ShantanuT01/DACTYL-Pretraining huggingface dataset:
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive understanding of turbulence. We develop and employ a hierarchical Bayesian fitting method to estimate the parameters describing the scaling relationships of the velocity power spectra of supersonic turbulence. We demonstrate the accuracy and other advantages of this technique compared with ordinary linear regression methods. Using synthetic power spectra, we show that the Bayesian method provides accurate parameter and error estimates. Commonly used normal linear regression methods can provide estimates that fail to recover the underlying slopes, up to 70% of the instances, even when considering the 2std.dev. uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in 3D numerical simulations. We model driven, isothermal, turbulence with rms Mach numbers in the highly supersonic regime M~15. We study the influence of purely solenoidal (divergence-free) and purely compressive (curl-free) forcing on the scaling exponent of the power spectrum. In simulations with solenoidal forcing and 1024^3 resolution, our results indicate that there is no extended inertial range with a constant scaling exponent. The bottleneck effect results in a curved power spectrum at all wave numbers and is more pronounced in the transversal modes compared with the longitudinal modes. Therefore, this effect is stronger in stationary turbulent flows driven by solenoidal forcing compared to the compressive one. The longitudinal spectrum driven with compressive forcing is the only spectrum with constant scaling exponent z=-1.94 +- 0.01, corresponding to slightly shallower slopes than the Burger's prediction.
We find that the true ground state of the dipolar spin ice system under [110]-magnetic fields is the ``Q=X'' structure, which is consistent with both experiments and Monte Carlo simulations. We then perform a Monte Carlo simulation to confirm that there exists a first order phase transition under the [110]-field. In particular this result indicates the existence of the first order phase transition to the ``Q=X'' phase in the field above 0.35 T for Dy2Ti2O7. We also show the magnetic field-temperature phase diagram to summarize the ordered states of this system.
Vertex operators in string theory come in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.
The studies focused on the Thermally-Pulsing Asymptotic Giant Branch phase experienced by low- and intermediate-mass stars are extremely important in many astrophysical contexts. In particular, a detailed computation of their chemical yields is essential for several issues, ranging from the chemical evolution of galaxies, to the mechanisms behind the formation of globular clusters. Among all the uncertainties affecting the theoretical modelling of this phase, and described in the literature, it remains to be fully clarified which results are severely affected by the use of inadequate low-temperature opacities, that are in most cases calculated on the basis of the original chemical composition of the stars, and do not consider the changes in the surface chemistry due to the occurrence of the third dredge-up and hot-bottom burning. Our investigation is aimed at investigating this point. By means of full evolutionary models including new set of molecular opacities computed specifically with the AESOPUS tool, we highlight which stellar models, among those present in the literature, need a substantial revision, mainly in relation to the predicted chemical yields. The interplay among convection, hot bottom burning and the low-temperature opacity treatment is also discussed
I report two new measures of the sudden change in the orbital period ($P$) across the nova eruption ($\Delta$P) and the steady period change in quiescence ($\dot{P}$) for classical novae (CNe) DQ Her and BT Mon. The fractional changes ($\Delta$P/P) in parts-per-million (ppm) are $-$4.46$\pm$0.03 for DQ Her and +39.6$\pm$0.5 for BT Mon. For BT Mon, the $\Delta$P/P value is not large enough (i.e., $>$1580 ppm) to allow for Hibernation in this system. The {\it negative} $\Delta$P/P for DQ Her is a confident counterexample of the Hibernation model for the evolution of cataclysmic variables. Further, published models of period changes by nova eruptions do not allow for such a negative value, so some additional mechanism is required, with this perhaps being due to asymmetric ejection of material. My program has also measured the first long-term $\dot{P}$ for CNe, with 0.00$\pm$0.02 for DQ Her and $-$2.3$\pm$0.1 for BT Mon, all with units of $10^{-11}$ days/cycle. These can be directly compared to the predictions of the Magnetic Braking model, where the long-term average $\dot{P}$ is a single universal function of $P$. The predicted values are -0.027 for DQ Her and -0.33 for BT Mon. For both novae, the measured $\dot{P}$ is significantly far from the predictions for Magnetic Braking. Further, the observed $\Delta$P for BT Mon imposes an additional {\it positive} period change of +0.60$\times$10$^{-11}$ days/cycle when averaged over the eruption cycle, so this system actually has a long-term {\it rise} in $P$.
