ShantanuT01/DACTYL-Pretraining huggingface dataset:
The dynamic behavior of the interfaces in the standard and random driven lattice gas models (DLG and RDLG respectively) is investigated via numerical Monte Carlo simulations in two dimensions. For $T\lesssim T_c$, the average interface width of the strips ($W$) was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value $W^{2}_{sat}$ only depends on the lattice size parallel to the external field axis $L_y$ and exhibits two distinct regimes: $W^{2}_{sat}\propto \ln$ $L_y$ for low temperatures, that crosses over to $W^{2}_{sat}\propto L_y^{2\alpha_I}$ near the critical zone, $\alpha_I=1/2$ being the roughness exponent of the interface. By using the relationship $\alpha_I=1/(1+\Delta_I)$, the anisotropic exponent for the interface of the DLG model was estimated, giving $\Delta_I\simeq 1$, in agreement with the computed value for anisotropic bulk exponent $\Delta_B$ with a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of $W$ at $T_c$ was also monitored and shows two growing stages: first one observes that $W \propto \ln$ $t$ for several decades, and in the following times one has $W\propto t^{\beta_I}$, where $\beta_{I}$ is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving $z_{\perp}^I\approx 4$, which is consistent with the dynamic exponent of the bulk critical transition $z_{\perp}^B$ in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.
Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems as nuclei, in particular for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.
Using Hubble Space Telescope/Space Telescope Imaging Spectrograph G140M spectroscopy, we investigate an absorption-line system at $z$=0.07489 in the spectrum of the quasi-stellar object PG 1543+489 ($z_{QSO}$=0.401). The sightline passes within $\rho = 66$ kpc of an edge-on $2L^*$ disk galaxy at a similar redshift, but the galaxy belongs to a group with four other galaxies within $\rho =160$ kpc. We detect H I [log $N$(H I/$cm^{-2}$) = 19.12$\pm$0.04] as well as N I, Mg II, Si II, and Si III, from which we measure a gas-phase abundance of [N/H] = $-1.0\pm 0.1$. Photoionization models indicate that the nitrogen-to-silicon relative abundance is solar, yet magnesium is underabundant by a factor of $\approx$ 2. We also report spatially resolved emission-line spectroscopy of the nearby galaxy, and we extract its rotation curve. The galaxy's metallicity is $\approx 8 \times$ higher than [N/H] in the absorber, and interestingly, the absorber velocities suggest that the gas at $\rho =$ 66 kpc is corotating with the galaxy's stellar disk, possibly with an inflow component. These characteristics could indicate that this sub-damped Ly$\alpha$ absorber system arises in a "cold-accretion" flow. However, the absorber abundance patterns are peculiar. We hypothesize that the gas was ejected from its galaxy of origin (or perhaps is a result of tidal debris from interactions between the group galaxies) with a solar nitrogen abundance, but that subsequently mixed with (and was diluted by) gas in the circumgalactic medium (CGM) or group. If the gas is bound to the nearby galaxy, this system may be an example of the gas "recycling" predicted by theoretical galaxy simulations. Our hypothesis is testable with future observations.
We study M/D-branes in a null-brane background. By taking a near horizon limit, one is left with cosmological models in the corresponding Poincar\'e patches. To deal with their usual horizons, we either extend these models to global AdS or remain in the Poincar\'e patch and apply a T-duality transformation whenever the effective radius of the compact dimension associated with the null-brane probes distances smaller than the string scale. The first scenario gives rise to null orbifolds in AdS spaces, which are described in detail. Their conformal boundaries are singular. The second has a dual gauge theory description in terms of Super Yang-Mills in the null-brane background. The latter is a good candidate for a non-perturbative definition of string theory in a time-dependent background.
We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the standard $L^p$-Wasserstein distances for $p \ge 1$. We present explicit lower bounds of the corresponding contraction rates. By employing the refined basic coupling and the coupling by reflection, the results are applied to Markov chains whose transitions include additive stochastic noises that are not necessarily isotropic. This can be useful in the study of Euler schemes for SDEs driven by L\'evy noises. In particular, motivated by recent works on the use of heavy tailed processes in Markov Chain Monte Carlo, we show that chains driven by the $\alpha$-stable noise can have better contraction rates than corresponding chains driven by the Gaussian noise, due to the heavy tails of the $\alpha$-stable distribution.
