On the Transition of a Mesoscopic System to a Macroscopic System

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

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Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment

Journal of Mathematical Biology ◽

10.1007/s00285-021-01599-x ◽

2021 ◽

Vol 82 (6) ◽

Author(s):

Pawan Kumar ◽

Jing Li ◽

Christina Surulescu

Keyword(s):

Multiscale Modeling ◽

Reaction Diffusion ◽

Tumor Grade ◽

Invasive Potential ◽

Macroscopic System ◽

Active Particles ◽

Reaction Diffusion Model ◽

Different Types ◽

Parabolic Scaling ◽

Parameter Ranges

AbstractGliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .

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QCD as a Mesoscopic System

10.1063/1.1996891 ◽

2005 ◽

Author(s):

Jacobus Verbaarschot

Keyword(s):

Mesoscopic System

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Measurement of the Intrinsic Dissipation of a Macroscopic System in the Quantum Regime

Physical Review Letters ◽

10.1103/physrevlett.82.5357 ◽

1999 ◽

Vol 82 (26) ◽

pp. 5357-5360 ◽

Cited By ~ 24

Author(s):

C. Cosmelli ◽

P. Carelli ◽

M. G. Castellano ◽

F. Chiarello ◽

G. Diambrini Palazzi ◽

...

Keyword(s):

Macroscopic System ◽

Quantum Regime ◽

Intrinsic Dissipation

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Lifelong Inclusive Education Service System in the Context of the 2030 Agenda for Sustainable Development

World Journal of Educational Research ◽

10.22158/wjer.v7n2p120 ◽

2020 ◽

Vol 7 (2) ◽

pp. p120

Author(s):

Feng -Xia ◽

Yongfen -Gu ◽

Meixian -Huang

Keyword(s):

Sustainable Development ◽

Inclusive Education ◽

Learning Opportunities ◽

Macroscopic System ◽

2030 Agenda ◽

The People ◽

Education Service ◽

Output Efficiency ◽

New Perspective ◽

Future Education

Transforming our World: The 2030 Agenda for Sustainable Development, which is issued by the United Nations in 2015, put forward 17 goals for sustainable development to promote worldwide peace and freedom. Among the 17 goals, one goes to the education vision, stating that “Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all”. This goal further and clearly describes the features of the future education: lifelong, inclusive, fair and high-quality. To make the dream true, every country should rethink the present education service and make reforms based on the national situation. In this context, this paper discusses the direction, construction, objects and layout of a lifelong inclusive education service suitable for present China’s national conditions, in hope of contributing Chinese wisdom to the “Community of shared future for mankind”. It is suggested in this paper that we should give priority to the construction and perfection of the macroscopic system and operating mechanisms for the lifelong inclusive education service in consideration of input and output efficiency; that we should update our mind and think of the education from a new perspective, that is, regard the lifelong inclusive education service as part of public service for all the people; that we should provide suitable education service for all students, regardless of age, race, disability, gender and wealth; that we should design and implement the educational projects reasonably and scientifically in order to better realize the goal.

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The diminishing role of hubs in dynamical processes on complex networks

Journal of The Royal Society Interface ◽

10.1098/rsif.2013.0568 ◽

2013 ◽

Vol 10 (88) ◽

pp. 20130568 ◽

Cited By ~ 27

Author(s):

Rick Quax ◽

Andrea Apolloni ◽

Peter M. A. Sloot

Keyword(s):

Interaction Network ◽

Macroscopic System ◽

Protein Protein Interaction ◽

Equilibrium Dynamics ◽

Qualitative Evidence ◽

Individual Unit ◽

System Of Units ◽

Protein Protein Interaction Network

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.

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