ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.
Chiral magnetism, wherein there is a preferred sense of rotation of the magnetization, has become a key aspect for future spintronic applications. It determines the chiral nature of magnetic textures, such as skyrmions, domain walls or spin spirals, and a specific magnetic chirality is often required for spintronic applications. Current research focuses on identifying and controlling the interactions that define the magnetic chirality. The influence of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) and, recently, the dipolar interactions have previously been reported. Here, we experimentally demonstrate that an indirect interlayer exchange interaction can be used as an additional tool to effectively manipulate the magnetic chirality. We image the chirality of magnetic domain walls in a coupled bilayer system using scanning electron microscopy with polarization analysis (SEMPA). Upon increasing the interlayer exchange coupling, we induce a transition of the magnetic chirality from clockwise rotating N\'eel walls to degenerate Bloch-N\'eel domain walls and we confirm our findings with micromagnetic simulations. In multi-layered systems relevant for skyrmion research a uniform magnetic chirality across the magnetic layers is often desired. Additional simulations show that this can be achieved for reduced iDMI values when exploiting the interlayer exchange interaction. This work opens up new ways to control and tailor the magnetic chirality by the interlayer exchange interaction.
The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.
Supermassive stars born from pristine gas in atomically-cooled haloes are thought to be the progenitors of supermassive black holes at high redshifts. However, the way they accrete their mass is still an unsolved problem. In particular, for accretion to proceed, a large amount of angular momentum has to be extracted from the collapsing gas. Here, we investigate the constraints stellar evolution imposes on this angular momentum problem. We present an evolution model of a supermassive Population III star including simultaneously accretion and rotation. We find that, for supermassive stars to form by accretion, the accreted angular momentum has to be about 1% of the Keplerian angular momentum. This tight constraint comes from the $\Omega\Gamma$-limit, at which the combination of radiation pressure and centrifugal force cancels gravity. It implies that supermassive stars are slow rotators, with a surface velocity less than 10-20% of their first critical velocity, at which the centrifugal force alone cancels gravity. At such low velocities, the deformation of the star due to rotation is negligible.
We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.
A model of population of ultraluminous X-ray sources with magnetised neutron stars (NULX) in a spiral galaxy with the star formation history similar to that in the thin disc of Milky Way is computed using a hybrid approach. First, applying analytical approximations (code BSE) we construct the ensemble of close binaries (CBS) which can be potential precursors of NULX. Next, evolution with accretion onto magnetised neutron stars (NS) is computed by the evolutionary code MESA. Accretion rate onto NS and X-ray luminosity are calculated for the models of sub- and supercritical discs and for the discs with advection. During accretion onto magnetised NS, super-Eddington luminosity $L_\mathrm{X}>10^{38}$ erg~s$^{-1}$ is attained already at the subcritical stage, when the energy release at the inner boundary of the disc defined by the NS magnetosphere is sub-Eddington. It is shown that standard evolution of CBS with an account of the peculiarities specific for accretion onto magnetised NS allows us to explain quantitatively observed characteristics of NULX (X-ray luminosities, NS spin periods, orbital periods and masses of visual components) without additional model assumptions on the collimation of X-ray emission from NS with high observed super-Eddington luminosity. In a model galaxy with star formation rate 3--5 $M_\odot {\rm yr^{-1}}$ there can exist several NULX. Discovery of a powerful wind from NULX with $L_{\mathrm X} \sim 10^{41}$ erg~s$^{-1}$ would be a signature of super-Eddington accretion onto magnetised NS.
In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. We prove the existence and uniqueness of global solution under suitable assumptions on the tension of beam and on the parameters of the problem. Afterwards, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
A method to separate a Slater determinant wave function with a two-center neck structure into spatially localized subsystems is proposed, and its potential applications are presented. An orthonormal set of spatially localized single-particle wave functions is obtained by diagonalizing the coordinate operator for the major axis of a necked system. Using the localized single-particle wave functions, the wave function of each subsystem is defined. Therefore, defined subsystem wave functions are used to obtain density distributions, mass centers, and energies of subsystems. The present method is applied to separations of Margenau--Brink cluster wave functions of $\alpha + \alpha$, $^{16}$O + $^{16}$O, and $\alpha + ^{16}$O into their subsystems, and also to separations of antisymmetrized molecular dynamics wave functions of $^{10}$Be into $\alpha$ + $^6$He subsystems. The method is simple and applicable to the separation of general Slater determinant wave functions that have neck structures into subsystem wave functions.
