ShantanuT01/DACTYL-Pretraining huggingface dataset:
A special Bianchi I universe is constructed in $~4D~$ string theory. Geometrically it represents a $~3D~$ anti-de-Sitter space crossed with a flat direction whereas in terms of an associated conformal field theory it is an extremal case of a gauged WZWN theory with target the coset $~SU(1,1) \times R^2 / R~$. Some of its properties are discussed.
Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of $A$-polynomials of knots.
The Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies, are investigated.
Two dimensional electronic systems under strong magnetic field form quantum Hall (QH) edge states, which propagate along the boundary of a sample with a dissipationless current. Engineering the pathway of these propagating one-dimensional chiral modes enables the investigation of quantum tunneling between adjacent QH states. Here, we report tunneling transport in spatially controlled networks of QH edge states in bilayer graphene. We observe resonant tunneling between co-propagating QH edges across barriers formed by electrically defining incompressible strips. Employing spectroscopic tunneling measurements enable the direct probing of the spatial profile, density of states, and compressibility of the QH edge states with an unprecedented energy resolution. The capability to engineer the QH edge network provides an opportunity to build future quantum electronic devices supported by rich underline physics.
We propose an expression for the classical limit of diagonal form factors in which we integrate the corresponding observable over the moduli space of classical solutions. In infinite volume the integral has to be regularized by proper subtractions and we present the one, which corresponds to the classical limit of the connected diagonal form factors. In finite volume the integral is finite and can be expressed in terms of the classical infinite volume diagonal form factors and subvolumes of the moduli space. We analyze carefully the periodicity properties of the finite volume moduli space and found a classical analogue of the Bethe-Yang equations. By applying the results to the heavy-heavy-light three point functions we can express their strong coupling limit in terms of the classical limit of the sine-Gordon diagonal form factors.
Charge transfer between metal nanoparticles and the supported TiO2 surface is primarily important for catalytic applications as it greatly affects the catalytic activity and the thermal stability of the deposited nanoparticles on the surface. Herein, a systematic spin-polarized density functional calculation is performed to evaluate the adsorption, diffusion, and charge state of several transition metal monomers on both stoichiometric and reduced rutile TiO2 (110) surface. The role of oxygen vacancy (Ov) with its accompanying excess electrons in influencing the activation of the monomers is examined. For pristine reduced surface, our hybrid functional calculation shows that only a small portion (around 5%) of the excess electrons occupy the topmost surface, which are mainly delocalized at the second nearest and third nearest fivefold coordinated Ti (Ti5c) atoms. The small amounts of excess electrons populating at the Ti5c atoms can be transferred to strongly electronegative adsorbates like Au and Pt thus enabling a moderate adsorption, whereas no stable adsorption at the Ti5c site is found for other less electronegative TM adatoms(Ag, Cu, Fe, Co, Ni and Pd) on the reduced surface and for all the adatoms on stoichiometric surface. This finding clarify the origin of the experimental observation of the adsorption of O2 and CO molecules at Ti5c sites in connection with charge transfer. In addition, the spatial redistribution of the excess electrons at Ti5c sites around the Ov upon the adsorption of the monomers is thoroughly examined. Our finding of an accumulation of excess electrons at the Ti5c sites around the monomers explains the critical role of the perimeter interface of the deposited nanoparticles in promoting the adsorption and activation of reactants observed in experiments.
For a non-endoscopic cohomological cuspidal automorphic representation of $\mathrm{GSp}_4 \times \mathrm{GL}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it. Both the construction and the verification of tame norm relations are based on Novodvorsky's integral formula for the $L$-function of $\mathrm{GSp}_4 \times \mathrm{GL}_2$.
We report temperature-dependent spin-Seebeck measurements on Pt/YIG bilayers and Pt/NiO/YIG trilayers, where YIG (Yttrium iron garnet, Y$_3$Fe$_5$O$_{12}$) is an insulating ferrimagnet and NiO is an antiferromagnet at low temperatures. The thickness of the NiO layer is varied from 0 to 10 nm. In the Pt/YIG bilayers, the temperature gradient applied to the YIG stimulates dynamic spin injection into the Pt, which generates an inverse spin Hall voltage in the Pt. The presence of a NiO layer dampens the spin injection exponentially with a decay length of $2 \pm 0.6$ nm at 180 K. The decay length increases with temperature and shows a maximum of $5.5 \pm 0.8$ nm at 360 K. The temperature dependence of the amplitude of the spin-Seebeck signal without NiO shows a broad maximum of $6.5 \pm 0.5$ $\mu$V/K at 20 K. In the presence of NiO, the maximum shifts sharply to higher temperatures, likely correlated to the increase in decay length. This implies that NiO is most transparent to magnon propagation near the paramagnet-antiferromagnet transition. We do not see the enhancement in spin current driven into Pt reported in other papers when 1-2 nm NiO layers are sandwiched between Pt and YIG.
