Efficient Simulation of Elastic Waves Propagation in Anisotropic Media

The paper deals with finite–difference (f-d) approach to simulation of elastic waves' propagation in anisotropic elastic media with general symmetry. Any implementation of this approach claims resolution of two key problems:

• construction of an effective f-d scheme itself; we propose to use the Lebedev's scheme (LS) being a natural generalization of Virieux staggered grid scheme (VS) widely used for isotropy; we prove that LS possesses better dispersion properties in comparison with well known Rotated Staggered Grids Scheme (RSGS).
• stable domain distension. The Perfectly Matched Layers(PML) useful for isotropic problems can be unstable in the case of anisotropy. Lebedev scheme allows one to use Optimal Grids (OG) which gives a possibility to implement efficient and low cost domain distension.

(© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experiment as an aid to structural seismic design

An overview of the available methods for simulating or estimating seismic effects on buildings and similar structural models as well as onin situ structures is given. The motivation is provided by noting severe damage even to modern buildings in the wake of strong earthquakes. The complex inelastic behavior of members and connections must be determined experimentally. Such information is essential for developing mathematical design models. Four available test methods, with examples, are described. One of these is the pseudo-static method of testing where a specimen is subjected to apriori selected cyclic forces or displacements. The second, the pseudo-dynamic method of testing, combines the above procedure with an on-line computer. In employing this approach it is possible to apply a random sequence of displacements corresponding to a previously recorded earthquake while taking into account the continuously changing structural stiffness. The third procedure employs a shaking table programmed to apply scaled earth-quake input based on available accelerograms. The fourth, a nondestructive method of testing of actual structures, consists of recording and interpreting ambient or forced vibrations in the elastic regime.     

On the peripheral spectrum of positive elements

Let A be an ordered Banach algebra with a unit \(\mathbf{e}\) and a cone \(A^+\). An element p of A is said to be an order idempotent if \(p^2 = p\) and \(0 \le p\le \mathbf{e}\). An element \(a\in A^+\) is said to be irreducible if the relation \((\mathbf{e}-p)ap = 0\), where p is an order idempotent, implies \(p = 0\) or \(p = \mathbf{e}\). For an arbitrary element a of A the peripheral spectrum \(\sigma _\mathrm{per}(a)\) of a is the set \(\sigma _\mathrm{per}(a) = \{\lambda \in \sigma (a):|\lambda | = r(a)\}\), where \(\sigma (a)\) is the spectrum of a and r(a) is the spectral radius of a. We investigate properties of the peripheral spectrum of an irreducible element a. Conditions under which \(\sigma _\mathrm{per}(a)\) contains or coincides with \(r(a)H_m\), where \(H_m\) is the group of all \(m^\mathrm{th}\) roots of unity, and the spectrum \(\sigma (a)\) is invariant under rotation by the angle \(\frac{2\pi }{m}\) for some \(m\in {\mathbb N}\), are given. The correlation between these results and the existence of a cyclic form of a is considered. The conditions under which a is primitive, i.e., \(\sigma _\mathrm{per}(a) = \{r(a)\}\), are studied. The necessary assumptions on the algebra A which imply the validity of these results, are discussed. In particular, the Lotz–Schaefer axiom is introduced and finite-rank elements of A are defined. Other approaches to the notions of irreducibility and primitivity are discussed. Conditions under which the inequalities \(0 \le b < a\) imply \(r(b) < r(a)\) are studied. The closedness of the center \(A_\mathbf{e}\), i.e., of the order ideal generated by \(\mathbf{e}\) in A, is proved.     

Four-regular graphs with rigid vertices associated to DNA recombination

Genome rearrangement and homological recombination processes have been modeled by Angeleska et al. [A. Angeleska, N. Jonoska, M. Saito, DNA recombinations through assembly graphs, Discrete Appl. Math. 157 (2009) 3020–3037] as 4-regular spacial graphs with rigid vertices, called assembly graphs. These graphs can also be represented by double occurrence words called assembly words. The rearranged DNA segments are modeled by certain types of paths in the assembly graphs called polygonal paths. The minimum number of polygonal paths visiting all vertices in a graph is called an assembly number for the graph.In this paper, we give formulas for counting certain types of assembly graphs and assembly words. Some of these formulas produce sequences not previously reported at the Online Encyclopedia of Integer Sequences (http://oeis.org). We provide a sharp upper bound for the number of polygonal paths in Hamiltonian sets of polygonal paths, and present a family of graphs that achieves this bound. We investigate changes in the assembly numbers as a result of graph compositions. Finally, we introduce a polynomial invariant for assembly graphs and show properties of this invariant.     

Non-eikonal effects in high-energy scattering IV. Inelastic scattering

We calculate amplitudes of inelastically scattered high-energy projectiles. For the example of scattering on ¹²C (T_p = 1 GeV) we demonstrate sizeable non-eikonal corrections in diffraction extrema even for relatively small q². At least part of the anomaly in the 3-distribution may be due to these non-eikonal effects.     

Delocalization in the anderson model due to a local measurement

We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model, and we discuss the experimental consequences.