ShantanuT01/DACTYL-Pretraining huggingface dataset:
Spectral index studies of halos, relics, and radio galaxies provide useful information on their origin and connection with merger processes. We present WSRT multi-wavelength observations of the galaxy cluster Abell 2255 at 25 cm, 85 cm, and 2 m. The spectral index images allowed us to study the integrated spectrum of halo and relic and to investigate the physical properties of the Beaver head-tail radio galaxy belonging to the cluster. In the radio halo, the spectral index is steeper at the center and flatter at the locations of the radio filaments, clearly detected at 25 cm. In the relics, the spectral index flattens, moving away from the cluster center. For the Beaver radio galaxy, the spectrum severely steepens from the head towards the end of the tail, because of the energy losses suffered by the relativistic particles. In the 2 m map, which is the first high-sensitivity image presented in the literature at such a long wavelength, a new Mpc-size emission region is detected between the known radio halo and the NW relic. Not detecting this feature in the more sensitive 85 cm observations implies that it must have a very steep spectrum (alpha <= -2.6). The observational properties of the radio halo suggest that either we are looking at a superposition of different structures (filaments in the foreground plus real halo in the background) seen in projection across the cluster center or that the halo is intrinsically peculiar. The newly detected extended region to the NW of the halo could be considered as an asymmetric extension of the halo itself. However, since radio halos are known in the literature as structures showing a regular morphology, the new feature could represent the first example of steep Mpc-size diffuse structures (MDS), detected around clusters at very low frequencies.
Multiple rebrightenings have been observed in the multiband afterglow of GRB 030329. Especially, a marked and quick rebrightening occurred at about t ~ 1.2 * 10^5 s. Energy injection from late and slow shells seems to be the best interpretation for these rebrightenings. Usually it is assumed that the energy is injected into the whole external shock. However, in the case of GRB 030329, the rebrightenings are so quick that the usual consideration fails to give a satisfactory fit to the observed light curves. Actually, since these late/slow shells coast freely in the wake of the external shock, they should be cold and may not expand laterally. The energy injection then should only occur at the central region of the external shock. Considering this effect, we numerically re-fit the quick rebrightenings observed in GRB 030329. By doing this, we were able to derive the beaming angle of the energy injection process. Our result, with a relative residual of only 5% - 10% during the major rebrightening, is better than any previous modeling. The derived energy injection angle is about 0.035. We assume that these late shells are ejected by the central engine via the same mechanism as those early shells that produce the prompt gamma-ray burst. The main difference is that their velocities are much slower, so that they catch up with the external shock very lately and manifest as the observed quick rebrightenings. If this were true, then the derived energy injection angle can give a good measure of the beaming angle of the prompt gamma-ray emission. Our study may hopefully provide a novel method to measure the beaming angle of gamma-ray bursts.
The derivation of Marko and Siggia's interpolation formula for the force-extension relation of the Worm-Like Chain Model (C.Bustamante, J.F.Marko, E.D.Siggia, and S.Smith, Science Vol.265, p.1599 (1994); J.F.Marko and E.D.Siggia, Macromolecules Vol.28, p.8759 (1995)) is retraced. Isotropy of space, resulting in rotational invariance of the free energy, is invoked together with analyticity. A new interpolation formula results for the force-extension relationship. It is as simple as the old one, but twice as close to the exact force-extension relationship. Application of the same reasoning to the second-order perturbative result obtained at strong force (J.D.Moroz and P.Nelson, Proc.Natl.Acad.Sci. USA Vol.94, p.14418 (1997)) results in yet a new interpolation formula, good to 1% at all forces.
Joining of dissimilar metals is required for numerous applications in industries such as chemical, energy and automotive. It is challenging due to differences in melting point, density, and thermal expansion of the metals being joined. Common welding techniques involve limiting melting and solidification to a narrow area leading to high thermal stresses and potentially brittle intermetallic phases. Furthermore, the geometric complexity of these welded joints can be rather limited. Additive Manufacturing (AM) presents new techniques for joining of dissimilar metals. One of the emerging methods is the building of functionally graded parts using Directed Energy Deposition (DED) to spatially vary composition. In this paper, a SS316L and C300 maraging steel couple were joined by DED and heat treated. 13 discrete composition layers were selected using metallurgical considerations, in order to ensure a smooth transition in properties and microstructure. The mechanical properties of the as-built joints were found to be similar to the SS part and no intermetallic phases were found in the interface.
