ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we deal with the solutions of systems of PDEs with bilateral inter-connected obstacles of min-max and max-min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the the values of a zero-sum switching game is studied.
Energy injection by supernovae may drive hot supersonic galactic winds in rapidly star-forming galaxies, driving metal-enriched gas into the circumgalactic medium and potentially accelerating cool gas. If sufficiently mass-loaded, such flows become radiative within the wind-driving region, reducing the overall mass outflow rate from the host galaxy. We show that this sets a maximum on the total outflow momentum for hot energy-driven winds. For a spherical wind of Solar metallicity driven by continuous star formation, $\dot p_\rm{max} \simeq 1.9\times10^4\ M_\odot/\rm{yr\ km/s}\ (\alpha/0.9)^{0.86}(R_\star/300\ \rm{pc})^{0.14}(\dot M_\star/20\ M_\odot/\rm{yr})^{0.86}$, where $\alpha$ is the fraction of supernova energy that thermalizes the wind, and $\dot M_\star$ and $R_\star$ are the star formation rate and radius of the wind-driving region. This maximum momentum for hot winds can also apply to cool, ionized outflows that are typically observed in starburst galaxies, if the hot wind undergoes bulk radiative cooling or if the hot wind transfers mass and momentum to cool clouds within the flow. We show that requiring the hot wind to undergo single-phase cooling on large scales sets a minimum on the total outflow momentum rate. These maximum and minimum outflow momenta have similar values, setting a characteristic momentum rate of hot galactic winds that can become radiative on large scales. We find that most observations of photoionized outflow wind momentum fall below the theoretical maximum and thus may be signatures of cooling hot flows. On the other hand, many systems fall below the minimum momentum required for bulk cooling, indicating that perhaps the cool material observed has instead been entrained in or mixed with the hot flow.
Difference in density of states for the spin's majority and minority bands in a ferromagnet changes the electrostatic potential along the domains, introducing the discontinuities of the potential at domain boundaries. The value of discontinuity oscillates with number of domains. Discontinuity depends on the positions of domain walls, their motion or collapse of domain walls in applied magnetic field. Large values of magnetoresistance are explained in terms of spin-accumulation. We suggest a new type of domain walls in nanowires of itinerant ferromagnets, in which the magnetization vector changes without rotation. Absence of transverse magnetization components allows considerable spin accumulation assuming the spin relaxation length, L_S, is large enough.
We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck L\'evy processes.
The paper aims at investigating two types of decay structure for linear symmetric hyperbolic systems with non-symmetric relaxation. Precisely, the system is of the type $(p,q)$ if the real part of all eigenvalues admits an upper bound $-c|\xi|^{2p}/(1+|\xi|^2)^{q}$, where $c$ is a generic positive constant and $\xi$ is the frequency variable, and the system enjoys the regularity-loss property if $p<q$. It is well known that the standard type $(1,1)$ can be assured by the classical Kawashima-Shizuta condition. A new structural condition was introduced in \cite{UDK} to analyze the regularity-loss type $(1,2)$ system with non-symmetric relaxation. In the paper, we construct two more complex models of the regularity-loss type corresponding to $p=m-3$, $q=m-2$ and $p=(3m-10)/2$, $q=2(m-3)$, respectively, where $m$ denotes phase dimensions. The proof is based on the delicate Fourier energy method as well as the suitable linear combination of series of energy inequalities. Due to arbitrary higher dimensions, it is not obvious to capture the energy dissipation rate with respect to the degenerate components. Thus, for each model, the analysis always starts from the case of low phase dimensions in order to understand the basic dissipative structure in the general case, and in the mean time, we also give the explicit construction of the compensating symmetric matrix $K$ and skew-symmetric matrix $S$.
We extend the Siegel-Walfisz theorem to a family of integer sequences that are characterized by constraints on the size of the prime factors. Besides prime powers, this family includes smooth numbers, almost primes and practical numbers.
