ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this document the density of electrically-charged positive and negative particles in a two component plasma (TCP) will be studied. Particularly, we focus on a two dimensional system confined in a large rectangular box for $\Gamma=2$ in the presence of two electric impurities. A method for solution, which will be called, {\it dimensional reduction}, will be applied in order to study the redistribution of electrically charged particles along the line joining both impurities. Numerical results, by means of a finite elements method approach, show, due to the electric field generated by the impurities, an increase in the density of charges of opposite sign in the neighborhood of each impurity. On the other hand, the presence of charges of the same sign diminishes in the same region due to the existing electric repulsion; some of the repelled particles accumulate in the border of the box. Numerical expansions around the borders of the impurities and the box show an almost linear power law relation of the net density for the particular cases that have been analyzed. It is also studied how the maximum and minimum values of the net density depend on the electric charges of the impurities, under some particular conditions.
The resistivity and Hall effect in CeNiSn are measured at temperatures down to 35 mK and in magnetic fields up to 20 T with the current applied along the {\it b} axis. The resistivity at zero field exhibits quadratic temperature dependence below $\sim$0.16 K with a huge coefficient of the $T^2$ term (54 $\mu$$\Omega$cm/K$^2$). The resistivity as a function of field shows an anomalous maximum and dip, the positions of which vary with field directions. Shubnikov-de Haas (SdH) oscillations with a frequency {\it F} of $\sim$100 T are observed for a wide range of field directions in the {\it ac} and {\it bc} planes, and the quasiparticle mass is determined to be $\sim$10-20 {\it m}$_e$. The carrier density is estimated to be $\sim10^{-3}$ electron/Ce. In a narrow range of field directions in the {\it ac} plane, where the magnetoresistance-dip anomaly manifests itself clearer than in other field directions, a higher-frequency ($F=300\sim400\text{T}$) SdH oscillation is found at high fields above the anomaly. This observation is discussed in terms of possible field-induced changes in the electronic structure.
It has been asserted in the literature that the analogy between the linear and first order slow motion approximation of Einstein equations of General Relativity (gravitomagnetic equations) and the Maxwell-Lorentz equations of electrodynamics breaks down if the gravitational potentials are time dependent.   In this work, we show that this assertion is not correct and it has arisen from an incorrect limit of the usual harmonic gauge condition, which drastically changes the physical content of the gravitomagnetic equations.
Despite the data labeling cost for the object detection tasks being substantially more than that of the classification tasks, semi-supervised learning methods for object detection have not been studied much. In this paper, we propose an Interpolation-based Semi-supervised learning method for object Detection (ISD), which considers and solves the problems caused by applying conventional Interpolation Regularization (IR) directly to object detection. We divide the output of the model into two types according to the objectness scores of both original patches that are mixed in IR. Then, we apply a separate loss suitable for each type in an unsupervised manner. The proposed losses dramatically improve the performance of semi-supervised learning as well as supervised learning. In the supervised learning setting, our method improves the baseline methods by a significant margin. In the semi-supervised learning setting, our algorithm improves the performance on a benchmark dataset (PASCAL VOC and MSCOCO) in a benchmark architecture (SSD).
The Coleman-Oort conjecture says that for large $g$ there are no positive-dimensional Shimura subvarieties of $\mathsf{A}_g$ generically contained in the Jacobian locus. Counterexamples are known for $g\leq 7$. They can all be constructed using families of Galois coverings of curves satisfying a numerical condition. These families are already classified in cases where: a) the Galois group is cyclic, b) it is abelian and the family is 1-dimensional, and c) $g\leq 9$. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for $g\leq 100$ there are no other families than those already known.
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric space, where the edge set is closed and nearby points have nearby graph neighborhoods.
The charge and spin Hall conductance of the two-dimensional hole gas within the Luttinger model with and without inversion symmetry breaking terms in a perpendicular magnetic field are studied, and two key phenomena are predicted. The sign of the spin Hall conductance is modulated periodically by the external magnetic field, which means a possible application in the future. Furthermore, a resonant spin Hall conductance in the two-dimensional hole gas with a certain hole density at a typical magnetic field is indicated, which implies a likely way to firmly establish the intrinsic spin Hall effect. The charge Hall conductance is unaffected by the spin-orbit coupling.
Contrary to wide-spread opinion that the final state interaction (FSI) enlarges the amplitude $<2\pi;I=0|K^0>$, we argue that FSI is not able to increase the absolute value of this amplitude.
