ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the kinetics of the redistribution of impurity atoms in the elastic fields of dislocations by computer simulation methods. A work consists of several stages. The first is the simulation of a dislocation core structure with a Burgers vector along [100] direction by using the modified molecular static method. The second is obtaining the coefficients that determine the influence of the components of the strain tensor on the diagonal elements of the matrix of diffusion coefficients and in the equations for fluxes of carbon atoms in bcc iron. The third stage is associated with modeling the diffusion characteristics of carbon atoms by the method of molecular dynamics in a crystal without defects. The fourth and final stage uses the data about atomic structure that we obtained at first stage, as well as the characteristics calculated in the second and third, is a simulation of the formation of segregations of interstitial atoms, which is based on solving diffusion equations that take into account the elastic deformations created by the dislocation. The complex of developed models is used to analyze the kinetics of segregation formation. 3D graphs illustrate the distribution of interstitial atoms in the vicinity of a dislocation for different times at certain temperatures.
The quantum theory of the ``spin light'' (electromagnetic radiation emitted by a massive neutrino propagating in dense matter due to the weak interaction of a neutrino with background fermions) is developed. In contrast to the Cherenkov radiation, this effect does not disappear even if the medium refractive index is assumed to be equal to unity. The formulas for the transition rate and the total radiation power are obtained. It is found out that radiation of photons is possible only when the sign of the particle helicity is opposite to that of the effective potential describing the interaction of a neutrino (antineutrino) with the background medium. Due to the radiative self-polarization the radiating particle can change its helicity. As a result, the active left-handed polarized neutrino (right-handed polarized antineutrino) converting to the state with inverse helicity can become practically ``sterile''. Since the sign of the effective potential depends on the neutrino flavor and the matter structure, the ``spin light'' can change a ratio of active neutrinos of different flavors. In the ultra relativistic approach, the radiated photons averaged energy is equal to one third of the initial neutrino energy, and two thirds of the energy are carried out by the final ``sterile'' neutrinos. This fact can be important for the understanding of the ``dark matter'' formation mechanism on the early stages of evolution of the Universe.
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the traveling fronts associated with the systems, and thus the present results complement recent papers \cite{GLS1, GLS2, GLS3, GLSR, GLY} that study the stability of traveling fronts.
We provide a rigorous definition of local realism. We show that the universal wave function cannot be a complete description of a local reality. Finally, we construct a local-realistic model for quantum theory.
The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2 particle polarized vertically up and down near the surface of a rotating body is $\hbar\Omega\sin\theta$. Here $\theta$ is the latitude and $\Omega = 2GJ/(c^2 R^3)$, where $J$ and $R$ are, respectively, the angular momentum and radius of the body. It seems that this relativistic quantum gravitational effect could be measurable in the foreseeable future.
We study the influence of magnetised crusts on torsional shear mode oscillations of magnetars. In this context, we employ magnetised crusts whose ground state properties are affected by Landau quantisation of electrons. The shear modulus of magnetised crusts is enhanced in strong magnetic fields $\geq 10^{17}$ G. Though we do not find any appreciable change in frequencies of fundamental torsional shear modes, frequencies of first overtones are significantly affected in strong magnetic fields. Furthermore, frequencies of torsional shear modes calculated with magnetised crusts are in good agreement with frequencies of observed quasi-periodic oscillations.
In this note we prove an estimate on the level sets of a function with $(p, q)$ growth that depends on the difference quotient of a bounded weak solution to a nonlocal double phase equation. This estimate is related to a self improving property of these solutions.
Based on the conception of quantum entanglement of Einstein-Podolsky-Rosen we construct generalized phase space representation associated with the entangled state |Gamma>_{e}, which is endowed with definite physical meaning. The set of states make up a complete and non-orthogonal representation. The Weyl ordered form of |Gamma>_{ee}_<Gamma| is derived which clearly exhibit the statistical behavior of marginal distribution of |Gamma>_{ee}_<Gamma|.The minimum uncertainty relation obeyed by |Gamma>_{e} is also demonstrated.
This Chapter provides a review of $\gamma$-ray sources lying at high Galactic latitudes. Their statistical properties and variability status, as well as studies involving cross correlations with lower frequency catalogs and multiwavelength observations, are summarized. The case for active galactic nuclei is analyzed with special emphasis, since they represent the largest population of high energy sources known to date. Other potential $\gamma$-ray emitters (including nearby starburst galaxies, normal galaxies, molecular clouds in the Galactic halo, galaxy clusters, and radio galaxies) that may appear in the next generation of $\gamma$-ray catalogs and, perhaps, that might have been already observed by EGRET as unidentified detections, are discussed.
