Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

The fantasy of authenticity: touring with Lacan

Amidst the plethora of research regarding the meaning of authenticity, there remains uncertainty as to the work authenticity performs in tourism. Existential authenticity conceptually shifts focus from the objects of touristic practice to a sense of Being, suggesting that authenticity can be achieved, albeit only in the liminal moments of tourism experiences. Psychoanalysis would contend otherwise – authenticity will always be beyond our reach. In a 2006 publication, Tim Oakes broaches the topic when discussing authenticity as “an abyss”. We revisit that idea, developing it further through the lens of Lacanian psychoanalysis to argue that authenticity is a fantasy. It is not an empty concept, however, but like all fantasies authenticity does important work, particularly in tourism marketing and touristic motivation and experience. To better understand how authenticity as a fantasy fosters tourism desire, it is necessary to develop a conceptual understanding of alienation in relation to tourism motivation. This paper moves alienation from the periphery to the center of tourism theories, demonstrates the dialectical relationship of authenticity/alienation, and posits that as a fantasy authenticity is a malleable concept that has the ability to contextualize the “something” that is missing from our lives. As such, it will remain salient in tourism

Lunar resources: Oxygen from rocks and soil

The first set of hydrogen reduction experiments to use actual lunar material was recently completed. The sample, 70035, is a coarse-grained vesicular basalt containing 18.46 wt. percent FeO and 12.97 wt. percent TiO2. The mineralogy includes pyroxene, ilmenite, plagioclase, and minor olivine. The sample was crushed to a grain size of less than 500 microns. The crushed basalt was reduced with hydrogen in seven tests at temperatures of 900-1050 C and pressures of 1-10 atm for 30-60 minutes. A capacitance probe, measuring the dew point of the gas stream, was used to follow reaction progress. Experiments were also conducted using a terrestrial basalt similar to some lunar mare samples. Minnesota Lunar Simulant (MLS-1) contains 13.29 wt. percent FeO, 2.96 wt. percent Fe2O3, and 6.56 wt. percent TiO2. The major minerals include plagioclase, pyroxene, olivine, ilmenite, and magnetite. The rock was ground and seived, and experiments were run on the less than 74- and 500-1168-micron fractions. Experiments were also conducted on less than 74-micron powders of olivine, pyroxene, synthetic ilmenite, and TiO2. The terrestrial rock and mineral samples were reduced with flowing hydrogen at 1100 C in a microbalance furnace, with reaction progress monitored by weight loss. Experiments were run at atmospheric pressure for durations of 3-4 hr. Solid samples from both sets of experiments were analyzed by Mossbauer spectroscopy, petrographic microscopy, scanning electron microscopy, tunneling electron microscopy, and x-ray diffraction. Apollo 17 soil 78221 was examined for evidence of natural reduction in the lunar environment. This sample was chosen based on its high maturity level (I sub s/FeO = 93.0). The FeO content is 11.68 wt. percent and the TiO2 content is 3.84 wt. percent. A polished thin section of the 90-150 micron size fraction was analyzed by petrographic microscopy and scanning electron microscopy

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

Wilderness state of mind: expanding authenticity

This paper challenges the overuse of existential authenticity as a categorical umbrella encapsulating touristic experience and contributes new insights to the way postmodern authenticity is defined in tourism research. To date, studies associated with postmodern authenticity have focused on the inauthentic and themed, with scholars contending that it speaks more to the consumptive, the superficial, and the trivial than to the substantive and meaningful. By working through a case study focused on nature tourists in pursuit of authentic wilderness experiences, this paper illustrates the ways postmodern authenticity encompasses much more than cynical authenticity, for while the American wilderness may be a hyperreal, and even hypernatural, simulacrum, nature tourists nevertheless report deep, meaningful, and " authentic " engagements with wilderness

The Genetic and Environmental Sources of Resemblance Between Normative Personality and Personality Disorder Traits

Recent work has suggested a high level of congruence between normative personality, most typically represented by the big five factors, and abnormal personality traits. In 2,293 Norwegian adult twins ascertained from a population-based registry, the authors evaluated the degree of sharing of genetic and environmental influences on normative personality, assessed by the Big Five Inventory (BFI), and personality disorder traits (PDTs), assessed by the Personality Inventory for DSM-S-Norwegian Brief Form (PID-5NBF). For four of the five BFI dimensions, the strongest genetic correlation was observed with the expected PID-5-NBF dimension (e.g., neuroticism with negative affectivity [+], conscientiousness with disinhibition [-]). However, neuroticism, conscientiousness, and agreeableness had substantial genetic correlations with other PID-S-NBF dimensions (e.g., neuroticism with compulsivity [+], agreeableness with detachment [-]). Openness had no substantial genetic correlations with any PID-5-NBF dimension. The proportion of genetic risk factors shared in aggregate between the BFI traits and the PID-5-NBF dimensions was quite high for conscientiousness and neuroticism, relatively robust for extraversion and agreeableness, but quite low for openness. Of the six PID-S-NBF dimensions, three (negative affectivity, detachment, and disinhibition) shared, in aggregate, most of their genetic risk factors with normative personality traits. Genetic factors underlying psychoticism, antagonism, and compulsivity were shared to a lesser extent, suggesting that they are influenced by etiological factors not well indexed by the BFI

Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling Using Polynomial Chaos

The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling.Peer reviewe

Fluctuation theorem for the effusion of an ideal gas

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.Comment: 11 pages, 10 figures, 2 table