The principle of least action and the geometric basis of D-branes

We analyze thoroughly the boundary conditions allowed in classical non-linear sigma models and derive from first principle the corresponding geometric objects, i.e. D-branes. In addition to giving classical D-branes an intrinsic and geometric foundation, D-branes in nontrivial H flux and D-branes embedded within D-branes are precisely defined. A well known topological condition on D-branes is replaced

Proximity and anomalous field-effect characteristics in double-wall carbon nanotubes

Proximity effect on field-effect characteristic (FEC) in double-wall carbon nanotubes (DWCNTs) is investigated. In a semiconductor-metal (S-M) DWCNT, the penetration of electron wavefunctions in the metallic shell to the semiconducting shell turns the original semiconducting tube into a metal with a non-zero local density of states at the Fermi level. By using a two-band tight-binding model on a ladder of two legs, it is demonstrated that anomalous FEC observed in so-called S-M type DWCNTs can be fully understood by the proximity effect of metallic phases.Comment: 4 pages, 4 figure

Random and free observables saturate the Tsirelson bound for CHSH inequality

Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation

Some integral inequalities on time scales

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.Comment: 8 page

Average transmission probability of a random stack

The transmission through a stack of identical slabs that are separated by gaps with random widths is usually treated by calculating the average of the logarithm of the transmission probability. We show how to calculate the average of the transmission probability itself with the aid of a recurrence relation and derive analytical upper and lower bounds. The upper bound, when used as an approximation for the transmission probability, is unreasonably good and we conjecture that it is asymptotically exact.Comment: 10 pages, 6 figure

Comparison of anisotropic rate-dependent models for modelling consolidation of soft clays

Two recently proposed anisotropic rate-dependent models are used to simulate the consolidation behaviour of two soft natural clays: Murro clay and Haarajoki clay. The rate-dependent constitutive models include the EVP-SCLAY1 model and the Anisotropic Creep Model (ACM). The two models are identical in the way the initial anisotropy and the evolution of anisotropy are simulated, but differ in the way the rate-effects are taken into consideration. The models are compared first at the element level against laboratory data and then at boundary value level against measured field data from instrumented embankments on Murro and Haarajoki clays. The numerical simulations suggest that at element the EVP-SCLAY1 model is able to give a better representation of the clay response under oedometric loading than ACM, when the input parameters are defined objectively. However, at boundary value level the issue is not as straightforward, and the appropriateness of the constitutive model may depend heavily on the in situ overconsolidation ratio (OCR)