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Making use of experimental data for bias extension, shearing, and point-load tests in large deformation regime for rectangular and square bi-pantographic specimens, we perform a numerical identification to fit the a priori parameters of a planar discrete spring model. The main objective of the work is to develop an automatized optimization process based on the Nelder–Mead simplex algorithm for identifying the constitutive parameters of discrete modeling of bi-pantographic structures, as well as assessing its descriptiveness and predictive capacity. The analysis allows to conclude that there exists a single set of parameters for the adopted discrete modeling such that it is descriptive and predictive for several different tests and for a wide range of deformations.

With the rapid development of the Internet, the amount of data increases sharply. In this network age, data have been generated, such as multimedia, social networks, and search records. Due to the generation of data, complex system discrete model technology is also widely used in all walks of life. Multimedia learning is a popular teaching mode in the world. Through the discrete model technology of the complex system, this paper deeply studies the impact of multimedia input on college students’ English ability. Because the modeling and sampling of complex systems are abstract and not fixed, approximation and control methods are adopted in discrete time, which greatly improves the reliability of the final research results. Compared with the original discrete modeling technology, this paper adds data sampling compression and assimilation technology on the basis of the original discrete modeling technology of the complex system. The results show that, by adding the technical application of controllable and observable systems, the discrete model of the whole complex system can reduce the error of the final output data. At the same time, this paper compresses and simplifies the data nodes at the microlevel. Macroscopically, it reduces the scale, especially the number of node data compression. The final result also realizes the data scale and greatly shortens the calculation time. This study has greatly improved the accuracy of the impact of multimedia on Chinese college students’ English ability in practical application.

An innovative method for modeling a complicated geotechnical problem combining the coarse and fine zones is to use the hybrid methods. The granular zone of a geotechnical system can be modeled by the discrete element method (DEM) and the fine zone by continuum-based methods. The advantage of this approach is the use of the capabilities of both methods. In the present research, by combining DEM and finite difference method (FDM), a 2D numerical laboratory framework is constructed. Simulation of a vertically loaded stone column installed in clay was chosen to examine the capabilities of the present approach. The contrast between the stone column aggregates, which usually consist of crushed stone with distinct behavior, and the host medium, which is clay with continuum behavior, makes the stone column suitable for this kind of coupled simulation. The coupled numerical model is validated by comparing the load–settlement response of the numerical model and the reported experimental results. Afterward, the failure mechanism of the stone column is evaluated. The column bulging was captured properly, and it was found that in addition to the bulging, the contraction occurs at the upper portion of the column. It was also found that at the early stages of loading, the compaction occurs in the column. However, at later stages of loading, the bulging will happen. Furthermore, the results showed that bulging decreases the internal stresses of the column. All of these achievements were obtained by micro and macro investigations. The obtained results indicate that the coupled DEM–FDM method is a robust approach to simulate the behavior of some geotechnical problems.

In this work, an including the switched evolution process discrete model of a DC–DC converter feeding a switched constant power load is proposed based on the Poincare mapping rule and matrix exponent method. Numerical simulations of the bifurcation scheme based on the proposed discrete model reveal the period-adding bifurcation structures of the system as multiple devils’ staircases. Further, the calculation of the stable regions of the multiple-period orbits of the nested period-adding bifurcation structures are illustrated. The experimental results verify the validity of the discrete model and analytical accuracy of the period-adding bifurcation characteristics of the system. The proposed model solves the difficulties associated with discrete modeling for power electronic nonlinear switched systems. The introduction of the switched evolution process in the proposed discrete model provides a specific mathematical model for studying the influence of the switched evolution process on the dynamics of power electronic nonlinear switched systems. This study is expected to be a foundation for the theory and further research on such power electronic nonlinear switched systems.

The discrete element method (DEM) is a general discrete modeling technique traditionally used to model granular material and discontinuous phenomena such as fracture and fragmentation of solids. We investigate the efficacy of DEM to model deformable elastic continua, cantilever beams in particular, and describe their mechanical behavior under loading. Of distinct interest is the ability of DEM to capture geometric nonlinearity in their large-displacement response. A case study is presented to demonstrate the utility of this approach in particle–structure problems that involve large structural displacements. We simulated an array of these cantilever beams in large elastic oscillations amidst a particulate environment, modeled using DEM. Mobile particles encounter the deflecting beams in their paths and can be redirected for capture based on net forces and moments that act on them. The dynamics of the ensuing particle–structure interactions is simulated, and factors regulating the efficiency of particle capture are examined.

