ShantanuT01/DACTYL-Pretraining huggingface dataset:
Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in heterogeneous materials, known as the fiber bundle model. We find three distinct regimes for fracture dynamics depending on the initial crack size. If the initial crack is smaller than a certain value, it does not affect the rupture dynamics and the critical stress. While for a larger initial crack, the growth of the crack leads to a breakdown of the entire system, and the critical stress depends on the crack size in a power-law manner with a nontrivial exponent. The exponent, as well as the limiting crack size, depend on the strength of heterogeneity and the range of stress relaxation in the system.
It is the aim of this paper to show how to construct Perelomov and Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some special values of the parameter corresponding to r = 1, the algebra covers the cases of the su(1,1) algebra, the su(2) algebra and the ordinary Weyl-Heisenberg or oscillator algebra. For r arbitrary, the generalized Weyl-Heisenberg algebra admits finite or infinite-dimensional representations depending on the values of the parameters. Coherent states of the Perelomov type are derived in finite and infinite dimensions through a Fock-Bargmann approach based on the use of complex variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in infinite dimension. In contrast, the construction of Barut-Girardello coherent states in finite dimension can be achieved solely at the price to replace complex variables by generalized Grassmann variables. Finally, some preliminary developments are given for the study of Bargmann functions associated with some of the coherent states obtained in this work.
Very recent eta and K+ photoproduction data on the proton from threshold up to E = 2.6 GeV are interpreted within a chiral constituent quark formalism, which embodies all known nucleon and hyperon resonances. Possible contributions from an additional S11 resonance are presented.
We analytically evaluate in the leading logarithm approximation the differential cross section for e^+ e^- -> e^+ \nu_e \bar{u} d. We compare our order \alpha^4 \alpha_s^0 leading-log result to the order \alpha^4 \alpha_s^0 exact result obtained from the GRC4F Monte Carlo program. Finally we use the Gluck, Reya, Schienbien distribution of partons in a virtual photon, which incorporates both evolution and nonperturbative strong interaction contributions, to obtain better estimates of the differential cross section.
We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH system on the regularity of the solution, and, in particular, the consequences for wave breaking, is discussed. Furthermore, the interplay between dissipative and conservative solutions is treated.
Quantum simulator with the ability to harness the dynamics of complex quantum systems has emerged as a promising platform for probing exotic topological phases. Since the flexibility offered by various controllable quantum systems has enabled to gain insight into quantum simulation of such complicated problems, analog quantum simulator has recently shown its feasibility to tackle problems of exploring topological phases. However, digital quantum simulation and detection of topological phases still remain elusive. Here, we develop and experimentally realize the digital quantum simulation of topological phase with a solid-state quantum simulator at room temperature. Distinct from previous works dealing with static topological phases, the topological phases emulated here are Floquet topological phases. Furthermore, we also illustrate the procedure of digitally simulating a quantum quench and observing the nonequilibrium dynamics of Floquet topological phases. By means of quantum quench, the 0- and {\pi}-energy topological invariants are unambiguously detected through measuring time-averaged spin polarizations. Our experiment opens up a new avenue to digitally simulate and detect Floquet topological phases with fast-developed programmable quantum simulators.
The alkali atoms, due to their small sizes and low charge ionic states, are most eligible to intercalate in the structural layers of V2O5. We have applied ab-initio density functional theory to study the dynamics of Li-ion in layers of {\alpha}-V2O5. The calculations are performed for two compositions, namely, Li0.08V2O5 and Li0.16V2O5, and show that there are unstable phonon frequencies. The unstable modes have large amplitude of Li atom along the b-axis of the orthorhombic unit cell indicating that such unstable modes could initiate Li-ion diffusion along b-axis. The ab-initio molecular dynamics simulations are performed up to 25 ps at 1200 K, which reveal one-dimensional diffusion of Li atoms. The diffusion pathways of Li atoms from the simulations seem to follow the eigenvectors of the unstable phonon modes obtained in the intercalated structure.
We discuss non-perturbative corrections to the neutrino sector, in the context of a D-brane Pati-Salam-like model, that can be obtained as a simple alternative to $SO(10)$ GUT's in theories with open and unoriented strings. In such D-brane models, exotic stringy instantons can correct the right-handed neutrino mass matrix in a calculable way, thus affecting mass hierarchies and modifying the see-saw mechanism to what we name exotic see-saw. For a wide range of parameters, a compact spectrum of right-handed neutrino masses can occur that gives rise to a predictive scenario for low energy observables. This model also provides a viable mechanism for Baryon Asymmetry in the Universe (BAU) through leptogenesis. Finally, a Majorana mass for the neutron is naturally predicted in the model, leading to potentially testable neutron-antineutron oscillations. Combined measurements in neutrino and neutron-antineutron sectors could provide precious informations on physics at the quantum gravity scale.
