Discrete Computational Model Research Articles

Rationalization of load distribution in multi-pair gearing based on a discrete contact model

Mechanisms and devices with multi – pair engagement of contact elements (transmission, connection, etc.) are widely used in mechanical engineering. The article considers an algorithm for rationalizing contact loading of parts of similar mechanisms and devices developed on the basis of a discrete computational model. The algorithm is based on the principle of entering the constructive step difference of contact elements.

Modelling and parameter identification of steel\u2013concrete composite beams in 3D rigid finite element method

This study presents spatial vibration modelling of steel–concrete composite beams. Structures of this type are commonly used as elements of composite floors and primary carrying girders in bridge structures. Two-dimensional models used to date did not enable analysis of all eigenmodes, specifically torsional, flexural horizontal, and distortional. A discrete computational model was developed in the convention of the rigid finite element method, the so-called RFEM model. It was assumed that the concrete slab and the steel I-section would be modelled separately. This approach realistically reflects the actual performance of the connection, comprising studs connecting the concrete slab and the steel section. The model was used to analyse two steel–concrete composite beams with different connector spacings. The paper presents the results of experiments conducted on the two composite beams. Their dynamic characteristics, including frequency and vibration modes, were determined with impulse response methods. Based on experimental research, identification of connection parameters with substitute longitudinal moduli of elasticity of reinforced concrete was conducted. A comparison of experimental results with those calculated with the model confirmed their good agreement.

Nonlinear Elastic and Inelastic Properties of Cells.

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

Multi-resolution in architecture as a design driver for additive manufacturing applications

Additive manufacturing is evolving toward more sophisticated territory for architects and designers, mainly through the increased use of scripting tools. Recognizing this, we present a design and fabrication pipeline comprised of a class of techniques for fabrication and methods of design through discrete computational models. These support a process responsive to varied design intents: this structured workflow expands the design and fabrication space of any input shape, without having to explicitly deal with the complexity of discrete models beforehand. We discuss a multi-resolution-based methodology that incorporates discrete computational methods, spatial additive manufacturing with both robotic and commercial three-dimensional printers, as well as, a free-oriented technique. Finally, we explore the impact of computational power on design outcome, examining in-depth the concept of resolution as a design driver.

Two-span bridge under moving load – numerical and experimental approach

From the point of view of bridge structures, the moving load is one of the most important components of the load. The analysis of the influence of moving load on bridges is carried out numerically or experimentally and can be traced in the literature since the year 1849. The first impulse was the collapse of the Chester Rail Bridge in England in the year 1847. The present paper analyses the effect of the moving load on a two-span bridge, both numerical and experimental way. The planar model of the vehicle and the bridge is adopted. The bridge is modeled as Bernoulli-Euler beam. The heavy vehicle is modeled as a discrete computational model with 8 degrees of freedom. Two approaches are used in numerical modeling. For the first time, the task is solved by the finite element method in the environment of the program system ADINA. The Newmark's method is used for the solution of equations of motion. The classic approach is used for the second time. A discrete computational model of a bridge with two degrees of freedom is used. Equations of motion are solved numerically in the environment of program system MATLAB by the Runge-Kutta 4th order method. The influence of vehicle speed on vertical deflections in the middle of individual bridge fields is analyzed in the speed range from 0 to 130 km/h with a step of 5 km/h. The detailed comparison of both numerical approaches is made at a vehicle speed of 70 km/h. The deflections of the bridge and the deflection of the vehicle are compared with each other. The correctness of the assumptions used in the numerical solutions was verified by measurement on a model beam in the laboratory. The results of the experimental tests were compared with the results of the numerical solution.

Simulating Small Neural Circuits with a Discrete Computational Model

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.

Discrete Computational Neural Dynamics Models for Solving Time-Dependent Sylvester Equation With Applications to Robotics and MIMO Systems

In this article, a neural dynamics model is constructed and investigated for solving time-dependent Sylvester equation with matrix inversion involved in the solving process. Besides, to eliminate the matrix inversion in the model, the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno method is leveraged to construct a new model. Moreover, the global convergence performance and the effectiveness of the two discrete computational models are testified by providing theoretical analyses and numerical experiments with comparisons to the existing solutions, respectively. Two applications to robotics and the multiple-input multiple-output system are given to elucidate the feasibility of the proposed models for solving time-dependent Sylvester equation.

Differential Privacy on Finite Computers

We consider the problem of designing and analyzing differentially private algorithms that can be implemented on discrete models of computation in strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomial-time algorithms.
 As a case study, we examine the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X.
 The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy \& Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X|, which can be exponential in the bit length of the input.
 