We present a new massive spin two field theory which has smooth massless limit based on BRS formalism. Our model contains a parameter a which extendes Fierz-Pauli's mass term. Although redundant scalar ghost exists in our model, physical degree of freedom is still five for the sake of existence of the Deser-Waldron type gauge symmetry. Origin of vDVZ discontiunity can be studied at the Fierz-Pauli limit a -> 1.
Recent exact $n\to\infty$ results for critical Casimir forces of the $O(n)$ $\phi^4$ model on a three-dimensional strip bounded by two planar free surfaces at a distance $L$ are surveyed. This model has long-range order below the bulk critical temperature $T_c$ if $L=\infty$, but remains disordered for all $T>0$ when $L<\infty$. A proper analysis of its scaling behavior near $T_c$ is quite challenging: Besides with bulk, boundary, and finite-size critical behaviors, one must deal with a nontrivial dimensional crossover. The model can be solved exactly in the limit $n\to\infty$ in terms of the eigenvalues and eigenenergies of a selfconsistent Schr\"odinger equation involving a potential $v(z)$ with the near-boundary singular behavior $v(z\to 0+)\approx -1/(4z^2)+4m/(\pi^{2}z)$, where $m=1/\xi_+(|t|)$ is the inverse bulk correlation length and $t\sim (T-T_c)/T_c$, and a corresponding singularity at the second boundary plane. The potential $v(z)$, the excess free energy, and the Casimir force have been determined numerically with high precision. Exact analytical results for a variety of properties such as series expansion coefficients of $v(z)$, the scattering data of $v(z)$ in the semi-infinite case $L=\infty$ for all $m\gtreqless 0$, and the low-temperature asymptotic behavior of the residual free energy and the Casimir force can be obtained by a combination of boundary-operator and short-distance expansions, proper extensions of inverse scattering theory, new trace formulae, and semiclassical expansions.
We show how Gromov's spaces of bounded geometries provide a general mathematical framework for addressing and solving many of the issues of $3D$-simplicial quantum gravity. In particular, we establish entropy estimates characterizing the asymptotic distribution of combinatorially inequivalent triangulated $3$-manifolds, as the number of tetrahedra diverges. Moreover, we offer a rather detailed presentation of how spaces of three-dimensional riemannian manifolds with natural bounds on curvatures, diameter, and volume can be used to prove that three-dimensional simplicial quantum gravity is connected to a Gaussian model determined by the simple homotopy types of the underlying manifolds. This connection is determined by a Gaussian measure defined over the general linear group $GL({\bf R},\infty)$. It is shown that the partition function of three-dimensional simplicial quantum gravity is well-defined, in the thermodynamic limit, for a suitable range of values of the gravitational and cosmological coupling constants. Such values are determined by the Reidemeister-Franz torsion invariants associated with an orthogonal representation of the fundamental groups of the set of manifolds considered. The geometrical system considered shows also critical behavior, and in such a case the partition function is exactly evaluated and shown to be equal to the Reidemeister-Franz torsion. The phase structure in the thermodynamical limit is also discussed. In particular, there are either phase transitions describing the passage from a simple homotopy type to another, and (first order) phase transitions within a given simple homotopy type which seem to confirm, on an analytical ground, the picture suggested by numerical simulations.
M. Von Korff introduced the $F$-signature of a normal projective variety, and computed the $F$-signature of the product of two projective lines $\mathbb{P}^1\times \mathbb{P}^1$. In this paper, we compute $F$-signatures of Hirzebruch surfaces.
We present the detailed analysis of genuine twist-3 contributions to the exclusive electroproduction amplitude of transversely polarized vector mesons. Using the formalism based on the QCD factorization in the momentum representation we calculated all the genuine twist-3 terms and found the total expression of this amplitude at 1/Q level. Generally speaking, these terms violate standard factorization owing to the existence of the infrared divergencies in the amplitude of hard sub-processes, although the strongest divergencies cancel due to the QCD equations of motion. We discuss the possible treatment of surviving divergencies.
In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and $L^\infty((0,T)\times\o)$, where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.
