ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the previous paper (hep-th/9712161) it was shown that the nonlinear Born-Infeld field equations supplemented by the "dynamical condition" (certain boundary condition for the field along the particle's trajectory) define perfectly deterministic theory, i.e. particle's trajectory is determined without any equations of motion. In the present paper we show that this theory possesses mathematically consistent Lagrangian and Hamiltonian formulations. Moreover, it turns out that the "dynamical condition" is already present in the definition of the physical phase space and, therefore, it is a basic element of the theory.
In this note we prove that the maximum length of a $d$-dimensional circuit code of spread $k$ equals $2^{d+O_k(\log^2d)}$, with the implied constant depending only on $k$.
We consider the dynamics and thermodynamics of a pair of magnetic dipoles interacting via their magnetic fields. We consider only the "spin" degrees of freedom; the dipoles are fixed in space. With this restriction it is possible to provide the general solution of the equations of motion in analytical form. Thermodynamic quantities, such as the specific heat and the zero field susceptibility are calculated by combining low temperature asymptotic series and a complete high temperature expansion. The thermal expectation value of the autocorrelation function is determined for the low temperature regime including terms linear in $T$. Furthermore, we compare our analytical results with numerical calculations based on Monte Carlo simulations.
Using an approach to open quantum systems based on the effective non-Hermitian Hamiltonian, we fully describe transport properties for a paradigmatic model of a coherent quantum transmitter: a finite sequence of square potential barriers. We consider the general case of asymmetric external barriers and variable coupling strength to the environment. We demonstrate that transport properties are very sensitive to the degree of opening of the system and determine the parameters for maximum transmission at any given degree of asymmetry. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, we show a double transition to a super-radiant regime where the transport properties and the structure of resonances undergo a strong change. We extend our analysis to the presence of disorder and to higher dimensions.
In this paper, we prove the uniform nonlinear structural stability of Hagen-Poiseuille flows with arbitrary large fluxes in the axisymmetric case. This uniform nonlinear structural stability is the first step to study Liouville type theorem for steady solution of Navier-Stokes system in a pipe, which may play an important role in proving the existence of solutions for the Leray's problem, the existence of solutions of steady Navier-Stokes system with arbitrary flux in a general nozzle. A key step to establish nonlinear structural stability is the a priori estimate for the associated linearized problem for Navier-Stokes system around Hagen-Poiseuille flows. The linear structural stability is established as a consequence of elaborate analysis for the governing equation for the partial Fourier transform of the stream function. The uniform estimates are obtained based on the analysis for the solutions with different fluxes and frequencies. One of the most involved cases is to analyze the solutions with large flux and intermediate frequency, where the boundary layer analysis for the solutions plays a crucial role.
Half of the energy ever emitted by stars and accreting objects comes to us in the FIR waveband and has yet to be properly explored. We propose a powerful Far-InfraRed Interferometer mission, FIRI, to carry out high-resolution imaging spectroscopy in the FIR. This key observational capability is essential to reveal how gas and dust evolve into stars and planets, how the first luminous objects in the Universe ignited, how galaxies formed, and when super-massive black holes grew. FIRI will disentangle the cosmic histories of star formation and accretion onto black holes and will trace the assembly and evolution of quiescent galaxies like our Milky Way. Perhaps most importantly, FIRI will observe all stages of planetary system formation and recognise Earth-like planets that may harbour life, via its ability to image the dust structures in planetary systems. It will thus address directly questions fundamental to our understanding of how the Universe has developed and evolved - the very questions posed by ESA's Cosmic Vision.
