ShantanuT01/DACTYL-Pretraining huggingface dataset:
The thermal transport properties of a two dimensional Fermi gas are explored, for the full range of temperatures and densities. The heat flux is established by solving the Uehling-Uhlebeck equation using a relaxation approximation given by Marle's collisional kernel and considering the temperature and chemical potential gradients as independent thermodynamic forces. It is shown that the corresponding transport coefficients are proportional to each other, which leads to the possibility of defining a generalized thermal force and a single transport coefficient. The behavior of such conductivity with the temperature and chemical potential is analyzed and a discussion on its dependence with the relaxation parameter is also included. The relevance and applications of the results are briefly addressed.
We present an initial overview of the filamentary structure in the Orion A molecular cloud utilizing a high angular and velocity resolution C$^{18}$O(1-0) emission map that was recently produced as part of the CARMA-NRO Orion Survey. The main goal of this study is to build a credible method to study varying widths of filaments which has previously been linked to star formation in molecular clouds. Due to the diverse star forming activities taking place throughout its $\sim$20 pc length, together with its proximity of 388 pc, the Orion A molecular cloud provides an excellent laboratory for such an experiment to be carried out with high resolution and high sensitivity. Using the widely-known structure identification algorithm, DisPerSE, on a 3-dimensional (PPV) C$^{18}$O cube, we identified 625 relatively short (the longest being 1.74 pc) filaments over the entire cloud. We study the distribution of filament widths using FilChaP, a python package that we have developed and made publicly available. We find that the filaments identified in a 2 square degree PPV cube do not overlap spatially, except for the complex OMC-4 region that shows distinct velocity components along the line of sight. The filament widths vary between 0.02 and 0.3 pc depending on the amount of substructure that a filament possesses. The more substructure a filament has, the larger is its width. We also find that despite this variation, the filament width shows no anticorrelation with the central column density which is in agreement with previous Herschel observations.
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of all orders. We prove that if the initial condition of the network is a set of i.i.d. random variables and independent of the synaptic weights, each component of the limit system is described as the sum of the corresponding coordinate of the initial condition with a centered Gaussian process whose covariance function can be described in terms of a modified Bessel function. This process is not Markovian. The convergence is in law almost surely with respect to the random weights. Our method is essentially based on the method of moments to obtain a Central Limit Theorem.
A jet is a considerable amount of plasma being ejected from the chromosphere or lower corona into the higher corona and is a common phenomenon. Usually, a jet is triggered by a brightening or a flare, which provides the first driving force to push plasma upward. In this process, magnetic reconnection is thought to be the mechanism to convert magnetic energy into thermal, nonthermal, and kinetic energies. However, most jets could reach an unusual high altitude and end much later than the end of its associated flare. This fact implies that there is another way to continuously transfer magnetic energy into kinetic energy even after the reconnection. The picture described above is well known in the community, but how and how much magnetic energy is released through a way other than reconnection is still unclear. By studying a prominence-like jet observed by SDO/AIA and STEREO-A/EUVI, we find that the continuous relaxation of the post-reconnection magnetic field structure is an important process for a jet to climb up higher than it could through only reconnection. The kinetic energy of the jet gained through the relaxation is 1.6 times that gained from the reconnection. The resultant energy flux is hundreds of times larger than the flux required for the local coronal heating, suggesting that such jets are a possible source to keep the corona hot. Furthermore, rotational motions appear all the time during the jet. Our analysis suggests that torsional Alfv\'en waves induced during reconnection could not be the only mechanism to release magnetic energy and drive jets.
We present a systematic analysis of molecular oxygen (O$_2$) adsorption trends on bimetallic PtNi clusters and their monometallic counterparts supported on MgO(100), by means of periodic DFT calculations for sizes between 25 up to 58 atoms. O$_2$ adsorption was studied on a variety of inequivalent sites for different structural motifs, such as truncated octahedral (TO), cuboctahedral (CO), icosahedral (Ih) and decahedral (Dh) geometries. We found that O$_2$ prefers to bind on top of two metal atoms, parallel to the cluster, with an average chemisorption energy of 1.09 eV (PtNi), 1.07 eV (Pt) and 2.09 eV (Ni), respectively. The largest adsorption energy values are found to be along the edges between two neighbouring (111)/(111) and (111)/(100) facets; while FCC and HCP sites located on the (111) facets may show a chemisorption value lower 0.3 eV where often fast O$_2$ dissociation easily occurs. Our results show that, even though it is difficult to disentangle the geometrical and electronic effects on the oxygen molecule adsorption, there is a strong correlation between the calculated general coordination number (GCN) and the chemisorp- tion map. Finally, the inclusion of dispersion corrections (DFT-D) leads to an overall increase on the calculated adsorption energy values but with a negligible alteration on the general O$_2$ adsorption trends.
