ShantanuT01/DACTYL-Pretraining huggingface dataset:
We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of the obstacle is assumed to be C^{1,1}-smooth. We prove that, when the obstacle boundary is merely Lipschitz, a log-log type stability still holds.
We solve the one dimensional Feshbach-Villars equation for spin-1/2 particle subjected to a scalar smooth potential. The eight component wave function is given in terms of the hypergeometric functions and via a limiting procedure, the wave functions of the step potential are deduced. These wave functions are used to test the validity of the boundary conditions deduced from the Feshbach-Villars transformation. The creation of pairs is predicted from the boundary condition of the charge density.
Given a set of red and blue points in the plane, a bichromatic line is a line containing at least one red and one blue point. We prove the following conjecture of Kleitman and Pinchasi (unpublished, 2003). Let P be a set of n red, and n or n-1 blue points in the plane. If neither colour class is collinear, then P determines at least |P|-1 bichromatic lines. In fact we are able to achieve the same conclusion under the weaker assumption that P is not collinear or a near-pencil.
In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a L$\acute{\mbox{e}}$vy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that the positive solutions will blow up in finite time in mean $L^{p}$-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrated the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by L$\acute{\mbox{e}}$vy noise has a global solution.
Current-voltage characteristics of a single-electron transistor with a vibrating quantum dot were calculated assuming vibrons to be in a coherent (non-equilibrium) state. For a large amplitude of quantum dot oscillations we predict strong suppression of conductance and the lifting of polaronic blockade by bias voltage in the form of steps in $I-V$ curves. The height of the steps differs from the prediction of the Franck-Condon theory (valid for equilibrated vibrons) and the current saturates at lower voltages then for the case, when vibrons are in equilibrium state.
In this paper we begin an exploration of several domination-related parameters (among which are the total, restrained, total restrained, paired, outer connected and   total outer connected domination numbers) in the generalized lexicographic product (GLP for short) of graphs. We prove that for each GLP of graphs there exist several equality chains containing these parameters. Some known results on standard lexicographic product of two graphs are generalized or/and extended. We also obtain results on well $\mu$-dominated GLP of graphs, where $\mu$ stands for any of the above mentioned domination parameters. In particular, we present a characterization of well $\mu$-dominated GLP of graphs in the cases when $\mu$ is the domination number or the total domination number.
We report 29Si nuclear magnetic resonance measurements of single crystals and aligned powders of URu2Si2 under pressure in the hidden order and paramagnetic phases. We find that the Knight shift decreases with applied pressure, consistent with previous measurements of the static magnetic susceptibility. Previous measurements of the spin lattice relaxation time revealed a partial suppression of the density of states below 30 K. This suppression persists under pressure, and the onset temperature is mildly enhanced.
We reconsider the massless up quark solution of the strong CP problem. We show that an anomaly free horizontal symmetry can naturally lead to a massless up quark and to a corresponding accidental anomalous symmetry. Reviewing the controversy about the phenomenological viability of $m_u=0$ we conclude that this possiblity is still open and can solve the strong CP problem. To appear in the Proceedings of The Yukawa Couplings and the Origins of Mass Workshop.
We present a deterministic entanglement purification protocol (EPP) working for currently available experiment technique. In this protocol, we resort to the robust time-bin entanglement to purify the polarization entanglement determinately, which is quite different from the previous EPPs. After purification, one can obtain a completely pure maximally entangled pair with the success probability of 100%, in principle. As the maximal polarization entanglement is of vice importance in long-distance quantum communication, this protocol may have a wide application.
The response of pseudoscalar and vector mesons to strong magnetic fields is studied within a simple constituent quark model using analogy with bound states of Positronium. Magnetic moments of charged vector mesons K*, D*, B* are predicted and it is found that Eta mesons have magnetic polarizability. In extremely strong magnetic fields, behaviour of J/Psi mesons is discussed. We speculate on the existence of an induced magnetic moment of Eta meson.
We report combined first-principle and tight-binding (TB) calculations to simulate the effects of chemical edge modifications on structural and electronic properties. The C-C bond lengths and bond angles near the GNR edge have considerable changes when edge carbon atoms are bounded to different atoms. By introducing a phenomenological hopping parameter $t_{1}$ for nearest-neighboring hopping to represent various chemical edge modifications, we investigated the electronic structural changes of nanoribbons with different widths based on the tight-binding scheme. Theoretical results show that addends can change the band structures of armchair GNRs and even result in observable metal-to-insulator transition.
We investigate the consequences of an increase in the envelope helium abundance of pre-helium flash red giants in globular clusters. Comparing predictions with the CM diagrams of a few crucial GC, one finds no evidence for a substantial increase in the surface helium content of HB members of these clusters, at least for objects in the RR Lyrae region or close to it. The possibility that the most peculiar giants belong to the asymptotic giant branch is discussed. The consequences of a delay in the helium flash are briefly examined.
