Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Classification of Low Dimensional Lie Super-Bialgebras

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In all the cases Poisson-Lie brackets on supergroups are found. Possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to be straightforward for all but one structures for super-E(2) group.Comment: 15 pages, LaTe

Spectral functions for medium-sized nuclei

The spectral functions for calcium and argon are constructed. It is verified that their predictions for the quasielastic electron-nucleus cross sections in the energy range ~1 GeV agree with the data. The argon spectral function is then used to obtain the quasielastic neutrino-nucleus cross section.Comment: 3 pages, 3 figures, presented at 5th International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region (NuInt07), Fermilab, USA, 30.05-3.06.200

Spectral function for 4^4He using the Chebyshev expansion in coupled-cluster theory

We compute spectral function for $^4$He by combining coupled-cluster theory with an expansion of integral transforms into Chebyshev polynomials. Our method allows to estimate the uncertainty of spectral reconstruction. The properties of the Chebyshev polynomials make the procedure numerically stable and considerably lower in memory usage than the typically employed Lanczos algorithm. We benchmark our predictions with other calculations in the literature and with electron scattering data in the quasi-elastic peak. The spectral function formalism allows one to extend ab-initio lepton-nucleus cross sections into the relativistic regime. This makes it a promising tool for modeling this process at higher energy transfers. The results we present open the door for studies of heavier nuclei, important for the neutrino oscillation programs.Comment: 12 pages, 5 figure

Truss-like Discrete Element Method Applied to Damage Process Simulation in Quasi-Brittle Materials

This paper discusses the combined application of the lattice discrete element method (LDEM) and the acoustic emission (AE) technique to analyze damage in quasi-brittle materials. These methods were used to study the damage in a concrete slab under pure-shear stress and a pre-fissured sandstone beam subjected to three-point bending. The first test was restricted to simulation results, whereas the second included experimental data. The discrete element method was used to perform the simulations for both tests, whereas the corresponding results and the information from the experiments were assessed using AE analysis tools. It was shown that the synergistic use of these two methods led to a comprehensive understanding of the two analyzed cases and offered an effective, generalizable approach for assessing damage processes in quasi-brittle materials

Damage Evolution in Quasi-Brittle Materials: Experimental Analysis by AE and Numerical Simulation

This work investigates the extension of a total-collapse prediction method to include local failures in quasi-brittle materials as they undergo damage processes. The analysis is experimentally conducted with acoustic emission data from a basalt specimen under a prescribed displacement loading test. The proposed failure index is compared with the well-established b-value to evaluate its usefulness; the simulation results are also used to further investigations. In particular, the simulations show that the parameter calculation can be carried out by indirectly estimating the elastic energy released within the system throughout the damage process, which cannot be measured directly. It is concluded that the proposed method is valid, consistently outperforming the b-value as a failure precursor throughout the experimental studies

Final State Interactions Effects in Neutrino-Nucleus Interactions

Final State Interactions effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of Formation Time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current $\pi^0$ production data in $\sim 1$ GeV neutrino flux experiments is demonstrated.Comment: 13 pages, 16 figure

Quantum E(2) groups and Lie bialgebra structures

Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group relations. There is one to one correspondence between Lie bialgebra structures on $e(2)$ and possible quantum deformations of $U(e(2))$ and $E(2)$.Comment: 8 pages, plain TEX, harvmac, to appear in J. Phys.

Analysis of Acoustic Emission Activity during Progressive Failure in Heterogeneous Materials: Experimental and Numerical Investigation

This work focuses on an experimental and numerical investigation into monitoring damage in a cube-shaped concrete specimen under compression. Experimental monitoring uses acoustic emission (AE) signals acquired by two independent measurement apparatuses, and the same damage process is numerically simulated with the lattice discrete element method (LDEM). The results from the experiment and simulation are then compared in terms of their failure load, final configurations, and the evolution of global parameters based on AE signals, such as the b-value coefficient and the natural time approach. It is concluded that the results from the AE analysis present a significant sensitivity to the characteristics of the acquisition systems. However, natural time methods are more robust for determining such differences, indicating the same general tendency for all three data sets