We survey nearby and vanishing cycles for both perverse sheaves and D-modules under analytic setting. Following ideas of A. Beilinson, M. Kashiwara and M. Saito, we explain in detail the proof of the comparison theorem between them in the sense of Riemann-Hilbert correspondence.
We study strangeness (K^+, K^-, and Lambda) production and flow in Ni+Ni collisions at 1-2 AGeV, based on the relativistic transport model including the strangeness degrees of freedom. We find that strangeness spectra and flow are sensitive to the properties of strange hadrons in nuclear medium. The predictions of the chiral perturbation theory that the K^+ feels a weak repulsive potential and K^- feels a strong attractive potential are in good agreement with recent experimental data from FOPI and KaoS collaborations.
Spin transfer driven excitations in magnetic nanostructures are characterized by a relatively large microwave emission linewidth (10 -100 MHz). Here we investigate the role of thermal fluctuations as well as of the non-linear amplitude-phase coupling parameter and the amplitude relaxation rate to explain the linewidth broadening of in-plane precession modes induced in planar nanostructures. Experiments on the linewidth broadening performed on MgO based magnetic tunnel junctions are compared to the linewidth obtained from macrospin simulations and from evaluation of the phase variance. In all cases we find that the linewidth varies linearly with temperature when the amplitude relaxation rate is of the same order as the linewidth and when the amplitude-phase coupling parameter is relatively small. The small amplitude-phase coupling parameter means that the linewidth is dominated by direct phase fluctuations and not by amplitude fluctuations, explaining thus its linear dependence as a function of temperature.
We report the selection and spectroscopic confirmation of 129 new late-type (K3-M6) members of the Tuc-Hor moving group, a nearby (~40 pc), young (~40 Myr) population of comoving stars. We also report observations for 13/17 known Tuc-Hor members in this spectral type range, and that 62 additional candidates are likely to be unassociated field stars; the confirmation frequency for new candidates is therefore 129/191 = 67%. We have used RVs, Halpha emission, and Li6708 absorption to distinguish contaminants and bona fide members. Our expanded census of Tuc-Hor increases the known population by a factor of ~3 in total and by a factor of ~8 for members with SpT>K3, but even so, the K-M dwarf population of Tuc-Hor is still markedly incomplete. The spatial distribution of members appears to trace a 2D sheet, with a broad distribution in X and Y, but a very narrow distribution (+/-5 pc) in Z. The corresponding velocity distribution is very small, with a scatter of +/-1.1 km/s about the mean UVW velocity. We also show that the isochronal age (20--30 Myr) and the lithium depletion age (40 Myr) disagree, following a trend seen in other PMS populations. The Halpha emission follows a trend of increasing EW with later SpT, as seen for young clusters. We find that members have been depleted of lithium for spectral types of K7.0-M4.5. Finally, our purely kinematic and color-magnitude selection procedure allows us to test the efficiency and completeness for activity-based selection of young stars. We find that 60% of K-M dwarfs in Tuc-Hor do not have ROSAT counterparts and would be omitted in Xray selected samples. GALEX UV-selected samples using a previously suggested criterion for youth achieve completeness of 77% and purity of 78%. We suggest new selection criteria that yield >95% completeness for ~40 Myr populations.(Abridged)
We study the problem of two Dirac particles interacting through non-relativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single particle, due to the non-trivial coupling between the center-of-mass and the relative coordinates, even in the presence of central potentials. We focus on the case of zero total momentum, which is equivalent to that of a single particle in a Sutherland lattice. We show that zero-energy states induce striking new features such as discontinuities in the relative wave function, for particles interacting through a step potential, and a concentration of relative density near the classical turning point, if particles interact via a Coulomb potential. In the latter case we also find that the two-body system becomes unstable above a critical coupling. These phenomena may have bearing on the nature of strong coupling phases in graphene.
A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.
We consider a directed graph on the 2-dimensional integer lattice, placing a directed edge from vertex $(i_1,i_2)$ to $(j_1,j_2)$, whenever $i_1 \le j_1$, $i_2 \le j_2$, with probability $p$, independently for each such pair of vertices. Let $L_{n,m}$ denote the maximum length of all paths contained in an $n \times m$ rectangle. We show that there is a positive exponent $a$, such that, if $m/n^a \to 1$, as $n \to \infty$, then a properly centered/rescaled version of $L_{n,m}$ converges weakly to the Tracy-Widom distribution. A generalization to graphs with non-constant probabilities is also discussed.
