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In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
Energy-based models provide a natural bridge between statistical physics and machine learning by representing data through structured energy landscapes. Boltzmann machines are a particularly compelling class of such models for capturing…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by…
The onset of plasticity in quenched martensitic microstructures is characterized by a low initial yield stress followed by an extremely strong initial hardening response, and then a sudden hardening saturation. Literature attributes this…
A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for…
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.…
Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
The dynamical nucleation of martensite in polycrystals is simulated by means of Lagrange-Rayleigh dynamics with Landau energetics, which is capable of obtaining the local stress as a result of the interplay of the potential of…
We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms…
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz…
The success of a quantum annealing algorithm requires a polynomial scaling of the energy gap. Recently it was shown that a two-dimensional transverse-field Ising model on a square lattice with nearest-neighbor $\pm J$ random coupling has a…
Scattering probes the internal structure of quantum systems. We calculate the two-particle elastic scattering phase shift for a short-ranged interaction on a quantum computer. Short-ranged interactions with a large scattering length or…
Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling…
We study the mechanics of temperature-driven reconstructive martensitic transformations in crystalline materials, within the framework of nonlinear elasticity theory. We focus on the prototypical case of the square-hexagonal transition in…
The time-dependent transport through single-molecule magnets coupled to magnetic or non-magnetic electrodes is studied in the framework of the generalized master equation method. We investigate the transient regime induced by the periodic…
We calculate ground-state properties of a many-quark system in the string-flip model using variational Monte Carlo methods. The many-body potential energy of the system is determined by finding the optimal grouping of quarks into hadrons.…
We explore the potential application of quantum annealing to address the protein structure problem. To this end, we compare several proposed ab initio protein folding models for quantum computers and analyze their scaling and performance…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…