The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently we showed that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $\alpha$ that set the scale of QG effects. In this paper we obtain the LIV for mesons and nucleons and apply it to study several effects, including the GZK anomaly.
The early optical emission of gamma-ray bursts gives an opportunity to understand the central engine and first stages of these events. About 30\% of GRBs present flares whose origin is still a subject of discussion. We present optical photometry of GRB 180620A with the COATLI telescope and RATIR instrument. COATLI started to observe from the end of prompt emission at $T+39.3$~s and RATIR from $T+121.4$~s. We supplement the optical data with the X-ray light curve from \emph{Swift}/XRT. %The optical and X-ray light curves show very unusual behavior with features clearly beyond the standard fireball model. We observe an optical flare from $T+110$ to $T+550$~s, with a temporal index decay $\alpha_\mathrm{O,decay}=1.32\pm 0.01$, and a $\Delta t/t=1.63$, which we interpret as the signature of a reverse shock component. After the initial normal decay the light curves show a long plateau from $T+500$ to $T+7800$~s both in X-rays and the optical before decaying again after an achromatic jet break at $T+7800$~s. Fluctuations are seen during the plateau phase in the optical. Adding to the complexity of GRB afterglows, the plateau phase (typically associated with the coasting phase of the jet) is seen in this object after the ``normal'' decay phase (emitted during the deceleration phase of the jet) and the jet break phase occurs directly after the plateau. We suggest that this sequence of events can be explained by a rapid deceleration of the jet with $t_d\lesssim 40$ s due to the high density of the environment ($\approx 100$ cm$^{-3}$) followed by reactivation of the central engine which causes the flare and powers the plateau phase.
Human skeleton, as a compact representation of human action, has received increasing attention in recent years. Many skeleton-based action recognition methods adopt graph convolutional networks (GCN) to extract features on top of human skeletons. Despite the positive results shown in previous works, GCN-based methods are subject to limitations in robustness, interoperability, and scalability. In this work, we propose PoseC3D, a new approach to skeleton-based action recognition, which relies on a 3D heatmap stack instead of a graph sequence as the base representation of human skeletons. Compared to GCN-based methods, PoseC3D is more effective in learning spatiotemporal features, more robust against pose estimation noises, and generalizes better in cross-dataset settings. Also, PoseC3D can handle multiple-person scenarios without additional computation cost, and its features can be easily integrated with other modalities at early fusion stages, which provides a great design space to further boost the performance. On four challenging datasets, PoseC3D consistently obtains superior performance, when used alone on skeletons and in combination with the RGB modality.
It is proven that the relativistic charged ball with its charge less than its mass (in natural units) cannot have a non-singular static configuration while its radius approaches its external horizon size. This conclusion does not depend on the details of charge distribution and the equation of state. The involved assumptions are (1) the ball is made of perfect fluid, (2) the energy density is everywhere non-negative.
A large fraction of the gas in the Galaxy is cold, dense, and molecular. If all this gas collapsed under the influence of gravity and formed stars in a local free-fall time, the star formation rate in the Galaxy would exceed that observed by more than an order of magnitude. Other star-forming galaxies behave similarly. Yet observations and simulations both suggest that the molecular gas is indeed gravitationally collapsing, albeit hierarchically. Prompt stellar feedback offers a potential solution to the low observed star formation rate if it quickly disrupts star-forming clouds during gravitational collapse. However, this requires that molecular clouds must be short-lived objects, raising the question of how so much gas can be observed in the molecular phase. This can occur only if molecular clouds form as quickly as they are destroyed, maintaining a global equilibrium fraction of dense gas. We therefore examine cloud formation timescales. We first demonstrate that supernova and superbubble sweeping cannot produce dense gas at the rate required to match the cloud destruction rate. On the other hand, Toomre gravitational instability can reach the required production rate. We thus argue that, although dense, star-forming gas may last only around a single global free-fall time, the dense gas in star-forming galaxies can globally exist in a state of dynamic equilibrium between formation by gravitational instability, and disruption by stellar feedback. At redshift z >~ 2, the Toomre instability timescale decreases, resulting in a prediction of higher molecular gas fractions at early times, in agreement with observations.
