ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a new type of diffuse interface model describing the evolution of a tumor mass under the effects of a chemical substance (e.g., a nutrient or a drug). The process is described by utilizing the variables $\varphi$, an order parameter representing the local proportion of tumor cells, and $\sigma$, representing the concentration of the chemical. The order parameter $\varphi$ is assumed to satisfy a suitable form of the Cahn-Hilliard equation with mass source and logarithmic potential of Flory-Huggins type (or generalizations of it). The chemical concentration $\sigma$ satisfies a reaction-diffusion equation where the cross-diffusion term has the same expression as in the celebrated Keller-Segel model. In this respect, the model we propose represents a new coupling between the Cahn-Hilliard equation and a subsystem of the Keller-Segel model. We believe that, compared to other models, this choice is more effective in capturing the chemotactic effects that may occur in tumor growth dynamics (chemically induced tumor evolution and consumption of nutrient/drug by tumor cells). Note that, in order to prevent finite time blowup of $\sigma$, we assume a chemical source term of logistic type. Our main mathematical result is devoted to proving existence of weak solutions in a rather general setting that covers both the two- and three- dimensional cases. Under more restrictive assumptions on coefficients and data, and in some cases on the spatial dimension, we prove various regularity results. Finally, in a proper class of smooth solutions we show uniqueness and continuous dependence on the initial data in a number of significant cases.
We study the effect of mesoscopic fluctuations on the validity of the Wiedemann--Franz (WF) law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, E_c, the WF law is satisfied for each specific sample but as the temperature is raised through E_c a sample-specific correction to the WF law of order 1/g appears (g is the dimensionless conductance) and then tends to zero again at high temperatures. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry, for which Lorenz number exhibits h/e flux-periodic Aharonov-Bohm oscillations.
We give meaning to differential equations with a rough path term and a Brownian noise term as driving signals. Such differential equations as well as the question of regularity of the solution map arise naturally and we discuss two applications: one revisits Clark's robustness problem in nonlinear filtering, the other is a Feynman--Kac type representation of linear RPDEs. En passant, we give a short and direct argument that implies integrability estimates for rough differential equations with Gaussian driving signals which is of independent interest.
We present SCUBA-2 450micron and 850micron observations of the Serpens MWC 297 region, part of the JCMT Gould Belt Survey of nearby star-forming regions. Simulations suggest that radiative feedback influences the star-formation process and we investigate observational evidence for this by constructing temperature maps. Maps are derived from the ratio of SCUBA-2 fluxes and a two component model of the JCMT beam for a fixed dust opacity spectral index of beta = 1.8. Within 40 of the B1.5Ve Herbig star MWC 297, the submillimetre fluxes are contaminated by free-free emission with a spectral index of 1.03+-0.02, consistent with an ultra-compact HII region and polar winds/jets. Contamination accounts for 73+-5 per cent and 82+-4 per cent of peak flux at 450micron and 850micron respectively. The residual thermal disk of the star is almost undetectable at these wavelengths. Young Stellar Objects are confirmed where SCUBA-2 850micron clumps identified by the fellwalker algorithm coincide with Spitzer Gould Belt Survey detections. We identify 23 objects and use Tbol to classify nine YSOs with masses 0.09 to 5.1 Msun. We find two Class 0, one Class 0/I, three Class I and three Class II sources. The mean temperature is 15+-2K for the nine YSOs and 32+-4K for the 14 starless clumps. We observe a starless clump with an abnormally high mean temperature of 46+-2K and conclude that it is radiatively heated by the star MWC 297. Jeans stability provides evidence that radiative heating by the star MWC 297 may be suppressing clump collapse.
Some repeating fast radio burst (FRB) sources exhibit complex polarization behaviors, including frequency-dependent depolarization, variation of rotation measure (RM), and oscillating spectral structures of polarized components. Very recently, Feng et al. (2022) reported that active repeaters exhibit conspicuous frequency-dependent depolarization and a strong correlation between RM scatter ($\sigma_{\rm RM}$) and the temporal scattering time ($\tau_{\rm s}$), $\sigma_{\rm RM}\propto\tau_{\rm s}^{1.0\pm0.2}$, both of which can be well described by multi-path propagation through a magnetized inhomogeneous plasma screen. This observation strongly suggests that the temporal scattering and RM scatter originate from the same region. Besides, a particular finding of note in Feng et al. (2022) is that the FRBs with compact persistent radio sources (PRS) tend to have extreme $\sigma_{\rm RM}$. In this work, we focus on some theoretical predictions on the relations among temporal scattering, depolarization by RM scatter, and PRS contributed by the magnetized plasma environment close to a repeating FRB source. The behaviors of the RM scatter imply that the magnetized plasma environment is consistent with a supernova remnant or a pulsar wind nebula, and the predicted $\sigma_{\rm RM}$-$\tau_{\rm s}$ relation is $\sigma_{\rm RM}\propto\tau_{\rm s}^{(0.54-0.83)}$ for different astrophysical scenarios. We further make a general discussion on PRS that does not depend on specific astrophysical scenarios. We show that the specific luminosity of a PRS should have a positive correlation with the RM contributed by the plasma screen. This is consistent with the observations of FRB 121102 and FRB 190520B.