We consider fully nonlinear uniformly elliptic cooperative systems with quadratic growth in the gradient, such as $$ -F_i(x, u_i, Du_i, D^2 u_i)- \langle M_i(x)D u_i, D u_i \rangle =\lambda c_{i1}(x) u_1 + \cdots + \lambda c_{in}(x) u_n +h_i(x), $$ for $i=1,\cdots,n$, in a bounded $C^{1,1}$ domain $\Omega\subset \mathbb{R}^N$ with Dirichlet boundary conditions; here $n\geq 1$, $\lambda \in\mathbb{R}$, $c_{ij},\, h_i \in L^\infty(\Omega)$, $c_{ij}\geq 0$, $M_i$ satisfies $0<\mu_1 I\leq M_i\leq \mu_2 I$, and $F_i$ is an uniformly elliptic Isaacs operator.   We obtain uniform a priori bounds for systems, under a weak coupling hypothesis that seems to be optimal. As an application, we also establish existence and multiplicity results for these systems, including a branch of solutions which is new even in the scalar case.
Input-output theory is invaluable for treating superconducting and photonic circuits connected by transmission lines or waveguides. However, this theory cannot in general handle situations in which retro-reflections from circuit components or configurations of beam-splitters create loops for the traveling-wave fields that connect the systems. Here, building upon the network-contraction theory of Gough and James [Commun. Math. Phys. 287, 1109 (2009)], we provide a compact and powerful method to treat any circuit that contains such loops so long as the effective cavities formed by the loops are sufficiently weak. Essentially all present-day on-chip superconducting and photonic circuits will satisfy this weakness condition so long as the reflectors that form the loops are not especially highly reflecting. As an example we analyze the problem of transmitting entanglement between two qubits connected by a transmission line with imperfect circulators, a problem for which the new method is essential. We obtain a full solution for the optimal receiver given that the sender employs a simple turn on/turn off. This solution shows that near-perfect transmission is possible even with significant retro-reflections.
The generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics was theoretically investigated in the context of non-equilibrium statistical mechanics. The recent study of the authors revealed that the Loewner evolution enables encoding the non-equilibrium (irreversible) processes into equilibrium (reversible) processes. In this study, by Gibbs entropy-based information-theoretic approaches, we formulated this encoding mechanism of the SLE to discuss its advantages as a mean to better describe non-equilibrium states. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curve, we reformulated the system's entropic properties in terms of the Kullback-Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectory was likewise discussed by decomposing its entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.
We employed first-principles density functional theory calculations guided by group-theoretical analysis and demonstrated the control of insulator-metal-insulator transition, polarization and two sublattice magnetization in (LaFeO$_3$)$_1$/(CaFeO$_3$)$_1$ superlattice via. multi structural mode coupling i.e., 'multimode coupling'. We have discovered a polar A-type charge disproportionation mode, Q$_{ACD}$ (analogous to the A-type antiferromagnetic ordering), and found that it couples with the trilinear coupling, $Q_{Tri}$ mode (common in $Pnma$ perovskite oxides and involves three structural modes), and lowers the symmetry further. By tuning the strength of the coupling between the participating modes, the polar metallic phase, polar zero bandgap semiconducting, and polar insulating phases can be obtained. Here, $Q_{Tri}$ switches the polarization direction, whereas, Q$_{ACD}$ can trigger insulator-metal-insulator transition along with the polarization switching. The mechanism is true for any transition metal superlattices constituted with $Pnma$ building blocks and with partially filled $e_g$ or $t_{2g}$ electron(s) at the transition metal sites.
We make use of the time-dependent density functional theory to derive a new formally exact expression for the dc resistivity of metals with impurities. This expression takes fully into account the dynamics of electron-electron interactions. Correction to the conventional $T$-matrix (phase-shifts) theory is treated within hydrodynamics of inhomogeneous viscous electron liquid. As a first application, we present calculations of the residual resistivity of aluminum as a function of the atomic number of the impurities. We show that the inclusion of many-body corrections considerably improves the agreement between theory and experiment.
We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit theorem gives rise to the continuous-state branching processes in varying environments studied recently by several authors.
Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: (i) designing a cost function with a local optimum at an acceptable solution, and (ii) developing an efficient numerical method to search for one (or multiple) of these local optima. While designing such functions is feasible in the noiseless case, the stability and location of local optima are mostly unknown under noise, occlusion, or missing data. In practice, this can result in undesirable local optima or not having a local optimum in the expected place. On the other hand, numerical optimization algorithms in high-dimensional spaces are typically local and often rely on expensive first or second order information to guide the search. To overcome these limitations, this paper proposes Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. Specifically, DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D point cloud registration, camera pose estimation, and image denoising. We show that DO performed comparably or outperformed state-of-the-art algorithms in terms of accuracy, robustness to perturbations, and computational efficiency.
We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents when the spatially inhomogeneous heat-bath and the periodic potential profile display an appropriate relative phase shift, $\phi$. By comparison with the collisionless limit, we determine the conditions for the most efficient transport among inelastic, elastic and non interacting rods. We show that the situation is complex as, depending on shape of the temperature profile, the current of one system may outperform the others.
The thermoelectric (TE) properties of a material are dramatically altered when electron-electron interactions become the dominant scattering mechanism. In the degenerate hydrodynamic regime, the thermal conductivity is reduced and becomes a {\it decreasing} function of the electronic temperature, due to a violation of the Wiedemann-Franz (WF) law. We here show how this peculiar temperature dependence gives rise to new striking TE phenomena. These include an 80-fold increase in TE efficiency compared to the WF regime, dramatic qualitative changes in the steady state temperature profile, and an anomalously large Thomson effect. In graphene, which we pay special attention to here, these effects are further amplified due to a doubling of the thermopower.
The quantum deformation concept is applied to a study of isovector pairing correlations in nuclei of the mass 40<A<100 region. While the non-deformed (q -> 1) limit of the theory provides a reasonable global estimate for strength parameters of the pairing interaction, the results show that the q-deformation plays a significant role in understanding higher-order effects in the interaction.
The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain A_inf-valued cohomology theory. We address some basic ring-theoretic questions about A_inf motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases A_inf, which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that vector bundles over the complement of the closed point in Spec A_inf do extend uniquely over the puncture; moreover, a similar statement holds in Huber's category of adic spaces.
We study the Brauer class rising from the obstruction to the existence of tautological line bundles on the Picard scheme of curves. We determine the period and index of the Brauer class in certain cases.
Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied.
Ultrafunctions are a particular class of functions defined on a hyperreal field $\mathbb{R}^{\ast}\supset\mathbb{R}$. They have been introduced and studied in some previous works. In this paper we introduce a particular space of ultrafunctions which has special properties, especially in term of localization of functions together with their derivatives. An appropriate notion of integral is then introduced which allows to extend in a consistent way the integration by parts formula, the Gauss theorem and the notion of perimeter. This new space we introduce, seems suitable for applications to PDE's and Calculus of Variations. This fact will be illustrated by a simple, but meaningful example.
Surface enhanced Raman spectra of Phenylalanine (Phe) in Ag colloidal solution have been recorded for Phe solutions of different pH. Spectral line-shape analyses of the enhanced modes, at 1005, 1380 and 1582 cm-1, between pH 4.5 and 10.5, have been carried out. The variation of spectral line-width with pH reveals two possible mechanisms in solution: (i) the fluctuation of pH in microscopic volume in an overall uniform pH solution and/or (ii) the motional narrowing caused by the intermolecular ionic interaction. We suggest that different charge states of the reference molecule are responsible for the observed bond softening with decrease in pH. The observed Raman shift and the Raman activity of the vibrational modes with maximum enhancement have been explained by carrying out DFT calculations.
Restoring face images from distortions is important in face recognition applications and is challenged by multiple scale issues, which is still not well-solved in research area. In this paper, we present a Sequential Gating Ensemble Network (SGEN) for multi-scale face restoration issue. We first employ the principle of ensemble learning into SGEN architecture design to reinforce predictive performance of the network. The SGEN aggregates multi-level base-encoders and base-decoders into the network, which enables the network to contain multiple scales of receptive field. Instead of combining these base-en/decoders directly with non-sequential operations, the SGEN takes base-en/decoders from different levels as sequential data. Specifically, the SGEN learns to sequentially extract high level information from base-encoders in bottom-up manner and restore low level information from base-decoders in top-down manner. Besides, we propose to realize bottom-up and top-down information combination and selection with Sequential Gating Unit (SGU). The SGU sequentially takes two inputs from different levels and decides the output based on one active input. Experiment results demonstrate that our SGEN is more effective at multi-scale human face restoration with more image details and less noise than state-of-the-art image restoration models. By using adversarial training, SGEN also produces more visually preferred results than other models through subjective evaluation.
