ShantanuT01/DACTYL-Pretraining huggingface dataset:
The rapid development of nanoscience and nanotechnology in the last two decades was stimulated by the emergence of scanning probe microscopy (SPM) techniques capable of accessing local material properties, including transport, mechanical, and electromechanical behavior on the nanoscale. Here, we analyze the general principles of electromechanical probing by piezoresponse force microscopy (PFM), a scanning probe technique applicable to a broad range of piezoelectric and ferroelectric materials. The physics of image formation in PFM is compared to Scanning Tunneling Microscopy and Atomic Force Microscopy in terms of the tensorial nature of excitation and the detection signals and signal dependence on the tip-surface contact area. It is shown that its insensitivity to contact area, capability for vector detection, and strong orientational dependence render this technique a distinct class of SPM. The relationship between vertical and lateral PFM signals and material properties are derived analytically for two cases: transversally-isotropic piezoelectric materials in the limit of weak elastic anisotropy, and anisotropic piezoelectric materials in the limit of weak elastic and dielectric anisotropies. The integral representations for PFM response for fully anisotropic material are also obtained. The image formation mechanism for conventional (e.g., sphere and cone) and multipole tips corresponding to emerging shielded and strip-line type probes are analyzed. Resolution limits in PFM and possible applications for orientation imaging on the nanoscale and molecular resolution imaging are discussed.
We investigate the norm maps of algebraic even $K$-groups of finite extensions of number fields. Namely, we show that they are surjective in most situations. In the event that they are not surjective, we give a criterion in determining when an element in the even $K$-group of the base field comes from a norm of an element from the even $K$-groups of the extension field. This latter criterion is only reliant on the real primes of the base field.
Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.
Modern numerical simulations of the formation of the first stars predict that the first stars formed in multiples. In those cases, the chemical yields of multiple supernova explosions may have contributed to the formation of a next generation star. We match the chemical abundances of the oldest observed stars in the universe to a database of theoretical supernova models, to show that it is likely that the first stars formed from the ashes of two or more progenitors.
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the experimental realisation of such a protocol is impeded by the large effort required to estimate the fidelity of an implemented gate. With a hierarchy of approximations we find a faithful approximation to the quantum process fidelity that can be estimated experimentally with reduced effort. Its practical use is demonstrated with the optimisation of a three-qubit quantum gate on a commercially available quantum processor.
To better understand the physical properties of accretion disks in high-mass star formation, we present a study of a 12 high-mass accretion disk candidates observed at high spatial resolution with the Australia Telescope Compact Array (ATCA) in the NH3 (4,4) and (5,5) lines. Almost all sources were detected in NH3, directly associated with CH3OH Class II maser emission. From the remaining eleven sources, six show clear signatures of rotation and/or infall motions. These signatures vary from velocity gradients perpendicular to the outflows, to infall signatures in absorption against ultracompact HII regions, to more spherical infall signatures in emission. Although our spatial resolution is ~1000AU, we do not find clear Keplerian signatures in any of the sources. Furthermore, we also do not find flattened structures. In contrast to this, in several of the sources with rotational signatures, the spatial structure is approximately spherical with sizes exceeding 10^4 AU, showing considerable clumpy sub-structure at even smaller scales. This implies that on average typical Keplerian accretion disks -- if they exist as expected -- should be confined to regions usually smaller than 1000AU. It is likely that these disks are fed by the larger-scale rotating envelope structure we observe here. Furthermore, we do detect 1.25cm continuum emission in most fields of view.
A short replay to the comment of Rossetti & Molendi (astro-ph/0702417) in answer to the paper of Fusco-Femiano, Landi & Orlandini 2007 regarding the presence of a nonthermal component in the Coma Cluster spectrum.