In recent times, several discrepancies at the level of $(2-3)\sigma$ have been observed in the decay processes mediated by flavour changing neutral current (FCNC) transitions $b \to s \ell^+ \ell^-$, which may be considered as the smoking-gun signal of New Physics (NP). These intriguing hints of NP have attracted a lot of attention and many attempts are made to look for the possible NP signature in other related processes, which are mediated through the same quark-level transitions. In this work, we perform a comprehensive analysis of the FCNC decays of $B$ meson to axial vector mesons $ K_1(1270)$ and $ K_1(1400)$, which are admixture of the $1^3P_1$ and $1^1P_1$ states $K_{1A}$ and $K_{1B}$, in a model independent framework. Using the $ B \to K_1$ form factors evaluated in the light cone sum rule approach, we investigate the rare exclusive semileptonic decays $ B \to K_1(1270) \mu^+ \mu^-$ and $ B \to K_1(1400) \mu^+ \mu^-$. Considering all the possible relevant operators for $b \to s \ell^+ \ell^-$ transitions, we study their effects on various observables such as branching fractions, lepton flavor universality violating ratio ($R_{K_1})$, forward-backward asymmetries, and lepton polarization asymmetries of these processes. These results will not only enhance the theoretical understanding of the mixing angle but also serve as a good tool for probing New Physics.
For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling. An effective Hamiltonian for the limit $|t|\ll V$ is given to lowest non-vanishing order by the ring exchange ($\sim t^{3}/V^{2}$). We show that the system can equivalently be described by hard-core bosons and map the model to a confining U(1) lattice gauge theory.
The Baryonic Tully-Fisher Relation (BTFR) is an empirical relation between baryonic mass and rotation velocity in disk galaxies. It provides tests of galaxy formation models in LCDM and of alternative theories like MOND. Observations of gas rich galaxies provide a measure of the slope and normalization of the BTFR that is more accurate (if less precise) than that provided by star dominated spirals, as their masses are insensitive to the details of stellar population modeling. Recent independent data for such galaxies are consistent with Mb = AVf^4 with A = 47+/-6 Msun (km/s)^-4. This is equivalent to MOND with $a_0 = 1.3 +/- 0.3 A/s/s. The scatter in the data is consistent with being due entirely to observational uncertainties. It is unclear why the physics of galaxy formation in LCDM happens to pick out the relation predicted by MOND. We introduce a feedback efficacy parameter E to relate halo properties to those of the galaxies they host. E correlates with star formation rate and gas fraction in the sense that galaxies that have experienced the least star formation have been most impacted by feedback.
The bipolar-hyper shell (BHS) model for the North Polar Spurs (NPS-E, -W, and Loop I) and counter southern spurs (SPS-E and -W) is revisited based on numerical hydrodynamical simulations. Propagations of shock waves produced by energetic explosive events in the Galactic Center are examined. Distributions of soft X-ray brightness on the sky at 0.25, 0.7, and 1.5 keV in a +/-50 deg x +/-50 deg region around the Galactic Center are modeled by thermal emission from high-temperature plasma in the shock-compressed shell considering shadowing by the interstellar HI and H2 gases. The result is compared with the ROSAT wide field X-ray images in R2, 4 and 6 bands. The NPS and southern spurs are well reproduced by the simulation as shadowed dumbbell-shaped shock waves. We discuss the origin and energetics of the event in relation to the starburst and/or AGN activities in the Galactic Center. [ High resolution pdf is available at http://www.ioa.s.u-tokyo.ac.jp/~sofue/htdocs/2016bhs/ ]
We study a generalized 1d periodic SPDE of Burgers type: $$ \partial_t u =- A^\theta u + \partial_x u^2 + A^{\theta/2} \xi $$ where $\theta > 1/2$, $-A$ is the 1d Laplacian, $\xi$ is a space-time white noise and the initial condition $u_0$ is taken to be (space) white noise. We introduce a notion of weak solution for this equation in the stationary setting. For these solutions we point out how the noise provide a regularizing effect allowing to prove existence and suitable estimates when $\theta>1/2$. When $\theta>5/4$ we obtain pathwise uniqueness. We discuss the use of the same method to study different approximations of the same equation and for a model of stationary 2d stochastic Navier-Stokes evolution.
SrRuO$_3$ (SRO) films are known to exhibit insulating behavior as their thickness approaches four unit cells. We employ electron energy$-$loss (EEL) spectroscopy to probe the spatially resolved electronic structures of both insulating and conducting SRO to correlate them with the metal$-$insulator transition (MIT). Importantly, the central layer of the ultrathin insulating film exhibits distinct features from the metallic SRO. Moreover, EEL near edge spectra adjacent to the SrTiO$_3$ (STO) substrate or to the capping layer are remarkably similar to those of STO. The site$-$projected density of states based on density functional theory (DFT) partially reflects the characteristics of the spectra of these layers. These results may provide important information on the possible influence of STO on the electronic states of ultrathin SRO.
