ShantanuT01/DACTYL-Pretraining huggingface dataset:
The contactless Surface Acoustic Wave (SAW) technique was implemented to probe the high-frequency (ac) conductivity in a high-mobility $p$-SiGe/Ge/SiGe structure in the integer quantum Hall (IQHE) regime. The structure was grown by low-energy plasma-enhanced chemical vapor deposition and comprised a two-dimensional channel formed in a compressively strained Ge layer. It was investigated at temperatures of 0.3 - 5.8 K and magnetic fields up to 18 T at various SAW intensities. In the IQHE regime, in minima of the conductivity oscillations with small filling factors, holes are localized. The ac conductivity is of the hopping nature and can be described within the "two-site" model. Furthermore, the dependence of the ac conductivity on the electric field of the SAW was determined. The manifestation of non-linear effects is interpreted in terms of nonlinear percolation-based conductivity.
In this article, we consider polynomials of the form $f(x)=a_0+a_{n_1}x^{n_1}+a_{n_2}x^{n_2}+\dots+a_{n_r}x^{n_r}\in \mathbb{Z}[x],$ where $|a_0|\ge |a_{n_1}|+\dots+|a_{n_r}|,$ $|a_0|$ is a prime power and $|a_0|\nmid |a_{n_1}a_{n_r}|$. We will show that under the strict inequality these polynomials are irreducible for certain values of $n_1$. In the case of equality, apart from its cyclotomic factors, they have exactly one irreducible non-reciprocal factor.
A powerful method pioneered by Swinnerton-Dyer allows one to study rational points on pencils of curves of genus 1 by combining the fibration method with a sophisticated form of descent. A variant of this method, first used by Skorobogatov and Swinnerton-Dyer in 2005, can be applied to study rational points on Kummer varieties. In this paper we extend the method to include an additional step of second descent. Assuming finiteness of the relevant Tate-Shafarevich groups, we use the extended method to show that the Brauer-Manin obstruction is the only obstruction to the Hasse principle on Kummer varieties associated to abelian varieties with all rational 2-torsion, under mild additional hypotheses.
We present an approximation to the matrix element for the process e+e- --> e+e-gamma, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed.
Lyman-alpha photons from the first radiating sources in the Universe play a pivotal role in 21-cm radio detections of Cosmic Dawn and the Epoch of Reionization. Comments are provided on the effect of the hyperfine structure of hydrogen on the rate of heating or cooling of the Intergalactic Medium. It is shown that heating of the still neutral hydrogen by the Cosmic Microwave Background is negligible, with a characteristic heating time of 1e27 s/ (1+z) at redshift z.
We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph. The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions. We argue from this representation that connected deSitter $n$-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory. Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field. This work has significant overlap with a paper by Marolf and Morrison, which is being released simultaneously.
The kinetic transport of electrons through graphene magnetic barriers is studied theoretically in presence of an external time harmonic scalar potential. The transmission coefficients are calculated in the framework of the non-perturbative Floquet theory using transfer matrix method. The time dependent scalar potential is found to suppress the usual Fabry-Perot oscillations occurring in the transmission through a constant vector potential barrier (corresponding to two oppositely directed delta-function magnetic barriers). Two types of asymmetric Fano resonances (FR) are noted and are discussed for the narrow barrier structure. One of them arises due to the oscillatory mode while the other due to the evanescent mode of the electron wave inside the barrier. In contrast, the oscillating field favors the transmission for rectangular magnetic barrier structure and also exhibits the FR due to the presence of bound state inside the barrier. The characteristic Fano line shape can be tuned by varying the amplitude of the oscillating potential. The detection of such FR offers an efficient tool for the identification of the quasi-bound and evanescent extended states inside the barrier not reported in the literature so far, for the case of graphene magnetic barrier structures.
We have shown that, as in the case of black holes, an ergosphere itself with no event horizon inside can evaporate spontaneously, giving energy radiation to spatial infinity until the ergoregion disappears. However, the feature of his quantum ergoregion instability is very much different from black hole radiation. It is rather analogous to a laser amplification. This analysis is based on the canonical quantization of a neutral scalar field in the presence of unstable modes characterized by complex frequencies in a simple model for a rapidly rotating star.
