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Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte…

Crawling is a common locomotion mechanism in soft robots and nonskeletal animals. In this work we propose modeling soft-robotic legged locomotion by approximating it with an equivalent articulated robot with elastic joints. For concreteness…

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…

This paper considers the current distributions that derive from finite amplitude perturbations of line-tied magnetic fields comprising hyperbolic field structures. The initial equilibrium on which we principally focus is a planar magnetic…

The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…

Over the past decade, autophoretic colloids have emerged as a prototypical system for studying self-propelled motion at microscopic scales, with promising applications in microfluidics, micromachinery, and therapeutics. Their motion in a…

We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched…

Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…

Polymer gels are comprised of a three-dimensional, cross-linked network that can typically withstand the mechanical deformation associated with both swelling and de-swelling. Thus, gels can be designed with smart behaviors that require both…

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well-defined internal mechanical motions to various initial deformations and that these…

We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…

The formation and destabilisation of viscoelastic filaments are of importance in many industrial and biological processes. Filament instabilities have been observed for viscoelastic fluids but recently also for soft elastic solids. In this…

We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…

We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…

When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when…

In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena…

A field-theoretical description of the behavior of compressible Ising systems with long-range interactions is presented. The description is performed in the two-loop approximation in three dimensions with the use of the Pade-Borel…

We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite size exact…