ShantanuT01/DACTYL-Pretraining huggingface dataset:
By a K3-surface with nine cusps I mean a compact complex surface with nine isolated double points $A_2$, but otherwise smooth, such that its minimal desingularisation is a K3-surface. In an earlier paper I showd that each such surface is a quotient of a complex torus by a cyclic group of order three. Here I try to classify these $K3$-surfaces, using the period map for complex tori. In particular I show:   A $K3$-surface with nine cusps carries polarizations only of degrees 0 or 2 modulo 6. This implies in particular that there is no quartic surface in projective three-space with nine cusps. (T. Urabe pointed out to me how to deduce this from a theorem of Nikulin.)   In an appendix I give explicit equations of quartic surfaces in three-space with eight cusps.
The meridional circulation plays an essential role in determining the basic mechanism of the dynamo action in case the of a low eddy diffusivity. Flux-transport dynamos with strong return flow and a deep stagnation point are discussed in the case of a positive $\alpha$-effect located in the overshoot layer and a rotation law consistent with helioseismology. By means of a linear dynamo model, it will be shown that the migration of the toroidal belts at lower latitudes and the periods of the activity cycles are consistent with the observations. Moreover, at variance with previous investigations, the typical critical dynamo numbers of dipolar solutions are significantly smaller that those of quadrupolar solutions even in the regime of strong flow.
We construct some new classes of topological black hole solutions in the context of mimetic gravity. We study the uncharged and charged black holes, separately. In the absence of a potential for the mimetic field, our solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking any kind of particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modification of the Schwarzschild spacetime. We also investigate the casual structure and physical properties of the solutions. The presence of the mimetic field changes the asymptotic behaviour of the spacetime. We observe that in the absence of a potential, our solutions are not asymptotically flat, while, in the presence of a negative constant potential for the mimetic field, the asymptotic behaviour of the solutions can be anti de-Sitter (AdS). Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in Einstein gravity and in mimentic gravity. In contrast to Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimentic gravity. Furthermore, we find stable bound orbits for massless particles.
Given two filtrations $\mathbb F \subset \mathbb G$, we study under which conditions the $\mathbb F$-optional projection and the $\mathbb F$-dual optional projection coincide for the class of $\mathbb G$-optional processes with integrable variation. It turns out that this property is equivalent to the immersion property for $\mathbb F$ and $\mathbb G$, that is every $\mathbb F$-local martingale is a $\mathbb G$-local martingale, which, equivalently, may be characterised using the class of $\mathbb F$-pseudo-stopping times. We also show that every $\mathbb G$-stopping time can be decomposed into the minimum of two barrier hitting times.
Twistor string theory is known to describe a wide variety of field theories at tree-level and has proved extremely useful in making substantial progress in perturbative gauge theory. We explore the twistor dual description of a class of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding 'flavour' branes to the topological B-model on super-twistor space and comment on the appearance of these objects. Evidence for the correspondence is provided by matching amplitudes on both sides.
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in the barriers, we find a quantization condition which is then solved to give a formula for the energy eigenvalues explicitly written in terms of the potential. In addition, constructing $N$ localized approximate eigenstates each of which matches on to that of the harmonic oscillator in one of the parabolic wells, and diagonalizing the Hamiltonian in the subspace spanned by the localized states on the assumption that the localized states form an orthogonal basis, we also find the same formula for the energy eigenvalues which the method of matching the wave functions gives. In the large-$N$ limit, the formula reproduces, at the leading order, the expression for the widths of the narrow energy bands of the Mathieu equation present in the mathematical literature. As there are differences between the $N$-well system in the large-$N$ limit and the fully periodic system, we include a two-dimensional model in which the quadratic minima are located on the vertices of a regular $N$-sided polygon with rotational symmetry of order $N$. We argue that the lowest band of the two-dimensional model closely resembles the tight-binding energy bands of the fully periodic one-dimensional system in that most of the eigenvalues are degenerate in the large-$N$ limit with the eigenfunctions satisfying the Bloch condition under the discrete rotations.
We show that an ensemble of identical d-level atoms can be efficiently described by d-1 collective oscillator degrees of freedom in the vicinity of a product state with all atoms in the same, but otherwise arbitrary single-particle state. We apply our description to two different kinds of spin squeezing: (i) when each spin-F atom is individually squeezed without creating interatomic entanglement and (ii) when a particular collective atomic oscillator mode is squeezed via quantum non-demolition (QND) measurement and feedback. When combined in sequence, the order of the two methods is relevant in the final degree of squeezing. We also discuss the role of the two kinds of squeezing when multi-sublevel atoms are used as quantum memories for light.
