ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $f(x,y)=0$ and $l(x,y)=0$ be respectively a singular and a regular analytic curve defined in the neighborhood of the origin of the complex plane. We study the family of analytic curves $f(x,y)-tl(x,y)^M=0$, where $t$ is a complex parameter. For all but a finite number of parameters the curves of this family have the same embedded topological type. The exceptional parameters are called special values.   We show that the number of nonzero special values does not exceed the number of components of the curve $f(x,y)=0$ counted without multiplicities. Then we apply this result to estimate the number of critical values at infinity of complex polynomials in two variables.
We study a one-dimensional plasmonic system with non-trivial topology: a chain of metallic nanoparticles with alternating spacing, which is the plasmonic analogue to the Su-Schreiffer-Heeger model. We extend previous efforts by including long range hopping with retardation and radiative damping, which leads to a non-Hermitian Hamiltonian with frequency dependence. We calculate band structures numerically and show that topological features such as quantised Zak phase persist due to chiral symmetry. This predicts parameters leading to topologically protected edge modes, which allows for positioning of disorder-robust hotspots at topological interfaces, opening up novel nanophotonics applications.
The nature of the several microlensing events observed by the MACHO team towards the LMC still remains controversial. Low-mass substellar objects and stars with masses larger than ~1 M_{sun} have been ruled out as major components of a MACHO galactic halo, while stars of half solar masses are the most probable candidates. In this paper we assess jointly the relative contributions of both red dwarfs and white dwarfs to the mass budget of the galactic halo. In doing so we use a Monte Carlo simulator which incorporates up-to-date evolutionary sequences of both red dwarfs and white dwarfs as well as detailed descriptions of our Galaxy and of the LMC. We explore the complete mass range between 0.08 and 1 M_{sun} as possible microlensing candidates and we compare the synthetic populations obtained with our simulator with the results obtained by the MACHO and EROS experiments. Our results indicate that, despite that the contribution of the red dwarf population increases by a factor of 2 the value of the optical depth obtained when taking into account the white dwarf population alone, it is still insufficient to explain the number of events claimed by the MACHO team. Finally, we find that the contribution to the halo dark matter of the whole population under study is smaller than 10% at the 95% conficence level.
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We briefly explain the physical mechanism leading to a power law pdf and provide a list of references for these results dating back from a quarter of century. We explain how the formulation in terms of the characteristic function developed by Takayasu et al. can be extended to exponents $\mu >2$, which explains the ``reason of the lucky coincidence''. The multidimensional generalization of (\ref{eq1}) and the available results are briefly summarized. The discovery of stretched exponential tails in the presence of the cut-off introduced in \cite{Taka} is explained theoretically. We end by briefly listing applications.
Special partial matchings (SPMs) are a generalisation of Brenti's special matchings. Let a \emph{pircon} be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Marietti's zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic $W$-sets constitute pircons. Together, these results extend a result of Can, Cherniavsky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.
Chiral spin liquids (CSLs) are time-reversal symmetry breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering, but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal symmetry breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model, which differ from their widely studied two-dimensional counterparts, namely, they exhibit a crystalline ordering of the $\mathbb{Z}_2$ gauge fluxes and thereby break some of the underlying lattice symmetries. We study the formation of these unconventional CSLs via extensive quantum Monte Carlo simulations and demonstrate that they are separated from the featureless paramagnet at high temperatures by a single first-order transition at which both time-reversal and lattice symmetries are simultaneously broken. Using variational approaches for the ground state, we explore the effect of varying the Kitaev couplings and find at least five distinct CSL phases, all of which possess crystalline ordering of the $\mathbb{Z}_2$ gauge fluxes. For some of these phases, the complementary itinerant Majorana fermions exhibit gapless band structures with topological features such as Weyl nodes or nodal lines in the bulk and Fermi arc or drumhead surface states.
Co$_{2}$FeSi/GaAs(111)B hybrid structures are grown by molecular-beam epitaxy and characterized by transmission electron microscopy (TEM) and x-ray diffraction. The Co$_{2}$FeSi films grow in an island growth mode at substrate temperatures $T_{S}$ between $T_{S}$~=~100$\thinspace^{\circ}$C and 425$\thinspace^{\circ}$C. The structures have a stable interface up to $T_{S}=275~^{\circ}$C. The films contain fully ordered $L2_{1}$ and partially ordered $B2$ phases. The spatial distribution of long-range order in Co$_{2}$FeSi is characterized using a comparison of TEM images taken with superlattice reflections and the corresponding fundamental reflections. The spatial inhomogeneities of long-range order can be explained by local non-stoichiometry due to lateral segregation or stress relaxation without formation of extended defects.