We consider the semilinear heat equation $$\partial_t u -\Delta u =f(u), \quad (x,t)\in \mathbb{R}^N\times [0,T),\qquad (1)$$ with $f(u)=|u|^{p-1}u\log^a (2+u^2)$, where $p>1$ is Sobolev subcritical and $a\in \mathbb{R}$. We first show an upper bound for any blow-up solution of (1). Then, using this estimate and the logarithmic property, we prove that the exact blow-up rate of any singular solution of (1) is given by the ODE solution associated with (1), namely $u' =|u|^{p-1}u\log^a (2+u^2)$. In other terms, all blow-up solutions in the Sobolev subcritical range are Type I solutions. Up to our knowledge, this is the first determination of the blow-up rate for a semilinear heat equation where the main nonlinear term is not homogeneous.
Quiescent black hole X-ray binaries (X-ray luminosities <1e34 erg/s) are believed to be fed by hot accretion flows that launch compact, relativistic jets. However, due to their low luminosities, quiescent jets have been detected in the radio waveband from only five systems so far. Here, we present radio observations of two quiescent black hole X-ray binaries with the Australia Telescope Compact Array. One system, GS 1124-684, was not detected. The other system, BW Cir, was detected over two different epochs in 2018 and 2020, for which we also obtained quasi-simultaneous X-ray detections with Chandra and Swift. BW Cir is now the sixth quiescent X-ray binary with a confirmed radio jet. However, the distance to BW Cir is uncertain, and we find that BW Cir shows different behaviour in the radio/X-ray luminosity plane depending on the correct distance. Estimates based on its G-type subgiant donor star place BW Cir at >25 kpc, while initial optical astrometric measurements from Gaia Data Release 2 suggested likely distances of just a few kpc. Here, we use the most recent measurements from Gaia Early Data Release 3 and find a distance d=7.1(+4.8/-3.9) kpc and a potential kick velocity PKV=165(+81/-17) km/s, with distances up to ~20 kpc possible based on its parallax and proper motion. Even though there is now less tension between the parallax and donor-star based distance measurements, it remains an unresolved matter, and we conclude with suggestions on how to reconcile the two measurements.
We calculate elliptic and triangular flow parameters of thermal photons using an event-by-event hydrodynamic model with fluctuating initial conditions at 200A GeV Au+Au collisions at RHIC and at 2.76A TeV Pb+Pb collisions at the LHC for three different centrality bins. The photon elliptic flow shows strong centrality dependence where $v_2(p_T)$ increases towards peripheral collisions both at RHIC and at the LHC energies. However, the triangular flow parameter does not show significant dependence to the collision centrality. The elliptic as well as the triangular flow parameters found to underestimate the PHENIX data at RHIC by a large margin for all three centrality bins. We calculate $p_T$ spectrum and anisotropic flow of thermal photons from 200A GeV Cu+Cu collisions at RHIC for 0--20\% centrality bin and compare with the results with those from Au+Au collisions. The production of thermal photon is found to decrease significantly for Cu+Cu collisions compared to Au+Au collisions. However, the effect of initial state fluctuation is found to be more pronounced for anisotropic flow resulting in larger $v_2$ and $v_3$ for Cu+Cu collisions. We study the correlation between the anisotropic flow parameters and the corresponding initial spatial anisotropies from their event by event distributions at RHIC and at the LHC energies. The linear correlation between $v_2$ and $\epsilon_2$ is found be stronger compared to the correlation between $v_3$ and $\epsilon_3$. In addition, the correlation coefficient is found to be larger at LHC than at RHIC.
We analyze sum rules for the $\Upsilon$ system with resummation of threshold effects on the basis of the nonrelativistic Coulomb approximation. We find for the pole mass of the bottom quark $m_b=4.75\pm 0.04 GeV$ and for the strong coupling constant $\al_s(M_Z)=0.118\pm 0.006$. The origin of the contradiction between two recent estimates obtained within the same formal framework is clarified.
We present optical (UBVJ), ultraviolet (FUV, NUV), and high resolution atomic hydrogen (HI) observations of the nearby blue compact dwarf (BCD), VII Zw 403. We find that VII Zw 403 has a relatively high HI mass-to-light ratio for a BCD. The rotation velocity is nominally 10-15 km/s, but rises to ~20 km/s after correction for the ~8-10 km/s random motions present in the gas. The velocity field is complex; including a variation in the position angle of the major axis going from the NE to the SW parts of the galaxy. Our high resolution HI maps reveal structure in the central gas, including a large, low-density HI depression or hole between the southern and northern halves of the galaxy, coincident with an unresolved x-ray source. Although interactions have been proposed as the triggering mechanism for the vigorous star formation occurring in BCDs, VII Zw 403 does not seem to have been tidally triggered by an external interaction, as we have found no nearby possible perturbers. It also doesn't appear to fall in the set of galaxies that exhibit a strong central mass density concentration, as its optical scale length is large in comparison to similar systems. However, there are some features that are compatible with an accretion event: optical/HI axis misalignment, a change in position angle of the kinematic axis, and a complex velocity field.
