ShantanuT01/DACTYL-Pretraining huggingface dataset:
Suppose $f,g$ are homogeneous polynomials of degree $d$ defining smooth hypersurfaces $X_f = V(f)\subset \mathbb{P}^{m-1}$ and $X_g = V(g)\subset\mathbb{P}^{n-1}$. Then the sum $f(x)+g(y)$ defines a smooth hypersurface $X=V(f(x)+g(y))\subset\mathbb{P}^{m+n-1}$ with an action of $\mu_d$ scaling the $g$ variables. Motivated by the work of Orlov, we construct a semi-orthogonal decomposition of the derived category of coherent sheaves on $[X/\mu_d]$ provided $d\geq \mathrm{max}\{m,n\}$.
Context: Observations of small carbon-bearing molecules such as CCH, C4H, c-C3H2, and HCO in the Horsehead Nebula have shown these species to have higher abundances towards the edge of the source than towards the center.   Aims: Given the determination of a wide range of values for zeta (s-1), the total ionization rate of hydrogen atoms, and the proposal of a column-dependent zeta(N_H), where N_H is the total column of hydrogen nuclei, we desire to determine if the effects of zeta(N_H) in a single object with spatial variation can be observable. We chose the Horsehead Nebula because of its geometry and high density.   Method: We model the Horsehead Nebula as a near edge-on photon dominated region (PDR), using several choices for zeta, both constant and as a function of column. The column-dependent zeta functions are determined by a Monte Carlo model of cosmic ray penetration, using a steep power-law spectrum and accounting for ionization and magnetic field effects. We consider a case with low-metal elemental abundances as well as a sulfur-rich case.   Results: We show that use of a column-dependent zeta(N_H) of 5(-15) s-1 at the surface and 7.5(-16) s-1 at Av = 10 on balance improves agreement between measured and theoretical molecular abundances, compared with constant values of zeta.
Detailed atmospheric abundances have been calculated for a sample of A-G supergiant stars with IR fluxes and/or high galactic latitudes. HD 172481 and HD 158616 show clear indications of being post-AGB stars that have experienced third dredge-up. HD 158616 is carbon-rich while the abundance pattern of HD 172481 and its large Li enhancement gives support to the hot bottom burning scenario that explains paucity of carbon-rich stars among AGB stars. HD 172324 is very likely a hot post-AGB star that shows a strong carbon deficiency. HD 725, HD 218753 and HD 331319 also appear to be evolved objects between the red giant and the AGB. HD 9167, HD 173638 with a few exceptions, reflect solar abundances and no signs of post red giant evolution. They are most likely young massive disk supergiants. Further analysis of proto-Planetary Nebula HDE 341617 reveals that He lines show signs of velocity stratification. The emission lines have weakened considerably since 1993. The envelope expands at 19 km s$^{-1}$ relative to the star. Atmospheric abundances, evolutionary tracks and isochrones are used to estimate masses and ages of all stars in the sample.
We present a description of a strongly driven multimode optomechanical system that shows the emergence of cooperative effects usually known from systems of atom-light interaction. Our calculations show that under application of a coherent pump field the system's response can be switched from a superradiant regime to a collective gain regime by varying the frequency detuning of the pump. In the superradiant regime, enhanced optical cooling of a single vibrational mode is possible, whereas the collective gain regime would potentially enable one to achieve almost thresholdless phonon laser action. The threshold pumping power scales as 1/N.
We present a detailed analysis of the neutrino-induced muon signals coming from neutralino pair-annihilations inside the Sun and the Earth with particular emphasis for light neutralinos. The theoretical model considered is an effective MSSM without gaugino-mass unification, which allows neutralinos of light masses (below 50 GeV). The muon events are divided in through-going and stopping muons, using the geometry of the Super-Kamiokande detector. In the evaluation of the signals, we take into account the relevant hadronic and astrophysics uncertainties and include neutrino oscillation and propagation properties in a consistent way. We derive the ranges of neutralino masses which could be explored at neutrino telescopes with a low muon-energy threshold (around 1 GeV) depending on the category of events and on the values of the various astrophysics and particle-physics parameters. A final analysis is focussed to the upward muon fluxes which could be generated by those neutralino configurations which are able to explain the annual modulation data of the DAMA/LIBRA experiment. We show how combining these data with measurements at neutrino telescopes could help in pinning down the features of the DM particle and in restraining the ranges of the many quantities (of astrophysics and particle-physics origins) which enter in the evaluations and still suffer from large uncertainties.