We study a variant of a problem considered by Dinaburg and Sinai on the statistics of the minimal solution to a linear Diophantine equation. We show that the signed ratio between the Euclidean norms of the minimal solution and the coefficient vector is uniformly distributed modulo one. We reduce the problem to an equidistribution theorem of Anton Good concerning the orbits of a point in the upper half-plane under the action of a Fuchsian group.
We investigate the classical phase space of 2-d string theory. We derive the linearised covariant equations for the spacetime fields by considering the most general deformation of the energy-momentum tensor which describes $c=1$ matter system coupled to 2-d gravity and by demanding that it respect conformal invariance. We derive the gauge invariances of the theory, and so investigate the classical phase space, defined as the space of all solutions to the equations of motion modulo gauge transformations. We thus clarify the origins of two classes of isolated states.
We use the Green's function formalism to discuss the role of strong correlations to the spatial structure of acceptor states doped into a two-dimensional Mott-Hubbard antiferromagnetic insulator. When the scattering between doped carriers, at the nesting wave vector ${\bf Q}=(\pi,\pi)$, is strong enough to produce a momentum dependent scattering rate, $\Gamma_{\bf k}$, the corresponding acceptor states become spatially anisotropic. As an example, we calculate the spatial structure of an acceptor state bound to an attractive two-dimensional Dirac delta potential, for a simple form of $\Gamma_{\bf k}$. We then discuss the role of such spatial anisotropy for the understanding of an apparent discrepancy between low temperature transport data and photoemission spectra in lightly doped La(2-x)Sr(x)CuO(4).
We have explored the possibility of driving pulsation modes in models of sdO stars in which the effects of element diffusion, gravitational settling and radiative levitation have been neglected so that the distribution of iron-peak elements remains uniform throughout the evolution. The stability of these models was determined using a non-adiabatic oscillations code. We analysed 27 sdO models from 16 different evolutionary sequences and discovered the first ever sdO models capable of driving high-radial order g-modes. In one model, the driving is by a classical kappa-mechanism due to the opacity bump from iron-peak elements at temperature ~200,000 K. In a second model, the driving result from the combined action of kappa-mechanisms operating in three distinct regions of the star: (i) a carbon-oxygen partial ionization zone at temperature ~2 10^6 K, (ii) a deeper region at temperature ~2 10^7 K, which we attribute to ionization of argon, and (iii) at the transition from radiative to conductive opacity in the core of the star.
We study the ionization and thermal evolution of the intergalactic medium during the epoch of \heii reionization by means of radiation hydrodynamical cosmological simulations. We post-process baryonic density fields from a standard optically-thin IGM simulation with a homogeneous galaxy-dominated UV background (UVB) which reionizes \hi and \hei at z=6.5 but does not have any contribution to the ionization of \heii. Quasars with luminosities proportional to the mass of the host halos are then introduced as point sources throughout the 100 Mpc simulation volume consistent with the Pei luminosity function. We evolve the spatial distribution of the \heii ionizing radiation field using a time-implicit variable tensor Eddington factor radiative transfer scheme. Simultaneously, we also solve for the local ionization of \heii to \heii and the associated photoheating of the gas. We find that the percolation of the \heiii regions is essentially complete by z=2.5. When comparing to a self-consistent optically thin simulation we find that in optically thick calculation the gas temperature is higher by a factor of approximately 1.7 at the mean gas density level. We use 300 random lines of sight to compute at $\bar{z} = 2.5 \pm 0.1$ a mean \heii \lya line transmission of $\bar{F} = 0.304 \pm 0.002$. We compare the broadening width of the \hi and \heii \lya lines to the results from the self-consistent optically thin simulation and find a shift by approximately 1.25 km/s of the b-parameter distribution. Estimating the relative broadening width between the two forests shows that the \heii median b-parameter is about 0.8 times the median \hi broadening width. This implies that the \heii absorbers are physically extended consistent with conclusions from observed lines of sight.
This paper presents a real-time approach for single-colored ball detection and tracking. The approach consists of two main phases. In a first offline calibration phase, the intrinsic parameters of the camera and the radial distortion are estimated, and a classification of colors is learned from a sample image of colored balls. The second phase consists of four main steps: (1) color segmentation of the input image into several regions based on the offline classification, (2) robust estimation of the circle parameters (3) refinement of the circle parameters, and (4) ball tracking. The experimental results showed that the approach presents a good compromise between suitability for real-time navigation and robustness to occlusions, background congestion and colors interference in the scene.