The Local Group hosts a number of star-forming dwarf galaxies that show evidence of periods of little to no star formation. We use a suite of cosmological simulations to study how star formation is reignited in such galaxies. We focus on isolated galaxies at $z=0$ with halo masses between 9.2$\times$10$^8$ M$_\odot$ and 8.4$\times$10$^9$ M$_\odot$, where star formation is typically shut off by reionization or by supernova feedback. Nearly 20% of these simulated galaxies later restart star formation, due to interactions with streams of gas in the intergalactic medium, indicating that this mechanism is relatively common in this mass range and that many isolated dwarfs at $z=0$ may not have been isolated throughout their histories. The source of this gas is not necessarily cosmic filaments. Rather, the dwarfs interact with gas thrown off by nearby galaxy mergers or streams extending from neighboring galaxies. While high ram pressure interactions of this nature lead to stripping, the encounters that reignite star formation are low density and/or low velocity and thus low ram pressure, resulting in compression of the hot gas in the halos of our dwarfs. The gas mass bound up in hot halos can be substantial -- at least an order of magnitude greater than the mass contained in HI. Consequently, we find that dwarfs that have experienced reignition tend to be more HI-rich and have a higher M$_{HI}$/M$_{*}$ ratio at $z=0$ than galaxies with continuous star formation. Using this fact, we identify galaxies in the Local Volume that might have "gappy" star formation histories, and can be studied by the Hubble Space Telescope or the James Webb Space Telescope.
We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with 1<p<\infty, and connect them to the Sobolev theory in R^n. In particular, we show that for quasiopen subsets of R^n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpel\"ainen and Mal\'y in 1992. As a by-product, we establish the quasi-Lindel\"of principle of the fine topology in metric spaces and study several variants of local Newtonian and Dirichlet spaces on quasiopen sets.
We report transport and thermodynamic properties of stoichiometric single crystals of the hexagonal iron-pnictide FeCrAs. The in-plane resistivity shows an unusual "non-metallic" dependence on temperature T, rising continuously with decreasing T from ~ 800 K to below 100 mK. The c-axis resistivity is similar, except for a sharp drop upon entry into an antiferromagnetic state at T_N 125 K. Below 10 K the resistivity follows a non-Fermi-liquid power law, rho(T) = rho_0 - AT^x with x<1, while the specific heat shows Fermi liquid behaviour with a large Sommerfeld coefficient, gamma ~ 30 mJ/mol K^2. The high temperature properties are reminiscent of those of the parent compounds of the new layered iron-pnictide superconductors, however the T -> 0 properties suggest a new class of non-Fermi liquid.
As deep networks become increasingly accurate at recognizing faces, it is vital to understand how these networks process faces. While these networks are solely trained to recognize identities, they also contain face related information such as sex, age, and pose of the face. The networks are not trained to learn these attributes. We introduce expressivity as a measure of how much a feature vector informs us about an attribute, where a feature vector can be from internal or final layers of a network. Expressivity is computed by a second neural network whose inputs are features and attributes. The output of the second neural network approximates the mutual information between feature vectors and an attribute. We investigate the expressivity for two different deep convolutional neural network (DCNN) architectures: a Resnet-101 and an Inception Resnet v2. In the final fully connected layer of the networks, we found the order of expressivity for facial attributes to be Age > Sex > Yaw. Additionally, we studied the changes in the encoding of facial attributes over training iterations. We found that as training progresses, expressivities of yaw, sex, and age decrease. Our technique can be a tool for investigating the sources of bias in a network and a step towards explaining the network's identity decisions.
We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.
We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any quadratic term of first time derivative that can leads to those vierbein forms of the Einstein equations without second time derivative term by the corresponding Euler-Lagrange equations. General relativity thus becomes a fully singular Lagrange system.
We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of the system. It is shown that at high frequencies there are two longitudinal sound modes with standard attenuation, while in the low frequency region there is one propagating sound mode and an over-damped phase mode. The crossover between these two regions is analyzed numerically and the dynamical structure factor is calculated. It is shown that the qualitative features of the experimentally observed spectra can be consistently described by our model.
