Numerical Modeling of Shock-Induced Damage for Granite under Dynamic Loading

Johnson-Holmquist constitutive model for brittle materials, coupled with a crack softening model, is used to describe the deviatoric and tensile crack propagation beneath impact crater in granite. Model constants are determined either directly from static uniaxial strain loading experiments, or indirectly from numerical adjustment. Constants are put into AUTODYN-2D from Century Dynamics to simulate the shock-induced damage in granite targets impacted by projectiles at different velocities. The agreement between experimental data and simulated results is encouraging. Instead of traditional grid-based methods, a Smooth Particle Hydrodynamics solver is used to define damaged regions in brittle media

A slave mode expansion for obtaining ab-initio interatomic potentials

Here we propose a new approach for performing a Taylor series expansion of the first-principles computed energy of a crystal as a function of the nuclear displacements. We enlarge the dimensionality of the existing displacement space and form new variables (ie. slave modes) which transform like irreducible representations of the space group and satisfy homogeneity of free space. Standard group theoretical techniques can then be applied to deduce the non-zero expansion coefficients a priori. At a given order, the translation group can be used to contract the products and eliminate terms which are not linearly independent, resulting in a final set of slave mode products. While the expansion coefficients can be computed in a variety of ways, we demonstrate that finite difference is effective up to fourth order. We demonstrate the power of the method in the strongly anharmonic system PbTe. All anharmonic terms within an octahedron are computed up to fourth order. A proper unitary transformation demonstrates that the vast majority of the anharmonicity can be attributed to just two terms, indicating that a minimal model of phonon interactions is achievable. The ability to straightforwardly generate polynomial potentials will allow precise simulations at length and time scales which were previously unrealizable

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Automatic generation of simplified weakest preconditions for integrity constraint verification

Given a constraint $c$ assumed to hold on a database $B$ and an update $u$ to be performed on $B$, we address the following question: will $c$ still hold after $u$ is performed? When $B$ is a relational database, we define a confluent terminating rewriting system which, starting from $c$ and $u$, automatically derives a simplified weakest precondition $wp(c,u)$ such that, whenever $B$ satisfies $wp(c,u)$, then the updated database $u(B)$ will satisfy $c$, and moreover $wp(c,u)$ is simplified in the sense that its computation depends only upon the instances of $c$ that may be modified by the update. We then extend the definition of a simplified $wp(c,u)$ to the case of deductive databases; we prove it using fixpoint induction

Design of ternary signals for MIMO identification in the presence of noise and nonlinear distortion

A new approach to designing sets of ternary periodic signals with different periods for multi-input multi-output system identification is described. The signals are pseudo-random signals with uniform nonzero harmonics, generated from Galois field GF(q), where q is a prime or a power of a prime. The signals are designed to be uncorrelated, so that effects of different inputs can be easily decoupled. However, correlated harmonics can be included if necessary, for applications in the identification of ill-conditioned processes. A design table is given for q les 31. An example is presented for the design of five uncorrelated signals with a common period N = 168 . Three of these signals are applied to identify the transfer function matrix as well as the singular values of a simulated distillation column. Results obtained are compared with those achieved using two alternative methods

The Cultural Reconstruction of Taboo Under Mama Uluk’s Leadership in Kampong Dukuh, a Sundanese Traditional Hamlet in Garut Regency West Java Indonesia

 Kampung Dukuh yang terletak di Desa Ciroyom, Kecamatan Cikelet Kabupaten Garut merupa- kan salah satu kampung adat yang ada di Jawa Barat yang memiliki banyak keunikan. Pamali sebagai salah satu sistem pengetahuan masyarakat adat Sunda. Pamali masih dipertahankan dalam kebu- dayaan masyarakat adat Kampung Dukuh. Walaupun tidak ada resiko yang tertulis ketika melaku- kan hal yang melanggar pamali, namun masyarakat kampung adat masih merasa takut durhaka atau dosa jika pamali tidak dilaksanakan dalam keseharian hidupnya. Sekaitan dengan hal ini, penelitian ini bertujuan menggambarkan berbagai larangan atau pamali yang telah direkonstruksi di masa kepemimpinan Mama Uluk di kampung Adat Dukuh Kabupaten Garut. Penelitian ini mengguna- kan metode kualitatif dengan teknik pengumpulan data wawancara dan pengamatan langsung. Hasil penelitian ini menjelaskan cara penyampaian larangan pada waktu yang telah ditentukan dan jenis larangan atau pamali atau pamali yang dipelihara dan terus diwariskankan secara turun temurun sampai saat ini dalam kehidupan sehari-hari seperti larangan di Makom Syech Jalil, Hutan Lindung dan bagaimana ketua adat (mama uluk) dalam kepemimpinannya merekonstruksi budaya tersebut dalam kehidupan keseharian mereka di kampung Dukuh kabupaten Garut.