ShantanuT01/DACTYL-Pretraining huggingface dataset:
Here we generalized a previous model of gravastar consisted of an internal de Sitter spacetime, a dynamical infinitely thin shell with an equation of state, but now we consider an external de Sitter-Schwarzschild spacetime. We have shown explicitly that the final output can be a black hole, a "bounded excursion" stable gravastar, a stable gravastar, or a de Sitter spacetime, depending on the total mass of the system, the cosmological constants, the equation of state of the thin shell and the initial position of the dynamical shell. We have found that the exterior cosmological constant imposes a limit to the gravastar formation, i.e., the exterior cosmological constant must be smaller than the interior cosmological constant. Besides, we have also shown that, in the particular case where the Schwarzschild mass vanishes, no stable gravastar can be formed, but we still have formation of black hole.
For an ordered subset $S = \{s_1, s_2,\dots s_k\}$ of vertices and a vertex $u$ in a connected graph $G$, the metric representation of $u$ with respect to $S$ is the ordered $k$-tuple $ r(u|S)=(d_G(v,s_1), d_G(v,s_2),\dots,$ $d_G(v,s_k))$, where $d_G(x,y)$ represents the distance between the vertices $x$ and $y$. The set $S$ is a metric generator for $G$ if every two different vertices of $G$ have distinct metric representations. A minimum metric generator is called a metric basis for $G$ and its cardinality, $dim(G)$, the metric dimension of $G$. It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae and tight bounds for the metric dimension of strong product graphs.
We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $\Omega$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(\Omega))$, $\varepsilon\geq0$, integrability properties of the second spatial derivatives and of the time derivative of the solutions. Hence, for suitable $p$ and exponents $r,\,q$, by Sobolev embedding theorems, we deduce global regularity of $u$ and $\nabla u$ in H\"older spaces. Finally we prove a global pointwise bound for the solution under the assumption $p>\frac{2n}{n+2}$.
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for the reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested for solving the general problem of reconstructing binary matrices that are given by their discrete X-rays in a number of directions, but more work have to be done to handle the ill-posedness of the problem. We can tackle this ill-posedness by limiting the set of possible solutions, by using appropriate a priori information, to only those which are reasonably typical of the class of matrices which contains the unknown matrix that we wish to reconstruct. Mathematically, this information is modelled in terms of a class of binary matrices to which the solution must belong. Several papers study the problem on classes of binary matrices on which some connectivity and convexity constraints are imposed. We study the reconstruction problem on some new classes consisting of binary matrices with periodicity properties, and we propose a polynomial-time algorithm for reconstructing these binary matrices from their orthogonal discrete X-rays.
We present a range of steady-state photoionization simulations, corresponding to different assumed shell geometries and compositions, of the unseen postulated rapidly expanding outer shell to the Crab Nebula. The properties of the shell are constrained by the mass that must lie within it, and by limits to the intensities of hydrogen recombination lines. In all cases the photoionization models predict very strong emission from high ionization lines that will not be emitted by the Crab's filaments, alleviating problems with detecting these lines in the presence of light scattered from brighter parts of the Crab. The NIR [Ne VI] $\lambda$7.652 $\mu$m line is a particularly good case; it should be dramatically brighter than the optical lines commonly used in searches. The C IV $\lambda1549\AA$ doublet is predicted to be the strongest absorption line from the shell, which is in agreement with HST observations. We show that the cooling timescale for the outer shell is much longer than the age of the Crab, due to the low density. This means that the temperature of the shell will actually "remember" its initial conditions. However, the recombination time is much shorter than the age of the Crab, so the predicted level of ionization should approximate the real ionization. In any case, it is clear that IR observations present the best opportunity to detect the outer shell and so guide future models that will constrain early events in the original explosion.
Consider two graphs G_1 and G_2 on the same vertex set V and suppose that G_i has m_i edges. Then there is a bipartition of V into two classes A and B so that for both i=1,2 the number of edges between A and B in G_i is (1+o(1))m_i/2. This answers a question of Bollobas and Scott. We also prove results about partitions into more than two vertex classes.
Results of relativistic calculations of the direct knockout (DKO) mechanism for the photon induced removal of a proton from a target nucleus over a wide range of energies and nuclei are presented. Spectroscopic factors used in the calculations are fixed from consistent analyses of the quasifree electron scattering process (e,e'p). The results indicate that within the uncertainties of the model, the knockout contributions are generally close to the experimental data for missing momenta below approximately 500 MeV/c. This is in disagreement with nonrelativistic analyses which often find that the direct knockout contribution can be quite small compared to the data and that meson exchange corrections can be important. The present study suggests that meson exchange current contributions may not be as large when treated in a relativistic framework. We also point out some difficulties we encountered in analyzing the data for a 12C target at photon energies below 80 MeV.