 In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee.
 One of our algorithms produces a sparse histogram as output.
 Its ``"per-bin accuracy" (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log|X|, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram.
 A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram; it is based on an (n+1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.

FE modeling of moving load effect on two span bridge

The problem of simulation of moving load effect on bridges is a relatively old problem. It was induced by the collapse of the Chester Rail Bridge in England in the year 1847 and can be traced in the literature since the year 1849. The new generation of young research workers is capable to contribute to the solution of the problem with new findings. The contribution is devoted to the modeling of the vehicle motion along a two-span bridge in the environment of the program system ADINA. The task is solved as a plane problem. It described the creation of a discrete computational model of vehicle with 8 degrees of freedom. The bridge is modeled using beam elements. It is assumed that the vehicle enters the bridge already vibrant. The vehicle and bridge response is modeled when vehicle driving at the speed of 70 km/h. The time course of oscillation of vehicle model's characteristic points and the oscillation of mid spans of individual bridge fields are shown graphically. Important results are given in numerical form. The Newmark's method is used for the solution of equations of motion.

Computational simulation of fracture behaviour in auxetic cellular structure by multiaxial loading

A computational simulation of fracture behaviour in auxetic cellular structure, subjected to multiaxial loading is presented in this paper. A fracture behaviour of the 3D (three-dimensional) chiral auxetic structure under multiaxial loading conditions was studied. The computational models were used to study the geometry effect of the unit cell on the Poisson’s ratio and fracture behaviour of the analysed chiral auxetic structure. A 3D computational model was built using FEM-code LS DYNA. The discrete computational model of chiral auxetic structure was built using beam finite elements. The lattice model of the analysed auxetic structure was positioned between rigid plates and assembled in a way to simulate a hydro-compression loading conditions. Between the contacting surfaces interactions in normal (contact) and tangential direction (friction) with the node-to-surface approach were simulated. A developed computational model offers insight in the fracture behaviour of considered auxetic cellular structure and helps to better understanding their crushing behaviour under impact multiaxial loading.

A Plugin Framework for Extending the Simulation Capabilities of FEBio

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new “plugin” framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

The Power of Writing, a Pebble Hierarchy and a Narrative for the Teaching of Automata Theory

In this work we study pebble automata. Those automata constitute an infinite hierarchy of discrete models of computation. The hierarchy begins at the level of finite state automata (0-pebble automata) and approaches the model of one-tape Turing machines. Thus, it can be argued that it is a complete hierarchy that covers, in a continuous way, all the models of automata that are important in the theory of computation. We investigate the use of this hierarchy as a narrative for the teaching of automata theory. We also investigate some fundamental questions concerning the power of pebble automata.

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primarystructures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one halfapproximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.

Application of local rules and cellular automata in representing protein translation and enhancing protein folding approximation

It is self-evident that the coarse-grained view of transcription and protein translation is a result of certain computations. Although there is no single definition of the term “computation,” protein translation can be implemented over mathematical models of computers. Protein folding, however, is a combinatorial problem; it is still unknown whether a fast, accurate, and optimal folding algorithm exists. The discovery of near-optimal folds depends on approximation algorithms and heuristic searches. The hydrophobic–hydrophilic (HP) model is a simplified representation of some of the realities of protein structure. Despite the simplified representation, the folding problem in the HP model was proven to be NP-complete. We use simple and local rules to model translation and folding of proteins. Local rules imply that at a certain level of abstraction an entity can move from a state to another based on its state and information collected from its neighborhood. Also, the rules are simple in a sense that they do not require complicated computation. We use one-dimensional cellular automata to describe translation of mRNA into protein. Cellular automata are discrete models of computation that use local interactions to produce a global behavior of some sort. We will also discuss how local rules can improve approximation algorithms of protein folding and give an example of a CA that accept a certain family of strings to achieve half H–H contacts.

Формалізований метод проектування застосувань в технології GPGPU

The method of researching systems with high-performance computing support, based on the transition systems apparatus (discrete computational model), is proposed. Two variants of synchronous product limitations of transition systems that model tha Nvidia CUDA approach are proposed. transition systems that represent two types of instructions, process of the warp instruction execution, and the process of warp scheduling were described. GPGPU application execution model was formalized and its correctness was proved. Two variants of the relevant Petri net which allowed automatic or semi-automatic detection of design errors were obtained. Problems in programming 2018; 2-3: 012-020

Doğalgaz Boru Hatlarında Dalga Bariyeri olarak Yapay Ana Kayanın Dalga Yayılışına Etkisi

Earthquakes have destructive influences onto lifeline engineering and especially leading to considerable economic loss to the underground structure. Underground structures are significant unit of lifeline engineering. . Applying horizontal wave barriers is used in civil engineering as an alternative solution to reduce the soil vibrations in the wave propagation region and surrounding of the structures to be protected. In this study, discrete computer model including non-linear soil conditions as well as radiation damping is improved for testing corresponding wave propagation of earthquake vibrations in the soil under 1999 Kocaeli earthquake strong ground motion and mitigation of buried pipeline responses. Extensive parametric investigations by using the developed numerical model for isolation systems have been executed to conceive the influence of different controlling parameters on the screening efficiency. Results indicated that WIB are very promising as a cut off frequency isolators by reduction of * 70% and a promising candidate for future application in the field.