The ground-state orbital occupancy of the Ru$^{4+}$ ion in Ca$_{2-x}$La$_x$RuO$_4$ [x=0, 0.05(1), 0.07(1) and 0.12(1)] was investigated by performing X-ray absorption spectroscopy (XAS) in the vicinity of the O K edge as a function of angle between the incident beam and the surface of the crystals. A minimal model of the hybridization between the O 2p states probed at the K edge and the Ru 4d orbitals was used to analyze the XAS data, allowing the ratio of hole occupancies $n_{xy}/n_{yz,zx}$ to be determined as a function of doping and temperature. For the samples displaying a low-temperature insulating ground-state ($x\leq0.07$), $n_{xy}/n_{yz,zx}$ is found to increase significantly with increasing doping. For x=0.12, which has a metallic ground-state, the XAS spectra are found to be independent of temperature, and not to be describable by the minimal hybridization model. To understand the origin of the evolution of the electronic structure across the phase diagram, we have performed theoretical calculations based on a model Hamiltonian, comprising electron-electron correlations, crystal field ($\Delta$) and spin-orbit coupling ($\lambda$), of a Ru-O-Ru cluster. Our calculations of the Ru hole occupancy as a function of $\Delta/\lambda$ establish that the enhancement of $n_{xy}/n_{yz,zx}$ is driven by significant changes to the crystal field as the tetragonal distortion of the RuO$_6$ octahedral changes from compressive to tensile with La doping. It also shows that the hole occupancy of the O 2p and Ru 4d orbitals display the same trend as a function of $\Delta/\lambda$, thus validating the minimal hybridization model. In essence, our results suggest that the predominant mechanism driving the emergence of the low-temperature metallic phase in La doped Ca$_2$RuO$_4$ is the structurally induced redistribution of holes within the t2g orbitals, rather that the injection of free carriers.
A brief introduction to the decoherent histories approach to quantum theory is given, with emphasis on its role in the discussion of the emergence of classicality from quantum theory. Some applications are discussed, including quantum-classical couplings, the relationship of the histories approach to quantum state diffusion, and the application of the histories approach to situations involving time in a non-trivial way.
We present a multiwavelength study of the Be/X-ray binary system XTE J1946+274 with the main goal of better characterizing its behavior during X-ray quiescence. We aim to shed light on the mechanism which triggers the X-ray activity for this source. XTE J1946+274 was observed by Chandra-ACIS during quiescence in 2013 March 12. In addition, this source has been monitored from the ground-based astronomical observatories of El Teide (Tenerife, Spain), Roque de los Muchachos (La Palma, Spain) and Sierra Nevada (Granada, Spain) since 2011 September, and from the TUBITAK National Observatory (Antalya, Turkey) since 2005 April. We have performed spectral and photometric temporal analyses in order to investigate the quiescent state and transient behavior of this binary system. In 2006, a long mass ejection event took place from the Be star, lasting for about seven years. We also found that a large Be circumstellar disk was present during quiescence, although major X-ray activity was not observed. We made an attempt to explain this scenario by assuming the permanently presence of a tilted and warped Be circumstellar disk. The 0.3-10 keV X-ray spectrum during quiescence was well fitted with either an absorbed blackbody or absorbed power-law models. The main parameters obtained for these models were kT=1.43+/-0.17 and Gamma=0.9+/-0.4 (with N_H~2-7E+22 cm-2). The 0.3-10 keV flux of the source was ~0.8E-12 erg-1 cm-2 s-1. Pulsations were found with P_pulse=15.757(1) s (MJD 56363.115) and an rms pulse fraction of 32.1(3)%. The observed X-ray luminosity during quiescent periods may be explained by the neutron star being in supersonic propeller regimen.
In this paper we construct pseudo random walks (symmetric and asymmetric) which converge in law to compositions of pseudoprocesses stopped at stable subordinators. We find the higher-order space-fractional heat-type equations whose fundamental solutions coincide with the law of the limiting pseudoprocesses. The fractional equations involve either Riesz operators or their Feller asymmetric counterparts. The main result of this paper is the derivation of pseudoprocesses whose law is governed by heat-type equations of real-valued order $\gamma>2$. The classical pseudoprocesses are very special cases of those investigated here.