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In this work, a modeling approach using the discrete states of molecules in an equilibrium lattice is introduced. The discrete states are considered in terms of probabilities to describe condensed phase mixtures. The molecules themselves are modeled with a dice-like geometry, providing the opportunity for up to six different energetic interaction sites per molecule. A link to real molecules is created by combining the model with a molecular sampling algorithm which determines the energetic interaction parameters for molecule clusters through a force field model. The comparison of model results with experimental data for the systems acetone – methanol and acetone – n-heptane shows that the deviations are comparable in magnitude to those of the UNIFAC model.

Gene expression profiles exhibit variability due to stochasticity in cellular processes such as transcription and translation. This variability results in probabilistic dynamics, where under the same conditions one may observe slightly or very different responses. A comprehensive analysis of the stochasticity in cellular processes is an important challenge in systems biology because biological networks are large and complex. Boolean networks are popular models for gene regulation due to their intuitive approach and relative simplicity for analysis. To incorporate the stochasticity of gene regulatory processes into the models, several stochastic extensions of the deterministic Boolean network framework have been developed. For simplicity of the presentation, we will focus on a class of stochastic models which we will refer to as Stochastic Discrete Dynamical Systems. However, the methods discussed in this chapter can also be applied in other stochastic settings such as Probabilistic Boolean Networks. This chapter will cover three important problems in stochastic discrete modeling: (1) long-term dynamical properties, (2) parameter estimation techniques, and finally, (3) optimal control methods and their limitations.

In this paper, a discrete particle method was evaluated and used in numerical simulations of low-velocity penetration in sand. Hemispherical, blunt, and ogival-nosed impactors were tested at striking velocities below 5 m/s. The tests were conducted in a dropped-object-rig where the resisting force from the sand was measured continuously during the experiments. This provided a basis for comparison for the simulations. The shapes of the force-penetration depth curves were different for the various impactors, but the ultimate penetration depths were similar in all tests that were done with the same impact velocity. Three-dimensional discrete particle simulations were generally capable of describing the behavior of the sand. However, the peak resisting force was underestimated, which led to a slight overestimation of the ultimate penetration depth. This discrete particle method has previously been evaluated at high impact velocities. The results presented in this study supplement past results and show that the method can also be used to describe the overall response of sand subjected to low-velocity penetration. © 2017. This is the authors’ accepted and refereed manuscript to the article. LOCKED until 11.1.2019 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

A reservoir geological model provides the basis for reservoir numerical simulation, development plans, and development decisions. Fracture-vug carbonate reservoirs can be of many types and have complex distributions, making reservoir modeling very difficult. Based on core, drilling, logging, and seismic data, reservoir identification methods and standards have been set up. The two-step method is used to build the geological model using multiscale and multitype data. The first step is to establish discrete geological models for cavernous, solution-vug, large-scale fracture, and small-scale fracture reservoirs. Specifically, the cavernous reservoir model is built based on well geological and sectional models, by considering high-resolution seismic-well inversion, with the constraints of the karst genetic model and using the deterministic modeling method. The solution-vug reservoir model is built by core and logging identification, with the constraint of interwell probability distribution based on seismic data, and using the multiattribute co-simulation method. Large-scale fractures are modeled based on 3-dimensional (3D) seismic interpretation and extracted seismic attributes. On the basis of single well fracture identification, the small-scale discrete fracture network model is built with the constraint of fracture development density and using the stochastic simulation method. In the second step, with four prepared types of discrete models, the parity assignment algorithm is used to integrate the four models into a fracture-vug reservoir 3D discrete distribution model, based on which, for different reservoir types, under the control of reservoir “facies”, the multiattribute model is established. This kind of model is applied for production well allocation, sidetracking, and water injection development. Field application has achieved good results.

Quantitative, predictive multiscale models show promise in accurately representing the behavior of complex biological systems across a wide range of spatial and temporal scales based on experimental and clinical data. Eventually, this allows for data integration, hypothesis generation, and prediction, and thus has the potential to significantly impact biomedical research. Biological processes can occur at the same scale as well as between scales, forming a complex system with multiple feedback and feed-forward loops. Advanced multiscale methods are therefore needed to begin to address these challenges. In this article, we discuss current advances in the development of multiscale modeling methods. We also discuss some key points in multiscale modeling-aided biomedical research.

A grand challenge in the production of materials is to design “smart” synthetic systems that can detect the presence of a “wound” or defect, but also actively re-establish the continuity and integrity of the damaged area. These defects of the material are difficult to detect and repair. Nanocontainers with self-healing materials are the new technology for smart nanocoating interfaces. In order to predict properties of final industrial products we need to understand a wide range of physics and chemistry phenomena and develop new integrated multiscale modeling to describe these complex processes. This chapter describes the solutions based on an innovative integrated modeling approach, including nano and macro scale, on a full-scale level, on real industrial problems in the automotive and aerospace industries. We used two different modeling approaches, discrete and continuum, as well as a mesoscopic bridge scale method to investigate coating substrates that contain nanoscale defects with healing agents. The discrete modeling uses the dissipative particle dynamics (DPD) method with usual three forces: repulsive, dissipative, and random forces, as well as additional forces that bound healing agents to metal substrate. The continuum modeling uses the finite element method (FEM) with different diffusivity and fluxes. The mesoscopic bridge scale method connects these two different approaches to the integrated bridge scale method. The chapter includes a case study with different concentrations of inhibitors inside the primer layer. The results of the finite element method show how much of the inhibitors in the nanocontainers are necessary to protect the metal surface that is treated with these healing agents. Further application of modeling coupled with data mining technology could encourage faster development of new active multi-level protective systems for future materials. These findings will provide guidelines for formulating nanocomposite coatings that effectively heal the surfaces through the self-assembly of the particles into the defects. Predictions for optimization of the microstructure and microstructural design based on a modeling approach can provide lower-cost novel materials and production lines.

