Temporal No-Linearity: An Alternative to Dark Energy

Mathematical compatibilities and constraints of a hypothetical 5D space-time with time referenced by two coordinates (3-2) have been revisited in detail in several recent papers. It has been prescribed from the GR the compatibility constraints of the FLRW metric in each temporal brane, to be restricted to Closed Universes, Smooth Initial Singularities, and “Open CTC”. In a first view, this leads to leaving these works considering mathematical games discarded by the Standard Candles data. However, if time would be referred by two coordinates, they would not be linearly related, and it will be mathematically stated that space-time may not be flat in any case because time-like branes geometry will never be. If so, the time scale “lived” over a two-time dimension geodesic necessarily is not constant over its linear projection on one of both coordinates. Consequently, the correlations between Redshift and Distance Modulus—Distance Ladder—may be corrected by a synchronization function (if a no-linear two-time geodesic trajectory over a “warped temporal geometry” is linearly divided into constant segments, then their projections are not linear in any case). We apply an example of time-trajectory over the time slices, matching the Standard Candle data for a Closed Universe dominated by matter (>90%) in a bulk 3-2 configuration, with open temporal branes and smooth singularity. If time can be referred by two coordinates, then there is no need of Darkness to explain astrophysical data and Universe can be closed.

A co-rotational updated Lagrangian formulation for a 2D beam element with consideration of the deformed curvature

A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.

Two Network Structure Indicators for Conventional Public Transit

The significance of network structure indicators for the planning and management of conventional public transit is widely acknowledged.In order to improve and enrich the conventional public transit assessment system,two network structure indicators are proposed.Firstly,according to the obvious defects lying in the traditional no-linear coefficient,the realistic no-linear coefficient γRNL,a modified no-linear coefficient indicator,is put forward,which takes into account the effects of barriers in a city.Secondly,to cover the gap of an indicator which can reflect the coverage homogeneity of a transit network,the length dimension LDis proposed on the basis of Fractal Theory.Finally,a case study is applied to verify the validity and practicability of the two indicators in problem diagnosis using regression analysis.The results validate that γRNLcan evaluate the detour of bus lines more reasonably than the previous no-linear coefficient because it reflects the layout of bus lines,and LDcan represent the rate of change of the network density,adding a new member to the scheme of network structure indicators for public transit.

Development of Upstream Data-Input Models to Estimate Downstream Peak Flow in Two Mediterranean River Basins of Chile

Accurate flood prediction is an important tool for risk management and hydraulic works design on a watershed scale. The objective of this study was to calibrate and validate 24 linear and non-linear regression models, using only upstream data to estimate real-time downstream flooding. Four critical downstream estimation points in the Mataquito and Maule river basins located in central Chile were selected to estimate peak flows using data from one, two, or three upstream stations. More than one thousand paper-based storm hydrographs were manually analyzed for rainfall events that occurred between 1999 and 2006, in order to determine the best models for predicting downstream peak flow. The Peak Flow Index (IQP) (defined as the quotient between upstream and downstream data) and the Transit Times (TT) between upstream and downstream points were also obtained and analyzed for each river basin. The Coefficients of Determination (R2), the Standard Error of the Estimate (SEE), and the Bland-Altman test (ACBA) were used to calibrate and validate the best selected model at each basin. Despite the high variability observed in peak flow data, the developed models were able to accurately estimate downstream peak flows using only upstream flow data.