ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston remains at the so called mechanical equilibrium. However, the temperatures and densities of the gases may differ across the piston. In that case some earlier studies by Gruber, Piasecki and others reveal a very slow motion (drift) of the piston in the direction of the hotter gas. At the same time the hotter gas slowly transfers its energy (heat) across the piston to the cooler gas. While the previous studies of this interesting phenomenon were only heuristic or experimental, we provide first rigorous proofs assuming that the velocity distribution of the ideal gas satisfies a certain ``cutoff'' condition.
In 1989, Ming Luo \cite{L2} showed that the Fibonacci number $U_n$ is Triangular if and only if $n=\pm1,2,4,8,10$. For this, he established a Jacobi Symbol Criterion. Moreover, he observed that this problem is equivalent to finding all integer points on two elliptic curves. In this paper, we prove a Jacobi Symbol Criterion for more general families of binary recurrences. In addition, applying the criterion and elementary methods, we determine all integer points on the elliptic curves $y^2=5x^2(x+3)^2+4(-1)^n$.
The method of averaging is used to investigate the phenomenon of capture into resonance for a model that describes a Keplerian binary system influenced by radiation damping and external normally incident periodic gravitational radiation. The dynamical evolution of the binary orbit while trapped in resonance is elucidated using the second order partially averaged system. This method provides a theoretical framework that can be used to explain the main evolutionary dynamics of a physical system that has been trapped in resonance.
We present near-infrared spectroscopic observations for a sample of ten optically faint luminous infrared galaxies (R-[24]> 14) using Keck NIRSPEC and Gemini NIRI. The sample is selected from a 24 micron Spitzer MIPS imaging survey of the NDWFS Bootes field. We measure accurate redshifts in the range 1.3<z<3.4. Based on either emission line widths or line diagnostics, we find that all ten galaxies harbor luminous AGN. Seven sources are type I AGN, exhibiting broad (>1900 km/s) Halpha or Hbeta emission lines; the remaining three are type II AGN. Given their large mid-IR luminosities and faint optical magnitudes, we might expect these sources to be heavily extincted quasars, and therefore only visible as type II AGN. The visibility of broad lines in 70% of the sources suggests that it is unlikely that these AGN are being viewed through the mid-plane of a dusty torus. For four of the sources we constrain the Halpha/Hbeta Balmer decrement and estimate the extinction to the emission line region to be large for both type I and type II AGN, with A_Halpha > 2.4-5 mag. Since the narrow-line region is also extincted and the UV continuum emission from the host galaxies is extremely faint, this suggests that much of the obscuration is contributed by dust on large (~kpc) scales within the host galaxies. These sources may be examples of "host-obscured" AGN which could have space densities comparable or greater to that of optically luminous type I AGN with similar bolometric luminosities.
We perform molecular dynamics simulations to investigate the effect of hydrogenation on the Poisson's ratio of graphene. It is found that the value for Poisson's ratio in graphene can be effectively tuned from positive to negative by varying the percentage of hydrogenation. Specifically, the Poisson's ratio decreases with the increase of the percentage of hydrogenation, and reaches a minimum value of -0.04 at the percentage of hydrogenation about 50%. The Poisson's ratio starts to increase with a further increase of the percentage of hydrogenation. The appearance of minimum negative Poisson's ratio in the hydrogenated graphene is attributed to the suppression of the hydrogenation-induced ripples during stretching of graphene. Our results demonstrate that hydrogenation is a valuable approach for the tuning of the Poisson's ratio from positive to negative in graphene.
The present status of the theoretical description of electromagnetic reactions on the deuteron above pion threshold is reviewed. Three major topics are considered: (i) retardation effects in $\pi$-meson exchange contributions to $NN$-interaction and meson exchange currents in deuteron photodisintegration above $\pi$-threshold in the $\Delta$-resonance region, (ii) off-shell effects in the one-body current treated in a simple pion cloud model in deuteron photodisintegration in and above the $\Delta$-resonance region, and (iii) final state interaction effects in photoproduction of $\pi$ and $\eta$ mesons on the deuteron.