Monolayer graphene is an example of materials with multi-valley electronic structure. In such materials, the valley index is being considered as an information carrier. Consequently, relaxation mechanisms leading to loss of valley information are of interest. Here, we calculate the rate of valley relaxation induced by charged impurities in graphene. A special model of graphene is applied, where the $p_z$ orbitals are two-dimensional Gaussian functions, with a spatial extension characterised by an effective Bohr radius $a_\textrm{eB}$. We obtain the valley relaxation rate by solving the Boltzmann equation, for the case of noninteracting electrons, as well as for the case when the impurity potential is screened due to electron-electron interaction. For the latter case, we take into account local-field effects and evaluate the dielectric matrix in the random phase approximation. Our main findings: (i) The valley relaxation rate is proportional to the electronic density of states at the Fermi energy. (ii) Charged impurities located in the close vicinity of the graphene plane, at distance $d \lesssim 0.3\,\textrm{\AA}$, are much more efficient in inducing valley relaxation than those farther away, the effect of the latter being suppressed exponentially with increasing graphene-impurity distance $d$. (iii) Both in the absence and in the presence of electron-electron interaction, the valley relaxation rate shows pronounced dependence on the effective Bohr radius $a_\textrm{eB}$. The trends are different in the two cases: in the absence (presence) of screening, the valley relaxation rate decreases (increases) for increasing effective Bohr radius. This last result highlights that a quantitative calculation of the valley relaxation rate should incorporate electron-electron interactions as well as an accurate knowledge of the electronic wave functions on the atomic length scale.
An $n$-dimensional algebraic variety in $({\mathbb C}^\times)^{2n}$ covers its amoeba as well as its coamoeba generically finite-to-one. We provide an upper bound for the volume of these amoebas as well as for the number of points in the inverse images under the amoeba and coamoeba maps.
We study rational curves of degree two on a smooth sextic 4-fold and their counting invariant defined using Donaldson-Thomas theory of Calabi-Yau 4-folds. By comparing it with the corresponding Gromov-Witten invariant, we verify a conjectural relation between them proposed by the author, Maulik and Toda.
We present a set of low resolution empirical SED templates for AGNs and galaxies in the wavelength range from 0.03 to 30 microns. These templates form a non-negative basis of the color space of such objects and have been derived from a combination 14448 galaxies and 5347 likely AGNs in the NDWFS Bootes field. We briefly describe how the templates are derived and discuss some applications of them. In particular, we discuss biases in commonly used AGN mid-IR color selection criteria and the expected distribution of sources in the current WISE satellite mission.
Cubic Half-Heusler Cu$_{1-x}$Co$_x$MnSb (0 $\leq$ $x$ $\leq$ 0.1) compounds have been investigated both experimentally and theoretically for their magnetic, transport and electronic properties in search of possible half metallic antiferromagnetism. The systems (Cu,Co)MnSb are of particular interest as the end member alloys CuMnSb and CoMnSb are semi metallic (SM) antiferromagnetic (AFM) and half metallic (HM) ferromagnetic (FM), respectively. Clearly, Co-doping at the Cu-site of CuMnSb introduces changes in the carrier concentration at the Fermi level that may lead to half-metallic ground state but there remains a persistent controversy whether the AFM to FM transition occurs simultaneously. Our experimental results reveal that the AFM to FM magnetic transition occurs through a percolation mechanism where Co-substitution gradually suppresses the AFM phase and forces FM polarization around every dopant cobalt. As a result a mixed magnetic phase is realized within this composition range while a nearly HM band structure is developed already at the 10% Co-doping. Absence of T$^2$ dependence in the resistivity variation at low T-region serves as an indirect proof of opening up an energy gap at the Fermi surface in one of the spin channels. This is further corroborated by the ab-initio electronic structure calculations that suggests a nearly ferromagnetic half-metallic ground state is stabilized by Sb-p holes produced upon Co doping.
Given two rational, properly parametrized space curves ${\mathcal C}_1$ and ${\mathcal C}_2$, where $\CCC_2$ is contained in some plane $\Pi$, we provide an algorithm to check whether or not there exist perspective or parallel projections mapping $\CCC_1$ onto $\CCC_2$, i.e. to recognize $\CCC_2$ as the projection of $\CCC_1$. In the affirmative case, the algorithm provides the eye point(s) of the perspective transformation(s), or the direction(s) of the parallel projection(s). The problem is mainly discussed from a symbolic point of view, but an approximate algorithm is also included.
