ShantanuT01/DACTYL-Pretraining huggingface dataset:
An annular magnetic memory that uses a spin-polarized current to switch the magnetization direction or helicity of a magnetic region is proposed. The device has magnetic materials in the shape of a ring (1 to 5 nm in thickness, 20 to 250 nm in mean radius and 8 to 100 nm in width), comprising a reference magnetic layer with a fixed magnetic helicity and a free magnetic layer with a changeable magnetic helicity. These are separated by a thin non-magnetic layer. Information is written using a current flowing perpendicular to the layers, inducing a spin-transfer torque that alters the magnetic state of the free layer. The resistance, which depends on the magnetic state of the device, is used to read out the stored information. This device offers several important advantages compared to conventional spin-transfer magnetic random access memory (MRAM) devices. First, the ring geometry offers stable magnetization states, which are, nonetheless, easily altered with short current pulses. Second, the ring geometry naturally solves a major challenge of spin-transfer devices: writing requires relatively high currents and a low impedance circuit, whereas readout demands a larger impedance and magnetoresistance. The annular device accommodates these conflicting requirements by performing reading and writing operations at separate read and write contacts placed at different locations on the ring.
We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting distribution of height $n$ by simple random walk on the critical Galton-Watson tree conditioned on non-extinction at generation $n$. We extend the results of arxiv:1502.05584 to prove that, with high probability, the mass of the harmonic measure $\mu_n$ carried by a random vertex uniformly chosen from height $n$ is approximately equal to $n^{-\lambda_\alpha}$, where the constant $\lambda_\alpha >\frac{1}{\alpha-1}$ depends only on the index $\alpha$. In the analogous continuous model, this constant $\lambda_\alpha$ turns out to be the typical local dimension of the continuous harmonic measure. Using an explicit formula for $\lambda_\alpha$, we are able to show that $\lambda_\alpha$ decreases with respect to $\alpha\in(1,2]$, and it goes to infinity at the same speed as $(\alpha-1)^{-2}$ when $\alpha$ approaches 1.
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT .
We summarize the screening theory of the integer quantized Hall effect (IQHE) and emphasize its two key mechanisms: first, the existence, in certain magnetic field intervals, of incompressible strips, with integer values of the local filling factor and quantized values of longitudinal and Hall resistivity, and second, the confinement of an imposed dissipative current to these strips, leading to the quantization of the global resistances. We demonstrate that, without any localization assumption, this theory explains the enormous experimental reproducibility of the quantized resistance values, as well as experimental results on the potential distribution in narrow Hall bars. We further demonstrate that inclusion of long-range potential fluctuations allows to apply the theory to wider Hall bars, and can lead to a broadening of the quantum Hall plateaus, whereas short-range disorder tends to narrow the plateaus.
Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen as small ellipses. The orientation and axial ratio of the ellipses could then be used to trace the properties of the lens. We introduce and solve an ordinary homogeneous linear first order differential equation which describes completely the radial cluster lens. It can be used to reconstruct the lens mappeing from the measured axial ratios of lensed background galaxies.
This is a theoretical study of finite voltage effects on the conductance, the shot noise power, and the third charge-transfer cumulant for graphene-based Corbino disk in the presence of external magnetic fields. Periodic magnetoconductance oscillations, predicted in Refs. [1,2], become invisible for relatively small source-drain voltages, as the current decays rapidly with magnetic field. Quantum interference still governs the behavior of higher charge-transfer cumulants.
We present evidence that $>25$ MeV solar proton events show a clustering in time at intervals of $\approx$ six months that persisted during the rising and peak phases of Solar Cycle 24. This phenomenon is most clearly demonstrated by considering events originating in the northern or southern solar hemispheres separately. We examine how these variations in the solar energetic particle (SEP) event rate are related to other phenomena, such as hemispheric sunspot numbers and areas, rates of coronal mass ejections, and the mean solar magnetic field. Most obviously, the SEP event rate closely follows the sunspot number and area in the same hemisphere. The $\approx$ six-month variations are associated with features in many of the other parameters we examine, indicating that they are just one signature of the episodic development of Cycle 24. They may be related to the "$\approx$150~day" periodicities reported in various solar and interplanetary phenomena during previous solar cycles. The clear presence of $\approx$six-month periodicities in Cycle 24 that evolve independently in each hemisphere conflicts with a scenario suggested by McIntosh et al. (2015, Nature Com. 6, 6491) for the variational time scales of solar magnetism.
