In the nonadiabatic dynamics across a quantum phase transition, the Kibble-Zurek mechanism predicts that the formation of topological defects is suppressed as a universal power law with the quench ...time. In inhomogeneous systems, the critical point is reached locally and causality reduces the effective system size for defect formation to regions where the velocity of the critical front is slower than the sound velocity, favoring adiabatic dynamics. The reduced density of excitations exhibits a much steeper dependence on the quench rate and is also described by a universal power law that we demonstrated in a quantum Ising chain.
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To answer some issues raised about the concept of fractional differentiation and integration based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental differences ...between the power law, exponential decay, Mittag-Leffler law and their possible applications in nature. We demonstrate the failure of the semi-group principle in modeling real-world problems. We use natural phenomena to illustrate the importance of non-commutative and non-associative operators under which the Caputo-Fabrizio and Atangana-Baleanu fractional operators fall. We present statistical properties of generator for each fractional derivative, including Riemann-Liouville, Caputo-Fabrizio and Atangana-Baleanu ones. The Atangana-Baleanu and Caputo-Fabrizio fractional derivatives show crossover properties for the mean-square displacement, while the Riemann-Liouville is scale invariant. Their probability distributions are also a Gaussian to non-Gaussian crossover, with the difference that the Caputo Fabrizio kernel has a steady state between the transition. Only the Atangana-Baleanu kernel is a crossover for the waiting time distribution from stretched exponential to power law. A new criterion was suggested, namely the Atangana-Gómez fractional bracket, that helps describe the energy needed by a fractional derivative to characterize a 2-pletic manifold. Based on these properties, we classified fractional derivatives in three categories: weak, mild and strong fractional differential and integral operators. We presented some applications of fractional differential operators to describe real-world problems and we proved, with numerical simulations, that the Riemann-Liouville power-law derivative provides a description of real-world problems with much additional information, that can be seen as noise or error due to specific memory properties of its power-law kernel. The Caputo-Fabrizio derivative is less noisy while the Atangana-Baleanu fractional derivative provides an excellent description, due to its Mittag-Leffler memory, able to distinguish between dynamical systems taking place at different scales without steady state. The study suggests that the properties of associativity and commutativity or the semi-group principle are just irrelevant in fractional calculus. Properties of classical derivatives were established for the ordinary calculus with no memory effect and it is a failure of mathematical investigation to attempt to describe more complex natural phenomena using the same notions.
•Semigroup principle failures to capture natural phenomena.•The future of modeling real world problem relies on fractional differential operators with non-index law property.•Atangana–Baleanu ...fractional differential operators are convolution of Riemann–Liouville–Caputo derivative with the Mittag–Leffler function.•Index law is not valid in fractional differentiation.
Recently fractional differential operators with non-index law properties have being recognized to have brought new weapons to accurately model real world problems particularly those with non-Markovian processes. This present paper has two double aims, the first was to prove the inadequacy and failure of index law fractional calculus and secondly to show the application of fractional differential operators with no index law properties to statistic and dynamical systems. To achieve this, we presented the historical construction of the concept of fractional differential operators from Leibniz to date. Using a matrix based on the fractional differential operators, we proved that, fractional operators obeying index law cannot model real world problems taking place in two states, more precisely they cannot describe phenomena taking place beyond their boundaries, as they are scaling invariant, more precisely our results show that, mathematical models based on these differential operators are not able to describe the inverse memory, meaning the full history of a physical problem cannot be described accurately using these derivatives with index law properties. On the other hand, we proved that, differential operators with no index-law properties are scaling variant, thus can describe situations taking place in different states and are able to localize the frontiers between two states. We present the renewal process properties included in differential equation build out of the Atangana–Baleanu fractional derivative and counting process, which is connected to its inter-arrival time distribution Mittag–Leffler distribution which is the kernel of these derivatives. We presented the connection of each derivative to a statistical family, for instance Riemann–Liouville–Caputo derivatives are connected to the Pareto statistic, which has no well-defined average when alpha is less than 1 corresponding to the interval where fractional operators mostly defined. We established new properties and theorem for the Atangana–Baleanu derivative of an analytic function, in particular we proved that, they are convolution of the Mittag–Leffler function with the Riemann–Liouville–Caputo derivatives. To see the accuracy of the non-index law derivative to in modeling real chaotic problems, 4 examples were considered, including the nine-term 3-D novel chaotic system, King Cobra chaotic system, the Ikeda delay system and chaotic chameleon system. The numerical simulations show very interesting and novel attractors. The king cobra system with the Atangana–Baleanu presented a very novel attractor where at the earlier time we observed a random walk and latter time we observed the real sharp of the cobra. The Ikeda model with Atangana–Baleanu presented different attractors for each value of fractional order, in particular we obtain a square and circular explosions. The results obtained in this paper show that, the future of modeling real world problem relies on fractional differential operators with non-index law property. Our numerical results showed that, to not model physical problems with fractional differential operators with non-singular kernel and imposing index law in fractional calculus is rightfully living with closed eyes without ever taking a risk to open them.