The nearly 100% linear polarization has been reported for a few fast radio bursts. This finding places severe limits on the emission mechanism. I argue that the totally polarized radiation could be generated in the course of relativistic magnetic reconnection in the outer magnetosphere of the magnetar. At the onset of the magnetar flare, a large scale magnetic perturbation forms a magnetic pulse, which propagates from the flare cite outwards. The pulse strongly compresses magnetospheric plasma and pushes it away. The high-frequency MHD waves are generated when the magnetic pulse reaches the current sheet separating, just beyond the light cylinder, the oppositely directed magnetic fields. Coalescence of magnetic islands in the reconnecting current sheet produces magnetosonic waves, which propagate away on the top of the magnetic pulse and escape in the far zone of the wind as radio waves polarized along the rotational axis of the magnetar. I estimate parameters of the outgoing radiation and show that they are compatible with the observed properties of FRBs.
The second order formalism for fermions provides a description of fermions that is very similar to that of scalars. We demonstrate that this second order formalism is equivalent to the standard Dirac formalism. We do so in terms of the conventional fermionic Feynman rules. The second order formalism has previously proven useful for the computation of fermion loops, here we describe how the corresponding rules can be applied to the calculation of amplitudes involving external fermions, including tree-level processes and processes with more than one fermion line. We comment on the supersymmetric identities relating fermions and scalars and the associated simplifications to perturbative calculations that are then more transparent.
We present a general model with universal extra dimensions in the presence of the bulk fermion masses and boundary localized kinetic terms, which are generically allowed by symmetries of five dimensional gauge theory. We provide a comprehensive analysis for a general UED model, including Kaluza-Klein mass spectra, their interactions with the SM particles, and constraints from LHC, electroweak tests, and dark matter experiments. Finally we show current bounds on the size of allowed universal bulk mass and universal brane-localized terms.
The VERITAS array of Cherenkov telescopes was used to observe ~130 blazars from 2007 to 2012. Of these, 25 were detected as very-high-energy (VHE; E > 100 GeV) sources. We present here the results of the analysis of 65 VERITAS non-detected blazars, including upper limits on their VHE flux. Results from a stacked analysis of the entire data set and of smaller sub-sets (defined as a function of the redshift and the blazar class) are presented and discussed.
Inspiralling binary systems of neutron stars or black holes are promising sources of gravitational radiation detectable by large-scale laser interferometric gravitational observatories, such as the US LIGO and Italian-French VIRGO projects. Accurate theoretical gravitational-waveform templates will be needed to carry out matched filtering data analysis of the detectors' output once they are on the air by the end of this decade. For all but the final, strongly general relativistic coalescence of the two bodies, high-order post-Newtonian methods are playing a major role in the theorists' efforts to develop the needed templates. This paper discusses the foundations of this method, and provides a compendium of useful formulae and results. Figures available upon request. (Invited talk given at the 8th Nishinomiya-Yukawa Memorial Symposium, October 28, 1993.)
We compute and analyze the evolution of primordial stars of masses at the ZAMS between 5 M_sun and 10 M_sun, with and without overshooting. Our main goals are to determine the nature of the remnants of massive intermediate-mass primordial stars and to check the influence of overshooting in their evolution. Our calculations cover stellar evolution from the main sequence phase until the formation of the degenerate cores and the thermally pulsing phase. We have obtained the values for the limiting masses of Population III progenitor stars leading to carbon-oxygen and oxygen-neon compact cores. Moreover, we have also obtained the limiting mass for which isolated primordial stars would lead to core-collapse supernovae after the end of the main central burning phases. Considering a moderate amount of overshooting the mass thresholds at the ZAMS for the formation of carbon-oxygen and oxygen-neon degenerate cores shifts to smaller values by about 2 M_sun. As a by-product of our calculations, we have also obtained the structure and composition profiles of the resulting compact remnants. Opposite to what happens with solar metallicity objects, the final fate of primordial stars is not straightforward determined from the mass of the compact cores at the end of carbon burning. Instead, the small mass-loss rates typically associated to stellar winds of low metallicity stars might allow the growth of the resulting degenerate cores up to the Chandrasekhar mass, on time scales one or two orders of magnitude shorter than the time required to loose the envelope. This would lead to the formation of supernovae for initial masses as small as about 5 M_sun.
