Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy-Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.Comment: new version with only minor change

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.Comment: 41 page

Circe

40,000 thieves enraptured by undulations of fine-spun jewel wisps and a chrysallis of nectar dreams-..

Artificial Intelligence : an online exploration of the public’s attitude towards the increased use of AI in today’s society and the associated future consequences

Throughout the past decade, Artificial Intelligence has been edging its way into our lives. The increased use of AI technology led to significant improvements in various industries and different aspects of life, but also comes with several risks and regulatory challenges that need to be adequately addressed. In light of these issues, existing academic research has investigated AI from a researcher’s perspective without explaining the expectations, fears, and thoughts of consumers. The present thesis aims to understand the consumers’ general attitude towards Artificial Intelligence. Hence, an online netnography was conducted to map the interests and thoughts on AI in online communities. Results show that most concerns and the general scepticism towards the technology have its origin in the theme of trust. The mistrust in governments, corporations and AI itself together with unclear accountability positions decelerate adoption and development. Reinforcing transparency and direct communication between providers and consumers is, therefore, considered to be a key aspect in introducing AI technology on a mainstream level. The underlying thesis contributes preliminary research findings to a yet rather neglected field within AI and holds practical implications for AI providers and AI enablers of all size. Implications include the optimal positioning in Artificial Intelligence and how to avoid or resolve common issues on the customer’s side with the commercial and social use of the technology.Ao longo da última década, a Inteligência Artificial tem vindo a conquistar o seu espaço nas nossas vidas. O uso crescente da tecnologia da IA levou a melhorias significativas em várias indústrias e em diferentes aspetos da vida, mas também apresenta vários riscos e desafios regulamentares que precisam de ser abordados adequadamente. À luz destas questões, a investigação académica existente investigou a IA a partir da perspetiva de um investigador sem explicar as expectativas, medos e pensamentos dos consumidores. O objetivo da presente tese é entender a atitude geral dos consumidores em relação à Inteligência Artificial. Assim, uma netnografia online foi conduzida com o objetivo de mapear os interesses e pensamentos das comunidades online sobre a IA. Os resultados mostram que a maioria das preocupações e o ceticismo geral em relação à tecnologia têm origem no tema da confiança. A desconfiança em governos, corporações e na própria IA, juntamente com posições pouco claras de responsabilidade, desaceleram a adoção e o desenvolvimento. Reforçar a transparência e a comunicação direta entre provedores e consumidores é, portanto, considerado um aspeto fundamental na introdução da tecnologia de IA a um nível profundo. A tese subjacente contribui com resultados de pesquisas preliminares para um campo ainda bastante negligenciado dentro da IA e tem implicações práticas para provedores de IA de todos os tamanhos. Estas implicações incluem, não só, o posicionamento ideal na Inteligência Artificial, bem como, evitar ou resolver problemas comuns do lado do cliente com o uso comercial e social da tecnologia

Visibility of Young's interference fringes: Scattered light from small ion crystals

We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.Comment: Main text: 5 pages, 4 figures. Supplemental Material: 2pages, 1 figur

On the passage from atomistic systems to nonlinear elasticity theory

We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the continuum theory which depends on the underlying atomistic interaction potentials and the lattice geometry. The interaction potentials to which our theory applies are general finite range models on multilattices which in particular can also account for multi-pole interactions and bond-angle dependent contributions. Furthermore, we discuss the applicability of the Cauchy-Born rule. Our class of limiting energy densities consists of general quasiconvex functions and the class of linearized limiting energies consistent with the Cauchy-Born rule consists of general quadratic forms not restricted by the Cauchy relations