相关论文: Quasicrystal problem -- on rigidity of non-periodi…
In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…
In this work, we prove that if a uniformly separated sequence in $\mathbb{R}^d$ is uniformly quasicrystalline and converges rapidly enough to a discrete set $X$ in $\mathbb{R}^d$ having the same separation radius as the sequence, then $X$…
This work is concerned with the quasineutral limit of the one-dimensional Vlasov-Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is threefold: first, we provide a proof of the fact that the formal…
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…
Phasonic degrees of freedom are unique to quasiperiodic structures, and play a central role in poorly-understood properties of quasicrystals from excitation spectra to wavefunction statistics to electronic transport. However, phasons are…
Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…
We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border…
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…
Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
The role that quasiparticles play in a strong interaction system with spontaneous symmetry breaking is examined. We find, using a non- perturbative cluster decomposition method, that the quasiparticles do not saturate the physical local…
For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…
The possibility that a short-range interacting system exhibits nonadditivity is investigated. After the discussion on the precise definition of additivity and its consequence, we show that it is possible when the system is in a…
Many new families of quasicrystal-forming magnetic alloys have been synthesized and studied in recent years. For small changes of composition, the alloys can go from quasiperiodic to periodic (approximant crystals) while conserving most of…
Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an "initial" time slice. But this is not the only way to specify boundary…
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This…
Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend…
A new solution for a general half-plane contact in the steady state is presented. The contacting bodies are subject to a set of constant loads - normal force, shear force and bulk tension parallel with the interface - together with an…