Some fraction of narrow absorption lines are physically associated to the quasar/host-galaxy materials (i.e., intrinsic NALs) like those of BALs and mini-BALs. The relation between these three types of absorption lines has not been understood yet, however one interpretation is that these absorption features correspond to different inclination angles. In this study, we search for intrinsic NALs in 11 BAL/mini-BAL quasar spectra retrieved from VLT/UVES public archive, in order to test a possible relation of intrinsic NALs and BALs/mini-BALs in the geometry models. We use partial coverage analysis to separate intrinsic NALs from ones which are associated to cosmologically intervening materials like foreground galaxies and intergalactic medium (i.e., intervening NALs). We identify one reliable and two possible intrinsic NAL systems out of 36 NAL systems in 9 BAL/mini-BAL quasar spectra after removing two quasars without clear BAL features. In spite of a small sample size, we placed a lower limit on the fraction of BAL/mini-BAL quasars that have at least one intrinsic C IV NAL ($\sim33^{+33}_{-18}\%$). This can be interpreted that intrinsic NAL absorbers exist everywhere regardless of inclination angle. We found that one of the intrinsic NAL systems detected in SDSS J121549.80-003432.1 is located at a large radial distance of R > 130 kpc, using a method of photoionization model with ground/excited-state lines. Considering the wide range of intrinsic NAL absorber distribution in inclination angles and radial distances, it suggests that origins and geometry of them are more complicated than we expected.
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of collective creations on the vacuum) in the stochastic limit satisfy a particular kind of Quantum Boltzmann (or free) commutational relations. This clarifies a general phenomenon of arising of Quantum Boltzmann relations in interacting systems.
The aim of this paper is to investigate the transition of a strongly magnetized neutron star into the accretion regime with very low accretion rate. For this purpose we monitored the Be-transient X-ray pulsar GRO J1008-57 throughout a full orbital cycle. The current observational campaign was performed with the Swift/XRT telescope in the soft X-ray band (0.5-10 keV) between two subsequent Type I outbursts in January and September 2016. The expected transition to the propeller regime was not observed. However, the transitions between different regimes of accretion were detected. In particular, after an outburst the source entered a stable accretion state characterised by the accretion rate of ~10^14-10^15 g/s. We associate this state with accretion from a cold (low-ionised) disc of temperature below ~6500 K. We argue that a transition to such accretion regime should be observed in all X-ray pulsars with certain combination of the rotation frequency and magnetic field strength. The proposed model of accretion from a cold disc is able to explain several puzzling observational properties of X-ray pulsars.
Hypergraph expanders are hypergraphs with surprising, non-intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of $3$-uniform hypergraph expanders with polylogarithmic degree. We generalize this construction, giving a simple construction of $r$-uniform hypergraph expanders for all $r \geq 3$.
Metal halide perovskites are an important class of emerging semiconductors. Their charge dynamics is poorly understood due to limited knowledge of defect physics and charge recombination mechanisms. Nevertheless, classical ABC and Shockley-Read-Hall (SRH) models are ubiquitously applied to perovskites without considering their validity. Herein, an advanced technique mapping photoluminescence quantum yield (PLQY) as a function of both the excitation pulse energy and repetition frequency is developed and employed to examine the validity of these models. While ABC and SRH fail to explain the charge dynamics in a broad range of conditions, the addition of Auger recombination and trapping to the SRH model enables a quantitative fitting of PLQY maps and low-power PL decay kinetics, and extracting trap concentrations and efficacies. Higher-power PL kinetics requires the inclusion of additional non-linear processes. The PLQY mapping developed herein is suitable for a comprehensive testing of theories and is applicable to any semiconductor.
We have studied the discrete electronic spectrum of closed metallic nanotube quantum dots. At low temperatures, the stability diagrams show a very regular four-fold pattern that allows for the determination of the electron addition and excitation energies. The measured nanotube spectra are in excellent agreement with theoretical predictions based on the nanotube band structure. Our results permit the complete identification of the electron quantum states in nanotube quantum dots.
We study the character sums \[\phi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left(x(x^{m}+a)(x^{n}+b)\right),\textrm{ and, } \psi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left((x^{m}+a)(x^{n}+b)\right)\] where $\phi$ is the quadratic character defined over $\mathbb{F}_q$. These sums are expressed in terms of Gaussian hypergeometric series over $\mathbb{F}_q$. Then we use these expressions to exhibit the number of $\mathbb{F}_q$-rational points on families of hyperelliptic curves and their Jacobian varieties.
We argue that multi-trace interactions in quantum field theory on the boundary of AdS space can be incorporated in the AdS/CFT correspondence by using a more general boundary condition for the bulk fields than has been considered hitherto. We illustrate the procedure for a renormalizable four-dimensional field theory with a $(\Tr \Phi^2)^2$ interaction. In this example, we show how the AdS fields with the appropriate boundary condition reproduce the renormalization group effects found in the boundary field theory. We also construct in related examples a line of fixed points with a nonperturbative duality, and a flow between two methods of quantization.