The purpose of this article is to study Newton polygons of certain abelian $L$-functions on curves. Let $X$ be a smooth affine curve over a finite field $\mathbb{F}_q$ and let $\rho:\pi_1(X) \to \mathbb{C}_p^\times$ be a finite character of order $p^n$. By previous work of the first author, the Newton polygon $\mathrm{NP}(\rho)$ lies above a `Hodge polygon' $\mathrm{HP}(\rho)$, which is defined using local ramification invariants of $\rho$. In this article we study the touching between these two polygons. We prove that $\mathrm{NP}(\rho)$ and $\mathrm{HP}(\rho)$ share a vertex if and only if a corresponding vertex is shared between the Newton and Hodge polygons of `local' $L$-functions associated to each ramified point of $\rho$. As a consequence, we determine a necessary and sufficient condition for the coincidence of $\mathrm{NP}(\rho)$ and $\mathrm{HP}(\rho)$.
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these algorithms is generally nonconvex, causing suboptimal solutions due to convergence to local, rather than global, minima. In this work, we introduce a variational quantum algorithm that uses classical Markov chain Monte Carlo techniques to provably converge to global minima. These performance gaurantees are derived from the ergodicity of our algorithm's state space and enable us to place analytic bounds on its time-complexity. We demonstrate both the effectiveness of our technique and the validity of our analysis through quantum circuit simulations for MaxCut instances, solving these problems deterministically and with perfect accuracy. Our technique stands to broadly enrich the field of variational quantum algorithms, improving and gauranteeing the performance of these promising, yet often heuristic, methods.
This article concerns the water wave problem in a three-dimensional domain of infinite depth and examines the modulational regime for weakly nonlinear wavetrains. We use the method of normal form transformations near the equilibrium state to provide a new derivation of the Hamiltonian Dysthe equation describing the slow evolution of the wave envelope. A precise calculation of the third-order normal form allows for a refined reconstruction of the free surface. We test our approximation against direct numerical simulations of the three-dimensional Euler system and against predictions from the classical Dysthe equation, and find very good agreement.
We investigate how the pressure in fluctuating shear flow depends on the shear rate $S$ and on the system size $L$ by studying fluctuating hydrodynamics under shear conditions. We derive anomalous forms of the pressure for two limiting values of the dimensionless parameter $\lambda=SL^2/\nu$, where $\nu$ is the kinematic viscosity. In the case $\lambda \ll 1$, the pressure is not an intensive quantity because of the influence of the long-range spatial correlations of momentum fluctuations. In the other limit $\lambda \gg 1$, the long-range correlations are suppressed at large distances, and the pressure is intensive. In this case, however, there is the interesting effect that the non-equilibrium correction to the pressure is proportional to $S^{3/2}$, which was previously obtained with the projection operator method [K. Kawasaki and J. D. Gunton, Phys. Rev. {\bf A 8}, 2048, (1973)].
In-medium nucleon-nucleon scattering cross sections are explored by comparing results of quantum molecular dynamics simulations to data on stopping and on elliptic and directed flow in intermediate-energy heavy-ion collisions. The comparison points to in-medium cross sections which are suppressed at low energies but not at higher energies. Positive correlations are found between the degree of stopping and the magnitudes of elliptic and directed flows.
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which describe queueing networks. Such a limit is typically obtained by the weak convergence of either stochastic processes or stationary distributions. We already have nice reviews and text books for them. However, this area is still actively studied, and it seems getting hard to have a comprehensive overview because mathematical results are highly technical. We try to fill this gap presenting technical background. Although those diffusion approximations have been well developed, there remains a big problem, which is difficulty to get useful information from the limiting diffusion processes. Their state spaces are multidimensional, whose dimension corresponds to the number of nodes for a single-class case and the number of customer types for a multi-class case. We now have a better view for the two dimensional case, but still know very little about the higher dimensional case. This intractability is somehow against a spirit of diffusion approximation. This motivates us to reconsider diffusion approximation from scratch. For this, we highlight the stationary distributions, and make clear a mechanism to produce diffusion approximations.
We report GHz longitudinal as well as shear acoustic phonons photoexcitation and photodetection using femtosecond laser pulses in a spin-crossover molecular crystal. From our experimental observation of time domain Brillouin scattering triggered by the photoexcitation of acoustic waves across the low-spin (LS) to high-spin (HS) thermal crossover, we reveal a link between molecular spin state and photoexcitation of coherent GHz acoustic phonons. In particular, we experimentally evidence an unconventional non-thermal pathway for the laser excitation of GHz phonons. We also provide experimental insight on the optical and mechanical parameters evolution across the LS/HS spin crossover temperature T$_{1/2}$.
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems.