We present the Feynman integral reduction program Kira 1.2 and describe its new features and other changes w.r.t. the previous versions. The main new features include a much faster equation generator, more flexible seed specification options, several predefined integral orderings, the reduction of systems of user-provided equations and a new technique to simplify coefficients by sampling variables over integers. Furthermore, we provide a collection of recommendations on how to use the program efficiently. This version has overall improvements in runtime for all reduction tasks compared to the previous versions of Kira.
This article studies real roots of the flow polynomial $F(G,\lambda)$ of a bridgeless graph $G$. For any integer $k\ge 0$, let $\xi_k$ be the supremum in $(1,2]$ such that $F(G,\lambda)$ has no real roots in $(1,\xi_k)$ for all graphs $G$ with $|W(G)|\le k$, where $W(G)$ is the set of vertices in $G$ of degrees larger than $3$. We prove that $\xi_k$ can be determined by considering a finite set of graphs and show that $\xi_k=2$ for $k\le 2$, $\xi_3=1.430\cdots$, $\xi_4=1.361\cdots$ and $\xi_5=1.317\cdots$. We also prove that for any bridgeless graph $G=(V,E)$, if all roots of $F(G,\lambda)$ are real but some of these roots are not in the set $\{1,2,3\}$, then $|E|\ge |V|+17$ and $F(G,\lambda)$ has at least 9 real roots in $(1,2)$.
Given hypergraphs H and F, an F-factor in H is a spanning subgraph consisting of vertex disjoint copies of F. Let K_4^3-e denote the 3-uniform hypergraph on 4 vertices with 3 edges. We show that for \gamma>0 there exists an integer n_0 such that every 3-uniform hypergraph $H$ of order n > n_0 with minimum codegree at least (1/2+\gamma)n and 4|n contains a (K_4^3-e)-factor. Moreover, this bound is asymptotically the best possible and we further give a conjecture on the exact value of the threshold for the existence of a (K_4^3-e)-factor. Therefore, all minimum codegree thresholds for the existence of F-factors are known asymptotically for 3-uniform hypergraphs F on 4 vertices.
Simulations of structure formation in the Universe predict accretion shock waves at the boundaries of the large-scale structures as sheets, filaments, and clusters of galaxies. If magnetic fields are present at these shocks, particle acceleration should take place, and could contribute to the observed cosmic rays of high energies. When the radio plasma of an old invisible radio lobe is dragged into such a shock wave, the relativistic electron population will be reaccelerated and the plasma becomes radio-luminous again. Such tracers of the accretion shock waves are observed at the boundaries of some clusters of galaxies: the so-called cluster radio relics, which are large regions of diffuse radio emission, without any parent galaxy nearby. The observed properties of the cluster radio relics are naturally explained by accretion shock waves. Radio relics therefore give the first evidence for the existence of accretion shocks of the large-scale structure formation and they allow investigations of the shock properties.
The thermodynamic properties of {\alpha}-Al and other phases (GP zones, {\theta}'', {\theta}' and {\theta}) in the Al-rich part of the Al-Cu system have been obtained by means of the cluster expansion formalism in combination with statistical mechanics. This information was used to build the Al-rich part of the Al-Cu phase-diagram taking into account vibrational entropic contributions for {\theta}', as those of the other phases were negligible. The simulation predictions of the phase boundaries between {\alpha}-Al and either {\theta}'', {\theta}' or {\theta} phases as a function of temperature are in good agreement with experimental data and extend the phase boundaries to a wider temperature range. The DFT calculations reveal the presence of a number of metastable Guinier-Preston-zone type configurations that may coexist with {\alpha}-Al and {\theta}'' at low temperatures. They also demonstrate that {\theta}' is the stable phase below 550K but it is replaced by {\theta} above this temperature due to the vibrational entropic contribution to the Gibbs energy of {\theta}'. This work shows how the combination of cluster expansion and statistical mechanics can be used to expand our knowledge of the phase diagram of metallic alloys and to provide Gibbs free energies of different phases that can be used as input in mesoscale simulations of precipitation.