I review the basic features of four dimensional Z_2 x Z_2 (shift) orientifolds with internal magnetic fields, describing two examples with N=1 supersymmetry. As in the corresponding six-dimensional examples, D9-branes magnetized along four internal directions can mimic D5-branes, even in presence of multiplets of image branes localized on different fixed tori. Chiral low-energy spectra can be obtained if the model also contains D5-branes parallel to the magnetized directions.
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of the $d$-dimensional toric code up to local unitary transformations and adding or removing ancilla qubits. Our result not only generalizes the proven equivalence for $d=2$, but also provides an explicit recipe of how to decouple independent components of the color code, highlighting the importance of colorability in the construction of the code. Moreover, for the $d$-dimensional color code with $d+1$ boundaries of $d+1$ distinct colors, we find that the code is equivalent to multiple copies of the $d$-dimensional toric code which are attached along a $(d-1)$-dimensional boundary. In particular, for $d=2$, we show that the (triangular) color code with boundaries is equivalent to the (folded) toric code with boundaries. We also find that the $d$-dimensional toric code admits logical non-Pauli gates from the $d$-th level of the Clifford hierarchy, and thus saturates the bound by Bravyi and K\"{o}nig. In particular, we show that the $d$-qubit control-$Z$ logical gate can be fault-tolerantly implemented on the stack of $d$ copies of the toric code by a local unitary transformation.
Context. We present very early optical lightcurves beginning 10 days before maximum of the Type IIn supernova 1998S, covering the first four months after discovery. Aims. We examine the light evolution and try to compare the lightcurves to two analytical models(Nakar & Sari(2010) and Rabinak & Waxman(2011)) for a red supergiant star. Methods. The photometry was carried at the 60-cm telescope of the Xinglong Station of China. Broadband filters Johnsons B, V and Cousins R were used. Results. The magnitude rose for the first few days and then dropped slowly afterwards. The two different models we use can fit the early lightcurves very well. The explosion date derived from the models is within the range of 1998 March 1.34 - 2.64(JD 2450873.84 - JD 2450875.14.) The radius of the progenitor is found to be ~ 300 Rsun and ~ 2000 Rsun for the model of Nakar & Sari(2010) and Rabinak & Waxman(2011) respectively. The constraint on mass and energy is not strong. The ranges of these two parameters are within that of a red supergiant.
We use early-time observations of He I 10830 \AA to measure the extent of upward mixing of radioactive material in SN 1987A. This work develops and extends the work of Graham (1988), and places constraints on actual explosion models. The presence of the He I 10830 \AA (2s^{3}S--2p^{3}P) line at $\geq 10$ days post-explosion implies re-ionisation by $\gamma$-rays from upwardly-mixed radioactive material produced during the explosion. Using the unmixed explosion model 10H (Woosley 1988) as well as mixed versions of it, we estimated the $\gamma$-ray energy deposition by applying a purely absorptive radiative transfer calculation. The deposition energy was used to find the ionisation balance as a function of radius, and hence the 2s$^{3}$S population density profile. This was then applied to a spectral synthesis model and the synthetic spectra were compared with the observations. Neither model 10H nor the mixed version, 10HMM, succeeded in reproducing the observed He I 10830 \AA line. The discrepancy with the data found for 10HMM is particularly significant, as this model has successfully reproduced the X-ray and $\gamma$-ray observations and the UVOIR light curve. We find that a match to the He I line profile is achieved by reducing the extent of mixing in 10HMM. Our reduced-mixing models also reproduce the observed $\gamma$-ray line light curves and the iron-group velocities deduced from late-time infrared line profiles. We suggest that the He I line method provides a more sensitive measure of the extent of mixing in a type II supernova explosion.
CO, $^{13}$CO and C$^{18}$O ${\it J}$ = 3--2 observations are presented of the Ophiuchus molecular cloud. The $^{13}$CO and C$^{18}$O emission is dominated by the Oph A clump, and the Oph B1, B2, C, E, F and J regions. The optically thin(ner) C$^{18}$O line is used as a column density tracer, from which the gravitational binding energy is estimated to be $4.5 \times 10^{39}$ J (2282 $M_\odot$ km$^2$ s$^{-2}$). The turbulent kinetic energy is $6.3 \times 10^{38}$ J (320 $M_\odot$ km$^2$ s$^{-2}$), or 7 times less than this, and therefore the Oph cloud as a whole is gravitationally bound. Thirty protostars were searched for high velocity gas, with eight showing outflows, and twenty more having evidence of high velocity gas along their lines-of-sight. The total outflow kinetic energy is $1.3 \times 10^{38}$ J (67 $M_\odot$ km$^2$ s$^{-2}$), corresponding to 21$\%$ of the cloud's turbulent kinetic energy. Although turbulent injection by outflows is significant, but does ${\it not}$ appear to be the dominant source of turbulence in the cloud. 105 dense molecular clumplets were identified, which had radii $\sim$ 0.01--0.05 pc, virial masses $\sim$ 0.1--12 $M_\odot$, luminosities $\sim$ 0.001--0.1 K~km s$^{-1}$ pc$^{-2}$, and excitation temperatures $\sim$ 10--50K. These are consistent with the standard GMC based size-line width relationships, showing that the scaling laws extend down to size scales of hundredths of a parsec, and to sub solar-mass condensations. There is however no compelling evidence that the majority of clumplets are undergoing free-fall collapse, nor that they are pressure confined.
