The second order nonlinear conductance of a two-dimensional mesoscopic conductor

We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating the various partial density of states, the sensitivity and the characteristic potential. Interesting spatial structure of these quantities are revealed. We present detailed results concerning the crossover behavior of the second order nonlinear conductance when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of interests such as the gauge invariance are also discussed.Comment: LaTe

Response of rigid piles during passive dragging

This paper develops a three-layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length ps of the soil movement. They are repeated for a series of linearly increasing ps (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free-head and capped piles. The solutions are presented in non-dimensional charts and elaborated through three examples. The study reveals the following: On-pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p-multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α=0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α=0.33-0.5 and 0.8-1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α=0.5-0.72 for moving clay under embankment loading. Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests. The normalised rotational stiffness is equal to 0.1-0.15 for the capped piles, which increases the pile displacement with depth. The three-layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design

Interaction homotopy and interaction homology

Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces. In this work, we present an algebraic topology framework to explore interactions between spaces. We introduce the concept of interaction spaces and investigate their homotopy, singular homology, and simplicial homology. Furthermore, we demonstrate that interaction singular homology serves as an invariant under interaction homotopy. We believe that the proposed framework holds potential for practical applications

Response of piles subjected to progressive soil movement

Model tests were conducted to investigate the behavior of vertically loaded, free head piles undergoing lateral soil movement using an experimental apparatus developed in house. This paper presents ten new tests on an instrumented model pile in dry sand, which provide the profiles of bending moment, shear force and pile deflection along the pile, the development of maximum bending moment Mmax, maximum shear force Tmax, and pile deflection y0 at the ground surface with soil movement. The tests reveal the effects of axial load P (at pile head), the distance between the tested pile and source of free soil movement Sb, sliding depths, and angle of soil movement (via loading angle) on the pile response. For instance, the axial loading P leads to extra bending moment and deflection in the passive pile; the Mmax reduces with increase in Sb; and the Mmax is proportional to the angle of soil movement. The elastic solution by Guo and Qin [Guo, W. D., Qin, H. Y., 2010, Thrust and Bending Moment of Rigid Piles Subjected to Moving Soil, Can. Geotech. J., Vol. 47, No. 2, pp. 180-196] was used to predict the development of Mmax and Tmax observed in the current tests, a boundary element analysis, and an in situ pile test, respectively. It provides satisfactory predictions for all cases against the measured data

Response of 20 laterally loaded piles in sand

Closed-form solutions and their associated spreadsheet program (GASLFP) were developed by the first author for laterally loaded free- head piles in elastic-plastic media. The solutions show behaviour of a laterally loaded pile is dominated by net limiting force per unit length (LFP) fully mobilised along the pile to a depth called slip depth. They are characterised by three parameters of Ng, α o and n (to describe the LFP) and the soil shear modulus (Gs). Conversely, these parameters may be deduced by matching the predicted with measured response. To facilitate practical design, in this paper, the input values of Ng, α o, n and Gs were deduced in light of measured response of 20 piles tested in sand. The result allows effect of pile types, installation action, and dry or submerged sand to be clarified. In addition, using analogy to pipeline-soil interaction, a new alternative expression described by the parameters kp, α o and n is proposed to construct the LFP. The use of the previous parameter Ng and the new kp is discussed at length. Critical responses for typical deflection levels have also been provided. This back-analysis is elaborated via three typical cases

Structure nonlinearity and response of laterally loaded piles

In light of a generic limiting force profile (LFP), closed·form solutions for laterally loaded free- and fixed- head piles in elastic-plastic media have been developed, and implemented by the first author into a spreadsheet program called GASLFP. The solutions offer an expeditious and sufficiently accurate prediction of response of lateral piles. Conversely, they allow input parameters to be deduced using measured pile response, as has been conducted for over 70 test (elastic) piles to date. Nevertheless. structure nonlinearity of pile body is an important issue at a large deflection. In this paper, a semi·empirical approach is established to capture pile response owing to structural nonlinearity. Expressions were provided for gaining cracking moment Mcr, flexural rigidity of cracked cross section Eplp. and ultimate bending moment Mult Against measured response of two laterally loaded single piles, back-estimation indicates that (1) the parameters for elastic piles are quite consistent with the previous findings for piles in sand and clay, (2) The proposed variations of Mcr, Eplp and Mult, for nonlinear piles provide good prediction of the pile response against measured data and (3) the modulus of rupture kr of 16.7 (clay) and 33.0(sand) are close 10 those adopted for structural beams, although a very high kr of 62.7 (thus resulting in higher Mcr, ) for a pi le in sand was deduced (shown elsewhere). The use of the kr for beams would render pile deflections of the later pile to be significantly overestimated. The conclusions may be incorporated into design of laterally loaded piles