ShantanuT01/DACTYL-Pretraining huggingface dataset:
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear elliptic system. We derive weak formulations of the coupled constraints, and review some new developments in the solution theory for the constraints in the cases of constant mean extrinsic curvature (CMC) data, near-CMC data, and arbitrarily prescribed mean extrinsic curvature data. We then outline some recent results on a priori and a posteriori error estimates for a broad class of Galerkin-type approximation methods for this system which includes techniques such as finite element, wavelet, and spectral methods. We then use these estimates to construct an adaptive finite element method (AFEM) for solving this system numerically, and outline some new convergence and optimality results. We then describe in some detail an implementation of the methods using the FETK software package, which is an adaptive multilevel finite element code designed to solve nonlinear elliptic and parabolic systems on Riemannian manifolds. We finish by describing a simplex mesh generation algorithm for compact binary objects, and then look at a detailed example showing the use of FETK for numerical solution of the constraints.
The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and their multiplicities. The analogous decomposition for the \mu-discriminant of polynomial is found.
This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common deformation of multiple zeta values and of Kaneko-Tsumura's recent multiple $T$-values. The first few graded dimensions, assuming that a grading by the weight does hold, are computed.
The spin wave excitations of the ideal S=5/2 Kagome lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted "zero energy mode," verifying a fundamental prediction for the Kagome lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low temperature magnetization and spin structure.
Fusion-evaporation cross-sections {\sigma}evr in reactions known for fusion hindrance phenomenon in coupled-channels calculations at below-barrier energies, are studied in terms of the dynamical cluster-decay model (DCM) of one of us (RKG) and Collaborators and the Wong formula extended by us, both based on proximity potential, by using the concept of "barrier modification" at sub-barrier energies, first advocated by Misicu and Esbensen for M3Y potential. The DCM is shown to contain the "barrier lowering" as its inbuilt characteristic, and the same is found essential, and introduced empirically, in the extended-Wong formula.
We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen-Macaulay modules, which we review in an Appendix.
We obtain a one parameter class of stationary rotating string cosmological models of which the well-known G$\ddot o $del Universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative.
We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in the non-equilibrium expansion parameter. The first prescription is based on a generalisation of the kinetic mesoscopic virial equation and expresses the pressure exerted on the walls in terms of the average of the virial of the inter-particle forces. In the second approach, the pressure and the surface tension are identified with the volume and area derivatives, respectively, of the partition function associated with the known stationary non-equilibrium distribution of the model. The third method is a mechanical approach and is related to the work necessary to deform the system. The pressure is obtained by comparing the expression of the work in terms of local stress and strain with the corresponding expression in terms of microscopic distribution. This is determined from the force balance encoded in the Born-Green-Yvon equation. Such a method has the advantage of giving a formula for the local pressure tensor and the surface tension even in inhomogeneous situations. By direct inspection, we show that the three procedures lead to the same values of the pressure, and give support to the idea that the partition function, obtained via the unified coloured noise approximation, is more than a formal property of the system, but determines the stationary non-equilibrium thermodynamics of the model.
We enumerate arrangements of $n$ couples, i.e. pairs of people, placed in a single-file queue, and consider four statistics from the vantage point of a distinguished given couple. In how many arrangements are exactly $p$ of the $n-1$ other couples i) interlaced with the given couple, ii) contained within them, iii) containing the given couple, and iv) lying outside the given couple? We provide generating functions which enumerate these arrangements and obtain the associated continuous asymptotic distributions in the $n\to\infty$ limit. The asymptotic distributions corresponding to cases i), iii), and iv) evince critical phenomena around the value $p_c=(n-1)/2$, such that the probability that 1) the couple is interlaced with more than half of the other couples, and 2) the couple is contained by more than half of the other couples, are both zero in the strict $n\to\infty$ limit. We further show that the cumulative probability that less than half of the other couples lie outside the given couple is $\pi/4$ in the limit, and that the associated distribution is uniform for $p<p_c$.
We consider a magnetic Schr\"odinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the assumption that they satisfy appropriate a priori bounds. We also give a similar stability result for the holonomy of the connection 1-form $X$.
