of a liquid additive (i.e., liquid-assisted grinding) minimized chain-degradation, enabling high-molecular-weight polymer synthesis.

Modeling epidemics by the lattice Boltzmann method.

In this paper, we demonstrate that the lattice Boltzmann method can be successfully adopted to investigate the dynamics of epidemics. Numerical simulations prove the excellent accuracy properties of the approach, which recovers the solution of the popular SIR model. Because spatial effects are naturally accounted for in the lattice Boltzmann formulation, the present scheme appears to be more competitive than traditional solution procedures. Interestingly, it allows us to simulate scenarios characterized by selective lockdown configurations.

Semi–analytical, piecewise temperature–time distributions in solid bodies of regular shape affected by uniform surface heat flux employing the Method Of Lines (MOL) and the eigenvalue method

The central objective of the present study is to generate an approximate, semi–analytical piecewise solution of the one-dimensional, unsteady heat conduction equation in regular solid bodies (large wall, long cylinder and sphere) with uniform heat flux at the exposed surfaces. The main obstacle in these heat conduction problems lies in the boundary condition of uniform heat flux that is non-homogeneous, and of course is not conducive to the direct utilization of the method of separation of variables. To circumvent this restrictive obstacle, the traditional solution procedure relies on the principle of superposition of solutions composed of three degraded sub-solutions: one sub-solution in terms of the space coordinate and time, another sub-solution in terms of the space coordinate and another sub-solution in terms of time. In the present study, we exploit a radical different approach applying the Method Of Lines (MOL) forthwith to the one-dimensional, unsteady, heat conduction equation with prescribed uniform heat flux. Essentially, MOL discretizes the spatial partial derivatives in the one-dimensional, unsteady, heat conduction equation, while leaving the time partial derivative continuous. Correspondingly, the MOL transformation gives way to an adjoint system of linear, ordinary differential equations of first order in time, which is solved analytically (not numerically) with the potent eigenvalue method in the platform of a symbolic algebra code. The outcome of the two-part computational procedure provides a sequence of semi-analytical piecewise temperature distributions at the pre-selected lines in the large wall, long cylinder and sphere, which are expressed in terms of linear combinations of exponential functions of time comprising the required set of eigenvalues and eigenvectors. At the end, it was determined that the semi-analytical piecewise surface, center and mean temperature-time distributions based on seven lines exhibit excellent quality in the entire time domain.

Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment

In this paper, we investigated a multi-objective inventory model under both stock-dependent demand rate and holding cost rate with fuzzy random coefficients. Chance constrained fuzzy random multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. In addition, the technique of fuzzy random simulation is applied to deal with general fuzzy random objective functions and fuzzy random constraints which are usually difficult to converted into their crisp equivalents. The purposed of this study is to determine optimal order quantity and inventory level such that the total profit and wastage cost are maximized and minimize for the retailer respectively. Finally, illustrate example is given in order to show the application of the proposed model.

A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate

In this paper, we developed a multi-objective multi-item inventory model with fuzzy rough coefficients. Here, we have considered both demand and holding cost which is a non-linear function of the instantaneous stock level. Chance-constrained fuzzy rough multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. By examining the various definitions and theoretical results of fuzzy rough variables, we have designed a Tr-Pos chance constrained technique to determine the optimal solutions of a fuzzy rough multi-objective inventory problem. Finally, a numerical example is provided to illustrate the present model, and a sensitivity analysis of the optimal solution with respect to the major parameters is carried out.

A Heuristic for the Multisource Weber Problem with Service Level Constraints

In this paper we develop a column-generation-based heuristic procedure to solve a generalized version of the multisource Weber problem where in addition to the transportation cost we also consider staffing level costs that arise due to consideration of service level constraints. Traditional solution procedures for the multisource Weber problem do not take into account the staffing costs. Our contribution is towards addressing this gap. We develop a lower bound for the problem using which we evaluate the performance of the heuristic procedure on problems of different sizes and cost parameters. Our computational experience indicates that problems with up to 100 customer regions can be solved using the heuristic within five minutes of computational time on average. The average gap is less than 5% for a majority of problem instances.

Mechanochemical preparation of copper iodide clusters of interest for luminescent devices.

