Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential

Computational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme. We specifically study the interface energy space as one of the most uncertain inputs in phase-field modeling and its impact on the shape and contact angle of a growing phase during heterogeneous solidification of secondary phase between solid and liquid phases. We evaluate and discuss methods for the study of sensitivity and propagation of uncertainty in these input parameters as reflected on the shape of the Cu6Sn5 intermetallic during growth over the Cu substrate inside the liquid Sn solder due to uncertain interface energies. The sensitivity results rank σSI,σIL, and σIL, respectively, as the most influential parameters on the shape of the intermetallic. Furthermore, we use variational autoencoder, a deep generative neural network method, and label spreading, a semi-supervised machine learning method for establishing correlations between inputs of outputs of the computational model. We clustered the microstructures into three categories (“wetting”, “dewetting”, and “invariant”) using the label spreading method and compared it with the trend observed in the Young-Laplace equation. On the other hand, a structure map in the interface energy space is developed that shows σSI and σSL alter the shape of the intermetallic synchronously where an increase in the latter and decrease in the former changes the shape from dewetting structures to wetting structures. The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME.

The Unity Principle – A New Paradigm in Theoretical Physics

Contemporary theoretical physics enters a deep crisis resulting from its positivistic and post-positivistic approach, which assumes that reality is mechanical and atomistic made of point-like particles or one-dimensional strings where the essence of matter, energy, space and time, gravity and other forces are undetectable mysteries. However, within this paper I will endeavour to show that the Universe (reality) is dialectical (relational) and is thus accessible by dialectical logic. The fundamental discovery of the Unity Principle derived on the base of dialectical logic is presented illustrating the exact mechanism how the physical Universe may work at its macro and micro levels. New fundamentals of theoretical physics are built

Energy Spaces, Dirichlet Forms and Capacities in a Nonlinear Setting

In this article we study lower semicontinuous, convex functionals on real Hilbert spaces. In the first part of the article we construct a Banach space that serves as the energy space for such functionals. In the second part we study nonlinear Dirichlet forms, as defined by Cipriani and Grillo, and show, as it is well known in the bilinear case, that the energy space of such forms is a lattice. We define a capacity and introduce the notion quasicontinuity associated with these forms and prove several results, which are well known in the bilinear case.

Almost conservation laws for stochastic nonlinear Schrödinger equations

In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R 3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

Orbital stability of periodic peakons for the generalized modified Camassa-Holm equation

<p style='text-indent:20px;'>This paper is devoted to studying the dynamical stability of periodic peaked solitary waves for the generalized modified Camassa-Holm equation. The equation is a generalization of the modified Camassa-Holm equation and it possesses the Hamiltonian structure shared by the modified Camassa-Holm equation. The equation admits the periodic peakons. It is shown that the periodic peakons are dynamically stable under small perturbations in the energy space.</p>