Related papers: Modeling of cluster structures in a material. Forc…
We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field $\varphi$ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…
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…
We use liquid state theory and computer simulations to gain insights into the shape of the structure factor for fluids of particles interacting via a combination of short-range attractions and long-range repulsions. Such systems can…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…
An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski…
We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated…
Short review of experimental and theoretical researches influence of inner boundaries at properties of composite materials. Reviewing articles that are made at the last, approximately, thirty years, and which demonstrate role of inner…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
The Clifford action on superspaces is analyzed with a view on generalized Dirac fields taking values in some Clifford supermodule. the stress is here on two principles: complexification and polarisation. For applications in field theory,…
Matter gets organized at several levels of structural rearrangements. At mesoscopic level one can distinguish between two types of rearrangements, conforming to different close-packing or densification conditions, appearing during different…
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two dimensions. This model is now extended to three dimensions. Two-dimensional tilings…
Assuming a second-order phase transition for the hadronization process, we attempt to associate intermittency patterns in high-energy hadronic collisions to fractal structures in configuration space and corresponding intermittency indices…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…