Search results for "lattices"
showing 10 items of 37 documents
Operators on Partial Inner Product Spaces: Towards a Spectral Analysis
2014
Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers.
Crack dynamics and crack surfaces in elastic beam lattices
1998
The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as t1/7. At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a “mirror-mist-mirror” crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the “mirror-mist-hackle”–type interface typical in many experimental situations. Peer reviewed
From Lattice Valued Theories to Lattice Valued Analysis
2015
We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.
Su certe classi di gruppi unipotenti
2005
We introduce some results characterizing unipotent algebraic groups having a chain as the lattice of connected subgroups and we discuss some consequent results.
Noise correlations of the ultracold Fermi gas in an optical lattice
2008
In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and BP (breach pair) state, are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at non-zero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results als…
Non-commutative Ring Learning with Errors from Cyclic Algebras
2022
AbstractThe Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well-chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by add…
Large-Scale Formation of DNA Origami Lattices on Silicon
2023
In recent years, hierarchical nanostructures have found applications in fields like diagnostics, medicine, nano-optics, and nanoelectronics, especially in challenging applications like the creation of metasurfaces with unique optical properties. One of the promising materials to fabricate such nanostructures has been DNA due to its robust self-assembly properties and plethora of different functionalization schemes. Here, we demonstrate the assembly of a two-dimensional fishnet-type lattice on a silicon substrate using cross-shaped DNA origami as the building block, i.e., tile. The effects of different environmental and structural factors are investigated under liquid atomic force microscopy…
Effect of Stiffness on the Micellization Behavior of Model H4T4 Surfactant Chains
2006
The micellization behavior of a series of model surfactants, all with four head and tail groups (H4T4) but with different degrees of chain stiffness, was studied using grand canonical Monte Carlo simulations on a cubic lattice. The critical micelle concentration, micellar size, and thermodynamics of micellization were examined. In all cases investigated, the critical micelle concentration was found to increase with increasing temperature as observed for nonionic surfactants in apolar or slightly polar solvents. At a fixed reduced temperature and increasing chain stiffness, in agreement with previous observations, it was found that the critical micelle concentration decreased and the average…
Disjointness of Lattice Elements
1992
We examine the relations between various disjointness properties in lattices with least elements, and in special lattices like section semicomplemented lattices and section complemented lattices.
Controlling Atom-Photon Bound States in an Array of Josephson-Junction Resonators
2022
Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light -matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here, we report on the concept and implementation of a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency -tunable artificial atoms. We study the atom-field interaction and access previously unexplored coupling regimes, in both the single-and double-excitation subspace. In addition, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispers…