The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

Aviation of the Future: What Needs to Change to Get Aviation Fit for the Twenty-First Century

The world around us has changed dramatically, particularly since the beginning of the twenty-first century, mainly due to the broad availability of the Internet. Inventions such as smart phones, apps, virtual face to face conversations, coupled with the rise of Facebook, Google, Amazon & Co. added a lot of speed to this development. The digital revolution empowers the consumer and determines ever increasing expectations. At the same time, latest tech developments such as artificial intelligence (AI), machine learning (ML), blockchain, voice and more create opportunities never seen before. However, the aviation industry to a large extent has remained stuck in legacy processes and their decades old technology. It also suffers from low profit margins. With a few exceptions, aviation management overall struggles on how to adapt to the real-time and agile environment. Digital transformation activities have started both in operational and commercial areas, but fundamental underlying platforms and culture change in most cases have not yet been addressed. This chapter explains reasons behind key pain points of the industry, what activities are ongoing and the main areas that need to change to get into shape for the current dynamic environment

Peridynamic model for fatigue cracks

The peridynamic theory of solid mechanics is an extension of the classical theory whose field equations can be applied on evolving discontinuities, such as cracks and dislocations. As such, it potentially offers increased generality in the modeling of the nucleation, growth, and mutual interaction of cracks and other defects. Although most applications of the peridynamic theory to date have concerned dynamic fracture, a recent advance extends the theory to fatigue cracking under cyclic loading. The method consists of a peridynamic bond failure criterion that depends on the history of cyclic bond strain. Each bond has associated with it a scalar variable called the remaining life that decays over many loading cycles. The bond breaks irreversibly when this variable becomes zero. By calibrating the model to S–N data and Paris law curves, the essential features of fatigue crack nucleation and growth are reproduced while retaining the main advantages of the peridynamic formulation. A mapping from simulation time to the number of loading cycles avoids the need to explicitly simulate large numbers of cycles. This discussion will cover the basic equations of the peridynamic theory and the new fatigue model. The calibration method for real materials will be discussed, demonstrating good agreement with laboratory test data in computational modeling of fatigue crack growth in an aluminum alloy. Extension of the fatigue model to variable cycling loading amplitude will also be discussed

Determination of horizon size in state-based peridynamics

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems

Kommunikáció a harangok nyelvén : kupuszinai példa

The most important manifestation of conveying information in a community is speech. Before information was conveyed by articulated human voice, gestures had a communicative function on a par with utterances, and this is, for the most part, still true today. Every community devised an acoustic code system of sounds created by the contact of certain objects, such as the chime of bells. Bells are not merely the privilege of churches, chapels and cemeteries. Castles, for instance, may have bells to summon the laborers for lunch, or a smaller bell may hang above the gatesto signal the arrival of gueststo the residents. However, bells are most often used in religious practice. Bell chimes form a part of sacred time, at the same time circumscribing and regulating it; and bell chimes also follow human life from the cradle to the grave. Messages may also be conveyed by bells: warnings, summons and announcements. Folk observations that deduce pending negative phenomena or events from the quality and the acoustic properties of bell chimes are now considered a part of folklore. In such cases, the coordinates that carry message value are the most important (tone, volume, rhythm, etc.). Bell chimes signal a metacommunication process between people, because we must not forget that the bells are sounded by people, and it is ultimately the people who send messages by the bell