The Self-similar-structure shell model (SSM) comes from the evolution of the conventional shell model (SM) and keeps the energy level of SM single particle harmonic oscillation motion. In SM, single particle motion is the positive harmonic oscillation and in SSM, the single particle motion is the negative harmonic oscillation. In this paper a nuclear evolution equation (NEE) is proposed. NEE describes the nuclear evolution process from gas state to liquid state and reveals the relations among SM, SSM and liquid drop model (DM). Based upon SSM and NEE theory, we propose the solution to long-standing problem of nuclear shell model single particle spin-orbit interaction energy . We demonstrate that the single particle motion in normal nuclear ground state is the negative harmonic oscillation of SSM[1][2][3][4]   Key words: negative harmonic oscillation, nuclear evolution equation, self-similar shell model
We present a set of experimentally feasible pulse sequences that implement any single-qubit gate on a singlet-triplet spin qubit and demonstrate that these new sequences are up to three times faster than existing sequences in the literature. We show that these sequences can be extended to incorporate built-in dynamical error correction, yielding gates that are robust to both charge and magnetic field noise and up to twice as fast as previous dynamically corrected gate schemes. We present a thorough comparison of the performance of our new sequences with that of several existing ones using randomized benchmarking, considering both quasistatic and $1/f^\alpha$ noise models. We provide our results both as a function of evolution time and as a function of the number of gates, which respectively yield both an effective coherence time and an estimate of the number of gates that can be performed within this coherence time. We determine which set of pulse sequences gives the best results for a wide range of noise strengths and power spectra. Overall, we find that the traditional, slower sequences perform best when there is no field noise or when the noise contains significant high-frequency components; otherwise, our new, fast sequences exhibit the best performance.
A 2-D version of the asymmetric exclusion model for granular sheared flows is presented. The velocity profile exhibits two qualitatively different behaviors, dependent on control parameters. For low friction, the velocity profile follows an exponential decay while for large friction the profile is more accurately represented by a Gaussian law. The phase transition occurring between these two behavior is identified by the appearance of correlations in the cluster size distribution. Finally, a mean--field theory gives qualitative and quantitative good agreement with the numerical results.
Hubble Space Telescope (HST) WFPC-2 I-band (F814W) images of three X-ray selected BL Lacertae objects (MS1221.8+2452, MS1407.9+5954, & MS2143.4+0704) reveal that each of these BL Lac objects is well-centered in an extended nebulosity that is consistent in brightness and morphology with being light from an elliptical galaxy at the previously reported redshifts of these BL Lac objects. Each of the detected host galaxies have radial surface brightness profiles that are well fit by a DeVaucouleurs' law with effective radii of between 3 to 12 kpc (H_0=50 km s^{-1} Mpc^{-1}, q_0 = 0). The absolute magnitudes of the host galaxies fall in the range -24.7 < M_I < -23.5, in the range of luminosities determined for other BL Lacertae object host galaxies. In addition to allowing the measurement of the host galaxy magnitudes and radial surface brightness profiles, the HST images allow a search for substructure in the host galaxies and the presence of close companion galaxies at spatial resolutions not yet achievable from the ground. While no evidence was found for any ``bars'' or spiral arms, ``boxy'' isophotes are present in the host galaxy of at least one of the three objects observed as part of this study (MS2143.4+0704). The apparent magnitudes and image properties of the companions of the BL Lac objects are catalogued as part of this work. The three BL Lacs appear to occur in diverse environments, from being fairly isolated (MS1221.8+2452) to possibly being a member of a rich group of galaxies (MS1407.9+5954).
Electrical spin transport and accumulation have been measured in highly Si doped Al0.3Ga0.7As utilizing a lateral spin transport device. Persistent photoconductivity allows for the tuning of the effective carrier density of the channel material in situ via photodoping. Hanle effect measurements are completed at various carrier densities and the measurements yield spin lifetimes on the order of nanoseconds, an order of magnitude smaller than in bulk GaAs. These measurements illustrate that this methodology can be used to obtain a detailed description of how spin lifetimes depend on carrier density in semiconductors across the metal-insulator transition.
We study the magnetization dynamics in a ferromagnet-insulator-superconductor tunnel junction and the associated buildup of the electrical polarization. We show that for an open circuit, the induced voltage varies strongly and nonmonotonically with the precessional frequency, and can be enhanced significantly by the superconducting correlations. For frequencies much smaller or much larger than the superconducting gap, the voltage drops to zero, while when these two energy scales are comparable, the voltage is peaked at a value determined by the driving frequency. We comment on the potential utilization of the effect for the low-temperature spatially-resolved spectroscopy of magnetic dynamics.
