ShantanuT01/DACTYL-Pretraining huggingface dataset:
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable. However, Dirac's treatment can be slightly modified to obtain, in some cases, a Hamiltonian description completely equivalent to the Lagrangian one. A recipe to deal with the different cases is provided, along with a few pedagogical examples.
Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles. Furthermore, based on the game-perspective we derive new variational formulations for first-order MFG systems with congestion. Finally, we use these findings to prove the existence of time-periodic solutions for viscous MFG systems with a coupling that is not a non-decreasing function of density.
Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift $z\sim 10$. They are often proposed as complementary tools to type-Ia supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance calibrations of GRBs usually make use one or some of the empirical luminosity correlations, such as $\tau_{\rm lag}-L$, $V-L$, $E_p-L$, $E_p-E_{\gamma}$, $\tau_{\rm RT}-L$ and $E_p-E_{\rm iso}$ relations. These calibrating methods are based on the underling assumption that the empirical luminosity correlations are universal over all redshift range. In this paper, we test the possible redshift dependence of six luminosity correlations by dividing GRBs into low-$z$ and high-$z$ classes according to their redshift smaller or larger than 1.4. It is shown that the $E_p-E_{\gamma}$ relation for low-$z$ GRBs is consistent with that for high-$z$ GRBs within $1\sigma$ uncertainty. The intrinsic scatter of $V-L$ relation is too larger to make a convincing conclusion. For the rest four correlations, however, low-$z$ GRBs differ from high-$z$ GRBs at more than $3\sigma$ confidence level. As such, we calibrate GRBs using the $E_p-E_{\gamma}$ relation in a model-independent way. The constraint of high-$z$ GRBs on the $\Lambda$CDM model gives $\Omega_M=0.302\pm 0.142(1\sigma)$, well consistent with the Planck 2015 results.
We study the effect of electron-phonon interactions on the electrical conductance of a helical edge state of a two-dimensional topological insulator. We show that the edge deformation caused by bulk acoustic phonons modifies the spin texture of the edge state, and that the resulting spin-phonon coupling leads to inelastic backscattering which makes the transport diffusive. Using a semiclassical Boltzmann equation we compute the electrical conductivity and show that it exhibits a metallic Bloch-Gr\"uneisen law. At temperatures on the order of the Debye temperature of the host material, spin-phonon scattering thus lowers the conductivity of the edge state drastically. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $\delta G \propto T^5$ at low temperatures. Relying only on parallel transport of the helical spin texture along the deformed edge, the coupling strength is determined by the host material's density and sound velocity. Our results impose fundamental limits for the finite-temperature conductivity of a helical edge channel.
We propose a review of the current knowledge about the synthesis, magnetic properties and applications of magnetic cylindrical nanowires and nanotubes. By "nano" we consider diameters reasonably smaller than a micrometer. At this scale, comparable to micromagnetic and transport length scales, novel properties appear. At the same time, this makes the underlying physics easier to understand due to the limiter number of degrees of freedom involved. The three-dimensional nature and the curvature of these objects contribute also to their specific properties, compared to patterns flat elements. While the topic of nanowires and later nanotubes started now decades ago, it is nevertheless flourishing, thanks to the progress of synthesis, theory and characterization tools. These give access to ever more complex and thus functional structures, and also shifting the focus from material-type measurements of large assemblies, to single-object investigations. We first provide an overview of common fabrication methods yielding nanowires, nanotubes and structures engineered in geometry~(change in diameter, shape) or material (segments, core-shell structures), shape or core-shell. We then review their magnetic properties: global measurements, magnetization states and switching, single domain wall statics and dynamics, and spin waves. For each aspect, both theory and experiments are surveyed. We also mention standard characterization techniques useful for these. We finally mention emerging applications of magnetic nanowires and nanotubes, along with the foreseen perspectives in the topic.
We fabricated a gated-vertical (In,Ga)As quantum dot with an Al2O3 gate insulator deposited using atomic layer deposition and investigated its electrical transport properties at low temperatures. The gate voltage dependence of the dI/dV-V characteristics shows clear Coulomb diamonds at 1.1K. The metal-insulator gate structure allowed us to control the number of electrons in the quantum dot from 0 to a large number estimated to be about 130.
