ShantanuT01/DACTYL-Pretraining huggingface dataset:
Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact via an attractive soft Coulomb potential. It is observed that the collapse in the particle system indeed takes place when the energy of the uniform state is put near or below the metastability-instability threshold (collapse energy), predicted by the mean-field theory. Similarly, the explosion in the particle system occurs when the energy of the core-halo state is increased above the explosion energy, where according to the mean field predictions the core-halo state becomes unstable. For a system consisting of 125 -- 500 particles, the collapse takes about $10^5$ single particle crossing times to complete, while a typical explosion is by an order of magnitude faster. A finite lifetime of metastable states is observed. It is also found that the mean-field description of the uniform and the core-halo states is exact within the statistical uncertainty of the molecular dynamics data.
In this paper, existence and uniqueness are proved for path-dependent McKean-Vlasov type SDEs with integrability conditions. Gradient estimates and Harnack type inequalities are derived in the case that the coefficients are Dini continuous in the space variable. These generalize the corresponding results derived for classical functional SDEs with singular coefficients.
We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massouli\'{e} [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network. We study the transient properties as well as the steady-state distribution of the model. In particular, for $\alpha\geq1$, we obtain bounds on the maximum number of flows in the network over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property for all $\alpha\geq1$. For the steady-state distribution, we obtain explicit exponential tail bounds on the number of flows, for any $\alpha>0$, by relying on a norm-like Lyapunov function. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [Ann. Appl. Probab. 19 (2009) 1719-1780], in steady state, for the case where $\alpha=1$ and under a local traffic condition.
Young and massive star clusters above a critical mass form thermally unstable clumps reducing locally the temperature and pressure of the hot 10$^{7}$~K cluster wind. The matter reinserted by stars, and mass loaded in interactions with pristine gas and from evaporating circumstellar disks, accumulate on clumps that are ionized with photons produced by massive stars. We discuss if they may become self-shielded when they reach the central part of the cluster, or even before it, during their free fall to the cluster center. Here we explore the importance of heating efficiency of stellar winds.
Antidot lattices, defined on a two-dimensional electron gas at a semiconductor heterostructure, are a well-studied class of man-made structures with intriguing physical properties. We point out that a closely related system, graphene sheets with regularly spaced holes ("antidots"), should display similar phenomenology, but within a much more favorable energy scale, a consequence of the Dirac fermion nature of the states around the Fermi level. Further, by leaving out some of the holes one can create defect states, or pairs of coupled defect states, which can function as hosts for electron spin qubits. We present a detailed study of the energetics of periodic graphene antidot lattices, analyze the level structure of a single defect, calculate the exchange coupling between a pair of spin qubits, and identify possible avenues for further developments.
Two graphene monolayers that are oppositely charged and placed close to each other are considered. Taking into account valley and spin degeneracy of electrons we analyze the symmetry of the excitonic insulator states in such a system and build a phase diagram that takes into account the effect of the symmetry breaking due to the external in-plane magnetic field and the carrier density imbalance between the layers.
Time-distance helioseismology uses cross-covariances of wave motions on the solar surface to determine the travel times of wave packets moving from one surface location to another. We review the methodology to interpret travel-time measurements in terms of small, localized perturbations to a horizontally homogeneous reference solar model. Using the first Born approximation, we derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for perturbations in sound-speed, density, pressure, and vector flows. While kernels for sound speed and flows had been computed previously, here we extend the calculation to kernels for density and pressure, hence providing a complete description of the effects of solar dynamics and structure on travel times. We treat three thermodynamic quantities as independent and do not assume hydrostatic equilibrium. We present a convenient approach to computing damped Green's functions using a normal-mode summation. The Green's function must be computed on a wavenumber grid that has sufficient resolution to resolve the longest lived modes. The typical kernel calculations used in this paper are computer intensive and require on the order of 600 CPU hours per kernel. Kernels are validated by computing the travel-time perturbation that results from horizontally-invariant perturbations using two independent approaches. At fixed sound-speed, the density and pressure kernels are approximately related through a negative multiplicative factor, therefore implying that perturbations in density and pressure are difficult to disentangle. Mean travel-times are not only sensitive to sound-speed, density and pressure perturbations, but also to flows, especially vertical flows. Accurate sensitivity kernels are needed to interpret complex flow patterns such as convection.
Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is surprisingly challenging. It introduces novel techniques for bounding the spectrum which are useful for a variety of walks on a variety of groups.
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It is argued that this could perhaps be accomplished by giving up the assumption that the objective ``state'' of a system is independent of a future measurement performed on the system. This idea is then applied in an example of quantum state estimation on a qubit system.
