ShantanuT01/DACTYL-Pretraining huggingface dataset:
A theoretical model is provided to address the parameters influencing the electronic properties of kink-structured carbon chain at 0K. It is studied by the principle of DFT and solving the numerical 1D time-independent Schr\"odinger equation of electron and phonon simultaneously. Two different lengths of branches A and B, are occupied alternatively to generate the asymmetric carbon chain. The ratio of the asymmetric branch length,RAB=A/B, plays an important role in the electronic density of states DOS around Fermi level Ef . The highest DOS(Ef) occurs if the RAB equals to 2 and while the Fermi level coincides with the Von-Hove singularity at RAB=3. The location of the singularity point relative to the Ef is controllable via branch length interestingly. By comparison with the symmetric case, tuning the branch length asymmetrically shows a stronger impact to shift the Ef to the singularity point. The numerical solution of the 1D time independent Schrodinger equation of phonon indicates that the kink reinforces the charge fluctuations but the fluctuations are minimized when the RAB goes up. Based on the simulation results, the electron phonon coupling of the carbon nanowire decreases with chain length. In comparison to the symmetric structure, the electron phonon coupling of the asymmetric carbon chain is higher. The maximum electron phonon coupling of the asymmetric carbon chain takes place at RAB=2 . However, the weakening of the electron phonon coupling is observed owing to ultrahigh concentration of kinks. The reduction of the electron phonon coupling of the carbon chain is occurred under pressure.
Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$.   The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.
The Linet-Tian metrics are solutions of the Einstein equations with a cosmological constant, $\Lambda$, that can be positive or negative. The linear instability of these metrics in the case $\Lambda <0$, has already been established. In the case $\Lambda>0$, it was found in a recent analysis that the perturbation equations admit unstable modes. The analysis was based on the construction of a gauge invariant function of the metric perturbation coefficients, called here $W(y)$. This function satisfied a linear second order equation that could be used to set up a boundary value problem determining the allowed, real or purely imaginary frequencies for the perturbations. Nevertheless, the relation of these solutions to the full spectrum of perturbations, and, therefore, to the evolution of arbitrary perturbations, remained open. In this paper we consider again the perturbations of the Linet-Tian metric with $\Lambda >0$, and show, using a form of the Darboux transformation, that one can associate with the perturbation equations a self adjoint problem that provides a solution to the completeness and spectrum of the perturbations. This is also used to construct the explicit relation between the solutions of the gauge invariant equation for $W(y)$, and the evolution of arbitrary initial data, thus solving the problem that remained open in the previous study. Numerical methods are then used to confirm the existence of unstable modes as a part of the complete spectrum of the perturbations, thus establishing the linear gravitational instability of the Linet-Tian metrics with $\Lambda >0$.
We experimentally demonstrate the nonlocal reversal of a partial-collapse quantum measurement on two-photon entangled state. Both the partial measurement and the reversal operation are implemented in linear optics with two displaced Sagnac interferometers, which are characterized by single qubit quantum process tomography. The recovered state is measured by quantum state tomography and its nonlocality is characterized by testing the Bell inequality. Our result will be helpful in quantum communication and quantum error correction.
We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the internal information is only partially provided near the boundary due to the high absorption property of the medium and the limitation of the equipment. Our main contribution is to prove a H\"older stability of the inverse problem in a subregion where the internal information is reliably provided based on the stability estimation of a Cauchy problem satisfied by the diffusion coefficient. The exponent of the H\"older stability converges to a positive constant independent of the subregion as the subregion contracts towards the boundary. Numerical experiments demonstrates that it is possible to locally reconstruct the diffusion and absorption coefficients for smooth and even discontinuous media.
Relaxor ferroelectrics are complex oxide materials which are rather unique to study the effects of compositional disorder on phase transitions. Here, we study the effects of quenched cubic random electric fields on the lattice instabilities that lead to a ferroelectric transition and show that, within a microscopic model and a statistical mechanical solution, even weak compositional disorder can prohibit the development of long-range order and that a random field state with anisotropic and power-law correlations of polarization emerges from the combined effect of their characteristic dipole forces and their inherent charge disorder. We compare and reproduce several key experimental observations in the well- studied relaxor PbMg$_{1/3}$Nb$_{2/3}$O$_3$-PbTiO$_3$.
We consider the self-similar fragmentation equation with a superquadratic fragmentation rate and provide a quantitative estimate of the spectral gap.
Schmidt's method for construction of luminosity function of galaxies is generalized by taking into account the dependence of density of galaxies from the distance in the near Universe. The logarithmical luminosity function (LLF) of field galaxies depending on morphological type is constructed. We show that the LLF for all galaxies, and also separately for elliptical and lenticular galaxies can be presented by Schechter function in narrow area of absolute magnitudes. The LLF of spiral galaxies was presented by Schechter function for enough wide area of absolute magnitudes: . Spiral galaxies differ slightly by parameter . At transition from early spirals to the late spirals parameter in Schechter function is reduced. The reduction of mean luminosity of galaxies is observed at transition from elliptical galaxies to lenticular galaxies, to early spiral galaxies, and further, to late spiral galaxies, in a bright end, . The completeness and the average density of samples of galaxies of different morphological types are estimated. In the range the mean number density of all galaxies is equal 0.127 Mpc-3.