The copper iodide complexes are known for their large variety of coordination geometries. Such diversity, while making it difficult to predict the final structure, permits the preparation of a great number of copper iodide complexes based on the same ligand. The target of the research was that of thoroughly exploring the chemistry of CuI and the ligand diphenyl-2-pyridyl phosphine (PN) by varying the stoichiometric ratio and/or the aggregation state. Six different compounds have been identified: [Cu4I4(PN)2], [Cu4I4(PN)2·(CH2Cl2)0.5], [CuI(PN)0.5]∞, [CuI(PN)3] whose structures have been determined during this study, CuI(PN)2 which was characterized by powder diffraction and [Cu2I2(PN)3] which has been already reported. The preparation routes are also different: synthesis in solution yielded [Cu4I4(PN)2·(CH2Cl2)0.5] and [CuI(PN)3] while [CuI(PN)0.5]∞ and CuI(PN)2 were obtained only via solid state reactions. These two latter examples confirmed that mechanochemistry is a valid route to explore the landscape of the possible structures of CuI derivatives. Crystallization by traditional solution procedures failed to give the desired crystal, so structure determination of the new compounds was tackled in two ways: by attempting crystal growth via solvothermal synthesis and by resolving the structure from X-ray powder diffraction data with "direct space" methods. What is more the photophysical properties of the complexes that could be obtained as sufficiently pure powders have also been investigated and are reported herein.

Superposition Principle for the Tensionless Contact of a Beam Resting on a Winkler or a Pasternak Foundation

AbstractA Green function–based approach is presented to address the nonlinear tensionless contact problem for beams resting on either a Winkler or a Pasternak two-parameter elastic foundation. Unlike the traditional solution procedure, this approach allows determination of the contact locus position independently from the deflection curves. By doing so, a general nonlinear connection between the loading and the contact locus is found, which enlightens the specific features of the loading that affect the position of the contact locus. It is then possible to build load classes sharing the property that their application leads to the same contact locus. Within such load classes, the problem is linear and a superposition principle holds. Several applications of the method are presented, including symmetric and nonsymmetric contact layouts, which can be hardly tackled within the traditional solution procedure. Whenever possible, results are compared with the existing literature.

An economic replacement model with probabilistic asset utilization

Traditional economic replacement analysis provides asset purchase and sale decisions over a given horizon based on expected purchase, operating, maintenance and salvage costs. As these costs are dependent on asset utilization, a constant or predetermined usage is generally assumed. However, due to randomness in operations, such as customer demand, these expected utilization schedules may not be realized in practice, thus invalidating the replacement schedule. This paper examines the effect of probabilistic asset utilization on replacement decisions through the use of dynamic programming. The solution determines minimum expected cost decisions for each state defined by the asset's age and cumulative utilization in each period. These decisions generalize the definition of the economic life of an asset to include age and cumulative utilization. Assumptions common to replacement analysis allow the state space to grow linearly with time, avoiding dynamic programming's ‘curse of dimensionality’. Examples with time invariant and variant economics are presented and compared to traditional solution procedures

An economic replacement model with probabilistic asset utilization

Traditional economic replacement analysis provides asset purchase and sale decisions over a given horizon based on expected purchase, operating, maintenance and salvage costs. As these costs are dependent on asset utilization, a constant or predetermined usage is generally assumed. However, due to randomness in operations, such as customer demand, these expected utilization schedules may not be realized in practice, thus invalidating the replacement schedule. This paper examines the effect of probabilistic asset utilization on replacement decisions through the use of dynamic programming. The solution determines minimum expected cost decisions for each state defined by the asset's age and cumulative utilization in each period. These decisions generalize the definition of the economic life of an asset to include age and cumulative utilization. Assumptions common to replacement analysis allow the state space to grow linearly with time, avoiding dynamic programming's `curse of dimensionality'. Examples with time invariant and variant economics are presented and compared to traditional solution procedures.

RTSS: An interactive decision support system for solving real time scheduling problems considering customer and job priorities with schedule interruptions

Scheduling is the process of organizing, choosing and timing resource usage in a facility (e.g. factory, hospital) to conclude all necessary activities for completing a job at a desired time. This is a common problem where there are multiple jobs and a variety of resources that are required to complete each one of them. The principal objectives in scheduling include efficient and effective resource utilization and improvement in overall system performance. Mathematical complexities in obtaining an optimal solution to scheduling problems force many assumptions into the existing solution. The importance and value of a customer or a job (based on historical data) are not included in such traditional solution procedures. In this paper, we present a decision support system (DSS) to solve scheduling problems that considers the value of a job and a customer. This real time scheduling system also permits many of the traditional assumptions and constraints of scheduling models to be relaxed. Schedule interruptions are permitted and the state of the facility is evaluated at the time of dispatching decisions. An expert system is used to generate alternatives in order to eliminate potential job lateness with reduced mathematical complexities of the scheduling algorithm. This DSS is developed as a tool for the decision maker to solve practical scheduling problems. Traditional research on dynamic job shop scheduling (DJSS) is largely based on combinatorial analysis. Unfortunately, the NP-complete nature of the problem forces many assumptions that limit the use of analytical methods in practical problem solving to be included in existing solution procedures. Customer and job priorities, based on historical data, are seldom included in scheduling models. Many complexities in solving scheduling problems can be reduced if restrictions on limiting resources can be modified in consultation with the decision maker. Such changes can alter the feasible solution space, and permit sound, profitable decisions to enter into the model. This technique is not practicable in a traditional mathematical approach to obtain a solution for the scheduling problem. In this paper, we present a decision support system for real time scheduling that not only allows changes in limiting resources but also permits planned and unplanned downtime of machines, customer order changes and utilization of equipment with multiple capabilities. Expert systems and solicited user input are used to modify resource constraints. This system combines the customer value, job value and the potential value of job and customer along with a traditional component of scheduling analysis to create a schedule. The impact of this system on classical job shop scheduling is also discussed.