We investigate the possibility of lens mass determination for a caustic crossing microlensing event based on a space telescope observation. We demonstrate that the parallax due to the orbital motion of a space telescope causes a periodic fluctuation of the light curve, from which the lens distance can be derived. Since the proper motion of the lens relative to the source is also measurable for a caustic crossing event, one can find a full solution for microlensing properties of the event, including the lens mass. To determine the lens mass with sufficient accuracy, the light curve near the caustic crossing should be observed within uncertainty of $\sim$ 1%. We argue that the Hubble Space Telescope observation of the caustic crossing supplied with ground-based observations of the full light curve will enable us to determine the mass of MACHOs, which is crucial for understanding the nature of MACHOs.
Exploiting some connections between the system $\nabla v\otimes\nabla v + 2$ sym $\nabla w = A$ and the isometric immersion problem in two dimensions, we provide a simple construction of $C^{1,\alpha}$ convex integration solutions for the former from the corresponding result for the latter.
Bremsstrahlung from relativistic electrons is considered under conditions when some transverse direction of momentum transfer is statistically preferred. It is shown that in the dipole approximation all the medium anisotropy effects can be accumulated into a special modulus-bound transverse vector, $\bm N$. To exemplify a target with $N^2\sim1$, we calculate radiation from electron incident at a small angle on an atomic row in oriented crystal. Radiation intensity and polarization dependence on the emission angle and frequency for constant $\bm N$ is investigated. Net polarization for the angle-integral cross-section is evaluated, which appears to be proportional to $N^2/2$, and decreases with the increase of the photon energy fraction. A prominent feature of the radiation angular distribution is the existence of an angle at which the radiation may be completely polarized, in spite of the target complete or partial isotropy -- that owes to existence of an origin-centered tangential circle for polarization in the fully differential radiation probability kernel. Possibilities for utilizing various properties of the polarized bremsstrahlung flux for preparation of polarized photon beams and for probing intrinsic anisotropy of the medium are analyzed.
We consider the equivalence relation ~ on the symmetric group S_n generated by the interchange of two adjacent elements a_i and a_{i+1} of w=a_1 ... a_n in S_n such that |a_i - a_{i+1}|=1. We count the number of equivalence classes and the sizes of equivalence classes. The results are generalized to permutations of multisets using umbral techniques. In the original problem, the equivalence class containing the identity permutation is the set of linear extensions of a certain poset. Further investigation yields a characterization of all finite graded posets whose flag h-vector takes on only the values -1, 0, 1.
Let $G$ be a connected graph and $d(a,b)$ be the distance between the vertices $a$ and $b$. A subset $U =\{u_1,u_2,\cdots,u_k\}$ of the vertices is called a resolving set for $G$ if for every two distinct vertices $a,b \in V(G)$, there is a vertex $u_\xi \in U$ such that $d(a,u_\xi)\neq d(b,u_\xi)$. A resolving set containing a minimum number of vertices is called a metric basis for $G$ and the number of vertices in a metric basis is its metric dimension denoted by $dim(G)$. A resolving set $U$ for $G$ is fault-tolerant if $U \setminus \{u\}$ is also a resolving set, for each $u \in U$, and the fault-tolerant metric dimension of $G$ is the minimum cardinality of such a set. In this paper we introduce the study of the fault-tolerant metric dimension of $P(n,2)$ with prism graph.
Several domination results have been obtained for maximal outerplanar graphs (mops). The classical domination problem is to minimize the size of a set $S$ of vertices of an $n$-vertex graph $G$ such that $G - N[S]$, the graph obtained by deleting the closed neighborhood of $S$, contains no vertices. In the proof of the Art Gallery Theorem, Chv\'{a}tal showed that the minimum size, called the domination number of $G$ and denoted by $\gamma(G)$, is at most $n/3$ if $G$ is a mop. Here we consider a modification by allowing $G - N[S]$ to have a maximum degree of at most $k$. Let $\iota_k(G)$ denote the size of a smallest set $S$ for which this is achieved. If $n \le 2k+3$, then trivially $\iota_k(G) \leq 1$. Let $G$ be a mop on $n \ge \max\{5,2k+3\}$ vertices, $n_2$ of which are of degree $2$. Upper bounds on $\iota_k(G)$ have been obtained for $k = 0$ and $k = 1$, namely $\iota_{0}(G) \le \min\{\frac{n}{4},\frac{n+n_2}{5},\frac{n-n_2}{3}\}$ and $\iota_1(G) \le \min\{\frac{n}{5},\frac{n+n_2}{6},\frac{n-n_2}{3}\}$. We prove that $\iota_{k}(G) \le \min\{\frac{n}{k+4},\frac{n+n_2}{k+5},\frac{n-n_2}{k+2}\}$ for any $k \ge 0$. For the original setting of the Art Gallery Theorem, the argument presented yields that if an art gallery has exactly $n$ corners and at least one of every $k + 2$ consecutive corners must be visible to at least one guard, then the number of guards needed is at most $n/(k+4)$. We also prove that $\gamma(G) \le \frac{n - n_2}{2}$ unless $n = 2n_2$, $n_2$ is odd, and $\gamma(G) = \frac{n - n_2 + 1}{2}$. Together with the inequality $\gamma(G) \le \frac{n+n_2}{4}$, obtained by Campos and Wakabayashi and independently by Tokunaga, this improves Chv\'{a}tal's bound. The bounds are sharp.
