Related papers: Systematic pathway generation and sorting in marte…

Despite the fundamental importance of solid-solid transformations in many technologies, the microscopic mechanisms remain poorly understood. Here, we explore the atomistic mechanisms at the migrating interface during solid-solid phase…

Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…

Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…

We propose a method for crystal structure prediction based on a new structure generation algorithm and on-lattice machine learning interatomic potentials. Our algorithm generates the atomic configurations assigning atomic species to sites…

A mathematical framework is proposed to predict the features of the (5 5 7) lath transformation in low-carbon steels based on energy minimisation. This theory generates a one-parameter family of possible habit planes and a selection…

We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into…

Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms local order parameters. This type of order plays a key role in the theory of the fractional quantum…

Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum…

In this paper, we present an automated parameter optimization method for trajectory generation. We formulate parameter optimization as a constrained optimization problem that can be effectively solved using Bayesian optimization. While the…

Structural transformations at interfaces are of profound fundamental interest as complex examples of phase transitions in low-dimensional systems. Despite decades of extensive research, no compelling evidence exists for structural…

Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…

The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution algorithm (DE). Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the generated…

Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…

Several types of numerical and combinatorial optimization algorithms have been used as useful tools to minimize functional forms. Generally, when those forms are non-linear or occur in problems without a specific optimization method,…

We perform a systematic symmetry classification of the Markov generators of classical stochastic processes. Our classification scheme is based on the action of involutive symmetry transformations of a real Markov generator, extending the…

Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…

This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles…

The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their…