Total Least Squares, Matrix Enhancement, and Signal Processing

The concept of least squares (LS) as applied to a system of generally inconsistent linear equations A x ≍ y plays a central role in algorithms used for solving a variety of important signal processing problems. In the standard LS approach, the smallest unconstrained Euclidean norm perturbation of vector y is sought so that the resultant perturbed system of linear equations A x = y + δ has a solution. Implicit in the LS problem formulation is the assumption that only y vector is subject to error. Depending on the nature of the application, however, system matrix A may also be subject to error. When both the system matrix and right side vector are imprecisely known, the use of a least-squares solution can lead to disappointingly poor results. To mitigate the effects of errors in both A and y the concept of total least squares (TLS) is invoked. In the standard TLS problem, the smallest unconstrained perturbation of the matrix-vector pair ( A, y ) is sought so that the perturbed system of equations [ A + Δ] x + = y + δ has a solution. In this paper, theoretical issues regarding TLS are first addressed in which a singular value decomposition approach is used to find the optimal unconstrained choices for the perturbations Δ and δ. The TLS concept is next extended to the case in which the perturbed matrix-vector pair ( A + Δ, y + δ ) identifying the perturbed linear equations is constrained to satisfy prescribed properties known (or hypothesized) to be possessed in the idealized case. These property constraints take on such disparate forms as requiring that the perturbed auxiliary matrix [ A + Δ − y − δ ] be positive definite Hermitian, block Toeplitz, or of a given nonfull rank. Property requirements of this nature characterize a variety of practical signal processing problems. Applications of these concepts to the problems of exponential data modeling and system identification are then made where improvements over more traditional solution procedures are realized. The notion of constrained data perturbations has also been successfully applied to the problems of synthesizing one-dimensional and higher dimensional linear systems, obtaining positive sequence approximations, and missing data interpolation.

INVESTIGATION OF EXCITATION SPECTRA OF EXACTLY SOLVABLE MODELS USING INVERSION RELATIONS

We study the excitations of two-dimensional classical vertex models and related one-dimensional quantum Hamiltonians. The main mathematical means we use are functional equations which are set up and solved for the excitation functions. The method is first applied to the eight-vertex model as a prototype and compared with the traditional solution procedure of the Bethe Ansatz. In the last part we investigate some q-state models, notably the biquadratic spin-1 quantum antiferromagnet and its generalizations, which recently attracted interest due to Haldane’s conjecture.

TOTAL SETUP LOT SIZING WITH QUANTITY DISCOUNTS*

ABSTRACTOften, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price‐break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules.This paper presents a total setup lot‐sizing model that reduces the computations required to find the least‐total‐cost quantity, given parameters from a supplier's price schedule.The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot‐sizing model is next developed to define a “critical interval” that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.

Some effects of surface tension on steep water waves. Part 3

This is the final part in the work on steady gravity–capillary waves by the author. On extending the work of Pierson & Fife (1961), the phenomenon of Wilton's ripples is resolved. These singularities of the traditional solution procedure are merely consequences of the non-uniformity in the ordering of the Fourier coefficients of the wave profile. Results presented here include wave properties and profiles. Near-resonant waves are also considered. Good agreement is found between this work and previous papers in the series as well as with other authors. An appendix contains all the results in numerical form. Minor algebraic errors in Wilton's original work are corrected.

An interactive procedure for minimizing makespan on parallel processors

Consider scheduling n independent, single operation jobs, all available at time zero, on m identical processors. Further, assume that each job must be processed by exactly one of these processors, and it is desired to minimize makespan. This paper reports a computationally efficient procedure for treating this problem, which utilizes human ingenuity to improve on a traditional solution procedure. Computational experience with the procedure indicates that good solutions to large problems are easily obtained; in fact out of 240 test problems, the optimal solution was found in every case. The entire procedure is simple enough for a shop foreman to be able to solve large problems by hand.