Relativistic jets are highly collimated plasma outflows emerging from accreting black holes. They are launched with a significant amount of magnetic energy, which can be dissipated to accelerate nonthermal particles and give rise to electromagnetic radiation at larger scales. Kink instabilities can be an efficient mechanism to trigger dissipation of jet magnetic energy. While previous works have studied the conditions required for the growth of kink instabilities in relativistic jets, the radiation signatures of these instabilities have not been investigated in detail. In this paper, we aim to self-consistently study radiation and polarization signatures from kink instabilities in relativistic jets. We combine large-scale relativistic magnetohydrodynamic (RMHD) simulations with polarized radiation transfer of a magnetized jet, which emerges from the central engine and propagates through the surrounding medium. We observe that a localized region at the central spine of the jet exhibits the strongest kink instabilities, which we identify as the jet emission region. Very interestingly, we find quasi-periodic oscillation (QPO) signatures in the light curve from the emission region. Additionally, the polarization degree appears to be anti-correlated to flares in the light curves. Our analyses show that these QPO signatures are intrinsically driven by kink instabilities, where the period of the QPOs is associated to the kink growth time scale. The latter corresponds to weeks to months QPOs in blazars. The polarization signatures offer unique diagnostics for QPOs driven by kink instabilities.
We consider the convex geometry of the cone of nonnegative quadratics over Stanley-Reisner varieties. Stanley-Reisner varieties (which are unions of coordinate planes) are amongst the simplest real projective varieties, so this is potentially a starting point that can generalize to more complicated real projective varieties. This subject has some suprising connections to algebraic topology and category theory, which we exploit heavily in our work.   These questions are also valuable in applied math, because they directly translate to questions about positive semidefinite (PSD) matrices. In particular, this relates to a long line of work concerning the extent to which it is possible to approximately check that a matrix is PSD by checking that some principle submatrices are PSD, or to check if a partial matrix can be approximately completed to full PSD matrix.   We systematize both these practical and theoretical questions using a framework based on algebraic topology, category theory, and convex geometry. As applications of this framework we are able to classify the extreme nonnegative quadratics over many Stanley-Reisner varieties. We plan to follow these structural results with a paper that is more focused on quantitative questions about PSD matrix completion, which have applications in sparse semidefinite programming.
The young binary system HD 350731 is a noteworthy laboratory for studying early-type binaries with similar components. We present here the analysis of differential multi-color photometric and spectroscopic observations for the double-lined detached system. Accurate absolute parameters were determined from the simultaneous solution of light and radial velocity curves for the first time. HD 350731 consists of two B8V-type components having masses and radii respectively of $M_{1}=2.91\pm0.13$ M$_{\odot}$, $M_{2}=2.80\pm0.14$ M$_{\odot}$, $R_{1}= 2.11 \pm0.05$ R$_{\odot}$ and $R_{2}=2.07\pm0.05$ R$_{\odot}$. The effective temperatures were determined based on analysis of disentangled spectra of the components and derived to be $12000\pm250$ K and $11830\pm300$ K for the primary and secondary components, respectively. The measured projected rotational velocities, 69.2$\pm$1.5 km s$^{-1}$ for primary and 70.1$\pm$1.7 km s$^{-1}$ for secondary, were found closer to the pseudo-synchronous velocities of the components. Comparison with evolutionary models suggests an age of 120$\pm$35 Myr. Kinematic analysis of the unevolved binary system HD 350731 revealed that it belongs to the young thin-disc population of the Galaxy.
We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.
Generalization of QCD motivated classical SU(2) Yang--Mills theory coupled to the scalar field is discussed. The massive scalar field, corresponding the scalar glueball, provides a confining potential for static, point-like, external sources. In case of massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions are compared with phenomenological potentials. The case of non-dynamical permittivity is also discussed.
PSR B1259-63 is a 48 ms radio pulsar in a highly eccentric 3.4 year orbit with a Be star SS 2883. Unpulsed gamma-ray, X-ray and radio emission components are observed from the binary system. It is likely that the collision of the pulsar wind with the anisotropic wind of the Be star plays a crucial role in the generation of the observed non-thermal emission. The 2007 periastron passage was observed in unprecedented details with Suzaku, Swift, XMM-Newton and Chandra missions. We present here the results of this campaign and compare them with previous observations. With these data we are able, for the first time, to study the details of the spectral evolution of the source over a 2 months period of the passage of the pulsar close to the Be star. New data confirm the pre-periastron spectral hardening, with the photon index reaching a value smaller than 1.5, observed during a local flux minimum. If the observed X-ray emission is due to the inverse Compton (IC) losses of the 10 MeV electrons, then such a hard spectrum can be a result of Coulomb losses, or can be related to the existence of the low-energy cut-off in the electron spectrum. Alternatively, if the X-ray emission is a synchrotron emission of very high energy electrons, the observed hard spectrum can be explained if the high energy electrons are cooled by IC emission in Klein-Nishina regime. Unfortunately the lack of simultaneous data in the TeV energy band prevents us from making a definite conclusion on the nature of the observed spectral hardening and, therefore, on the origin of the X-ray emission.