3D hand pose tracking/estimation will be very important in the next generation of human-computer interaction. Most of the currently available algorithms rely on low-cost active depth sensors. However, these sensors can be easily interfered by other active sources and require relatively high power consumption. As a result, they are currently not suitable for outdoor environments and mobile devices. This paper aims at tracking/estimating hand poses using passive stereo which avoids these limitations. A benchmark with 18,000 stereo image pairs and 18,000 depth images captured from different scenarios and the ground-truth 3D positions of palm and finger joints (obtained from the manual label) is thus proposed. This paper demonstrates that the performance of the state-of-the art tracking/estimation algorithms can be maintained with most stereo matching algorithms on the proposed benchmark, as long as the hand segmentation is correct. As a result, a novel stereo-based hand segmentation algorithm specially designed for hand tracking/estimation is proposed. The quantitative evaluation demonstrates that the proposed algorithm is suitable for the state-of-the-art hand pose tracking/estimation algorithms and the tracking quality is comparable to the use of active depth sensors under different challenging scenarios.
In the sixth of the series of papers reporting on a large reverberation mapping (RM) campaign of active galactic nuclei (AGNs) with high accretion rates, we present velocity-resolved time lags of H$\beta$ emission lines for nine objects observed in the campaign during 2012$-$2013. In order to correct the line-broadening caused by seeing and instruments before the analysis of velocity-resolved RM, we adopt Richardson-Lucy deconvolution to reconstruct their H$\beta$ profiles. The validity and effectiveness of the deconvolution are checked out by Monte Carlo simulation. Five among the nine objects show clear dependence of time delay on velocity. Mrk 335 and Mrk 486 show signatures of gas inflow whereas the clouds in the broad-line regions (BLRs) of Mrk 142 and MCG +06-26-012 tend to be radial outflowing. Mrk 1044 is consistent with the case of virialized motions. The lags of the rest four are not velocity-resolvable. The velocity-resolved RM of super-Eddington accreting massive black holes (SEAMBHs) shows that they have diversity of the kinematics in their BLRs. Comparing with the AGNs with sub-Eddington accretion rates, we do not find significant differences in the BLR kinematics of SEAMBHs.
We show that the borderline cases in the proof of the positive energy theorem for initial data sets, on spin manifolds, in dimensions $n\ge 3$, are only possible for initial data arising from embeddings in Minkowski space-time.
Robust statistical observables can be used to extract the novel isospin fluctuations from background contributions in K-short K-plus measurements in nuclear collisions. To illustrate how this can be done, we present new HIJING and UrQMD computations of these observables.
We present a fast and efficient tight-binding (TB) method for simulating scanning tunneling microscopy (STM) imaging of adsorbate molecules on ultrathin insulating films. Due to the electronic decoupling of the molecule from the metal surface caused by the presence of the insulating overlayer, the STM images of the frontier molecular orbitals can be simulated using a very efficient scheme, which also enables the analysis of phase shifts in the STM current. Au-pentacene complex adsorbed on a NaCl bilayer on Cu substrate provides an intricate model system, which has been previously studied both experimentally and theoretically. Our calculations indicate that the complicated shape of the molecular orbitals may cause multivalued constant current surfaces -- leading to ambiguity of the STM image. The results obtained using the TB method are found to be consistent with both DFT calculations and experimental data.
A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge detection algorithms designed to detect faint edges in noisy images. In our formalism we view edge detection as a search in a discrete, though potentially large, set of feasible curves. First, we derive approximate expressions for the detection threshold as a function of curve length and the complexity of the search space. We then present two edge detection algorithms, one for straight edges, and the second for curved ones. Both algorithms efficiently search for edges in a large set of candidates by hierarchically constructing difference filters that match the curves traced by the sought edges. We demonstrate the utility of our algorithms in both simulations and applications involving challenging real images. Finally, based on these principles, we develop an algorithm for fiber detection and enhancement. We exemplify its utility to reveal and enhance nerve axons in light microscopy images.
The influence of an initial momentum on the appearance of "quantum resonances" in the delta-kicked rotor system is explored experimentally. We show that for certain initial momenta, a resonance can be negated entirely, whereas at others a resonance can be made to appear. At a larger number of kicks, all resonances are shown to narrow. We show that as a consequence, the individual "diffraction peaks" may split. We compare our results to numerical simulations as well as analytical theory.
