Slow cracklike dynamics at the onset of frictional sliding

We propose a friction model which incorporates interfacial elasticity and whose steady state sliding relation is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches. In 1D and upon the application of sideway loading, we demonstrate the existence of transient cracklike fronts whose velocity is independent of sound speed, which we propose to be analogous to the recently discovered slow interfacial rupture fronts. Most importantly, the properties of these transient inhomogeneously loaded fronts are determined by steady state front solutions at the minimum of the sliding friction law, implying the existence of a new velocity scale and a "forbidden gap" of rupture velocities. We highlight the role played by interfacial elasticity and supplement our analysis with 2D scaling arguments.     

Rigidity and the Lower Bound Theorem for Doubly Cohen–Macaulay Complexes

We prove that for d≥3, the 1-skeleton of any (d?1)-dimensional doubly Cohen–Macaulay (abbreviated 2-CM) complex is generically d-rigid. This implies that Barnette’s lower bound inequalities for boundary complexes of simplicial polytopes (Barnette, D. Isr. J. Math. 10:121–125, 1971; Barnette, D. Pac. J. Math. 46:349–354, 1973) hold for every 2-CM complex of dimension ≥2 (see Kalai, G. Invent. Math. 88:125–151, 1987). Moreover, the initial part (g ₀,g ₁,g ₂) of the g-vector of a 2-CM complex (of dimension ≥3) is an M-sequence. It was conjectured by Björner and Swartz (J. Comb. Theory Ser. A 113:1305–1320, 2006) that the entire g-vector of a 2-CM complex is an M-sequence.     

'Genome order index' should not be used for defining compositional constraints in nucleotide sequences

A “genome order index,” defined as S = a² + c² + t² + g², where a, c, t, and g are the nucleotide frequencies of A, C, T, and G, respectively, was used to suggest that there exist genome-specific constraints on nucleotide composition. We show that the “evidence” for constraint, S < 1/3, is in fact a mathematical property that is always true regardless of data. Moreover, we show that S is strictly equivalent to and derivable from the Shannon H-function and has no advantage over it.     

Bending MeV proton beams by means of a glass capillary tube

We study in a preliminary and simplified manner the possibility of bending submicron beams by means of glass capillary tubes. We show that protons of 20 MeV can be guided within a 10 nm diameter helical tube, for a distance of 0.55 cm, with the beam bending in the transverse direction by 0.16 mm. Although these distances are not large and the angle of incidence of the beam is very small, applications of great interest warrant further investigation of this study.     

The length of closed geodesics on random Riemann surfaces

Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers’ theorem gives a global bound on the length of the first 3g ? 3 geodesics. We use Brooks and Makover’s construction of random Riemann surfaces to investigate the distribution of short (< log(g)) geodesics on random Riemann surfaces. We calculate the expected value of the shortest geodesic, and show that if one orders geodesics by length \({\gamma_1\le \gamma_2\le \cdots \le \gamma_i ,\ldots}\), then for fixed k, if one allows the genus to go to infinity, the length of γ _k is independent of the genus.     

Geodesics and almost geodesic cycles in random regular graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d_G(u, v) is at least d_C(u, v)?e(n). Let ω(n) be any function tending to infinity with n. We consider a random d‐regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n) = log_d?1log_d?1n+ ω(n) and |C| = 2log_d?1n+ O(ω(n)). Along the way, we obtain results on near‐geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. Copyright © 2010 John Wiley & Sons, Ltd. J Graph Theory 66:115‐136, 2011     

New imine compounds and their copper complexes: synthesis,characterization and comparative investigations of morphologic,mesomorphic, thermotropic,thermo-optical and thermodynamical properties

Investigations of the morphologic, mesomorphic, thermotropic, thermo-optical and thermodynamical properties of new imine compounds and their copper complexes, synthesized by our group, have been carried out. Temperature transformations of typical textures for mesophases, taking place in imine compounds and copper complexes, and the peculiarities of the biphasic regions at the direct and reverse mesophase–isotropic liquid and isotropic liquid–mesophase phase transitions have been investigated.