The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future $e^+ e^-$ colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass $m_0$, gaugino mass $m_{1/2}$ and trilinear coupling $A$, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low $\tb$ solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high $\tb$ case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into $b$ and $\tau$ pairs. The main production mechanisms for the heavy Higgs particles are the associated $AH$ production and $H^+H^-$ pair production with cross sections of the order of a few fb.
The baryonic and dark matter fractions in the universe can be both generated by the same baryogenesis mechanism, simultaneously and with comparable amounts, if dark matter is constituted by the baryons of the mirror world, a parallel hidden sector with the same (or similar) microphysics as that of the observable world.
We present the Forgotten Quadrant Survey (FQS), an ESO large project that used the 12m antenna of the Arizona Radio Observatory to map the Galactic Plane in the range 220\deg$<l<$240\deg and -2.5\deg$<b<$0\deg, both in $^{12}$CO(1-0) and $^{13}$CO(1-0), at a spectral resolution of 0.65 km s$^{-1}$ and 0.26 km s$^{-1}$. Our dataset allows us to easily identify how the molecular dense gas is organised at different spatial scales: from the giant clouds with their denser filamentary networks, down to the clumps and cores that host the newborn stars and to obtain reliable estimates of their key physical parameters. We present the first release of the FQS data and discuss their quality. Spectra with 0.65 km s$^{-1}$ velocity channels have a noise ranging from 0.8 K to 1.3 K for $^{12}$CO(1-0) and from 0.3 K to 0.6 K for $^{13}$CO(1-0). In this paper, we used the $^{12}$CO(1-0) spectral cubes to produce a catalogue of 263 molecular clouds. This is the first selfconsistent, statistical catalogue of molecular clouds of the outer Galaxy, obtained with a subarcminute spatial resolution and therefore able to detect not only the classical giant molecular clouds, but also the small clouds and to resolve the cloud structure at the subparsec scale up to a distance of a few kpc. We found two classes of objects: structures with size above a few parsecs that are typical molecular clouds and may be self-gravitating, and subparsec structures that cannot be in gravitational equilibrium and are likely transient or confined by external pressure. We used the ratio between the Herschel H$_2$ column density and the integrated intensity of the CO lines to calculate the CO conversion factor and we found mean values of (3.3$\pm$1.4)$\times 10^{20}$ cm$^{-2}$(K km s$^{-1})^{-1}$ and (1.2$\pm$0.4)$\times 10^{21}$ cm$^{-2}$(K km s$^{-1})^{-1}$, for $^{12}$CO(1-0) and $^{13}$CO(1-0), respectively.
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.
Thermodynamic experiments as well as Raman scattering have been used to study the magnetic instabilities in the spin-tetrahedra systems Cu_2Te_2O_5X_2, X=Cl and Br. While the phase transition observed in the Cl system at T_o=18.2 K is consistent with 3D AF ordering, the phase transition at T_o=11.3 K in the Br system has several unusual features. We propose an explanation in terms of weakly coupled tetrahedra with a singlet-triplet gap and low lying singlets.
In this paper, we present a method which combines the flexibility of the neural algorithm of artistic style with the speed of fast style transfer networks to allow real-time stylization using any content/style image pair. We build upon recent work leveraging conditional instance normalization for multi-style transfer networks by learning to predict the conditional instance normalization parameters directly from a style image. The model is successfully trained on a corpus of roughly 80,000 paintings and is able to generalize to paintings previously unobserved. We demonstrate that the learned embedding space is smooth and contains a rich structure and organizes semantic information associated with paintings in an entirely unsupervised manner.
We study the formation of fluid vorticity and the hyperon polarization in heavy-ion collisions at NICA energies in the framework of the Parton-Hadron-String Dynamic Model, taking into account both hadronic and quark-gluonic (partonic) degrees of freedom. The vorticity properties in peripheral Au+Au collisions at $\sqrt{s_{NN}}=$7.7\,GeV are demonstrated and confronted with other models. The obtained result for the $\Lambda$ polarization is in agreement with the experimental data by the STAR collaboration, whereas the model is not able to explain the observed high values of the anti-hyperon $\bar\Lambda$ polarization.
