Design of Four-Patch Multi-Stable Composite Laminates for Shape Morphing Applications

Thin bistable composite laminates can be used for shape morphing applications by virtue of their material properties and asymmetric ply layup. These laminates are called bistable because they can be snapped into two or more stable shapes. A single bistable patch can result in simple cylindrical shapes and when multiple such patches are assembled into a single multi-patch laminate they result in more complex shapes and multiple stable shapes that can find wide practical use in shape morphing applications. Analytical models exist that can approximate the stable shapes of the laminates from the input of material properties and laminate geometry. And these models correlate with FEA and experiment to a satisfactory degree and could be used for the design of multi patch laminates. In this research, we make use of these analytical models that solve for a four-patch grid laminate and create a design method based on optimization to solve the reverse problem to arrive at the laminate parameters given the target shape(s). Two approaches are presented wherein one targets a single stable shape and the other targets two stable shapes which are the shapes before and after snap through. This work would be useful to understand how multi-patch laminates could be designed using optimization.

Method for Identification of the Power of a Source of Thermal Energy By Solving the Internal Reverse Problem of Thermal Conductivity

Запропоновано підхід до вирішення внутрішньої оберненої задачі теплопровідності (ОЗТ) на основі використання принципу регуляризації Тихонова та методу функцій впливу. Потужність джерела енергії подано у вигляді лінійної комбінації сплайнів Шьонберга першого порядку, а температуру — у вигляді лінійної комбінації функцій впливу. Метод функцій впливу дає можливість використовувати один і той же вектор невідомих коефіцієнтів для джерел енергії та температури. Невідомі коефіцієнти визначено за допомогою розв’язання системи рівнянь, яка є наслідком необхідної умови мінімуму функціонала Тихонова з ефективним алгоритмом пошуку параметра регуляри­зації, використання якого дає можливість одержати сталий розв’язок ОЗТ. Для регуляри­зації розв’язку ОЗТ в цьому функціоналі використовується також стабілізуючий функ­ціонал з параметром регуляризації як мультиплікативним множником. Наведено обчис­лю­вальні результати ідентифікації потужності теплової енергії по температурі, яка вимірюється з похибкою, що характеризується випадковою величиною, розподіленою за нормальним законом.

Enhancing network modularity to mitigate catastrophic forgetting

Catastrophic forgetting occurs when learning algorithms change connections used to encode previously acquired skills to learn a new skill. Recently, a modular approach for neural networks was deemed necessary as learning problems grow in scale and complexity since it intuitively should reduce learning interference by separating functionality into physically distinct network modules. However, an algorithmic approach is difficult in practice since it involves expert design and trial and error. Kashtan et al. finds that evolution under an environment that changes in a modular fashion leads to the spontaneous evolution of a modular network structure. In this paper, we aim to solve the reverse problem of modularly varying goal (MVG) to obtain a highly modular structure that can mitigate catastrophic forgetting so that it can also apply to realistic data. First, we confirm that a configuration with a highly modular structure exists by applying an MVG against a realistic dataset and confirm that this neural network can mitigate catastrophic forgetting. Next, we solve the reverse problem, that is, we propose a method that can obtain a highly modular structure able to mitigate catastrophic forgetting. Since the MVG-obtained neural network can relatively maintain the intra-module elements while leaving the inter-module elements relatively variable, we propose a method to restrict the inter-module weight elements so that they can be relatively variable against the intra-module ones. From the results, the obtained neural network has a highly modular structure and can learn an unlearned goal faster than without this method.

Inverse problems of structural mechanics

The paper presents a brief review of the main ideas on the extensive class of inverse problems in structural mechanics relating to the identification of design models, technical condition monitoring and finding damages. The numerical implementation of identified incorrectness of inverse problems requires regularization. References include works describing the cases of practical application of reverse problem solutions.

Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra

The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering. In this paper, its solution, in reverse problem, was investigated for specific data using three different methods. It is presented by solving it with the method of Euler angles as well as with the use of quaternion and dual-quaternion algebra, after first giving some basic mathematical theory. After research, not only were three artificial sets of data used, which were structured in a specific way and forced into specific transformations to be solved, but also a real geodesy problem was tested, in order to identify the sensitivity and problems of each method. Statistical analysis of the results was performed by each method, while it was found that there were significant deviations in rotations and translations in the method of Euler angles and dual quaternions, respectively.

Reverse Quantum Mechanics: A Path to Realism.

This paper is essentially a quantum challenge: starting from simple assumptions, we argue about an ontological approach to quantum mechanics. In this paper, we will focus only on the assumptions.While these assumptions seems to solve the ontological aspect of theory many others epistemological problems arise. For these reasons, in order to prove these assumptions, we need to find a consistent mathematical context (i.e. time reverse problem, quantum entanglement, implications on quantumfields, Schr¨odinger cat states, the role of observer, the role of mind ).

NUMERICAL MODELING OF THE JOINT TRANSFER OF MOISTURE AND HEAT IN THE SOIL

The topic of the scientific article is “Numerical modeling of the joint transfer of moisture and heat in the soil”. In the work boundary reverse problem for the system of equations of heat transfer and moisture is studied. Using the data, obtained from the solution of the direct problem, the reverse problem is solved. The iteration method for solving boundary reverse problem is developed on the basis of the mathematical model of the heat and moisture transfer. Numerical calculations are carried out. The algorithm for solving the boundary value problem is modeled on the programming language Java, which is able to implement checking to the unique solubility and find the numerical solutions for the different source data.

The puzzle of unbarred galaxies

Nearly two thirds of spiral galaxies are either strongly or weakly barred, yet a significant fraction of disc galaxies do not have a bar. Now we understand that there are at least three ways of making bars, i.e., bar instability, tidal interaction, and secular bar growth by orbit trapping of a seed bar. However, the reverse problem of avoiding bar formation in unbarred galaxies may be more challenging than we thought. It is shocking that we still do not understand how the bar instability is avoided in real galaxies such as M33, and this puzzle may be central to the outstanding issue of what determines the distribution of bar strengths in galaxies.