The Chevalier & Clegg (1985) spherical wind is widely used to model galactic outflows. Efforts are underway to understand the production of multiphase gas in such outflows. Since the important scales for the multiphase gas are very small compared to the size of the wind, it is very useful to have a local model of the cold gas interacting with a volume-filling expanding wind. In this note we explicitly derive the governing hydrodynamic equations in such a local box for the first time. We highlight that the expansion in a wind occurs only in the transverse direction, and this results in anisotropic source terms in the momentum equation. Our equations will be very useful in realistic modelling of the small scale structure of multiphase galactic outflows. [original note does not include an abstract]
Internal symmetries can be used to classify multiple solutions to the time energy canonical commutation relation (TE-CCR). The dynamical behavior of solutions to the TE-CCR posessing particular internal symmetries involving time reversal differ significantly from solutions to the TE-CCR without those particular symmetries, implying a connection between the internal symmetries of a quantum system, its internal unitary dynamics, and the TE-CCR.
It has recently been shown that a simple empirical formula, in terms of the mass number and the valence nucleon numbers, is able to describe the main trends of the lowest excitation energies of the natural parity even multipole states up to $10^+$ in even-even nuclei throughout the entire periodic table. In an effort to understand why such a simple formula is so capable, we investigate the possibility of associating each term of the empirical formula with the specific part of the measured excitation energy graph.
The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal and one obtains a long time diffusive tail in the decay of autocorrelation function (ACF). Some variations of the model with different coupling schemes and with anisotropy are also studied and we find normal diffusion in all of them. A systematic finite size analysis of the Heisenberg model also suggests diffusive spreading of fluctuation, contrary to previous claims of anomalous diffusion.
Electron Spin Resonance (ESR) measurements performed on the filled skutterudite system Ce1-x$YbxFe4P12 (x< 0.003) unequivocally reveal the coexistence of two Yb3+ resonances, associated with sites of considerably different occupations and temperature behaviors. Detailed analysis of the ESR data suggests a scenario where the fraction of oversized (Fe2P3)4 cages that host Yb ions are filled with a low occupation of on-center Yb3+ sites and a highly occupied T-dependent distribution of off-center Yb3+ sites. Analysis of the 171Yb3+ (I=1/2) isotope hyperfine splittings reveal that these two sites are associated with a low (~ 1 GHz) and a high (> 15 GHz) rattling frequency, respectively. Our findings introduce Yb3+ in Th symmetry systems and uses the Yb3+ ESR as a sensitive microscopic probe to investigate the Yb3+ ions dynamics.
We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covered by the Wilsonian renormalization group approach. In the framework of pionless effective field theory, also extended by the inclusion of a long-range interaction of separable type, we demonstrate that Weinberg's power counting scheme is consistent in the sense that it leads to a systematic order-by-order expansion of the scattering amplitude.
In this paper we report multifrequency single pulse polarization observations of the PSR B0329+54 normal mode using the Giant Meterwave Radio Telescope at 325 and 610 MHz and the Effelsberg Observatory at 2695 MHz. Our observations show that towards the central part of the polarization position-angle traverse there is an unusual ``arc''-like structure, which is comprised of a broadband ``kink'' and a frequency-dependent ``spot.'' The features are intimately connected with the intensity dependence of the core component: the stronger emission arrives earlier and its linear polarization is displaced farther along the ``kink''. Moreover, at high intensities, the circular polarization is --/+ antisymmetric; the nearly complete positive circular is characteristic of the weaker, later core subpulses. We find that the ``kink'' emission is associated with the extraordinary (X) propagation mode, and hence propagation effects do not appear capable of producing the core component's broadband, intensity-dependent emission. Rather, the overall evidence points to a largely geometric interpretation in which the ``kink'' provides a rare glimpse of the accelerating cascade or height-dependent amplifier responsible for the core radiation.
We present in this paper a covariant quantization of the ``massive'' vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian manifold. The correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time is essential in our approach. We introduce the Wightman-G\"arding axiomatic for vector field on dS space. The Hilbert space structure and the unsmeared field operators $K_\alpha(x)$ are also defined. This work is in the direct continuation of previous one concerning the scalar and the spinor cases.
In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.
We are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification.   We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA optimizes the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings, and avoids rank-deficient embeddings. Using this new regularizer allows us to adapt the large-scale WSABIE procedure and to leverage the Adam stochastic optimization algorithm, which results in an algorithm that scales gracefully to very large data-sets. Also, we derive a kernelized version which allows to take advantage of state-of-the-art features for re-identification when data-set size permits kernel computation.   Benchmarks on recent and standard re-identification data-sets show that our method beats existing state-of-the-art techniques both in term of accuracy and speed. We also provide experimental analysis to shade lights on the properties of the regularizer we use, and how it improves performance.
