ShantanuT01/DACTYL-Pretraining huggingface dataset:
The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.
The Fermi Large Area Telescope (Fermi LAT) collaboration has recently reported on 50 months of measurements of the isotropic Extragalactic Gamma Ray Background (EGRB) spectrum between $100\mbox{MeV}$ and $820\mbox{GeV}$. Ultrahigh Energy Cosmic Ray (UHECR) protons interact with the Cosmic Microwave Background (CMB) photons and produce cascade photons of energies $10\mbox{MeV}\mbox{-}1\mbox{TeV}$ that contribute to the EGRB flux. We examine seven possible evolution models for UHECRs and find that UHECR sources that evolve as the Star Formation Rate (SFR), medium low luminosity active galactic nuclei type-1 ($L = 10^{43.5}\mbox{erg sec}^{-1}$ in the $[0.5\mbox{-}2]\mbox{KeV}$ band), and BL Lacertae objects (BL Lacs) are the most acceptable given the constraints imposed by the observed EGRB. Other possibilities produce too much secondary $\gamma$-radiation. In all cases, the decaying dark matter contribution improves the fit at high energy, but the contribution of still unresolved blazars, which would leave the smallest role for decaying dark matter, may yet provide an alternative improvement.   The possibility that the entire EGRB can be fitted with resolvable but not-yet-resolved blazars, as recently claimed by Ajello et al. (2015), would leave little room in the EGRB to accommodate $\gamma$-rays from extragalactic UHECR production, even for many source evolution rates that would otherwise be acceptable. We find that, under the assumption of UHECRs being mostly protons, there is not enough room for producing extragalactic UHECRs with AGN, GRB, or even SFR source evolution. Sources that evolve as BL Lacs on the other hand, would produce much less secondary $\gamma$-radiation and would remain a viable source of UHECRs, provided that they dominate.
A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{45}$Ti, $^{46}$Ti, $^{46}$V and $^{48}$Cr to assess how proton-neutron pair correlations emerge under different scenarios. We also study how the presence of a one-body spin-obit interaction affects the contribution of the various pairing modes.
We report on the systematic characterization of photoluminescence (PL) lifetimes in NV- and NV0 centers in 2 MeV H+ implanted type Ib diamond samples by means of a time correlated single photon counting (TCSPC) microscopy technique. A dipole-dipole resonant energy transfer model was applied to interpret the experimental results, allowing a quantitative correlation of the concentration of both native (single substitutional nitrogen atoms) and ion-induced (isolated vacancies) PL-quenching defects with the measured PL lifetimes. The TCSPC measurements were carried out in both frontal (i.e. laser beam probing the main sample surface along the same normal direction of the previously implanted ions) and lateral (i.e. laser beam probing the lateral sample surface orthogonally with respect to the same ion implantation direction) geometries. In particular, the latter geometry allowed a direct probing of the centers lifetime along the strongly nonuniform damage profiles of MeV ions in the crystal. The extrapolation of empirical quasi-exponential decay parameters allowed the systematic estimation of the mean quantum efficiency of the centers as a function of intrinsic and ion-induced defect concentration, which is of direct relevance for the current studies on the use of diamond color centers for photonic applications.
In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy conditions, the smoothness of the joint density of the solution for this system has been studied by E. Nualart in [11]. The purpose of this paper is further to study the lower and upper bounds of the density. The main tools are the Malliavin calculus and the method developed by Kohatasu-Higa in [6] or E. Nualart and Quer-Sardanyons in [12].
We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size $k$ are reconfigurable in an $n$-vertex interval graph, then there is a reconfiguration sequence of length $\mathcal{O}(k\cdot n^2)$. We also provide a construction in which the shortest reconfiguration sequence is of length $\Omega(k^2\cdot n)$.   As a counterpart to these results, we also establish that $\textsf{Independent Set Reconfiguration}$ is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.
