ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present detailed investigations in single crystals of two recently reported quaternary intermetallic compounds EuRhAl$_4$Si$_2$ and EuIrAl$_4$Si$_2$ employing magnetization, electrical resistivity in zero and applied fields, heat capacity and $^{151}$Eu M\"{o}ssbauer spectroscopy measurements. The two compounds order antiferromagnetically at $T_{\rm N1}$ = 11.7 and 14.7\,K, respectively, each undergoing two magnetic transitions: the first from paramagnetic to incommensurate modulated antiferromagnetic, the second at lower temperature to a commensurate antiferromagnetic phase as confirmed by heat capacity and M\"{o}ssbauer spectra. The magnetic properties in the ordered state present a large anisotropy despite Eu$^{2+}$ being an $S$-state ion for which the single-ion anisotropy is expected to be weak. Two features in the magnetization measured along the $c$-axis are prominent. At 1.8\,K, a ferromagnetic-like jump occurs at very low field to a value one third of the saturation magnetization (1/3 M$_0$) followed by a wide plateau up to 2\,T for T = Rh and 4\,T for T = Ir. At this field value, a sharp hysteretic spin-flop transition occurs to a fully saturated state (M$_0$). Surprisingly, the magnetization does not return to origin when the field is reduced to zero in the return cycle, as expected in an antiferromagnet. Instead, a remnant magnetization 1/3 M$_0$ is observed and the magnetic loop around the origin shows hysteresis. This suggests that the zero field magnetic structure has a ferromagnetic component, and we present a model with up to third neighbor exchange and dipolar interaction which reproduces the magnetization curves and hints to an "up-up-down" magnetic structure in zero field.
The space of complete collineations is a compactification of the space of matrices of fixed dimension and rank, whose boundary is a divisor with normal crossings. It was introduced in the 19th century and has been used to solve many enumerative problems.   We show that this venerable space can be understood using the latest quotient constructions in algebraic geometry. Indeed, there is a detailed analogy between the complete collineations and the moduli space of stable pointed curves of genus zero. The remarkable results of Kapranov exhibiting the latter space as a Chow quotient, Hilbert quotient, and so on, all have counterparts for complete collineations.   This analogy encompasses Vainsencher's construction of the complete collineations, as well as a form of the Gel'fand-MacPherson correspondence. There is also a tangential relation with the Gromov-Witten invariants of Grassmannians. The symmetric and anti-symmetric versions of the problem are considered as well.   An appendix explains the original motivation, which came from the space of broken Morse flows for the moment map of a circle action.
The decisive role of magnetic anisotropy even in systems with small anisotropy is illustrated for the honeycomb-layered antiferromagnets The decisive role of magnetic anisotropy in honeycomb layered Li$_3$Ni$_2$SbO$_6$ and Na$_3$Ni$_2$SbO$_6$ with $A$ = Li and Na. Both systems evolve long range magnetic order below $T_{\rm N}$ = 14 and 16.5~K, respectively. The magnetic phase diagrams obtained from static magnetisation studies up to 15~T imply competing antiferromagnetic phases and a tricritical point at $T_{\rm N}$. The phase boundaries are visible in the dynamic response of the antiferromagnetic resonance modes, too, which investigation by means of high frequency/high field electron spin resonance enables precise determination of magnetic anisotropy. The anisotropy gap amounts to $\Delta = 360 \pm 2$~GHz in Na$_3$Ni$_2$SbO$_6$ while in Li$_3$Ni$_2$SbO$_6$ orthorhombicity is associated with $\Delta = 198 \pm 4$ and $218 \pm 4$~GHz. Above $T_{\rm N}$, the data imply short-range antiferromagnetic order up to at least 80~K. The data suggest a crucial role of anisotropy for selecting the actual spin structure at $B=0$~T.
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of crossing the barrier scales as $ 1/\sqrt{n} $ as we rescale space by $ \sqrt{n} $ and time by $ n $, we obtain a non trivial scaling limit which behaves like reflected Brownian motion until its local time at the origin reaches an independent exponential variable. It then follows reflected Brownian motion on the other side of the origin until its local time at the origin reaches another exponential level, and so on. We give a martingale problem characterisation of this process as well as another construction and an explicit formula for its transition density. This result has applications in the field of population genetics where such a random walk is used to trace the position of one's ancestor in the past in the presence of a barrier to gene flow.
