The logarithm on time scales

We briefly present the well-studied exponential function on a time scale and pose the problem of finding an appropriate logarithm function on a time scale.     

Double Solutions of Impulsive Dynamic Boundary Value Problems on a Time Scale

A double fixed-point theorem is applied to obtain the existence of at least two positive solutions of a right focal boundary value problem for a second order impulsive dynamic equation on a time scale.     

XGobi: Interactive Dynamic Data Visualization in the X Window System

Abstract

XGobi is a data visualization system with state-of-the-art interactive and dynamic methods for the manipulation of views of data. It implements 2-D displays of projections of points and lines in high-dimensional spaces, as well as parallel coordinate displays and textual views thereof. Projection tools include dotplots of single variables, plots of pairs of variables, 3-D data rotations, various grand tours, and interactive projection pursuit. Views of the data can be reshaped. Points can be labeled and brushed with glyphs and colors. Lines can be edited and colored. Several XGobi processes can be run simultaneously and linked for labeling, brushing, and sharing of projections. Missing data are accommodated and their patterns can be examined; multiple imputations can be given to XGobi for rapid visual diagnostics. XGobi includes an extensive online help facility. XGobi can be integrated in other software systems, as has been done for the data analysis language S, the geographic information system (GIS) Arc View?, and the interactive multidimensional scaling program XGvis. XGobi is implemented in the X Window System? for portability as well as the ability to run across a network.     

Visualizing Marked Spatial and Origin-Destination Point Patterns With Dynamically Linked Windows

We present dynamic linked graphs for exploratory analysis of spatial marked point processes data and give an introduction to our exploratory graphical analysis tool, called Marked Point Processes Exploratory Analysis (MaPPEA). In particular, we consider point processes with events marked with another spatial event representing origin-destination data types. Using linked windows brushing, MaPPEA provides an illustration of the structure and relationships between marks and locations of point patterns. The main feature is the dynamically changing, spatially localized graphical summary of the mark distribution. Many different graphical summaries are available, and they are updated dynamically as the user moves the mouse on the map showing the events. The methods are illustrated with data on car theft location and the eventual car retrieval location and on trees’ locations and their associated marks. This article has supplementary material online.     

Patient-specific model of lung deformation using spatially dependent constitutive parameters

Breathing-induced spatially dependent lung deformation is predicted using patient-specific elastic properties with the contact–impact analysis model. The lung geometry is derived from 4D CT scan data of real patients. The spatially varying Young’s modulus for the patient is obtained from a previous study that used inverse deformation of the lung. The compact–impact analysis is implemented using the finite element method. The predicted lung deformation is compared with the results based on linear elasticity. The results are consistent with physiology, indicating large deformations near the diaphragm and smaller values at remote locations on the lobe. The effect of non-linearity of elastic property is most significant at the remote locations where the diaphragm-induced deformation is significantly attenuated.     

Optimal vehicle suspension characteristics for increased structural fatigue life

Heavy off-road vehicle suspension systems face unique challenges. The ride comfort versus handling compromise in these vehicles has been frequently investigated using mathematical optimisation. Further challenges exist due to the large variations in vehicle sprung mass. A passive suspension system can only provide optimal isolation at a single payload. The designer of such a suspension system must therefore make a compromise between designing for a fully-laden or unladen payload state. This work deals with suspension optimisation for vehicle structural life. The paper mainly addresses two questions: (1) What are the suspension characteristics required to ensure optimal isolation of the vehicle structure from road loads? and (2) If such optimal suspension characteristics can be found, how sensitive are they to changes in vehicle payload? The study aims to answer these questions by examining a Land Rover Defender 110 as test vehicle. An experimentally validated non-linear seven degree-of-freedom mathematical model of the test vehicle is constructed for the use in sensitivity studies. Mathematical optimisation is performed using the model in order to find the suspension characteristics for optimal structural life for the vehicle under consideration. Sensitivity studies are conducted to determine the robustness of the optimal characteristics and their sensitivity to vehicle payload variation. Recommendations are made for suspension characteristic selection for optimal structural life.     

On the response of rubbers at high strain rates—III. Effect of hysteresis

In this series of papers, we examine the propagation of waves of finite deformation in rubbers through experiments and analysis; in the present paper, Part III, the effect of hysteretic material behavior on the free retraction of prestretched rubber is considered. A rubber strip stretched to many times its initial length is released at one end and the resulting unloading is examined. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Simple waves as well as shock waves are observed in these unloading experiments. The measurements are modeled using a power-law model of the material behavior. The hysteretic material response and the formation of shocks are characterized.     

水平层状岩体边坡动力响应中的结构面效应研究

根据应力波传播原理分析了水平层状岩体边坡中应力波传播特征,建立了应力波在该类边坡中传播的模型。利用离散元软件UDEC分析了不同频率垂向压缩应力波作用下边坡动力响应规律中的结构面效应。结果表明:边坡中的水平层面对坡顶的动力响应有明显影响。低频应力波作用下,水平层状岩体边坡坡顶的垂向峰值速度较均质坡体相同部位的峰值速度的增加值随坡高增加而增大。较高频率应力波作用时,边坡顶部靠近坡面的垂向峰值速度高于无结构面边坡相同部位的峰值速度,远离坡面时情况相反; 坡顶垂向峰值速度大小呈周期性变化,输入应力波频率越大该变化频次越高。研究结果将有助于进一步揭示各种不同岩体结构类型边坡在动力荷载作用下损伤机理及破坏模式。     

GPS RTK技术用于滑坡动态实时变形监测的研究

为了研究GPS RTK技术用于滑坡动态变形监测的精度和可靠性,本文结合某类滑坡的大型物理模型试验,在滑坡体上布设了若干监测点,并用GPS RTK技术、全站仪三维测量技术和GPS单历元定位技术实时跟踪监测了该滑坡在自然状态下从稳定到产生破坏的全部过程。通过对监测数据的处理和分析,获得了RTK技术用于滑坡变形监测的可靠性和精度等技术参数,即在基准站和流动站同步观测到的卫星数在7颗以上且RTK系统的数据链能够正常工作的情况下,RTK测量的平面和高程精度就能分别控制在15mm和20mm以内。研究结果表明,RTK技术在一定条件下完全可用于滑坡灾害的动态实时变形监测。     

Dynamics of dual pontoon floating structure for cage aquaculture in a two-dimensional numerical wave tank

The trend of using floating structures with cage aquaculture is becoming more popular in the open sea. The purpose of this paper is to investigate the dynamic properties of a dual pontoon floating structure (DPFS) when attached to a fish net by using physical and numerical models. A two-dimensional (2-D) fully nonlinear numerical wave tank (NWT), based on the boundary element method (BEM), is developed to calculate the wave forces on the DPFS. The wave forces on a fish net system are then evaluated using a modified Morison equation. The comparisons of dynamic behaviors between numerical simulations and experimental measurements on the DPFS show good agreement. Results also display that a fish net system causes the resonant response of body motions and mooring forces to be slightly lower due to the net's damping effect. Finally, for designing the rearing space of cage aquaculture, the influences which net depth and net width have on the DPFS dynamic responses are also presented in this paper.