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"This book explains the hypoplastic modelling framework. It is divided into two parts, the first of which is devoted to principles of hypoplasticity. First, the basic features of soils mechanical behaviour are introduced, namely non-linearity and asymptotic properties. These features are then incorporated into simple one-dimensional hypoplastic equations for compression and shear. Subsequently, a hypoplastic equivalent of the Modified Cam-Clay model is developed in 2D space using stress and strain invariants to demonstrate key similarities and differences between elasto-plastic and hypoplastic formulations. Lastly, the mathematical structure of hypoplastic models is explained by tracing their historical development, from the early trial-and-error models to more recent approaches. In turn, Part II introduces specific hypoplastic models for soils. First, two reference models for sand and clay are defined. After summarising their mathematical formulations, calibration procedures are described and discussed. Subsequently, more advanced modelling approaches are covered: the intergranular strain concept incorporating the effects of small strain stiffness and cyclic loading, viscohypoplasticity for predicting rate effects, soil structure to represent structured and bonded materials and soil anisotropy. The book concludes with a description of partial saturation and thermal effects: topics that are increasingly important to the disciplines of energy and environmental geotechnics.Selecting a constitutive model and its parameters is often the most important and yet challenging part of any numerical analysis in geotechnical engineering. Hypoplasticity involves a specific class of soil constitutive models, which are described in detail here. The book offers an essential resource, both for model users who need a more advanced model for their geotechnical calculations and are mainly interested in parameter calibration procedures, and for model developers who are seeking a comprehensive understanding of the mathematical structure of hypoplasticity."

"Themes that are highlighted include :

• the role of language : the models developed for engineering design have resulted in new ways of talking about technological systems
• communities of practice : related to the previous point, particular engineering communities have particular ways of sharing and developing knowledge
• graphical (re)presentation : engineers have developed many ways of reducing quite complex mathematical models to more simple representations
• reification : highly abstract mathematical models are turned into ‘objects’ that can be manipulated almost like components of a physical system
• machines : not only the currently ubiquitous digital computer, but also older analogue devices, slide rules, physical models, wind tunnels and other small-scale simulators, as well as mechanical, electrical and electronic analogue computers
• mathematics and modelling as a bridging tool between disciplines

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"Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling."

"Terorisme sebagai fenomena sosial yang terus mengalami perubahan seiring jalannya waktu, merupakan masalah yang memerlukan penyelesaian dengan menggunakan berbagai pendekatan. Salah satu pendekatan yang dilakukan dalam penelitian ini adalah pendekatan matematika berupa pemodelan. Suatu model matematika penyebaran dan penangan terorisme ini dilakukan bertujuan untuk memberikan gambaran atau informasi mengenai bagaimana dinamika penyebaran dan penangan terorisme tersebut berlangsung. Model matematika penyebaran dan penanganan terorisme ini dirancang dengan menggunakan asumsi-asumsi dan pengelompokan kelas, yaitu kelas umum atau general (G), kelas bibit atau calon fanatik atau seed (S), kelas teroris atau fanatik aktif atau active fanatic (FA), dan kelas teroris yang sedang mendapatkan penanganan di lapas atau fanatic in prison (FP). Hasil penelitian yang dilakukan secara analisis menunjukan bahwa sistem tersebut memiliki titik ekuilibrium bebas terorisme E0 = (1;0;0;0) yang stabil asimtotis lokal pada semua kondisi dan titik ekuilibrium terorisme E = (g; s;va ;vp) yang stabil asimtotis lokal pada kondisi tertentu. Kesimpulan ini juga ditunjang oleh hasil dan simulasi numerik yang dilakukan.

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Terrorism as a social phenomenon that continues to change, is a problem that requires solution using a variety of approaches. One approach taken in this study is a mathematical modeling approach. A mathematical model of the transmission and treatment of terrorism carried out aims to provide information about how the dynamics of transmission and treatment of terrorism took place in the society. A mathematical model of transmission and treatment of terrorism is designed using assumptions and class groupings, namely the general class (G), class of seed (S), class of active terrorists or fanatics (FA), and class of terrorists who are getting treatment in prisons (FP). The results of the analysis show that the system has the terrorism-free equilibrium point E0 = (1;0;0;0) which is locally asymptotically stable point in all conditions, and the terrorism equilibrium point E = (g; s;v a ;v p) which is locally asymptotically stable under certain conditions. This conclusion is supported by the results of numerical simulations are performed."

"Ketidaktepatan kedatangan kereta menyebabkan terganggunya jadwal yang sudah disusun. Sehingga diperlukan pengalokasian ulang kereta ke peron guna mengatasi gangguan tersebut. Dalam pengalokasian kereta ke peron, terdapat tiga hal yang perlu diminimumkan, yaitu lamanya waktu berhenti kereta pada area luar stasiun, penempatan kereta ke peron dengan kondisi yang kurang baik, dan perpindahan peron bagi kereta yang akan tiba di menit-menit akhir. Pada skripsi ini akan dibentuk model pemrograman linier bilangan bulat campuran untuk meminimumkan ketiga hal di atas dan akan diselesaikan dengan menggunakan metode branch and bound. Hasil optimal dari model pemrograman linier bilangan bulat campuran tersebut adalah keputusan terhadap peron yang akan ditempati oleh kereta yang tiba pada area luar stasiun dan kapan seharusnya kereta berangkat dari area luar stasiun menuju peron.

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Inaccuracy of train arrival causes disturbance of the schedule that has been arranged. So the reallocation of train to platform needed in order to solve that disturbance. In allocating the train to platform, there are three things that should minimized, that is duration of the train stops outside the station, placement of the train to the poorly platform, and last minute reassignment of train to platform.

In this paper will be formed the model of mixed integer linear programming to minimize three points above and will be solved by using the branch and bound method. The optimal results of the mixed integer linear programming model is decisions of the platform that will be occupied by a train which arrived outside the station and when the train should leave from outside the station to the platform."