Related papers: Optimization of the branching pattern in coherent …
We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
Numerical simulations of a thin layer of turbulent flow in stably stratified conditions within the Boussinesq approximation have been performed. The statistics of energy transfer among scales have been investigated for different values of…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
The reverse martensitic ("austenitic") transformation upon heating of equiatomic nickel-titanium nanoparticles with diameters between 4 and 17 nm is analyzed by means of molecular-dynamics simulations with a semi-empirical model potential.…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian,…
We use the phase-field method to study the martensitic transformation at the nanoscale. For nanosystems such as nanowires and nanograins embedded in a stiff matrix, the geometric constraints and boundary conditions have an impact on…
Motivated by experimental observations on CuAlNi single crystals, we present a theoretical investigation of non-planar austenite-martensite interfaces. Our analysis is based on the nonlinear elasticity model for martensitic transformations…
Entropy barriers and ageing states appear in martensitic structural-transition models, slowly re-equilibrating after temperature quenches, under Monte Carlo dynamics. Concepts from protein folding and ageing harmonic oscillators turn out to…
We present a phase-field approximation of sharp-interface energies defined on partitions, designed for modeling grain boundaries in polycrystals. The independent variable takes values in the orthogonal group $\mathrm{O}(d)$ modulo a lattice…
The objective of this article is to compare different surface energies for multi-well singular perturbation problems associated with martensitic phase transformations involving higher order laminates. We deduce scaling laws in the singular…
We report a detailed numerical investigation of a recently introduced two dimensional model for square-to-rectangle martensitic transformation that explains several unusual features of the martensitic transformation. This model includes…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling…
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…
The energy transition entails a rapid uptake of renewable energy sources. Besides physical changes within the grid infrastructure, energy storage devices and their smart operation are key measures to master the resulting challenges like,…