In architecture and computer-aided design, wireframes (i.e., line-based models) are widely used as basic 3D models for design evaluation and fast design iterations. However, unlike a full design file, a wireframe model lacks critical information, such as detailed shape, texture, and materials, needed by a conventional renderer to produce 2D renderings of the objects or scenes. In this paper, we bridge the information gap by generating photo-realistic rendering of indoor scenes from wireframe models in an image translation framework. While existing image synthesis methods can generate visually pleasing images for common objects such as faces and birds, these methods do not explicitly model and preserve essential structural constraints in a wireframe model, such as junctions, parallel lines, and planar surfaces. To this end, we propose a novel model based on a structure-appearance joint representation learned from both images and wireframes. In our model, structural constraints are explicitly enforced by learning a joint representation in a shared encoder network that must support the generation of both images and wireframes. Experiments on a wireframe-scene dataset show that our wireframe-to-image translation model significantly outperforms the state-of-the-art methods in both visual quality and structural integrity of generated images.
The synthesis of embedded silicon carbide was carried out in N type silicon samples having (100) and (111) orientations using high dose implantation of carbon ions at room temperature. The variation of dose was employed to get dose dependence of silicon carbide formation. Postimplant annealing at 1000 C in order to anneal out the implantion induced defects and to get silicon carbide precipitates in silicon matrix. Detailed Fourier tarnsform infrared spectroscopy analysis and x-ray diffraction studies confirms the formation of cubic phase of silicon carbide. The grain size of the silicon carbide precipitates is estimated to a few nano meters. The silicon carbide precipitates have been found to exhibit a better crystalline order in silicon (100) samples than in silicon (111) samples.The x-ray diffraction results also indicate the amorphization of bombarded region of the silicon samples. After annealing the amorphized region got recrystalized into a polycrystalline phase of silicon.
We present Chandra X-ray images of Tycho's supernova remnant that delineate its outer shock as a thin, smooth rim along the straight northeastern edge and most of the circular western half. The images also show that the Si and S ejecta are highly clumpy, and have reached near the forward shock at numerous locations. Most of the X-ray spectra that we examine along the rim show evidence of line emission from Si and S ejecta, while the continuum is well-represented by either a thermal or nonthermal model. If the continuum is assumed to be thermal, the electron temperatures at the rim are all similar at about 2 keV, while the ionization ages are very low, because of the overall weakness of the line emission. These electron temperatures are substantially below those expected for equilibration of the electron and ion temperatures, assuming shock velocities inferred from radio and X-ray expansion measurements; the electron to mean temperature ratios are <~0.1-0.2, indicating that collisionless heating of the electrons at the shock is modest. The nonthermal contribution to these spectra may be important, but cannot be strongly constrained by these data. It could account for as much as half of the flux in the 4-6 keV energy range, based on an extrapolation of the hard X-ray spectrum above 10 keV.
We demonstrate numerically on large spin lattices that one can write skyrmions in a thin magnetic film with a magnetic dipole of a few tens of nanometer in size. Nucleation of non-chiral skyrmions as well as chiral skyrmions formed by the Dzyaloshinskii-Moriya interaction has been investigated. Analytical model is developed that agrees with numerical results. It is shown that skyrmions can be written though a number of scenarios that depend on the experimental technique and parameters of the system. In one scenario, that branches into subscenarios of different topology, the magnetic dipole on approaching the film creates a skyrmion-antiskyrmion pair. As the dipole moves closer to the film it induces collapse of the antiskyrmion and creation of a non-zero topological charge due to the remaining skyrmion. In a different scenario the dipole moving parallel to the film nucleates a skyrmion at the boundary and then drags it inside the film. Possible implementations of these methods for writing topologically protected information in a magnetic film are discussed.
We are interested in stationary "fluid" random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE can be obtained by filtering a coalescing motion with respect to a subnoise containing the Gaussian part of its noise. Thus, the coalescing motion cannot be described by a white noise.
This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the {\it classical} model and the BA model. Note that the number of step added edges for the mixed model is random and non-uniformly bounded. By developing a comparing argument, phase transition on the degree distributions of the mixed model is revealed: while the {\it pure} classical model possesses a {\it exponential} degree sequence, the {\it pure} BA model and the mixed model possess {\it power law} degree sequences. As an application of the methodology, phase transition on the degree sequence of {\it another} mixed model with {\it hard copying} is also studied, especially, in the power law region, the inverse power can take any value greater than 1.
A third post-Newtonian (3 PN) equation of motion for an inspiralling binary consisting of two spherical compact stars with strong internal gravity is derived under harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in a sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3 PN equation of motion and an energy of the binary orbital motion in case of the circular orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of the mass frame. It is argued that the 3 PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.
For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to obtain weighted norm inequalities for the operator L. We apply our results to obtain weighted (Lp, Lq) boundedness of the Riesz potentials and of the related fractional maximal operators for the Dunkl transform. Finally, we prove a weighted generalized Sobolev inequality.