We have found for the first time a Balmer edge feature in the Big Blue Bump emission of a quasar. The feature is seen in the polarized flux spectrum of the quasar, where all the emissions from outside the nucleus are scraped off and removed. The existence of the Balmer-edge absorption feature directly indicates that the Big Blue Bump is indeed thermal and optically-thick.
We consider a two-dimensional rigid rotator system coupled to a two-dimensional heat bath. The Caldeira-Leggett (Brownian) model for the rotator and the spin-Boson model have been used to describe such systems, but they do not possess rotational symmetry, they cannot describe the discretized rotational bands in absorption and emission spectra that have been found experimentally. Here, to address this problem, we introduce a rotationally invariant system-bath (RISB) model that is described by two sets of harmonic-oscillator baths independently coupled to the rigid rotator as sine and cosine functions of the rotator angle. Due to a difference in the energy discretization of the total Hamiltonian, the dynamics described by the RISB model differ significantly from those described by the rotational Caldeira-Legget (RCL) model, while both models reduce to the Langevin equation for a rotator in the classical limit. To demonstrate this point, we compute the rotational absorption spectrum defined by the linear response function of a rotator dipole. For this purpose, we derive a quantum master equation for the RISB model in the high-temperature Markovian case. We find that the spectral profiles of the calculated signals exhibit a transition from quantized rotational bands to a single peak after spectrum collapse. This is a significant finding, because previous approaches cannot describe such phenomena in a unified manner.
When deriving a formula for the Hall conductivity of interacting electrons in Phys. Rev. B 86, 165133, we have relied on an unjustified implicit assumption that a certain gauge choice could be made. Only under this condition would the formula follow. If this condition fails, the formula we derived does not lead to the exactly quantized value of the Hall conductance in fractional Chern insulators.
We investigate the shadow cast by a rotating braneworld black hole, in the Randall-Sundrum scenario. In addition to the angular momentum, the tidal charge term deforms the shape of the shadow. For a given value of the rotation parameter, the presence of a negative tidal charge enlarges the shadow and reduces its deformation with respect to Kerr spacetime, while for a positive charge, the opposite effect is obtained. We also analyze the case in which the combination of the rotation parameter and the tidal charge results in a naked singularity. We discuss the observational prospects corresponding to the supermassive black hole at the Galactic center.
We study a compactification of the moduli space of theta characteristics, giving a modular interpretation of the geometric points and describing the boundary stratification. This space is different from the moduli space of spin curves. The modular description and the boundary stratification of the new compactification are encoded by a tropical moduli space. We show that this tropical moduli space is a refinement of the moduli space of spin tropical curves. We describe explicitly the induced decomposition of its cones.
Lithium intercalated anatase used in Li-ion batteries has some special features: coexistence of Li-rich and Li-poor phases as well as two possible positions for Li ions in the oxygen tetrahedron. A theoretical description of the compound considering those peculiarities is presented. As shown by the performed symmetry analysis, the intercalation induced lattice deformation can be accompanied by the ordering of antiferroelectric type (internal piezoeffect). In the following step, a qualitative illustration of the phase separation in the lithiated anatase is given within the Landau expansion at the proper choice of coefficients. A microscopic model for description of the compound is also proposed which combines features of the Mitsui and Blume-Emery-Griffits models and utilizes the symmetry analysis results. Various ground state and temperature-dependent phase diagrams of the model are studied to find a set of model parameters corresponding to the lithiated anatase. A phase separation into the empty and half-filled phases in a wide temperature range has been found closely resembling the phase coexistence in the intercalated crystal. In the framework of the model, the two-position Li subsystem could have the ordering of ferro- or antiferroelectric types which, however, has not been yet observed by the experiment.
We present SPLOT, a small scale pilot survey to test the potential of snapshot (single epoch) linear imaging polarimetry as a supplementary tool to traditional transient follow-up. Transients exist in a vast volume of observational parameter space and polarimetry has the potential to highlight sources of scientific interest and add value to near real-time transient survey streams. We observed a sample of $\sim 50$ randomly selected optical transients with the EFOSC2 and SofI instruments, on the 3.6m New Technology Telescope (NTT) to test the feasibility of the survey. Our sample contained a number of interesting individual sources: a variety of supernovae, X-ray binaries, a tidal disruption event, blazar outbursts, and, by design, numerous transients of unknown nature. We discuss the results, both for the individual sources and the survey in detail. We provide an overview on the success and limitations of SPLOT and also describe a novel calibration method for removing instrumental polarisation effects from Nasymth-mounted telescopes. We find that a SPLOT-like survey would be a benefit to the large scale future transient survey streams such as LSST. The polarimetric measurements have added scientific value to a significant number of the sources and, most importantly, has shown the potential to highlight unclassified transient sources of scientific interest for further study.