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582-1586, 1996) and Perelson and Nelson (SIAM Rev 41:3-44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. One of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

With the growing number of cars in the world, there are corresponding problems that society needs to solve. In metropolises, intersections are generators of traffic jams and traffic accidents. The introduction of unmanned autonomous vehicles is one of the solutions to increase safety on the road. To avoid traffic jams, it is necessary to optimize road traffic. This article proposes a model of the intersection management system. The system aims to organize a conflict-free, safe, and optimal traversal of AVs within the framework of the intelligent transport system of a smart city. The model assumes that at each intersection there are objects of transport infrastructure responsible for building routes at the intersection. To assess the feasibility of the presented model, the authors developed a custom software simulator of a network of urban intersections and conducted experiments. Based on simulation experiments, the use of the developed model can significantly reduce the time spent by unmanned vehicles to overcome the intersection compared to traffic lights.

Simulations of neural activity are commonly based on differential equations. We address the question what can be achieved with a simplified discrete model. The proposed model resembles artificial neural networks enriched with additional biologically inspired features. A neuron has several states, and the state transitions follow endogenous patterns which roughly correspond to firing behavior observed in biological neurons: oscillatory, tonic, plateauing, etc. Neural interactions consist of two components: synaptic connections and extrasynaptic emission of neurotransmitters. The dynamics is asynchronous and event-based; the events correspond to the changes in neurons activity. This model is innovative in introducing discrete framework for modeling neurotransmitter interactions which play the important role in neuromodulation. We simulate rhythmic activity of small neural ensembles like central pattern generators (CPG). The modeled examples include: the biphasic rhythm generated by the half-center mechanism with the post-inhibitory rebound (like the leech heartbeat CPG), the triphasic rhythm (like in pond snail feeding CPG) and the pattern switch in the system of several neurons (like the switch between ingestion and egestion in Aplysia feeding CPG). The asynchronous dynamics allows to obtain multi-phasic rhythms with phase durations close to their biological prototypes. The perspectives of discrete modeling in biological research are discussed in the conclusion.

Microtransit is a new, technology-enabled, on-demand transportation mode in which small shuttles provide shared rides through flexible routing and scheduling in response to customers’ requests for rides. It can potentially offer greater efficiency and more equitable service than ride-hailing services, and it may fill gaps in traditional transit services.Thus far, the early shape of the microtransit customer market remains unclear. Specifically, why some people are interested in microtransit while others are not remains an open question. For people who have never used it, what factors could work as facilitators or barriers in their willingness to adopt microtransit? Who are early adopters of microtransit? Aiming to fill this gap, in 2021, researchers at the University ofCalifornia, Davis conducted focus groups and an online survey of SmaRT Ride adopters and users of other means of transportation in the Sacramento area.View the NCST Project Webpage &nbsp

The mechanical responses of steel fiber–reinforced concrete (SFRC) thermally damaged at high temperature needs a deeper evaluation via a mesoscopic model that explicitly treats the fibers. ...