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis $I(\infty)=\{0\}\times\mathbf{Z}$. Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. the horizontal direction) random forest spanning $\mathbf{Z}^2$, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations.
The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes of the string are elliminated. The U(\infty) gauge theory is described by noninteracting planar surfaces and the 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. We pay special attention to the case D=2 where the sum over surfaces can be performed explicitly, and demonstrate that it reproduces the known exact results for the free energy and Wilson loops in the continuum limit. In D=4 dimensions, our lattice string model reproduces the strong coupling phase of the gauge theory. The weak coupling phase is described by a more complicated string whose world surface may have windows. A possible integration measure in the space of continuous surfaces is suggested.
We analyze orbits of stars and dark matter out to three effective radii for 42 galaxies formed in cosmological zoom simulations. Box orbits always dominate at the centers and $z$-tubes become important at larger radii. We connect the orbital structure to the formation histories and specific features (e.g. disk, counter-rotating core, minor axis rotation) in two-dimensional kinematic maps. Globally, fast rotating galaxies with significant recent in situ star formation are dominated by $z$-tubes. Slow rotators with recent mergers have significant box orbit and $x$-tube components. Rotation, quantified by the $\lambda_R$-parameter often originates from streaming motion of stars on $z$-tubes but sometimes from figure rotation. The observed anti-correlation of $h_3$ and $V_0 / \sigma$ in rotating galaxies can be connected to a dissipative formation history leading to high $z$-tube fractions. For galaxies with recent mergers in situ formed stars, accreted stars and dark matter particles populate similar orbits. Dark matter particles have isotropic velocity dispersions. Accreted stars are typically radially biased ($\beta \approx 0.2 - 0.4$). In situ stars become tangentially biased (as low as $\beta \approx -1.0$) if dissipation was relevant during the late assembly of the galaxy. We discuss the relevance of our analysis for integral field surveys and for constraining galaxy formation models.
New virial black-hole mass estimates are presented for a sample of 72 AGN covering three decades in optical luminosity. Using a model in which the AGN broad-line region (BLR) has a flattened geometry, we investigate the M_{bh)-L_{bulge} relation for a combined 90-object sample, consisting of the AGN plus a sample of 18 nearby inactive elliptical galaxies with dynamical black-hole mass measurements. It is found that, for all reasonable mass-to-light ratios, the M_{bh}-L_{bulge} relation is equivalent to a linear scaling between bulge and black-hole mass. The best-fitting normalization of the M_{bh}-M_{bulge} relation is found to be M_{bh}=0.0012M_{bulge}, in agreement with recent black-hole mass studies based on stellar velocity dispersions. Furthermore, the scatter around the M_{bh}-L_{bulge} relation for the full sample is found to be significantly smaller than has been previously reported (\Delta \log M_{bh}=0.39 dex). Finally, using the nearby inactive elliptical galaxy sample alone, it is shown that the scatter in the M_{bh}-L_{bulge} relation is only 0.33 dex, comparable to that of the M_{bh}-sigma relation. These results indicate that reliable black-hole mass estimates can be obtained for high redshift galaxies.
We report our theoretical results on spin conductivity in antiferromagnets by focusing on the role of the magnetic toroidal quadrupole (MTQ) in electron systems. The MTQ is characterized as a time-reversal-odd rank-2 polar tensor degree of freedom in electrons, which is distinct from conventional rank-1 magnetic and magnetic toroidal dipoles. Based on a microscopic $sd$ model analysis for a tetragonal system under both collinear and noncollinear antiferromagnetic orderings, we clarify that the MTQ becomes a source of an extrinsic spin conductivity even with neither a uniform magnetization nor spin-orbit coupling. We also list all the magnetic point groups to accommodate the MTQs as a primary order parameter as well as the candidate antiferromagnetic materials.
With any integral lattice \Lambda in n-dimensional euclidean space we associate an elementary abelian 2-group I(\lambda) whose elements represent parts of the dual lattice that are similar to \Lambda. There are corresponding involutions on modular forms for which the theta series of \Lambda is an eigenform; previous work has focused on this connection. In the present paper I(\Lambda) is considered as a quotient of some finite 2-subgroup of O_n(\R). We establish upper bounds, depending only on n, for the order of I(\Lambda), and we study the occurrence of similarities of specific types.
