ShantanuT01/DACTYL-Pretraining huggingface dataset:
The 5d5 iridate CaIrO3 is isostructural with the post-perovskite phase of MgSiO3, recently shown to occur under extreme pressure in the lower Earth's mantle. It therefore serves as an analogue of post-perovskite MgSiO3 for a wide variety of measurements at ambient conditions or achievable with conventional multianvile pressure modules. By multireference configuration-interaction calculations we here provide essential information on the chemical bonding and magnetic interactions in CaIrO3. We predict a large antiferromagnetic superexchange of 120 meV along the c axis, the same size with the interactions in the cuprate superconductors, and ferromagnetic couplings smaller by an order of magnitude along a. CaIrO3 can thus be regarded as a j = 1/2 quasi-one-dimensional antiferromagnet. While this qualitatively agrees with the stripy magnetic structure proposed by resonant x-ray diffraction, the detailed microscopic picture emerging from our study, in particular, the highly uneven admixture of t2g components, provides a clear prediction for resonant inelastic x-ray scattering experiments.
In this work we study some regularity properties associated to the initial value problem (IVP) \begin{equation}\label{main1} \left\{ \begin{array}{ll} \partial_{t}u-\partial_{x_{1}}(-\Delta)^{\alpha/2} u+u\partial_{x_{1}}u=0, \quad 0< \alpha\leq 2,& \\ u(x,0)=u_{0}(x),\quad x=(x_{1},x_{2},\dots,x_{n})\in \mathbb{R}^{n},\, n\geq 2,\quad t\in\mathbb{R},& \\ \end{array} \right. \end{equation} where $(-\Delta)^{\alpha/2}$ denotes the $n-$dimensional fractional Laplacian.   We show that solutions to the IVP (0.1) with initial data in a suitable Sobolev space exhibit a local smoothing effect in the spatial variable of $\frac{\alpha}{2}$ derivatives, almost everywhere in time. One of the main difficulties that emerge when trying to obtain this regularizing effect underlies that the operator in consideration is non-local, and the property we are trying to describe is local, so new ideas are required. Nevertheless, to avoid these problems, we use a perturbation argument replacing $(-\Delta)^{\frac{\alpha}{2}}$ by $(I-\Delta)^{\frac{\alpha}{2}},$ that through the use of pseudo-differential calculus allows us to show that solutions become locally smoother by $\frac{\alpha}{2}$ of a derivative in all spatial directions.   As a by-product, we use this particular smoothing effect to show that the extra regularity of the initial data on some distinguished subsets of the Euclidean space is propagated by the flow solution with infinity speed.
Wilson loops are calculated within the AdS/CFT correspondence by finding a classical solution to the string equations of motion in AdS_5 x S^5 and evaluating its action. An important fact is that this sigma-model used to evaluate the Wilson loops is integrable, a feature that has gained relevance through the study of spinning strings carrying large quantum numbers and spin-chains. We apply the same techniques used to solve the equations for spinning strings to find the minimal surfaces describing a wide class of Wilson loops. We focus on different cases with periodic boundary conditions on the AdS_5 and S^5 factors and find a rich array of solutions. We examine the different phases that appear in the problem and comment on the applicability of integrability to the general problem.
We investigate the decay mechanism in the B^- -> phi phi K^- decay with the phi phi invariant mass below the charm threshold and in the neighborhood of the eta_c invariant mass region. Our approach is based on the use of factorization model and the knowledge of matrix elements of the weak currents. For the B meson weak transition we apply form factor formalism, while for the light mesons we use effective weak and strong Lagrangians. We find that the dominant contributions to the branching ratio come from the eta, eta' and eta(1490) pole terms of the penguin operators in the decay chains B^- -> eta (eta', eta(1490)) K^- -> phi phi K^-. Our prediction for the branching ratio is in agreement with the Belle's result.
For the 1D-frustrated ferromagnetic J_1-J_2 model with interchain coupling added, we analyze the dynamical and static structure factor S(k,omega), the pitch angle phi of the magnetic structure, the magnetization curve of edge-shared chain cuprates, and focus on LiCuVO4 for which neither a perturbed spinon nor a spin wave approach can be applied. phi is found to be most sensitive to the interplay of frustration and quantum fluctuations. For LiVCuO4 the obtained exchange parameters J are in accord with the results for a realistic 5-band extended Hubbard model and LSDA + U predictions yielding alpha=J_2/|J_1| about 0.75 in contrast to 5.5 > alpha > 1.42 suggested in the literature. The alpha-regime of the empirical phi-values in NaCu2O2 and linarite are considered, too.
We study a simple exactly solvable 2D model describing the interaction of a localized particle with an impurity. The localization potential $V(x)=-\alpha \delta (x)$ causes the particle to be trapped in the y-axis, and the `impurity' is modeled by a straight impenetrable edge extending along the positive x-axis. We show that the problem described can be treated as the Sommerfeld diffraction from an infinite edge. We use the model to present qualitative arguments on the nature of interaction of polarized light traveling along an optical fiber with external impurities.
Discrete symmetry breaking and possible restoration at finite temperature $T$ are analysed in 2D Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass $m$ is proven to be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the mean field approximation used in the auxialiary scalar field approach. Reproducing of the non-zero critical temperature $T_c=0.567 m(0)$, ($m(0)$ is the dynamical fermion mass at T=0), shows the equivalence between the real-time and the imaginary-time thermal field theory in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the $\ln(T_c/T)$ behavior of $m^2$ at $T\stackrel{<}{\sim} T_c$ can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.
We have numerically studied the properties of the interface induced in the ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary conditions. The fractal dimension $d_f$ of the interface was determined. The corresponding SLE parameter $\kappa$ was estimated to be $\kappa\simeq 3.18(6)$, compatible with previous estimate. On the other hand, we estimated $\kappa$ independently from the probability of passage of the interface at the left of a given point. The numerical data are well reproduced by the Schramm theoretical prediction and the fit leads to $\kappa\simeq 3.245(10)$, in agreement with the first estimate. This provides evidences that the geometric properties of spin interfaces in the random 3-state Potts model may be described by chordal ${\rm SLE}_\kappa$.
We use recent X-ray observations of the intracluster medium (ICM) of the galaxy group NGC 5813 to confront theoretical studies of ICM thermal evolution with the newly derived ICM properties. We argue that the ICM of the cooling flow galaxy group NGC 5813 is more likely to be heated by mixing of post-shock jets' gas residing in hot bubbles with the ICM, than by shocks or turbulent-heating. Shocks thermalize only a small fraction of their energy in the inner regions of the cooling flow; in order to adequately heat the inner part of the ICM, they would overheat the outer regions by a large factor, leading to its ejection from the group. Heating by mixing, that was found to be much more efficient than turbulent-heating and shocks-heating, hence, rescues the outer ICM of NGC 5813 from its predestined fate according to cooling flow feedback scenarios that are based on heating by shocks.
We introduce a modified version of the Hirshfeld charge analysis method and demonstrate its accurateness by calculating the charge transfer between the paramagnetic molecule NO2 and graphene. The charge transfer between paramagnetic molecules and a graphene layer as calculated with ab initio methods can crucially depend on the size of the supercell used in the calculation. This has important consequences for adsorption studies involving paramagnetic molecules such as NO2 physisorbed on graphene or on carbon nanotubes.
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end points. Our main result is a stability estimate consists of two parts: the data discrepancy and the high frequency tail.
