On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

Catalogue of extreme wave events in Ireland: revised and updated for 14680 BP - 2017

This paper aims to extend and update the survey of extreme wave events in Ireland that was previously carried out by O’Brien et al. (2013). The original catalogue highlighted the frequency of such events dating back as far as the turn of the last ice age through to 2012. Ireland’s marine territory extends far beyond its coastline and is one of the largest seabed territories in Europe. It is therefore not surprising that extreme waves have continued to occur regularly since 2012, particularly considering the severity of weather during the winters of 2013-14 and 2015-16. In addition, a large number of storm surges have been identified since the publication of the original catalogue. This paper updates the O’Brien et al. (2013) catalogue to include events up to the end of 2016. Storm surges are included as a new category and events are categorised into long waves (tsunamis and storm surges) and short waves (storm and rogue waves). New results prior to 2012 are also included and some of the events previously documented are reclassified. Important questions regarding public safety, services and the influence of climate change are also highlighted

Complete characterization of convergence to equilibrium for an inelastic Kac model

Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability distribution if and only if the symmetrized initial distribution belongs to the standard domain of attraction of a symmetric stable law, whose index $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. This result is then used: (1) To state that the class of all stationary solutions coincides with that of all symmetric stable laws with index $\alpha$. (2) To determine the solution of a well-known stochastic functional equation in the absence of extra-conditions usually adopted

Non-Invasive Driver Drowsiness Detection System.

Drowsiness when in command of a vehicle leads to a decline in cognitive performance that affects driver behavior, potentially causing accidents. Drowsiness-related road accidents lead to severe trauma, economic consequences, impact on others, physical injury and/or even death. Real-time and accurate driver drowsiness detection and warnings systems are necessary schemes to reduce tiredness-related driving accident rates. The research presented here aims at the classification of drowsy and non-drowsy driver states based on respiration rate detection by non-invasive, non-touch, impulsive radio ultra-wideband (IR-UWB) radar. Chest movements of 40 subjects were acquired for 5 m using a lab-placed IR-UWB radar system, and respiration per minute was extracted from the resulting signals. A structured dataset was obtained comprising respiration per minute, age and label (drowsy/non-drowsy). Different machine learning models, namely, Support Vector Machine, Decision Tree, Logistic regression, Gradient Boosting Machine, Extra Tree Classifier and Multilayer Perceptron were trained on the dataset, amongst which the Support Vector Machine shows the best accuracy of 87%. This research provides a ground truth for verification and assessment of UWB to be used effectively for driver drowsiness detection based on respiration

A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter

Dust enshrouded star-forming activity in Arp 299

We present mid-infrared spectro-imaging (5 - 16 microns) observations of the infrared luminous interacting system Arp 299 (=Mrk171 =IC694+NGC3690) obtained with the ISOCAM instrument aboard ISO. Our observations show that nearly 40% of the total emission at 7 and 15 microns is diffuse, originating from the interacting disks of the galaxies. Moreover, they indicate the presence of large amounts of hot dust in the main infrared sources of the system and large extinctions toward the nuclei. While the observed spectra have an overall similar shape, mainly composed of Unidentified Infrared Bands (UIB) in the short wavelength domain, a strong continuum at ~ 13 microns and a deep silicate absorption band at 10 microns, their differences reveal the varying physical conditions of each component. For each source, the spectral energy distribution (SED) can be reproduced by a linear combination of a UIB "canonical" spectral template and a hot dust continuum due to a 230-300 K black body, after independently applying an extinction correction to both of them. We find that the UIB extinction does not vary much throughout the system (A_V ~ 5 mag) suggesting that most UIBs originate from less enshrouded regions. IC694 appears to dominate the infrared emission of the system and our observations support the interpretation of a deeply embedded nuclear starburst located behind an absorption of about 40 mag. The central region of NGC3690 displays a hard radiation field characterized by a [NeIII]/[NeII] ratio > 1.8. It also hosts a strong continuum from 5 to 16 microns which can be explained as thermal emission from a deeply embedded (A_V ~ 60 mag) compact source, consistent with the mid-infrared signature of an active galactic nucleus (AGN), and in agreement with recent X-ray findings.Comment: to be published in Astronomy and Astrophysics - 12 page