We illustrate in a simple setting the instantaneous shock tracking approach to stability of viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a choice of the definition of instanteous location of a viscous shock-- we show that this choice is time-asymptotically equivalent both to the natural choice of least-squares fit pointed out by Goodman and to a simple phase condition used by Gu\`es, M\'etivier, Williams, and Zumbrun in other contexts. More generally, we show that it is asymptotically equivalent to any location defined by a localized projection
In this paper, we are concerned with semiclassical states to the following Sobolev critical Dirac equation with degenerate potential, \begin{align*} -\textnormal{i} \eps \alpha \cdot \nabla u + a \beta u + V(x) u=|u|^{q-2} u + |u| u \quad \mbox{in} \,\, \R^3, \end{align*} where $u:\mathbb{R}^3\rightarrow \mathbb{C}^4$, $2<q<3$, $\eps>0$ is a small parameter, $a>0$ is a constant, $\alpha=(\alpha_1, \alpha_2, \alpha_3)$, $\alpha_j$ and $\beta$ are $4 \times 4$ Pauli-Dirac matrices. We construct an infinite sequence of higher topological type semiclassical states with higher energies concentrating around the local minimum points of the degenerate potential $V$. The solutions are obtained from a minimax characterization of higher dimensional symmetric linking structure, which correspond to critical points of the underlying energy functional at energy levels where compactness condition breaks down. Our approach is variational, which mainly relies on penalization method and blow-up arguments along with local type Pohozaev identity.
IceCube is a 1 km^3 neutrino telescope currently under construction at the South Pole. The detector will consist of 5160 optical sensors deployed at depths between 1450 m and 2450 m in clear Antarctic ice distributed over 86 strings. An air shower array covering a surface area of 1 km2 above the in-ice detector will measure cosmic ray air showers in the energy range from 300 TeV to above 1 EeV. The detector is designed to detect neutrinos of all flavors: electron-, muon-, and tau-neutrinos. With 59 strings in operation in 2009, construction is 67% complete. Based on data taken to date, the observatory meets its design goals. Selected results will be presented.
We provide a new formulation of the Local Friendliness no-go theorem of Bong et al [Nat. Phys. 16, 1199 (2020)] from fundamental causal principles, providing another perspective on how it puts strictly stronger bounds on quantum reality than Bell's theorem. In particular, quantum causal models have been proposed as a way to maintain a peaceful coexistence between quantum mechanics and relativistic causality, while respecting Leibniz's methodological principle. This works for Bell's theorem but does not work for the Local Friendliness no-go theorem, which considers an extended Wigner's Friend scenario. More radical conceptual renewal is required; we suggest that cleaving to Leibniz's principle requires extending relativity to events themselves.
Along with the running of Large Hadron Collider (LHC) located at CERN in November 2009, a large number of data samples of $B_c$ meson have been collected and some hadronic $B_c$ decay modes have been measured by the LHC experiments. In view of the special and important roles of $B_c$ meson decays playing in the heavy flavor sector, we here give a short review on the status of two body hadronic decays $B_c \to M_1 M_2$ at both experimental and theoretical aspects. For the theoretical progresses, specifically, we will show lots of theoretical studies on two body hadronic $B_c$ decays involving pseudoscalar, vector, scalar, axial-vector, even tensor meson(s) in the final states by employing the perturbative QCD (pQCD) factorization approach. We will present a general analysis about the two-body hadronic decays of the heavy $B_c$ meson and also provide some expectations for the future developments.
In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\left. \begin{array}{rl} u_t+\partial_x^3 u+\partial_x \partial_y^2 u +u \partial_x u &\hspace{-2mm}=0,\qquad\qquad (x,y)\in\mathbb R^2,\; t\in\mathbb R,\\ u(x,y,0)&\hspace{-2mm}=u_0(x,y). \end{array} \right\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$H^s(\mathbb R^2) \cap L^2((1+x^2+y^2)^{r} dx dy),$$ with $s,r\in\mathbb R$.
We have extended the ANTARES code to simulate the coupling of pulsation with convection in Cepheid-like variables in an increasingly realistic way, in particular in multidimensions, 2D at this stage. Present days models of radially pulsating stars assume radial symmetry and have the pulsation-convection interaction included via model equations containing ad hoc closures and moreover parameters whose values are barely known. We intend to construct ever more realistic multidimensional models of Cepheids. In the present paper, the first of a series, we describe the basic numerical approach and how it is motivated by physical properties of these objects which are sometimes more, sometimes less obvious. - For the construction of appropriate models a polar grid co-moving with the mean radial velocity has been introduced to optimize radial resolution throughout the different pulsation phases. The grid is radially stretched to account for the change of spatial scales due to vertical stratification and a new grid refinement scheme is introduced to resolve the upper, hydrogen ionisation zone where the gradient of temperature is steepest. We demonstrate that the simulations are not conservative when the original weighted essentially non-oscillatory method implemented in ANTARES is used and derive a new scheme which allows a conservative time evolution. The numerical approximation of diffusion follows the same principles. Moreover, the radiative transfer solver has been modified to improve the efficiency of calculations on parallel computers. We show that with these improvements the ANTARES code can be used for realistic simulations of the convection-pulsation interaction in Cepheids. We discuss the properties of several models which include the upper 42% of a Cepheid along its radial coordinate, assume different opening angles, and are suitable for an in-depth study of convection and pulsation.