The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function. We prove that it has a density function which we can explicitly construct. Moreover, we prove an asymptotic formula for the number of zeros of the Lerch zeta-function on the right side of the critical line, whose main term is associated with the density function.
We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order to avoid stressed bonds may change the phase diagram. In contrast to what happens on random graphs and in some recent numerical studies at zero temperature, we do not find a true intermediate phase separating the usual rigid and floppy ones.
By using our recent generalization of the colliding waves concept to metric-affine gravity theories, and also our generalization of the advanced and retarded time coordinate representation in terms of Jacobi functions, we find a general class of colliding wave solutions with fourth degree polynomials in metric-affine gravity. We show that our general approach contains the standard second degree polynomials colliding wave solutions as a particular case.
For G = GL_2, PGL_2 and SL_2 we prove that the perverse filtration associated to the Hitchin map on the cohomology of the moduli space of twisted G-Higgs bundles on a Riemann surface C agrees with the weight filtration on the cohomology of the twisted G character variety of C, when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.
We argue that the process gamma +A \to J/psi + gap + X at large momentum transfer provides a quick and effective way to test onset of a novel perturbative QCD regime of strong absorption for the interaction of small dipoles at the collider energies. We find that already the first heavy ion run at the LHC will allow to study this reaction with sufficient statistics via ultraperipheral collisions hence probing the interaction of q\bar q dipoles of sizes ~ 0.2 fm with nuclear media down to x ~ 10^{-5}.
Due to thermal pulses, asymptotic giant branch (AGB) stars experience periods of convective mixing that provide ideal conditions for slow neutron-capture nucleosynthesis. These processes are affected by large uncertainties and are still not fully understood. By the lucky coincidence that about a quarter of all post-AGB stars turn hydrogen-deficient in a final flash of the helium-burning shell, they display nuclear processed material at the surface providing an unique insight to nucleosynthesis and mixing. We present results of non-local thermodynamic equilibrium spectral analyses of the extremely hot, hydrogen-deficient, PG 1159-type central stars of the Skull Nebula NGC 246 and the "Galactic Soccerballs" Abell 43 and NGC 7094.
We consider the irreducibility of Generalised Laguerre Polynomials for negative integral values given by $L_n^{(-1-n-s)}(x)=\displaystyle\sum_{j=0}^{n}\binom{n-j+s}{n-j}\frac{x^j}{j!}.$ For different values of $s,$ this family gives polynomials which are of great interest. It was proved earlier that for $0 \leq s \leq 60,$ these polynomials are irreducible over $\mathbb{Q}.$ In this paper we improve this result upto $s \leq 88.$
Cosmology and other scientific results from the WMAP mission require an accurate knowledge of the beam patterns in flight. While the degree of beam knowledge for the WMAP one-year and three-year results was unprecedented for a CMB experiment, we have significantly improved the beam determination as part of the five-year data release. Physical optics fits are done on both the A and the B sides for the first time. The cutoff scale of the fitted distortions on the primary mirror is reduced by a factor of ~2 from previous analyses. These changes enable an improvement in the hybridization of Jupiter data with beam models, which is optimized with respect to error in the main beam solid angle. An increase in main-beam solid angle of ~1% is found for the V2 and W1-W4 differencing assemblies. Although the five-year results are statistically consistent with previous ones, the errors in the five-year beam transfer functions are reduced by a factor of ~2 as compared to the three-year analysis. We present radiometry of the planet Jupiter as a test of the beam consistency and as a calibration standard; for an individual differencing assembly, errors in the measured disk temperature are ~0.5%.
For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to nonlinear equations and eigenvalue problems.