Properties of entangled photon pairs generated in spontaneous parametric down-conversion are investigated in interference experiments. Strong energy correlations are demonstrated in a direct way. If a signal photon is detected behind a narrow spectral filter, then interference appears in the Mach-Zehnder interferometer placed in the route of the idler photon, even if the path difference in the interferometer exceeds the coherence length of the light. Narrow time correlations of the detection instants are demonstrated for the same photon-pair source using the Hong-Ou-Mandel interferometer. Both these two effects may be exhibited only by an entangled state.
The $\Gamma$-limit for a sequence of length functionals associated with a one parameter family of Riemannian manifolds is computed analytically. The Riemannian manifold is of `two-phase' type, that is, the metric coefficient takes values in $\{1,\beta\}$, with $\beta$ sufficiently large. The metric coefficient takes the value $\beta$ on squares, the size of which are controlled by a single parameter. We find a family of examples of limiting Finsler metrics that are piecewise affine with infinitely many lines of discontinuity. Such an example provides insight into how the limit metric behaves under variations of the underlying microscopic Riemannian geometry, with implications for attempts to compute such metrics numerically.
The first-order metal-insulator transition (MIT) in paramagnetic $V_{2}O_{3}$ is studied within the ab-initio scheme LDA+DMFT, which merges the local density approximation (LDA) with dynamical mean field theory (DMFT). With a fixed value of the Coulomb $U=6.0 eV$, we show how the abrupt pressure driven MIT is understood in a new picture: pressure-induced decrease of the trigonal distortion within the strong correlation scenario (which is not obtained within LDA). We find good quantitative agreement with $(i)$ switch of the orbital occupation of $(a_{1g},e_{g1}^{\pi}, e_{g2}^{\pi})$ and the spin state S=1 across the MIT, $(ii)$ thermodynamics and $dc$ resistivity, and $(iii)$ the one-electron spectral function, within this new scenario.
In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the Perron-Frobenius theorem, and, with regard to the case of reversible Markov chain, via the principal eigenvalue approach; (ii) for regime-switching diffusions with countable state spaces by means of a finite partition trick and an M-Matrix theory. We then apply our theory to study the stabilization for linear switching models. Several examples are given to demonstrate our theory.
We investigate the large time behavior of solutions to the spatially homogeneous linear Boltzmann equation from a semigroup viewpoint. Our analysis is performed in some (weighted) $L^{1}$-spaces. We deal with both the cases of hard and soft potentials (with angular cut-off). For hard potentials, we provide a new proof of the fact that, in weighted $L^{1}$-spaces with exponential or algebraic weights, the solutions converge exponentially fast towards equilibrium. Our approach uses weak-compactness arguments combined with recent results of the second author on positive semigroups in $L^{1}$-spaces. For soft potentials, in $L^{1}$-spaces, we exploits the convergence to ergodic projection for perturbed substochastic semigroup to show that, for very general initial datum, solutions to the linear Boltzmann equation converges to equilibrium in large time. Moreover, for a large class of initial data, we also prove that the convergence rate is at least algebraic. Notice that, for soft potentials, no exponential rate of convergence is expected because of the absence of spectral gap.
Near-infrared medium-resolution spectra of seven bright brown dwarfs are presented. The spectra were obtained with the Infrared Camera (IRC) on board the infrared astronomical satellite AKARI, covering 2.5--5.0 um with a spectral resolution of approximately 120. The spectral types of the objects range from L5 to T8, and enable us to study the spectral evolution of brown dwarfs. The observed spectra are in general consistent with the predictions from the previous observations and photospheric models. We find that the CO fundamental band around 4.6 um is clearly seen even in the T8 dwarf 2MASS J041519-0935, confirming the presence of non-equilibrium chemical state in the atmosphere. We also identify the CO_2 fundamental stretching-mode band at 4.2 um for the first time in the spectra of late-L and T-type brown dwarfs.   We analyze the observed spectra by comparing with the predicted ones based on the Unified Cloudy Model (UCM). Although overall spectral energy distributions (SEDs) can be reasonably fitted with the UCM, observed CO and CO_2 bands in late-L and T-dwarfs are unexpectedly stronger than the model predictions assuming local thermodynamical equilibrium (LTE). We examine the vertical mixing model and find that this model explains the CO band at least partly in the T-dwarfs 2MASS J041519-0935 and 2MASS J055919-1404. The CO fundamental band also shows excess absorption against the predicted one in the L9 dwarf SDSS J083008+4828. Since CO is already highly abundant in the upper photospheres of late-L dwarfs, the extra CO by vertical mixing has little effect on the CO band strengths, and the vertical mixing model cannot be applied to this L-dwarf. A more serious problem is that the significant enhancement of the CO_2 4.2 um band in both the late-L and T dwarfs cannot be explained at all by the vertical mixing model. The enhancement of the CO_2 band remains puzzling.