A theory of the trion and biexciton in a nanowire (NW) in the framework of the effective-mass model using the Born-Oppenheimer approximation is presented. We consider the formation of trions and biexcitons under the action of both the lateral confinement and the localization potential. The analytical expressions for the binding energy and eigenfunctions of the trion and biexciton are obtained and expressed by means of matrix elements of the effective one-dimensional cusp-type Coulomb potentials whose parameters are determined self-consistently by employing the same eigenfunctions of the confined electron and hole states. Our calculations for the ZnO/ZnMgO, CdSe/ZnS and CdSe/CdS core/shell cylindrical shaped NWs show that the trion and biexciton binding energy in NWs are size-dependent and for the same input parameters the biexciton binding energy in NWs is always larger than the binding energy of the trion. The trion and biexciton remain stable in CdSe/ZnS NW with the increase of the dielectric shell, while in ZnO/ZnMgO NW they become unstable when the surrounding dielectric shell exceeds 2.5 nm and 2 nm for each, respectively. The associative ionization of biexciton antibonding states into trion bonding states is studied. Based on the results for size dependence of biexciton binding energy and probability associative ionization an optimal radius for optoelectronic application NW is suggested.
Aperiodicity and un-conventional rotational symmetries allow quasicrystalline structures to exhibit unprecedented physical and functional properties. In magnetism, artificial ferromagnetic quasicrystals exhibited knee anomalies suggesting reprogrammable magnetic properties via nonstochastic switching. However, the decisive roles of short-range exchange and long-range dipolar interactions have not yet been clarified for optimized reconfigurable functionality. We report broadband spin-wave spectroscopy and X-ray photoemission electron microscopy on different quasicrystal lattices consisting of ferromagnetic Ni81Fe19 nanobars arranged on aperiodic Penrose and Ammann tilings with different exchange and dipolar interactions. We imaged the magnetic states of partially reversed quasicrystals and analyzed their configurations in terms of the charge model, geometrical frustration and the formation of flux-closure loops. Only the exchange-coupled lattices are found to show aperiodicity-specific collective phenomena and non-stochastic switching. Both, exchange and dipolarly coupled quasicrystals show magnonic excitations with narrow linewidths in minor loop measurements. Thereby reconfigurable functionalities in spintronics and magnonics become realistic.
The magnetization switching of a thin ferromagnetic layer placed on top of a heavy metal (such as Pt, Ta or W) driven by an in-plane current has been observed in recent experiments. The magnetization dynamics of these processes is studied in a full micromagnetic framework which takes into account the transfer-torque from spin Hall effect due to the spin-orbit coupling. Simulations indicate that the reversal occurs via nucleation of complex magnetization patterns. In particular, magnetic bubbles appear during the reversal of the magnetization in the perpendicular configuration while for the in-plane configuration, nucleation of vortexes are observed.
We prove a comparison theorem between the d-plane Radon transform and the Fourier-Laplace transform for D-modules. This generalizes results of Brylinski and d'Agnolo-Eastwood.
Differential cross-section and single polarization observables in the process gamma p --> K^+ Lambda are investigated within a constituent quark model and a dynamical coupled-channel formalism. The effects of two new nucleon resonances and of the K*(892)- and K1(1270)-exchanges are briefly presented.