The availability of compact, low-cost magnetic resonance imaging instruments would further broaden the substantial impact of this technology. We report highly sensitive detection of magnetic resonance using low-stress silicon nitride (SiN$_x$) membranes. We use these membranes as low-loss, high-frequency mechanical oscillators and find they are able to mechanically detect spin-dependent forces with high sensitivity enabling ultrasensitive magnetic resonance detection. The high force detection sensitivity stems from their high mechanical quality factor $Q\sim10^6$ combined with the low mass of the resonator. We use this excellent mechanical force sensitivity to detect the electron spin magnetic resonance using a SiN$_x$ membrane as a force detector. The demonstrated force sensitivity at 300 K is 4 fN/$\sqrt{\mathrm{Hz}}$, indicating a potential low temperature (4 K) sensitivity of 25 aN/$\sqrt{\mathrm{Hz}}$. Given their sensitivity, robust construction, large surface area and low cost, SiN$_x$ membranes can potentially serve as the central component of a compact room-temperature ESR and NMR instrument that has superior spatial resolution to conventional approaches.
We consider a Bertrand type estimate for primes splitting completely. As one of its applications, we show the finiteness of trivial solutions of Diophantine equation about the factorial function over number fields except for the case the rational number field.
We determine the maximum number of rational points on a curve over $\mathbb{F}_2$ with fixed gonality and small genus.
A role of different components in the wave function of the weakly bound light nuclei states was studied within the framework of the cluster model, taking into account of orbitals "polarization". It was shown that a limited number of structures associated with the different modes of nucleon motion can be of great importance for such systems. Examples of simple and quite flexible trial wave functions are given for the nuclei $^8$Be, $^6$He. Expressions for the microscopic wave functions of these nuclei were found and used for the calculation of basic nuclear characteristics, using well known central-exchange nucleon-nucleon potentials.
We show here that quadruple lenses can be useful laboratories to probe whether the potential of the lensing galaxy is purely elliptical or whether an additional distortion is present in the deflector plane. For this test we only have to know the relative image positions of the quadruple lens system and the (relative) center of light position of the lensing galaxy. Furthermore we introduce new methods which easily allow us to determine the location (rotation angle relative to the image positions) of the major axis of the lensing galaxy. In due course we can determine the parity of the four images as well. We apply these methods to the 8 currently known quadruple lenses and find that in the case of MG 0414+0534, CLASS 1608+656 and HST 12531-2914 it is impossible to accommodate the relative image positions and the galaxy position with any elliptical potential whereas the other five cases can be described very well with a simple elliptical potential. This method will have important impacts for $\chi^2$-fits and the reconstruction of galaxy models for quadruple lenses.
Various cosmological models in frames of $F(T)$ gravity are considered. The general scheme of constructing effective dark energy models with various evolution is presented. It is showed that these models in principle are compatible with $\Lambda$CDM model. The dynamics of universe governed by $F(T)$ gravity can mimics $\Lambda$CDM evolution in past but declines from it in a future. We also construct some dark energy models with the "real" (non-effective) equation-of-state parameter $w$ such that $w\leq-1$. It is showed that in $F(T)$ gravity the Universe filled phantom field not necessarily ends its existence in singularity. There are two possible mechanisms permitting the final singularity. Firstly due to the nonlinear dependence between energy density and $H^{2}$ ($H$ is the Hubble parameter) the universe can expands not so fast as in the general relativity and in fact Little Rip regime take place instead Big Rip. We also considered the models with possible bounce in future. In these models the universe expansion can mimics the dynamics with future singularity but due to bounce in future universe begin contracts.
We propose a scheme for teleporting an atomic center-of-mass wave function between distant locations. The scheme uses interactions in cavity quantum electrodynamics to facilitate a coupling between the motion of an atom trapped inside a cavity and external propagating light fields. This enables the distribution of quantum entanglement and the realization of the required motional Bell-state analysis.
A tutorial introduction to the Kondo effect, the RKKY interaction, and a renormalization group treatment to analyze the competition between the two.
Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier density probability measure of the graphene sheet, we show that the density fluctuation ($\zeta^{-1}$) is related to the disorder strength ($n_i$), the interaction parameter ($r_s$) and the average density ($\bar{n}$) via the relation $\zeta^{-1}\propto r_sn_i^2\bar{n}^{-1}$ for which $\bar{n}\rightarrow 0$ leads to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in agreement with the previous works. The general equation governing the two-body distribution probability is obtained and analyzed. We present the analytical solution for some limits which is used for calculating density-density response function. We show that the resulting function shows power-law behaviors in terms of $\zeta$ with fractional exponents which are reported. The disorder-averaged polarization operator is shown to be a decreasing function of momentum like ordinary 2D parabolic band systems. It is seen that a disorder-driven momentum $q_{\text{ch}}$ emerges in the system which controls the behaviors of the screened potential. We show that in small densities an instability occurs in which imaginary part of the dielectric function becomes negative and the screened potential changes sign. Corresponding to this instability, some oscillations in charge density along with a screening-anti-screening transition are observed. These effects become dominant in very low densities, strong disorders and strong interactions, the state in which EHPs appear. The total charge probability measure is another quantity which has been investigated in this paper.
The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modelling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on the 8th of September 2017, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-centre approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the 'thin target' approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in a good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally-driven modelling of individual solar flares, including manifestations of energetic particles in the corona, as well as inner heliosphere.
We calculated the magnetic anisotropy constant Ku of MnBi using a first principles approach, and obtained a negative Ku in agreeable with experimental results. Furthermore, we also found a band filling dependence indicating that a slight decrease in the valence electron number will change Ku from negative to positive. When some of the Bi is replaced with Sn to decrease the valence electron number, the Ku value of MnBi1-xSnx drastically changes to a positive value, Ku~2 MJ/m3, for x > 0.05.
We investigate nil-Temperley-Lieb algebras of type A. We give a general description of the structure of monomials formed by the generators. We also show that the dimensions of these algebras are the famous Catalan numbers by providing a bijection between the monomials and Dyck paths. We show that the distribution of these monomials by degree is the same as the distribution of Dyck paths by the sum of the heights of the peaks minus the number of peaks.
Seymour's Decomposition Theorem for regular matroids states that any matroid representable over both GF(2) and GF(3) can be obtained from matroids that are graphic, cographic, or isomorphic to R10 by 1-, 2-, and 3-sums. It is hoped that similar characterizations hold for other classes of matroids, notably for the class of near-regular matroids. Suppose that all near-regular matroids can be obtained from matroids that belong to a few basic classes through k-sums. Also suppose that these basic classes are such that, whenever a class contains all graphic matroids, it does not contain all cographic matroids. We show that in that case 3-sums will not suffice.
In metric formalism, Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields $F(R)\propto R^\frac{3}{2}$ along with the conserved current $\frac{d}{dt} (a\sqrt R)$ in Robertson-Walker metric and nothing else. However, Roshan et.al. had claimed in $\mathrm{Phys. Lett. \textbf{B668}, 238 (2008)}$ \cite{o} that Noether symmetry in the context of Palatini $F(\Re)$ theory of gravity admits $F(\Re)\propto \Re^{s}$, (where $s$ is an arbitrary constant) in matter domain era in Friedmann- Robertson-Walker universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general. Here, it is shown that Noether Symmetry admits $F(\Re)\propto\Re^\frac{3}{2}$ along with a conserved current $\Sigma_{0} {a}[\frac{\dot a}{a}+ \frac{\dot\Phi}{2\Phi}]$ in Palatini gravity. Thus, their claim is not right.
Let $G$ be a simple graph of order $n$. A dominating set of $G$ is a set $S$ of vertices of $G$ so that every vertex of $G$ is either in $S$ or adjacent to a vertex in $S$. The domination polynomial of $G$ is the polynomial $D(G,x)=\sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. In this paper we show that cycles are determined by their domination polynomials.
We find the exact size of a maximal non-commuting set in unipotent uppertriangular linear group $UU_4(\mathbb{F}_q)$ in terms of a non-commuting geometric structure (Refer Definition [10]), where $\mathbb{F}_q$ is the finite field with $q$ elements. Then we get bounds on the size of such a set by explicitly finding certain non-commuting sets in the non-commuting structure.
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function modulo 2 and 3.
Nuclei at both the neutron- and proton-drip lines are studied. In the cluster-core model, the halo-structure of all the observed and proposed cases of neutron- or proton-halos is investigated in terms of simple potential energy surfaces calculated as the sum of binding energies, Coulomb repulsion, nuclear proximity attraction and the centrifugal potential for all the possible cluster+core configurations of a nucleus. The clusters of neutrons and protons are taken to be unbound, with additional Coulomb energy added for proton-clusters. The model predictions agree with the available experimental studies but show some differences with the nucleon separation energy hypothesis, particularly for proton-halo nuclei. Of particular interest are the halo-structures of $^{11}N$ and $^{20}Mg$. The calculated potential energy surfaces are also useful to identify the new magic numbers and molecular structures in exotic nuclei. In particular, N=6 is a possible new magic number for very neutron-deficient nuclei, but Z=N=2 and Z=8 seem to remain magic even for such nuclei, near the drip line.