The evolution of dynamical perturbations is examined in nuclear multifragmentation in the frame of Vlasov equation. Both plane wave and bubble type of perturbations are investigated in the presence of surface (Yukawa) forces. An energy condition is given for the allowed type of instabilities and the time scale of the exponential growth of the instabilities is calculated. The results are compared to the mechanical spinodal region predictions. PACS: 25.70 Mn
The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source Poisson models, models based on aggregated renewal sequences, and models built from aggregated on-off sources. The versions of these models with finite variance transmission rate share the following pattern: if the sources connect at a fast rate over time the cumulative statistical fluctuations are fractional Brownian motion, if the connection rate is slow the traffic fluctuations are described by a stable L\'evy process, while the limiting fluctuations for the intermediate scaling regime are given by fractional Poisson motion.
Let $\mathbb{F}_q$ denote a finite field of odd cardinality $q$, $\mathbb{A}=\mathbb{F}_q[T]$ the polynomial ring over $\mathbb{F}_q$ and $k=\mathbb{F}_q(T)$ the rational function field over $\mathbb{F}_q$. In this paper, we compute the average value of the size of the group $K_2(\mathcal{O}_{\gamma D})$, where $\mathcal{O}_{\gamma D}$ denotes the integral closure of $\mathbb{A}$ in $k(\sqrt{\gamma D})$, $D$ is a monic, square-free polynomial of even degree and $\gamma$ is a fixed generator of $\mathbb{F}_q^*$.
Recent IR observations indicate that many massive binary systems present dust formation episodes, in regions close to the stars, during the periastron passage. These systems are known to be high-energy sources, and it is believed that wind collisions are the origin of the emission. In this work we show that wind collisions not only increase the X-ray emission but also allow dust formation. As an application we study eta Car, which presents, near periastron, an increase in the X-ray emission followed by a sudden decrease that lasts for about a month. We reproduce this feature calculating the optical depth due to dust formation along the orbital period.
We present a sample of 80 candidate strongly lensed galaxies with flux density above 100mJy at 500{\mu}m extracted from the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS), over an area of 600 square degrees. Available imaging and spectroscopic data allow us to confirm the strong lensing in 20 cases and to reject it in one case. For other 8 objects the lensing scenario is strongly supported by the presence of two sources along the same line of sight with distinct photometric redshifts. The remaining objects await more follow-up observations to confirm their nature. The lenses and the background sources have median redshifts z_L = 0.6 and z_S = 2.5, respectively, and are observed out to z_L = 1.2 and z_S = 4.2. We measure the number counts of candidate lensed galaxies at 500{\mu}m and compare them with theoretical predictions, finding a good agreement for a maximum magnification of the background sources in the range 10-20. These values are consistent with the magnification factors derived from the lens modelling of individual systems. The catalogue presented here provides sub- mm bright targets for follow-up observations aimed at exploiting gravitational lensing to study with un-precedented details the morphological and dynamical properties of dusty star forming regions in z >~ 1.5 galaxies.
We present a methodology for probing the details of electronic susceptibility through minimally-invasive nuclear magnetic resonance techniques. Specifically, we classify electron-mediated long-range interactions in an ensemble of nuclear spins by revealing their effect on simple spin echo experiments. We find that pulse strength and applied field orientation dependence of these spin echo measurements resolves the spatial extent and anisotropy of electronic spin susceptibility. This work provides an alternate explanation to NMR results in superconducting and magnetically-ordered systems. The methodology has direct applications for sensing and characterizing emergent electronic phases.
Let $X_1$, $X_2$, $\ldots$, $X_n$ be a sequence of coherent random variables, i.e., satisfying the equalities $$ X_j=\mathbb{P}(A|\mathcal{G}_j),\qquad j=1,\,2,\,\ldots,\,n,$$ almost surely for some event $A$. The paper contains the proof of the estimate $$\mathbb{P}\Big(\max_{1\le i < j\le n}|X_i-X_j|\ge \delta\Big) \leq \frac{n(1-\delta)}{2-\delta} \wedge 1,$$ where $\delta\in (\frac{1}{2},1]$ is a given parameter. The inequality is sharp: for any $\delta$, the constant on the right cannot be replaced by any smaller number. The argument rests on several novel combinatorial and symmetrization arguments, combined with dynamic programming. Our result generalizes the two-variate inequality of K. Burdzy and S. Pal and in particular provides its alternative derivation.
Spin-phonon interactions are central to many interesting phenomena, ranging from superconductivity to magnetoelectric effects. Yet, they are believed to have a negligible influence on the structural behavior of most materials. For example, magnetic perovskite oxides often undergo structural transitions accompanied by magnetic signatures whose minuteness suggests that the underlying spin-phonon couplings are largely irrelevant. Here we present an exception to this rule, showing that novel effects can occur as a consequence. Our first-principles calculations reveal that spin-phonon interactions are essential to reproduce the experimental observations on the phase diagram of magnetoelectric multiferroic BiCoO$_{3}$. Moreover, we predict that, under compression, these couplings lead to an unprecedented temperature-driven double-reentrant sequence of ferroelectric transitions. We propose how to modify BiCoO$_{3}$ via chemical doping to reproduce such striking effects at ambient conditions, thereby yielding useful multifunctionality.