Methods. We perform numerical simulations of the evolution of the cosmic web for the conventional LCDM model. The simulations cover a wide range of box sizes L = 256 - 4000 Mpc/h, mass and force resolutions and epochs from very early moments z = 30 to the present moment z = 0. We calculate density fields with various smoothing lengths to find the dependence of the density field on smoothing scale. We calculate PDF and its moments - variance, skewness and kurtosis. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale, the amplitude of fluctuations and the redshift. During the evolution the reduced skewness $S_3= S/\sigma$ and reduced kurtosis $S_4=K/\sigma^2$ present a complex behaviour: at a fixed redshift curves of $S_3(\sigma)$ and $S_4(\sigma)$ steeply increase with $\sigma$ at $\sigma\le 1$ and then flatten out and become constant at $\sigma\ge2$. If we fix the smoothing scale $R_t$, then after reaching the maximum at $\sigma\approx 2$, the curves at large $\sigma$ start to gradually decline. We provide accurate fits for the evolution of $S_{3,4}(\sigma,z)$. Skewness and kurtosis approach at early epochs constant levels, depending on smoothing length: $S_3(\sigma) \approx 3$ and $S_4(\sigma) \approx 15$. Conclusions. Most of statistics of dark matter clustering (e.g., halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the $\sigma$ with the relatively modest correction to explicit dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of moments on evolutionary epoch $z$ and smoothing length $R_t$ is very different, together they determine the evolution of $S_{3,4}(\sigma)$ uniquely. The evolution of $S_3$ and $S_4$ cannot be described by current theoretical approximations.
We report the successful electrical creation of spin polarization in p-type Si at room temperature by using an epitaxial MgO(001) tunnel barrier and Fe(001) electrode. Reflection high-energy electron diffraction observations revealed that epitaxial Fe/MgO(001) tunnel contacts can be grown on a (2 x 1) reconstructed Si surface whereas tunnel contacts grown on the (1 x 1) Si surface were polycrystalline. Transmission electron microscopy images showed a more flat interface for the epitaxial Fe/MgO/Si compared to that of the polycrystalline structure. For the Fe/MgO/p-Si devices, the Hanle and inverted Hanle effects were clearly observed at 300 K by using a three-terminal configuration, proving that spin polarization can be induced in the Si at room temperature. Effective spin lifetimes deduced from the width of the Hanle curve were 95 +/- 6 ps and 143 +/- 10 ps for the samples with polycrystalline and epitaxial MgO tunnel contacts, respectively. The observed difference can be qualitatively explained by the local magnetic field induced by the larger roughness of the interface of the polycrystalline sample. The sample with epitaxial Fe/MgO tunnel contact showed higher magnitude of the spin accumulation with a nearly symmetric behavior with respect to the bias polarity whereas that of the polycrystalline MgO sample exhibited a quite asymmetric evolution. This might be attributed to the higher degree of spin polarization of the epitaxial Fe/MgO(001) tunnel contact, which acts as a spin filter. Our experimental results suggest that an epitaxial MgO barrier is beneficial for creating spins in Si.
In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections to the Kahler potential. We analyse the two-loop corrections on the Coulomb branch for a complex deformation. For an arbitrary chiral field in the Cartan subalgebra we reduce the problem of computing the two-loop Kahler potential to that of diagonalising the mass matrix, we then present the result in a manifestly superconformal form. The mass matrix diagonalisation is performed for the case of the chiral background that induces the breaking pattern SU(N) -> SU(N-2)*U(1)^2. Then, for the gauge group SU(3), the Kahler potential is explicitly computed to the two-loop order.
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem. It is shown that, with any given system of gravitating bodies, one may associate a one-parameter family of similar systems, the parameter measuring the gravitational field-strength. After a specific change of units, the derivation of asymptotic expansions becomes straightforward. Two hypotheses could be made as to which time variable has to be used in the expansion. The first one leads to an "asymptotic" post-Newtonian approximation (PNA) with instantaneous propagation, differing from the standard PNA in that, in the asymptotic PNA, all fields are expanded. The second hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA) allowing to describe propagation effects, but it is not compatible with the Newtonian limit. It is shown that the standard PNA is not compatible with the application of the usual method of asymptotic expansions as envisaged here.