We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches for yielding binary codes, our method is based on a dimensionality-reduction criterion that its resulting mapping is designed to preserve the image relationships entailed by the inner products of sparse codes, rather than those implied by the Euclidean distances in the ambient space. While the proposed formulation does not require computing any sparse codes, the underlying computation model still inevitably involves solving an unmanageable eigenproblem when extremely high-dimensional descriptors are used. To overcome the difficulty, we consider the column-sampling technique and presume a special form of rotation matrix to facilitate subproblem decomposition. We test our method on several challenging image datasets and demonstrate its effectiveness by comparing with state-of-the-art binary coding techniques.
A graph K is square-free if it contains no four-cycle as a subgraph. A graph K is multiplicative if GxH -> K implies G -> K or H -> K, for all graphs G,H. Here GxH is the tensor (or categorical) graph product and G -> K denotes the existence of a graph homomorphism from G to K. Hedetniemi's conjecture states that all cliques K_n are multiplicative. However, the only non-trivial graphs known to be multiplicative are K_3, odd cycles, and still more generally, circular cliques $K_{p/q}$ with 2 <= p/q < 4. We make no progress for cliques, but show that all square-free graphs are multiplicative. In particular, this gives the first multiplicative graphs of chromatic number higher than 4. Generalizing, in terms of the box complex, the topological insight behind existing proofs for odd cycles, we also give a different proof for circular cliques.
We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, while if the energy is lower than the threshold the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as function of inter-atomic distance and temperature by using renormalization group and Monte Carlo simulations. The phase diagram, the equation of state, the isothermal modulus and the thermal expansion are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as function of the inter-atomic distance.
An analysis of the iron L-shell emission in the publicly available spectrum of the Capella binary system, as obtained by the High Energy Transmission Grating Spectrometer on board the Chandra X-ray Observatory, is presented. The atomic-state model, based on the HULLAC code, is shown to be especially adequate for analyzing high-resolution x-ray spectra of this sort. Almost all of the spectral lines in the 10 - 18 Angstrom wavelength range are identified. It is shown that, for the most part, these lines can be attributed to emission from L-shell iron ions in the Capella coronae. Possibilities for electron temperature diagnostics using line ratios of Fe16+ are demonstrated. It is shown that the observed iron-L spectrum can be reproduced almost entirely by assuming a single electron temperature of kTe= 600 eV. This temperature is consistent with both the measured fractional ion abundances of iron and with the temperature derived from ratios of Fe16+ lines. A volume emission measure of 1053 cm-3 is calculated for the iron L-shell emitting regions of the Capella coronae indicating a rather small volume of 1029 cm3 for the emitting plasma if an electron density of 1012 cm-3 is assumed.
The bulk piezoelectric response, as measured by the piezoelectric modulus tensor (\textbf{d}), is determined by a combination of charge redistribution due to strain and the amount of strain produced by the application of stress (stiffness). Motivated by the notion that less stiff materials could exhibit large piezoelectric responses, herein we investigate the piezoelectric modulus of van der Waals-bonded quasi-2D ionic compounds using first-principles calculations. From a pool of 869 known binary and ternary quasi-2D materials, we have identified 135 non-centrosymmetric crystals of which 48 systems are found to have \textbf{d} components larger than the longitudinal piezoelectric modulus of AlN (a common piezoelectric for resonators), and three systems with the response greater than that of PbTiO$_3$, which is among the materials with largest known piezoelectric modulus. None of the identified materials have previously been considered for piezoelectric applications. Furthermore, we find that large \textbf{d} components always couple to the deformations (shearing or axial) of van der Waals "gaps" between the layers and are indeed enabled by the weak intra-layer interactions.