Parton recombination corrections to the standard spin-dependent Altarelli-Parisi evolution equation are considered in a nonlinear evolution equation. The properties of this recombination equation and its relation with the spin-averaged form are discussed.
Following a cell-method due to van Kampen for the calculation of a coarse-grained free energy functional for the van der Waals gas, we compute a corresponding entropy functional from microscopic principles. This entropy functional is one of the building blocks of the recently developed GENERIC framework. This framework allows to obtain in a thermodynamically consistent way the continuum hydrodynamic equations for a fluid able to display liquid-vapor coexistence. Surface tension appears naturally and the resulting model describes interfaces as diffuse regions, much in the same spirit as the gradient theory for equilibrium situations. We suggest that using interfacial forces in the integral form obtained in the microscopic derivation instead of third order derivatives of the density field might represent an advantage from a computational point of view.
A comprehensive study of impurity-induced magnetism in nonmagnetically (Mg${}^{2+}$) and magnetically (Co${}^{2+}$) doped PbNi${}_{2}$V${}_{2}$O${}_{8}$ compounds is given, using both macroscopic dc susceptibility and local-probe electron spin resonance (ESR) techniques. Magnetic coupling between impurity-liberated spins is estimated from a linewidth of low-temperature ESR signal in Mg-doped samples. In addition, in the case of magnetic cobalt dopants the impurity-host magnetic exchange is evaluated from the Co-induced contribution to the linewidth in the paramagnetic phase. The experimentally observed severe broadening of the ESR lines in the magnetically doped compounds with respect to nonmagnetic doping is attributed to a rapid spin-lattice relaxation of the Co${}^{2+}$ ions, which results in a bottleneck-type of temperature dependence of the induced linewidth. The exchange parameters obtained from the ESR analysis offer a satisfactory explanation of the observed low-temperature magnetization in doped samples.
We investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. For Reissner-Nordstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system. We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour. However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena. For Born-Infeld black holes we define a new thermodynamic quantity B conjugate to the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We demonstrate that this quantity is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.
X-ray transients, such as accreting neutron stars, periodically undergo outbursts, thought to be caused by a thermal-viscous instability in the accretion disk. Usually outbursts of accreting neutron stars are identified when the accretion disk has undergone an instability, and the persistent X-ray flux has risen to a threshold detectable by all sky monitors on X-ray space observatories. Here we present the earliest known combined optical, UV, and X-ray monitoring observations of the outburst onset of an accreting neutron star low mass X-ray binary system. We observed a significant, continuing increase in the optical i'-band magnitude starting on July 25, 12 days before the first X-ray detection with Swift/XRT and NICER (August 6), during the onset of the 2019 outburst of SAX J1808.4-3658. We also observed a 4 day optical to X-ray rise delay, and a 2 day UV to X-ray delay, at the onset of the outburst. We present the multiwavelength observations that were obtained, discussing the theory of outbursts in X-ray transients, including the disk instability model, and the implications of the delay. This work is an important confirmation of the delay in optical to X-ray emission during the onset of outbursts in low mass X-ray binaries, which has only previously been measured with less sensitive all sky monitors. We find observational evidence that the outburst is triggered by ionisation of hydrogen in the disk.
Tailoring the functional properties of advanced organic/inorganic heterogeonous devices to their intended technological applications requires knowledge and control of the microscopic structure inside the device. Atomistic quantum mechanical simulation methods deliver accurate energies and properties for individual configurations, however, finding the most favourable configurations remains computationally prohibitive. We propose a 'building block'-based Bayesian Optimisation Structure Search (BOSS) approach for addressing extended organic/inorganic interface problems and demonstrate its feasibility in a molecular surface adsorption study. In BOSS, a likelihood-free Bayesian scheme accelerates the identification of material energy landscapes with the number of sampled configurations during active learning, enabling structural inference with high chemical accuracy and featuring large simulation cells. This allowed us to identify several most favourable molecular adsorption configurations for $\mathrm{C}_{60}$ on the (101) surface of $\mathrm{TiO}_2$ anatase and clarify the key molecule-surface interactions governing structural assembly. Inferred structures were in good agreement with detailed experimental images of this surface adsorbate, demonstrating good predictive power of BOSS and opening the route towards large-scale surface adsorption studies of molecular aggregates and films.
