ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a theoretical study of the deuterated species detectability in various types of extragalactic star-forming regions based on our predictions of chemical abundances. This work is motivated by the past and current attempts at observing deuterated species in external galaxies such as NGC~253, IC~342 and the LMC. Here, we investigate the influence of the density, the temperature, the FUV radiation field, the cosmic ray ionisation, and the metallicity on the fractional abundances and D/H abundance ratios of about 20 deuterated species. Without modelling any particular source, we determined how the deuterium chemistry behaves in different physical environments such as starburst, cosmic-rays enhanced environments, low metallicity and high redshift galaxies. In general, our predicted column densities seem in good agreement with those derived from the current limited dataset of observations in external galaxies. We provide, for the first time, a list of key deuterated species whose abundances are high enough to be possibly detectable by the Atacama Large Millimeter Array (ALMA) and Herschel, as a function of galactic nuclear activity and redshift.
The constraints imposed by chiral symmetry on hadron correlation functions in nuclear medium are discussed. It is shown that these constraints imply a certain structure for the in-medium hadron correlators and lead to the cancelation of the order $\rho m_\pi$ term in the in-medium nucleon correlator. We also consider the effect of mixing of the chiral partners correlation functions arising from the interaction of nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. The different scenarios of such restoration are briefly discussed.
We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion $U$ while there is no finite average moment in the ground states at lower densities.
Theoretically calculated power spectra are compares with observed solar p-mode velocity power spectra over a range of mode degree and frequency. The depth for the sources responsible for exciting p-modes of frequency 2.0 mHz is determined from the asymmetry of their power spectra and found to be about 800 km below the photosphere for quadrupole sources and 150 km if sources are dipole. The source depth for high frequency oscillations of frequency greater than about 6 mHz is 180 (50) km for quadrupole (dipole) sources.
Temperature dependent crystal structures of the quasi-one-dimensional ladder material BaFe2Se3 are examined. Combining the optical second harmonic generation (SHG) experiments and neutron diffraction measurements, we elucidate the crystal structure with Pmn2_1 space group in the low-temperature phase below Ts2 = 400 K, further above Neel temperature. This low-temperature phase loses the spatial inversion symmetry, where a resultant macroscopic polarization emerges along the rung direction. The transition is characterized by block-type lattice distortions with the magneto-striction mechanism. Change in the electrical resistivity and the magnetic susceptibility across the polar-nonpolar transition also suggests a modification of the electronic states reflecting the structural instability. Consistency and discrepancy with the existing theory are discussed.
We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that besides coherence properties, these states exhibit a squeezing and a deformation (cooling) of the phase--space trajectories, both of which strongly depend on the form of the nonlinear function. The presence of the extra nonlinear term in the phase of the wave functions has also relevant consequences on photon statistics and correlation properties. The non quadratic structure of the associated Hamiltonians suggests that these states be generated in connection with multiphoton processes in media with higher nonlinearities.
Self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters $ \beta_d$ and $ \beta_h $, so that the former controls the distance ($ d $) between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths. The probability measure for local movements is supposed to be the one for the "true self-avoiding walk" multiplied by a factor exponentially decaying with $ d $. After a transient behavior for short times, a variety of behaviors have been observed for large times depending on the value of $\beta_d$ and $\beta_h$. Our statistical analysis reveals that the system undergoes a crossover between two (small and large $\beta_d$) regimes identified in large times ($t$). In the small $\beta_d$ regime, the random walkers (identified by the position of the legs of the spider) remain on average in a fixed non-zero distance in the large time limit, whereas in the second regime (large $\beta_d$s), the absorbing force between the walkers dominates the other stochastic forces. In the latter regime, $ d $ decays in a power-law fashion with the logarithm of time. When the system is mapped to a growth process (represented by a height field which is identified by the number of visits for each point), the roughness and the average height show different behaviors in two regimes, i.e., they show power-law with respect to $t$ in the first regime, and $\log t$ in the second regime. The fractal dimension of the random walker traces and the winding angle are shown to consistently undergo a similar crossover.