Trillions of chemical reactions occur in the human body every second, where the generated products are not only consumed locally but also transported to various locations in a systematic manner to sustain homeostasis. Current solutions to model these biological phenomena are restricted in computability and scalability due to the use of continuum approaches where it is practically impossible to encapsulate the complexity of the physiological processes occurring at diverse scales. Here we present a discrete modeling framework defined on an interacting graph that offers the flexibility to model multiscale systems by translating the physical space into a metamodel. We discretize the graph-based metamodel into functional units composed of well-mixed volumes with vascular and cellular subdomains; the operators defined over these volumes define the transport dynamics. We predict glucose drift governed by advective-dispersive transport in the vascular subdomains of an islet vasculature and cross-validate the flow and concentration fields with finite-element based COMSOL simulations. Vascular and cellular subdomains are coupled to model the nutrient exchange occurring in response to the gradient arising out of reaction and perfusion dynamics. The application of our framework for modeling biologically relevant test systems shows how our approach can assimilate both multi-omics data from in vitro - in vivo studies and vascular topology from imaging studies for examining the structure-function relationship of complex vasculatures. The framework can advance simulation of whole-body networks at user-defined levels and is expected to find major use in personalized medicine and drug discovery. Graphical abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=199 SRC="FIGDIR/small/460337v1_ufig1.gif" ALT="Figure 1"> View larger version (41K): org.highwire.dtl.DTLVardef@16ff682org.highwire.dtl.DTLVardef@1a1101dorg.highwire.dtl.DTLVardef@1291b39org.highwire.dtl.DTLVardef@1ba65d6_HPS_FORMAT_FIGEXP M_FIG C_FIG SignificanceWithin a tissue, the short-range and long-range communications that sustain metabolism is mediated by the vessels perfusing through the cells. When blood flows through the vasculature, nutrient exchange occurs from cell-to-vessel in accordance with the concentration gradients arising out of cellular and vascular dynamics. Therefore, the topology of blood flow and the anatomical arrangement of cells act as primary determinants influencing the functional response of a tissue. We introduce a graph-based model for understanding the multi-scale connectivity observed across functional networks in a tissue. Our approach offers the flexibility to couple different scales by defining each component to the desired scale so as to balance the need for completeness without compromising on necessary details to answer the questions of interest.

In this article, we study the issues of stabilization of the systems consisting of interacting objects – structures or processes. The results were obtained using the graph theory. To calculate the degree of influence of objects on each other, both direct influences between the vertices and indirect ones are taken into account. The problem of stability of systems is studied. Conditions for the stability of a system with nonlinear interactions are found. The questions of the system stabilization under the influence of the evolutionary mechanism, realizing the response of objects to the impact, are examined. An approach is proposed that sets the evolution of the original system by including response reactions that increase or decrease the weight of the arcs. Examples are given and conditions are specified under which the unbalanced original graph of mutual influences comes to a stable two-class structure.

The dynamics of individual behavior are related to the dynamics of the social structures in which individuals are embedded. This implies that in order to study social mechanisms such as social selection or peer influence, we need to model the evolution of social networks and the attributes of network actors as interdependent processes. The stochastic actor-oriented model is a statistical approach to study network-attribute coevolution based on longitudinal data. In its standard specification, the coevolving actor attributes are assumed to be measured on an ordinal categorical scale. Continuous variables first need to be discretized to fit into such a modeling framework. This article presents an extension of the stochastic actor-oriented model that does away with this restriction by using a stochastic differential equation to model the evolution of a continuous attribute. We propose a measure for explained variance and give an interpretation of parameter sizes. The proposed method is illustrated by a study of the relationship between friendship, alcohol consumption, and self-esteem among adolescents.

Chilled water system of central air conditioning is a typical hybrid system; variable frequency behavior with amplitude limited of pumps reflects continuous and discrete dynamic characteristics. The way of energy-saving is variable water volume, via variable frequency behavior of pumps to gain adjustment of power consumption. Facing the situation of the variable frequency pumps with parallel operation, single continuous or discrete modeling cannot reflect the hybrid features. Thus, the control method will have some questions, such as bad energy-saving effect, difficult accurate adjustment of cold capacity, and low running energy efficiency. However, hybrid system modeling can reflect hybrid dynamic behavior of pumps, which is combining continuous and discrete features. The questions of nonlinear and multiparameters can be solved by control method based on hybrid system. Here, an optimum control method is proposed with the principle of the minimum, by setting the minimum power consumption as the performance function in fixed time, which realizes variable control of pumps and accurate adjustment of temperature inside room. At last, it shows the system characteristics and energy-saving affection by hybrid system modeling and the optimum control method.