We consider the Wiener sausage for a Brownian motion up to time $t$ associated with a closed ball in even dimensional cases. We obtain the asymptotic expansion of the expected volume of the Wiener sausage for large $t$. The result says that the expansion has many $\log$ terms, which do not appear in odd dimensional cases.
Realistic caloric curves are obtained for $^{197}Au + ^{197}Au$ reaction with incident energy ranging from 35 to 130 MeV/nucleon in the dynamic statistical multifragmentation model. It is shown that for excitation energy 3 to 8 MeV/nucleon, the temperature remains constant in the range 5 to 6 MeV, which is close to experiment. The mechanism of energy deposition through the tripartition of colliding system envisaged in this model together with inter-fragment nuclear interaction are found to play important role. A possible signature of liquid-gas phase transition is seen in the specific heat distribution calculated from these caloric curves, and the critical temperature is found to be $\sim$ 6 to 6.5 MeV.
We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as $\chi(T)^{-1} - \chi(0)^{-1} \propto T^{\gamma}$, we find that $\chi(0)^{-1}$ decreases with increasing pressure and vanishes to zero at the critical pressure $P_{\rm c} \simeq 2$ GPa, with $\gamma~ (\simeq 0.5)$ unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above $P_{\rm c}$, the approximant undergoes a magnetic transition at $T \simeq 100$ mK. These results are contrasted with the fact that, in the quasicrystal, the quantum criticality is robust against the application of pressure. The applicability of the so-called $T/H$ scaling to the approximant is also discussed.
Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with certain block structures, and establish a CLT for the corresponding linear spectral statistics via the large-deviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be block-Wigner-type matrices. Further, we show that for certain estimator of such renormalized adjacency matrices, which will be no longer Wigner-type but share long-range non-decaying weak correlations among the entries, the linear spectral statistics of such estimators will still share the same limiting behavior as those of the block-Wigner-type matrices, thus enabling hypothesis testing about stochastic block model.
In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions.   Then we present a certain family of noncommutative random matrix models for the $(\alpha,q)$--deformed Gaussian random variables
We consider unitary transformations on a bipartite system A x B. To what extent entails the ability to transmit information from A to B the ability to transfer information in the converse direction? We prove a dimension-dependent lower bound on the classical channel capacity C(A<--B) in terms of the capacity C(A-->B) for the case that the bipartite unitary operation consists of controlled local unitaries on B conditioned on basis states on A. This can be interpreted as a statement on the strength of the inevitable backaction of a quantum system on its controller.   If the local operations are given by the regular representation of a finite group G we have C(A-->B)=log |G| and C(A<--B)=log N where N is the sum over the degrees of all inequivalent representations. Hence the information deficit C(A-->B)-C(A<--B) between the forward and the backward capacity depends on the "non-abelianness" of the control group. For regular representations, the ratio between backward and forward capacities cannot be smaller than 1/2. The symmetric group S_n reaches this bound asymptotically. However, for the general case (without group structure) all bounds must depend on the dimensions since it is known that the ratio can tend to zero.
We further explore the consequences of treating the X(3872) meson as a tetraquark bound state by analyzing its one-photon decay X => \gamma + J/psi in the framework of our approach developed in previous papers which incorporates quark confinement in an effective way. To introduce electromagnetism we gauge a nonlocal effective Lagrangian describing the interaction of the X(3872) meson with its four constituent quarks by using the P-exponential path-independent formalism. We calculate the matrix element of the transition X => \gamma+ J/psi and prove its gauge invariance. We evaluate the X=> \gamma + J/psi decay width and the longitudinal/transverse composition of the J/psi in this decay. For a reasonable value of the size parameter of the X(3872) meson we find consistency with the available experimental data. We also calculate the helicity and multipole amplitudes of the process, and describe how they can be obtained from the covariant transition amplitude by covariant projection.
We use the high angular resolution in the near-infrared of the WFC3 on HST to determine YHVz color-color selection criteria to identify and characterize 1.5<z<3.5 galaxies in the HUDF09 and ERS (GOODS-South) fields. The WFC3 NIR images reveal galaxies at these redshifts that were undetected in the rest-frame UV HUDF/GOODS images, as well as true centers and regular disks in galaxies classified as highly irregular in rest-frame UV light. Across the 1.5<z<2.15 redshift range, regular disks are unveiled in the WFC3 images of ~25% of both intermediate and high mass galaxies, i.e., above 10^10 Msun. Meanwhile, galaxies maintaining diffuse and/or irregular morphologies in the rest-frame optical light---i.e., not yet dynamically settled---at these epochs are almost entirely restricted to masses below 10^11 Msun. In contrast at 2.25 < z < 3.5 these diffuse and/or irregular structures overwhelmingly dominate the morphological mix in both the intermediate and high mass regimes, while no regular disks, and only a small fraction (25%) of smooth spheroids, are evident above 10^11 Msun. Strikingly, by 1.5 < z < 2.25 roughly 2 out of every 3 galaxies at the highest masses are spheroids. In our small sample, the fraction of star-forming galaxies at these mass scales decreases concurrently from ~60% to ~5%. If confirmed, this indicates that z~2 is the epoch of both the morphological transformation and quenching of star-formation which assemble the first substantial population of massive ellipticals.
