ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the energy critical four dimensional semi-linear heat equation \[ \partial_{t}v-\Delta v-v^{3}=0, \quad(t,x)\in \mathbb{R}\times \mathbb{R}^4. \] Formal computation of Filippas et al. (R. Soc. Lond. Proc. 2000) conjectures the existence of a sequence of type II blow-up solutions with various blow-up rates \[ \|v(t)\|_{L^\infty(\mathbb{R}^4)}\approx \frac{|\log(T-t)|^{\frac{2L}{2L-1}}}{(T-t)^L} ,\quad L=1,2,\cdots.\] Schweyer (J. Funct. Anal. 2012) rigorously constructs a type II blow-up solution for the case $L=1$. In this paper, we show the existence of type II blow-up solution for $L=2$. The method here could be generalized to deal with all the cases $L\geq 2$.
When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided. Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids. However, little is known about the level repulsion when more than two quasiparticles are present; for example, in an open quantum system where a quasiparticle can spontaneously decay into many particle continuum. Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine resolution neutron spectroscopy study of magnetic quasiparticles in a frustrated quantum magnet BiCu2PO6, we observe a renormalization of quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states. Our results have a broadimplication for understanding open quantum systems described by non-hermitian Hamiltonian.
We study the limit behaviour of a class of random walk models taking values in the $d$-dimensional unit standard simplex, $d\ge 1$, defined as follows. From an interior point $z$, the process chooses one of the $d+1$ vertices of the simplex, with probabilities depending on $z$, and then the particle randomly jumps to a new location $z'$ on the segment connecting $z$ to the chosen vertex. In some specific cases, using properties of the Beta distribution, we prove that the limiting distributions of the Markov chain are, in fact, Dirichlet. We also consider a related history-dependent random walk model in $[0,1]$ based on an urn-type scheme. We show that this random walk converges in distribution to the arcsine law.
Two high-resolution optical spectra of the R Coronae Borealis star UW Cen in decline are discussed. A spectrum from mid-1992 when the star had faded by three magnitudes shows just a few differences with the spectrum at maximum light. The ubiquitous sharp emission lines seen in R CrB at a similar drop below maximum light are absent. In contrast, a spectrum from mid-2002 when the star was five magnitudes below maximum light shows an array of sharp emission lines and a collection of broad emission lines. Comparisons are made with spectra of R CrB obtained during the deep 1995-1996 minimum. The many common features are discussed in terms of a torus-jet geometry.
We extend the `topological inflation' of Linde and Vilenkin to {\em unstable} monopoles. This allows the monopole to decay; not inflating eternally, as topological inflation demands. Such a situation happens naturally in some Grand Unified Theories --- such as supersymmetric flipped-$SU(5)$. We analyse analytically the dynamics of inflating monopoles to determine the equations governing the expansion, additionally recovering the bound on the scale of symmetry breaking found numerically by Sakai {\em et. al.} The latter half of this paper is devoted to the Cosmology of inflating unstable monopoles --- which is an example of an inhomogeneous cosmology. We describe how such a monopole may be formed and how long it inflates for --- finding it to be a random process. We then derive how cosmological parameters, such as density and temperature, are distributed at the end of inflation, and how the Universe reheats as the monopole decays. The general conclusion of this work is that such inflation creates a local region of relatively flat, homogenous and isotropic Universe surrounded by pre-GUT matter.
We use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet formulae for super-Yang-Mills or supergravity, the scattering equations for conformal supergravity are not in general refined by MHV degree. Nevertheless, we obtain a concise worldsheet formula for any number of scalars and gravitons which we lift to a manifestly supersymmetric formula using four types of vertex operators. The theory also contains states with non-plane wave boundary conditions and we show that the corresponding amplitudes can be obtained from plane-wave amplitudes by applying momentum derivatives. Such derivatives are subtle to define since the formulae are intrinsically four-dimensional and on-shell, so we develop a method for computing momentum derivatives of spinor variables.
The SL(2,R)/U(1) gauged Wess-Zumino-Witten model is an exact conformal field theory describing a black hole in two-dimensional space-time. The free field approach of Bershadsky and Kutasov is a suitable formulation of this CFT in order to compute physically interesting quantities of this black hole. We find the space-time interpretation of this model for k=9/4 and show that it reproduces the metric and the dilaton found by Dijkgraaf, E. Verlinde and H. Verlinde in the mini-superspace approximation. We compute the two- and three-point functions of tachyons interacting in the black hole background and analyse in detail the form of the four-point tachyon scattering amplitude. We discuss the connection to the c=1 matrix model and the deformed matrix model of Jevicki and Yoneya.