Two systems are homometric if they are indistinguishable by diffraction. We first make a distinction between Bragg and diffuse scattering homometry, and show that in the last case, coherent diffraction can allow the diffraction diagrams to be differentiated. The study of the Rudin-Shapiro sequence, homometric to random sequences, allows one to manipulate independently two-point and four-point correlation functions, and to show their effect on the statistics of speckle patterns. Consequences for the study of real materials is discussed.
This paper presents a novel hierarchical coding scheme for light fields based on transmittance patterns of low-rank multiplicative layers and Fourier disparity layers. The proposed scheme learns stacked multiplicative layers from subsets of light field views determined from different scanning orders. The multiplicative layers are optimized using a fast data-driven convolutional neural network (CNN). The spatial correlation in layer patterns is exploited with varying low ranks in factorization derived from singular value decomposition on a Krylov subspace. Further, encoding with HEVC efficiently removes intra-view and inter-view correlation in low-rank approximated layers. The initial subset of approximated decoded views from multiplicative representation is used to construct Fourier disparity layer (FDL) representation. The FDL model synthesizes second subset of views which is identified by a pre-defined hierarchical prediction order. The correlations between the prediction residue of synthesized views is further eliminated by encoding the residual signal. The set of views obtained from decoding the residual is employed in order to refine the FDL model and predict the next subset of views with improved accuracy. This hierarchical procedure is repeated until all light field views are encoded. The critical advantage of proposed hybrid layered representation and coding scheme is that it utilizes not just spatial and temporal redundancies, but efficiently exploits the strong intrinsic similarities among neighboring sub-aperture images in both horizontal and vertical directions as specified by different predication orders. Besides, the scheme is flexible to realize a range of multiple bitrates at the decoder within a single integrated system. The compression performance analyzed with real light field shows substantial bitrate savings, maintaining good reconstruction quality.
In a warm dark matter (WDM) cosmology, the first objects to form at z>=20 are one dimensional filaments with mean length on the order of the WDM free-streaming scale. Gao and Theuns recently claimed by using high-resolution hydrodynamic simulations that the eventual collapse of these WDM filaments along their longest axes may seed the supermassive black holes that power high-z quasars. In this picture, it is supposed that the high-z quasar luminosity function should reflect how abundant the WDM filaments are in the early universe. We derive analytically the mass function of early-universe filaments with the help of the Zel'dovich approximation. Then, we determine the rate of its decrease in the mass section corresponding to the free streaming scale of a WDM particle of mass m_v. Adjusting the value of m_v, we fit the slope of the analytic model to that of the high-z quasar luminosity function measured from the Sloan Digital Sky Survey DR3. A new WDM constraint from this feasibility study is found to be consistent with the lightest super-symmetric partner.
Radio relics in galaxy clusters are associated with powerful shocks that (re)accelerate relativistic electrons. It is widely believed that the acceleration proceeds via diffusive shock acceleration. In the framework of thermal leakage, the ratio of the energy in relativistic electrons to the energy in relativistic protons should should be smaller than $K_{\rm e/p} \sim 10^{-2}$. The relativistic protons interact with the thermal gas to produce $\gamma$-rays in hadronic interactions. Combining observations of radio relics with upper limits from $\gamma$-ray observatories can constrain the ratio $K_{\rm e/p}$. In this work we selected 10 galaxy clusters that contain double radio relics, and derive new upper limits from the stacking of $\gamma$-ray observations by FERMI. We modelled the propagation of shocks using a semi-analytical model, where we assumed a simple geometry for shocks and that cosmic ray protons are trapped in the intracluster medium. Our analysis shows that diffusive shock acceleration has difficulties in matching simultaneously the observed radio emission and the constraints imposed by FERMI, unless the magnetic field in relics is unrealistically large ($\gg 10 ~\rm \mu G$). In all investigated cases (also including realistic variations of our basic model and the effect of re-acceleration) the mean emission of the sample is of the order of the stacking limit by FERMI, or larger. These findings put tension on the commonly adopted model for the powering of radio relics, and imply that the relative acceleration efficiency of electrons and protons is at odds with predictions of diffusive shock acceleration, requiring $K_{\rm e/p} \geq 10-10^{-2}$.
We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra. With this scheme we also get a quantum superalgebra $U_{t}(sl(2/1)$.