In 1994, based on Roberts' counterexample to Hilbert's fourteenth problem, A'Campo-Neuen constructed an example of a linear action of a 12-dimensional commutative unipotent group H_0 on a 19-dimensional vector space V such that the algebra of invariants k[V]^{H_0} is not finitely generated. We consider a certain extension H of H_0 by a one-dimensional torus and prove that H is epimorphic in SL(V). In particular, the homogeneous space SL(V)/H provides a new example of a homogeneous space with epimorphic stabilizer that admits no projective embeddings with small boundary.
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.
For medical image analysis, segmentation models trained on one or several domains lack generalization ability to unseen domains due to discrepancies between different data acquisition policies. We argue that the degeneration in segmentation performance is mainly attributed to overfitting to source domains and domain shift. To this end, we present a novel generalizable medical image segmentation method. To be specific, we design our approach as a multi-task paradigm by combining the segmentation model with a self-supervision domain-specific image restoration (DSIR) module for model regularization. We also design a random amplitude mixup (RAM) module, which incorporates low-level frequency information of different domain images to synthesize new images. To guide our model be resistant to domain shift, we introduce a semantic consistency loss. We demonstrate the performance of our method on two public generalizable segmentation benchmarks in medical images, which validates our method could achieve the state-of-the-art performance.
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$ with $q=\frac{2n}{n-2}$~: $$\inf_{\|u\|_{L^q}=1}\int_\Omega (1+|x|^\beta |u|^k)|\nabla u|^2.$$ We show that minimizers exist only in the range $\beta<kn/q$ which corresponds to a dominant non-linear term. On the contrary, the linear influence for $\beta\geq kn/q$ prevents their existence.
We find the leakage current through a double quantum dot in the Pauli spin blockade regime accounting for inelastic (spin-flip) cotunneling processes. Taking the energy-dependence of this spin-flip mechanism into account allows for an accurate description of the current as a function of applied magnetic fields, gate voltages, and an inter-dot tunnel coupling. In the presence of an additional local dephasing process or nonuniform magnetic field, we obtain a simple closed-form analytical expression for the leakage current giving the full dependence on an applied magnetic field and energy detuning. This work is important for understanding the nature of leakage, especially in systems where other spin-flip mechanisms (due, e.g., to hyperfine coupling to nuclear spins or spin-orbit coupling) are weak, including silicon and carbon-nanotube or graphene quantum dots.
We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $p_{g}=\left( \gamma-1\right) \rho_{g},$ where $\gamma$ is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universe. The ghost field Einstein permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.
We summarise the recent results in 1810.08093, where the Type IIB AdS$_6$ solutions T-dual to the Brandhuber-Oz solution to massive Type IIA supergravity are shown to fit within an extension to allow for delocalized 5- and 7-branes of the global AdS$_6 \times S^2$ solutions constructed by D'Hoker, Gutperle and Uhlemann. We show that the Abelian T-dual solution provides an explicit example of a Riemann surface with the topology of an annulus.
A superprocess limit for an interacting birth-death particle system modelling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not hold. We use a martingale problem approach and a separation of the slow (trait) and fast (age) scales. While the trait marginals converge in a pathwise sense to a superprocess, the age distributions, on another time scale, average to equilibria that depend on traits. The convergence of the whole process depending on trait and age, only holds for finite-dimensional time-marginals. We apply our results to the study of examples illustrating different cases of trade-off between competition and senescence.
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-differential operator. The well-posedness of the direct problem is examined in the distribution sense and the regularity of the solution is discussed for the given rough source. For the inverse problem, the strength of the random source, involved in the principal symbol of its covariance operator, is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band with probability one. Numerical experiments are presented to illustrate the validity and effectiveness of the proposed method for the case that the random source is the white noise.
Let $\mathcal S=\{s_1<s_2<s_3<\ldots\}$ be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For $X\ge2$ we denote by $g(X)$ the largest gap between consecutive elements of $\mathcal S$ that do not exceed $X$. We prove that for $X \to +\infty$ the lower bound $$g(X)\geq \left(\frac{390}{449}-o(1)\right)\ln X$$ holds.   This estimate is twice the recent estimate by R. Dietmann and C. Elsholtz.