This paper presents a discrete model of non-synaptic interactions between neurons, which are performed by special chemical agents, neurotransmitters. In this model, all signals are broadcast: each neuron’s activity can be perceived by all other neurons that are sensitive to its neurotransmitter. The purpose of leaving synapses out is to demonstrate the importance of heterochemical1 interactions in the nervous system. Transmitter-specific neurons are described as finite automatons, which are a generalization of the traditional formal neuron. In a network consisting of such neurons, all connections are functional and not structural. This feature makes it possible to explain rapid reconfigurations of activity patterns in the generation of different rhythms by neuron ensembles, which are observed in living systems. We discuss and justify the choice of a discrete mathematical framework for simulation of heterochemical interactions.

In this paper the formulas for Fibonacci distribution and golden proportion regularities in oscillation spectra of oscillator systems are presented in frame of MEMS elements parameters probabilistic discrete modeling. Established ratios allow to calculate the statistical mean, standard deviation and confidence limits of system parameters.

In this paper, a model for two-component systems of six-sided dice in a simple cubic lattice is developed, based on a basic cluster approach previously proposed. The model represents a simplified picture of liquid mixtures of molecules with different interaction sites on their surfaces, where each interaction site can be assigned an individual energetic property to account for cooperative effects. Based on probabilities that characterize the sequential construction of the lattice using clusters, explicit expressions for the Shannon entropy, synonymously used as thermodynamic entropy, and the internal energy of the system are derived. The latter are used to formulate the Helmholtz free energy that is minimized to determine thermodynamic bulk properties of the system in equilibrium. The model is exemplarily applied to mixtures that contain distinct isomeric configurations of molecules, and the results are compared with the Monte-Carlo simulation results as a benchmark. The comparison shows that the model can be applied to distinguish between isomeric configurations, which suggests that it can be further developed towards an excess Gibbs-energy, respectively, activity coefficient model for chemical engineering applications.

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.

An unstructured discrete fracture model (UDFM) is developed in this study to simulate the two-dimensional fluid flow in the complex fractured tight oil reservoirs. The model applies a control-volume finite-difference (CVFD) discretization scheme with the two-point flux-approximation (TPFA) to evaluate the transmissibility list. Discretization process of the mathematical model is greatly simplified by three differential operators that are defined to represent the expressions of divergence, gradient and average as their original forms, and thus, enable rapid prototyping of the numerical model. The discretized equation system is solved by a modified Newton's method, in which the Jacobian matrix is computed by the automatic differentiation (AD) technique. Our model is validated with the simulation results obtained by the commercial reservoir simulator, Eclipse. To test the model's potential in field-scale application, we implement it in five large-scale complex fractured systems that are radial domains with a uniform diameter of 1000 m but different fracture densities: 382/km2, 509/km2, 636/km2, 764/km2 and 1018/km2. Simulation results not only indicate the robustness of our model in simulating complex fractured systems but also highlight the significant effects of fracture network configuration and fracture density on the development features of fractured tight oil reservoirs.

Discrete modeling is a concept to establish thermodynamics on Shannon entropy expressed by variables that characterize discrete states of individual molecules in terms of their interacting neighbors in a mixture. To apply this method to condensed-phase lattice fluids, this paper further develops an approach proposed by Vinograd which features discrete Markov-chains for the sequential lattice construction and rigorous use of Shannon information as thermodynamic entropy, providing an in-depth discussion of the modeling concept evolved. The development comprises (1) improved accuracy compared to Monte Carlo data and (2) an extension from a two-dimensional to a three-dimensional simple lattice. The resulting model outperforms the quasichemical approximation proposed by Guggenheim, a frequently used reference model for the simple case of spherical molecules with uniform energetic surface properties. To illustrate its potential as a starting point for developing gE-models in chemical engineering applications, t...

A modeling approach to efficiently incorporate Prandtl-Ishlinskii-type hysteresis coupling behaviour into an otherwise linear-dynamic system is proposed. For a simplified elastic drive train with a nonlinear hysteretic coupling torque, the coupled full system dynamics is first formulated in continuous time. Then, a novel piecewise-affine representation is proposed that allows direct, exact time-discretization of the sensitive coupling dynamics, retaining the resonance properties accurately. Sensitivities of coupled-system measurements for variations in the coupled model parameters, including hysteresis component parameters, are expressed, and an output-error parameter identification problem is stated. The efficiency of the proposed model structure is validated by a model parameterized based on measurement data. These results provide a promising starting point for a fully coupled, realtime-capable system model architecture.