This paper is devoted to investigation of the fractional order fuzzy dynamical system, in our case, modeling the recent pandemic due to corona virus (COVID-19). The considered model is analyzed for ...exactness and uniqueness of solution by using fixed point theory approach. We have also provided the numerical solution of the nonlinear dynamical system with the help of some iterative method applying Caputo as well as Attangana-Baleanu and Caputo fractional type derivative. Also, random COVID-19 model described by a system of random differential equations was presented. At the end we have given some numerical approximation to illustrate the proposed method by applying different fractional values corresponding to uncertainty.
Introduction: Medical students represent a new generation of medical thought, and if they have a favourable attitude towards organ donation this will greatly encourage its promotion.
Objective: To ...analyse the attitude of medical students in Spanish universities towards the donation of their own organs and to determine the factors affecting this attitude.
Material and Methods: Type of study: A sociological, interdisciplinary, multicentre, and observational study in Spain. Study population: Students studying a degree in medicine enrolled in Spain (n = 34,000). Sample size: A sample of 9598 students (confidence of 99% and precision of ±1%), stratified by geographical area and academic year. Instrument of measurement: A validated questionnaire of attitude towards organ donation and transplantation (PCID-DTO RIOS) was self-administered and completed anonymously.
Results: The questionnaire completion rate was 95.7% (n = 9.275). 80% were in favour of donation, 2% against and 18% were undecided. The following main variables were related to a favourable attitude: being of the female sex (Odds Ratio = 1.739); being in the sixth year of the degree (OR = 2.506); knowing a donor (OR = 1.346); having spoken about the subject with one's family (OR = 2.132) and friends (OR = 1.333); having a family circle that is in favour, more specifically, having a father (OR = 1.841), mother (OR = 2.538) or partner in favour (OR = 2.192); being a blood donor (OR = 2.824); acceptance of the mutilation of the body if it were necessary (OR = 2.958); and being an atheist or an agnostic (OR = 1.766).
Conclusions: Spanish medical students generally have a favourable attitude towards organ donation, although 20% are not in favour.
Complex topological configurations are fertile ground for exploring emergent phenomena and exotic phases in condensed-matter physics. For example, the recent discovery of polarization vortices and ...their associated complex-phase coexistence and response under applied electric fields in superlattices of (PbTiO
)
/(SrTiO
)
suggests the presence of a complex, multi-dimensional system capable of interesting physical responses, such as chirality, negative capacitance and large piezo-electric responses
. Here, by varying epitaxial constraints, we discover room-temperature polar-skyrmion bubbles in a lead titanate layer confined by strontium titanate layers, which are imaged by atomic-resolution scanning transmission electron microscopy. Phase-field modelling and second-principles calculations reveal that the polar-skyrmion bubbles have a skyrmion number of +1, and resonant soft-X-ray diffraction experiments show circular dichroism, confirming chirality. Such nanometre-scale polar-skyrmion bubbles are the electric analogues of magnetic skyrmions, and could contribute to the advancement of ferroelectrics towards functionalities incorporating emergent chirality and electrically controllable negative capacitance.
We present results from the most comprehensive radio monitoring campaign towards the closest star to our Sun, Proxima Centauri. We report 1.1–3.1 GHz observations with the Australia Telescope Compact ...Array over 18 consecutive days in April 2017. We detected radio emission from Proxima Centauri for most of the observing sessions, which spanned ~1.6 orbital periods of the planet Proxima b. The radio emission is stronger at the low-frequency band, centered around 1.6 GHz, and is consistent with the expected electron-cyclotron frequency for the known star’s magnetic field intensity of ~600 gauss. The 1.6 GHz light curve shows an emission pattern that is consistent with the orbital period of the planet Proxima b around the star Proxima, with its maxima of emission happening near the quadratures. We also observed two short-duration flares (a few minutes) and a long-duration burst (about three days) whose peaks happened close to the quadratures. We find that the frequency, large degree of circular polarization, change in the sign of circular polarization, and intensity of the observed radio emission are all consistent with expectations from electron cyclotron-maser emission arising from sub-Alfvénic star–planet interaction. We interpret our radio observations as signatures of interaction between the planet Proxima b and its host star Proxima. We advocate for monitoring other dwarf stars with planets to eventually reveal periodic radio emission due to star–planet interaction, thus opening a new avenue for exoplanet hunting and the study of a new field of exoplanet–star plasma interaction.
