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Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates, the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces., Comment: 27 pages, 15 figures

Alarm management systems have become indispensable in modern industry. Alarms inform the operator of abnormal situations, particularly in the case of equipment failures. Due to the interconnections between various parts of the system, each fault can affect other sections of the system operating normally. As a result, the fault propagates through faultless devices, increasing the number of alarms. Hence, the timely detection of the major fault that triggered the alarm by the operator can prevent the following consequences. However, due to the complexity of the system, it is often impossible to find precise relations between the underlying fault and the alarms. As a result, the operator needs support to make an appropriate decision immediately. Modeling alarms based on the historical alarm data can assist the operator in determining the root cause of the alarm. This research aims to model the relations between industrial alarms using historical alarm data in the database. Firstly, alarm data is collected, and alarm tags are sequenced. Then, these sequences are converted to numerical vectors using word embedding. Next, a self-attention-based BiLSTM-CNN classifier is used to learn the structure and relevance between historical alarm data. After training the model, this model is used for online fault detection. Finally, as a case study, the proposed model is implemented in the well-known Tennessee Eastman process, and the results are presented.

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the undeformed and deformed configurations. All the phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions.

This paper gives a numerically stable method to compute H-basis which is based on the computing a minimal basis for the module of syzygies using singular value decomposition. We illustrate the performance of this method by means of various examples.

In this study, the effect of alumina and modified alumina nanoparticles in a PMMA/alumina nanocomposite was investigated. To attain this goal, the glass transition behavior of poly methyl methacrylate (PMMA), PMMA/alumina and PMMA/hydroxylated alumina nanocomposites were investigated by molecular dynamic simulations (MD). All the MD simulations were performed using the Materials Studio 6.0 software package of Accelrys. To obtain the glass transition temperature, the variation of density vs. temperature was obtained. The temperature at which the slope of the density-temperature curve observably changes is defined as the glass transition temperature (Tg). The effect of alumina nanoparticles on the Tg was related to the free volume and the mobility of chain segments and the interaction between the alumina nanoparticles and the polymer. The mobility of the chain segments was investigated based on the mean square displacement and radius gyration. The results show that the increasement the Tg of the PMMA/hydroxylated alumina nanocomposite is more than that of the PMMA/alumina nanocomposite due to the modification of the alumina nanoparticles.

A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gr\"{o}bner basis with respect to the lexicographic order induced by $x_1 > \cdots > x_n > y_1> \cdots > y_n$. In this paper, we generalize this notion and study the so called $m-$closed graphs. We find equivalent condition to $3-$closed property of an arbitrary tree $T$. Using it, we classify a class of $3-$closed trees. The primary decomposition of this class of graphs is also studied., Comment: 13 pages, 4 figures