Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.

On Parameter Identification for Reaction-Dominated Pore-Scale Reactive Transport Using Modified Bee Colony Algorithm

Parameter identification is an important research topic with a variety of applications in industrial and environmental problems. Usually, a functional has to be minimized in conjunction with parameter identification; thus, there is a certain similarity between the parameter identification and optimization. A number of rigorous and efficient algorithms for optimization problems were developed in recent decades for the case of a convex functional. In the case of a non-convex functional, the metaheuristic algorithms dominate. This paper discusses an optimization method called modified bee colony algorithm (MBC), which is a modification of the standard bees algorithm (SBA). The SBA is inspired by a particular intelligent behavior of honeybee swarms. The algorithm is adapted for the parameter identification of reaction-dominated pore-scale transport when a non-convex functional has to be minimized. The algorithm is first checked by solving a few benchmark problems, namely finding the minima for Shekel, Rosenbrock, Himmelblau and Rastrigin functions. A statistical analysis was carried out to compare the performance of MBC with the SBA and the artificial bee colony (ABC) algorithm. Next, MBC is applied to identify the three parameters in the Langmuir isotherm, which is used to describe the considered reaction. Here, 2D periodic porous media were considered. The simulation results show that the MBC algorithm can be successfully used for identifying admissible sets for the reaction parameters in reaction-dominated transport characterized by low Pecklet and high Damkholer numbers. Finite element approximation in space and implicit time discretization are exploited to solve the direct problem.

Yablo’s Paradox, the Liar, and Referential Contradictions from a Graph Theory Point of View

F -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘... affirms the falsity of...’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of F -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory.

Skeptical Reasoning with Preferred Semantics in Abstract Argumentation without Computing Preferred Extensions

We address the problem of deciding skeptical acceptance wrt. preferred semantics of an argument in abstract argumentation frameworks, i.e., the problem of deciding whether an argument is contained in all maximally admissible sets, a.k.a. preferred extensions. State-of-the-art algorithms solve this problem with iterative calls to an external SAT-solver to determine preferred extensions. We provide a new characterisation of skeptical acceptance wrt. preferred semantics that does not involve the notion of a preferred extension. We then develop a new algorithm that also relies on iterative calls to an external SAT-solver but avoids the costly part of maximising admissible sets. We present the results of an experimental evaluation that shows that this new approach significantly outperforms the state of the art. We also apply similar ideas to develop a new algorithm for computing the ideal extension.

SEARCH FOR UNCERTAINTY REGIONS OF KINETIC CONSTANTS IN MODELING PROCESSES OF NON-BREAK POLYMERIZATION OF DIENES

Рассматриваются процессы полимеризации на катализаторах Циглера-Натта. Исследован вопрос о механизме процессов как необходимом наборе элементарных стадий кинетической схемы. Приведена общая схема допустимых стадий процесса, включающая стадии инициирования, роста цепи, передач цепи и обрыва цепи. Указано, что часть элементарных реакций может быть убрана из кинетической схемы за счет способа приготовления самого катализатора, а часть - на основании получаемых кинетических зависимостей. Но гипотеза о наличии или отсутствии элементарных стадий может быть доказана не только экспериментальным, но и вычислительным путем. Приводимые в работе табличные данные свидетельствуют о практически нулевом значении константы скорости элементарной стадии материального обрыва цепи - дезактивации активных центров, что, в свою очередь, вызывает оптимизацию кинетической схемы. Тогда рассматриваемые процессы могут быть отнесены к типу безобрывной полимеризации. Составление кинетической и математической моделей для исследуемых процессов позволяет поставить прямые и обратные кинетические задачи. Решение последних может быть получено методом многократного решения прямых кинетических задач и сравнения расчетных значений молекулярных характеристик с их экспериментальными аналогами. Однако целесообразнее проводить предварительный этап нахождения областей локальных минимумов по оптимизируемым значениям констант путем построения базисной поверхности и при поиске допустимых наборов значений констант скоростей оперировать найденными областями минимумов This paper considers the processes of polymerization on Ziegler-Natta catalysts. The question of the mechanism of the processes as a necessary set of elementary stages of the kinetic scheme is investigated. A general scheme of the permissible stages of the process is given, including the stages of initiation, chain growth, chain transfers and chain termination. It is indicated that part of the elementary reactions can be removed from the kinetic scheme due to the method of preparation of the catalyst itself, and part on the basis of the obtained kinetic dependences. However, the hypothesis about the presence or absence of elementary stages can be proved not only experimentally but also computationally. The tabular data presented in the work indicate a practically zero value of the rate constant of the elementary stage of material chain termination - deactivation of active centers, which, in turn, leads to optimization of the kinetic scheme. Then the processes under consideration can be attributed to the type of non-break polymerization. Compilation of kinetic and mathematical models for the processes under study makes it possible to pose direct and inverse kinetic problems. The solution of the latter can be obtained by the method of multiple solution of direct kinetic problems and comparison of the calculated values of molecular characteristics with their experimental counterparts. However, it is more expedient to carry out the preliminary stage of finding the regions of local minima by the optimized values of the constants by constructing the base surface. When searching for admissible sets of values of the rate constants, operate with the found areas of minima

ADAPTIVE GUARANTEED ESTIMATION OF A CONSTANT SIGNAL UNDER UNCERTAINTY OF MEASUREMENT ERRORS

In the guaranteed estimation problems under uncertainty relative to disturbances and meas-urement errors, the admissible sets of their possible values are determined. The solution is chosen due to conditions of guaranteed bounded estimates optimization corresponding to the worst realiza-tion of disturbances and measurement errors. The result of the guaranteed estimation is an unim-provable bounded estimate (information set), which turns to be overly pessimistic (reinsurance) if a prior admissible set of measurement errors is too large compared to their realized values. The admis-sible sets of disturbances and measurement errors can turn to be only rough upper estimates on a short observation interval. The goal of research is the accuracy enhancement problem of guaran-teed estimation when measurement errors are not realized in the worst way, i.e. the environment in which the object operates does not behave as aggressively as it is built in a priori data on the permis-sible set of error values. Research design. The problem of adaptive guaranteed estimation of a con-stant signal from noisy measurements is considered. The adaptive filtering problem is, according to the results of measurement processing, from the whole set of possible realizations of errors, to choose the one that would generate the measurement sequence. Results. An adaptive guaranteed estimation algorithm is presented. The adaptive algorithm construction is based on a multi-alternative method based on the Kalman filter bank. The method uses a set of filters, each of which is tuned to a specific hypoth-esis about the measurement error model. Filter residuals are used to compute estimates of realized measurement errors. The choice of the realization of possible errors is performed using a function that has the meaning of the residual variance over a short time interval. Conclusion. The computa-tional scheme of the adaptive algorithm, the numerical example, and comparative analysis of ob-tained estimates are presented.

Transient stability analysis of power grids with admissible and maximal robust positively invariant sets

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid’s bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.

Characterizing strongly admissible sets

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility (in contrast to grounded semantics) ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable.