ShantanuT01/DACTYL-Pretraining huggingface dataset:
We predict cosmological constraints for forthcoming surveys using Superluminous Supernovae (SLSNe) as standardisable candles. Due to their high peak luminosity, these events can be observed to high redshift (z~3), opening up new possibilities to probe the Universe in the deceleration epoch. We describe our methodology for creating mock Hubble diagrams for the Dark Energy Survey (DES), the "Search Using DECam for Superluminous Supernovae" (SUDSS) and a sample of SLSNe possible from the Large Synoptic Survey Telescope (LSST), exploring a range of standardisation values for SLSNe. We include uncertainties due to gravitational lensing and marginalise over possible uncertainties in the magnitude scale of the observations (e.g. uncertain absolute peak magnitude, calibration errors). We find that the addition of only ~100 SLSNe from SUDSS to 3800 Type Ia Supernovae (SNe Ia) from DES can improve the constraints on w and Omega_m by at least 20% (assuming a flat wCDM universe). Moreover, the combination of DES SNe Ia and 10,000 LSST-like SLSNe can measure Omega_m and w to 2% and 4% respectively. The real power of SLSNe becomes evident when we consider possible temporal variations in w(a), giving possible uncertainties of only 2%, 5% and 14% on Omega_m, w_0 and w_a respectively, from the combination of DES SNe Ia, LSST-like SLSNe and Planck. These errors are competitive with predicted Euclid constraints, indicating a future role for SLSNe for probing the high redshift Universe.
In Theorem 1.5 of [5] an estimate from below is given for nonnegative supersolutions of parabolic equations in terms of the measure of the set where the right-hand side is less than $-1$. The given proof contains many interesting details which are certainly useful in many other situations. However, as long as the statement of Theorem 1.5 of \cite{JL} is concerned, it can be proved in a much shorter way, which we present here.
In this paper we prove global bounds on the spatial gradient of viscosity solutions to second order linear and nonlinear parabolic equations in $(0,T) \times \R^N$. Our assumptions include the case that the coefficients be both unbounded and with very mild local regularity (possibly weaker than the Dini continuity), the estimates only depending on the parabolicity constant and on the modulus of continuity of coefficients (but not on their $L^{\infty}$-norm). Our proof provides the analytic counterpart to the probabilistic proof used in Priola and Wang (J. Funct. Anal. 2006) to get this type of gradient estimates in the linear case. We actually extend such estimates to the case of possibly unbounded data and solutions as well as to the case of nonlinear operators including Bellman-Isaacs equations. We investigate both the classical regularizing effect (at time $t>0$) and the possible conservation of Lipschitz regularity from $t=0$, and similarly we prove global H\"older estimates under weaker assumptions on the coefficients. The estimates we prove for unbounded data and solutions seem to be new even in the classical case of linear equations with bounded and H\"older continuous coefficients. Applications to Liouville type theorems are also given in the paper. Finally, we compare in an appendix the analytic and the probabilistic approach discussing the analogy between the doubling variables method of viscosity solutions and the probabilistic coupling method.
It is now believed that magnetohydrodynamic equilibria can exist in stably stratified stars due to the seminal works of Braithwaite & Spruit (2004) and Braithwaite & Nordlund (2006). What is still not known is whether magnetohydrodynamic equilibria can exist in a barotropic star, in which stable stratification is not present. It has been conjectured by Reisenegger (2009) that there will likely not exist any magnetohydrodynamical equilibria in barotropic stars. We aim to test this claim by presenting preliminary MHD simulations of barotropic stars using the three dimensional stagger code of Nordlund & Galsgaard (1995).
Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple structure. To explain these discrepancies we derive a stochastic growth equation that describes the evolution of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. Exploring the connection between the ion-sputtering problem and the Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that morphological transitions may take place when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied. Furthermore, the discussed methods allow us to calculate analytically the ion-induced surface diffusion coefficient, that can be compared with experiments. Finally, we use numerical simulations of a one dimensional sputtering model to investigate certain aspects of the ripple formation and roughening.
We carry out the Hamiltonian formulation of the three- dimensional gravitational teleparallelism without imposing the time gauge condition, by rigorously performing the Legendre transform. Definition of the gravitational angular momentum arises by suitably interpreting the integral form of the constraint equation Gama^ik=0 as an angular momentum equation. The gravitational angular momentum is evaluated for the gravitational field of a rotating BTZ black hole.
We have performed an isophotal analysis of galaxies in the distant (z=0.4) cluster Cl0939+4713 (Abell 851), using post-refurbished Hubble Space Telescope images. Morphological type estimates for the galaxies are given. A rigorous comparison of the properties of the types shows that early-type galaxies in Cl0939+4713 are, within the present statistical or systematic errors, indistinguishable from their counterparts in Coma in all their studied properties, namely ellipticity profile, slope of the color-magnitude relation from the near-ultraviolet to the near-infrared colors, mean surface brightness and luminosity function in the restframe photographic J band, homogeneity in color (around the color-magnitude relation). Furthermore ellipticals and lenticulars are separately homogeneous in their mean surface brightness, and have similar relative mean surface brightnesses in both clusters. Spirals are overabundant in Cl0939+4713 with respect to Coma, but twice less than previously estimated, and are more similar to field spirals than to cluster spirals. We suggest that the differences in the photometric properties of the spirals in the two clusters arise from differences in cluster gas density distribution which ultimately bring star formation in the spirals to a stop in Coma, but not in Cl0939+4713. The morphological types are segregated along a privileged direction that coincides with the position angle of the major axis of the outer X-ray isophotes in the cluster, just like in Coma and Perseus.
We measure the fluctuations of the position of a Brownian particle confined by an optical trap in an aging gelatin droplet after a fast quench. Its linear response to an external perturbation is also measured. We compute the spontaneous heat flux from the particle to the bath due to the nonequilibrium formation of the gel. We show that the mean heat flux is quantitatively related to the violation of the equilibrium fluctuation-dissipation theorem as a measure of the broken detailed balance during the aging process.
We report a measurement of the Type Ia supernova (SN Ia) rate in galaxy clusters at 0.9 < z < 1.45 from the Hubble Space Telescope (HST) Cluster Supernova Survey. This is the first cluster SN Ia rate measurement with detected z > 0.9 SNe. Finding 8 +/- 1 cluster SNe Ia, we determine a SN Ia rate of 0.50 +0.23-0.19 (stat) +0.10-0.09 (sys) SNuB (SNuB = 10^-12 SNe L_{sun,B}^-1 yr^-1). In units of stellar mass, this translates to 0.36 +0.16-0.13 (stat) +0.07-0.06 (sys) SNuM (SNuM = 10^-12 SNe M_sun^-1 yr^-1). This represents a factor of approximately 5 +/- 2 increase over measurements of the cluster rate at z < 0.2. We parameterize the late-time SN Ia delay time distribution with a power law (proportional to t^s). Under the assumption of a cluster formation redshift of z_f = 3, our rate measurement in combination with lower-redshift cluster SN Ia rates constrains s = -1.41 +0.47/-0.40, consistent with measurements of the delay time distribution in the field. This measurement is generally consistent with expectations for the "double degenerate" scenario and inconsistent with some models for the "single degenerate" scenario predicting a steeper delay time distribution at large delay times. We check for environmental dependence and the influence of younger stellar populations by calculating the rate specifically in cluster red-sequence galaxies and in morphologically early-type galaxies, finding results similar to the full cluster rate. Finally, the upper limit of one host-less cluster SN Ia detected in the survey implies that the fraction of stars in the intra-cluster medium is less than 0.47 (95% confidence), consistent with measurements at lower redshifts.
We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into $GL_n$. Existing theorems require that the residual representation have 'big' image, in a certain technical sense. Our theorems are based on a strengthening of the Taylor-Wiles method which allows one to weaken this hypothesis.
Garbagnati has constructed certain surfaces of general type that are bidouble planes as well as double covers of K3 surfaces. In this note, we study the Chow groups (and Chow motive) of these surfaces.
We provide new evidence for the gauge/string duality between the baryonic branch of the cascading SU(k(M+1)) \times SU(kM) gauge theory and a family of type IIB flux backgrounds based on warped products of the deformed conifold and R^{3,1}. We show that a Euclidean D5-brane wrapping all six deformed conifold directions can be used to measure the baryon expectation values, and present arguments based on kappa-symmetry and the equations of motion that identify the gauge bundles required to ensure worldvolume supersymmetry of this object. Furthermore, we investigate its coupling to the pseudoscalar and scalar modes associated with the phase and magnitude, respectively, of the baryon expectation value. We find that these massless modes perturb the Dirac-Born-Infeld and Chern-Simons terms of the D5-brane action in a way consistent with our identification of the baryonic condensates. We match the scaling dimension of the baryon operators computed from the D5-brane action with that found in the cascading gauge theory. We also derive and numerically evaluate an expression that describes the variation of the baryon expectation values along the supergravity dual of the baryonic branch.
The classical Orr-Sommerfeld equations are the resolvent equations of the linearized Navier Stokes equations around a stationary shear layer profile in the half plane. In this paper, we derive pointwise bounds on the Green function of the Orr Sommerfeld problem away from its critical layers.
Self-similarity was recently introduced as a measure of inter-class congruence for classification of actions. Herein, we investigate the dual problem of intra-class dissimilarity for classification of action styles. We introduce self-dissimilarity matrices that discriminate between same actions performed by different subjects regardless of viewing direction and camera parameters. We investigate two frameworks using these invariant style dissimilarity measures based on Principal Component Analysis (PCA) and Fisher Discriminant Analysis (FDA). Extensive experiments performed on IXMAS dataset indicate remarkably good discriminant characteristics for the proposed invariant measures for gender recognition from video data.
The inevitable spread in properties of the toroidal obscuration of active galactic nuclei (AGNs) invalidates the widespread notion that type 1 and 2 AGNs are intrinsically the same objects, drawn randomly from the distribution of torus covering factors. Instead, AGNs are drawn \emph{preferentially} from this distribution; type 2 are more likely drawn from the distribution higher end, type 1 from its lower end. Type 2 AGNs have a higher IR luminosity, lower narrow-line luminosity and a higher fraction of Compton thick X-ray obscuration than type 1. Meaningful studies of unification statistics cannot be conducted without first determining the intrinsic distribution function of torus covering factors.
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way the complexity order of the standard Monte Carlo algorithm ($\varepsilon^{-3}$ in the case of a first order scheme and $\varepsilon^{-2.5}$ in the case of a second order scheme) can be reduced down to $\varepsilon^{-2+\delta}$ for any $\delta\in [0,0.25)$ with $\varepsilon$ being the precision to be achieved. These theoretical results are illustrated by several numerical examples.
The chain-like system Ba_{3}Cu_{3}Sc_4O_{12} has potentially interesting magnetic properties due to the presence of Cu^{2+} and a structure-suggested low-dimensionality. We present magnetization M versus magnetic field H and temperature T, T- and H-dependent heat-capacity C_{p}, ^{45}Sc nuclear magnetic resonance (NMR), muon spin rotation ({\mu}SR), neutron diffraction measurements and electronic structure calculations for Ba_{3}Cu_{3}Sc_{4}O_{12}. The onset of magnetic long-range antiferromagnetic order at T_{N} ~16 K is consistently evidenced from the whole gamut of our data. A significant sensitivity of T_{N} to the applied magnetic field H (T_{N}~0 K for H=70 kOe) is also reported. Coupled with a ferromagnetic Curie-Weiss temperature ({\theta}_{CW}~65 K) in the susceptibility (from a 100 K-300 K fit), it is indicative of competing ferromagnetic and antiferromagnetic interactions. These indications are corroborated by our density functional theory based electronic structure calculations where we find the presence of significant ferromagnetic couplings between some copper ions whereas AF couplings were present between some others. Our experimental data, backed by our theoretical calculations, rule out one-dimensional magnetic behaviour suggested by the structure and the observed long-range order is due to the presence of non-negligible magnetic interactions between adjacent as well as next-nearest chains.
Numerical simulations of magneto-convection have greatly expanded our understanding of stellar interiors and stellar magnetism. Recently, fully compressible hydrodynamical simulations of full-star models have demonstrated the feasibility of studying the excitation and propagation of pressure and internal gravity waves in stellar interiors, which would allow for a direct comparison with asteroseismological measurements. However, the impact of magnetic fields on such waves has not been taken into account yet in three-dimensional simulations. We conduct a proof of concept for the realization of three-dimensional, fully compressible, magneto-hydrodynamical numerical simulations of stellar interiors with the RAMSES code. We adapted the RAMSES code to deal with highly subsonic turbulence, typical of stellar convection, by implementing a well-balanced scheme in the numerical solver. We then ran and analyzed three-dimensional hydrodynamical and magneto-hydrodynamical simulations with different resolutions of a plane-parallel convective envelope on a Cartesian grid. Both hydrodynamical and magneto-hydrodynamical simulations develop a quasi-steady, turbulent convection layer from random density perturbations introduced over the initial profiles. The convective flows are characterized by small-amplitude fluctuations around the hydrodynamical equilibrium of the stellar interior, which is preserved over the whole simulation time. Using our compressible well-balanced scheme, we were able to model flows with Mach numbers as low as $\mathcal{M} \sim 10^{-3}$, but even lower Mach number flows are possible in principle. In the magneto-hydrodynamical runs, we observe an exponential growth of magnetic energy consistent with the action of a small-scale dynamo. (Abridged)
Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and one-half spin) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic interaction vertices which we refer to as first-derivative form and higher-derivative form. All cubic interaction vertices are built by using the first-derivative form.
This paper presents a simple, one-dimensional model of a randomly advected passive scalar. The model exhibits anomalous inertial range scaling for the structure functions constructed from scalar differences. The model provides a simple computational test for recent ideas regarding closure and scaling for randomly advected passive scalars. Results suggest that high order structure function scaling depends on the largest velocity eddy size, and hence scaling exponents may be geometry-dependent and non-universal.
We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for $\de$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with $|\om(n)-\log_2 n|\le (\log_2 n)^{\de}$ obey the Poisson distribution law.
A large fraction of the previously estimated WMAP CMB quadrupole signal would be an artefact of incorrect Doppler dipole subtraction if the hypothesis of a small timing interpolation error were correct. Observations of bright foreground objects constitute part of the time-ordered-data (TOD). Scans of an object in different directions should be shifted by the would-be timing error, causing a blurring effect. Three half-years of the calibrated, filtered WMAP TOD are compiled individually for the four W band differencing assemblies (DA's), with no masking of bright objects, giving 12 maps for each timing offset. Percentiles of the temperature-fluctuation distribution in each map at HEALPix resolution N_side=2048 are used to determine the dependence of all-sky image sharpness on the timing offset. In the W band, the 99.999% percentile, i.e. the temperature fluctuation in the approx 503-rd brightest pixel, is the least noisy percentile. Using this statistic, the hypothesis that a -25.6 ms offset relative to the timing adopted by the WMAP collaboration gives a focus at least as sharp as the uncorrected timing is rejected at 4.6\sigma significance. The Q and V band maps also reject the -25.6 ms offset hypothesis at high statistical significance. The requirement that the correct choice of timing offset must maximise image sharpness implies that the hypothesis of a timing error in the WMAP collaboration's compilation of the WMAP calibrated, filtered TOD is rejected at high statistical significance in each of the Q, V and W wavebands. However, the hypothesis that a timing error was applied during calibration of the raw TOD, leading to a dipole-induced difference signal, is not excluded by this method.
DEEP is a two-phase spectral survey of faint field galaxies with the Keck Telescopes. The goals include exploring galaxy formation and evolution, mapping distant large scale structures, and constraining cosmology. DEEP, since its inception in the early 1990's, has been distinguished by an emphasis on studying the kinematics and masses of distant galaxies. The major DEEP survey in the second phase (DEEP2) is scheduled to begin in 2002 using a new spectrograph and will mainly aim for a sample of 50,000 galaxies to I ~ 23. Until then, the first phase of DEEP science programs will have been concentrating on using existing Keck spectrographs to undertake spectral surveys of over 1000 galaxies that have also been observed with HST. I will highlight the study of rotation curves of distant spirals; the fundamental plane of faint, high-redshift E/S0s; the narrow velocity widths seen in luminous blue compact galaxies; and the diversity of kinematics seen in a small sample of high redshift (z ~ 3) galaxies. These DEEP pilot programs have clearly demonstrated the feasibility, importance, and potential of using kinematics to better understand distant galaxies.
We report microscopic mechanisms for an unusual magnetization reversal behavior in Co/Pt multilayers where some of the first-order reversal curves protrude outside of the major loop. Transmission x-ray microscopy reveals a fragmented stripe domain topography when the magnetic field is reversed prior to saturation, in contrast to an interconnected pattern when reversing from a saturated state. The different domain nucleation and propagation behaviors are due to unannihilated domains from the prior field sweep. These residual domains contribute to random dipole fields that impede the subsequent domain growth and prevent domains from growing as closely together as for the interconnected pattern.
We consider the spatial spin correlations around a partially screened spin-1 magnetic moment in a metal exhibiting the underscreened Kondo effect. We find that the underscreening of the impurity spin results in spatial spin correlations that are more pronounced as compared to the fully screened Kondo effect; their power-law decay is weaker because of characteristic logarithmic corrections at large distances. The spin correlator also changes sign as a function of distance to the impurity allowing for ferromagnetic correlations between conduction electron spin density and the local moment. The numerical findings are shown to be in agreement with the predictions deriving from an effective ferromagnetic Kondo Hamiltonian.
We consider the Dirichlet boundary value problem for nonlinear systems of partial differential equations with p-structure. We choose two representative cases: the "full gradient case", corresponding to a p-Laplacian, and the "symmetric gradient case", arising from mathematical physics. The domain is either the "cubic domain" (see the definition below) or a bounded open subset of R^3 with a smooth boundary. We are interested in regularity results, up to the boundary, for the second order derivatives of the velocity field. Depending on the model and on the range of p, p<2 or p>2, we prove different regularity results. It is worth noting that in the full gradient case with p<2 we cover the degenerate case and obtain W^{2,q}-global regularity results, for arbitrarily large values of q.
This paper gives the first affirmative answer to the question of the global existence of Boltzmann equations without angular cutoff in the $L^\infty$-setting. In particular, we show that when the initial data is close to equilibrium and the perturbation is small in $L^2 \cap L^\infty$ with a polynomial decay tail, the Boltzmann equation has a global solution in the weighted $L^2\cap L^\infty$-space. In order to overcome the difficulties arising from the singular cross-section and the low regularity, a De Giorgi type argument is crafted in the kinetic context with the help of the averaging lemma. More specifically, we use a strong averaging lemma to obtain suitable $L^p$-estimates for level-set functions. These estimates are crucial for constructing an appropriate energy functional to carry out the De Giorgi argument. Similar as in \cite{AMSY}, we extend local solutions to global ones by using the spectral gap of the linearised Boltzmann operator. The convergence to the equilibrium state is then obtained as a byproduct with relaxations shown in both $L^2$ and $L^\infty$-spaces.