Production of lepton pairs in gamma p -> e-e+ p reaction is studied at photon energies up to 1 GeV. We show that even if lepton charge is not measured there are extensive kinematical regimes where the nuclear process dominates over the Bethe-Heitler contribution. The decomposition is performed of the unpolarized cross section for the virtual Compton scattering in terms of response functions. These are expressed in terms of a polarization density matrix of the virtual photon and are shown to be sensitive to the properties of baryon resonances in the first and the second resonance regions. In the analysis a unitary K-matrix model is used, based on an effective Lagrangian including nucleon, mesons, and baryon resonances with masses up to 1.7 GeV. Results of the model are compared with data for real-photon Compton scattering and predictions are given for observables in photoproduction of lepton pairs.
We construct examples of algebraic surfaces with interesting fundamental groups.
In this paper, we study a nonlocal degenerate parabolic equation of order {\alpha} + 2 for 0<{\alpha}<2. The equation is a generalization of the one arising in the modeling of hydraulic fractures studied by Imbert and Mellet in 2011. Using the same approach, we prove the existence of solutions for this equation for 0<{\alpha}<2 and for nonnegative initial data satisfying appropriate assumptions. The main difference is the compactness results due to different Sobolev embeddings. Furthermore, for {\alpha} > 1, we construct a nonnegative solution for nonnegative initial data under weaker assumptions.
Observed power spectrum of matter found in Papers I and II is compared with analytical power spectra. Spatially flat cold and mixed dark matter models with cosmological constant and open models are considered. The primordial power spectrum of matter is determined using the power spectrum of matter and the transfer functions of analytical models. The primordial power spectrum has a break in amplitude. We conclude that a scale-free primordial power spectrum is excluded if presently available data on the distribution of clusters and galaxies represent the true mass distribution of the Universe.
In this paper, we focus on the coordinate representation in human pose estimation. While being the standard choice, heatmap based representation has not been systematically investigated. We found that the process of coordinate decoding (i.e. transforming the predicted heatmaps to the coordinates) is surprisingly significant for human pose estimation performance, which nevertheless was not recognised before. In light of the discovered importance, we further probe the design limitations of the standard coordinate decoding method and propose a principled distribution-aware decoding method. Meanwhile, we improve the standard coordinate encoding process (i.e. transforming ground-truth coordinates to heatmaps) by generating accurate heatmap distributions for unbiased model training. Taking them together, we formulate a novel Distribution-Aware coordinate Representation for Keypoint (DARK) method. Serving as a model-agnostic plug-in, DARK significantly improves the performance of a variety of state-of-the-art human pose estimation models. Extensive experiments show that DARK yields the best results on COCO keypoint detection challenge, validating the usefulness and effectiveness of our novel coordinate representation idea. The project page containing more details is at https://ilovepose.github.io/coco
This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or elementary statements concerning constants and inequalities for which we are not aware of existing published material or expressions detailed enough for our purpose. We claim no originality on the theoretical results and rely on standard methods in most cases, except that we keep track of the constants and provide constructive estimates.
For the metallic nanoparticles, smaller than the free electron path, an impact of the particle's surface on the nonlocal effects emerging is shown. Light-induced current inside the particle begins to depend on the spatial derivatives of the field that leads to modification of Maxwell's equations. Consequently, the results of Mie theory as well as definitions of the dielectric function and optical conductivity should be revisited. For the sphere-shaped nanoparticle, the explicit expression for the high-frequency current with account of nonlocality is obtained. The dependence of the nonlocal contribution on the light frequency and particle's size is discussed.
We study the effect of the domain wall on electronic transport properties in wire of ferromagnetic 3$d$ transition metals based on the linear response theory. We considered the exchange interaction between the conduction electron and the magnetization, taking into account the scattering by impurities as well. The effective electron-wall interaction is derived by use of a local gauge transformation in the spin space. This interaction is treated perturbatively to the second order. The conductivity contribution within the classical (Boltzmann) transport theory turns out to be negligiblly small in bulk magnets, due to a large thickness of the wall compared with the fermi wavelength. It can be, however, significant in ballistic nanocontacts, as indicated in recent experiments. We also discuss the quantum correction in disordered case where the quantum coherence among electrons becomes important. In such case of weak localization the wall can contribute to a decrease of resistivity by causing dephasing. At lower temperature this effect grows and can win over the classical contribution, in particular in wire of diameter $L_{\perp}\lesssim \ell_{\phi}$, $\ell_{\phi}$ being the inelastic diffusion length. Conductance change of the quantum origin caused by the motion of the wall is also discussed.