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a piecewise $C^2$ function with a discontinuity at a point. Due to the variable entropy condition with a discontinuity at the entrance, the corresponding solution has a nonzero vorticity and contains a contact discontinuity $x_2=g_D(x_1)$. We construct such a solution via Helmholtz decomposition. The key step is to decompose the Rankine-Hugoniot conditions on the contact discontinuity via Helmholtz decomposition so that the compactness of approximated solutions can be achieved. Then we apply the method of iteration to obtain a piecewise smooth subsonic flow with a contact discontinuity and nonzero vorticity. We also analyze the asymptotic behavior of the solution at far field.
Two dimensional electron gases (2DEGs) at surfaces and interfaces of semiconductors are described straightforwardly with a 1D self-consistent Poisson-Schr\"{o}dinger scheme. However, their band energies have not been modeled correctly in this way. Using angle-resolved photoelectron spectroscopy we study the band structures of 2DEGs formed at sulfur-passivated surfaces of InAs(001) as a model system. Electronic properties of these surfaces are tuned by changing the S coverage, while keeping a high-quality interface, free of defects and with a constant doping density. In contrast to earlier studies we show that the Poisson-Schr\"{o}dinger scheme predicts the 2DEG bands energies correctly but it is indispensable to take into account the existence of the physical surface. The surface substantially influences the band energies beyond simple electrostatics, by setting nontrivial boundary conditions for 2DEG wavefunctions.
A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We characterize the maximum noncontextual and quantum values of these inequalities, and provide evidence supporting the conjecture that the maximum quantum violation of these inequalities is exactly singled out by the exclusivity principle.
In this paper, we establish a connection between the 1/k-Eulerian polynomials introduced by Savage and Viswanathan (Electron. J. Combin. 19(2012), P9) and k-Stirling permutations. We also introduce the dual set of Stirling permutations.
We derive an effective Lagrangian in the quasi-antiferromagnetic approximation that allows to describe the magnetization dynamics for uniaxial f-d (rare-earth - transition metal) ferrimagnet near the magnetization compensation point in the presence of external magnetic field. We perform calculations for the parameters of GdFeCo, a metallic ferrimagnet with compensation point that is one of the most promising materials in ultrafast magnetism. Using the developed approach, we find the torque that acts on the magnetization due to ultrafast demagnetization pulse that can be caused either by ultrashort laser or electrical current pulse. We show that the torque is non-zero only in the non-collinear magnetic phase that can be acquired by applying external magnetic field to the material. The coherent response of magnetization dynamics amplitude and its timescale exhibits critical behavior near certain values of the magnetic field corresponding to a spin-flop like phase transition. Understanding the underlying mechanisms for these effects opens the way to efficient control of the amplitude and the timescales of the spin dynamics, which is one of the central problems in the field of ultrafast magnetism.
Magnetic elements have an intensity contrast that depends on the type of region they are located in (e.g. quiet Sun, or active region plage). Observed values also depend on the spatial resolution of the data. Here we investigate the contrast-magnetic field dependence in active region plage observed near disk center with Sunrise during its second flight in 2013. The wavelengths under study range from the visible at 525\,nm to the near ultraviolet (NUV) at 300\,nm and 397\,nm. We use quasi-simultaneous spectropolarimetric and photometric data from the Imaging Magnetograph eXperiment (IMaX) and the Sunrise Filter Imager (SuFI), respectively. We find that in all wavelength bands, the contrast exhibits a qualitatively similar dependence on the line-of-sight magnetic field, $B_{\rm LOS}$, as found in the quiet Sun, with the exception of the continuum at 525\,nm. There, the contrast of plage magnetic elements peaks for intermediate values of $B_{\rm LOS}$ and decreases at higher field strengths. By comparison, the contrast of magnetic elements in the quiet Sun saturates at its maximum value at large $B_{\rm LOS}$. We find that the explanation of the turnover in contrast in terms of the effect of finite spatial resolution of the data is incorrect with the evidence provided by the high-spatial resolution Sunrise data, as the plage magnetic elements are larger than the quiet Sun magnetic elements and are well-resolved. The turnover comes from the fact that the core pixels of these larger magnetic elements are darker than the quiet Sun. We find that plages reach lower contrast than the quiet Sun at disk center at wavelength bands formed deep in the photosphere, such as the visible continuum and the 300\,nm band. This difference decreases with formation height and disappears in the Ca\,{\sc ii} H core, in agreement with empirical models of magnetic element atmospheres.