It is argued that the spatial homogeneity of the early universe need not be explained as having evolved from a previous inhomogeneous state. Rather, a homogeneous cosmic initial condition follows from the Second Law of Thermodynamics applied to gravitating systems.
The Einstein-Gordon equations for Friedmann-Robertson-Walker (FRW) geometries in feedback reaction with the quartically self-interacting physical field, arisen from the "inner parity" spontaneous breaking, are explicitly formulated. The Hamiltonian density non-positive extrema would classically forbid both spatially closed and flat homogeneous and isotropic worlds if these were to allow the physical field to (repeatedly) go through and to (finally) settle down in a ground state. In this respect, the fixed point exact solutions of the spontaneous Z_2-symmetry breaking Einstein-Gordon equations (mandatory) describe (k=-1)-FRW manifolds which actually are either Milne or anti-de Sitter Universes. Setting the Z_2-invariance breaking scale at the one of the electroweak symmetry, we speculate on the cosmological implications of the Higgs-anti-de Sitter bubbles and derive a set of particular closed-form solutions to the S_2-cobordism with a spatially flat FRW Universe.
The level statistics of SU(3)-SU(3)* transitional region of IBM is described by the nearest neighbor spacing distribution statistics. The energy levels are determined by using the SO(6)representation of eigenstates. By employing the MLE technique, the parameter of Abul-Magd distribution is estimated where suggest less regular dynamics for transitional region in compare to dynamical symmetry limits. Also, the O(6)dynamical symmetry which is known as the critical point of this transitional region, describes a deviation to more regular dynamics.
Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of the $p$-Laplacian type diffusion is also considered.
Strongly noncircular outer stellar disks have been found in two unbarred SA0 galaxies by analyzing spectroscopic data on the rotation of stars and photometric data on the shape and orientation of the isophotes. In NGC 502, the oval distortion of the disk is manifested as two elliptical rings, the inner and the outer ones, covering wide radial zones between the bulge and the disk and at the outer edge of the stellar disk. Such a structure may be a consequence of the so-called "dry" minor merger - multiple accretion of gas-free satellites. In NGC 5485, the kinematical major axis does not coincide with the orientation of isophotes in the disk-dominated region, and for this galaxy the conclusion about its global triaxial structure is unavoidable.
We argue that the Gopakumar-Vafa interpretation of the topological string partition function can be used to compute and resum certain non-perturbative brane instanton effects of type II CY compactifications. In particular the topological string A-model encodes the non-perturbative corrections to the hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d N=2 IIB models. We also discuss the reduction to 4d N=1 by fluxes and/or orientifolds and/or D-branes, and the prospects to resum brane instanton contributions to non-perturbative superpotentials. We argue that the connection between non-perturbative effects and the topological string underlies the continuity of non-perturbative effects across lines of BPS stability. We also confirm this statement in mirror B-model matrix model examples, relating matrix model instantons to non-perturbative D-brane instantons. The computation of non-perturbative effects from the topological string requires a 3d circle compactification and T-duality, relating effects from particles and instantons, reminiscent of that involved in the physical derivation of the Kontsevich-Soibelmann wall-crossing formula.
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just two genetic types. Short bursts of selection acting in opposing directions drive to maintain both types at intermediate frequencies, while the fluctuations due to 'genetic drift' work to eliminate variation in the population.   We consider first a population with no spatial structure, modelled by an adaptation of the Lambda (or generalised) Fleming-Viot process, and derive a stochastic differential equation as a scaling limit. This amounts to a limit result for a Lambda-Fleming-Viot process in a rapidly fluctuating random environment. We then extend to a population that is distributed across a spatial continuum, which we model through a modification of the spatial Lambda-Fleming-Viot process with selection. In this setting we show that the scaling limit is a stochastic partial differential equation. As is usual with spatially distributed populations, in dimensions greater than one, the 'genetic drift' disappears in the scaling limit, but here we retain some stochasticity due to the fluctuations in the environment, resulting in a stochastic p.d.e. driven by a noise that is white in time but coloured in space.   We discuss the (rather limited) situations under which there is a duality with a system of branching and annihilating particles. We also write down a system of equations that captures the frequency of descendants of particular subsets of the population and use this same idea of 'tracers', which we learned from Hallatschek and Nelson (2008) and Durrett and Fan (2016), in numerical experiments with a closely related model based on the classical Moran model.