Elemental abundances of CH stars can provide observational constraints for theoretical studies on the nucleosynthesis and evolution of low- and intermediate-mass stars. However, available abundance data in literature are quite scanty. In our pursuit to generate a homogeneous database of elemental abundances of CH stars we have performed a detailed chemical abundance study for a sample of 12 potential CH star candidates based on high resolution spectroscopy. We present first time abundance analysis for the objects HE 0308-1612, CD-28 1082, HD 30443, and HD 87853. For the other objects, although limited information is available, detailed chemical composition studies are missing. Our analysis shows CD-28 1082 to be a very metal-poor object with [Fe/H] = -2.45 and enriched in carbon with [C/Fe] = 2.19. With a ratio of [Ba/Eu] ~ 0.02 the star satisfies the classification criteria of a CEMP-r/s star. The objects CD-38 2151 with [Fe/H] = -2.03 and HD 30443 with [Fe/H] ~ -1.68 are found to show the characteristic properties of CH stars. HE 0308-1612 and HD 87853 are found to be moderately metal-poor with [Fe/H]~ -0.73; while HE 0308-1612 is moderately enhanced with carbon ([C/Fe] ~ 0.78) and shows the spectral properties of CH stars, the abundance of carbon could not be estimated for HD 87853. Among the two moderately metal-poor objects, HD 87080 ([Fe/H] = -0.48) shows near solar carbon abundance, and HD 176021 ([Fe/H] = -0.63) is mildly enhanced in carbon with [C/Fe] = 0.52. HD 176021 along with HD 202020 a known binary, exhibit the characteristic properties of CH stars as far as the heavy element abundances are concerned. Five objects in our sample show spectral properties that are normally seen in barium stars.
By integrating the Seiberg-Witten differential equation in a special path, we write ordinary gauge fields in terms of their non-commutative counterparts up to three non-commutative gauge fields. We then use this change of variables to write ordinary abelian Dirac-Born-Infeld action in terms of non-commutative fields. The resulting action is then compared with various low energy contact terms of world-sheet perturbative string scattering amplitudes from non-commutative D$p$-brane. We find completely agreement between the field theory and string theory results. Hence, it shows that perturbative string theory knows the solution of the Seiberg-Witten differential equation.
It was recently pointed out by Barrau, Martineau and Renevey that the mass of the Schwarzschild black hole immersed in a heat bath tends to infity in a finite time. We show that this singularity problem in the black hole mass may be avoided, if the stretched horizon of the black hole is constructed out of a fixed, finite number of discrete constituents, and an appropriate counting is applied to the energy eigenstates of the hole.
We present a novel high resolution contactless technique for thermal conductivity determination and thermal field mapping based on creating a thermal distribution of phonons using a heating laser, while a second laser probes the local temperature through the spectral position of a Raman active mode. The spatial resolution can be as small as $300$ nm, whereas its temperature accuracy is $\pm 2$ K. We validate this technique investigating the thermal properties of three free-standing single crystalline Si membranes with thickness of 250, 1000, and 2000 nm. We show that for 2-dimensional materials such as free-standing membranes or thin films, and for small temperature gradients, the thermal field decays as $T(r) \propto ln(r)$ in the diffusive limit. The case of large temperature gradients within the membranes leads to an exponential decay of the thermal field, $T \propto exp[-A \cdot ln(r)]$. The results demonstrate the full potential of this new contactless method for quantitative determination of thermal properties. The range of materials to which this method is applicable reaches far beyond the here demonstrated case of Si, as the only requirement is the presence of a Raman active mode.
We present a novel approach aimed at identifying the key chemical elements to search for the (missing) descendants of very massive first stars exploding as Pair Instability Supernovae (PISN). Our simple and general method consists in a parametric study accounting for the unknowns related to early cosmic star-formation and metal-enrichment. Our approach allow us to define the most likely [Fe/H] and abundance ratios of long-lived stars born in inter-stellar media polluted by the nucleosynthetic products of PISN at a > 90%, 70%, and 50% level. In agreement with previous works, we show that the descendants of very massive first stars can be most likely found at [Fe/H]~ -2. Further, we demonstrate that to search for an under-abundance of [(N, Cu, Zn)/Fe] < 0 is the key to identify these rare descendants. The "killing elements" N, Zn, and Cu are not produced by PISN, so that their sub-Solar abundance with respect to iron persists in environments polluted by further generations of normal core-collapse supernovae up to a 50% level. We show that the star BD +80 245, which has [Fe/H]= -2.2, [N/Fe]= -0.79, [Cu/Fe]=-0.75, and [Zn/Fe]= -0.12 can be the smoking gun of the chemical imprint from very massive first stars. To this end we acquired new spectra for BD +80 245 and re-analysed those available from the literature accounting for Non-Local Thermodynamic Equilibrium corrections for Cu. We discuss how to find more of these missing descendants in ongoing and future surveys to tightly constrain the mass distribution of the first stars.