Numerical investigation of microstructure effect on mechanical properties of bi-continuous and particulate reinforced composite materials

In this paper, numerical simulations are proposed to investigate mechanical properties of bi-continuous and particulate reinforced composite materials using a non-local voxel-based discrete computational model. Special focus of this article is the effect of 3D microstructure and its heterogeneity on elastic deformation and fracture behaviors. First, a review on model formulation is presented. Model parameters are derived in terms of material constants using the concept of energy equivalency. Interface representation and numerical homogenization scheme are discussed. Following this, numerical investigations on the effects of interface properties and inclusion characteristics, i.e. the volume fraction and material constants, on homogenized elastic constants and fracture behaviors of statistically isotropic bi-phase composites are performed. The effective elastic constants predicted by the proposed model agree well with analytical results. Fracture simulation demonstrates good capability of the proposed model for the microstructure-sensitive failure analysis. Conclusions and future work are drawn based on the proposed study.

Discrete computational shear strength models for 5-, 6-, and 11-circular-hoop and spiral transverse reinforcement

Based on the actual, discrete locations of interception points between the critical shear crack and transverse reinforcement, this study developed the discrete computational shear strength models for 5-, 6-, and 11-circular-hoop and spiral reinforcement. Moreover, conventional simplified calculation method was revised for use for 5-, 6-, and 11-circular-hoop and spiral reinforcement. Examination of the difference between the discrete computational shear strength models and simplified calculation shows that the error of the simplified calculation increases with increasing ratios of spacing to diameter of circular hoops or spirals. Limiting values of spacing to diameter ratios were proposed to control the error of the simplification calculation to be equal to or less than 10%. Plots of modification factors were proposed to be used with the simplification calculation when the spacing to diameter ratio is large.

Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment

Through a first-generation computational mechanics avatar that directly links advanced X-ray computed tomographic experimental techniques to a discrete computational model, we present a case study where we made the first attempt to characterize and model the grain-scale response inside the shear band of a real specimen of Caicos ooids subjected to triaxial compression. The avatar has enabled, for the first time, the transition from faithful representation of grain morphologies in X-ray tomograms of granular media to a morphologically accurate discrete computational model. Grain-scale information is extracted and upscaled into a continuum finite element model through a hierarchical multiscale scheme, and the onset and evolution of a persistent shear band is modeled, showing excellent quantitative agreement with experiment in terms of both grain-scale and continuum responses in the post-bifurcation regime. More importantly, consistency in results across characterization, discrete analysis and continuum response from multiscale calculations are found, achieving the first and long sought-after quantitative breakthrough in grain-scale analysis of real granular materials.

Noise analysis of genome-scale protein synthesis using a discrete computational model of translation.

Noise in genetic networks has been the subject of extensive experimental and computational studies. However, very few of these studies have considered noise properties using mechanistic models that account for the discrete movement of ribosomes and RNA polymerases along their corresponding templates (messenger RNA (mRNA) and DNA). The large size of these systems, which scales with the number of genes, mRNA copies, codons per mRNA, and ribosomes, is responsible for some of the challenges. Additionally, one should be able to describe the dynamics of ribosome exchange between the free ribosome pool and those bound to mRNAs, as well as how mRNA species compete for ribosomes. We developed an efficient algorithm for stochastic simulations that addresses these issues and used it to study the contribution and trade-offs of noise to translation properties (rates, time delays, and rate-limiting steps). The algorithm scales linearly with the number of mRNA copies, which allowed us to study the importance of genome-scale competition between mRNAs for the same ribosomes. We determined that noise is minimized under conditions maximizing the specific synthesis rate. Moreover, sensitivity analysis of the stochastic system revealed the importance of the elongation rate in the resultant noise, whereas the translation initiation rate constant was more closely related to the average protein synthesis rate. We observed significant differences between our results and the noise properties of the most commonly used translation models. Overall, our studies demonstrate that the use of full mechanistic models is essential for the study of noise in translation and transcription.