In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital relaxation. The direct numerical study of these processes is challenging because the fast orbital motion imposed by the central black hole requires very small timesteps. An alternative approach, pioneered by Gauss, is to use the secular approximation of smearing out the $N$ stars over their Keplerian orbits, using $K$ nodes along each orbit. In this study we propose three novel improvements to this method. First, we re-formulate the discretisation of the rates of change of the variables describing the orbital states to ensure that all conservation laws are exactly satisfied. Second, we replace the pairwise sum over nodes by a multipole expansion up to order $\ell_{\mathrm{max}}$, reducing the overall computational costs from $O(N^2K^2)$ to $O(NK\ell_{\mathrm{max}}^2)$. Finally, we show that the averaged dynamical system is equivalent to $2N$ interacting unit spin vectors and provide two time integrators: a second-order symplectic scheme and a fourth-order Lie-group Runge-Kutta method, both of which are straightforward to generalize to higher order. These new simulations recover the diffusion coefficients of stellar eccentricities obtained through analytical calculations of the secular dynamics.
Electronic properties of ultrathin dielectric films consistently attract much attention since they play important roles in various electronic devices, such as field effect transistors and memory elements. Insulating properties of the gate oxide in transistors represent the key factor limiting Moore's law. The dielectric strength of the insulating film limits how much energy can be stored in nanocapacitors. The origin of the electric current in the nanometer-scale insulating barrier remains unexplained. Here we present an optically transparent Al-Al2O3-graphene nanocapacitor suitable for studying electronic transport in calibrated nanoscale dielectric films under high electric fields and with light exposure. The controllable flow of photons provides an additional powerful probe helping to resolve the puzzle of the electric conductivity in these high-quality insulating films. The dielectric alumina, Al2O3, is deposited by atomic layer deposition technology. With this device we observe a photon-assisted field emission effect, in which the effective barrier height is reduced by a quantity equal to the photon energy. Our main finding is a reversed photoeffect. Namely, at sufficiently high bias voltages the current through the dielectric film decreases as the light intensity increases. Moreover, higher photon energies correlate with stronger decreases of the current. To explain this reversed photoeffect, we present a qualitative model based on a conjecture that electrons leak into the dielectric and form charged sandpile-like branching patterns, which facilitate transport, and which can be dispersed by light.
We apply the perturbative chiral quark model to the study of the low-energy pi-N interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave pi-N scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p^2) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e^2) radiative corrections to the pi-N scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the pi(-)p atom in the 1s state, which is relevant for the experiment "Pionic Hydrogen" at PSI.
To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.
We classify birationally rigid orbifold Fano 3-folds of index one defined by $5 \times 5$ Pfaffians. We give a sharp criterion for birational rigidity of these families based on the type of singularities that the varieties admit. Various conjectures are born out of our study, highlighting a possible approach to the classification of terminal Fano 3-folds. The birationally rigid cases are the first known rigid examples of Fanos that are not (weighted) complete intersection.
Red giants in the updated APOGEE-Kepler catalogue, with estimates of mass, chemical composition, surface gravity and effective temperature, have recently challenged stellar models computed under the standard assumption of solar calibrated mixing length. In this work, we critically reanalyse this sample of red giants, adopting our own stellar model calculations. Contrary to previous results, we find that the disagreement between the effective temperature scale of red giants and models with solar calibrated mixing length disappears when considering our models and the APOGEE-Kepler stars with scaled solar metal distribution. However, a discrepancy shows up when alpha-enhanced stars are included in the sample. We have found that assuming mass, chemical composition and effective temperature scale of the APOGEE-Kepler catalogue, stellar models generally underpredict the change of temperature of red giants caused by alpha-element enhancements at fixed [Fe/H]. A second important conclusion is that the choice of the outer boundary conditions employed in model calculations is critical. Effective temperature differences (metallicity dependent) between models with solar calibrated mixing length and observations appear for some choices of the boundary conditions, but this is not a general result
Within $R^2$ gravity, we study the linear stability of strongly gravitating spherically symmetric configurations supported by a polytropic fluid. All calculations are carried out in the Jordan frame. It is demonstrated that, as in general relativity, the transition from stable to unstable systems occurs at the maximum of the curve mass-central density of the fluid.
