ShantanuT01/DACTYL-Pretraining huggingface dataset:
In long-wavelength moir\'e patterns of homobilayer semiconductors, the layer pseudospin of electrons is subject to a sizable Zeeman field that is spatially modulated from the interlayer coupling in moir\'e. By interference of this spatial modulation with a homogeneous but dynamically tunable component from out-of-plane electric field, we show that the spatial-temporal profile of the overall Zeeman field therefore features a topological texture that can be controlled in an ultrafast timescale by a terahertz field or an interlayer bias. Such dynamical modulation leads to the emergence of an in-plane electric field for low energy carriers, which is related to their real space Berry curvature -- the moir\'e magnetic field -- through the Faraday's law of induction. These emergent electromagnetic fields, having opposite signs at the time reversal pair of valleys, can be exploited to manipulate valley and spin in the moir\'e landscape under the control by a bias pulse or a terahertz irradiation.
This survey article collects a few of my favorite open problems of Branko Gr\"{u}nbaum.
We show that the failure of the usual Verdier duality on Bun(G) leads to a new duality functor on the category of D-modules, and we study its relation to the operation of Eisenstein series.
Large aromatic carbon nanostructures are cornerstone materials due to their increasingly active role in functional devices, but their synthesis in solution encounters size and shape limitations. New on-surface strategies facilitate the synthesis of large and insoluble planar systems with atomic-scale precision. While dehydrogenation is usually the chemical zipping reaction building up large aromatic carbon structures, mostly benzenoid structures are being produced. Here, we report on a new cyclodehydrogenation reaction transforming a sterically stressed precursor with conjoined cove regions into planar carbon platform by incorporating azulene moieties in their interior. Submolecular resolution STM is used to characterize this exotic large polycyclic aromatic compound on Au(111) yielding unprecedented insight into a dehydrogenative intramolecular aryl-aryl coupling reaction. The resulting polycyclic aromatic carbon structure shows a [18]annulene core hosting peculiar pore states confined at the carbon cavity.
We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a simple numerical implementation based on finite differences and step-wise approximations of parabolic dendritic branches of arbitrary orientation. Results of the two-dimensional model are verified against reference benchmark solutions for steady, unsteady, and buoyant flow, as well as steady-state dendritic growth in the diffusive regime. Simulations of equiaxed growth under forced flow yield dendrite tip velocities within 10% of quantitative phase-field results from the literature. Finally, we perform illustrative simulations of polycrystalline solidification using physical parameters for an aluminum-10wt%copper alloy. Resulting microstructures show notable differences when taking into account natural buoyancy in comparison to a purely diffusive transport regime. The resulting model opens new avenues for computationally and quantitatively investigating the influence of fluid flow and gravity-induced buoyancy upon the selection of dendritic microstructures. Further ongoing developments include an equivalent formulation for directional solidification conditions and the implementation of the model in three dimensions, which is critical for quantitative comparison to experimental measurements.
We are concerned with the Moser-Trudinger problem \begin{equation*} \begin{cases} -\Delta u=\lambda ue^{u^2}~~&\mbox{in}~\Omega,\\[0.5mm] u>0 ~~ &{\text{in}~\Omega},\\[0.5mm] u=0~~&\mbox{on}~\partial \Omega, \end{cases} \end{equation*} where $\Omega \subset \mathbb{R}^2$ is a smooth bounded domain and $\lambda>0$ is sufficiently small. Qualitative analysis for Moser-Trudinger nonlinearities has been studied in recent decades, however there is still a lot of clarity about this issue, even for a low energy. The reason is that this problem is a critical exponent for dimension two and will lose compactness. Here by using a variety of local Pohozaev identities, we qualitatively analyze the positive solutions of Moser-Trudinger problem with a low energy, which contains the Morse index, non-degeneracy, asymptotic behavior, uniqueness and symmetry of solutions. Since the fundamental solution of $-\Delta$ in $\Omega \subset \mathbb{R}^2$ is in logarithmic form and the corresponding bubble is exponential growth, more precise asymptotic behavior of the solutions is needed, which is of independent interest. Moreover, to obtain our results, some ODE's theory will be used to a prior estimate of the solutions and some elliptic theory in dimension two will play a crucial role.