The optimal phase covariant cloning machine (PQCM) broadcasts the information associated to an input qubit into a multi-qubit systems, exploiting a partial a-priori knowledge of the input state. This additional a priori information leads to a higher fidelity than for the universal cloning. The present article first analyzes different experimental schemes to implement the 1->3 PQCM. The method is then generalized to any 1->M machine for odd value of M by a theoretical approach based on the general angular momentum formalism. Finally different experimental schemes based either on linear or non-linear methods and valid for single photon polarization encoded qubits are discussed.
This paper proposes an affinity fusion graph framework to effectively connect different graphs with highly discriminating power and nonlinearity for natural image segmentation. The proposed framework combines adjacency-graphs and kernel spectral clustering based graphs (KSC-graphs) according to a new definition named affinity nodes of multi-scale superpixels. These affinity nodes are selected based on a better affiliation of superpixels, namely subspace-preserving representation which is generated by sparse subspace clustering based on subspace pursuit. Then a KSC-graph is built via a novel kernel spectral clustering to explore the nonlinear relationships among these affinity nodes. Moreover, an adjacency-graph at each scale is constructed, which is further used to update the proposed KSC-graph at affinity nodes. The fusion graph is built across different scales, and it is partitioned to obtain final segmentation result. Experimental results on the Berkeley segmentation dataset and Microsoft Research Cambridge dataset show the superiority of our framework in comparison with the state-of-the-art methods. The code is available at https://github.com/Yangzhangcst/AF-graph.
Although d-complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on their local structure. These posets are a mutual generalization of rooted trees, shapes, and shifted shapes. They possess Stanley's hook product property for their P-partition generating functions and Schutzenberger's well defined jeu de taquin rectification property. The original definition of d-complete poset was lengthy, but more succinct definitions were later developed. Here several definitions are shown to be equivalent. The basic properties of d-complete posets are summarized. Background and a partial bibliography for these posets is given.
Band-to-band tunneling (BTBT) devices have recently gained a lot of interest due to their potential for reducing power dissipation in integrated circuits. We have performed extensive simulations for the BTBT operation of carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) using the non-equilibrium Green's functions formalism for both ballistic and dissipative quantum transport. In comparison with recently reported experimental data (Y. Lu et al, J. Am. Chem. Soc., v. 128, p. 3518-3519, 2006), we have obtained strong evidence that BTBT in CNT-MOSFETs is dominated by optical phonon assisted inelastic transport, which can have important implications on the transistor characteristics. It is shown that under large biasing conditions two-phonon scattering may also become important.
We investigate the question whether there is a real difference in the light change between stars classified as semiregular (SRV) or irregular (Lb) variables by analysing photometric light curves of 12 representatives of each class. Using Fourier analysis we try to find a periodic signal in each light curve and determine the S/N of this signal. For all stars, independent of their variability class we detect a period above the significance threshold. No difference in the measured S/N between the two classes could be found. We propose that the Lb stars can be seen as an extension of the SRVs towards shorter periods and smaller amplitudes. This is in agreement with findings from other quantities which also showed no marked difference between the two classes.
We compare the semi-analytic models of galaxy formation of Fu et al. (2010), which track the evolution of the radial profiles of atomic and molecular gas in galaxies, with gas fraction scaling relations derived from the COLD GASS survey (Saintonge et al 2011). The models provide a good description of how condensed baryons in galaxies with gas are partitioned into stars, atomic and molecular gas as a function of galaxy stellar mass and surface density. The models do not reproduce the tight observed relation between stellar surface density and bulge-to-disk ratio for this population. We then turn to an analysis of the"quenched" population of galaxies without detectable cold gas. The current implementation of radio-mode feedback in the models disagrees strongly with the data. In the models, gas cooling shuts down in nearly all galaxies in dark matter halos above a mass of 10**12 M_sun. As a result, stellar mass is the observable that best predicts whether a galaxy has little or no neutral gas. In contrast, our data show that quenching is largely independent of stellar mass. Instead, there are clear thresholds in bulge-to-disk ratio and in stellar surface density that demarcate the location of quenched galaxies. We propose that processes associated with bulge formation play a key role in depleting the neutral gas in galaxies and that further gas accretion is suppressed following the formation of the bulge, even in dark matter halos of low mass.
We study the tunneling probability of a massive ($m_w$) uncharged scalar packet out from a near-extremal, static charged black hole (with mass $M$ and charge $Q\lesssim M$). We show that there is indeed a net probability that a massive uncharged particle tunnels out from the black hole so that the final state (with new mass $M'\equiv M-m_w < Q$) does violate the cosmic censorship conjecture. Nevertheless, the typical time for such a black hole to discharge (i.e, to absorb charge $-Q$ from its surroundings and then become neutral) is much smaller than the tunneling time; therefore, the violation is never attained in practice. Even for a completely isolated black hole (should it exist), the standard time dilation near the horizon stretches the typical violation time scale to unobservable values.