Compilation of papers presented by the VERITAS Collaboration at the 35th International Cosmic Ray Conference (ICRC), held July 12 through July 20, 2017 in Busan, South Korea.
Abridged.   Low-metallicity star-forming dwarf galaxies are prime targets to understand the chemical enrichment of the interstellar medium. The HI region provides important constraints on the dispersal and mixing of heavy elements released by successive star-formation episodes. Our primary objective is to study the enrichment of the HI region and the interplay between star-formation history and metallicity evolution.   We observed the most metal-poor star-forming galaxy in the Local Universe, I Zw 18, with Hubble/COS. The abundances in the neutral gas are derived from far-UV absorption-lines (HI, CII, CII*, NI, OI, ...) and are compared to the abundances in the HII region. Models are constructed to calculate the ionization structure and the thermal processes. We investigate the gas cooling in the HI region through physical diagnostics drawn from the fine-structure level of C+.   We find that HI region abundances are lower by a factor of ~2 as compared to the HII region. There is no differential depletion on dust between the HI and HII region. Using sulfur as a metallicity tracer, we calculate a metallicity of 1/46 solar (vs. 1/31 in the HII region). From the study of abundance ratios, we propose that C, N, O, and Fe are mainly produced in massive stars. We argue that the HI envelope may contain pockets of pristine gas with a metallicity essentially null. Finally, we derive the physical conditions in the HI region by investigating the CII* absorption line. The cooling rate derived from CII* is consistent with collisions with H atoms in the diffuse neutral gas. We calculate the star-formation rate from the CII* cooling rate assuming that photoelectric effect on dust is the dominant gas heating mechanism. Our determination is in good agreement with the values in the literature if we assume a low dust-to-gas ratio (~2000 times lower than the Milky Way value).
In this paper we demonstrate experimentally the implementation of a niobium-trilayer junction with an aluminum-oxide tunnel barrier, embedded in a high-gap superconducting niobium-titanium-nitride circuit. Previously reported heating by quasiparticle trapping is removed by inserting a normal metal layer of gold between the niobium junction and the niobium-titanium-nitride layer. We analyze in dc-characterization measurements the cooling of the nonequilibrium quasiparticles in various device geometries having different gold layer thickness and shape. Our work is concluded with remarks for future heterodyne mixer experiments using our device technology.
We present a mean-field model of the dense nuclear matter equation of state designed for use in computationally demanding hadronic transport simulations. Our approach, based on the relativistic Landau Fermi-liquid theory, allows us to construct a family of equations of state spanning a wide range of possible bulk properties of dense QCD matter. We implement the developed model in the hadronic transport code SMASH, and show that the resulting dynamic behavior reproduces theoretical expectations for the thermodynamic properties of the system based on the underlying equation of state. In particular, we show that pair distribution functions calculated from hadronic transport simulation data are consistent with theoretical expectations based on the second-order cumulant ratio, and can be used as a signature of crossing the phase diagram in the vicinity of a critical point. We additionally present a novel method that may enable a measurement of the speed of sound and its derivative with respect to the baryon number density in heavy-ion collisions. Application of our approach to available experimental data implies that the derivative of the speed of sound is non-monotonic in systems created in collisions at intermediate to low energies, which in turn may be connected to non-trivial features in the underlying equation of state.
Halide perovskites are a promising class of materials for optoelectronic applications, due to their excellent optoelectronic performance. However, they suffer several dynamical degradation problems, the characterization of which is challenging in experiments. Atomic scale simulations can provide valuable insights, however, the high computational cost of traditional quantum mechanical methods such as DFT makes it difficult to model dynamical processes in large perovskite systems. In this work, we present a re-parameterized GFN1-xTB method for the accurate description of structural and dynamical properties of CsPbBr\textsubscript{3}, CsPbI\textsubscript{3}, and CsPb(I\textsubscript{1-x}Br\textsubscript{x})\textsubscript{3}. Our molecular dynamics simulations show that the phase stability is strongly correlated to the displacement of ions in the perovskites. In the low temperature orthorhombic phase, the directional movement of the Cs cations decreases contact with the surrounding halides, initiating a transition to the non-perovskite phase. However, this loss of contact can be compensated by increased halide displacement, once enough thermal energy is available, resulting in a transition to the tetragonal or cubic phases. Furthermore, we find the mixing of halides increase halide displacement over a significant range of temperatures, resulting in lower phase transition temperatures and therefore improved phase stability.