Stir bar sorptive extraction (SBSE) has generated growing interest due to its high effectiveness for the extraction of non-polar and medium-polarity compounds from liquid samples or liquid extracts. ...In particular, in recent years, a large amount of new analytical applications of SBSE has been proposed for the extraction of natural compounds, pollutants and other organic compounds in foods, biological samples, environmental matrices and pharmaceutical products. The present review summarizes and discusses the theory behind SBSE and the most recent developments concerning its effectiveness. In addition, the main results of recent analytical approaches and their applications, published in the last three years, are described. The advantages, limitations and disadvantages of SBSE are described and an overview of future trends and novel extraction sorbents and supports is given.
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•Summary of the most important aspect for the development of a robust method based on SBSE.•Review of the latest applications in analytical chemistry employing SBSE.•Review of the unresolved limitations and issues of SBSE.•Present and future trends in SBSE are discussed.
Open cluster kinematics with Gaia DR2 Soubiran, C.; Cantat-Gaudin, T.; Romero-Gómez, M. ...
Astronomy and astrophysics (Berlin),
11/2018, Letnik:
619
Journal Article
Recenzirano
Odprti dostop
Context. Open clusters are very good tracers of the evolution of the Galactic disc. Thanks to Gaia, their kinematics can be investigated with an unprecedented precision and accuracy. Aims. The ...distribution of open clusters in the 6D phase space is revisited with Gaia DR2. Methods. The weighted mean radial velocity of open clusters was determined, using the most probable members available from a previous astrometric investigation that also provided mean parallaxes and proper motions. Those parameters, all derived from Gaia DR2 only, were combined to provide the 6D phase-space information of 861 clusters. The velocity distribution of nearby clusters was investigated, as well as the spatial and velocity distributions of the whole sample as a function of age. A high-quality subsample was used to investigate some possible pairs and groups of clusters sharing the same Galactic position and velocity. Results. For the high-quality sample of 406 clusters, the median uncertainty of the weighted mean radial velocity is 0.5 km s−1. The accuracy, assessed by comparison to ground-based high-resolution spectroscopy, is better than 1 km s−1. Open clusters nicely follow the velocity distribution of field stars in the close solar neighbourhood as previously revealed by Gaia DR2. As expected, the vertical distribution of young clusters is very flat, but the novelty is the high precision to which this can be seen. The dispersion of vertical velocities of young clusters is at the level of 5 km s−1. Clusters older than 1 Gyr span distances to the Galactic plane of up to 1 kpc with a vertical velocity dispersion of 14 km s−1, typical of the thin disc. Five pairs of clusters and one group with five members might be physically related. Other binary candidates that have been identified previously are found to be chance alignments.
The jigsaw of PRRSV virulence Ruedas-Torres, I.; Rodríguez-Gómez, I.M.; Sánchez-Carvajal, J.M. ...
Veterinary microbiology,
September 2021, 2021-09-00, 20210901, Letnik:
260
Journal Article
Recenzirano
Odprti dostop
•High mortality, severe clinical signs and lesions are associated with selected PRRSV strains.•Terminology used during the description of “virulent” PRRSV outbreaks is revised.•Immunopathological ...characteristics of “virulent” and classical PRRSV strains are reviewed.•An approximation to the criteria to define a “virulent” PRRSV strain is proposed.
Porcine reproductive and respiratory syndrome virus (PRRSV) is the causative agent of the, probably, most economically important disease for the pig industry worldwide. This disease, characterised by producing reproductive failure in sows and respiratory problems in growing pigs, appeared in the late 1980s in the United States and Canada. Since its appearance, strains capable of producing higher mortality rates as well as greater severity in clinical signs and lesions than classical strains have been identified. However, since the first reports of these “virulent” PRRSV outbreaks, no homogeneity and consensus in their description have been established. Moreover, to the authors’ knowledge, there is no published information related to the criteria that a PRRSV strain should fulfil to be considered as a “virulent” strain. In this review, we revise the terminology used and gather the information related to the main characteristics and differences in clinical signs, lesions, viral replication and tropism as well as immunological parameters between virulent and classical PRRSV strains and propose a first approximation to the criteria to define a virulent PRRSV strain.
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