Recently, it has been shown that (4+1)-dimensional Yang-Mills theory may be written as a (3+1)-dimensional BPS Skyrme model, in which the Skyrme field is coupled to an infinite tower of vector mesons. Truncating this tower to a single vector meson yields an extension of the standard Skyrme model to a theory of pions coupled to the rho meson, with the significant simplification that no additional free parameters are introduced. The present paper is concerned with this truncated theory and results are presented for Skyrmions with baryon numbers one to four. The approach involves the use of an extended version of the Atiyah-Manton construction, in which the Skyrme field is approximated by the holonomy of a Yang-Mills instanton. It is found that the coupling to the rho meson significantly reduces Skyrmion binding energies, to produce an improved comparison with the experimental data on nuclei. A truncation that includes both a vector and an axial vector meson is also investigated, providing a model of pions, the rho meson and the a1 meson. Binding energies are further reduced by the inclusion of this additional meson, shifting the Skyrmion energies a little closer to those of nuclei. Fixing the energy unit by equating the energy of the baryon number four Skyrmion to the He-4 mass, yields masses for all lower baryon numbers that are within 20 MeV of the experimental values, which is an error that is four times smaller than in the standard Skyrme model.
A nearly platonic graph is a k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for a finite graph to have exactly one disparate face, and offer some conjectures, including the conjecture that graphs with two disparate faces come in a small set of families.
We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.
Structures of excited states in $^{11}$B are investigated with a method of $\beta$-$\gamma$ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various excited states with developed cluster core structures are suggested in positive- and negative-parity states. For negative-parity states, we suggest a band with a $2\alpha+t$ cluster structure. This band starts from the $3/2^{-}_{3}$ state and can correspond to the experimental band observed recently. In positive-parity states, two $\alpha$ core cluster structures with surrounding nucleons are found. A $K^\pi=1/2^+$ band is suggested to be constructed from a remarkably developed cluster structure with a large prolate deformation. We discuss features of the cluster structure in association with molecular orbital structures of $^{10}$Be.
We conduct dislocation dynamics (DD) simulations of Fe periodic single crystals under tensile load at several high strain rates and temperatures. The simulations are enabled by the recent development of temperature-dependent dislocation mobility relations obtained from atomistic calculations. The plastic evolution in the simulations is governed by rapid initial dislocation multiplication, followed by a saturation of the flow stress when the subpopulation of slow plastic carriers becomes stabilized by dislocation annihilation. Above 500 K, edge dislocations coexist with screw dislocations and contribute proportionaly to the value of the flow stress. The DD simulations are used to interpret shock-loading experiments in Fe in terms of the relative importance of different strengthening mechanisms. We find that in the $10^4$-to-$10^6$ s$^{-1}$ strain rate regime, work hardening explains the hardening of shock-loaded bulk Fe crystals.
We present a new type of phase-change behavior relevant for information storage applications, that can be observed in 2D systems with cluster-forming ability. The temperature-based control of the ordering in 2D particle systems depends on the existence of a crystal-to-glass transition. We perform molecular dynamics simulations of models with soft interactions, demonstrating that the crystalline and amorphous structures can be easily tuned by heat pulses. The physical mechanism responsible for this behavior is a self-assembled polydispersity, that depends on the cluster-forming ability of the interactions. Therefore, the range of real materials that can perform such a transition is very wide in nature, reading from colloidal suspensions to vortex matter. The state of the art in soft matter experimental setups, controlling interactions, polydispersity and dimensionality, makes it a very fertile ground for practical applications.