Recent advances in 3D vision have demonstrated the strengths of photometric bundle adjustment. By directly minimizing reprojected pixel errors, instead of geometric reprojection errors, such methods can achieve sub-pixel alignment accuracy in both high and low textured regions. Typically, these problems are solved using a forwards compositional Lucas-Kanade formulation parameterized by 6-DoF rigid camera poses and a depth per point in the structure. For large problems the most CPU-intensive component of the pipeline is the creation and factorization of the Hessian matrix at each iteration. For many warps, the inverse compositional formulation can offer significant speed-ups since the Hessian need only be inverted once. In this paper, we show that an ordinary inverse compositional formulation does not work for warps of this type of parameterization due to ill-conditioning of its partial derivatives. However, we show that it is possible to overcome this limitation by introducing the concept of a proxy template image. We show an order of magnitude improvement in speed, with little effect on quality, going from forwards to inverse compositional in our own photometric bundle adjustment method designed for object-centric structure from motion. This means less processing time for large systems or denser reconstructions under the same real-time constraints. We additionally show that this theory can be readily applied to existing methods by integrating it with the recently released Direct Sparse Odometry SLAM algorithm.
Motion prediction is a critical part of self-driving technology, responsible for inferring future behavior of traffic actors in autonomous vehicle's surroundings. In order to ensure safe and efficient operations, prediction models need to output accurate trajectories that obey the map constraints. In this paper, we address this task and propose a novel ellipse loss that allows the models to better reason about scene compliance and predict more realistic trajectories. Ellipse loss penalizes off-road predictions directly in a supervised manner, by projecting the output trajectories into the top-down map frame using a differentiable trajectory rasterizer module. Moreover, it takes into account actor dimensions and orientation, providing more direct training signals to the model. We applied ellipse loss to a recently proposed state-of-the-art joint detection-prediction model to showcase its benefits. Evaluation on large-scale autonomous driving data strongly indicates that the method allows for more accurate and more realistic trajectory predictions.
We present a detailed molecular-dynamics study of the melting, freezing, and coalescence of gold nanoclusters within the framework of the embedded-atom method. Concerning melting, we find the process to first affect the surface (``premelting''), then to proceed inwards. The curve for the melting temperature vs cluster size is found to agree reasonably well with predictions of phenomenological models based on macroscopic concepts, in spite of the fact that the clusters exhibit polymorphism and structural transitions. Upon quenching, we observe a large hysterisis of the transition temperature, consistent with recent experiments on lead. In contrast, we find macroscopic sintering theories to be totally unable to describe the coalescing behaviour of two small clusters. We attribute this failure to the fact that the nanocrystals are facetted, while the sintering theories are formulated for macroscopically smooth crystallites. The time for coalescence from our calculations is predicted to be much longer than expected from the macroscopic theory. This has important consequences for the morphology of cluster-assembled materials.
The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe$_{3-x}$GeTe$_2$ were investigated by bulk dc magnetization around the paramagnetic (PM) to ferromagnetic (FM) phase transition. The Fe$_{3-x}$GeTe$_2$ single crystals grown by self-flux method with Fe deficiency $x \approx 0.36$ exhibit bulk FM ordering below $T_c = 152$ K. The M\"{o}ssbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents $\beta = 0.372(4)$ with a critical temperature $T_c = 151.25(5)$ K and $\gamma = 1.265(15)$ with $T_c = 151.17(12)$ K are obtained by the Kouvel-Fisher method whereas $\delta = 4.50(1)$ is obtained by a critical isotherm analysis at $T_c = 151$ K. These critical exponents obey the Widom scaling relation $\delta = 1+\gamma/\beta$, indicating self-consistency of the obtained values. With these critical exponents the isotherm $M(H)$ curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation $m = f_\pm(h)$, where $m$ and $h$ are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg ($d = 3, n = 3$) spins coupled with the attractive long-range interactions between spins that decay as $J(r)\approx r^{-(3+\sigma)}$ with $\sigma=1.89$.
We show that the spontaneous symmetry breaking can be defined also for finite systems based on the properly defined jump probability between the ground states in the 2d and 3d Ising models on a square and a cubic lattice respectively. Our analysis reveals the existence of an interval in the temperature (control parameter) space within which the spontaneous symmetry breaking takes place. The upper limit of this region is the pseudocritical point where the symmetric vacuum bifurcates in energetically degenerate non-symmetric vacua, initiating the spontaneous symmetry breaking process. The lower limit, identified as the temperature value at which the spontaneous symmetry breaking is completed, is characterized by maximal characteristic time for the decay of magnetization (order parameter) auto-correlations. We argue that this anomalous enhancement of auto-correlations is attributed to the transition from type I to on-off intermittency in the order parameter dynamics. Possible phenomenological implications of this behaviour are briefly discussed.
