From point particles to body points DiCarlo, Antonio; Podio-Guidugli, Paolo
Mathematics in engineering,
01/2022, Volume:
4, Issue:
1
Journal Article
Peer reviewed
Open access
Given a spacetime background against which to observe it, a material system in motion can be modeled discretely, as a collection of particles called 'point masses', or continuously, as a dense and ...deformable object (a body, in the language of continuum mechanics) occupying a region consisting of 'material points'. In that the discrete and continuous descriptions have a common conceptual framework, the scale gap can be got over, provided a coarsening procedure is devised. Here we restrict attention to kinematics, and consider four such bottom-up procedures, two statistical and two deterministic, to derive a macroscopic velocity field from a microscopic one. We show that, to do this, introducing space and time mesoscopic scales is of the essence. We also show under what assumptions a macroscopic motion of the given material system can be associated with a microscopically-informed velocity field. Interestingly, no matter what coarsening procedure one chooses, the points of the resulting continuous description of the system's motion carry intrinsic physical information and may be persistently labelled: we propose to call them body points.
In this paper, I determine the minimum amount of information that continuum mechanics needs to obtain from Newtonian molecular dynamics, in order to avail itself of stress-strain responses uniformly ...valid for a vast range of macroscopic regimes, being quantitatively determined by microscopic physical properties. Described from the opposite, bottom-up point of view, the procedure I put forward uses the basic kinematic and dynamical machinery of continuum mechanics to upscale molecular dynamics to the macroscopic level in a practicable and efficient way.
•The stress is uniquely identified in terms of molecular quantities in a direct, general, and computable way.•The contribution from molecular dynamics to continuum mechanics is recognised.•An ...effective hierarchical multiscale method is introduced.
Giving the continuum notion of stress a quantitative atomistic basis is a long-standing issue. It is argued here that a completely satisfactory solution to this problem came from totally unexpected quarters, being contained (implicitly) in the Parrinello-Rahman method of molecular dynamics. Until now, the latent theoretical potential of this method passed unnoticed by molecular dynamics practitioners—who regarded it as a mere computational device— and even more so among scholars of continuum mechanics. The supreme irony is that Parrinello and Rahman themselves knew very little, if any, of continuum mechanics, and could not care less of it. Their unintentional contribution, expounded and extended in this paper, is a major testimony to the heuristic power of computational science. In their quest for a molecular dynamics method suited for studying solid-state phase transitions they were led, by an intrinsic necessity, to allow the computational cell to change its shape in exactly the same way as an infinitesimally small piece of a deformable medium is assumed to do in standard continuum mechanics.
Research efforts in the twenty-first century have been paramount to the discovery and development of novel pharmacological treatments in a variety of diseases resulting in improved life expectancy. ...Yet, cardiac disease remains a leading cause of morbidity and mortality worldwide. Over time, there has been an expansion in conditions such as atrial fibrillation (AF) and heart failure (HF). Although past research has elucidated specific pathways that participate in the development of distinct cardiac pathologies, the exact mechanisms of action leading to disease remain to be fully characterized. Protein turnover and cellular bioenergetics are integral components of cardiac diseases, highlighting the importance of mitochondria and endoplasmic reticulum (ER) in driving cellular homeostasis. More specifically, the interactions between mitochondria and ER are crucial to calcium signaling, apoptosis induction, autophagy, and lipid biosynthesis. Here, we summarize mitochondrial and ER functions and physical interactions in healthy physiological states. We then transition to perturbations that occur in response to pathophysiological challenges and how this alters mitochondrial-ER and other intracellular organelle interactions. Finally, we discuss lifestyle interventions and innovative therapeutic targets that may be used to restore beneficial mitochondrial and ER interactions, thereby improving cardiac function.
An early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the ...elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing.
Display omitted
•New research direction in solid modeling.•Algebraic relationships between CSG and boundary representations of PL solids.•Arrangements are isomorphic to the finite Boolean algebra of regularized sets.•This algebra is isomorphic to a linear vector space of 3-chains.•Operations on CSG and b-reps reduce to composition of algebraic operations. operations.