Non-perturbative quantum gravity effects might allow a black-to-white hole transition. We revisit this increasingly popular hypothesis by taking into account the fundamentally random nature of the bouncing time. We show that if the primordial mass spectrum of black holes is highly peaked, the expected signal can in fact match the wavelength of the observed fast radio bursts. On the other hand, if the primordial mass spectrum is wide and smooth, clear predictions are suggested and the sensitivity to the shape of the spectrum is studied.
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime $a(t) \sim t^{\beta}$ with $\beta$ close to 3/2 a spatially flat universe is a good fit to these data.
We have theoretically studied the spin structure factors of Heisenberg model on honeycomb lattice in the presence of longitudinal magnetic field, i.e. magnetic field perpendicular to the honeycomb plane, and Dzyaloshinskii-Moriya interaction. The possible effects of next nearest neighbor exchange constant are investigated in terms of anisotropy in the Heisenberg interactions. This spatial anisotropy is due to the difference between nearest neighbor exchange coupling constant and next nearest neighbor exchange coupling constant. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to higher frequency with magnetic field. Also the intensity of dynamical transverse spin structure factor is not affected by magnetic field. However the Dzyaloshinskii Moriya interaction strength causes to decrease the intensity of dynamical transverse spin structure factor. The increase of magnetic field does not varied the frequency position of peaks in dynamical longitudinal spin susceptibility however the intensity reduces with magnetic field. Our results show static transverse structure factor is found to be monotonically decreasing with magnetic field and temperature for different vlaues of next nearest neighbor coupling exchange constant.
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $\alpha-\alpha$ fishbone potential by simultaneously fitting to two-$\alpha$ resonance energies, experimental phase shifts and three-$\alpha$ binding energies. We found that essentially a simple gaussian can provide a good description of two-$\alpha$ and three-$\alpha$ experimental data without invoking three-body potentials.
We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the D-brane bubbles. Different regions of moduli space are associated with D5-branes of various topologies; singularities in the moduli space are associated with topology change. T-duality on toroidal topologies maps between mirror string realizations of the field theory.
We report on a search for short-period intensity variations in the green-line FeXIV 530.3 nm emission from the solar corona during the 21 August 2017 total eclipse viewed from Idaho in the United States. Our experiment was performed with a much more sensitive detection system, and with better spatial resolution, than on previous occasions (1999 and 2001 eclipses), allowing fine details of quiet coronal loops and an active-region loop system to be seen. A guided 200-mm-aperture Schmidt-Cassegrain telescope was used with a state-of-the-art CCD camera having 16-bit intensity discrimination and a field-of-view 0.43 degree x 0.43 degree that encompassed approximately one third of the visible corona. The camera pixel size was 1.55 arcseconds, while the seeing during the eclipse enabled features of approx. 2 arcseconds (1450 km on the Sun) to be resolved. A total of 429 images were recorded during a 122.9 second portion of the totality at a frame rate of 3.49 images per second. In the analysis, we searched particularly for short-period intensity oscillations and travelling waves, since theory predicts fast-mode magneto-hydrodynamic (MHD) waves with short periods may be important in quiet coronal and active-region heating. Allowing first for various instrumental and photometric effects, we used a wavelet technique to search for periodicities in some 404 000 pixels in the frequency range 0.5-1.6 Hz (periods: 2 second to 0.6 second). We also searched for travelling waves along some 65 coronal structures. However, we found no statistically significant evidence in either. This negative result considerably refines the limit that we obtained from our previous analyses, and it indicates that future searches for short-period coronal waves may be better directed towards Doppler shifts as well as intensity oscillations.