Epitaxial graphene films were formed on the Si-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. A high-k gate stack on epitaxial graphene is realized by inserting a fully oxidized nanometer thin aluminum film as a seeding layer followed by an atomic-layer deposition process. The electrical properties of epitaxial graphene films are sustained after gate stack formation without significant degradation. At low temperatures, the quantum-Hall effect in Hall resistance is observed along with pronounced Shubnikov-de Hass oscillations in diagonal magneto-resistance of gated epitaxial graphene on SiC (0001).
The pressure dependence of melting temperatures for boron carbide and B4C-carbon eutectic has been studied up to 8 GPa, and it was found that in both cases the melting curves exhibit negative slope (-13\pm6 K/GPa), that is indicative of higher density of the melt as compared to the solid phase.
Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of their collimation angle. Modeling a jet break requires an understanding of the "jet spreading" process, whereby the jet transitions from a collimated outflow into the spherical Sedov-Taylor solution at late times. Currently, direct numerical calculations are the most accurate way to capture the deceleration and spreading process, as analytical models have previously given inaccurate descriptions of the dynamics. Here (in paper I) we present a new, semi-analytical model built empirically by performing relativistic numerical jet calculations and measuring the relationship between Lorentz factor and opening angle. We then calculate the Lorentz factor and jet opening angle as a function of shock radius and compare to the numerical solutions. Our analytic model provides an efficient means of computing synthetic GRB afterglow light curves and spectra, which is the focus of paper II.
This paper is an extension of our last 1D, N = 4 supersymmetric SYK paper [arXiv:2103.11899]. In this paper we introduced the complex linear supermultiplet (CLS), which is "usefully inequivalent" to the chiral supermultiplet. We construct three types of models based on the complex linear supermultiplet containing quartic interactions from modified CLS kinetic term, quartic interactions from 3-pt vertices integrated over the whole superspace, and 2(q-1)-pt interactions generated via superpotentials respectively. A strong evidence for the inevitability of dynamical bosons for 1D, N = 4 SYK is also presented.
Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline x)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of varieties whose Galois group is isomorphic to $\mathbb{Z}_p$. Our goal of this paper is to study the Newton polygon of the $L$-function associated to a finite character of $\mathbb{Z}_p$ and a generic polynomial whose convex hull is an $n$-dimensional paralleltope $\Delta$. We denote this polygon by $\mathrm{GNP}(\Delta)$. We prove a lower bound of $\mathrm{GNP}(\Delta)$, which is called the improved Hodge polygon $\mathrm{IHP}(\Delta)$. We show that $\mathrm{IHP}(\Delta)$ lies above the usual Hodge polygon $\mathrm{HP}(\Delta)$ at certain infinitely many points, and when $p$ is larger than a fixed number determined by $\Delta$, it coincides with $\mathrm{GNP}(\Delta)$ at these points. As a corollary, we roughly determine the distribution of the slopes of $\mathrm{GNP}(\Delta)$.
We have used 3-D smoothed particle hydrodynamical simulations to study the basic properties of the outflow that is created by a protostellar jet in a dense molecular cloud. The dynamics of the jet/cloud interaction is strongly affected by the cooling in the shocked gas behind the bow shock at the head of the jet. We show that this cooling is very rapid, with the cooling distance of the gas much less than the jet radius. Thus, although ambient gas is initially driven away from the jet axis by the high thermal pressure odf the post-shock gas, rapid cooling reduces the pressure and the outflow subsequently evolves in a momentum-conserving snowplow fashion. The velocity of the ambient gas is high in the vicinity of the jet head, but decreases rapidly as more material is swept up. Thus, this type of outflow produces extremely high velocity clumps of post shock gas which resemble the features seen in outflows. We have investigated the transfer of momentum from the jet to the ambient medium as a function of the jet parameters. We show that a low Mach number (<6) jet slows down rapidly because it entrains ambient material along its sides. On the other hand, the beam of a high Mach number jet is separated from the ambient gas by a low density cocoon of post-shock gas, and this jet transfers momentum to the ambient medium principally at the bow-shock. In high Mach number jets, as those from young stellar objects, the dominant interaction is therefore at the bow shock at the head of the jet.