Since the beginning of the 20th century, it is known that the spontaneous bending of heterogeneous bilayered plates correlates with the self-stress due to the contrast in the material properties of ...the two layers, and that this correlation can be exploited to gauge the internal stress state. Over the last decades, ever-growing device miniaturization has made stress assessment and even stress engineering an area of major technological interest. In this paper, we obtain two effective 2D models accounting for the spontaneous bending of devices comprised of a thin substrate and a much thinner coating by applying a
Γ
-convergence technique to the standard 3D linear hyperelastic model of a bilayered plate. Our procedure is characterized by the introduction of two distinct smallness parameters plus three independent energy scaling parameters.
Proto-Plasm: parallel language for adaptive and scalable modelling of biosystems Bajaj, Chandrajit; DiCarlo, Antonio; Paoluzzi, Alberto
Philosophical transactions - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences,
09/2008, Volume:
366, Issue:
1878
Journal Article
Peer reviewed
Open access
This paper discusses the design goals and the first developments of Proto-Plasm, a novel computational environment to produce libraries of executable, combinable and customizable computer models of ...natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the Proto-Plasm platform is still in its infancy. Its computational framework-language, model library, integrated development environment and parallel engine-intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. Proto-Plasm may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a Proto-Plasm program. Here we exemplify the basic functionalities of Proto-Plasm, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions.
Since 1995, rates of end-stage renal disease have risen dramatically in patients living with HIV infection. However, given the concern for higher rates of acute rejection in this patient population, ...the immunologic threat posed by HIV infection is a specter clinicians must continually confront. Living donor transplantation may negate this risk; this study aims to assess the benefit of living donor transplantation in this population and to ascertain the immunologic risk faced by patients who are HIV-infected. The 2021 UNOS database was queried, and all HIV-infected kidney transplant recipients since 1987 were identified. Recipients were stratified based on deceased (DDKT) vs living (LDKT) donor status. Overall survival, allograft survival, acute rejection, panel reactive antibody (PRA) percentage, and crossmatch positivity were compared between groups. One thousand two hundred twenty-six patients underwent DDKT, and 304 patients underwent LDKT. Living donor kidney transplantation demonstrated greater overall survival (P = .045) and graft survival (P < .001). However, no difference in acute rejection was noted between the cohorts, and no difference in overall or graft survival was evident based on PRA percentage. Crossmatch positive status did not negatively affect graft survival. Patients with HIV undergoing LDKT fared better than those undergoing DDKT. Nevertheless, patients at higher immunologic risk-elevated PRA% and crossmatch positivity-did not experience graft loss at a higher rate than patients at lower immunologic risk. These results were valid in both DDKT and LDKT cohorts. These findings suggest that infection with HIV does not overtly increase patients' immunologic risk, and concerns surrounding transplantation in this population may be overestimated.
With increased complexity of geometric data, topological models play an increasingly important role beyond boundary representations, assemblies, finite elements, image processing, and other ...traditional modeling applications. While many graph- and index-based data structures have been proposed, no standard representation has emerged as of now. Furthermore, such representations typically do not deal with representations of mappings and functions and do not scale to support parallel processing, open source, and client-based architectures. We advocate that a proper mathematical model for all topological structures is a (co)chain complex: a sequence of (co)chain spaces and (co)boundary mappings. This in turn implies all topological structures may be represented by a collection of sparse matrices. We propose a Linear Algebraic Representation (LAR) scheme for mod 2 (co)chain complexes using CSR matrices and show that it supports a variety of topological computations using standard matrix algebra, without any overhead in space or running time. A full open source implementation of LAR is available and is being used for a variety of applications.
•A proper mathematical model for all topological structures is a (co)chain complex.•We propose a linear algebraic representation (LAR) scheme for representing such complexes.•The LAR scheme is fully implemented using sparse matrices.•The LAR scheme provides efficient support for topological queries and constructions.
Display omitted
We show how to construct, by exploiting adiabatic time and length scale separation between atomistic and continuum mechanics, a multiscale scheme for continuum dynamics free from macroscopic ...constitutive modeling. To do so, we introduce a new set of degrees of freedom that simultaneously represent the macroscopic and the microscopic dynamics, based on a space tessellation. In this new formulation, the dynamics of the macroscopic fields steers the microscopic particle dynamics by producing the conditions under which they evolve and, concurrently, the particle dynamics drives the evolution of the macroscopic fields by providing them with atomistically based constitutive information. Under conditions of adiabatic separation both in time and length scales, it is possible to decimate the tessellating cells and let the macroscopic equations of motion be driven by the time average of the terms coupling them with the microscopic degrees of freedom.
PDF