The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails, which map to a particular temperature of interacting self-avoiding trails, showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self-avoiding walks. On the other hand, it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model. In this work we simulate the standard equilibrium interacting self-avoiding trail model on the square lattice up to lengths over $2,000,000$ steps and show that the results of the kinetic growth simulations are, in fact, entirely in accord with standard simulations of the temperature dependent model. In this way we verify that the collapse transition of interacting self-avoiding walks and trails are indeed in different universality classes in two dimensions.
Monolayers of semiconducting transition metal dichalcogenides exhibit intriguing fundamental physics of strongly coupled spin and valley degrees of freedom for charge carriers. While the possibility of exploiting these properties for information processing stimulated concerted research activities towards the concept of valleytronics , maintaining control over spin-valley polarization proved challenging in individual monolayers. A promising alternative route explores type II band alignment in artificial van der Waals heterostructures. The resulting formation of interlayer excitons combines the advantages of long carrier lifetimes and spin-valley locking . Here, we demonstrate direct magnetic manipulation of valley polarization in a WSe2/MoSe2 heterostructure through giant valley Zeeman splitting of interlayer transitions. Remarkably, even after non-selective injection, the observed $g$ factor as large as $-15$ induces near-unity polarization of long-lived excitons with 100 ns lifetimes under magnetic fields. The demonstrated control of the spin-valley physics highlights the exceptional aspects of novel, artificially designed material systems and their promise for atomically-thin valleytronic devices.
The acene series represents a unique model system to investigate the intriguing electronic properties of extended pi electron structures in the one-dimensional limit, which are important for applications in electronics and spintronics and for the fundamental understanding of electronic transport. Here we present the on-surface generation of the longest acene obtained so far: Dodecacene. Scanning tunneling spectroscopy gives access to the energy position and spatial distribution of its electronic states on the Au(111) surface. We observe that, after a progressive closing of the gap and a stabilization to about 1 eV at the length of decacene and undecacene, the energy gap of dodecacene unexpectedly increases to 1.4 eV. Considering the acene series as an exemplary general case, we discuss the evolution with length of the single tunneling resonances in comparison with ionization energy, electronic affinity, and optical gap.
We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to $\mathcal{O}(\epsilon^2)$ in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N$^3$LL resummation.
The Extragalactic Background Light (EBL) from the infrared (IR) through the ultraviolet (UV) is dominated by emission from stars, either directly or through absorption and reradiation by dust. It can thus give information on the star formation history of the universe. However, it is difficult to measure directly due to foreground radiation fields from the Galaxy and solar system. Gamma-rays from extragalactic sources at cosmological distances (blazars and gamma-ray bursts) interact with EBL photons creating electron-positron pairs, absorbing the gamma-rays. Given the intrinsic gamma-ray spectrum of a source and its redshift, the EBL can in principle be measured. However, the intrinsic gamma-ray spectra of blazars and GRBs can vary considerably from source to source and the from the same source over short timescales. A maximum intrinsic spectrum can be assumed from theoretical grounds, to give upper limits on the EBL absorption from blazars at low redshift with very high energy (VHE) gamma-ray observations with ground-based Atmospheric Cherenkov telescopes. The Fermi-LAT observations of blazars and GRBs can probe EBL absorption at higher redshifts. The lower energy portion of the LAT spectrum of these sources is unattenuated by the EBL, so that extrapolating this to higher energies can give the maximum intrinsic spectrum for a source. Comparing this to the observed higher energy LAT spectrum will then give upper limits on the EBL absorption. For blazars which have been detected by both the Fermi-LAT and at higher energies by Cherenkov telescopes, combined LAT-VHE observations can put more stringent constraints on the low redshift EBL. These procedures above can also be reversed: for sources with an unknown redshift, a given EBL model and gamma-ray spectrum can lead to an upper limit on the source's redshift.