The braneworld cosmological model was constructed by embedding a 3-brane into a higher dimensional bulk background geometry and the usual matter of our universe was assumed to be confined in the brane while the gravity can propagate in the bulk. By considering that the bulk geometry is anisotropic, after reviewed the separable solution for the bulk metric and the result that the anisotropic property of the bulk can support the perfect fluid kind of the matter in the brane, we develop a formalism of the cosmological perturbation for this kind of anisotropic braneworld model. As in isotropic case, we can also decompose the perturbation into scalar, vector and tensor modes, we find that the formalism for the anisotropic braneworld cosmological perturbation are very different from the isotropic case. The anisotropic effect can be reflected in the tensor modes which dominated the cosmological gravitation waves. Finally, we also discussed the perturbed Einstein equations governed the dynamics of the bulk geometry and the brane with the junction conditions.
We prove a $C^{1,\alpha}$ interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity of a special class of nonlinear operators.
Tribological characteristics of nanotube-based nanoelectromechanical systems (NEMS) exemplified by a gigahertz oscillator are studied. Various factors that influence the tribological properties of the nanotube-based NEMS are quantitatively analyzed with the use of molecular dynamics calculations of the quality factor (Q-factor) of the gigahertz oscillator. We demonstrate that commensurability of the nanotube walls can increase the dissipation rate, while the structure of the wall ends and the nanotube length do not influence the Q-factor. It is shown that the dissipation rate depends on the interwall distance and the way of fixation of the outer wall and is significant in the case of a poor fixation for the nanotubes with a large interwall distance. Defects are found to strongly decrease the Q-factor due to the excitation of low-frequency vibrational modes. No universal correlation between the static friction forces and the energy dissipation rate is established. We propose an explanation of the obtained results on the basis of the classical theory of vibrational-translational relaxation. Significant thermodynamics fluctuations are revealed in the gigahertz oscillator by molecular dynamics simulations and analyzed in the framework of the fluctuation-dissipation theorem. Possibility of designing the NEMS with a desirable Q-factor and their applications are discussed on the basis of the above results.
An origin of the Optical/UV radiation from tidal disruption events (TDEs) has recently been discussed for different scenarios, but observational support is generally missing. In this Letter, we test applicability of the `Wind-Driven model' (Uno & Maeda 2020) to a sample of UV/Optical TDEs. With the model, we aim to derive the physical properties of the Optical/UV TDEs, such as mass-loss rates and characteristic radii. The model assumes optically thick continuous outflows like stellar winds, and one key question is how the wind-launched radius is connected to physical processes in TDEs. As one possibility, through a comparison between the escape velocities estimated from their black-hole masses and the wind velocities estimated from observed line widths, we propose that the outflow is launched from the self-interaction radius ($R_{\rm SI}$) where the stellar debris stretched by the tidal force intersects; we show that the escape velocities at $R_{\rm SI}$ are roughly consistent with the wind velocities. By applying the model to a sample of Optical/UV TDE candidates, we find that explosive mass ejections ($\gtrsim 10 ~M_{\odot}{\rm yr^{-1}}$) from $R_{\rm SI}$ ($\sim 10^{14}{\rm ~cm}$) can explain the observed properties of TDEs around peak luminosity. We also apply the same framework to a peculiar transient, AT2018cow. The model suggests that AT2018cow is likely a TDE induced by an intermediate-mass black hole ($M_{\rm BH} \sim 10^{4}~M_{\odot}$).
Due to the rapid development of World Wide Web (WWW) and imaging technology, more and more images are available in the Internet and stored in databases. Searching the related images by the querying image is becoming tedious and difficult. Most of the images on the web are compressed by methods based on discrete cosine transform (DCT) including Joint Photographic Experts Group(JPEG) and H.261. This paper presents an efficient content-based image indexing technique for searching similar images using discrete cosine transform features. Experimental results demonstrate its superiority with the existing techniques.
The main objective of the present work is to discuss the global existence and stability of solutions to the porous medium equations on Riemannian manifolds with singularities. Several different types of solutions are considered. Our proof is based on a Poincare inequality on function space defined on manifolds with singularities.
In this paper, we evaluate a synthetic framework to be used in the field of gaze estimation employing deep learning techniques. The lack of sufficient annotated data could be overcome by the utilization of a synthetic evaluation framework as far as it resembles the behavior of a real scenario. In this work, we use U2Eyes synthetic environment employing I2Head datataset as real benchmark for comparison based on alternative training and testing strategies. The results obtained show comparable average behavior between both frameworks although significantly more robust and stable performance is retrieved by the synthetic images. Additionally, the potential of synthetically pretrained models in order to be applied in user's specific calibration strategies is shown with outstanding performances.