We give some remarks on our papers with Minamide and Yanagida on Bridgeland stability conditions. We also give a remark on stability conditions on Enriques surfaces, and give another proof of the projectivity of the coarse moduli spaces of semi-stable objects, which were obtained by Nuer.
In the history of condensed matter physics, reinvestigation of a well-studied material with enhanced quality sometimes led to important scientific discoveries. A well-known example is the discovery of fractional quantum Hall effect in high quality GaAs/AlGaAs heterojunctions. Here we report the first single crystal growth and magnetoresistance (MR) measurements of the silver chalcogenide $\beta $-Ag$_2$Se (Naumannite), a compound has been known for the unusual, linear-field-dependent MR in its polycrystalline form for over a decade. With the quantum limit (QL) as low as 3 Tesla, a moderate field produced by a superconductor magnet available in many laboratories can easily drive the electrons in Ag$_2$Se to an unprecedented state. We observed significant negative longitudinal MR beyond the QL, which was understood as a `charge-pumping' effect between the novel fermions with opposite chiralities. Characterization of the single-crystalline Ag$_2$Se and the fabrication of electric devices working above the QL, will represent a new direction for the study of these exotic electrons.
One significant drawback of a spectroscopic ellipsometry (SE) technique is its time-consuming and often complicated analysis procedure necessary to assess the optical functions of thin-film and bulk samples. Here, to solve this inherent problem of a traditional SE method, we present a new general way that allows full automation of SE analyses for crystalline-phase semiconductors exhibiting complex absorption features. In particular, we have modified a scheme established in our previous study, which performs a non-linear SE fitting analysis only in a low energy region at the beginning, while the analyzed energy region is gradually expanded toward higher energy by incorporating addition optical transition peaks. In this study, we have further developed a unique analyzing-energy search algorithm, in which a proper analyzing-energy region is determined to incorporate the feature of a new transition peak. In the developed method, a drastic improvement over the previous simple approach has been confirmed for expressing complex dielectric functions consisting of sharp and broad absorption peaks. The proposed method (Delta M method) has been applied successfully to analyze perovskite-based crystalline samples, including hybrid perovskite (CH3NH3PbI3) and chalcogenide perovskites (SrHfS3 and BaZrS3). In the automated analyses of these semiconductors, 7-8 transition peaks are introduced automatically to describe sample dielectric functions, while structural parameters, such as thin-film and roughness thicknesses, are also determined simultaneously. The established method can drastically reduce an analysis time to a level that allows the automatic inspection of daily varying material optical properties and expands the application area of spectroscopic ellipsometry considerably.
The longitudinal and transverse structure functions are calculated for inclusive electron scattering from ${}^{12}$C and ${}^{40}$Ca in the quasielastic and dip region. The microscopic model presented here incorporates two-body currents derived from one-pion exchange and intermediate $\Delta$ excitation. The reaction mechanism involves both one-nucleon and two-nucleon knockout processes. It is demonstrated that, even for quasielastic kinematics, two-body currents give a substantial contribution to the transverse structure function. Furthermore, the observed excess of transverse strength in the dip region between the quasielastic and delta peak can be partially ascribed to direct two-nucleon knockout following photoabsorption on a two-body current.