Within the framework of the improved isospin dependent quantum molecular dynamics (ImIQMD) model, the dynamics of strangeness (K$^{0,+}$, $\Lambda$ and $\Sigma^{-,0,+}$) production in heavy-ion collisions near threshold energies is investigated systematically, in which the strange particles are considered to be mainly produced by the inelastic collisions of baryon-baryon and pion-baryon. The collisions in the region of supra-saturation densities of the dense baryonic matter formed in heavy-ion collisions dominate the yields of strangeness production. The total multiplicities as functions of incident energies and collision centralities are calculated with the Skyrme parameter SLy6. The excitation function of strangeness production is analyzed and also compared with the KaoS data for the K$^{+}$ production in the reactions $^{12}$C+$^{12}$C and $^{197}$Au+$^{197}$Au.
This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $\mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking $R=t^{-\frac{d}{d+1}}$ it is shown that this point process converges in distribution, as $t\to\infty$, to a Poisson point process on $\mathbb{R}^d\setminus\{0\}$ whose intensity measure has power-law density proportional to $\|x\|^{-(d+1)}$ with respect to the Lebesgue measure. A bound on the speed of convergence in terms of the Kantorovich-Rubinstein distance is provided as well. In the background is a general functional Poisson approximation theorem on abstract Poisson spaces. Implications on the weak convergence of the convex hull of the intersection point process and the convergence of its $f$-vector are also discussed, disproving and correcting thereby a conjecture of Devroye and Toussaint [J.\ Algorithms 14.3 (1993), 381--394] in computational geometry.
Black holes are more than just odd-looking curiosities in gravity theory. They uniquely intertwine the basic principles of General Relativity with those of Quantum Theory. Just by demanding that they nevertheless obey acceptable laws of dynamics, just like stars and planets, we hit upon strange structures that must play key roles in the quantum effects that we expect in the gravitational force at ultrashort distance scales. It is explained why, in our approach to address the problem of information conservation, the usual expression for the temperature of Hawking's radiation is off by a factor 2.
Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.
The suppression of magnetic order with pressure concomitant with the appearance of pressure- induced superconductivity was recently discovered in CrAs. Here we present a neutron diffraction study of the pressure evolution of the helimagnetic ground-state towards and in the vicinity of the superconducting phase. Neutron diffraction on polycrystalline CrAs was employed from zero pressure to 0.65 GPa and at various temperatures. The helimagnetic long-range order is sustained under pressure and the magnetic propagation vector does not show any considerable change. The average ordered magnetic moment is reduced from 1.73(2) {\mu}B at ambient pressure to 0.4(1) {\mu}B close to the critical pressure Pc=0.7 GPa, at which magnetic order is completely suppressed. The width of the magnetic Bragg peaks strongly depends on temperature and pressure, showing a maximum in the region of the onset of superconductivity. We interpret this as associated with competing ground-states in the vicinity of the superconducting phase.
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's theorem combined with Belinfante's "symmetrization" method applied to the group of displacements provide a conserved vector, a "superpotential" and a energy-momentum that are independent of any divergence added to the Hilbert Lagrangian of the perturbations. The energy-momentum is symmetrical and divergenceless only on backgrounds that are Einstein spaces in the sense of A.Z.Petrov.
I give a pedagogical introduction into flavour-changing neutral current interactions of kaons and their role to reveal or constrain physics beyond the Standard Model (SM). Then I discuss the measure $\epsilon_K^\prime$ of direct CP violation in $K\to \pi\pi$ decays, which deviates from the SM prediction by $2.8\sigma$. A supersymmetric scenario with flavour mixing among left-handed squarks can accomodate the measured value of $\epsilon_K^\prime$ even for very heavy sparticles, outside the reach of the LHC. The considered scenario employs mass splittings among the right-handed up and down squarks (to enhance $\epsilon_K^\prime$) and a gluino which is heavier than the left-handed strange-down mixed squarks by at least a factor of 1.5 (to suppress excessive contribution to $\epsilon_K$, the measure of indirect CP violation). The branching ratios of the rare decays $K^+ \to \pi^+ \nu \bar\nu$ and $K_L \to \pi^0 \nu \bar\nu$, to be measured by the NA62 and KOTO-step2 experiments, respectively, are only moderately affected. These measurements have the capability to either falsify the model or to constrain the CP phase associated with strange-down squark mixing accurately.