We have investigated the magnetic behavior of ball-milled fine particles of well-known Kondo lattices, CeAu2Si2, CePd2Si2 and CeAl2, by magnetization and heat-capacity studies in order to understand the magnetic behavior when the particle size is reduced. These compounds have been known to order antiferromagnetically in the bulk form near (TN=) 10, 10 and 3.8 K respectively. We find that the features due to magnetic ordering get suppressed to temperatures below 1.8 K in the case of fine particles of ternary alloys, though trivalence of Ce as inferred from the effective moment remains unchanged. In contrast to this, in CeAl2, there appears to be a marginal enhancement of TN, when the particle size is reduced to less than a micron. These results can be consistently understood by proposing that there is relatively more 4f-localization as the particle size is reduced, resulting in weakening of exchange interaction strength.
In this work we compare the predictions of two representative hadronic interaction models, EPOS 1.99, and QGSJET II-03 with several extensive air showers (EAS) parameters for proton and iron primaries in the energy range $10^{17}$ - $10^{19} eV$ using CORSIKA-6990. The EAS parameters depth of shower maximum, shower size, size of muon shower, muon number distribution, electron number distribution,size of hadron shower, hadron energy sum, electron muon correlations, and, hadron energy spectra are studied in this paper.
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the P\'eclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type.   Addendum and Erratum   The expression for the effective diffusion of an inertial, periodically driven Brownian particle in an asymmetric, periodic potential is compared with the step number diffusion which is extracted from the corresponding coarse grained hopping process specifying the number of covered spatial periods within each temporal period. The two expressions are typically different and involve the correlations between the number of hops.
Using the merger of local density approximation and dynamical mean field theory, we show how electronic correlations increase the thermopower of Na$_{0.7}$CoO$_2$ by 200%. The newly revealed mechanism is an asymmetric shift of (quasi) electrons and holes away from the Fermi level, concurrent with an asymmetry of the respective (group) velocities. Exploiting this effect in bandstructure and correlation engineering may lead to a substantial increase of the thermoelectric figure of merit.
We apply the Dynamical Mean Field Theory to calculate the low-density limit of the optical conductivity in the Holstein model. This non perturbative treatment allows to span continuously from the weak-coupling quasi-free electron behaviour to the strong-coupling small polaron picture. New features arise in the intermediate coupling regime: i) a noticeable transfer of spectral weight towards low frequencies occurs at low temperatures, when coherent processes acquire importance; ii) thermally activated Polaron Interband Transitions appear at non zero temperature, whose spectral weight has a non monotonic temperature behaviour. We propose an interpretation of the infrared active vibrations (IRAV) observed in the optical spectra of the underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.
We consider the anomalous dimensions of restricted Schur polynomials constructed using n~O(N) complex adjoint scalars Z and m complex adjoint scalars Y. We fix m<<n so that our operators are almost half BPS. At leading order in m/n this system corresponds to a dilute gas of m free magnons. Adding the first correction of order m/n to the anomalous dimension, which arises at two loops, we find non-zero magnon interactions. The form of this new operator mixing is studied in detail for a system of two giant gravitons with four strings attached.
The `theoretical' existence of traversable Lorentzian wormholes in the classical, macroscopic world is plagued by the violation of the well--known energy conditions of General Relativity. In this brief article we show : (i) how the extent of violation can be quantified using certain volume integrals (ii) whether this `amount of violation' can be minimised for some specific cut--and--paste geometric constructions. Examples and possibilities are also outlined.