We present a semi-analytical approach to the interaction of two (originally) Kerr black holes through a head-on collision process. An expression for the rate of emission of gravitational radiation is derived from an exact solution to the Einstein's field equations. The total amount of gravitational radiation emitted in the process is calculated and compared to current numerical investigations. We find that the spin-spin interaction increases the emission of gravitational wave energy up to 0.2% of the total rest mass. We discuss also the possibility of spin-exchange between the holes.
We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.
A new genre of Spin-Transfer Torque (STT) MRAM is proposed, in which bi-directional writing is achieved using thermoelectrically controlled magnonic current as an alternative to conventional electric current. The device uses a magnetic tunnel junction (MTJ), which is adjacent to a non-magnetic metallic and a ferrite film. This film stack is heated or cooled by a Peltier element which creates a bi-directional magnonic pulse in the ferrite film. Conversion of magnons to spin current occurs at the ferrite-metal interface, and the resulting spin-transfer torque is used to achieve sub-nanosecond precessional switching of the ferromagnetic free layer in the MTJ. Compared to electric current driven STT-MRAM with perpendicular magnetic anisotropy (PMA), thermoelectric STT-MRAM reduces the overall magnetization switching energy by more than 40% for nano-second switching, combined with a write error rate (WER) of less than 10-9 and a lifetime of 10 years or higher. The combination of higher thermal activation energy, sub-nanosecond read/write speed, improved tunneling magneto-resistance (TMR) and tunnel barrier reliability make thermoelectric STT-MRAM a promising choice for future non-volatile memory applications.
We show that for every infinite collection $\mathcal{R}$ of disjoint equivalent rays in a graph $G$ there is a subdivision of the hexagonal half-grid in $G$ such that all its vertical rays belong to $\mathcal{R}$. This result strengthens Halin's grid theorem by giving control over which specific set of rays is used, while its proof is significantly shorter.
In this paper, based on the principles of linear response theory, we compute the longitudinal DC conductivity associated with Lifshitz like fixed points in the presence of chiral anomalies in ($ 3+1 $) dimensions. In our analysis, apart from having the usual anomalous contributions due to chiral anomaly, we observe an additional and pure \textit{parity odd} effect to the magnetoconductivity which has its origin in the broken Lorentz (boost) invariance at a Lifshitz fixed point. We also device a holographic set up in order to compute ($ z=2 $) Lifshitz contributions to the magnetoconductivity precisely at strong coupling and low charge density limit.
A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We show that except for some small exceptions of order less than 54, each of these graphs is either a prism of order 6k with k odd, a M\"obius ladder, or it falls into one of two infinite families, each family containing one graph for every order of the form 6k with k odd.
We consider a solution $u(\cdot,t)$ to an initial boundary value problem for time-fractional diffusion-wave equation with the order $\alpha \in (0,2) \setminus \{ 1\}$ where $t$ is a time variable. We first prove that a suitable norm of $u(\cdot,t)$ is bounded by $\frac{1}{t^{\alpha}}$ for $0<\alpha<1$ and $\frac{1}{t^{\alpha-1}}$ for $1<\alpha<2$ for all large $t>0$. Moreover we characterize initial values in the cases where the decay rates are faster than the above critical exponents. Differently from the classical diffusion equation $\alpha=1$, the decay rate can give some local characterization of initial values. The proof is based on the eigenfunction expansions of solutions and the asymptotic expansions of the Mittag-Leffler functions for large time.
Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E.G.D. Cohen, Phys. Rev. E \textbf{76}, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviation-like principle. As example, it is studied the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a L\'{e}vy noise is also analyzed in detail.
This paper deals with a source separation strategy based on second-order statistics, namely, on data covariance matrices estimated at several lags. In general, ``blind'' approaches to source separation do not assume any knowledge on the mixing operator; however, any prior information about the possible structure of the mixing operator can improve the solution. Unlike ICA blind separation approaches, where mutual independence between the sources is assumed, our method only needs to constrain second-order statistics, and is effective even if the original sources are significantly correlated. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used a database that simulates the one expected from the instruments that will operate onboard ESA's Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere. The assumption was made that the emission spectra of the galactic foregrounds can be parametrised, thus reducing the number of unknowns for system identification to the number of the foreground radiations. We performed separation in several sky patches, featuring different levels of galactic contamination to the CMB, and assuming several noise levels, including the ones derived from the Planck specifications.