Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems

We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with $H=T+V$ where $T$ is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational method for maximizing the entropy subject to the average energy and normalization constraints. The analytical results show (i) that the non-extensive thermodynamics formalism should be called into question to explain experimental results described by extended exponential distributions exhibiting long tails, i.e. $q$-exponentials with $q>1$, and (ii) that in the thermodynamic limit the theory is only consistent in the range $0\leq q\leq1$ where the distribution has finite support, thus implying that configurations with e.g. energy above some limit have zero probability, which is at variance with the physics of systems in contact with a heat reservoir. We also discuss the ($q$-dependent) thermodynamic temperature and the generalized specific heat.Comment: To appear in EuroPhysics Letter

Trajectories and Platoon-forming Algorithm for Intersections with Heterogeneous Autonomous Traffic

The anticipated launch of fully autonomous vehicles presents an opportunity to develop and implement novel traffic management systems. Intersections are one of the bottlenecks for urban traffic, and thus offer tremendous potential for performance improvements of traffic flow if managed efficiently. Platoon-forming algorithms, in which vehicles are grouped together with short inter-vehicular distances just before arriving at an intersection at high speed, seem particularly promising in this aspect. In this work, we present an intersection access control system based on platoon-forming for heterogeneous autonomous traffic. The heterogeneity of traffic arises from vehicles with different acceleration capabilities and safety constraints. We focus on obtaining computationally fast and interpretable closed-form expressions for safe and efficient vehicle trajectories that lead to platoon formation, and show that these trajectories are solutions to certain classes of optimisation problems. Additionally, we conduct a numerical study to obtain approximations for intersection capacity as a result of such platoon formation.Comment: 42 pages, 16 figures. 3D Animations included as ancillary file

Statistics of precursors to fingering processes

We present an analysis of the statistical properties of hydrodynamic field fluctuations which reveal the existence of precursors to fingering processes. These precursors are found to exhibit power law distributions, and these power laws are shown to follow from spatial $q$-Gaussian structures which are solutions to the generalized non-linear diffusion equation.Comment: 7 pages incl. 5 figs; tp appear in Europhysics Letter

The XMM Newton and INTEGRAL observations of the supergiant fast X-ray transient IGR J16328-4726

The accretion mechanism producing the short flares observed from the Supergiant Fast X-ray Transients (SFXT) is still highly debated and forms a major part in our attempts to place these X-ray binaries in the wider context of the High Mass X-ray Binaries. We report on a 216 ks INTEGRAL observation of the SFXT IGR J16328-4726 (August 24-27, 2014) simultaneous with two fixed-time observations with XMM Newton (33ks and 20ks) performed around the putative periastron passage, in order to investigate the accretion regime and the wind properties during this orbital phase. During these observations, the source has shown luminosity variations, from 4x10^{34} erg/s to 10^{36} erg/s, linked to spectral properties changes. The soft X-ray continuum is well modeled by a power law with a photon index varying from 1.2 up to 1.7 and with high values of the column density in the range 2-4x10^{23}/cm^2. We report on the presence of iron lines at 6.8-7.1 keV suggesting that the X-ray flux is produced by accretion of matter from the companion wind characterized by density and temperature inhomogeneities

Hybrid Amperometric and Potentiometric Sensing Based on a CMOS ISFET Array

Potentiometry and amperometry are some of the most important techniques for electroanalytical applications. Integrating these two techniques on a single chip using CMOS technology paves the way for more analysis and measurement of chemical solutions. In this paper, we describe the integration of electrode transducers (amperometry) on an ion imager based on an ISFET array (potentiometry). In particular, this integration enables the spatial representation of the potential distribution of active electrodes in a chemical solution under investigation

The Rayleigh-Brillouin Spectrum in Special Relativistic Hydrodynamics

In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to non-equilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic non-equilibrium thermodynamics. The answer will clearly require deeper examination of this problem.Comment: 13 pages, no figures. Accepted for publication in Phys. Rev.

High frequency longitudinal and transverse dynamics in water

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q,\omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed. The study of their temperature- and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c_0) (viscous limit) to the infinite frequency sound velocity (c_\infinity) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q,\omega) as soon as the purely viscous regime is left.Comment: 28 pages, 12 figure

Effect of Stimulus Orientation on Visual Function in Children with Refractive Amblyopia.