We discuss the condensation of relativistic spin-one fields at high chemical potential. This phenomenon leads to the spontaneous breaking of rotational invariance, together with the breaking of internal symmetries.
We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path via appropriate notions of test functions and rough jets. These objects will be defined as controlled processes with respect to the driving rough path. We show that this notion is compatible with the seminal results of Lions and Souganidis and with the recent results of Friz and coauthors on fully non-linear SPDEs with rough drivers.
Three-body calculations of (d,p) and (p,d) reactions involving one-neutron halo nuclei 11Be and 15C are performed using the framework of Faddeev-type scattering equations. Important effects of the optical potential nonlocality are found improving the description of the experimental data. The obtained values for the neutron spectroscopic factor are consistent with estimations from other approaches.
We measure the sum of the neutrino particle masses using the three-dimensional galaxy power spectrum of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) CMASS galaxy sample. Combined with the cosmic microwave background (CMB), supernova (SN) and additional baryonic acoustic oscillation (BAO) data, we find upper 95 percent confidence limits of the neutrino mass $\Sigma m_{\nu}<0.340$ eV within a flat $\Lambda$CDM background, and $\Sigma m_{\nu}<0.821$ eV, assuming a more general background cosmological model. The number of neutrino species is measured to be $N_{\rm eff}=4.308\pm0.794$ and $N_{\rm eff}=4.032^{+0.870}_{-0.894}$ for these two cases respectively. We study and quantify the effect of several factors on the neutrino measurements, including the galaxy power spectrum bias model, the effect of redshift-space distortion, the cutoff scale of the power spectrum, and the choice of additional data. The impact of neutrinos with unknown masses on other cosmological parameter measurements is investigated. The fractional matter density and the Hubble parameter are measured to be $\Omega_M=0.2796\pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $\Lambda$CDM) and $\Omega_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ km/s/Mpc (more general background model). Based on a Chevallier-Polarski-Linder (CPL) parametrisation of the equation-of-state $w$ of dark energy, we find that $w=-1$ is consistent with observations, even allowing for neutrinos. Similarly, the curvature \Omega_K and the running of the spectral index $\alpha_s$ are both consistent with zero. The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $\Lambda$ CDM) and $r<0.440$ (95 percent CL, more general background model).
Solar eruptions generally refer to coronal mass ejections (CMEs) and flares. Both are important sources of space weather. Solar flares cause sudden change in the ionization level in the ionosphere. CMEs cause solar energetic particle (SEP) events and geomagnetic storms. A flare with unusually high intensity and/or a CME with extremely high energy can be thought of examples of extreme events on the Sun. These events can also lead to extreme SEP events and/or geomagnetic storms. Ultimately, the energy that powers CMEs and flares are stored in magnetic regions on the Sun, known as active regions. Active regions with extraordinary size and magnetic field have the potential to produce extreme events. Based on current data sets, we estimate the sizes of one-in-hundred and one-in-thousand year events as an indicator of the extremeness of the events. We consider both the extremeness in the source of eruptions and in the consequences. We then compare the estimated 100-year and 1000-year sizes with the sizes of historical extreme events measured or inferred.
We apply various conventional tests of integrability to the supersymmetric nonlinear Schr\"odinger equation. We find that a matrix Lax pair exists and that the system has the Painlev\'e property only for a particular choice of the free parameters of the theory. We also show that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. We are unable to construct a zero curvature formulation of the equations based on OSp(2$|$1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schr\"odinger equation which appears to possess the Painlev\'e property.
We study the probability distribution function (pdf) of the position of a L\'evy flight of index 0<\alpha<2 in presence of an absorbing wall at the origin. The solution of the associated fractional Fokker-Planck equation can be constructed using a perturbation scheme around the Brownian solution (corresponding to \alpha = 2), as an expansion in \epsilon = 2 - \alpha. We obtain an explicit analytical solution, exact at the first order in \epsilon, which allows us to conjecture the precise asymptotic behavior of this pdf, including the first subleading corrections, for any \alpha. Careful numerical simulations, as well as an exact computation for \alpha = 1, confirm our conjecture.