The transition to a hidden metastable state in 1T-TaS2 is investigated in real time using coherent time-resolved femtosecond spectroscopy. Relying on spectral differences between phonon modes in the equilibrium states and in the metastable state, and temperature-tuning the metastable state lifetime, we perform stroboscopic measurements of the electronic response and switching of coherent oscillation frequency through the transition. Very fast coherent switching of the collective mode frequency is observed (400 fs), comparable to the electronic timescale (300 fs). A slower, 4.7 ps process is attributed to lattice relaxation. The observations are described well by a fast electronic band structure transformation into the metastable state, consistent with a topological transition.
We construct non-Lipshitz flow in $H^s$ for the cubic nonlinear Schr\"odinger equation on the 2-torus of revolution with a Lipshitz or smooth metric . The non-Lipshitz property holds for all $s<2/3$ for Lipshitz metric and $s<1/2$ for smooth metric. Both coincide with the Sobolev exponents for uniform local well-posedness.
We present application examples of a graphical method for the efficient construction of potential matrix elements in quantum physics or quantum chemistry. The simplicity and power of this method are illustrated through several examples. In particular, a complete set of potential matrix elements for electron-Lithium scattering are derived for the first time using this method, which removes the frozen core approximation adopted by previous studies. This method can be readily adapted to study other many-body quantum systems.
This paper is about the $n+2$-dimensional gravitational contraction of inhomogeneous fluid without heat flux in the framework of $f(R)$ metric theory of gravity. Matching conditions for two regions of a star has been derived by using the Darmois junction conditions. For the analytic solution of equations of motion in modified $f(R)$ theory of gravity, we have taken scalar curvature as constant. Hence final result of gravitational collapse in this frame work is the existence of black hole and cosmological horizons, both of these form earlier than singularity. It has been shown that constant curvature term $f(R_{0})$ ($R_0$ is constant scalar curvature) slows down the collapsing process.
A printing process for high-resolution transfer of all components for organic electronic devices on plastic substrates has been developed and demonstrated for pentacene (Pn), poly (3-hexylthiophene) and carbon nanotube (CNT) thin-film transistors (TFTs). The nanotransfer printing process allows fabrication of an entire device without exposing any component to incompatible processes and with reduced need for special chemical preparation of transfer or device substrates. Devices on plastic substrates include a Pn TFT with a saturation, field-effect mobility of 0.09 cm^2 (Vs)^-1 and on/off ratio approximately 10^4 and a CNT TFT which exhibits ambipolar behavior and no hysteresis.
We investigate consequences of the discovery that Fe II emission in quasars, one of the spectroscopic signatures of "Eigenvector 1", may originate in infalling clouds. Eigenvector 1 correlates with the Eddington ratio L/L_Edd so that Fe II/Hbeta increases as L/L_Edd increases. We show that the "force multiplier", the ratio of gas opacity to electron scattering opacity, is ~ 10^3 - 10^4 in Fe II-emitting gas. Such gas would be accelerated away from the central object if the radiation force is able to act on the entire cloud. As had previously been deduced, infall requires that the clouds have large column densities so that a substantial amount of shielded gas is present. The critical column density required for infall to occur depends on L/L_Edd, establishing a link between Eigenvector 1 and the Fe II/Hbeta ratio. We see predominantly the shielded face of the infalling clouds rather than the symmetric distribution of emitters that has been assumed. The Fe II spectrum emitted by the shielded face is in good agreement with observations thus solving several long-standing mysteries in quasar emission lines.