We have elucidated the dynamic phase transition features and finite-size scaling analysis of the triangular lattice system under the presence of a square-wave magnetic field. It has been found that as the value of half-period of the external field reaches its critical value, whose location is estimated by means of Binder cumulant, the system presents a dynamic phase transition between dynamically ordered and disordered phases. Moreover, at the dynamic phase transition point, finite-size scaling of the Monte Carlo results for the dynamic order parameter and susceptibility give the critical exponents $\beta/\nu=0.143\pm0.004$ and $\gamma/\nu=1.766\pm0.036$, respectively. The obtained critical exponents show that present magnetic system belongs to same universality class with the two-dimensional equilibrium Ising model.
We compare the actual WMAP maps with artificial, purely statistical maps of the same harmonic content to argue that there are, with confidence level 99.7 %, ring-type structures in the observed cosmic microwave background.
We present an analytic enumeration of the metastable states, $N_s$, in a periodic long-range Josephson array frustrated by a transverse field. We find that the configurational entropy, $S_{conf} \equiv \ln N_s$, is extensive and scales with frustration, confirming that the non-random system is glassy. We also find that $S_{conf}$ is different from that of its disordered analogue, despite that fact that the two models share the same dynamical equations.
The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.
We analyze the photo-production helicity amplitudes for the positive parity excited baryons in the context of the $1/N_c$ expansion of QCD. The results show that sub-leading corrections in $1/N_c$ are important and that, while 1-body effective operators are dominant, there is some evidence for the need of 2-body effects.
From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special boundary points (LCSLs) given by normal crossing divisors. We find local isomorphisms between the $E(3,6)$ systems and the associated GKZ systems defined locally on the parameter space and cover the entire parameter space. Parallel structures are conjectured in general for hypergeometric system $E(n,m)$ on Grassmannians. Local solutions and mirror symmetry will be described in a companion paper \cite{HLTYpartII}, where we introduce a K3 analogue of the elliptic lambda function in terms of genus two theta functions.
In the thesis we present a new method for parametrizing algebraic varieties over the field of characteristic zero. The problem of parametrizing is reduced to a problem of finding an isomorphism of algebras.   We introduce the Lie algebra of a variety as a Lie algebra related to its group of automorphisms. Constructing an isomorphism of this one and some classical Lie algebra (for example the algebra of matrices of the zero trace) then leads to parametrizing the variety. The problem of finding an isomorphism of Lie algebras is further reduced to trivializing an associative algebra, which means finding an isomorphism of the algebra and a full matrix algebra. The last is a classical problem in number theory, when regarded over algebraically non-closed fields. We give algorithms for trivializing algebras of degrees up to 4 over number fields.   In our work we used the method to parametrize Del Pezzo surfaces of degrees 8 and 9 over number fields. The algorithms are implemented for the case of the field of the rationals.
The antiferromagnetic mixed valence ternary oxide $\alpha$-CoV$_{3}$O$_{8}$ displays disorder on the Co$^{2+}$ site that is inherent to the $Ibam$ space group. The zero field structural and dynamic properties of $\alpha$-CoV$_{3}$O$_{8}$~have been investigated using a combination of neutron and x-ray diffraction, DC susceptibility, and neutron spectroscopy. The low temperature magnetic and structural properties are consistent with a random macroscopic distribution of Co$^{2+}$ over the 16$k$ metal sites. However, by applying the sum rules of neutron scattering we observe the collective magnetic excitations are parameterized with an ordered Co$^{2+}$ arrangement and critical scattering consistent with a three dimensional Ising universality class. The low energy spectrum is well-described by Co$^{2+}$ cations coupled $via$ a three dimensional network composed of competing ferromagnetic and stronger antiferromagnetic superexchange within the $ab$ plane and along $c$, respectively. While the extrapolated Weiss temperature is near zero, the 3D dimensionality results in long range antiferromagnetic order at $T\rm{_{N}}\sim$ 19 K. A crystal field analysis finds two bands of excitations separated in energy at $\hbar \omega$ $\sim$ 5 meV and 25 meV, consistent with a $j\rm{_{eff}}=\frac{1}{2}$ ground state with little mixing between spin-orbit split Kramers doublets. A comparison of our results to the random 3D Ising magnets and other compounds where spin-orbit coupling is present indicate that the presence of an orbital degree of freedom, in combination with strong crystal field effects and well-separated $j\rm{_{eff}}$ manifolds may play a key role in making the dynamics largely insensitive to disorder.