In studies of accreting black holes in binary systems, empirical relations have been proposed to quantify the coupling between accretion processes and ejection mechanisms. These processes are probed respectively by means of X-ray and radio/optical-infrared observations. The relations predict, given certain accretion conditions, the expected energy output in the form of a jet. We investigated this coupling by studying the black hole candidate Swift J1753.5-0127, via multiwavelength coordinated observations over a period of ~4 years. We present the results of our campaign showing that, all along the outburst, the source features a jet that is fainter than expected from the empirical correlation between the radio and the X-ray luminosities in hard spectral state. Because the jet is so weak in this system the near-infrared emission is, unusually for this state and luminosity, dominated by thermal emission from the accretion disc. We briefly discuss the importance and the implications of a precise determination of both the slope and the normalisation of the correlations, listing some possible parameters that broadband jet models should take into account to explain the population of sources characterized by a dim jet. We also investigate whether our data can give any hint about the nature of the compact object in the system, since its mass has not been dynamically measured.
For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients $c_{i,j}$. We calculate the Weyl binomial coefficients: normal order coefficients of the element $(D+U)^n$ in the Weyl algebra. We extend all these results to the $q$-analogue of the Weyl algebra. We discuss further generalizations using $i$-rook numbers.
Micro-Raman scattering and electron field emission characteristics of silicon nanowires (SiNWs) synthesized by metal assisted chemical etching (MACE) are investigated. Scanning electron microscopy images reveal the growth of well aligned vertical SiNWs. Raman shift and size relation from bond-polarizability model has been used to calculate exact confinement sizes in SiNWs. The Si optical phonon peak for SiNWs showed a downshift and an asymmetric broadening with decreasing diameter of the SiNWs due to quantum confinement of optical phonons. The field emission characteristics of these SiNWs are studied based by carrying out current-voltage measurements followed by a theoretical analysis using Fowler-Nordheim equation. The electron field emission increased with decreasing diameter of SiNWs. Field emission from these SiNWs exhibits significant enhancement in turn-on field and total emission current with decreasing nanowire size. The reported results in the current study indicate that MACE is a simple technique to prepare well-aligned SiNWs with potentials for applications in field emission devices.
An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star-product formula $\exp[i\epsilon_{\alpha\beta}\partial^\alpha \partial^\beta]$. Using Pochhammer formula, integration over these parameters is carried over a Riemann surface associated with the expression of the type $z^x (1-z)^y$ where $x$ and $y$ are arbitrary real numbers.
In this paper we calculate the contributions to the branching ratio of $B_s \to \gamma\gamma$ from the charged Pseudo-Goldstone bosons appeared in one generation Technicolor model. We find that the theoretical values of the branching ratio, $BR(B_s\to\gamma\gamma)$, including the contributions of PGBs, $P^\pm$ and $P^{\pm}_8$, are much different from the $SM$ prediction. The new physics effects can be enhance 2-3 levels to $SM$ result. It is shown that the decay $B_s\to \gamma\gamma$ can give the test the new physics signals from the technicolor model.
A self-driving perception model aims to extract 3D semantic representations from multiple cameras collectively into the bird's-eye-view (BEV) coordinate frame of the ego car in order to ground downstream planner. Existing perception methods often rely on error-prone depth estimation of the whole scene or learning sparse virtual 3D representations without the target geometry structure, both of which remain limited in performance and/or capability. In this paper, we present a novel end-to-end architecture for ego 3D representation learning from an arbitrary number of unconstrained camera views. Inspired by the ray tracing principle, we design a polarized grid of "imaginary eyes" as the learnable ego 3D representation and formulate the learning process with the adaptive attention mechanism in conjunction with the 3D-to-2D projection. Critically, this formulation allows extracting rich 3D representation from 2D images without any depth supervision, and with the built-in geometry structure consistent w.r.t. BEV. Despite its simplicity and versatility, extensive experiments on standard BEV visual tasks (e.g., camera-based 3D object detection and BEV segmentation) show that our model outperforms all state-of-the-art alternatives significantly, with an extra advantage in computational efficiency from multi-task learning.
We prove that a non--zero Jacobi form of arbitrary level $N$ and square--free index $m_1m_2$ with $m_1|N$ and $(N,m_2)=1$ has a non--zero theta component $h_\mu$ with either $(\mu,2m_1m_2)=1$ or $(\mu,2m_1m_2)\nmid 2m_2$. As an application, we prove that a non--zero Siegel cusp form $F$ of degree $2$ and an odd level $N$ in the Atkin--Lehner type newspace is determined by fundamental Fourier coefficients up to a divisor of $N$.
Let $G$ be a simple graph. A total dominator coloring of $G$, is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number $\chi_d^t(G)$ of $G$, is the minimum number of colors among all total dominator coloring of $G$. For any $k \in \mathbb{N}$, the $k$-subdivision of $G$ is a simple graph $G^{\frac{1}{k}}$ which is constructed by replacing each edge of $G$ with a path of length $k$. In this paper, we study the total dominator chromatic number of $k$-subdivision of $G$.
A direct relation between the conformal formalism for 2d-quantum gravity and the W-constrained KP hierarchy is found, without the need to invoke intermediate matrix model technology. The Kontsevich-Miwa transform of the KP hierarchy is used to establish an identification between W constraints on the KP tau function and decoupling equations corresponding to Virasoro null vectors. The Kontsevich-Miwa transform maps the $W^{(l)}$-constrained KP hierarchy to the $(p^\prime,p)$ minimal model, with the tau function being given by the correlator of a product of (dressed) $(l,1)$ (or $(1,l)$) operators, provided the Miwa parameter $n_i$ and the free parameter (an abstract $bc$ spin) present in the constraints are expressed through the ratio $p^\prime/p$ and the level $l$.
The anisotropy parameter $\beta$ characterizes the extent to which orbits in stellar systems are predominantly radial or tangential, and is likely to constrain, for the stellar halo of the Milky Way, scenarios for its formation and evolution. We have measured the anisotropy $\beta$ as a function of Galactocentric radius from $5-100$ kpc for over 8600 metal poor ([Fe/H] $<-1.3$) halo K giants from the LAMOST catalog with line-of-sight velocities and distances, matched to proper motions from the second $Gaia$ data release. We construct full 6-D positions and velocities for the K giants to directly measure the 3 components of the velocity dispersion $(\sigma_r, \sigma_\theta, \sigma_\phi)$ (in spherical coordinates). We find that the orbits in the halo are radial over our full Galactocentric distance range reaching over 100 kpc. The anisotropy remains remarkably unchanged with Galactocentric radius from approximately 5 to 25 kpc, with an amplitude that depends on the metallicity of the stars, dropping from $\beta \approx 0.9$ for $-1.8 \leq$ [Fe/H] $< -1.3$ (for the bulk of the stars) to $\beta \approx 0.6$ for the lowest metallicities ([Fe/H] $< -1.8$). Considering our sample as a whole, $\beta\approx0.8$ and, beyond 25 kpc, the orbits gradually become less radial and anisotropy decreases to $\beta<0.3$ past 100 kpc. Within 8 kpc, $\beta<0.8$. The measurement of anisotropy is affected by substructure and streams, particularly beyond a Galactocentric distance of approximately 25 kpc, where the Sagittarius stream is prominent in the data. These results are complimentary to recent analysis of simulations by Loebman et al. and of SDSS/$Gaia$ DR1 data by Belokurov et al.
Crystal and magnetic structures of the mineral centennialite CaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O are investigated by means of synchrotron x-ray diffraction and neutron diffraction measurements complemented by density functional theory (DFT) and pseudofermion functional renormalization group (PFFRG) calculations. CaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O crystallizes in the $P\bar{3}m1$ space group and Cu$^{2+}$ ions form a geometrically perfect kagome network with antiferromagnetic $J_1$. No intersite disorder between Cu$^{2+}$ and Ca$^{2+}$ ions is detected. CaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O enters a magnetic long-range ordered state below $T_\text{N}=7.2$~K, and the $\mathbf{q}=\mathbf{0}$ magnetic structure with negative vector spin chirality is obtained. The ordered moment at 0.3~K is suppressed to $0.58(2)\mu_\text{B}$. Our DFT calculations indicate the presence of antiferromagnetic $J_2$ and ferromagnetic $J_d$ superexchange couplings of a strength which places the system at the crossroads of three magnetic orders (at the classical level) and a spin-$\frac{1}{2}$ PFFRG analysis shows a dominance of $\mathbf{q}=\mathbf{0}$ type magnetic correlations, consistent with and indicating proximity to the observed $\mathbf{q}=\mathbf{0}$ spin structure. The results suggest that this material is located close to a quantum critical point and is a good realization of a $J_1$-$J_2$-$J_d$ kagome antiferromagnet.
Using the Lanczos method we determine the phase diagram of the 2-leg AF-Heisenberg ladder with alternating dimerization. It consists of a resonating valence bond phase and a dimer phase separated by a critical line. Our results are in good agreement with previous conjectures obtained with the non linear sigma model.
Field-road models are reaction-diffusion systems which have been recently introduced to account for the effect of a road on propagation phenomena arising in epidemiology and ecology. Such systems consist in coupling a classical Fisher-KPP equation to a line with fast diffusion accounting for a road. A series of works investigate the spreading properties of such systems when the road is a straight line and the field a half-plane. Here, we take interest in the case where the field is a cone. Our main result is that the spreading speed is not influenced by the angle of the cone.
We present three-dimensional eccentric disc models of the nucleus of M31, modelling the disc as a linear combination of thick rings of massless stars orbiting in the potential of a central black hole. Our models are nonparametric generalisations of the parametric models of Peiris & Tremaine. The models reproduce well the observed WFPC2 photometry, the detailed line-of-sight velocity distributions from STIS observations along P1 and P2, together with the qualitative features of the OASIS kinematic maps. We confirm Peiris & Tremaine's finding that nuclear discs aligned with the larger disc of M31 are strongly ruled out. Our optimal model is inclined at 57 degrees with respect to the line of sight of M31 and has a position angle of 55 degrees. It has a central black hole of mass 10^8 solar masses, and, when viewed in three dimensions, shows a clear enhancement in the density of stars around the black hole. The distribution of orbit eccentricities in our models is similar to Peiris & Tremaine's model, but we find significantly different inclination distributions, which might provide valuable clues to the origin of the disc.
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are obtained for two distinct cases. In the case of dimension two, we obtain four partial characterization results. An analytical result with full generality is not available in this case, and it seems to be out of reach with existing techniques. For dimension greater or equal to three, we obtain a full characterization of the set of aggregate distributions, which is the first complete characterization result of this type in the literature for any choice of continuous marginal distributions.
Aims: We investigate the nature of the source GDS J033218.92-275302.7at redshift ~ 5.56. Methods: The SED of the source is well sampled by 16 bands photometry, from UV-optical, near infrared and mid-infrared (MID-IR).The detection of signal in the MID-IR Spitzer/IRAC bands 5.8, 8.0 um -- where the nebular emission contribution is less effective -- suggests the presence of a Balmer break, signature of an underlying stellar population formed at earlier epochs. The optical spectrum shows a clear Lya emission line together with semi-forbidden NIV] 1483.3-1486.5 also in emission. Results: From the SED fitting and the Lya modelling it turns out that the source seems to have an evolved component with stellar mass of ~5 x10^(10) Msolar and age ~ 0.4 Gyrs, and a young component with an age of ~ 0.01 Gyrs and SFR in the range of 30-200 Msolar yr^(-1). The limits on the effective radius derived from the ACS/z850 and VLT/Ks bands indicate that this galaxy is denser than the local ones with similar mass. A relatively high nebular gas column density is favored from the Lya line modelling (NHI>=10^(21) cm^(-2)). A vigorous outflow (~ 450 km/s) has been measured from the optical spectrum,consistent with the Lya modelling. From ACS observations it turns out that the region emitting Lya photons is spatially compact and of the same order of the effective radius estimated at the ~1400A rest-frame wavelength, whose emission is dominated by the stellar continuum and/or AGN. The gas is blown out from the central region,but given the mass of the galaxy it is uncertain whether it will pollute the IGM to large distances. We argue that a burst of star formation in a dense gas environment is active (possibly containing hot and massive stars and/or a low luminosity AGN), superimposed to an already formed fraction of stellar mass (abridged).