Coronal mass ejections (CMEs) and coronal jets are two types of common solar eruptive phenomena, which often independently happen at different spatial scales. In this work, we present a stereoscopic observation of a large-scale CME flux rope arising from an unwinding blowout jet in a multipolar complex magnetic system. Based on a multi-band observational analysis, we find that this whole event starts with a small filament whose eruption occurs at a coronal geyser site after a series of homologous jets. Aided by magnetic field extrapolations, it reveals that the coronal geyser site forms above an elongate opposite-polarity interface, where the emergence-driven photospheric flux cancellation and repetitive reconnection are responsible for those preceding recurrent jets and also contribute to the ultimate filament destabilization. By interacting with overlying fields, the erupting filament breaks one of its legs and results in an unwinding blowout jet. Our estimation suggests that around 1.4$-$2.0 turns of twist release in its jet spire. This prominent twist transport in jet spire rapidly creates a newborn larger-scale flux rope from the jet base to a remote site. Soon after its formation, this large-scale flux rope erupts towards the outer coronae causing an Earth-directed CME. In its source region, two sets of distinct post-flare loops form in succession, indicating this eruption involves two-stage of flare magnetic reconnection. This work not only reveals a real magnetic coupling process between different eruptive activities but provides a new hint for understanding the creation of large-scale CME flux ropes during the solar eruption.
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilities can be negative, and events can cancel out. An illustration of the power of quantumized algorithms is the ability to efficiently solve the satisfiability problem, something that many believe is beyond the capability of classical computers. This paper proves that the lambda-q calculus is not only capable of solving satisfiability but can also simulate such complex systems as quantum computers. Since satisfiability is believed to be beyond the capabilities of quantum computers, the lambda-q calculus may be strictly stronger.
A simple macroscopic model for the vehicular traffic flow with hysteresis is proposed. The model includes drivers' hysteresis behavior into the classical Lighthill-Whitham-Richard (LWR) model. One novelty of the model is how the hysteresis is modeled based on hysteresis behavior reported in literature. By comparing wave patterns producible by the classical LWR model versus this model, the effect of hysteresis can be revealed. For this purpose, wave pattern analysis is carried out by construction of viscous waves and Riemann solvers of the model. Examples of solutions for initial data corresponding to some real world setups or experimental observations are constructed. Many of them qualitatively agree with experimental observations and intuition. These result shows that the model not only keeps the successful part of the LWR model, but also demonstrates many wave patterns observed real world traffic that LWR fails to exhibit, such as stop-and-go waves and many other traffic patterns. A mechanism for formation and decay of stop-and-go patterns and traffic jams is revealed. Furthermore, acceleration shocks in congested zone are predicted, which can serve as fronts of stop-and-go patterns.
This paper addresses the problem of head detection in crowded environments. Our detection is based entirely on the geometric consistency across cameras with overlapping fields of view, and no additional learning process is required. We propose a fully unsupervised method for inferring scene and camera geometry, in contrast to existing algorithms which require specific calibration procedures. Moreover, we avoid relying on the presence of body parts other than heads or on background subtraction, which have limited effectiveness under heavy clutter. We cast the head detection problem as a stereo MRF-based optimization of a dense pedestrian height map, and we introduce a constraint which aligns the height gradient according to the vertical vanishing point direction. We validate the method in an outdoor setting with varying pedestrian density levels. With only three views, our approach is able to detect simultaneously tens of heavily occluded pedestrians across a large, homogeneous area.
We report the transmission over a wide frequency range (far infrared - visible) of pristine and hole-doped, free-standing carbon nanotube films at temperatures between 50 K and 300 K. Optical constants are estimated by Kramers-Kronig analysis of transmittance. We see evidence in the far infrared for a gap below 10 meV. Hole doping causes a shift of spectral weight from the first interband transition into the far infrared. Temperature dependence in both the doped and undoped samples is restricted to the far-infrared region.
We analyze the multifrequency behavior of the quasar 3C 454.3 during three prominent \gamma-ray outbursts: 2009 Autumn, 2010 Spring, and 2010 Autumn. The data reveal a repeating pattern, including a triple flare structure, in the properties of each \gamma-ray outburst, which implies similar mechanism(s) and location for all three events. The multi-frequency behavior indicates that the lower frequency events are co-spatial with the \gamma-ray outbursts, although the \gamma-ray emission varies on the shortest timescales. We determine that the variability from UV to IR wavelengths during an outburst results from a single synchrotron component whose properties do not change significantly over the different outbursts. Despite a general increase in the degree of optical linear polarization during an outburst, the polarization drops significantly at the peak of the \gamma-ray event, which suggests that both shocks and turbulent processes are involved. We detect two disturbances (knots) with superluminal apparent speeds in the parsec-scale jet associated with the outbursts in 2009 Autumn and 2010 Autumn. The kinematic properties of the knots can explain the difference in amplitudes of the \gamma-ray events, while their millimeter-wave polarization is related to the optical polarization during the outbursts. We interpret the multi-frequency behavior within models involving either a system of standing conical shocks or magnetic reconnection events located in the parsec-scale millimeter-wave core of the jet. We argue that \gamma-ray outbursts with variability timescales as short as ~ 3 hr can occur on parsec scales if flares take place in localized regions such as turbulent cells.
