相关论文: Quasi-rigidity: some uniqueness issues
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
A basic problem in the science of realistic granular matter is the plethora of heuristic models of the stress field in the absence of a first-principles theory. Such a theory is formulated here, based on the idea that static granular…
Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector…
A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…
The {\it number rigidity} of a stationary point process $\mathsf{P}$ entails that for a bounded set $A$ the knowledge of $\mathsf{P}$ on $A^{c}$ a.s. determines $\mathsf{P}(A)$; the $k$-order rigidity means the moments of $\mathsf{P}1_{A}$…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…
A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with…
A wide range of disordered materials, from biological to geological assemblies, feature discrete elements undergoing large shape changes. How significant geometrical variations at the microscopic scale affect the response of the assembly,…
Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is…
We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of non-periodic tilings and one-dimensional sequences of symbols seen as ground states of…
The conditions for forming quasicrystals and their approximants are stringent, normally requiring multiple length scales to stabilize the quasicrystalline order. Here we report an unexpected finding that the approximants and motifs of…
Quasi-brittle behavior where macroscopic failure is preceded by stable damaging and intensive cracking activity is a desired feature of materials because it makes fracture predictable. Based on a fiber bundle model with global load sharing…
Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach…
A theoretical framework for the calculation of shear and bulk viscosities of hadronic matter at finite temperature is presented. The framework is based on the quasi-particle picture. It allows for an arbitrary number of hadron species with…
The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy…
Using the Jacobian matrix, we obtain theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the…