In the present work, we have done a comprehensive study of low-lying energy spectrum for oxygen and fluorine chains using $ab~initio$ no core shell model. We have used inside nonlocal outside Yukawa (INOY) potential, which is a two body interaction but also has the effect of three body forces by short range and nonlocal character. Also, we have performed calculations with N3LO and N2LOopt interactions and compared corresponding results with the experimental data and phenomenological USDB interaction. We have reached up to $N_{max}$=6 for $^{18-21}$O and $^{18-19}$F, $N_{max}$=4 for other oxygen and fluorine isotopes, respectively. We have also discussed the binding energy of oxygen and fluorine chains. Over binding in the ground state (g.s.) energy in neutron rich oxygen isotopes is observed in our largest model space calculations.
The subsequent coalescence of low--mass halos over cosmic time is thought to be the major formation channel of massive spiral galaxies like the Milky Way and the Andromeda Galaxy (M31). The gaseous halo of a massive galaxy is considered to be the reservoir of baryonic matter persistently fueling the star formation in the disk. Because of its proximity, M31 is the ideal object for studying the structure of the halo gas in great detail. Using the latest neutral atomic hydrogen (HI) data of the Effelsberg-Bonn HI Survey (EBHIS) allows comprising a comprehensive inventory of gas associated with M31. The primary aim is to differentiate between physical structures belonging to the Milky Way Galaxy and M31 and accordingly to test the presence of a M31 neutral gaseous halo. Analyzing the spatially fully sampled EBHIS data makes it feasible to trace coherent HI structures in space and radial velocity. To disentangle Milky Way and M31 HI emission we use a new approach, along with the traditional path of setting an upper radial velocity limit, by calculating a difference second moment map. We argue that M31's disk is physically connected to an asymmetric HI halo of tens of kpc size, the M31 cloud. We confirm the presence of a coherent low-velocity HI filament located in between M31 and M33 aligned at the sky with the clouds at systemic velocity. The physical parameters of the HI filament are comparable to those of the HI clouds at systemic velocity. We also detected an irregularly shaped HI cloud that is is positionally located close to but offset from the stellar body of And XIX.
In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Levy noise and regime-switching described by Markov chain can derive the heavy-tailed property of the stationary distribution. In this work, the different role played by Levy measure and regime-switching process is clearly characterized.
Charge and spin-Peierls instabilities in quarter-filled (n=1/2) compounds consisting of coupled ladders and/or zig-zag chains are investigated. Hubbard and t-J models including local Holstein and/or Peierls couplings to the lattice are studied by numerical techniques. Next nearest neighbor hopping and magnetic exchange, and short-range Coulomb interactions are also considered. We show that, generically, these systems undergo instabilities towards the formation of Charge Density Waves, Bond Order Waves and (generalized) spin-Peierls modulated structures. Moderate electron-electron and electron-lattice couplings can lead to a coexistence of these three types of orders. In the ladder, a zig-zag pattern is stabilized by the Holstein coupling and the nearest-neighbor Coulomb repulsion. In the case of an isolated chain, bond-centered and site-centered 2k_F and 4k_F modulations are induced by the local Holstein coupling. In addition, we show that, in contrast to the ladders, a small charge ordering in the chains, strongly enhances the spin-Peierls instability. Our results are applied to the NaV_2O_5 compound (trellis lattice) and various phases with coexisting charge disproportionation and spin-Peierls order are proposed and discussed in the context of recent experiments. The role of the long-range Coulomb potential is also outlined.
I think the title and content of the recent Letter by Georgeot and Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As long as the classical Arnold map is considered, the classical computational algorithm can be made exactly equivalent with the quantum one. The claimed advantage of the Letter's quantum algorithm disappears if we correctly restrict the statistical analysis for the classical Arnold system.
This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field to compute flow lines, or streamlines. The local Universe is then partitioned into volumes corresponding to gravitational basins, also called watersheds, among the different end-points of the velocity flow lines. This new methodology is first tested on numerical cosmological simulations, used as benchmark for the method, and then applied to the {\it Cosmic-Flows} project observational data in order to to pay particular attention to the nearby superclusters including ours. More extensive tests on both simulated and observational data will be discussed in an accompanying paper.