We consider a thin soft adhesive interphase between dissimilar elastic media. The material of the intermediate layer is modelled by elasto-plastic pressure-sensitive constitutive law. An asymptotic procedure, together with a novel formulation of the deformation theory of plasticity for pressure-sensitive materials, is used in order to derive nonlinear transmission conditions for the corresponding imperfect zero-thickness interface. A FEM analysis of the original three-phase structure is performed to validate the transmission conditions for the simplified bimaterial structure.
We investigate the chemo-kinematic properties of the Milky Way disc by exploring the first year of data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), and compare our results to smaller optical high-resolution samples in the literature, as well as results from lower resolution surveys such as GCS, SEGUE and RAVE. We start by selecting a high-quality sample in terms of chemistry ($\sim$ 20.000 stars) and, after computing distances and orbital parameters for this sample, we employ a number of useful subsets to formulate constraints on Galactic chemical and chemodynamical evolution processes in the Solar neighbourhood and beyond (e.g., metallicity distributions -- MDFs, [$\alpha$/Fe] vs. [Fe/H] diagrams, and abundance gradients). Our red giant sample spans distances as large as 10 kpc from the Sun.   We find remarkable agreement between the recently published local (d $<$ 100 pc) high-resolution high-S/N HARPS sample and our local HQ sample (d $<$ 1 kpc). The local MDF peaks slightly below solar metallicity, and exhibits an extended tail towards [Fe/H] $= -$1, whereas a sharper cut-off is seen at larger metallicities. The APOGEE data also confirm the existence of a gap in the [$\alpha$/Fe] vs. [Fe/H] abundance diagram. When expanding our sample to cover three different Galactocentric distance bins, we find the high-[$\alpha$/Fe] stars to be rare towards the outer zones, as previously suggested in the literature. For the gradients in [Fe/H] and [$\alpha$/Fe], measured over a range of 6 $ < $ R $ <$ 11 kpc in Galactocentric distance, we find a good agreement with the gradients traced by the GCS and RAVE dwarf samples. For stars with 1.5 $<$ z $<$ 3 kpc, we find a positive metallicity gradient and a negative gradient in [$\alpha$/Fe].
We present the experimental evidence of RF demodulation by a graphene monolayer embedded in a coplanar structure. The demodulator was tested in the frequency range from 100 MHz to 25 GHz using amplitude modulated input signals. An input power of 0 dBm (1 mW) was used which is the typical power emitted for short range wireless communication systems, such as Bluetooth. The graphene demodulator exhibits good signal response in the frequency range associated to industrial, scientific and medical (ISM) radio band (2.4 GHz).
White-light flares (WLFs), first observed in 1859, refer to a type of solar flares showing an obvious enhancement of the visible continuum emission. This type of enhancement often occurs in most energetic flares, and is usually interpreted as a consequence of efficient heating in the lower solar atmosphere through non-thermal electrons propagating downward from the energy release site in the corona. However, this coronal-reconnection model has difficulty in explaining the recently discovered small WLFs. Here we report a C2.3 white-light flare, which are associated with several observational phenomena: fast decrease in opposite-polarity photospheric magnetic fluxes, disappearance of two adjacent pores, significant heating of the lower chromosphere, negligible increase of hard X-ray flux, and an associated U-shaped magnetic field configuration. All these suggest that this white-light flare is powered by magnetic reconnection in the lower part of the solar atmosphere rather than by reconnection higher up in the corona.
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this article, we obtain generalizations of these character formulas, by using a bijection on integer partitions, namely the Littlewood decomposition, for which we prove new properties. As applications, we derive signed generating functions for subsets of integer partitions, and new hook length formulas.