A general form of the polarization matrix valid for any type of electromagnetic radiation (plane waves, multipole radiation etc.) is defined in terms of a certain bilinear form in the field-strength tensor. The quantum counterpart is determined as an operator matrix with normal-ordered elements with respect to the creation and annihilation operators. The zero-point oscillations (ZPO) of polarization are defined via difference between the anti-normal and normal ordered operator polarization matrices. It is shown that ZPO of the multipole field are stronger than those described by the model of plane waves and are concentrated in a certain neighborhood of a local source.
In spite of the enormous success of the Standard Model (SM), we have strong reasons to expect the presence of new physics beyond the SM at higher energies. The idea of the Grand Unification of all the known interactions in nature is perhaps the main reason behind these expectations. Low-energy Supersymmetry is closely linked with grand unification as a solution of the hierarchy problem associated with the ratio M_GUT / M_Z. In these lectures we will provide a general overview of Grand Unification and Supersymmetry with special emphasis on their phenomenological consequences at low energies. We will analyse the flavour and CP problems of Supersymmetry and try to identify in these associated low-energy observables possible indications of the existence of a Grand Unified theory at high energies.
We present a new semi-supervised domain adaptation framework that combines a novel auto-encoder-based domain adaptation model with a simultaneous learning scheme providing stable improvements over state-of-the-art domain adaptation models. Our framework holds strong distribution matching property by training both source and target auto-encoders using a novel simultaneous learning scheme on a single graph with an optimally modified MMD loss objective function. Additionally, we design a semi-supervised classification approach by transferring the aligned domain invariant feature spaces from source domain to the target domain. We evaluate on three datasets and show proof that our framework can effectively solve both fragile convergence (adversarial) and weak distribution matching problems between source and target feature space (discrepancy) with a high `speed' of adaptation requiring a very low number of iterations.
The field of exoplanet research has revitalized interest in M dwarfs, which have become favorite targets of Doppler and transit surveys. Accurate measurements of their basic properties such as masses, radii, and effective temperatures have revealed significant disagreements with predictions from stellar evolution theory in the sense that stars are larger and cooler than expected. These anomalies are believed to be due to high levels of activity in these stars. The evidence for the radius discrepancies has grown over the years as more and more determinations have become available; however, fewer of these studies include accurate determinations of the temperatures. The ubiquitous mass-radius diagrams featured in many new discovery papers are becoming more confusing due to increased scatter, which may be due in part to larger than realized systematic errors affecting many of the published measurements. A discussion of these and other issues is given here from an observer's perspective, along with a summary of theoretical efforts to explain the radius and temperature anomalies.
The theory of multiverse and wormholes suggests that the parameters of the Standard Model are fixed in such a way that the radiation of the $S^{3}$ universe at the final stage $S_{rad}$ becomes maximum, which we call the maximum entropy principle. Although it is difficult to confirm this principle generally, for a few parameters of the Standard Model, we can check whether $S_{rad}$ actually becomes maximum at the observed values. In this paper, we regard $S_{rad}$ at the final stage as a function of the weak scale ( the Higgs expectation value ) $v_{h}$, and show that it becomes maximum around $v_{h}={\cal{O}}(300\text{GeV})$ when the dimensionless couplings in the Standard Model, that is, the Higgs self coupling, the gauge couplings, and the Yukawa couplings are fixed. Roughly speaking, we find that the weak scale is given by \begin{equation} v_{h}\sim\frac{T_{BBN}^{2}}{M_{pl}y_{e}^{5}},\nonumber\end{equation} where $y_{e}$ is the Yukawa coupling of electron, $T_{BBN}$ is the temperature where the Big Bang Nucleosynthesis starts and $M_{pl}$ is the Planck mass.
The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.