Using a functional renormalization group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization group technique allows us to analyze the problem for both weak and strong electron-phonon coupling. We show that, in contrast results from conventional weak coupling studies, electron-phonon interactions can dominate electron-electron interactions because of retardation effects.
We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general relativity and M{\o}ler's tetrad theory of gravitation.
Globular Clusters (GCs) are generally treated as natural validators of simple stellar population (SSP) models. However, there are still some differences between real GCs and SSPs. In this work we use a direct $N$-body simulation code {\hf Nbody6} to study the influences of dynamical interactions, metallicity and primordial binaries on Milky Way globular clusters' integrated properties. Our models start with $N=100,000$ stars, covering a metallicity range $Z=0.0001-0.02$, a subset of our models contain primordial binaries, resulting in a binary fraction as currently observed at a model age of GCs.Stellar evolution and external tidal field representative for an average Milky Way GC are taken into consideration. The integrated colours and Lick indices are calculated using BaSeL and Bluered stellar spectral libraries separately.   By including dynamical interactions, our model clusters show integrated features (colours up to 0.01mag bluer, H$\beta$ up to 0.1\AA $ $ greater and [MgFe]$'$ 0.05\AA $ $ smaller) making the clusters appear slightly younger than the model clusters without dynamical interactions. This effect is caused mainly by the preferential loss of low-mass stars which have a stronger contribution to redder passbands as well as different spectral features compared to higher-mass stars. In addition, this effect is larger at lower metallicities. On the contrary, the incorporation of primordial binaries reduces this effect.
One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by replacing $X$ with a proper algebraic stack. We show, however, that it also holds when $X$ is replaced by many examples of algebraic stacks which are not proper, including many global quotient stacks. This leads us to revisit the definition of properness for stacks.   We introduce the notion of a formally proper morphism of stacks and study its properties. We develop methods for establishing formal properness in a large class of examples. Along the way, we prove strong h-descent results which hold in the setting of derived algebraic geometry but not in classical algebraic geometry. Our main applications are algebraicity results for mapping stacks and the stack of coherent sheaves on a flat and formally proper stack.
We optimize the design of future spectroscopic redshift surveys for constraining the dark energy via precision measurements of the baryon acoustic oscillations (BAO), with particular emphasis on the design of the Wide-Field Multi-Object Spectrograph (WFMOS). We develop a model that predicts the number density of possible target galaxies as a function of exposure time and redshift. We use this number counts model together with fitting formulae for the accuracy of the BAO measurements to determine the effectiveness of different surveys and instrument designs. We search through the available survey parameter space to find the optimal survey with respect to the dark energy equation-of-state parameters according to the Dark Energy Task Force Figure-of-Merit, including predictions of future measurements from the Planck satellite. We optimize the survey to test the LambdaCDM model, assuming that galaxies are pre-selected using photometric redshifts to have a constant number density with redshift, and using a non-linear cut-off for the matter power spectrum that evolves with redshift. We find that line-emission galaxies are strongly preferred as targets over continuum emission galaxies. The optimal survey covers a redshift range 0.8 < z < 1.4, over the widest possible area (6000 sq. degs from 1500 hours observing time). The most efficient number of fibres for the spectrograph is 2,000, and the survey performance continues to improve with the addition of extra fibres until a plateau is reached at 10,000 fibres. The optimal point in the survey parameter space is not highly peaked and is not significantly affected by including constraints from upcoming supernovae surveys and other BAO experiments.
The problem under consideration in this thesis has, actually, two aspects. The first one concerns the case when a nucleon is in free space that is in vacuum, while the second one studies a nucleon embedded into a nuclear environment. Both of these two aspects have been considered in the framework of chiral topological models of QCD. The whole content of the thesis may be divided into two main parts. In the first part the original Skyrme model with finite pion mass has been extended by inclusion of the light scalar - isoscalar sigma - meson. The Lagrangian has been further extended by explicit inclusion of sigma, rho and omega - mesons as well. In order to get a more complete picture of NN potential the appropriate meson - nucleon vertex form - factors are obtained. The second part of the thesis considers a nucleon immersed into a nuclear medium. For this purpose a medium modified Skyrme Lagrangian has been proposed. The Lagrangian describes well such well known medium effects as decreasing of nucleon mass and increasing of its size (swelling). We studied also a system with finite temperature also. The temperature effects are taken into account by using the method of termofield dynamics (TFD). The corresponding critical temperatures for each meson - nucleon system are calculated .