In this paper, we establish the second order estimates of solutions to the first initial-boundary value problem for general Hessian type fully nonlinear parabolic equations on Riemannian manifolds. The techniques used in this article can work for a wide range of fully nonlinear PDEs under very general conditions.
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of individual clusters over the states of an ideal gas is replaced by the averaging over the states of a non-correlated crystal using single-particle cell potentials. As a result, we arrive at the expansion of the partition function in correlations on the basis of single-particle functions corresponding to the multiplicative approximation. The cell potentials defining these functions are found from the condition of the minimum of the remainder in the constructed decomposition.
The MAGIC telescope located on the Roque de los Muchachos on the Canary Island La Palma at a height of 2200 m a.s.l. is able to point to the sea. This permits a search for air shower signatures induced by particles coming out of the Earth. An analytical approximation results in tau neutrino effective areas from ~10^3 m^2 (at 100 TeV) to 10^5 m^2 (at 1 EeV) for an observation angle of about 1 degree below the horizon, rapidly diminishing with further inclination. Taking into account the huge effective area, this configuration was investigated for its suitability to search for ultra-high energy (UHE) tau-neutrino signatures. The outcome of simulations for tau-neutrino signatures will be presented, models for astrophysical neutrino sources reviewed, and estimated event rates in MAGIC are shown.
Expansions in non-integer bases have been investigated abundantly since their introduction by R\'enyi. It was discovered by Erd\H{o}s et al. that the sets of numbers with a unique expansion have a much more complex structure than in the integer base case. The present paper is devoted to the continuity properties of these maps with respect to the Hausdorff metric.
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings the solution is negative on a non-negligible set.
Starting from a recent model where the Kbar N amplitudes are evaluated from the chiral Lagrangians using a coupled channel unitary method, we evaluate here the scattering length for K^- deuteron scattering. We find that the double scattering contribution is very large compared to the impulse approximation and that the charge exchange contribution of this rescattering is as large as the sequential K^- scattering on the two nucleons. Higher order rescattering corrections are evaluated using coupled channels with K^- and Kbar^0 within the integral form of the fixed centre approximation to the Faddeev equations. The higher order corrections involving intermediate pions and hyperons are found negligible.
In this paper, we study the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the relaxation operator, Fokker-Planck operator and linearized Boltzmann operator are considered. By constructing equivalent temporal energy functionals, time rates of the solution approaching equilibrium in some Hilbert spaces are obtained when the spatial domain takes the whole space or torus and when there is a confining force or not. The main tool of the proof is the macro-micro decomposition combined with Kawashima's argument on dissipation of the hyperbolic-parabolic system. Finally, a Korn-type inequality with probability measure is provided to deal with dissipation of momentum components.
We construct the Lagrangeans of N=3 and N=4 two-form supergravities. The two-form gravity theories are classically equivalent to the Einstein gravity theories and can be formulated as gauge theories. The gauge algebras used here can be identified with the subalgebra of N=3 superconformal algebra and SU(2)\times SU(2)\times U(1)-extended N=4 superconformal algebra.
Let $\xi$ be a Gaussian white noise on $\mathbb R^d$ ($d=1,2,3$). Let $(\xi_\varepsilon)_{\varepsilon>0}$ be continuous Gaussian processes such that $\xi_\varepsilon\to\xi$ as $\varepsilon\to0$, defined by convolving $\xi$ against a mollifier. We consider the asymptotics of the parabolic Anderson model (PAM) with noise $\xi_{\varepsilon(t)}$ for large time $t\gg1$, and the Dirichlet eigenvalues of the Anderson Hamiltonian (AH) with potential $\xi_{\varepsilon(t)}$ on large boxes $(-t,t)^d$, where the parameter $\varepsilon(t)$ vanishes as $t\to\infty$. We prove that the asymptotics in question exhibit a phase transition in the rate at which $\varepsilon(t)$ vanishes, which distinguishes between the behavior observed in the AH/PAM with continuous Gaussian noise and white noise. By comparing our main theorems with previous results on the AH/PAM with white noise, our results show that some asymptotics of the latter can be accessed with solely elementary methods, and we obtain quantitative estimates on the difference between the AH/PAM with white noise and its continuous-noise approximations as $t\to\infty$.
