Past excavations in Samaria, capital of biblical Israel, yielded a corpus of Hebrew ink on clay inscriptions (ostraca) that documents wine and oil shipments to the palace from surrounding localities. ...Many questions regarding these early 8th century BCE texts, in particular the location of their composition, have been debated. Authorship in countryside villages or estates would attest to widespread literacy in a relatively early phase of ancient Israel's history. Here we report an algorithmic investigation of 31 of the inscriptions. Our study establishes that they were most likely written by two scribes who recorded the shipments in Samaria. We achieved our results through a method comprised of image processing and newly developed statistical learning techniques. These outcomes contrast with our previous results, which indicated widespread literacy in the kingdom of Judah a century and half to two centuries later, ca. 600 BCE.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The relationship between the expansion of literacy in Judah and composition of biblical texts has attracted scholarly attention for over a century. Information on this issue can be deduced from ...Hebrew inscriptions from the final phase of the first Temple period. We report our investigation of 16 inscriptions from the Judahite desert fortress of Arad, dated ca. 600 BCE—the eve of Nebuchadnezzar’s destruction of Jerusalem. The inquiry is based on new methods for image processing and document analysis, as well as machine learning algorithms. These techniques enable identification of the minimal number of authors in a given group of inscriptions. Our algorithmic analysis, complemented by the textual information, reveals a minimum of six authors within the examined inscriptions. The results indicate that in this remote fort literacy had spread throughout the military hierarchy, down to the quartermaster and probably even below that rank. This implies that an educational infrastructure that could support the composition of literary texts in Judah already existed before the destruction of the first Temple. A similar level of literacy in this area is attested again only 400 y later, ca. 200 BCE.
Most surviving biblical period Hebrew inscriptions are ostraca-ink-on-clay texts. They are poorly preserved and once unearthed, fade rapidly. Therefore, proper and timely documentation of ostraca is ...essential. Here we show a striking example of a hitherto invisible text on the back side of an ostracon revealed via multispectral imaging. This ostracon, found at the desert fortress of Arad and dated to ca. 600 BCE (the eve of Judah's destruction by Nebuchadnezzar), has been on display for half a century. Its front side has been thoroughly studied, while its back side was considered blank. Our research revealed three lines of text on the supposedly blank side and four "new" lines on the front side. Our results demonstrate the need for multispectral image acquisition for both sides of all ancient ink ostraca. Moreover, in certain cases we recommend employing multispectral techniques for screening newly unearthed ceramic potsherds prior to disposal.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In this work we investigate the Runge–Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows. ...The flows considered are subsonic, transonic and supersonic flows in complex geometries, and also can be either steady or unsteady flows. All of these problems are considered to be a very stiff.
We then introduce an acceleration method for the compressible Navier–Stokes equations. We start with the multigrid method for pure subsonic flow, including reactive flows. We then add the Rossow–Swanson–Turkel RK/Implicit smoother that enables performing all these complex flow simulations with a reasonable CFL number. We next discuss the RK/Implicit smoother for time dependent problem and also for low Mach numbers. The preconditioner includes an intrinsic low Mach number treatment inside the smoother operator. We also develop a modified Roe scheme with a corresponding flux Jacobian matrix. We then give the extension of the method for real gas and reactive flow. Reactive flows are governed by a system of inhomogeneous Navier–Stokes equations with very stiff source terms. The extension of the RK/Implicit smoother requires an approximation of the source term Jacobian. The properties of the Jacobian are very important for the stability of the method. We discuss what the chemical physics theory of chemical kinetics tells about the mathematical properties of the Jacobian matrix. We focus on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian. We present the implementation of the method for turbulent flow. We use a two RANS turbulent model – one equation model – Spalart–Allmaras and a two-equation model – k–ω SST model. The last extension is for two-phase flows with a gas as a main phase and Eulerian representation of a dispersed particles phase (EDP). We present some examples for such flow computations inside a ballistic evaluation rocket motor.
The numerical examples in this work include transonic flow about a RAE2822 airfoil, about a M6 Onera wing, NACA0012 airfoil at very low Mach number, two-phase flow inside a Ballistic evaluation motor (BEM), a turbulent reactive shear layer and a time dependent Sod's tube problem.