Polarized neutron diffraction experiments have been performed on multiferroic materials $R$Mn$_{2}$O$_{5}$ ($R=$Ho, Er) under electric fields in the ferroelectric commensurate (CM) and the low-temperature incommensurate (LT-ICM) phases, where the former has the highest electric polarization and the latter has reduced polarization. It is found that, after cooling in electric fields down to the CM phase, the magnetic chirality is proportional to the electric polarization. Also we confirmed that the magnetic chirality can be switched by the polarity of the electric polarization in both the CM and LT-ICM phases. These facts suggest an intimate coupling between the magnetic chirality and the electric polarization. However, upon the transition from the CM to LT-ICM phase, the reduction of the electric polarization is not accompanied by any reduction of the magnetic chirality, implying that the CM and LT-ICM phases contain different mechanisms of the magnetoelectric coupling.
We present an one-dimensional numerical study of Alfven waves propagating along a radial magnetic field. Neglecting losses, any spherical Alfven wave, no matter how small its initial amplitude is, becomes nonlinear at sufficiently large radii. From previous simulations of Alfven waves in plane parallel atmospheres we did expect the waves to steepen and produce current sheets in the nonlinear regime, which was confirmed by our new calculations. On the other hand we did find that even the least nonlinear waves were damped out almost completely before 10 solar radii. A damping of that kind is required by models of Alfven wave-driven winds from old low-mass stars as these winds are mainly accelerated within a few stellar radii.
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.
The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the solution of a suitable stochastic PDE defined on the graph associated with the Hamiltonian. Firstly, we deal with the case that the stochastic perturbation is given by a singular spatially homogeneous Wiener process taking values in the space of Schwartz distributions. As in previous works, we assume here that the derivative of the period of the motion on the level sets of the Hamiltonian does not vanish. Then, in the second part, without assuming this condition on the derivative of the period, we study a weaker type of convergence for the solutions of a suitable class of linear SPDEs.
New kinds of supersymmetry arise in supersymmetric $\sg$-models describing the motion of spinning point-particles in classical backgrounds, for example black-holes, or the dynamics of monopoles. Their geometric origin is the existence of Killing-Yano tensors. The relation between these concepts is explained and examples are given. --- Contribution to Proceedings Quarks-94; Vladimir, Russia (1994).
Let $H$ and $K$ be subsets of the vertex set $V(Q_d)$ of the $d$-cube $Q_d$ (we call $H$ and $K$ configurations in $Q_d$). We say $K$ is an \emph{exact copy} of $H$ if there is an automorphism of $Q_d$ which sends $H$ to $K$. If $d$ is a positive integer and $H$ is a configuration in $Q_d$, we define $\pi(H,d)$ to be the limit as $n$ goes to infinity of the maximum fraction, over all subsets $S$ of $V(Q_n)$, of sub-$d$-cubes of $Q_n$ whose intersection with $S$ is an exact copy of $H$. We determine $\pi(C_8,4)$ and $\pi(P_4,3)$ where $C_8$ is a "perfect" 8-cycle in $Q_4$ and $P_4$ is a "perfect" path with 4 vertices in $Q_3$, and make conjectures about $\pi(C_{2d},d)$ and $\pi(P_{d+1},d)$ for larger values of $d$. In our proofs there are connections with counting the number of sequences with certain properties and with the inducibility of certain small graphs. In particular, we needed to determine the inducibility of two vertex disjoint edges in the family of bipartite graphs.