We consider partial zeta functions $\zeta(s,c)$ associated with ray classes $c$'s of a totally real field. Stark's conjecture implies that an appropriate product of $\exp(\zeta'(0,c))$'s is an algebraic number which is called a Stark unit. Shintani gave an explicit formula for $\exp(\zeta'(0,c))$ in terms of Barnes' multiple gamma function. Yoshida ``decomposed'' Shintani's formula: he defined the symbol $X(c,\iota)$ satisfying that $\exp(\zeta'(0,c))=\prod_{\iota} \exp(X(c,\iota))$ where $\iota$ runs over all real embeddings of $F$. Hence we can decompose a Stark unit into a product of $[F:\mathbb Q]$ terms. The main result is to show that $([F:\mathbb Q]-1)$ of them are algebraic numbers. We also study a relation between Yoshida's conjecture on CM-periods and Stark's conjecture.
These lectures give a detailed introduction to constructing and analyzing string vacua suitable for phenomenological model building, with particular emphasis on F-theory flux vacua. Topics include (1) general challenges and overview of some proposed scenarios, (2) an extensive introduction to F-theory and its relation to M-theory and perturbative IIB string theory, (3) F-theory flux vacua and moduli stabilization scenarios, (4) a practical geometrical toolkit for constructing string vacua from scratch, (5) statistics of flux vacua, and (6) explicit models.
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $\rho$ and $\phi$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $\rho$ and $\phi$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $\rho$ and $\phi$ production data provided we use a set of light quark masses with $m_{u,d}$ < $m_{s}$ ~ 0.14 GeV.
A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion coefficient. It is shown that no particularly natural, unique interpretation of the equation is possible. This phenomenon is reflected in the behavior of numerical schemes for its resolution and points to similar issues that potentially affect its nonlinear counterpart.
We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations.
Let $X$ be an algebraic variety, defined over the rationals. This paper gives upper bounds for the number of rational points on $X$, with height at most $B$, for the case in which $X$ is a curve or a surface. In the latter case one excludes from the counting function those points that lie on lines in the surface. The bounds are uniform for all $X$ of a given degree. They are best possible in the case of curves. As an application it is shown that if $F$ is an irreducible binary form of degree 3 or more then almost all integers represented by $F$ have essentially one such representation.
There is a very natural map from the configuration space of n distinct points in Euclidean 3-space into the flag manifold U(n)/U(1)^n, which is compatible with the action of the symmetric group. The map is well-defined for all configurations of points provided a certain conjecture holds, for which we provide numerical evidence. We propose some additional conjectures, which imply the first, and test these numerically. Motivated by the above map, we define a geometrical multi-particle energy function and compute the energy minimizing configurations for up to 32 particles. These configurations comprise the vertices of polyhedral structures which are dual to those found in a number of complicated physical theories, such as Skyrmions and fullerenes. Comparisons with 2-particle and 3-particle energy functions are made. The planar restriction and the generalization to hyperbolic 3-space are also investigated.
We report the discovery of the first radio pulsar associated with NGC 6712, an eclipsing black widow (BW) pulsar, J1853$-$0842A, found by high-sensitivity searches using the Five-hundred-meter Aperture Spherical radio Telescope. This 2.15 ms pulsar is in a 3.56 hr compact circular orbit with a very low mass companion likely of mass 0.018 to 0.036 $M_{\rm \odot}$ and exhibits eclipsing of the pulsar signal. Though the distance to PSR J1853$-$0842A predicted from its dispersion measure ($155.125 \pm 0.004$ cm$^{-3}$ pc) and Galactic free electron density models are about 30\% smaller than that of NGC 6712 obtained from interstellar reddening measurements, this is likely due to limited knowledge about the spiral arms and Scutum stellar cloud in this direction. Follow-up timing observations spanning 445 days allow us to localize the pulsar's position to be 0.14 core radii from the center of NGC 6712 and measure a negative spin-down rate for this pulsar of $-2.39(2)\times10^{-21}\rm s s^{-1}$. The latter cannot be explained without the acceleration of the GC and decisively supports the association between PSR J1853--0842A and NGC 6712. Considering the maximum GC acceleration, Galactic acceleration, and Shklovskii effect, we place an upper limit on the intrinsic spin-down rate to be $1.11\times10^{-20}\rm~s~s^{-1}$. From an analysis of the eclipsing observations, we estimate the electron density of the eclipse region to be about $1.88\times10^6\rm cm^{-3}$. We also place an upper limit of the accretion rate from the companion is about $3.05\times10^{-13}~M_{\rm \odot}\rm~yr^{-1}$ which is comparable with some other BWs.