The mean-field Landau-type theory is used to analyze the polarization properties of epitaxial ferroelectric thin films grown on dissimilar cubic substrates, which induce biaxial compressive stress in the film plane. The intrinsic effect of the film surfaces on the spontaneous polarization is taken into account via the concept of the extrapolation length. The theory simultaneously allows for the influence of the misfit strain imposed on the film lattice by a thick substrate. Numerical calculations are performed for PbTiO3 and BaTiO3 films under an assumption of the polarization reduction in surface layers. The film mean polarization is calculated as a function of film thickness, temperature, and misfit strain. It is shown that the negative intrinsic size effect is reduced in epitaxial films due to the in-plane compression of the film lattice. At room temperature, strong reduction of the mean polarization may take place only in ultrathin films (thickness ~ 1 nm). Theoretical predictions are compared with the available experimental data on polarization properties of BaTiO3 films grown on SrRuO3 coated SrTiO3.
Isotopic abundance ratios 24^Mg:25^Mg:26^Mg are derived for 20 stars from high- resolution spectra of the MgH A-X 0-0 band at 5140AA. With the exception of the weak g-band giant HR 1299, the stars are dwarfs that sample the metallicity range -1.8 < [Fe/H] <0.0. The abundance of 25^Mg amd 26^Mg relative to the dominant isotope 24^Mg decreases with decreasing [Fe/H] in fair accord with predictions from a recent model of galactic chemical evolution in which the Mg isotopes are synthesised by massive stars. Several stars appear especially enriched in the heavier Mg isotopes suggesting contamination by material from the envelopes of intermediate-mass AGB stars.
We calculate ab initio the gravitational potential energy per unit area for a gravitationally coupled multi-component galactic disk of stars and gas, which is given as the integration over vertical density distribution, vertical gravitational force, and vertical distance. This is based on the method proposed by Camm for a single-component disk, which we extend here for a multi-component disk by deriving the expression of the energy explicitly at any galactocentric radius R. For a self-consistent distribution, the density and force are obtained by jointly solving the equation of vertical hydrostatic equilibrium and the Poisson equation. Substituting the numerical values for the density distribution and force obtained for the coupled system, in the derived expression of the energy, we find that the energy of each component remains unchanged compared to the energy for the corresponding single-component case. We explain this surprising result by simplifying the above expression for the energy of a component analytically, which turns out to be equal to the surface density times the squared vertical velocity dispersion of the component. However, the energy required to raise a unit test mass to a certain height z from the mid-plane is higher in the coupled case. The system is therefore more tightly bound closer to the mid-plane, and hence it is harder to disturb it due to an external tidal encounter.
This paper provides an estimate of the sum of a homogeneous polynomial $P$ of degree $\nu$ and mean zero over the lattice points inside a sphere of radius $R$. It is proved that $$ \sum_{\mathbf x \in \mathbb Z^3 \atop |\mathbf x| \le R} P(\mathbf x) = O_{\epsilon,P}(R^{\nu + 83/64 + \epsilon}) $$
We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module case.
Radial velocities, elemental abundances, and accretion properties of members of star-forming regions (SFRs) are important for understanding star and planet formation. While infrared observations reveal the evolutionary status of the disk, optical spectroscopy is fundamental to acquire information on the properties of the central star and on the accretion characteristics. 2MASS archive data and the Spitzer c2d survey of the Chamaeleon II dark cloud have provided disk properties of a large number of young stars. We complement these data with spectroscopy with the aim of providing physical stellar parameters and accretion properties. We use FLAMES/UVES+GIRAFFE observations of 40 members of Cha II to measure radial velocities through cross-correlation technique, Li abundances by means of curves of growth, and for a suitable star elemental abundances of Fe, Al, Si, Ca, Ti, and Ni using the code MOOG. From the equivalent widths of the Halpha, Hbeta, and the HeI-5876, 6678, 7065 Angstrom emission lines, we estimate the mass accretion rates, dMacc/dt, for all the objects. We derive a radial velocity distribution for the Cha II stars (<Vrad>=11.4+-2.0 km/s). We find dMacc/dt prop. to Mstar^1.3 and to Age^(-0.82) in the 0.1-1.0 Msun mass regime, and a mean dMacc/dt for Cha II of ~7*10^(-10) Msun/yr. We also establish a relationship between the HeI-7065 Angstrom line emission and the accretion luminosity. The radial velocity distributions of stars and gas in Cha II are consistent. The spread in dMacc/dt at a given stellar mass is about one order of magnitude and can not be ascribed entirely to short timescale variability. Analyzing the relation between dMacc/dt and the colors in Spitzer and 2MASS bands, we find indications that the inner disk changes from optically thick to optically thin at dMacc/dt~10^(-10) Msun/yr. Finally, the disk fraction is consistent with the age of Cha II.
We extend our previous computations to show that there are 585355 Carmichael numbers up to $10^{17}$. As before, the numbers were generated by a back-tracking search for possible prime factorisations together with a ``large prime variation''. We present further statistics on the distribution of Carmichael numbers.
We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.