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Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems,…
The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure…
High-entropy alloys (HEAs) are solid solutions of multiple elements with equal atomic ratios which present an innovative pathway for de novo alloy engineering. While there exist extensive studies to ascertain the important structural…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…
When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the…
Kinematic quantities for finite elastic and plastic deformations are defined via an approach that does not rely on auxiliary elements like reference frame and reference configuration, and that gives account of the inertial-noninertial…
An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods. Moreover, two…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
We present two applications of the integro-differential volume equation for the eigenstrain, building on Eshelby's inclusion method [15,16], in the contexts of both static and dynamic linear elasticity. The primary objective is to address…
Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy data, there may exist characteristic…
In small volumes, sample dimensions are known to strongly influence mechanical behavior, especially strength and crystal plasticity. This correlation fades away at the so-called mesoscale, loosely defined at several micrometers in both…
Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields.…
Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential…
Plastic deformations in crystals often produce textures in the form of randomly oriented patches of the unstressed lattice. We use a novel mesoscopic Landau-type model of crystal plasticity to show that in such textures large…
There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
In two-dimensional Lennard-Jones glasses, mechanical probing reveals that local yield surfaces are dominated by regions with a positive second derivative of the yield stress with respect to the loading angle. Each feature corresponds to a…