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.
Some exact identities connecting the one- and two-particle Green's functions in the presence of spin-orbit coupling have been derived. These identities is similar to the usual Ward identity in the particle or charge transport theory and a satisfying spin transport theory in spin-orbit coupling system should also preserve these identities.
We use the standard Runge-Kutta method to solve the set of basic equations describing black hole accretion flows composed of two-temperature plasma. We do not invoke any extra energy transport mechanism such as thermal conduction and do not specify any ad hoc outer boundary condition for the advection-dominated accretion flow (ADAF) solution. We find that in the case of high viscosity and non-zero radiative cooling, the ADAF solution can have an asymptotic approach to the Shakura-Sunyaev disk (SSD) solution, and the SSD-ADAF transition radius is close to the central black hole. Our results further prove the mechanism of thermal instability-triggered SSD-ADAF transition suggested previously by Takeuchi & Mineshige and Gu & Lu.
The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJKs photometry reaching stars in the oldest turn-off point all over the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy in the Star Formation History (SFH) that can be expected from VMC data, in particular for the LMC. To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground MW stars and background galaxies. We perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimization of a chi-squared-like statistics. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known Age--Metallicity Relation (AMR). It turns out that, for a given sky area, the random errors for ages older than ~0.4 Gyr seem to be independent of the crowding. For a spatial resolution of ~0.1 sqdeg, the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the smaller stellar statistics for stars younger than ~0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR(t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that the propagation of the errors in these parameters in the SFR(t) implies systematic errors below 30%.
Keck/LRIS multi-object spectroscopy has been carried out on 140 of some of the lowest and highest surface brightness faint (19 < R < 22) dwarf galaxy candidates in the core region of the Coma Cluster. These spectra are used to measure redshifts and establish membership for these faint dwarf populations. The primary goal of the low surface brightness sample is to test our ability to use morphological and surface brightness criteria to distinguish between Coma Cluster members and background galaxies using high resolution HST/ACS images. Candidates were rated as expected members, uncertain, or expected background. From 93 spectra, 51 dwarf galaxy members and 20 background galaxies are identified. Our morphological membership estimation success rate is ~100% for objects expected to be members and better than ~90% for galaxies expected to be in the background. We confirm that low surface brightness is a very good indicator of cluster membership. High surface brightness galaxies are almost always background with confusion arising only from the cases of the rare compact elliptical galaxies. The more problematic cases occur at intermediate surface brightness. Many of these galaxies are given uncertain membership ratings, and these were found to be members about half of the time. Including color information will improve membership determination but will fail for some of the same objects that are already mis-identified when using only surface brightness and morphology criteria. Compact elliptical galaxies with B-V colors ~0.2 magnitudes redward of the red sequence in particular require spectroscopic follow-up. In a sample of 47 high surface brightness, UCD candidates, 19 objects have redshifts which place them in the Coma Cluster. Redshift measurements are presented and the use of indirect means for establishing cluster membership is discussed.
A new Vaidya-type generalisation of Kerr space-time is constructed by requiring the Kerr mass and angular momentum per unit mass to depend upon a variable which has a simple geometrical origin. The matter distribution introduced in this way radiates mass and angular momentum at future null infinity. The Vaidya generalisation of the Schwarzschild space-time is a special case of the newly found solution.
We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.