Concrete fracture can be simulated in static regime, however, it is a dynamical process. For very slow loading rates, the kinetic energy is negligible compared to the energy dissipated by fracturing, and the influence of inertia can be neglected. In all other cases, neglecting the influence of inertia forces can lead to improper results. With increasing loading rate, increase in strength and energy dissipation as well as changes in crack pattern can be observed. The contribution presents dynamical simulations of experiments on concrete specimens under various displacement rates, from very slow, quasi-static, to high displacement rates. The simulations are calculated using discrete particle model, the material is represented by a system of interconnected ideally rigid polyhedral particles. The solution of equations of motion is calculated using implicit time integration Newmark scheme. The constitutive behavior of the material is strain rate independent. For high strain rates the influence of inertia forces dominates and is mainly responsible for increase in loading forces as well as for change in the crack pattern and crack branching. The results obtained with the model are compared to experimental data from literature.

In this paper, a new approach for back analysis of a geogrid reinforced soil (GRS) wall failure is presented. A new zero-thickness cohesive fracture element is utilized to simulate the slip surface behind the GRS wall. This element can simulate displacement discontinuity as well as tractions across the shear band effectively. The numerical results are compared with the measured values from the physical test as well as the obtained values from the typical finite element method. This paper demonstrates that the proposed finite element algorithm via discrete modeling of the shear band can effectively improve the quality of numerical back analysis of the soil failure which explains its necessity.

Despite the high vulnerability of historic structures to earthquakes, the approaches for evaluating seismic demand and capacity still appear inadequate and there is little consensus on the most appropriate assessment methods to use. To develop an improved knowledge on the seismic behavior of masonry structures and the reliability of analysis tools, two real-scale specimens were tested on a shake table, and several experts were invited to foresee failure mechanism and seismic capacity within a blind prediction test. Once unveiled, experimental results were simulated using multi-block dynamics, finite elements, or discrete elements. This article gathers the lessons learned and identifies issues requiring further attention. A combination of engineering judgment and numerical models may help to identify the collapse mechanism, which is as essential as it is challenging for the seismic assessment. To this purpose, discrete modeling approaches may lead to more reliable results than continuous ones. Even when the correct mechanism is identified, estimating the seismic capacity remains difficult, due to the complexity and randomness of the seismic response, and to the sensitivity of numerical tools to input variables. Simplified approaches based on rigid body dynamics, despite the considerable experience and engineering judgment required, provide as good results as do advanced simulations., info:eu-repo/semantics/publishedVersion

International audience; In this paper we show the discrete modeling of the heat equation on an open cell metallic foam, exploiting its geometric structure. The topology of the material is described using the incidence matrices of a so called k‐complex. Together with the discrete constitutive equations, a finite‐dimensional model in port‐Hamiltonian form is found.

In this paper the discrete implementation of a sensorless IM drive with stator current error based MRAS-type speed estimator is analyzed. The system is discretized using analogue emulation method. Two numerical integration methods, Forward Euler and Modified Euler, are compared in simulation and experimental tests. The comparison is confirmed by ITAE criterion. Moreover, the stability improvement method of the tested speed estimator, developed in continuous time domain, is used and tested in the discrete modeling and implementation. This approach also validate the stable operation of the tested speed estimation method in full operating range of the drive system.

Industrial robots are used in a variety of industry branches, especially where precision is needed. This paper deals with modeling and control of a positioning process for an industrial robot part of the hot rolling chain, that must extract with accuracy heated billets from a rotary hearth furnace. The model is a discrete one, obtained from a continuous form, by using some digitizing methods and different values of sampling time. The authors used Zero-order hold method, simple and Tustin substitutions. The best fitted model is obtained by comparing root means square deviation for each resulted discrete model. The proposed control is a discrete PI control law, implemented and validated using computer simulation software. The parameters result quite easily from closed loop Ziegler Nichols method, but require further tuning to improve transient response performances.

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.