About one percent of giants\upcite{Brown1989} are detected to have anomalously high lithium (Li) abundances in their atmospheres, conflicting directly with the prediction of the standard stellar evolution models\upcite{Iben1967}, and making the production and evolution of Li more intriguing, not only in the sense of the Big Bang nucleosynthesis\upcite{Cyburt2016,Spite1982} or the Galactic medium\upcite{Tajitsu2015}, but also the evolution of stars. Decades of efforts have been put into explaining why such outliers exist\upcite{Sackmann1999, Denissenkov2004, Charbonnel2010}, yet the origins of Li-rich giants are still being debated. Here we report the discovery of the most Li-rich giant known to date, with a super-high Li abundance of 4.51. This rare phenomenon was snapshotted together with another short-term event that the star is experiencing its luminosity bump on the red giant branch. Such high Li abundance indicates that the star might be at the very beginning of its Li-rich phase, which provides a great opportunity to investigate the origin and evolution of Li in the Galaxy. A detailed nuclear simulation is presented with up-to-date reaction rates to recreate the Li enriching process in this star. Our results provide tight constraints on both observational and theoretical points of view, suggesting that low-mass giants can produce Li inside themselves to a super high level via $^{7}$Be transportation during the red giant phase.
We prove that in every $2$-colouring of the edges of $K_\mathbb{N}$ there exists a monochromatic infinite path $P$ such that $V(P)$ has upper density at least ${(12+\sqrt{8})}/{17} \approx 0.87226$ and further show that this is best possible. This settles a problem of Erd\H{o}s and Galvin.
The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,\omega)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.
The time-odd triaxial relativistic mean field approach is developed and applied to the investigation of the ground-state properties of light odd-mass nuclei near the double-closed shells. The nuclear magnetic moments including the isoscalar and isovector ones are calculated and good agreement with Schmidt values is obtained. Taking $^{17}$F as an example, the splitting of the single particle levels (around $~0.7$ MeV near the Fermi level), the nuclear current, the core polarizations, and the nuclear magnetic potential, i.e., the spatial part of the vector potential, due to the violation of the time reversal invariance are investigated in detail.
Sunspot penumbrae show high-velocity patches along the periphery. The high-velocity downflow patches are believed to be the return channels of the Evershed flow. We aim to investigate their structure in detail using Hinode SOT/SP observations. We employ Fourier interpolation in combination with spatially coupled height dependent LTE inversions of Stokes profiles to produce high-resolution, height-dependent maps of atmospheric parameters of these downflows and investigate their properties. High-speed downflows are observed over a wide range of viewing angles. They have supersonic line-of-sight velocities, some in excess of 20km/s, and very high magnetic field strengths, reaching values of over 7 kG. A relation between the downflow velocities and the magnetic field strength is found, in good agreement with MHD simulations. The coupled inversion at high resolution allows for the accurate determination of small-scale structures. The recovered atmospheric structure indicates that regions with very high downflow velocities contain some of the strongest magnetic fields that have ever been measured on the Sun.
We review the state of the art in the problem of counting the number open knight tours, since the publication in internet of a computation of this quantity.
We prove formulas for the number of Jordan blocks of the maximal size for local monodromies of one-parameter degenerations of complex algebraic varieties where the bound of the size comes from the monodromy theorem. In case the general fibers are smooth and compact, the proof calculates some part of the weight spectral sequence of the limit mixed Hodge structure of Steenbrink. In the singular case, we can prove a similar formula for the monodromy on the cohomology with compact supports, but not on the usual cohomology. We also show that the number can really depend on the position of singular points in the embedded resolution even in the isolated singularity case, and hence there are no simple combinatorial formulas using the embedded resolution in general.
In this article, we discuss some classical problems in combinatorics which can be solved by exploiting analogues between graph theory and the theory of manifolds. One well-known example is the McMullen conjecture, which was settled twenty years ago by Richard Stanley by interpreting certain combinatorial invariants of convex polytopes as the Betti numbers of a complex projective variety. Another example is the classical parallel redrawing problem, which turns out to be closely related to the problem of computing the second Betti number of a complex compact $(\C^*)^n$-manifold.
Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin Weyl tensors are found in a closed form and are shown to have the double copy origin. The effect of higher-spin fields to form a strictly positive scalar condensate for any values of higher-spin charges is observed.