We study the properties of all major HVC complexes from a sample compiled 1991 by Wakker & van Woerden (WvW). We use the Leiden/Argentine/Bonn all sky 21-cm line survey and decompose the profiles into Gaussian components. We find a well defined multi-component structure for most of the HVC complexes. The cold HVC phase has lines with typical velocity dispersions of sigma = 3 km/s and exists only within more extended broad line regions, typically with sigma = 12 km/s. The motions of the cores relative to the envelopes are characterized by Mach numbers M = 1.5. The center velocities of the cores within a HVC complex have typical dispersions of 20 km/s. Remarkable is the well defined two-component structure for some prominent HVC complexes in the outskirts of the Milky Way: Complex H, the Magellanic Stream and the Leading Arm. There might be some indications for an interaction between HVCs and disk gas at intermediate velocities. This is possible for complex H, M, C, WB, WD, WE, WC, R, G, GCP, and OA, but not for complex A, MS, ACVHV, EN, WA, and P. Conclusions: The line widths, determined by us, imply that estimates of HVC masses, as far as derived from the WvW database, need to be scaled up by a factor 1.4. Correspondingly, guesses for the external pressure of a confining coronal gas need to be revised upward by a factor of 2. The HVC multi-phase structure implies in general that currently the halo pressure is significantly underestimated. In consequence, the HVC multi-phase structure may indicate that most of the complexes are circum-galactic. HVCs have turbulent energy densities which are an order of magnitude larger than that of comparable clumps in the Galactic disk.
A systematic study of the temperature dependence of the shapes and pairing gaps of some isotopes in the rare-earth region is made in the relativistic Hartree-BCS theory. Thermal response to these nuclei is always found to lead to a phase transition from the superfluid to the normal phase at a temperature $T_{\Delta}\sim 0.4 - 0.8$ MeV and a shape transition from prolate to spherical shapes at $T_c\sim 1.0 - 2.5$ MeV. These shape transition temperatures are appreciably higher than the corresponding ones calculated in the non-relativistic framework with the pairing plus quadrupole interaction. Study of nuclei with continued addition of neutron pairs for a given isotope shows that with increased ground state deformation, the transition to the spherical shape is delayed in temperature. A strong linear correlation between $T_{\Delta}$ and the ground state pairing gap $\Delta^0$ is observed; a well- marked linear correlation between $T_c$ and the ground state quadrupole defromation $\beta_2^{0}$ is also seen. The thermal evolution of the hexadecapole deformation is further presented in the paper.
Recent work in quantum loop cosmology suggests the universe undergoes a bounce when evolving from a previous collapsing phase. However, with non-inflationary matter sources, the scenario appears to strongly violate the holography bound S\leq A/4 during the bounce, where A now represents the cross-sectional area of the bounce. We also give a simple argument why any inflationary phase after the bounce is unlikely due to prior dissipation of a scalar field kinetic energy phase into regular matter components.
We consider a model of two qubits dissipating into both local and global environments (generally at non-zero temperatures), with the possibility of interpolating between purely local dissipation and purely global one. The corresponding dissipative dynamical map is characterized in terms of its Kraus operators focusing on the stationary regime. We then determine conditions under which entanglement can be induced by the action of such a map. It results (rather counterintuitively) that in order to have entanglement in the presence of local environment, this latter must be at nonzero temperature.
Star formation activities in the NGC 2024 FIR 4 region were studied by imaging centimeter continuum sources and water maser sources using several archival data sets from the Very Large Array. The continuum source VLA 9 is elongated in the northwest-southeast direction, consistent with the FIR 4 bipolar outflow axis, and has a flat spectrum in the 6.2-3.6 cm interval. The three water maser spots associated with FIR 4 are also distributed along the outflow axis. One of the spots is located close to VLA 9, and another one is close to an X-ray source. Examinations of the positions of compact objects in this region suggest that the FIR 4 cloud core contains a single low-mass protostar. VLA 9 is the best indicator of the protostellar position. VLA 9 may be a radio thermal jet driven by this protostar, and it is unlikely that FIR 4 contains a high-mass young stellar object (YSO). A methanol 6.7 GHz maser source is located close to VLA 9, at a distance of about 100 AU. The FIR 4 protostar must be responsible for the methanol maser action, which suggests that methanol class II masers are not necessarily excited by high-mass YSOs. Also discussed are properties of other centimeter continuum sources in the field of view and the water masers associated with FIR 6n. Some of the continuum sources are radio thermal jets, and some are magnetically active young stars.
In this paper we study integro-differential equations like the anisotropic fractional Laplacian. As in [Silvestre, Indiana University Mathematics Journal 55, 2006], we adapt the De Giorgi technique to achieve the $C^{\gamma}$-regularity for solutions of class $C^{2}$ and use the geometry found in [Caffarelli, Leit\~ao, and Urbano, Math. Ann. 360, 2014] to get an ABP estimate, a Harnack inequality and the interior $C^{1, \gamma}$ regularity for viscosity solutions.