There are evidences that the human right atrium and sinoatrial node (SAN) are functionally separated except at discrete SAN-atrial electrical junctions. We hypothesize that such anatomy could be a source of re-entry around the SAN. A model was developed which reconstructs the human right atrium anatomy. The activity of a myocyte was simulated by a timed automaton with continuous and discrete transitions reproducing the known stages of the action potential of the cellular membrane. A stochastic 2D network of timed automata was designed to model the grid of the right atrium. Discrete modeling allowed us to specify directly the rate of SAN to atrium pathways. Also, the influence of (1) atrial tissue fibrosis, via probability for transversal intercellular network connections, and of (2) impairment of individual cells via probability of a cell to excite, were controlled. The simulations provided a critical relationship between atrial anatomy and the rhythm of heart excitations. It occurred that at probability of 1/8 of SAN-atrium pathways (randomly chosen), the occurrence of the normal rhythm attained the highest probability - close to 1, in large intervals for the density of transversal intercellular connections, and for the levels of cellular impairment.

A discrete model of multitransmitter interactions between neurons in a common extracellular space (ECS) is proposed. Neurons in the model are heterogeneous in three different senses. They differ in (i) the type of endogenous change in the membrane potential, (ii) the type of secreted neurotransmitter, and (iii) the set of receptors, wherein each receptor is sensitive to a particular neurotransmitter. The model is characterized by the broadcast nature transmission of the signals: the neurotransmitter appeared in the ECS is treated as an input signal for all neurons with receptors sensitive to it. It is shown that the extrasynaptic interaction of neurons combined with multitransmitter environment enables to reproduce the rhythms generated by simple natural neural networks.

This paper presents a novel framework for the discrete modeling of the large-scale triaxial test of rock clasts, considering both the realistic particle shapes and veritable flexible boundary condition. First, real-shaped particle models for the tested rock clasts are precisely reconstructed using the close-range photogrammetry technique. The rubber membrane was modeled by a series of bonded particles. Then, the laboratory procedures of the triaxial test, i.e., sample preparation, isotropic compression, and shearing, are reproduced in the DEM simulations with consideration of the veritable confining boundary. To ensure more reliable numerical results, a systematic DEM calibration framework is established to determine the modeling parameters based on a series of calibration experiments, including tensile test, suspension test, clast-membrane sliding test, and large-scale triaxial test. Finally, the proposed method is applied to investigate the effects of confining pressure on the macro- and micro-mechanical behaviors of rock clasts. The presented works lay a foundation for further studies on revealing the mechanisms of the conventional triaxial test, e.g., the effect of end restraint and rubber membrane. Moreover, the proposed systematic framework for calibration of modeling parameters can be applied to precisely capture the real mechanical properties of various types of granular rock-like materials in DEM simulations.

Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamic models that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background and application to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models for strongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approach is based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete local compositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of its partition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement to systems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis for introducing the co...

International audience; The paper presents investigations on the penetration tests in granular material. A discrete numerical study is proposed for the modeling of penetration tests in constant velocity conditions and also in impact conditions. The model reproduces qualitatively the mechanical response of samples of granular material, compared to classical experimental results. Penetration tests are conducted at constant velocity and from impact, with similar penetration rates ranging from 25 mm.s-1 to 5000 mm.s-1. In constant velocity condition, the value of tip force remains steady as long as the penetration velocity induces a quasi–static regime in the granular material. However, the tip force increases rapidly in the dense flow regime corresponding to higher penetration rate. Impact tip force increases with the impact velocity. Finally, the tip forces obtained from impact penetration tests are smaller compared to the one obtained in constant velocity conditions in both quasi–static and dense flow regimes.