Understanding the dynamics of photoionization-induced solitons in gas-filled hollow-core photonic crystal fibers

We present in detail our developed model [Saleh et al., Phys. Rev. Lett. 107] that governs pulse propagation in hollow-core photonic crystal fibers filled by an ionizing gas. By using perturbative methods, we find that the photoionization process induces the opposite phenomenon of the well-known Raman self-frequency red-shift of solitons in solid-core glass fibers, as was recently experimentally demonstrated [Hoelzer et al., Phys. Rev. Lett. 107]. This process is only limited by ionization losses, and leads to a constant acceleration of solitons in the time domain with a continuous blue-shift in the frequency domain. By applying the Gagnon-B\'{e}langer gauge transformation, multi-peak `inverted gravity-like' solitary waves are predicted. We also demonstrate that the pulse dynamics shows the ejection of solitons during propagation in such fibers, analogous to what happens in conventional solid-core fibers. Moreover, unconventional long-range non-local interactions between temporally distant solitons, unique of gas plasma systems, are predicted and studied. Finally, the effects of higher-order dispersion coefficients and the shock operator on the pulse dynamics are investigated, showing that the resonant radiation in the UV [Joly et al., Phys. Rev. Lett. 106] can be improved via plasma formation.Comment: 9 pages, 10 figure

Enhancing Cricket Performance Analysis with Human Pose Estimation and Machine Learning

Cricket has a massive global following and is ranked as the second most popular sport globally, with an estimated 2.5 billion fans. Batting requires quick decisions based on ball speed, trajectory, fielder positions, etc. Recently, computer vision and machine learning techniques have gained attention as potential tools to predict cricket strokes played by batters. This study presents a cutting-edge approach to predicting batsman strokes using computer vision and machine learning. The study analyzes eight strokes: pull, cut, cover drive, straight drive, backfoot punch, on drive, flick, and sweep. The study uses the MediaPipe library to extract features from videos and several machine learning and deep learning algorithms, including random forest (RF), support vector machine, k-nearest neighbors, decision tree, linear regression, and long short-term memory to predict the strokes. The study achieves an outstanding accuracy of 99.77% using the RF algorithm, outperforming the other algorithms used in the study. The k-fold validation of the RF model is 95.0% with a standard deviation of 0.07, highlighting the potential of computer vision and machine learning techniques for predicting batsman strokes in cricket. The study’s results could help improve coaching techniques and enhance batsmen’s performance in cricket, ultimately improving the game’s overall quality

A Novel Approach to Railway Track Faults Detection Using Acoustic Analysis.

Regular inspection of railway track health is crucial for maintaining safe and reliable train operations. Factors, such as cracks, ballast issues, rail discontinuity, loose nuts and bolts, burnt wheels, superelevation, and misalignment developed on the rails due to non-maintenance, pre-emptive investigations and delayed detection, pose a grave danger and threats to the safe operation of rail transport. The traditional procedure of manually inspecting the rail track using a railway cart is both inefficient and prone to human error and biases. In a country like Pakistan where train accidents have taken many lives, it is not unusual to automate such approaches to avoid such accidents and save countless lives. This study aims at enhancing the traditional railway cart system to address these issues by introducing an automatic railway track fault detection system using acoustic analysis. In this regard, this study makes two important contributions: data collection on Pakistan railway tracks using acoustic signals and the application of various classification techniques to the collected data. Initially, three types of tracks are considered, including normal track, wheel burnt and superelevation, due to their common occurrence. Several well-known machine learning algorithms are applied such as support vector machines, logistic regression, random forest and decision tree classifier, in addition to deep learning models like multilayer perceptron and convolutional neural networks. Results suggest that acoustic data can help determine the track faults successfully. Results indicate that the best results are obtained by RF and DT with an accuracy of 97%

Intermittent magnetic field excitation by a turbulent flow of liquid sodium

The magnetic field measured in the Madison Dynamo Experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.Comment: 5 pages, 7 figure