We present the analysis of the variability of HD 170699, a COROT star showing the characteristics of a non evolutionary Delta Scuti star with high rotational velocity. There is a clear period of 10.45 c/d with 5.29 mmag amplitude in the y filter. From the data, it can be seen that the star shows multi-periodicity and it is necessary to add more frequencies to adjust the observations
Our it ab initio calculations show that spin-orbit coupling is crucial to understand the electronic structure of the Si(557)-Au surface. The spin-orbit splitting produces the two one-dimensional bands observed in photoemission, which were previously attributed to spin-charge separation in a Luttinger liquid. This spin splitting might have relevance for future device applications. We also show that the apparent Peierls-like transition observed in this surface by scanning tunneling microscopy is a result of the dynamical fluctuations of the step-edge structure, which are quenched as the temperature is decreased.
Perovskites have attracted much attention due to their remarkable optical properties. While it is well established that excitons dominate their optical response, the impact of higher excitonic states and formation of phonon sidebands in optical spectra still need to be better understood. Here, we perform a theoretical study on excitonic properties of monolayered hybrid organic perovskites -- supported by temperature-dependent photoluminescence measurements. Solving the Wannier equation, we obtain microscopic access to the Rydberg-like series of excitonic states including their wavefunctions and binding energies. Exploiting the generalized Elliot formula, we calculate the photoluminescence spectra demonstrating a pronounced contribution of a phonon sideband for temperatures up to 50 K -- in agreement with experimental measurements. Finally, we predict temperature-dependent linewidths of the three energetically lowest excitonic transitions and identify the underlying phonon-driven scattering processes.
We consider a model for a Z'-boson coupled only to baryon minus lepton number and hypercharge. Besides the usual right-handed neutrinos, we add a pair of fermions with a fractional lepton charge, which we therefore call leptinos. One of the leptinos is taken to be odd under an additional Z_2 charge, the other even. This allows for a natural (inverse) seesaw mechanism for neutrino masses. The odd leptino is a candidate for dark matter, but has to be resonantly annihilated by the Z'-boson or the Higgs-boson responsible for giving mass to the former. Considering collider and cosmological bounds on the model, we find that the Z'-boson and/or the extra Higgs-boson can be seen at the LHC. With more pairs of leptinos leptogenesis is possible.
Organic semiconductors find increasing importance in spin transport devices due to the modulation and control of their properties through chemical synthetic versatility. The organic materials are used as interlayers between two ferromagnet (FM) electrodes in organic spin valves (OSV), as well as for magnetic spin manipulation of metal-organic complexes at the molecular level. In the latter, specifically, the substrate-induced magnetic switching in a paramagnetic molecule has been evoked extensively, but studied by delicate surface spectroscopies. Here we present evidence of the substantial magnetic switching in a nanosized thin film of the paramagnetic molecule, tris(8-hydroxyquinoline)iron(III) (Feq3) deposited on a FM substrate, using the magnetoresistance response of electrical spin-injection in an OSV structure, and the inverse-spin-Hall effect induced by state-of-art pulsed microwave spin-pumping. We show that interfacial spin control at the molecular level may lead to a macroscopic organic spin transport device, thus, bridging the gap between organic spintronics and molecular spintronics.
Ton 34 recently transitioned from non-absorbing quasar into a BALQSO.Here, we report new HST-STIS observations of this quasar. Along with CIV absorption, we also detect absorption by NV+Ly alpha and possibly OVI+Ly beta. We follow the evolution of the CIV BAL, and find that, for the slower outflowing material, the absorption trough varies little (if at all) on a rest-frame timescale of 2 yr. However, we detect a strong deepening of the absorption in the gas moving at larger velocities (-20,000 - -23,000 km s-1). The data is consistent with a multistreaming flow crossing our line of sight to the source. The transverse velocity of the flow should be few thousand km s-1, similar to the rotation velocity of the BLR gas (2,600 km s-1). By simply assuming Keplerian motion, these two components must have similar locations, pointing to a common outflow forming the BLR and the BAL. We speculate that BALs, mini-BALs, and NALs, are part of a common, ubiquitous, accretion-disk outflow in AGN, but become observable depending on the viewing angle towards the flow. The absorption troughs suggest a wind covering only 20% of the emitting source, implying a maximum size of 10^-3 pc for the clouds forming the BAL/BLR medium. This is consistent with constraints of the BLR clouds from X-ray occultations. Finally, we suggest that the low excitation broad emission lines detected in the spectra of this source lie beyond the wind, and this gas is probably excited by the shock of the BAL wind with the surrounding medium.