We present the analysis of a peculiar W~Virginis (pWVir) type-II Cepheid, OGLE-LMC-T2CEP-211 ($P_{puls}=9.393\,d$), in a double-lined binary system ($P_{orb}=242\,d$), which shed light on virtually unknown evolutionary status and structure of pWVir stars. The dynamical mass of the Cepheid (first ever for a type-II Cepheid) is $0.64\pm{}0.02\,M_\odot$ and the radius $R=25.1\pm{}0.3\,R_\odot$. The companion is a massive ($5.67\,M_\odot$) main-sequence star obscured by a disk. Such configuration suggests a mass transfer in the system history. We found that originally the system ($P_{orb}^{init}=12\,d$) was composed of $3.5$ and $2.8\,M_\odot$ stars, with the current Cepheid being more massive. The system age is now $\sim{}$200 My, and the Cepheid is almost completely stripped of hydrogen, with helium mass of $\sim{}92\%$ of the total mass. It finished transferring the mass 2.5 My ago and is evolving towards lower temperatures passing through the instability strip. Comparison with observations indicate a reasonable $2.7\cdot{}10^{-8}\,M_\odot/y$ mass loss from the Cepheid. The companion is most probably a Be main-sequence star with $T=22000\,K$ and $R=2.5\,R_\odot$. Our results yield a good agreement with a pulsation theory model for a hydrogen-deficient pulsator, confirming the described evolutionary scenario. We detected a two-ring disk ($R_{disk}\sim\,116\,R_{\odot}$) and a shell ($R_{shell}\sim\,9\,R_{\odot}$) around the companion, that is probably a combination of the matter from the past mass transfer, the mass being lost by the Cepheid due to wind and pulsations, and a decretion disk around a rapidly rotating secondary. Our study together with observational properties of pWVir stars suggests that their majority are products of a similar binary evolution interaction.
The growth rate of cosmic structure is a powerful cosmological probe for extracting information on the gravitational interactions and dark energy. In the late time Universe, the growth rate becomes non-linear and is usually probed by measuring the two point statistics of galaxy clustering in redshift space up to a limited scale, retaining the constraint on the linear growth rate f. In this letter, we present an alternative method to analyse the growth of structure in terms of local densities, i.e. f(Delta). Using N-body simulations, we measure the function of f(Delta) and show that structure grows faster in high density regions and slower in low density regions. We demonstrate that f(Delta) can be modelled using a log-normal Monte Carlo Random Walk approach, which provides a means to extract cosmological information from f(Delta). We discuss prospects for applying this approach to galaxy surveys.
We briefly report on NLO QCD corrections to the $pp \to t\bar{t} B +X$ process, where $B$ stands for $H,\,W^\pm$ or $Z$. In the calculation all double-, single and non-resonant Feynman diagrams, interferences and finite-width effects are included for the top quark and $W^\pm/Z$ gauge bosons. Numerical results are shown at the differential cross section level for various factorisation and renormalisation scale settings and a few PDF sets. The main theoretical uncertainties associated with neglected higher-order terms in the perturbative expansion and with different parametrisations of the PDFs are also discussed. Furthermore, we compare our complete predictions for $pp\to t\bar{t} B+X$ in multi-lepton final states to the calculation in the narrow-width approximation.
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C^1 boundary, the other stated for sets with finite perimeter.
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments.   We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. This enables us to demonstrate that the role of quantum measurement suggested is incorrect, and further, that the use of information theory to resolve Szilard's paradox is both unnecessary and insufficient. Finally we show that, if the concept of 'active information' is extended to cover thermal density matrices, then many of the conceptual problems raised by this paradox appear to be resolved.
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to solve this equation in a straightforward manner just by solving the Schrodinger equation and taking the stochastic expectation value of its solutions after an adequate modification. Using the linear entropy as a figure of merit (basically the loss of quantum coherence) the distinction of four kinds of environments is suggested.
Consider a fibered power of an elliptic surface. We characterize its subvarieties that contain a Zariski dense set of points that are torsion points in fibers with complex multiplication. This result can be viewed as a mix of the Manin-Mumford and Andr\'e-Oort Conjecture and is related to a conjecture of Pink. The main technical tool is a new height inequality. We also use it to give another proof of a case of Gubler's result on the Bogomolov Conjecture over function fields.
The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-B$\ddot{a}$cklund transformation of ZMS equation is obtained.