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance equations and equations for the chemical potentials, depending on the relative velocities, supplemented with initial and homogeneous Neumann boundary conditions. Global-in-time existence of bounded weak solutions to the quasilinear parabolic system and their exponential decay to the homogeneous steady state are proved. The mathematical difficulties are due to the singular Maxwell-Stefan diffusion matrix, the cross-diffusion coupling, and the lack of standard maximum principles. Key ideas of the proofs are the Perron-Frobenius theory for quasi-positive matrices, entropy-dissipation methods, and a new entropy variable formulation allowing for the proof of nonnegative lower and upper bounds for the concentrations.
This paper deals with regularity theory for two-phase free boundary variational problems ruled by degenerate elliptic operators.
We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).
We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we prove a slightly more general result).
We prove L^1 --> L^\infty estimates for the linear Schroedinger equation in three dimensions. The potential is assumed to belong to certain L^p spaces, but no pointwise decay estimates and no additional regularity is required.
It is known that projective minimal models satisfy the celebrated Miyaoka-Yau inequalities. In this article, we extend these inequalities to the set of all smooth, projective and non-uniruled varieties.
Our knowledge of flavour dynamics has undergone a `quantum jump' since just before the turn of the millenium: direct CP violation has been firmly established in $K_L \to \pi \pi$ decays in 1999; the first CP asymmetry outside $K_L$ decays has been discovered in 2001 in $B_d \to \psi K_S$, followed by $B_d \to \pi^+\pi^-$, $\eta^{\prime}K_S$ and $B \to K^{\pm}\pi^{\mp}$ establishing direct CP violation also in the beauty sector. Counterintuitive, yet central features of quantum mechanics like meson-antimeson oscillations and EPR correlations have been crucial in making such effects observable.   The CKM dynamics of the Standard Model (SM) of HEP allow a description of CP insensitive and sensitive $B$, $K$ and $D$ transitions that is impressively consistent even on the quantitative level. We know now that at least the lion's share of the observed CP violation is provided by the SM. Yet these novel successes do not invalidate the theoretical arguments for it being incomplete. We have also more direct evidence for New Physics, namely neutrino oscillations, the observed baryon number of the Universe, dark matter and dark energy. While the New Physics anticipated at the TeV scale is not likely to shed any light on the SM's mysteries of flavour, detailed and comprehensive studies of heavy flavour transitions will be essential in diagnosing salient features of that New Physics. Strategic principles for such studies are outlined.
An attempt has been made to explore the galactic dynamics via the rotational velocity beyond the Einstein's geometric theory of gravity. It is inspired from the geometric relation obtained in the power law $f(R)$ gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein-Hilbert action (taking $R$ as $f(R)\propto R^{1+\delta}$) at the galactic scales for the explanation of cosmological dark matter problem and obtain the contribution of dynamical $f(R)$ background geometry in accelerating the test mass. In the weak field limits, we obtain the effective acceleration of the test mass due to a massive spherically symmetric source in $f(R)$ background and develop an equation for the rotational velocity. We test the viability of the model by tracing the motion of test mass outside the typical galactic visible boundaries without considering any dark matter halo profile. We obtain a nice agreement in the outer regions (up to few tens of kpc beyond the visible boundary) of the typical galaxy by using the known galaxy data.\\ We further explore the galactic dynamics for a galaxy NGC 1052 of which the dark matter deficient galaxies, i.e., DF2 and DF4 are a part (satellite galaxies) and discuss plots of the dynamical feature of rotation curves in $f(R)$ background for the model parameter $\delta<<1$ and interpret the results for its satellite galaxies.
Images of the circumstellar ejecta associated with the post-red supergiant IRC +10420 show a complex ejecta with visual evidence for episodic mass loss. In this paper we describe the transverse motions of numerous knots, arcs and condensations in the inner ejecta measured from second epoch {\it HST/WFPC2} images. When combined with the radial motions for several of the features, the total space motion and direction of the outflows show that they were ejected at different times, in different directions, and presumably from separate regions on the surface of the star. These discrete structures in the ejecta are kinematically distinct from the general expansion of the nebula and their motions are dominated by their transverse velocities. They are apparently all moving within a few degrees of the plane of the sky. We are thus viewing IRC +10420 nearly pole-on and looking nearly directly down onto its equatorial plane. We also discuss the role of surface activity and magnetic fields on IRC +10420's recent mass loss history.