Learning to predict the long-term future of video frames is notoriously challenging due to inherent ambiguities in the distant future and dramatic amplifications of prediction error through time. Despite the recent advances in the literature, existing approaches are limited to moderately short-term prediction (less than a few seconds), while extrapolating it to a longer future quickly leads to destruction in structure and content. In this work, we revisit hierarchical models in video prediction. Our method predicts future frames by first estimating a sequence of semantic structures and subsequently translating the structures to pixels by video-to-video translation. Despite the simplicity, we show that modeling structures and their dynamics in the discrete semantic structure space with a stochastic recurrent estimator leads to surprisingly successful long-term prediction. We evaluate our method on three challenging datasets involving car driving and human dancing, and demonstrate that it can generate complicated scene structures and motions over a very long time horizon (i.e., thousands frames), setting a new standard of video prediction with orders of magnitude longer prediction time than existing approaches. Full videos and codes are available at https://1konny.github.io/HVP/.
The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and multiple links of the same direction between any two nodes. Scaling exponents in the range of 1-2 are obtained through Monte Carlo simulations and various clustering coefficients are calculated, one of which, $C_{\rm out}$, is of order $10^{-1}$, indicating the network resembles a small-world. The out-degree distribution has an exponential cut-off for large out-degree.
We consider linear age-structured population equations with diffusion. Supposing maximal regularity of the diffusion operator, we characterize the generator and its spectral properties of the associated strongly continuous semigroup. In particular, we provide conditions for stability of the zero solution and for asynchronous exponential growth.
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classical one. We also show that, depending on the size of the slits, the predictions of quantum approach could be apparently different with those of the aforementioned stochastic description
The Sun affects the Earth's physical phenomena in multiple ways, in particular the material in interplanetary space comes from coronal expansion in the form of inhomogeneous plasma flow (solar wind), which is the primary source of the interplanetary medium. Ground-based Interplanetary Scintillation (IPS) observations are an important and effective method for measuring solar wind speed and the structures of small diameter radio sources. We discuss one mode of ground-based single-station observations: Single-Station Single-Frequency (SSSF) mode. To realize the SSSF mode, a new system has been established at Urumqi Astronomical Observatory (UAO), China, and a series of experimental observations were carried out successfully from May to December, 2008.
We review recent results obtained for charge asymmetric systems at Fermi energies. Observables sensitive to the isospin dependent part of nuclear interaction are discussed, providing information on the symmetry energy behavior below normal density.
The Vista Variables in the Via Lactea (VVV) ESO Public Survey consists in a near-infrared time-series survey of the Galactic bulge and inner disk, covering 562 square degrees of the sky, over a total timespan of more than 5 years. In this paper, we provide an updated account of the current status of the survey, especially in the context of stellar variability studies. In this sense, we give a first description of our efforts towards the construction of the VVV Variable Star Catalog (VVV-VSC).
Direct detection experiments rule out fermion dark matter that is a chiral representation of the electroweak gauge group. Non-chiral real, complex and singlet representations, however, provide viable fermion dark matter candidates. Although any one of these candidates will be virtually impossible to detect at the LHC, it is shown that they may be detected at future planned direct detection experiments. For the real case, an irreducible radiative coupling to quarks may allow a detection. The complex case in general has an experimentally ruled out tree-level coupling to quarks via Z-boson exchange. However, in the case of two SU(2)_L doublets, a higher dimensional coupling to the Higgs can suppress this coupling, and a remaining irreducible radiative coupling may allow a detection. Singlet dark matter could be detected through a coupling to quarks via Higgs exchange. Since all non-chiral dark matter can have a coupling to the Higgs, at least some of its mass can be obtained from electroweak symmetry breaking, and this mass is a useful characterization of its direct detection cross-section.
The feasibility of Veselago lensing in graphene with a p-n junction is investigated numerically for realistic injection leads. Two different set-ups with two narrow leads are considered with absorbing or reflecting side edges. This allows us to separately determine the influence of scattering on electron focusing for the edges and the p-n interface. Both semiclassical and tight-binding simulations show a distinctive peak in the transmission probability that is attributed to the Veselago lensing effect. We investigate the robustness of this peak on the width of the injector, the position of the p-n interface and different gate potential profiles. Furthermore, the influence of scattering by both short- and long-range impurities is considered.