A lot has been learnt in the 15 years since the first data on jet modification at the Relativistic Heavy Ion Collider (RHIC). These proceedings will describe the portion of the theory that is unassailable, and attempt to chart a course for the next period of precision measurements and related calculations. In particular, we will focus on the emerging series of higher order calculations, which may reveal the scale, energy and temperature dependence of jet transport coefficients, as well as develop ingredients for a future NLO calculation of jet modification. Connections with the underlying degrees of freedom in the Quark Gluon Plasma (QGP) will be explored. We will discuss the challenges faced by Monte-Carlo event generators and their comparison with a broad spectrum of jet modification data. First principles calculations of transport coefficients, and the determination of new transport coefficients which encapsulate the transition of energy momentum from the jet scale to the medium scale will also be discussed.
In an earlier work, we gave an Apollonian-like pictorial representation for the ample cone for a class of K3 surfaces. This raises a natural question: Does the Apollonian packing itself represent the ample cone for a K3 surface? In this note, we answer this question in the affirmative.
The origin of kpc-scale holes in the atomic hydrogen (H I) distributions of some nearby dwarf irregular galaxies presents an intriguing problem. Star formation histories (SFHs) derived from resolved stars give us the unique opportunity to study past star forming events that may have helped shape the currently visible H I distribution. Our sample of five nearby dwarf irregular galaxies spans over an order of magnitude in both total H I mass and absolute B-band magnitude and is at the low mass end of previously studied systems. We use Very Large Array H I line data to estimate the energy required to create the centrally dominant hole in each galaxy. We compare this energy estimate to the past energy released by the underlying stellar populations computed from SFHs derived from data taken with the Hubble Space Telescope. The inferred integrated stellar energy released within the characteristic ages exceeds our energy estimates for creating the holes in all cases, assuming expected efficiencies. Therefore, it appears that stellar feedback provides sufficient energy to produce the observed holes. However, we find no obvious signature of single star forming events responsible for the observed structures when comparing the global SFHs of each galaxy in our sample to each other or to those of dwarf irregular galaxies reported in the literature. We also fail to find evidence of a central star cluster in FUV or Halpha imaging. We conclude that large H I holes are likely formed from multiple generations of star formation and only under suitable interstellar medium conditions.
Let $L=diag(1,1,\ldots,1,-1)$ and $M=diag(1,1,\ldots,1,-2)$ be the lattices of signature $(n,1)$. We consider the groups $\Gamma=SU(L,\mathcal{O}_K)$ and $\Gamma'=SU(M,\mathcal{O}_K)$ for an imaginary quadratic field $K=\mathbb{Q}(\sqrt{-d})$ of discriminant $D$ and it's ring of integers $\mathcal{O}_K$, $d$ odd and square free. We compute the Hirzebruch-Mumford volume of the factor spaces $\mathbb{B}^n/\Gamma$ and $\mathbb{B}^n/\Gamma'$. The result for the factor space $\mathbb{B}^n/\Gamma$ is due to Zeltinger, but as we're using it to prove the result for $\mathbb{B}^n/\Gamma'$ and it is hard to find his article, we prove the first result here as well.
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents corresponding to the survival probability of particles and monomers. The overall behavior agrees qualitatively with the mean-field theory. This theory also provides a useful approximation for the decay exponents, as well as the limiting mass distribution.
We consider the semilinear heat equation in large dimension $d\geq 11$ $$ \partial_t u =\Delta u+|u| ^{p-1}u, \ \ p=2q+1, \ \ q\in \mathbb N $$ on a smooth bounded domain $\Omega\subset \mathbb R^d$ with Dirichlet boundary condition. In the supercritical range $p\geq p(d)>1+\frac{4}{d-2}$ we prove the existence of a countable family $(u_\ell)_{\ell \in \mathbb N}$ of solutions blowing-up at time $T>0$ with type II blow up: $$ \parallel u_{\ell}(t) \parallel_{L^{\infty}} \sim C (T-t)^{-c_\ell} $$ with blow-up speed $c_\ell>\frac{1}{p-1}$. They concentrate the ground state $Q$ being the only radially and decaying solution of $\Delta Q+Q^p=0$: $$ u(x,t)\sim \frac{1}{\lambda (t)^{\frac{2}{p-1}}}Q\left(\frac{x-x_0}{\lambda (t)} \right), \ \lambda\sim C(u_n)(T-t)^{\frac{c_\ell(p-1)}{2}} $$ at some point $x_0\in \Omega$. The result generalizes previous works on the existence of type II blow-up solutions, which only existed in the radial setting. The present proof uses robust nonlinear analysis tools instead, based on energy methods and modulation techniques. This is the first non-radial construction of a solution blowing up by concentration of a stationary state in the supercritical regime, and provides a general strategy to prove similar results for dispersive equations or parabolic systems and to extend it to multiple blow ups.