We model the formation of Auriga's Wheel - a recently discovered collisional ring galaxy. Auriga's Wheel has a number of interesting features including a bridge of stars linking the neighbouring elliptical to the ring galaxy, and evidence for components of expansion and rotation within the ring. Using N-body/SPH modelling, we study collisions between an elliptical galaxy and a late-type disk galaxy. A near direct collision, with a mildy inclined disk, is found to reasonably reproduce the general system morphology ~50 Myr following the collision. The collision must have a relatively low velocity (initially ~150 km s^{-1}) in order to form the observed bridge, and simultaneously match the galaxies separation. Our best-match model suggests the total disk galaxy is ~5 times more massive than the elliptical. We find that the velocity of expansion of the ring is sensitive to the mass of the elliptical, while insensitive to the encounter velocity. We evolve our simulation beyond the current epoch to study the future destiny of the galaxy pair. In our model, the nucleus moves further away from the plane of the ring in the direction of the stellar bridge. The nucleus eventually merges with the elliptical galaxy ~100 Myr after the present time. The ring continues to expand for ~200 Myr before collapsing back. The low initial relative velocity of the two galaxies will eventually result in a complete merger.
We performed an iron abundance determination of the hot, hydrogen deficient post-AGB star PG1159-035, which is the prototype of the PG1159 spectral class and the GW Vir pulsators, and of two related objects (PG1520+525, PG1144+005), based on the first detection of Fe VIII lines in stellar photospheres. In another PG1159 star, PG1424+535, we detect Fe VII lines. In all four stars, each within Teff = 110,000 - 150,000 K, we find a solar iron abundance. This result agrees with our recent abundance analysis of the hottest PG1159 stars (Teff = 150,000 - 200,000 K) that exhibit Fe X lines. On the whole, we find that the PG1159 stars are not significantly iron deficient, in contrast to previous notions.
The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour $Z_2$ symmetric braneworlds with a negative bulk cosmological constant.
By using a phenomenologically successful Woods-Saxon potential, I study the shape and shell structure of (A) neutron drip line nuclei with 10 \leq N \leq 60, (B) neutron-rich nuclei related to the r- process with 40 \leq N \leq 90, and (C) one-particle spectra in the potential provided by the nucleus 70Fe as a representative of so-called N=40 "island of inversion (IoI)" nuclei. First, the shell structure that is unique in very weakly-bound neutrons is systematically studied, and the approximate neutron number of odd-N nuclei at which spherical (or deformed) halos can be found is pinned down. Second, the difference of the shell structure in r-process nuclei from that in stable nuclei is examined. Third, the similarity and the difference between the shell structure of N=20 IoI nuclei and that of N=40 IoI nuclei are analyzed. As a result of it, it is concluded that in Fe and Cr isotopes the deformation called "N=40 IoI" continuing up to N=50 is unlikely.
The asymptotics of the "$(k,\ell)$ hook" sums $S_{k,\ell}^{(2z)}(n)$ (see~\eqref{the.sums.1}) were calculated in~\cite{berele}. It was recently realized that in~\cite[Section 7]{berele} there are few misprints and certain confusion with regard to the notations, so that the precise asymptotics of $S_{k,\ell}^{(2z)}(n)$ is not clear. Here we add more details and carefully repeat these calculations, which lead to explicit values for the asymptotics of $S_{k,\ell}^{(2z)}(n).$
We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density $\rho$ of particles, from a low-density phase with all particles immobile for $\rho \le \rho_c = \frac{1}{n+1}$, to an active state for $\rho > \rho_c$. The mean fraction of movable particles in the active steady state varies as $(\rho - \rho_c)^{\beta}$, for $\rho$ near $\rho_c$. We show that for the model with range $n$, the exponent $\beta =n$, and thus can be made arbitrarily large.
Let $\alpha,\beta$ be real numbers such that $\alpha>1$ is irrational and of finite type, and let $c$ be a real number in the range $1<c<\frac{14}{13}$. In this paper, it is shown that there are infinitely many Piatetski-Shapiro primes $p = \left\lfloor n^c \right\rfloor$ in the non-homogenous Beatty sequence $\big(\left\lfloor\alpha m+\beta\right\rfloor\big)_{m=1}^\infty$.
Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In this article, after a comparative study between Fermi metric of a uniformly rotating eccentric observer and the spacetime metric in the same observer's frame obtained through the modified Franklin transformation, we consider rotational phenomena including transverse Doppler effect and Sagnac effect in both formalisms and compare their predictions. We also discuss length measurements in the two formalisms.
Let $A$ and $B$ be additive sets of $\mathbb{Z}_{2k}$, where $A$ has cardinality $k$ and $B=v.\complement A$ with $v\in\mathbb{Z}_{2k}^{\times}$. In this note some bounds for the cardinality of $A+B$ are obtained, using four different approaches. We also prove that in a special case the bound is not sharp and we can recover the whole group as a sumset.