We use an X-ray stacking technique to investigate the evolution of the mean X-ray luminosity of ~21,000 red galaxies at 0.3 < z < 0.9 as a function of their stellar mass and redshift. The red galaxies are selected from the 9.3 deg^2 Bootes field of the NOAO Deep Wide-Field Survey (NDWFS). The mean X-ray luminosity is an order of magnitude larger than we would expect from stellar sources alone and therefore must be primarily due to AGN emission. The X-ray luminosities (L_x ~ 10^41 ergs/s) imply that these must be sources with relatively low accretion rates and/or accretion efficiencies onto their central super-massive black hole (SMBH). The mean X-ray luminosity increases significantly as a function of optical luminosity and stellar mass, implying that more massive galaxies have higher nuclear accretion rates than lower mass galaxies. We calculate that the mean X-ray luminosity evolves as (1+z)^3.3+/-1.5. This suggests a global decline in the mean AGN activity of normal early-type galaxies from z~1 to the present. If accreting at typical AGN efficiencies, SMBHs within red galaxies accreted an insignificant proportion of their mass in this time.
We formulate an endoreversible finite-time Carnot cycle model based on the assumptions of local equilibrium and constant energy flux, where the efficiency and the power are expressed in terms of the thermodynamic variables of the working substance. By analyzing the entropy production rate caused by the heat transfer in each isothermal process during the cycle, and using an endoreversible condition applied to the linear response regime, we identify the thermodynamic flux and force of the present system and obtain a linear relation that connects them. We calculate the efficiency at maximum power in the linear response regime by using the linear relation, which agrees with the Curzon-Ahlborn efficiency known as the upper bound in this regime. This reason is also elucidated by rewriting our model into the form of the Onsager relations, where our model turns out to satisfy the tight-coupling condition leading to the Curzon-Ahlborn efficiency.
Using a capacity approach, and the theory of measure's perturbation of Dirichlet forms, we give the probabilistic representation of the General Robin boundary value problems on an arbitrary domain $\Omega$, involving smooth measures, which give arise to a new process obtained by killing the general reflecting Brownian motion at a random time. We obtain some properties of the semigroup directly from its probabilistic representation, and some convergence theorems, and also a probabilistic interpretation of the phenomena occurring on the boundary.
Quantum searching for one of $N$ marked items in an unsorted database of $n$ items is solved in $\mathcal{O}(\sqrt{n/N})$ steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross-Pitaevskii type quadratic nonlinearity, Childs and Young discovered an unstructured quantum search algorithm with a complexity $\mathcal{O}( \min \{ 1/g \, \log (g n), \sqrt{n} \} ) $, which can be used to find a marked item after $o(\log(n))$ repetitions, where $g$ is the nonlinearity strength [PhysRevA.93.022314]. In this work we develop a structured search on a complete graph using a time dependent nonlinearity which obtains one of the $N$ marked items with certainty. The protocol has runtime $\mathcal{O}((N^{\perp} - N) / (G \sqrt{N N^{\perp}}) ) if N^{\perp} > N$, where $N^{\perp}$ denotes the number of unmarked items and $G$ is related to the time dependent nonlinearity. If $N^{\perp} \leq N$, we obtain a runtime $\mathcal{O}( 1 )$. We also extend the analysis to a quantum search on general symmetric graphs and can greatly simplify the resulting equations when the graph diameter is less than 5.
For the lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4.
By considering the $M_2$-rank of an overpartition as well as a residual crank, we give another combinatorial refinement of the congruences $\overline{\mbox{spt}}_2(3n)\equiv \overline{\mbox{spt}}_2(3n+1)\equiv 0\pmod{3}$. Here $\overline{\mbox{spt}}_2(n)$ is the total number of occurrences of the smallest parts among the overpartitions of $n$ where the smallest part is even and not overlined. Our proof depends on Bailey's Lemma and the rank difference formulas of Lovejoy and Osburn for the $M_2$-rank of an overpartition. This congruence, along with a modulo $5$ congruence, has previously been refined using the rank of an overpartition.