We show that the recent derivation that triangleland's topology and geometry is $S^2$ from Heron's formula does not extend to quadrilaterals by considering Brahmagupta, Bretschneider and Coolidge's area formulae. That $N$-a-gonland is more generally $CP^{N - 2}$ (with $CP^1 = S^2$ recovering the triangleland sphere) follows from Kendall's extremization that is habitually used in Shape Theory, or the generalized Hopf map. We further explain our observation of non-extension in terms of total area not providing a shape quantity for quadrilaterals. It is rather the square root of of sums of squares of subsystem areas that provides a shape quantity; we clarify this further in representation-theoretic terms. The triangleland $S^2$ moreover also generalizes to $d$-simplexlands being $S^{d(d + 1)/2 - 1}$ topologically by Casson's observation. For the 3-simplex - alias tetrahaedron - while volume provides a shape quantity and is specified by the della Francesca-Tartaglia formula, the analogue of finding Heron eigenvectors is undefined. $d$-volume moreover provides a shape quantity for the $d$-simplex, specified by the Cayley-Menger formula generalization of the Heron and della Francesca-Tartaglia formulae. While eigenvectors can be defined for the even-$d$ Cayley-Menger formulae, the dimension count does not however work out for these to provide on-sphere conditions. We finally point out the multiple dimensional coincidences behind the derivation of the space of triangles from Heron's formula. This article is a useful check on how far the least technically involved derivation of the smallest nontrivial shape space can be taken. This is significant since Shape Theory is a futuristic branch of mathematics, with substantial applications in both Statistics (Shape Statistics) and Theoretical Physics (Background Independence: of major relevance to Classical and Quantum Gravitational Theory).
We demonstrate that from a low energy perspective a viable breaking of the electroweak symmetry, as present in nature, can be achieved without the (negative sign) $\mu^2$ mass term in the Higgs potential, thereby avoiding completely the appearance of relevant operators, featuring coefficients with a positive mass dimension, in the theory. We show that such a setup is self consistent and not ruled out by Higgs physics. In particular, we point out that it is the lightness of the Higgs boson that allows for the electroweak symmetry to be broken dynamically via operators of $D\geq 4$, consistent with the power expansion. Beyond that, we entertain how this scenario might even be preferred phenomenologically compared to the ordinary mechanism of electroweak symmetry breaking, as realized in the Standard Model, and argue that it can be fully tested at the LHC. In an appendix, we classify UV completions that could lead to such a setup, considering also the option of generating all scales dynamically.
We consider the zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and Cauchy-Kowaleskaya theorem, Maekawa proved the local in time convergence of the Navier-Stokes equations in the half- plane to the Euler equations outside a boundary layer and to the Prandtl equations in the boundary layer. In this paper, we develop the direct energy method to generalize Maekawa's result to the half-space.
We show that the interaction of a particle with a directionally solidified interface induces the onset of morphological instability provided that the particle-interface distance falls below a critical value. This instability occurs at pulling velocities that are below the threshold for the onset of the Mullins-Sekerka instability. The expression for the critical distance reveals that this instability is manifested only for certain combinations of the physical and processing parameters. Its occurence is attributed to the reversal of the thermal gradient in the melt ahead of the interface and behind the particle.
A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a systematic scheme for constructing the dual descriptions is developed. The method, a purely Lagrangian approach, is based on a first order parent Lagrangian, from which the dual partners are generated. In particular, a family of theories which are dual to the massive spin two Fierz-Pauli field, both free and coupled to an external source, is constructed in terms of a third rank tensor which is taken as the basic configuration variable.
Let $C: y^2=ax^4+bx^2+c$, be an elliptic curve defined over $\mathbb Q$. A set of rational points $(x_i,y_i) \in C(\mathbb Q)$, $i=1,2,\cdots,$ is said to be a sequence of consecutive squares if $x_i= (u + i)^2$, $i=1,2,\cdots$, for some $u\in \mathbb Q$. Using ideas of Mestre, we construct infinitely many elliptic curves $C$ with sequences of consecutive squares of length at least $6$. It turns out that these 6 rational points are independent. We then strengthen this result by proving that for a fixed $6$-term sequence of consecutive squares, there are infinitely many elliptic curves $C$ with the latter sequence forming the $x$-coordinates of six rational points in $C(\mathbb Q)$.
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration.