Equation of motion of an uncharged arbitrarily shaped dust particle under the effects of (stellar) electromagnetic radiation and thermal emission is derived. The resulting relativistically covariant equation of motion is expressed in terms of standard optical parameters. Relations between energy and mass of the incoming and outgoing radiation are obtained, together with relations between radiation energy and mass of the particle. The role of the diffraction nicely fits the relativistic formulation of the momentum of the outgoing radiation.   The inequality 0 < $\bar{Q}'_{pr, 1} / \bar{Q}'_{ext}$ < 2 is a simple relativistic consequence for the Poynting-Robertson (P-R) effect ($\bar{Q}'_{ext}$ and $\bar{Q}'_{pr, 1}$ are dimensionless efficiency factors for the extinction and radial direction of the radiation pressure, integrated over stellar spectrum). The condition for the P-R effect is $\vec{p}'_{o}$ = (1 - $\bar{Q}'_{pr, 1} / \bar{Q}'_{ext}$) $\vec{p}'_{i}$, where $\vec{p}'_{i}$ and $\vec{p}'_{o}$ are incoming and outgoing radiation momenta (per unit time) measured in the proper frame of reference of the particle. The case of "perfectly absorbing spherical dust particle", within geometrical optics approximation, corresponds to the condition $\vec{p}'_{o}$ = 0.5 $\vec{p}'_{i}$. As for arbitrarily shaped dust particle, the condition 0 < $\bar{C}'_{pr, 1}$ / $\bar{C}'_{ext}$ < 2 / ($1 ~+~ \sum_{j=2}^{3} \bar{C}'_{pr, j} / \bar{C}'_{pr, 1}$) holds for cross sections of extinction and radiation pressure components. The condition can add a new information to the results obtained from observations, measurements and numerical calculations of the optical properties of the particle.
Amorphous silicon materials and its alloys become extensively used in some technical applications involving large area of the microelectronic and optoelectronic devices. However, the amorphous-crystalline transition, segregation and diffusion processes still have numerous unanswered questions. In this work we study the Sb diffusion into an amorphous Si film by means of Secondary Neutral Mass Spectrometry (SNMS). Amorphous Si/Si1-xSbx/Si tri-layer samples with 5 at% antimony concentration were prepared by DC magnetron sputtering onto Si substrate at room temperature. Annealing of the samples were performed at different temperature in vacuum (p<10-7 mbar) and 100 bar high purity (99.999%) Ar pressure. During annealing a rather slow mixing between the Sb-alloyed and the amorphous Si layers was observed. Supposing concentration independent diffusion, the evaluated diffusion coefficients are in the range of ~10-21 m2s-1 at 823 K.
We present the results of our photoelectric $UBV$ observations of the yellow symbiotic star LT Del over 2010-2018. The binary system LT Del, which consists of a bright K giant and a compact hot star with a temperature of $\sim$100 000 K, has an orbital period of 476 days. In 2017 the variable experienced a second low-amplitude ($\Delta V\sim 0.^{m}7$) outburst in the history of its studies whose maximum occurred at an orbital phase of 0.15$\pm$0.05. The outburst duration was $\sim$60 days. The $B-V$ and $U-B$ colors in the outburst became noticeably bluer. A difference in the photometric behavior of the star in the 1994 and 2017 outburst has been detected. In the orbital cycle preceding the 2017 outburst a secondary minimum with a depth of $0.^{m}15$ and $0.^{m}20$ appeared in the $B$ and $V$ light curves, respectively, whose cause is discussed. The phase light and color curves are presented and explained; the position of the star on the color-color diagram is interpreted. We have estimated the parameters of the cool and hot components of the system based on the distance determination from Gaia DR2.
