Related papers: How useful are formal hierarchies? A case study on…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…
Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Micro-plasticity theories and models are suitable to explain and predict mechanical response of devices on length scales where the influence of the carrier of plastic deformation - the dislocations - cannot be neglected or completely…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are…
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is,…
Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…
Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a…
Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in…
Materials are often heterogeneous at various length scales, with variations in grain structure, defects, and composition which has a strong influence on the emergent macroscopic plastic behavior. In particular, heterogeneities lead to…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of…
Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…