相关论文: Multi-field approach in mechanics of structural so…

We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of…

The development of complex multicellular organisms from a single parent cell is a highly orchestrated process that cells conduct collectively without central guidance, creating intricate dynamic patterns essential for development and…

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…

We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living…

We construct multi-field generalisations of the Cosserat continuum model on the basis of the square lattice model that takes into account rotational degree of freedom of microstructural elements. This approach allows us to model not only…

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…

Recent studies on metamorphic petrology as well as microstructural observations suggest the influence of mechanical effects upon chemically active metamorphic minerals. Thus, the understanding of such a coupling is crucial to describe the…

We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second…

A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…

The Method of Continuous Molecular Fields is a universal approach to predict various properties of chemical compounds, in which molecules are represented by means of continuous fields (such as electrostatic, steric, electron density…

Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…

A multiscale scheme combining molecular dynamics (MD) and microscopic phase-field theory is proposed to study the structural phase transformations in solids with inhomogeneous strain field. The approach calculates strain response based on…

We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…

The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…

Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space…

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…

While biological crystallization processes have been studied on the microscale extensively, models addressing the mesoscale aspects of such phenomena are rare. In this work, we investigate whether the phase-field theory developed in…

Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the…

Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach and discuss its application…