In our previous paper we have elaborated a certain signed count of real lines on real projective n-dimensional hypersurfaces of degree 2n-1. Contrary to the honest "cardinal" count, it is independent of the choice of a hypersurface, and by this reason provides a strong lower bound on the honest count. In this count the contribution of a line is its local input to the Euler number of a certain auxiliary vector bundle. The aim of this paper is to present other, in a sense more geometric, interpretations of this local input. One of them results from a generalization of Segre species of real lines on cubic surfaces and another from a generalization of Welschinger weights of real lines on quintic threefolds.
By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given physical system. In particular, we show how the constraints due to the Ward identities, which implement the conservation laws associated with the various symmetries, help to minimize the number of independent running variables. This use of the Ward identities is examined both in the case of a stable phase and of a critical phenomenon. In the first case we consider the problems of interacting fermions and bosons. In one dimension general and specific Ward identities are sufficient to show the non-Fermi-liquid character of the interacting fermion system, and also allow to describe the crossover to a Fermi liquid above one dimension. This crossover is examined both in the absence and presence of singular interaction. On the other hand, in the case of interacting bosons in the superfluid phase, the implementation of the Ward identities provides the asymptotically exact description of the acoustic low-energy excitation spectrum, and clarifies the subtle mechanism of how this is realized below and above three dimensions. As a critical phenomenon, we discuss the disorder-driven metal-insulator transition in a disordered interacting Fermi system. In this case, through the use of Ward identities, one is able to associate all the disorder effects to renormalizations of the Landau parameters. As a consequence, the occurrence of a metal-insulator transition is described as a critical breakdown of a Fermi liquid.
We study the universality in gravitational waves emitted from non-rotating neutron stars characterized by different equations of state (EOS). We find that the quasi-normal mode frequencies of such waves, including the $w$-modes and the $f$-mode, display similar universal scaling behaviours that hold for most EOS. Such behaviours are shown to stem from the mathematical structure of the axial and the polar gravitational wave equations, and the fact that the mass distribution function can be approximated by a cubic-quintic polynomial in radius. As a benchmark for other realistic neutron stars, a simple model of neutron stars is adopted here to reproduce the pulsation frequencies and the generic scaling behaviours mentioned above with good accuracy.
We present a baseline sensitivity analysis of the Hydrogen Epoch of Reionization Array (HERA) and its build-out stages to one-point statistics (variance, skewness, and kurtosis) of redshifted 21 cm intensity fluctuation from the Epoch of Reionization (EoR) based on realistic mock observations. By developing a full-sky 21 cm lightcone model, taking into account the proper field of view and frequency bandwidth, utilising a realistic measurement scheme, and assuming perfect foreground removal, we show that HERA will be able to recover statistics of the sky model with high sensitivity by averaging over measurements from multiple fields. All build-out stages will be able to detect variance, while skewness and kurtosis should be detectable for HERA128 and larger. We identify sample variance as the limiting constraint of the variance measurement while skewness and kurtosis measurements will be primarily limited by thermal noise. The sensitivity can be improved by performing frequency binning and windowing. In addition, we find that strong sample variance fluctuation in the kurtosis measured from an individual field of observation indicates the present of outlying cold or hot regions in the underlying fluctuations, a feature that can potentially be used as an EoR bubble indicator. This manuscript is altered from the originally published paper to reflect corrections in the erratum.
The temperature dependence of the liquid-drop fission barrier is considered, the critical temperature for the liquid-gas phase transition in nuclear matter being a parameter. Experimental and calculated data on the fission probability are compared for highly excited $^{188}$Os. The calculations have been made in the framework of the statistical model. It is concluded that the critical temperature for the nuclear liquid--gas phase transition is higher than 16 MeV.
In the general process of eliminating dynamic variables in Markovian models, there exists a difference in the irreversible entropy production between the original and reduced dynamics. We call this difference the hidden entropy production, since it is an invisible quantity when only the reduced system's view is provided. We show that this hidden entropy production obeys a new integral fluctuation theorem for the generic case where all variables are time-reversal invariant, therefore supporting the intuition that entropy production should decrease by coarse graining. It is found, however, that in cases where the condition for our theorem does not hold, entropy production may also increase due to the reduction. The extended multibaker map is investigated as an example for this case.
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber leading to a severely ill-conditioned huge coefficient matrix. To understand and tackle such challenges, it is crucial to analyze how the solution of the 2D Helmholtz equation depends on (perturbed) boundary and source data for large wavenumbers. In fact, this stability analysis is critical in the error analysis and development of effective numerical schemes. Therefore, in this paper, we analyze and derive several new sharp wavenumber-explicit stability bounds for the 2D Helmholtz equation with inhomogeneous mixed boundary conditions: Dirichlet, Neumann, and impedance. We use Fourier techniques, the Rellich's identity, and a lifting strategy to establish these stability bounds. Some examples are given to show the optimality of our derived wavenumber-explicit stability bounds.