We study the shadow of a charged rotating black hole in $f(R)$ gravity. This black hole is characterized by mass, $M$, spin, $a$, electric charge, $Q$ and $R_{0}$ which is proportional to cosmological constant. We analyze the image of the black hole's shadow in four types 1) at $r\rightarrow\infty$, 2) at $r\rightarrow r_{o}$, in vacuum, 3) at $r\rightarrow\infty$, 4) at $r\rightarrow r_{o}$, for an observer at the presence of plasma. Moreover, we investigate the effect of spin, charge and modfication of gravity on the shape of shadow. In addition, we use two observables, the radius $R_{s}$ and the distortion parameter $\delta_{s}$, characterizing the apparent shape. We show that for all cases, the shadow becomes smaller with increasing electric charge. Also, by increasing the rotation parameters, circular symmetry of the image of black hole's shadow will change. Furthermore, in the presence of plasma, plasma parameter also effects on size of the shadow.
The intermediate- to high-mass star-forming region IRAS 20343+4129 is an excellent laboratory to study the influence of high- and intermediate-mass young stellar objects on nearby starless dense cores, and investigate for possible implications in the clustered star formation process. We present 3 mm observations of continuum and rotational transitions of several molecular species (C2H, c-C3H2, N2H+, NH2D) obtained with the Combined Array for Research in Millimetre-wave Astronomy, as well as 1.3 cm continuum and NH3 observations carried out with the Very Large Array, to reveal the properties of the dense gas. We confirm undoubtedly previous claims of an expanding cavity created by an ultracompact HII region associated with a young B2 zero-age main sequence (ZAMS) star. The dense gas surrounding the cavity is distributed in a filament that seems squeezed in between the cavity and a collimated outflow associated with an intermediate-mass protostar. We have identified 5 millimeter continuum condensations in the filament. All of them show column densities consistent with potentially being the birthplace of intermediate- to high-mass objects. These cores appear different from those observed in low-mass clustered environments in sereval observational aspects (kinematics, temperature, chemical gradients), indicating a strong influence of the most massive and evolved members of the protocluster. We suggest a possible scenario in which the B2 ZAMS star driving the cavity has compressed the surrounding gas, perturbed its properties and induced the star formation in its immediate surroundings.
We use variable-temperature (150--300\,K) single-crystal X-ray diffraction to re-examine the interplay between structure and dynamics in the ambient phase of the isotropic negative thermal expansion (NTE) material Cd(CN)$_2$. We find strong experimental evidence for the existence of low-energy vibrational modes that involve off-centering of Cd$^{2+}$ ions. These modes have the effect of increasing network packing density---suggesting a mechanism for NTE that is different to the generally-accepted picture of correlated Cd(C/N)$_4$ rotation modes. Strong local correlations in the displacement directions of neighbouring cadmium centres are evident in the existence of highly-structured diffuse scattering in the experimental X-ray diffraction patterns. Monte Carlo simulations suggest these patterns might be interpreted in terms of a basic set of `ice-rules' that establish a mapping between the dynamics of Cd(CN)$_2$ and proton ordering in cubic ice VII.
Semiconductor nanowire lasers can produce guided coherent light emission with miniaturized geometry, bringing about new possibility for a variety of applications including nanophotonic circuits, optical sensing, and on-chip and chip-to-chip optical communications. Here, we report on the realization of single-mode room-temperature lasing from 890 nm to 990 nm utilizing a novel design of single nanowires with GaAsSb-based multiple superlattices as gain medium under optical pumping. The wavelength tunability with comprehensively enhanced lasing performance is shown to result from the unique nanowire structure with efficient gain materials, which delivers a lasing quality factor as high as 1250, a reduced lasing threshold ~ 6 kW cm-2 and a high characteristic temperature ~ 129 K. These results present a major advancement for the design and synthesis of nanowire laser structures, which can pave the way towards future nanoscale integrated optoelectronic systems with stunning performance.
We investigate a stochastic model describing a column of grains in the jamming limit, in the presence of a low vibrational intensity. The key control parameter of the model, $\epsilon$, is a representation of granular shape, related to the reduced void space. Regularity and irregularity in grain shapes, respectively corresponding to rational and irrational values of $\epsilon$, are shown to be centrally important in determining the statics and dynamics of the compaction process.