We present a ray tracing code to compute integrated cosmological observables on the fly in AMR N-body simulations. Unlike conventional ray tracing techniques, our code takes full advantage of the time and spatial resolution attained by the N-body simulation by computing the integrals along the line of sight on a cell-by-cell basis through the AMR simulation grid. Moroever, since it runs on the fly in the N-body run, our code can produce maps of the desired observables without storing large (or any) amounts of data for post-processing. We implemented our routines in the RAMSES N-body code and tested the implementation using an example of weak lensing simulation. We analyse basic statistics of lensing convergence maps and find good agreement with semi-analytical methods. The ray tracing methodology presented here can be used in several cosmological analysis such as Sunyaev-Zel'dovich and integrated Sachs-Wolfe effect studies as well as modified gravity. Our code can also be used in cross-checks of the more conventional methods, which can be important in tests of theory systematics in preparation for upcoming large scale structure surveys.
The Pluecker relations are equations which describe decomposable multivectors in $\bigwedge V$. We review all known versions, give some new ones, and decompose them into irreducible parts for the $GL(V)$-representations.
We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindstr\"om's lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.
We develop a formalism to calculate the fluctuation-induced interactions in periodic systems. The formalism, which combines the scattering theory with the C method borrowed from electromagnetic gratings studies, is suitable and efficient for the calculation of the Casimir forces involving surface relief gratings. We apply the developed technique to obtain the energy and lateral force for simple 1-D sinusoidal gratings. Using this formalism we derived known asymptotic expressions that were previously obtained through perturbative approximations. At close separation, our numerical results match those obtained by the proximity force approximation and its first correction using the derivative expansion.
We present BIMA observations of a 2$\arcmin$ field in the northeastern spiral arm of M31. In this region we find six giant molecular clouds that have a mean diameter of 57$\pm$13 pc, a mean velocity width of 6.5$\pm$1.2 \kms, and a mean molecular mass of 3.0 $\pm$ 1.6 $\times$ 10$^5$\Msun. The peak brightness temperature of these clouds ranges from 1.6--4.2 K. We compare these clouds to clouds in M33 observed by \citet{wilson90} using the OVRO millimeter array, and some cloud complexes in the Milky Way observed by \cite{dame01} using the CfA 1.2m telescope. In order to properly compare the single dish data to the spatially filtered interferometric data, we project several well-known Milky Way complexes to the distance of Andromeda and simulate their observation with the BIMA interferometer. We compare the simulated Milky Way clouds with the M31 and M33 data using the same cloud identification and analysis technique and find no significant differences in the cloud properties in all three galaxies. Thus we conclude that previous claims of differences in the molecular cloud properties between these galaxies may have been due to differences in the choice of cloud identification techniques. With the upcoming CARMA array, individual molecular clouds may be studied in a variety of nearby galaxies. With ALMA, comprehensive GMC studies will be feasible at least as far as the Virgo cluster. With these data, comparative studies of molecular clouds across galactic disks of all types and between different galaxy disks will be possible. Our results emphasize that interferometric observations combined with the use of a consistent cloud identification and analysis technique will be essential for such forthcoming studies that will compare GMCs in the Local Group galaxies to galaxies in the Virgo cluster.
The supersymmetric extensions of the Schr\"odinger algebra are reviewed.
Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly investigated via moment recurrence techniques in quantum statistical mechanics. On that basis, we carry out numerical analyses for Ag, Cu, and Ni with the Sutton-Chen many-body potential. Our results reveal that the well-known Arrhenius law is insufficient to describe the proliferation of vacancies. Specifically, anharmonic effects lead to a strong nonlinearity in the Gibbs energy of vacancy formation. Our physical picture is well supported by previous simulations and experiments.
The chameleon gravity model postulates the existence of a scalar field that couples with matter to mediate a fifth force. If it exists, this fifth force would influence the hot X-ray emitting gas filling the potential wells of galaxy clusters. However, it would not influence the clusters' weak lensing signal. Therefore, by comparing X-ray and weak lensing profiles, one can place upper limits on the strength of a fifth force. This technique has been attempted before using a single, nearby cluster (Coma, $z=0.02$). Here we apply the technique to the stacked profiles of 58 clusters at higher redshifts ($0.1<z<1.2$), including 12 new to the literature, using X-ray data from the XMM Cluster Survey (XCS) and weak lensing data from the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). Using a multi-parameter MCMC analysis, we constrain the two chameleon gravity parameters ($\beta$ and $\phi_{\infty}$). Our fits are consistent with general relativity, not requiring a fifth force. In the special case of $f(R)$ gravity (where $\beta = \sqrt{1/6}$), we set an upper limit on the background field amplitude today of $|f_{\rm{R0}}| < 6 \times 10^{-5}$ (95% CL). This is one of the strongest constraints to date on $|f_{\rm{R0}}|$ on cosmological scales. We hope to improve this constraint in future by extending the study to hundreds of clusters using data from the Dark Energy Survey.
