Related papers: Stanley decompositions and localization
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced…
Quasi-static tensile experiments were performed for a model disordered solid consisting of a two-dimensional raft of polydisperse floating granular particles with capillary attractions. The ductility is tuned by controlling the capillary…
We study scaling properties of the localized eigenstates of the random dimer model in which pairs of local site energies are assigned at random in a one dimensional disordered tight-binding model. We use both the transfer matrix method and…
A deposition process with particles having realistic intermediate stickiness is studied in 2+1 dimensions. At each stage of the deposition process, for any given configuration, a newly depositing particle gives rise to allowed set of…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite…
Localizing behaviors of neural networks to a subset of the network's components or a subset of interactions between components is a natural first step towards analyzing network mechanisms and possible failure modes. Existing work is often…
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a…
The transverse spatial attributes of an optical beam can be decomposed into the position, momentum and orbital angular momentum observables. The position and momentum of a beam is directly related to the quadrature amplitudes, whilst the…
The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we…
We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the…
We investigate the localization of two interacting particles in one-dimensional random potential. Our definition of the two-particle localization length, $\xi$, is the same as that of v. Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)] and…
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital…
At low temperature, a quasi-one-dimensional ensemble of atoms with attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass…
The effect of disorder on magnonic transport in low-dimensional magnetic materials is studied in the framework of a classical spin model. Numerical investigations give insight into scattering properties of the systems and show the existence…
In this paper we define specialization and microlocalization for subanalytic sheaves. Applying these functors to the sheaves of tempered and Whytney holomorphic functions we get a unifying description of tempered and formal…
Given arbitrary monomial ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $K$, we investigate the Stanley depth of powers of the sum $I+J$, and their quotient rings, in $A\otimes_K B$ in terms of those of $I$ and $J$. Our…