In tall and light structures, such as transmission towers, wind turbines, and light-gauge steel structures, there is an increasing application of pile cap with helical pile foundation systems to resist the uplift loads due to the effects of windstorms and earthquakes. There is a lack of knowledge, published literature, or analysis methods to account for the effects of the pile cap, helical pile group, and soil interactions on the holistic response of the foundations, particularly, for the load conditions creating net uplift loads. In the lack of such, discrete modeling approaches are frequently employed in practice. These approaches isolate each system component and analyze them individually, neglecting the interactions between them. In an attempt to bridge this knowledge gap, this study proposes a system-level modeling methodology for the holistic analysis of pile cap systems in dry soil and static load conditions, while accounting for the effects of interactions between system components and the inherent material nonlinearities. The methodology employs a three-stage process in which the material and interaction properties are calibrated with the experimental benchmark specimens. The failure mechanisms are also experimentally verified based on the relative displacement of the piles. Important modeling considerations are discussed, and experimental benchmark specimens are provided to assist practitioners in accurately performing system-level analyses. The effectiveness of the proposed methodology is discussed, and the responses obtained, including the load–displacement responses, load capacities, and failure modes, are compared with those obtained from the discrete modeling approaches. The results demonstrate that discrete modeling approaches significantly underestimate the load capacity while not accurately predicting the governing behavior and the failure modes.

This paper presents a modeling method that models the quasi-Z-network with three different states instead of two. A new model is developed which could be exclusively decided by the input DC voltage and the AC load condition. This model is then used to design a discrete time domain version of integral state feedback controller that could extend the control validity of quasi-Z-network over a large range of input DC voltage and AC load. Experimental results are provided to show the feasibility of above modeling method and controller design. The feature of control validity is left for future investigation. Discrete modeling and digital controller design of H-bridge inverter are investigated. Programming method to compensate delay of PWM module of F28335 DSP and its successful operation will be illustrated using hardware prototype.

Understanding sensitivity is an important step to study system robustness and adaptability. In this work, we model and investigate intra-cellular networks via discrete modeling approach, which assigns a set of discrete values and a deterministic update rule to each model element. The models can be analyzed formally or simulated in a stochastic manner. We propose a comprehensive framework to study sensitivity in these models. In the framework, we define element influence (activity) and sensitivity with respect to the state distribution of the modeled system. Previous sensitivity analysis approaches all assume uniform state distribution, which is usually not true in biology. We perform both static and dynamic sensitivity analysis, the former assuming uniform state distribution, and the latter using a distribution estimated from stochastic simulation trajectories under a particular scenario. Additionally, we extended the element update functions to include weights according to these computed influences. Adding weights generates a weighted directed graph, and therefore, enables identifying key elements in the model and dominant signaling pathways that determine the behavior of the overall model. In the end, we apply our sensitivity analysis framework on pathway extraction in the intra-cellular networks that control T cells differentiation.

Background The hypothalamic-pituitary-adrenal (HPA) axis is a central regulator of stress response and its dysfunction has been associated with a broad range of complex illnesses including Gulf War Illness (GWI) and Chronic Fatigue Syndrome (CFS). Though classical mathematical approaches have been used to model HPA function in isolation, its broad regulatory interactions with immune and central nervous function are such that the biological fidelity of simulations is undermined by the limited availability of reliable parameter estimates. Method Here we introduce and apply a generalized discrete formalism to recover multiple stable regulatory programs of the HPA axis using little more than connectivity between physiological components. This simple discrete model captures cyclic attractors such as the circadian rhythm by applying generic constraints to a minimal parameter set; this is distinct from Ordinary Differential Equation (ODE) models, which require broad and precise parameter sets. Parameter tuning is accomplished by decomposition of the overall regulatory network into isolated sub-networks that support cyclic attractors. Network behavior is simulated using a novel asynchronous updating scheme that enforces priority with memory within and between physiological compartments. Results Consistent with much more complex conventional models of the HPA axis, this parsimonious framework supports two cyclic attractors, governed by higher and lower levels of cortisol respectively. Importantly, results suggest that stress may remodel the stability landscape of this system, favoring migration from one stable circadian cycle to the other. Access to each regime is dependent on HPA axis tone, captured here by the tunable parameters of the multi-valued logic. Likewise, an idealized glucocorticoid receptor blocker alters the regulatory topology such that maintenance of persistently low cortisol levels is rendered unstable, favoring a return to normal circadian oscillation in both cortisol and glucocorticoid receptor expression. Conclusion These results emphasize the significance of regulatory connectivity alone and how regulatory plasticity may be explored using simple discrete logic and minimal data compared to conventional methods. Electronic supplementary material The online version of this article (10.1186/s12918-018-0599-1) contains supplementary material, which is available to authorized users.