We characterize the orientation of polar plumes as a tracer of the large-scale coronal magnetic field configuration. We monitor in particular the north and south magnetic pole locations and the magnetic opening during 2007-2008 and provide some understanding of the variations in these quantities. The polar plume orientation is determined by applying the Hough-wavelet transform to a series of EUV images and extracting the key Hough space parameters of the resulting maps. The same procedure is applied to the polar cap field inclination derived from extrapolating magnetograms generated by a surface flux transport model. We observe that the position where the magnetic field is radial (the Sun's magnetic poles) reflects the global organization of magnetic field on the solar surface, and we suggest that this opens the possibility of both detecting flux emergence anywhere on the solar surface (including the far side) and better constraining the reorganization of the corona after flux emergence.
Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, $\beta_0^{\rm mid} = p_{\rm gas} / p_B$. For $10^5 \geq \beta_0^{\rm mid} \geq 10$ the effective $\alpha$-viscosity parameter scales as a power-law. Dynamo activity persists up to and including $\beta_0^{\rm mid} = 10^2$, at which point the entire vertical column of the disc is magnetic pressure-dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state $\beta^{\rm mid}$ in our simulations is well-matched by the analytic model of Begelman et al. (2015) describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.
We present the results of 15 years of monitoring lensed quasars, which was conducted by the COSMOGRAIL programme at the Leonhard Euler 1.2m Swiss Telescope. The decade-long light curves of 23 lensed systems are presented for the first time. We complement our data set with other monitoring data available in the literature to measure the time delays in 18 systems, among which nine reach a relative precision better than 15% for at least one time delay. To achieve this, we developed an automated version of the curve-shifting toolbox PyCS to ensure robust estimation of the time delay in the presence of microlensing, while accounting for the errors due to the imperfect representation of microlensing. We also re-analysed the previously published time delays of RX J1131$-$1231 and HE 0435$-$1223, by adding six and two new seasons of monitoring, respectively, and confirming the previous time-delay measurements. When the time delay measurement is possible, we corrected the light curves of the lensed images from their time delay and present the difference curves to highlight the microlensing signal contained in the data. To date, this is the largest sample of decade-long lens monitoring data, which is useful to measure $H_0$ and the size of quasar accretion discs with microlensing as well as to study quasar variability.
Shear flows have an important impact on the dynamics in an assortment of different astrophysical objects including accreditation discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a fundamental understanding of the motion in stellar interiors where turbulent motions, mixing processes, as well as magnetic field generation takes place. Here, a linear stability analysis for a fully compressible fluid in a two-dimensional Cartesian geometry is carried out. Our study focuses on determining the critical Richardson number for different Mach numbers and the destabilising effects of high thermal diffusion. We find that there is a deviation of the predicted stability threshold for moderate Mach number flows along with a significant effect on the growth rate of the linear instability for small P\'eclet numbers. We show that in addition to a Kelvin-Helmholtz instability a Holmboe instability can appear and we discuss the implication of this in stellar interiors.
We present a method to calculate the Landau levels and the corresponding edge states of two dimensional (2D) crystals using as a starting point their electronic structure as obtained from standard density functional theory (DFT). The DFT Hamiltonian is represented in the basis of maximally localized Wannier functions. This defines a tight-binding Hamiltonian for the bulk that can be used to describe other structures, such as ribbons, provided that atomic scale details of the edges are ignored. The effect of the orbital magnetic field is described using the Peierls substitution in the hopping matrix elements. Implementing this approach in a ribbon geometry, we obtain both the Landau levels and the dispersive edge states for a series of 2D crystals, including graphene, Boron Nitride, MoS$_2$ , Black Phosphorous, Indium Selenide and MoO$_3$ . Our procedure can readily be used in any other 2D crystal, and provides an alternative to effective mass descriptions.