Let $S \subset \mathbb P^3$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this article we study the configuration of points of certain reduced zero dimensional subschemes on $S$ satisfying Cayley-Bacharach property, which leads to the existence of non-trivial sections of a general memeber of the moduli space for small $c_2$. Using this study we will make an attempt to prove Mestrano-Simpson conjecture on the number of irreducible components of $\mathcal{M}(H, 11)$ and prove the conjecture partially. We will also show that $\mathcal{M}(H, c_2)$ is irreducible for $c_2 \le 10$ .
We study magnetoresistivity oscillations in a high-mobility two-dimensional electron system subject to both microwave and dc electric fields. First, we observe that the oscillation amplitude is a periodic function of the inverse magnetic field and is strongly suppressed at microwave frequencies near half-integers of the cyclotron frequency. Second, we obtain a complete set of conditions for the differential resistivity extrema and saddle points. These findings indicate the importance of scattering without microwave absorption and a special role played by microwave-induced scattering events antiparallel to the electric field.
The hydrodynamic state of the interstellar medium (ISM) heated and randomly stirred by supernovae (SNe) is investigated. We use a three-dimensional non-ideal hydrodynamic ISM model in a domain extending 0.5 x 0.5 kpc horizontally and 2 kpc vertically to explore the relative importance of various physical and numerical effects on the multi-phase, turbulent ISM. We include both Type I and II SNe, the latter occurring only in dense regions. First we investigate the role of the thermal instability in the temperature range 300-6100 K, comparing results obtained for two different cooling functions, one susceptible to the instability, the other stable. The presence of thermal instability in the system is mainly visible as the tendency of the gas to avoid the relevant temperature range, as it quickly evolves towards either colder or warmer phases. Nevertheless, the formation of dense structures for both cooling functions appears to be dominated by expanding and colliding supernova remnants, rather than by the thermal instability. As we need to include a finite thermal conduction coefficient to resolve the thermal instability with our uniform grid, we also explore the effects of changing Prandtl number on the system. The purely divergent SN forcing is found to produce significant amounts of vorticity. The relative vorticity is around 0.6-0.7 for the highest Prandtl numbers explored, Pr=40, and is observed to diminish almost by a factor of two for the lowest Prandtl numbers studied, Pr=1. Rotation laws with angular velocity decreasing or increasing outwards are investigated, enabling us to separate the contributions to kinetic helicity due to rotation and shear. When angular velocity decreases outwards, these two contributions partly cancel each other, resulting in a smaller net helicity.
This paper describes an effective and efficient image classification framework nominated distributed deep representation learning model (DDRL). The aim is to strike the balance between the computational intensive deep learning approaches (tuned parameters) which are intended for distributed computing, and the approaches that focused on the designed parameters but often limited by sequential computing and cannot scale up. In the evaluation of our approach, it is shown that DDRL is able to achieve state-of-art classification accuracy efficiently on both medium and large datasets. The result implies that our approach is more efficient than the conventional deep learning approaches, and can be applied to big data that is too complex for parameter designing focused approaches. More specifically, DDRL contains two main components, i.e., feature extraction and selection. A hierarchical distributed deep representation learning algorithm is designed to extract image statistics and a nonlinear mapping algorithm is used to map the inherent statistics into abstract features. Both algorithms are carefully designed to avoid millions of parameters tuning. This leads to a more compact solution for image classification of big data. We note that the proposed approach is designed to be friendly with parallel computing. It is generic and easy to be deployed to different distributed computing resources. In the experiments, the largescale image datasets are classified with a DDRM implementation on Hadoop MapReduce, which shows high scalability and resilience.
Using mechanical exfoliation combined with a controlled double step transfer procedure we demonstrate that single layers of antimony can be readily produced. These flakes are not significantly contaminated upon exposure to ambient conditions and they do not react with water. DFT calculations confirm our experimental observations and predict a band gap of 1.2-1.3 eV (ambient conditions) for single layer antimonene, which is smaller than that calculated under vacuum conditions at 0 K. Our work confirms antimonene as a highly stable 2D material with promising relevant applications in optoelectronics.
Beginning with the Legendre transform construction of hyperk\"ahler metrics, we analyze the ALF version of the D_n metrics. We determine the constraint equation obtained from extremizing the $w$ coordinate of the generating function F(z,\bar{z},u,\bar{u},w) and study its behavior as we send two of the mass parameters of the $D_n$ metric to zero. We find that the constraint equation enforces the limit that the metric becomes that of multi-Taub-NUT.
In this paper we introduce a maximal divisorial set in the arc space of a variety. The generalized Nash problem is reduced to a translation problem of the inclusion of two maximal divisorial sets. We study this problem and show a counter example to the most natural expectation even for a non-singular variety.