We use the most up-to-date cosmological evolution models of star-forming (SF) galaxies and radio sources to compute the extragalactic number counts and the cosmic background from 408MHz to 12THz. The model of SF galaxies reproduces the constraints obtained by Spitzer, Herschel, and ground-based submm/mm experiments: number counts, redshift distribution of galaxies, cosmic background intensity and anisotropies. The template SEDs of this model are extrapolated to the radio adding synchrotron, free-free, and spinning dust emissions. To fix the synchrotron intensity, we use the IR/radio flux ratio, q70, and a spectral index beta=-3. For a constant q70, our model added to the AGN contribution provides a good fit to the number counts from 12THz to 408MHz and to the CIB. Spinning dust accounts for up to 20% of the cosmic microwave background produced by SF galaxies, but for less than 10% of the total background when AGN are included. The SF galaxies account for 77.5% of the number counts at 1.4GHz for a flux of 1e-4Jy. However, the model does not explain the CRB measured with the ARCADE2 experiment. Considering the case when q70 decreases strongly with redshift, this still does not explain the ARCADE2 results. It also yields to an overestimate of the low-flux number counts in the radio. Thus, we rule out a steep variation of q70 with redshift at least for z<3.5. Adding a population of faint SF galaxies at high redshift (Lir<1e11Lsun and 4<z<6), which would reproduce the ARCADE2 results, leads to predictions of the CIB much higher than what is observed, ruling out this as the explanation for the ARCADE2 results. Considering our findings and previous studies, we conclude that if the radio emission measured by ARCADE2 is astrophysical in origin, it has to originate in the Galaxy or in a new kind of radio sources (with no mid- to far-IR counterparts) or emission mechanism still to be discovered.
Observations of the clustering of galaxies can provide useful information about the distribution of dark matter in the Universe. In order to extract accurate cosmological parameters from galaxy surveys, it is important to understand how the distribution of galaxies is biased with respect to the matter distribution. The large-scale bias of galaxies can be quantified either by directly measuring the large-scale ({\lambda} >~ 60 hinv Mpc) power spectrum of galaxies or by modeling the halo occupation distribution of galaxies using their clustering on small scales ({\lambda} <~ 30 hinv Mpc). We compare the luminosity dependence of the galaxy bias (both the shape and the normalization) obtained by these methods and check for consistency. Our comparison reveals that the bias of galaxies obtained by the small scale clustering measurements is systematically larger than that obtained from the large scale power spectrum methods. We also find systematic discrepancies in the shape of the galaxy bias-luminosity relation. We comment on the origin and possible consequences of these discrepancies which had remained unnoticed thus far.
According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to describe the metrics on their spaces of vacua by means of the hyperk\"ahler quotient construction. To check the identification of moduli spaces a comparison is made with field theory predictions. For SU(2) theory with k fundamental hypermultiplets the Coulomb branch is expected to be the D_k ALF gravitational instanton, so our results lead to a construction of such spaces. In the special case of SU(2) theory with four or fewer fundamental hypermultiplets we calculate the complex structures on the moduli spaces and compare them with field-theoretical results. We also discuss some puzzles with brane realizations of three-dimensional N=4 theories.
A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy landscape analysis, implies that the density of states of an O(n) spin model on a lattice can be effectively approximated, at least close to the phase transition, in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. In the present paper we show that such a relation exactly holds, albeit in a slightly modified form, in the special cases of the mean-field XY model and of the one-dimensional XY model. We also discuss the possible consequences of this result for the general case.
During the last three decades, many papers have reported the existence of a luminosity-metallicity or mass-metallicity (M-Z) relation for all kinds of galaxies: The more massive galaxies are also the ones with more metal-rich interstellar medium. We have obtained the mass-metallicity relation at different lookback times for the same set of galaxies from the Sloan Digital Sky Survey (SDSS), using the stellar metallicities estimated with our spectral synthesis code STARLIGHT. Using stellar metallicities has several advantages: We are free of the biases that affect the calibration of nebular metallicities; we can include in our study objects for which the nebular metallicity cannot be measured, such as AGN hosts and passive galaxies; we can probe metallicities at different epochs of a galaxy evolution.   We have found that the M-Z relation steepens and spans a wider range in both mass and metallicity at higher redshifts for SDSS galaxies. We also have modeled the time evolution of stellar metallicity with a closed-box chemical evolution model, for galaxies of different types and masses. Our results suggest that the M-Z relation for galaxies with present-day stellar masses down to 10^10 solar masses is mainly driven by the star formation history and not by inflows or outflows.