•The RK/Implicit smoother scheme was expanded to solve multi-physics flow problems.•The method combined with multigrid and low-Mach preconditioning methods.•We develop Roe-based upwind scheme with intrinsic modifications to low Mach number.•We study implication of Le-Chatelier's principle on chemical Jacobian source terms.
We compute the scattering of unsteady acoustic waves about complex three-dimensional bodies with high order accuracy. The geometry of a scattering body is defined with the help of CAD. Its surface is ...represented as a collection of non-overlapping patches, each parameterized independently by means of high order splines (NURBS). As a specific example, we consider a submarine-like scatterer constructed using five different patches.
The acoustic wave equation on the region exterior to the scatterer is solved by first reducing it to a system of Calderon's boundary operator equations. The latter are obtained using the method of difference potentials coupled with a compact fourth order accurate finite difference scheme. When solving the boundary operator equations, we employ Huygens' principle. It allows us to work on a sliding time window of non-increasing duration rather than keep the entire temporal history of the solution at the boundary.
The proposed methodology demonstrates grid-independent computational complexity at the boundary and sub-linear complexity with respect to the grid dimension. It efficiently handles complex non-conforming geometries on Cartesian grids with no penalty for either accuracy or stability due to the cut cells. Its performance does not deteriorate over arbitrarily long simulation times. The exact treatment of artificial outer boundaries is inherently built in. Finally, multiple similar problems can be solved efficiently at a low individual cost per problem. This is important when, for example, the boundary condition on the surface changes but the scattering body stays the same.
•Calderon's boundary equations and Huygens' principle to compute acoustic scattering.•Scattering surface represented by CAD with patched parameterization.•High-order accurate approximations to compute Calderon's operators.•Grid-independent computational complexity at the boundary.•Non-conforming geometries on Cartesian grids preserving accuracy and stability.
The inverse problem of identifying a small unknown inclusion or cavity in an elastic medium is considered. Important applications are structural damage identification, medical imaging and geophysical ...exploration; the latter is the focus of the present investigation. It is assumed that the (isotropic but possibly heterogeneous) material properties of the medium are known, except for the presence of a small inclusion of a different material or of a small cavity. The goal is to find the location, size and shape of the inclusion or cavity. Identification is performed using full waveform inversion (FWI) and the adjoint method for the efficient calculation of the gradient of the misfit function. The identification is accomplished by considering a single unknown material‐property field. The inclusion manifests itself in the inverse solution as a local region where the unknown material property becomes significantly different than the known background property. The limiting case of cavity identification requires special treatment in the minimization process to avoid failure, as Bürchner et al. showed empirically for the scalar wave equation. Their ρ$$ \rho $$‐scaling approach, whose success is explained mathematically here for the first time, is extended to elastodynamics. The performance of the proposed method is demonstrated via numerical examples, involving two geophysical models: a homogeneous model and the heterogeneous Marmousi model, which is a standard testing model in geophysical research.
We propose a numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even for high wavenumbers. The proposed ...scheme incorporates physics informed elements from the field of dispersion-relation-preserving (DRP) schemes into a convolutional optimization machine learning algorithm. We test the proposed method and demonstrate that it performs better than classical and DRP explicit methods for a wide range of wavenumbers.
•A data-driven numerical scheme.•Useful in the setting of high wavenumbers and coarse grids.•Incorporates physics-informed elements into the problem.
Several studies have presented compact fourth order accurate finite difference approximation for the Helmholtz equation in two or three dimensions. Several of these formulae allow for the wave number ...k to be variable. Other papers have extended this further to include variable coefficients within the Laplacian which models non-homogeneous materials in electromagnetism.
Later papers considered more accurate compact sixth order methods but these were restricted to constant k. In this paper we extend these compact sixth order schemes to variable k in both two and three dimensions. Results on 2D and 3D problems with known analytic solutions verify the sixth order accuracy. We demonstrate that for large wave numbers, the second order scheme cannot produce comparable results with reasonable grid sizes.
We develop a compact fourth‐order scheme for the three‐dimensional elastic wave equation in frequency space, using the first‐order velocity‐stress formulation. The scheme is implemented numerically ...for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one‐directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second‐order scheme.
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