A {\em special four-cycle } $F$ in a triple system consists of four triples {\em inducing } a $C_4$. This means that $F$ has four special vertices $v_1,v_2,v_3,v_4$ and four triples in the form $w_iv_iv_{i+1}$ (indices are understood $\pmod 4$) where the $w_j$s are not necessarily distinct but disjoint from $\{v_1,v_2,v_3,v_4\}$. There are seven non-isomorphic special four-cycles, their family is denoted by $\cal{F}$. Our main result implies that the Tur\'an number $\text{ex}(n,{\cal{F}})=\Theta(n^{3/2})$. In fact, we prove more, $\text{ex}(n,\{F_1,F_2,F_3\})=\Theta(n^{3/2})$, where the $F_i$-s are specific members of $\cal{F}$. This extends previous bounds for the Tur\'an number of triple systems containing no Berge four cycles.   We also study $\text{ex}(n,{\cal{A}})$ for all ${\cal{A}}\subseteq {\cal{F}}$. For 16 choices of $\cal{A}$ we show that $\text{ex}(n,{\cal{A}})=\Theta(n^{3/2})$, for 92 choices of $\cal{A}$ we find that $\text{ex}(n,{\cal{A}})=\Theta(n^2)$ and the other 18 cases remain unsolved.
In this work, we study the effect of the magnetic dilution of Cr$^{3+}$ on the LaCrO$_3$ half doped with Al. Pure and half-doped samples were prepared by combustion method using urea as fuel. The crystal structure was investigated by X-ray diffraction. Rietveld analysis reveal a structural phase transition caused by the increase of the chemical pressure due difference of Al$^{3+}$ and Cr$^{3+}$ ionic radii. SEM images shows that the samples exhibit a spherical formation and irregular morphologies. Magnetization measurements as a function of temperature reveal an antiferromagnetic order in both samples with a large decrease of T$_N$ (N\'eel temperature) with Al doping. The reduction of frustration factor and the increase of the magnetic moment of the doped sample could be attributed to the breaking of the long-range antiferromagnetic order. The magnetic hysteresis loops show a typical antiferromagnetic behavior with a slightly spin canting for the doped sample.
This article is concerned with the dynamic behaviour of two immiscible and incompressible fluids in a cylindrical domain, which are separated by a sharp interface. In case that the heavy fluid is situated on top of the light fluid, one expects that the fluid on top sags down into the lower phase. This effect is known as the Rayleigh-Taylor-Instability. We present a rather complete analysis of the corresponding free boundary problem which involves a contact angle. Our main result implies the existence of a critical surface tension with the following property. In case that the surface tension of the interface separating the two fluids is smaller than the critical surface tension, one has Rayleigh-Taylor-Instability. On the contrary, if the interface has a greater surface tension than the critical value, the instability effect does not occur and one has exponential stability of a flat interface. The last part of this article is concerned with the bifurcation of nontrivial equilibria in multiple eigenvalues. The invariance of the corresponding bifurcation equation with respect to rotations and reflections yields the existence of bifurcating subcritical equilibria. Finally it is proven that the bifurcating equilibria are unstable.
Aims: We investigate magnetic tracers in the photosphere and the chromosphere of the ultra-rapid rotator ($P\sim0.32d$) V530 Per, a cool member of the open cluster $\alpha$ Persei, to characterize the short-term variability of the magnetic activity and large-scale magnetic field of this prototypical young, rapidly rotating solar-like star. Methods: With time-resolved spectropolarimetric observations spread over four close-by nights, we reconstructed the brightness distribution and large-scale magnetic field geometry of V530 Per through Zeeman-Doppler imaging. Simultaneously, we estimated the short-term variability of the surface through latitudinal differential rotation. Using the same data set, we also mapped the spatial distribution of prominences through tomography of H$\alpha$ emission. Results: As in our previous study, a large dark spot occupies the polar region of V530 Per with smaller, dark, and bright spots at lower latitudes. The large-scale magnetic field is dominated by a toroidal, mostly axisymmetric component. The maximal radial field strength is equal to $\sim1$ kG. The surface differential rotation is consistent with a smooth Sun-like shear d$\Omega = 0.053 \pm 0.004$ rad.d$^{-1}$, close to the solar shear level. The prominence pattern displays a stable component that is confined close to the corotation radius. We also observe rapidly evolving H$\alpha$ emitting structures, over timescales ranging from minutes to days. The fast H$\alpha$ evolution was not linked to any detected photospheric changes in the spot or magnetic coverage.
We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices.