Discrete Models for Particle Packings

AbstractDiscrete computational models for the viscosities, sintering rates, and transport properties of sintering particle packings are presented. The packing is represented by a set of nodes (the particle centroids) connected by links (inter-particle contacts). The models for the mechanical behavior enforce equilibrium for each particle which leads to a set of simultaneous equations for the particle motion. Electrical or thermal transport through inter-particle contacts is modelled by imposing zero net flux at a node which also leads to a set of simultaneous equations for the value of potential at each particle center. The model is used to simulate the compaction of spheres to generate a threedimensional random packing. Statistical properties of the computed packing such as packing fraction, percolation threshold, and coordination number are compared with those of an experimental random packing. Results are also presented for the effective conductivity of mixtures of particles with very different conductivities.

Download Full-text

Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽

10.3390/sym13061063 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1063

Author(s):

Vladimir Mityushev ◽

Zhanat Zhunussova

Keyword(s):

Effective Conductivity ◽

Dimensional Space ◽

Elementary Function ◽

Voronoi Tessellation ◽

Random Packing ◽

Periodicity Cell ◽

Algebraic Equations ◽

Optimal Packing ◽

Linear Algebraic Equations ◽

Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

Download Full-text

A Review of Cell-Based Computational Modeling in Cancer Biology

JCO Clinical Cancer Informatics ◽

10.1200/cci.18.00069 ◽

2019 ◽

pp. 1-13 ◽

Cited By ~ 58

Author(s):

John Metzcar ◽

Yafei Wang ◽

Randy Heiland ◽

Paul Macklin

Keyword(s):

Stem Cells ◽

Computational Modeling ◽

Single Cell ◽

Stromal Cells ◽

Cancer Biology ◽

Large Scale ◽

Computational Models ◽

Three Dimensional ◽

Discrete Models ◽

Simulation Studies

Cancer biology involves complex, dynamic interactions between cancer cells and their tissue microenvironments. Single-cell effects are critical drivers of clinical progression. Chemical and mechanical communication between tumor and stromal cells can co-opt normal physiologic processes to promote growth and invasion. Cancer cell heterogeneity increases cancer’s ability to test strategies to adapt to microenvironmental stresses. Hypoxia and treatment can select for cancer stem cells and drive invasion and resistance. Cell-based computational models (also known as discrete models, agent-based models, or individual-based models) simulate individual cells as they interact in virtual tissues, which allows us to explore how single-cell behaviors lead to the dynamics we observe and work to control in cancer systems. In this review, we introduce the broad range of techniques available for cell-based computational modeling. The approaches can range from highly detailed models of just a few cells and their morphologies to millions of simpler cells in three-dimensional tissues. Modeling individual cells allows us to directly translate biologic observations into simulation rules. In many cases, individual cell agents include molecular-scale models. Most models also simulate the transport of oxygen, drugs, and growth factors, which allow us to link cancer development to microenvironmental conditions. We illustrate these methods with examples drawn from cancer hypoxia, angiogenesis, invasion, stem cells, and immunosurveillance. An ecosystem of interoperable cell-based simulation tools is emerging at a time when cloud computing resources make software easier to access and supercomputing resources make large-scale simulation studies possible. As the field develops, we anticipate that high-throughput simulation studies will allow us to rapidly explore the space of biologic possibilities, prescreen new therapeutic strategies, and even re-engineer tumor and stromal cells to bring cancer systems under control.

Download Full-text

A precise algorithm to detect voids in polydisperse circle packings

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0421 ◽

2015 ◽

Vol 471 (2182) ◽

pp. 20150421 ◽

Cited By ~ 2

Author(s):

Eckard Specht

Keyword(s):

A Priori ◽

Packing Fraction ◽

Heuristic Methods ◽

Large Problem ◽

Optimal Packing ◽

Contact Graph ◽

Benchmark Instances ◽

Circle Packings ◽

And Shifts ◽

Particle Packings

Computer simulations are the primary tool for studying polydisperse particle packings quanti- tatively. For the problem of packing N unequal circles in a larger container circle, nothing is known a priori about the optimal packing (i.e. the packing with the highest packing fraction). Simulations usually start from a random initial configuration with the aim to finish with a dense final packing. Unfortunately, smaller circles often get stuck in trapped positions and prevent the rest of the packing from growing larger. Hence, the knowledge of the structure of unoccupied areas or holes inside a packing is important to be able to move trapped circles into free circular places or voids . A novel algorithm is proposed for detecting such voids in two-dimensional arbitrary circle packings by a decomposition of the contact graph. Combined with a clever object jumping strategy and together with other heuristic methods like swaps and shifts, this approach increases the packing fraction ϕ significantly. Its effectiveness for jumping across the maximally random jammed barrier ( ϕ MRJ ≈0.8575 in the large- N limit) for small benchmark instances as well as for large problem sizes (up to N ≈10 3 ) is demonstrated.

Download Full-text

Modeling of word translation: Activation flow from concepts to lexical items

Bilingualism Language and Cognition ◽

10.1017/s1366728912000612 ◽

2012 ◽

Vol 16 (2) ◽

pp. 343-353 ◽

Cited By ~ 5

Author(s):

ARDI ROELOFS ◽

TON DIJKSTRA ◽

SVETLANA GERAKAKI

Keyword(s):

Continuous Flow ◽

Computational Models ◽

Word Production ◽

Discrete Models ◽

Empirical Observation ◽

Bilingual Speakers ◽

Continuous Models ◽

Discrete Flow ◽

Word Translation ◽

Lexical Items

Whereas most theoretical and computational models assume a continuous flow of activation from concepts to lexical items in spoken word production, one prominent model assumes that the mapping of concepts onto words happens in a discrete fashion (Bloem & La Heij, 2003). Semantic facilitation of context pictures on word translation has been taken to support the discrete-flow model. Here, we report results of computer simulations with the continuous-flow WEAVER++ model (Roelofs, 1992, 2006) demonstrating that the empirical observation taken to be in favor of discrete models is, in fact, only consistent with those models and equally compatible with more continuous models of word production by monolingual and bilingual speakers. Continuous models are specifically and independently supported by other empirical evidence on the effect of context pictures on native word production.

Download Full-text

Strain dependent vorticity in sheared granular media

EPJ Web of Conferences ◽

10.1051/epjconf/202124902010 ◽

2021 ◽

Vol 249 ◽

pp. 02010

Author(s):

Dong Wang ◽

Joshua A. Dijksman ◽

Jonathan Barés ◽

Hu Zheng

Keyword(s):

Flow Field ◽

Granular Media ◽

Total Surface Area ◽

Packing Fraction ◽

Differential Method ◽

Displacement Fields ◽

Data Set ◽

Quantitative Metrics ◽

Particle Packings ◽

Strain Dependent

Displacement fields in sheared particle packings often display vortex-like structures that reveal essential features about the mechanical state of the collection of particles. There are several metrics to quantify these flow field features, yet extracting such quantitative metrics from flow field or particle tracking data involves making numerous choices on the time and length scales over which to average. Here we employ a much used experimental data set on sheared disk packings to explore how such arbitrary data mining choices affect the obtained results. We focus on calculating the strain dependent vorticity, as this metric is a differential method hence potentially sensitive to the way it is computed. We find that the total surface area with an absolute vorticity above a certain threshold approaches a plateau value as shear progresses. This plateau value exhibits a non-monotonic dependence on packing fraction. We also show which range of choices yields results that can support an analysis method independent, physical interpretation of the flow field data.

Download Full-text

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

International Journal of Architectural Computing ◽

10.1177/1478077120924802 ◽

2020 ◽

Vol 18 (3) ◽

pp. 218-234

Author(s):

Manuel Ladron de Guevara ◽

Luis Ricardo Borunda ◽

Daragh Byrne ◽

Ramesh Krishnamurti

Keyword(s):

Additive Manufacturing ◽

Computational Methods ◽

Computational Models ◽

Three Dimensional ◽

Discrete Models ◽

Computational Power ◽

Manufacturing Applications ◽

The Impact

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.

Download Full-text