Purpose: We investigated and characterized the patterns of meridional anisotropies in newly diagnosed refractive amblyopes using pattern onset–offset visual evoked potentials (POVEPs) and psychophysical grating acuity (GA). Methods: Twenty-five refractive amblyopes were recruited and compared with non-amblyopic controls from our previous study. Monocular POVEPs were recorded in response to sinewave 4 cycles per degree (cpd) grating stimuli oriented along each individual participants' principal astigmatic meridians, which were approximately horizontal (meridian 1) and vertical (meridian 2). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed along the same meridians using a two-alternative non-forced-choice technique. The C3 amplitudes and peak latencies of the POVEPs and GAs were compared across meridians for both groups (refractive amblyopes and controls) using linear mixed models (monocular) and ANOVA (binocular), and post hoc analysis was conducted to determine if meridional anisotropies in this cohort of amblyopes were related to low (≤1.50 diopters [D]), moderate (1.75–2.75 D) and high (≥3.00 D) astigmatism. Results: In the newly diagnosed refractive amblyopes, there were no significant meridional anisotropies across all outcome measures, but the post hoc analysis demonstrated that C3 amplitude was significantly higher in those with low (P = 0.02) and moderate (P = 0.004) astigmatism compared to those with high astigmatism. Refractive amblyopes had poorer GA and C3 amplitudes compared to controls by approximately two lines on the logMAR chart (monocular: P = 0.013; binocular: P = 0.014) and approximately 6 µV (monocular: P = 0.009; binocular: P = 0.027), respectively. Conclusions: Deleterious effects of high astigmatism was evident in newly diagnosed refractive amblyopes, but the neural deficits do not seem to be orientation-specific for the stimulus parameters investigated

Electrophysiological and Psychophysical Studies of Meridional Anisotropies in Children With and Without Astigmatism.

Purpose: We investigated the pattern of meridional anisotropies, if any, for pattern onset-offset visual evoked potential (POVEPs) responses and psychophysical grating acuity (GA) in children with normal letter visual acuity (20/20 or better). Methods: A total of 29 children (aged 3-9 years), nine of whom were astigmatic (AS), were recruited. Orientation-specific monocular POVEPs were recorded in response to sinewave grating stimuli oriented along the subjects' principal AS meridians. Horizontal and vertical gratings were designated Meridians 1 and 2, respectively, for nonastigmatic patients (Non-AS). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed monocularly and binocularly along the same meridians using the same stimuli by a 2-alternative-forced-choice staircase technique. The C3 amplitudes and peak latencies of the POVEP and GAs were compared across meridians using linear mixed models (monocular) and ANOVA (binocular). Results: There were significant meridional anisotropies in monocular C3 amplitudes regardless of astigmatism status (P = 0.001): Meridian 2 (mean ± SE Non-AS, 30.13 ± 2.07 μV; AS, 26.53 ± 2.98 μV) was significantly higher than Meridian 1 (Non-AS, 26.14 ± 1.87 μV; AS, 21.68 ± 2.73 μV; P = 0.019), but no meridional anisotropies were found for GA or C3 latency. Binocular C3 amplitude in response to horizontally oriented stimuli (180°, 29.71 ± 3.06 μV) was significantly lower than the oblique (45°, 36.62 ± 3 .05 μV; P = 0.03 and 135°, 35.95 ± 2.92 μV; P = 0.04) and vertical (90°, 37.82 ± 3.65 μV; P = 0.02) meridians, and binocular C3 latency was significantly shorter in response to vertical than oblique gratings (P ≤ 0.001). Conclusions: Meridional anisotropy was observed in children with normal vision. The findings suggest that horizontal gratings result in a small, but significantly lower POVEP amplitude than for vertical and oblique gratings

High frequency dynamics in a monatomic glass

The high frequency dynamics of glassy Selenium has been studied by Inelastic X-ray Scattering at beamline BL35XU (SPring-8). The high quality of the data allows one to pinpoint the existence of a dispersing acoustic mode for wavevectors ($Q$) of $1.5<Q<12.5$ nm$^{-1}$, helping to clarify a previous contradiction between experimental and numerical results. The sound velocity shows a positive dispersion, exceeding the hydrodynamic value by $\approx$ 10% at $Q<3.5$ nm$^{-1}$. The $Q^2$ dependence of the sound attenuation $\Gamma(Q)$, reported for other glasses, is found to be the low-$Q$ limit of a more general $\Gamma(Q) \propto \Omega(Q)^2$ law which applies also to the higher $Q$ region, where $\Omega(Q)\propto Q$ no longer holds.Comment: Phys. Rev. Lett. (Accepted