The influence of triaxial deformation $\gamma$ on the purely collective form of wobbling motion in even-even nuclei are discussed based on the triaxial rotor model. It is found that the harmonic approximation is realized well when $\gamma=30^{\circ}$ for the properties of energy spectra and electric quadrupole transition probabilities, while this approximation gets bad when $\gamma$ deviates from $30^{\circ}$. A recent data from Coulomb excitation experiment, namely $3_1^+$ and $2_2^+$ for the $^{110}$Ru are studied and might be suggested as the bandhead of the wobbling bands. In addition, two types of angular momentum geometries for wobbling motion, stemming from different $\gamma$ values, are exhibited by azimuthal plots.
Scene flow is a description of real world motion in 3D that contains more information than optical flow. Because of its complexity there exists no applicable variant for real-time scene flow estimation in an automotive or commercial vehicle context that is sufficiently robust and accurate. Therefore, many applications estimate the 2D optical flow instead. In this paper, we examine the combination of top-performing state-of-the-art optical flow and stereo disparity algorithms in order to achieve a basic scene flow. On the public KITTI Scene Flow Benchmark we demonstrate the reasonable accuracy of the combination approach and show its speed in computation.
We describe an algorithm to compute the zeta function of any non-hyperelliptic genus 3 plane curve $C$ over a finite field with automorphism group $G = \mathbb{Z} / 2 \mathbb{Z}$. This algorithm computes in the Monsky-Washnitzer cohomology of~the curve. Using the relation between the Monsky-Washnitzer cohomology of $C$ and its quotient $E := C/G$, the computation splits into 2 parts: one in a subspace of the Monsky-Washnitzer cohomology and a second which reduces to the point counting on an elliptic curve $E$. The former corresponds to the dimension $2$ abelian surface $\mathrm{ker}(\mathrm{Jac}(C) \rightarrow E)$, on which we can compute with lower precision and with matrices of smaller dimension. Hence we obtain a faster algorithm than working directly on the curve $C$.
We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the amount of work an agent can extract depends on how well it can guess the micro-state of the system. In general it depends both on the agent's knowledge and risk-tolerance, because the agent can bet on facts that are not certain and thereby risk failure of the work extraction. We derive strikingly simple expressions for the extractable work in the extreme cases of effectively zero- and arbitrary risk tolerance respectively, thereby enveloping all cases. Our derivation makes a connection between heat engines and the smooth entropy approach. The latter has recently extended Shannon theory to encompass finite sized and internally correlated bit strings, and our analysis points the way to an analogous extension of statistical mechanics.
We revisit the issue of memory effects, i.e. effects giving rise to a net cumulative change of the configuration of test particles, using a toy model describing the emission of radiation by a compact source and focusing on the scalar, hence non-radiative, part of the Riemann curvature. Motivated by the well known fact that gravitational radiation is accompanied by a memory effect, i.e. a permanent displacement of the relative separation of test particles, present after radiation has passed, we investigate the existence of an analog effect in the non-radiative part of the gravitational field. While quadrupole and higher multipoles undergo oscillations responsible for gravitational radiation, energy, momentum and angular momentum are conserved charges undergoing non-oscillatory change due to radiation emission. We show how the source re-arrangement due to radiation emission produce time-dependent scalar potentials which induce a time variation in the scalar part of the Riemann curvature tensor. As a result, on general grounds a velocity memory effect appears, depending on the inverse of the square of the distance of the observer from the source, thus making it almost impossible to observe, as shown by comparison to the planned gravitational detector noise spectral densities.
This paper presents a general existence and uniqueness result for harmonic maps with prescribed singularities into non-positively curved targets, and surveys a number of applications to general relativity. It is based on a talk delivered by the author at The 11th Mathematical Society of Japan Seasonal Institute, The Role of Metrics in the Theory of Partial Differential Equations.