In the s = 1/2 antiferromagnetic spin chain material TiPO4 the formation of a spin gap takes place in a two step process with two characteristic temperatures, T*=111 K and TSP=74 K. We observe an unusual lattice dynamics over a large temperature regime as well as evidence for an orbital instability preceding the spin-Peierls transition. We relate different intrachain exchange interactions of the high temperature compared to the spin-Peierls phase to a modification of the orbital ordering pattern. In particular, our observation of a high energy excitation of mixed electronic and lattice origin suggests an exotic dimerization process different from other spin-Peierls materials.
Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a N\'eel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin $S=1/2$ dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both a SO(4) formulation and bond-operators.
We study Shimura curves of PEL type in the space of polarised abelian varieties $A^{\delta}_p$ generically contained in the ramified Prym locus. We generalise to ramified double covers, the construction done in [10] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is ${\mathbb P}^1$. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.
In the present work, we address a class of Cahn-Hilliard equations characterized by a nonlinear diffusive dynamics and possibly containing an additional sixth order term. This model describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases (a surfactant) is added. However, the model is also closely connected with other Cahn-Hilliard-type equations relevant in different types of applications. We first discuss the existence of a weak solution to the sixth-order model in the case when the configuration potential of the system is of singular (e.g., logarithmic) type. Then, we study the behavior of the solutions in the case when the sixth order term is let tend to 0, proving convergence to solutions of the fourth order system in a special case. The fourth order system is then investigated by a direct approach and existence of a weak solution is shown under very general conditions by means of a fixed point argument. Finally, additional properties of the solutions, like uniqueness and parabolic regularization are discussed, both for the sixth order and for the fourth order model, under more restrictive assumptions on the nonlinear diffusion term.
Galaxy haloes contain fundamental clues about the galaxy formation and evolution process: hierarchical cosmological models predict haloes to be ubiquitous, and to be (at least in part) the product of past merger and/or accretion events. The advent of wide-field surveys in the last two decades has revolutionized our view of our own Galaxy and its closest "sister", Andromeda, revealing copious tidal streams from past and ongoing accretion episodes, as well as doubling the number of their known faint satellites. The focus shall now be shifted to galaxy haloes beyond the Local Group: resolving individual stars over significant areas of galaxy haloes will enable estimates of their ages, metallicities and gradients. The valuable information collected for galaxies with a range of masses, morphologies and within diverse environments will ultimately test and quantitatively inform theoretical models of galaxy formation, and shed light onto the many challenges faced by simulations on galactic scales.
The x-ray process is modelled using integer compositions as a two dimensional analogue of the object being x-rayed, where the examining rays are modelled by diagonal lines with equation $x-y=n$ for non negative integers $n$. This process is essentially parameterised by the degree to which the x-rays are contained inside a particular composition. So, characterising the process translates naturally to obtaining a generating function which tracks the number of "staircases" which are contained inside arbitrary integer compositions of $n$. More precisely, we obtain a generating function which counts the number of times the staircase $1^+2^+3^+\cdots m^+$ fits inside a particular composition. The main theorem establishes this generating function \begin{equation*} F= \dfrac {k_{m}-\frac {qx^{m}y}{1-x}k_{m-1}}{(1-q)x^{\binom {m+1}{2}}\left(\frac{y}{1-x}\right)^{m}+\frac{1-x-xy}{1-x}\left(k_{m}-\frac{qx^{m}y}{1-x}k_{m-1}\right)}. \end{equation*} where \begin{equation} k_{m}=\sum_{j=0}^{m-1}x^{mj-\binom {j}{2}}\left(\frac {y}{1-x}\right)^{j}. \end{equation} Here $x$ and $y$ respectively track the composition size and number of parts, whilst $q$ tracks the number of such staircases contained.
The "main sequence of galaxies" $-$ defined in terms of the total star formation rate $\psi$ vs. the total stellar mass $M_*$ $-$ is a well-studied tight relation that has been observed at several wavelengths and at different redshifts. All earlier studies have derived this relation from integrated properties of galaxies. We recover the same relation from an analysis of spatially-resolved properties, with integral field spectroscopic (IFS) observations of 306 galaxies from the CALIFA survey. We consider the SFR surface density in units of log(M$_{\odot}$ yr$^{-1}$ Kpc$^{-2}$) and the stellar mass surface density in units of log(M$_{\odot}$ Kpc$^{-2}$) in individual spaxels which probe spatial scales of 0.5-1.5 Kpc. This local relation exhibits a high degree of correlation with small scatter ($\sigma = 0.23$ dex), irrespective of the dominant ionisation source of the host galaxy or its integrated stellar mass. We highlight: $(i)$ the integrated star formation main sequence formed by galaxies whose dominant ionisation process is related to star formation, for which we find a slope of 0.81 $\pm 0.02$; (ii) the spatially-resolved relation obtained with the spaxel analysis, we find a slope of 0.72 $\pm 0.04$; (iii) for the integrated main sequence we identified also a sequence formed by galaxies that are dominated by an old stellar population, which we have called the retired galaxies sequence.