Related papers: The first-order flexibility of a crystal framework
The multipole concept, which characterizes the spacial distribution of scalar and vector objects by their angular dependence, has already become widely used in various areas of physics. In recent years it has become employed to…
We predict an inhomogeneous phase of superfluid 3He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, $D_{c_2}(T)<D<D_{c_1}(T)$,…
This work represents the first chapter of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures. We are interested in the range of temperatures, where most electronic…
The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme…
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an…
Phases of matter are conventionally characterized by order parameters describing the type and degree of order in a system. For example, crystals consist of spatially ordered arrays of atoms, an order that is lost as the crystal melts. Like-…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
The theory of nematic-smectic phase transition in the system of uniform semi-flexible chains with hard-core repulsion is presented. Both the general density-functional formalism the tube-model calculation show that the flexibility of the…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in…
Tree models for rigidity percolation are introduced and solved. A probability vector describes the propagation of rigidity outward from a rigid border. All components of this ``vector order parameter'' are singular at the same rigidity…
In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find…
We report a phenomenological theory for the kinetic arrest (KA) of a first-order phase transition, taking the Mott metal-insulator transition in $V_2O_3$ as a test case. By defining a order parameter $\phi$ related to the monoclinic…
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
We develop and analyze a two-mode phase-field-crystal model to describe fcc ordering. The model is formulated by coupling two different sets of crystal density waves corresponding to <111> and <200> reciprocal lattice vectors, which are…
The first-order flex space of the bar-joint framework $G_P$ of a parallelogram tiling $P$ is determined in terms of an explicit free basis. Applications are given to braced parallelogram frameworks and to quasicrystal frameworks associated…
We demonstrate that first-order phase transitions in 1+1-dimensional nonequilibrium systems with fluctuating ordered phases are impossible, provided that there are no additional conservation laws, long-range interactions, macroscopic…
The structural relaxation of amorphous materials is described as arising from the superposition of elementary processes with varying activation energies. We show that it is possible to obtain the kinetic parameters of these processes from…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…