A Unified Numerical Framework Model for Simulating Flow, Transport, and Heat Transfer in Porous and Fractured Media Yu-Shu Wu Earth Sciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA ABSTRACT It has long been recognized that a common ground exists between governing equations used for describing various flow and transport phenomena in porous media. Put another way they are all generally based on the same form of mass and/or energy conservation laws. This implies that there may exist a unified formulation and numerical scheme applicable to modeling all of these physical processes. This paper explores such a possibility and proposes a generalized framework, as well as a mathematical formulation for modeling all known transport phenomena in porous media. Based on this framework, a unified numerical approach is developed and tested using multidimensional, multiphase flow, isothermal and nonisothermal reservoir simulators. In this approach, a spatial domain of interest is discretized with an unstructured grid, then a time discretization is carried out with a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly, using Newton iteration. In addition, the fracture medium is handled using a general dual- continuum concept with continuum or discrete modeling methods. A number of applications are discussed to demonstrate that with this unified approach, modeling a particular porous- medium flow and transport process simply becomes a matter of defining a set of state variables, along with their interrelations or mutual influence. 1. INTRODUCTION Since the late 1950s, significant progress has been made in developing and applying numerical simulation techniques in petroleum engineering [3,1,12,17] and in groundwater literature [9,10]. Because of its generality and effectiveness in handling subsurface multiphase flow and transport problems, the numerical simulation technique has become the major tool used by scientists and engineers in studies of flow and transport processes within a porous medium. Numerical modeling approaches currently used for simulating multiphase flow and transport processes are generally based on methodologies developed for petroleum and geothermal reservoir simulations, as well as groundwater modeling. They involve solving fully coupled formulations describing these processes, using finite-difference or finite-element schemes with a volume-averaging approach. Continual research effort, driven by the need to develop underground natural resources and resolve subsurface contamination problems, has developed and provided many numerical modeling approaches and models for field applications. Mathematical modeling techniques

Publisher Summary Discrete modeling is known to be the most appropriate approach for simulating cracking in masonry. The fact that in many cases, masonry lies beyond the limit of application of continuum modeling, due to its heterogeneity, is outlined in this chapter. In many cases masonry lies beyond the scope of a homogeneous, continuum mechanics description. This fact and the knowledge that the joints in masonry are the weak links make a discrete strategy particularly appropriate to model cracking, shear slipping, and crushing in masonry. The chapter presents an interface material model that captures the main failure modes in masonry joints. Of particular importance is the accurate description of shearing dilatancy or uplift, as this leads to volume increases when confined, causes wedging and associated stress build-up. It is imperative to incorporate the reduction in the dilatancy coefficient with shearing displacement and normal compression, whose mechanisms smoothen the shear surface.

Publisher Summary This chapter explores the theory and the application of the arithmetic approach, which is motivated by and implemented through modern high speed digital computer technology. A conservative arithmetic formulation of the Hamiltonian approach is developed by a discrete calculus of variations by Newtonian mechanics. Other discrete models developed include classical cavity flow, conservative harmonic oscillations, discrete biological population dynamics, biological circularization and gastrulation, atmospheric streaming, ocean wave generation due to earthquakes, and conservative interactions in which the potentials are anisotropic. Radiative transfer on discrete spaces is also examined in the chapter. However, the discretization of certain integral relationships can lead to arithmetic formulations, which are conservative because they conserve discrete energy. However, this “discrete energy” is different from the energy of the continuous formulation. Modeled quantum mechanically, a three-bead-two-rod discrete classical approach, is developed for modeling macromolecules and is applied successfully to the study of polymers. Conservative computer logic and two types of sequential circuitry are already developed, while computer systems analysis theory is being developed for the discrete modeling of both natural and social systems.

Publisher Summary General-activity simulation program (GASP) is a simulation language that provides an organizational structure to build models that simulate the dynamic performance of systems on a digital computer. The organizational structure of GASP allows the variables that define system performance to be described by equations and logical conditions. System descriptions written in terms of difference or differential equations are referred to as continuous models. System descriptions written in terms of discrete changes based on logical conditions are referred to as discrete models. GASP supports the modeling of both continuous and discrete models and a combination of the two. The organizational structure of GASP specifies where and how system equations are written and the procedure for defining logical conditions that affect system variables. In GASP, an event approach is taken that specifies that discrete changes can only occur at event times. GASP can perform the time advancement functions required by a simulation model and call specific user-written routines to obtain system performance updates and system performance changes. GASP IV is used extensively for both discrete modeling, such as the study of inventory and queueing systems, and continuous modeling, such as car and aircraft dynamic analysis. GASP has been used to study steel making operations, electroplating procedures, the manufacturing of plastic tubing, and the production of corn syrup. Other areas where combined simulation is receiving attention is in crop planning and harvesting, environmental pollution analysis, ecological planning, transportation, computer and communication studies, and computer-aided manufacturing. GASP has also provided the basis for generalized network simulation languages and for a generalized crop simulation language.

A new type of modeling, called discrete modeling, is developed. The approach is consistent with and requires the power provided by digital computers. Instead of utilizing a continuum approach, the models incorporate local molecular and long range type forces into n-body simulations. Extensive computer examples are described and discussed.