Developing from researches on heterogeneous modelling and voxel-based design, as well as on digital materials and discrete assembly, the paper describes current developments of Wasp, a software tool for hierarchical discrete modelling of objects as aggregations of modular parts, with focus on the generation of architectural objects. By conceptualizing the discrete nature of the final objects already within the software, it becomes possible to model heterogenous artefacts composed of basic parts, which are reversibly joined into a complete aggregation. Within such framework, users are provided with different aggregation procedures to select rule sequences producing the desired outcomes, as well as basic utilities for part collisions avoidance, visualization and editing of the produced geometries. To increase control over designed objects, the framework has been extended to include hierarchical modelling with multi-resolution parts, more advanced generation and editing functions for voxel fields, multi-channel scalar fields and global constraints. Overall, the aim of the framework is to allow modelling of objects as aggregations of discrete units with reversible connections, hence allowing the production of architectural entities which could be assembled, disassembled, and reconfigured during their lifecycle.

Mixing sand or soil with small pieces of tire is common practice in civil engineering applications. Although the properties of the soil are changed, it is environmentally friendly and sometimes economical. Nevertheless, the mechanical behavior of such mixtures is still not fully understood and more numerical investigations are required. This paper presents a novel approach for the modeling of sand–tire mixtures based on the discrete element method. The sand grains are represented by rigid agglomerates whereas the tire grains are represented by deformable agglomerates. The approach considers both grain shape and deformability. The micromechanical parameters of the contact law are calibrated based on experimental results from the literature. The effects of tire content and confining pressure on the stress–strain response are investigated in detail by performing numerical triaxial compression tests. The main results indicate that both strength and stiffness of the samples decrease with increasing tire content. A tire contact of 40% is identified as the boundary between rubber-like and sand-like behavior.

The flat, two dimensional materials play important role in the research and industrial applications in the last 15 years. The new materials with flat atomic structures are discovered almost every month. The focus of the paper is on the discrete modeling of the single layer molybdenum disulphide based material (SLMoS2). Two methods, based on the molecular statics and molecular dynamics of estimation of material properties and numerical simulations at the nanolevel are described and discussed.

An accurate discrete model is presented here for the analysis of simply supported web-core sandwich plates. In this model, the face plates are analysed using the equations of 3D elasticity and for the webs a plane stress idealization is used to model the kinematics of transverse bending while simple one-dimensional classical models are employed for lateral bending and torsion. Thus, this model accounts for the non-classical effects of transverse shear deformation and transverse thickness-stretch in the face-plates and the webs. It is shown that this model is capable of accurately capturing the effects of secondary local bending of the face-plates between the webs on the displacement and stress fields. Results obtained by this rigorous approach are used to highlight the errors of the commonly used model based on the classical hairbrush hypothesis for the face-plates.

Purpose – The purpose of this paper is to discretely model rockfill materials considering the irregular shape of the particles and their crushability. The scientific goal was to investigate the influence of particle crushability and shape on the mechanical behavior of rockfill materials. Design/methodology/approach – The method of generating irregular-shaped particles was based on the observation that most rockfill grains can be approximately circumscribed by an ellipsoid. Two shape descriptors were used to make the virtual particles closely replicate the geometric features of natural rockfill grains. The combined finite-discrete element method (FDEM) was used to numerically simulate a drained, tri-axial compression test. The particle assemblies were subjected to tri-axial compression under strain controlled conditions while a constant confining pressure was maintained. Findings – The non-breakable particles showed a remarkable ability to dilate as a result of a higher inter-particle locking effect. Dilat...

The information technologies have evolved in such a way that communication between computers or hosts has become common, so much that the worldwide organization (governments and corporations) depends on it; what could happen if these computers stop working for a long time is catastrophic. Unfortunately, networks are attacked by malware such as viruses and worms that could collapse the system. This has served as motivation for the formal study of computer worms and epidemics to develop strategies for prevention and protection; this is why in this paper, before analyzing epidemiological models, a set of formal definitions based on set theory and functions is proposed for describing 21 concepts used in the study of worms. These definitions provide a basis for future qualitative research on the behavior of computer worms, and quantitative for the study of their epidemiological models.

The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta’s sense. The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.