Fatigue Damage of a Single-Edge Notched Beam Specimen Under Variable Amplitude Loading with Similar Probabilistic and Cycle Counting Statistics

Fatigue life estimation under variable amplitude (VA) loading is still a major unresolved engineering problem. The linear cumulative damage rule (LDR) based methodology is inadequate to predict fatigue damage or useful remaining life if the fatigue loading is complex (not sinusoidal). In addition, the LDR based damage estimation methods rely on statistics of various cycle counting methodologies (e.g., rain-flow counting) where the load interaction effects are being ignored. It has been shown that the damage estimation fails if two load-time (load-cycle) histories with different temporal dynamics have the same or similar load spectra. A robust damage estimation should take the temporal dynamics, i.e., the overload/underload information, stress memory statistics, into consideration. In this extended abstract, the shortcomings of the LDR based methods will be presented through a comparison where two VA load spectra with similar stress history and cycle counting statistics were applied to a singled-edge notched beam specimen

Zombies: a simple discrete model of the apocalypse

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course

Zombies: a simple discrete model of the apocalypse

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course

Chaos in the Gauge/Gravity Correspondence

We study the motion of a string in the background of the Schwarzschild black hole in AdS_5 by applying the standard arsenal of dynamical systems. Our description of the phase space includes: the power spectrum, the largest Lyapunov exponent, Poincare sections and basins of attractions. We find convincing evidence that the motion is chaotic. We discuss the implications of some of the quantities associated with chaotic systems for aspects of the gauge/gravity correspondence. In particular, we suggest some potential relevance for the information loss paradox.Comment: 29 pages, 11 figure

Chaos around Holographic Regge Trajectories

Using methods of Hamiltonian dynamical systems, we show analytically that a dynamical system connected to the classical spinning string solution holographically dual to the principal Regge trajectory is non-integrable. The Regge trajectories themselves form an integrable island in the total phase space of the dynamical system. Our argument applies to any gravity background dual to confining field theories and we verify it explicitly in various supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and the AdS soliton. Having established non-integrability for this general class of supergravity backgrounds, we show explicitly by direct computation of the Poincare sections and the largest Lyapunov exponent, that such strings have chaotic motion.Comment: 28 pages, 5 figures. V3: Minor changes complying to referee's suggestions. Typos correcte

Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and Newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system)

Sleep quality, the neglected outcome variable in clinical studies focusing on locomotor system; a construct validation study

Background: In addition to general health and pain, sleep is highly relevant to judging the well-being of an individual. Of these three important outcome variables, however, sleep is neglected in most outcome studies. Sleep is a very important resource for recovery from daily stresses and strains, and any alteration of sleep will likely affect mental and physical health, especially during disease. Sleep assessment therefore should be standard in all population-based or clinical studies focusing on the locomotor system. Yet current sleep assessment tools are either too long or too specific for general use. Methods: Based on a literature review and subsequent patient-based rating of items, an expert panel designed a four-item questionnaire about sleep. Construct validation of the questionnaire in a random sample of the German-speaking Swiss population was performed in 2003. Reliability, correlation, and tests for internal consistency and validity were analyzed. Results: Overall, 16,634 (70%) out of 23,763 eligible individuals participated in the study. Test-retest reliability coefficients ranged from 0.72 to 0.87, and a Cronbach’s alpha of 0.83 indicates good internal consistency. Results show a moderate to good correlation between sleep disturbances and health perception, and between sleep disturbances and overall pain. Conclusions: The Sleep Standard Evaluation Questionnaire (SEQ-Sleep) is a reliable and short tool with confirmed construct validity for sleep assessment in population-based observational studies. It is easy to administer and therefore suitable for postal surveys of the general population. Criterion validity remains to be determined