We re-examine the properties of the high-velocity and extremely low mass white dwarf LP 400-22 and its close companion. Based on an extended observation timeline we determined a binary period of P= 1.01016 d, somewhat longer than the previously published period, and a mass function f(M_2)= 0.180 M_solar implying a mass for the companion M_2 > 0.41 M_solar. We also re-appraised the mass and cooling age of the white dwarf using low-metallicity (Z=0.001) evolutionary models appropriate for an old halo member, M_1 = 0.19 M_solar and t_cool~1.8 Gyr, and we infer a mass of 0.85 - 1.0 M_solar for the progenitor of the white dwarf. We discuss the likely origin of this system.
By constructing a large, uniform galaxy cluster catalog from the SDSS data, we have found that cluster galaxies evolve both spectrally and morphologically. By studying the morphology--cluster-centric-radius relation, we have found two characteristic environments where galaxy morphologies change dramatically. We found passive spiral galaxies in the infalling region of clusters. They are likely to be a galaxy population in transition due to the cluster environment. We also studied E+A galaxies, which have also been thought to be cluster originated. We found that E+As live in all environments including the field region.
Recently a new maximally supersymmetric, dyonically gauged supergravity in four-dimenions has been constructed. This theory admits several supersymmetric AdS solutions, and a Chern- Simons-matter dual theory has been proposed for a solution with an unbroken SU(3) symmetry. The gravity side and the field theory side of the free energy computation show nice agreements at superconformal point. With a view to a study of non-conformal deformations, in this paper we study a consistent truncation of the full theory where SU(3) is broken to U(1)$^2$. We elucidate the geometry of the scalar sector, and also present the superpotentials in both $\mathcal{N} = 2$ and $\mathcal{N} = 1$ supergravity formulation.
Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of $p$. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with $p>2$, there are still a few GRBs suggestive of a hard ($p<2$) electron energy spectrum. Our previous work showed that GRB 091127 gave strong evidence for a double power-law hard electron energy (DPLH) spectrum with $1<p_1<2$, $p_2>2$ and an "injection break" assumed as $\gamma_{\rm b}\propto \gamma^q$ in the highly relativistic regime, where $\gamma$ is the bulk Lorentz factor of the jet. In this paper, we show that GRB 060614 and GRB 060908 provide further evidence for such a DPLH spectrum. We interpret the multi-band afterglow of GRB 060614 with the DPLH model in an homogeneous interstellar medium by taking into account a continuous energy injection process, while for GRB 060908, a wind-like circumburst density profile is used. The two bursts, along with GRB 091127, suggest a similar behavior in the evolution of the injection break, with $q\sim0.5$. Whether this represents a universal law of the injection break remains uncertain and more such afterglow observations are needed to test this conjecture.
We prove that any quasirandom dense large graph in which all degrees are equal and even can be decomposed into any given collection of two-factors (2-regular spanning subgraphs). A special case of this result gives a new solution to the Oberwolfach problem.
In orthodontic treatment, a full tooth model consisting of both the crown and root is indispensable in making the treatment plan. However, acquiring tooth root information to obtain the full tooth model from CBCT images is sometimes restricted due to the massive radiation of CBCT scanning. Thus, reconstructing the full tooth shape from the ready-to-use input, e.g., the partial intra-oral scan and the 2D panoramic image, is an applicable and valuable solution. In this paper, we propose a neural network, called ToothInpaintor, that takes as input a partial 3D dental model and a 2D panoramic image and reconstructs the full tooth model with high-quality root(s). Technically, we utilize the implicit representation for both the 3D and 2D inputs, and learn a latent space of the full tooth shapes. At test time, given an input, we successfully project it to the learned latent space via neural optimization to obtain the full tooth model conditioned on the input. To help find the robust projection, a novel adversarial learning module is exploited in our pipeline. We extensively evaluate our method on a dataset collected from real-world clinics. The evaluation, comparison, and comprehensive ablation studies demonstrate that our approach produces accurate complete tooth models robustly and outperforms the state-of-the-art methods.