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$ order accurate Runge-Kutta scheme. The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors determined by comparing numerical and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations. The main part of our investigations is, however, centered on construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content. Remarkably the applied new method is unprecedented in that it allows to construct initial data for highly boosted and spinning black holes, essentially for the full physical allowed ranges of these parameters. In addition, the use of the evolutionary form of the constraints is free from applying any sort of boundary conditions in the strong field regime.
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w_{12}, led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a "Klazar violator" vertex in an increasing ordered tree and observe that w_{12} counts what we call Klazar trees--increasing ordered trees with no Klazar violators. A highlight of the paper is a bijection from n-edge increasing ordered trees to perfect matchings of [2n]={1,2,...,2n} that sends Klazar violators to even numbers matched to a larger odd number. We find the distribution of the latter matches and, in particular, establish the one-summation explicit formula sum_{k=1}^{lfloor n/2 rfloor}(2k-1)!!^2 StirlingPartition{n+1}{2k+1} for the number of perfect matchings of [2n] with no even-to-larger-odd matches. The proofs are mostly bijective.
Global magnetic fields of flare stars can evolve rapidly, in time scale of hundreds or dozens of days. We believe, that such changes result from rapid superposition of local magnetic fields generated by differential rotation of those stars. We discuss possible mechanisms of generation and dissipation of local and global magnetic fields in sample flare stars OT Ser and YZ CMi. We propose mechanism of magnetic braking of these stars, in which differential rotation generates local magnetic fields, and eventually energy accumulated in local fields is radiated away by flares. We obtained estimates of the rotational energy and the energy of the global magnetic field of OT Ser and YZ CMi. We also show that the energy of the local magnetic fields dissipated during superflare of YZ CMi on 9 February 2008 (UT 20:22:00) did not influence the global magnetic field of this star.
The observed delay-time distribution (DTD) of Type-Ia supernovae (SNe Ia) is a valuable probe of SN Ia progenitors and physics, and of the role of SNe Ia in cosmic metal enrichment. The SN Ia rate in galaxy clusters as a function of cluster redshift is an almost-direct measure of the DTD, but current estimates have been limited out to a mean redshift z=1.1, corresponding to time delays, after cluster star-formation, of over 3.2 Gyr. We analyze data from a Hubble Space Telescope monitoring project of 12 galaxy clusters at z=1.13-1.75, where we discover 29 SNe, and present their multi-band light curves. Based on the SN photometry and the apparent host galaxies, we assess cluster membership and SN type, finding 11 cases that are likely SNe Ia in cluster galaxies and 4 more cases which are possible but not certain cluster SNe Ia. We conduct simulations to estimate the SN detection efficiency, the experiment's completeness, and the photometric errors, and perform photometry of the cluster galaxies to derive the cluster stellar masses. Separating the cluster sample into high-z and low-z bins, we obtain rest-frame SN Ia rates per unit formed stellar mass of $2.2 ^{+2.6}_{-1.3}\times 10^{-13}{\rm yr}^{-1}{\rm M}_\odot^{-1}$ at a mean redshift z=1.25, and $3.5^{+6.6}_{-2.8} \times 10^{-13}{\rm yr}^{-1}{\rm M}_\odot^{-1}$ at z=1.58. Combining our results with previous cluster SN Ia rates, we fit the DTD, now down to delays of 1.5 Gyr, with a power-law dependence, $t^\alpha$, with $\alpha=-1.30^{+0.23}_{-0.16}$. We confirm previous indications for a Hubble-time-integrated SN Ia production efficiency that is several times higher in galaxy clusters than in the field, perhaps caused by a peculiar stellar initial mass function in clusters, or by a higher incidence of binaries that will evolve into SNe Ia.
Twirl operations, which convert impure singlet states into Werner states, play an important role in many schemes for entanglement purification. In this paper we describe strategies for implementing twirl operations, with an emphasis on methods suitable for ensemble quantum information processors such as nuclear magnetic resonance (NMR) quantum computers. We implement our twirl operation on a general two-spin mixed state using liquid state NMR techniques, demonstrating that we can obtain the singlet Werner state with high fidelity.