We present results from an optical imaging and spectroscopic monitoring campaign on the young, low-mass eruptive variable star V1647 Orionis. The star and associated nebulosity (McNeil's Nebula) were observed over the period February 2004 to February 2006 with observations commencing a few months after the original outburst event occurred. Using the Gemini North telescope, we obtained multi-band optical imaging photometry and medium-resolution long-slit spectroscopy of V1647 Ori on an approximately monthly interval. During this period, V1647 Ori remained at, or close to, peak brightness and then faded by 5 magnitudes to close to its pre-outburst brightness. This implies an outburst timescale of around 27 months. Spectral features seen in both emission and absorption varied considerably during the monitoring period. For example, the Halpha line changed significantly in both intensity and profile. We present and discuss the observed photometric and spectroscopic changes and consider how this eruptive event relates to the early formative stages of low-mass stars.
A generalized action for strings which is a sum of the Nambu-Goto and the extrinsic curvature (the energy integral of the surface) terms, is used to couple strings to gravity. It is shown that the conical singularity has deficit angle that has contributions from both the above terms. It is found that the effect of extrinsic curvature is to oppose that of the N-G action for the temperature of the black-hole and to modify the entropy-area relation.
In this paper I prove that for any prime $p$ there is a constant $C_p>0$ such that for any $n>0$ and for any $p$-power $q$ there is a smooth, projective, absolutely irreducible curve over $\mathbb{F}_q$ of genus $g\leq C_p q^n$ without points of degree smaller than $n$.
It is still a challenge to assess the merger fraction of galaxies at different cosmic epochs in order to probe the evolution of their mass assembly. Using the Illustris cosmological simulations, we investigate the relation between the separation of galaxies in a pair, both in velocity and projected spatial separation space, and the probability that these interacting galaxies will merge in the future. From this analysis, we propose a new set of criteria to select close pairs of galaxies along with a new corrective term to be applied to the computation of the galaxy merger fraction. We then probe the evolution of the major and minor merger fraction using the latest MUSE deep observations over the HUDF, HDFS, COSMOS-Gr30 and Abell 2744 regions. From a parent sample of 2483 galaxies with spectroscopic redshifts, we identify 366 close pairs spread over a large range of redshifts ($0.2<z<6$) and stellar masses ($10^7-10^{11}M_{\odot}$). Using the stellar mass ratio between the secondary and primary galaxy as a proxy to split the sample into major, minor and very minor mergers, we found a total of 183 major, 142 minor and 47 very minor close pairs corresponding to a mass ratio range of 1:1-1:6, 1:6-1:100 and lower than 1:100, respectively. Due to completeness issues, we do not consider the very minor pairs in the analysis. Overall, the major merger fraction increases up to $z\approx 2-3$ reaching 25% for pairs with the most massive galaxy with a stellar mass $M^*\geq 10^{9.5}M_{\odot}$. Beyond this redshift, the fraction decreases down to $\sim 5$% at $z\approx 6$. The evolution of the minor merger fraction is roughly constant with cosmic time, with a fraction of 20% at $z<3$ and a slow decrease between $3\leq z \leq6$ to 8-13%.
In this paper, we study the existence and multiplicity of weak solutions to a general type of Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces. Specifically, we appeal to Critical Point Theory to prove the existence of non-trivial solutions under the so-called Ambrosetti-Rabinowitz condition. We also state the existence of ground-state solutions. Moreover, multiplicity results which yield the existence of an unbounded sequence of solutions are also provided. Finally, we show existence under a weak-type Ambrosetti-Rabinowitz condition formulated in the framework of Orlicz spaces.
We consider finite time blowup solutions of the $L^2$-critical cubic focusing nonlinear Schr\"odinger equation on $\R^2$. Such functions, when in $H^1$, are known to concentrate a fixed $L^2$-mass (the mass of the ground state) at the point of blowup. Blowup solutions from initial data that is only in $L^2$ are known to concentrate at least a small amount of mass. In this paper we consider the intermediate case of blowup solutions from initial data in $H^s$, with $1 > s > s_Q$, where $s_Q \le \sQ$. Our main result is that such solutions, when radially symmetric, concentrate at least the mass of the ground state at the origin at blowup time.
We give a new proof that there are infinitely many primes, relying on van der Waerden's theorem for coloring the integers, and Fermat's theorem that there cannot be four squares in an arithmetic progression. We go on to discuss where else these ideas have come together in the past.