We study Rabi rotations arising in intensity-dependent photon echoes from an ensemble of self-assembled InGaAs quantum dots. To achieve a uniform distribution of intensities within the excited ensemble, we introduce flattop intensity profiles of picosecond laser pulses. This allows us to overcome the damping of Rabi rotations imposed by the spatial inhomogeneity of Rabi frequencies by a Gaussian laser profile. Using photon echo polarimetry, we distinguish between the coherent optical responses from exciton and trion ensembles. Here, we demonstrate that a photo-induced charging of the quantum dots leads to a significant reduction of the number of neutral quantum dots under resonant excitation with intensive optical pulses with areas exceeding $\frac{\pi}{2}$. The trion ensemble shows robust Rabi rotations when the area of the refocussing pulse is increased up to 5.5$\pi$. We analyze the remaining attenuation of Rabi rotations by theoretical modeling of excitation induced dephasing, inhomogeneity of dipole moments, and coupling to acoustic phonons. The latter is identified as the dominating mechanism resulting in a loss of optical coherence during the action of the involved optical pulses.
General 2d dilaton theories, containing spherically symmetric gravity and hence the Schwarzschild black hole as a special case, are quantized by an exact path integral of their geometric (Cartan-) variables. Matter, represented by minimally coupled massless scalar fields is treated in terms of a systematic perturbation theory. The crucial prerequisite for our approach is the use of a temporal gauge for the spin connection and for light cone components of the zweibeine which amounts to an Eddington Finkelstein gauge for the metric. We derive the generating functional in its most general form which allows a perturbation theory in the scalar fields. The relation of the zero order functional to the classical solution is established. As an example we derive the effective (gravitationally) induced 4-vertex for scalar fields.
For energies relevant to future linear colliders, $\sqrt{s} \gsim 500$ GeV, the WW fusion channel dominates the Higgs boson production cross section $e^+ e^- \to \bar{\nu} \nu h^0$. We have calculated the one-loop corrections to this process due to fermion and sfermion loops in the context of the MSSM. As a special case, the contribution of the fermion loops in the SM has also been studied. In general, the correction is negative and sizeable of the order of 10 percent, the bulk of it being due to fermion loops.
We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.
Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series of virtual Euler characteristics was conjectured to be a rational function when X is simply connected. We conjecture here the rationality of more general descendent series with insertions obtained from the Chern characters of the tautological sheaf. We prove the rationality of descendent series in Hilbert scheme cases for all curve classes and in Quot scheme cases when the curve class is 0.
The surfaces considered are real, rational and have a unique smooth real $(-2)$-curve. Their canonical class $K$ is strictly negative on any other irreducible curve in the surface and $K^2>0$. For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the $(-2)$-curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the $(-2)$-curve.
The Abelian distribution has been studied recently in models for neural avalanches. This paper uncovers new properties about the moments of the distribution, ways in which these properties can be useful are indicated.
Here, we report the synthesis and magnetic properties of a new triangular lattice antiferromagnet Ba$_3$CoTa$_2$O$_9$. The effective spin of Co$^{2+}$ is found to be $J=1/2$ at low temperatures due to the combined effect of crystal field and spin-orbit coupling. Ba$_3$CoTa$_2$O$_9$ undergoes two successive magnetic phase transitions at $T_{N1}\simeq0.70$~K and $T_{N2}\simeq0.57$~K in zero applied field, which is typical for triangular antiferromagnets with the easy-axis magnetic anisotropy. With increasing field, the transition anomalies are found to shift toward low temperatures, confirming the antiferromagnetic nature of the transitions. At higher fields, the transition peaks in the heat capacity data disappear and give way to a broad maximum, which can be ascribed to a Schottky anomaly due to the Zeeman splitting of spin levels. The $H-T$ phase diagram of the compound shows three distinct phases. The possible nature of these phases is discussed.