Diauxic Growth at the Mesoscopic Scale

In the present paper, we study a diauxic growth that can be generated by a class of model at the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale, similarly to the logistic scale, one may ask whether models on mesoscopic or microscopic scales may lead to such a behavior. The present paper is the first step towards the developing of the mesoscopic models that lead to a diauxic growth at the macroscopic scale. We propose various nonlinear mesoscopic models conservative or not that lead directly to some diauxic growths.

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Multiscale Post-Seismic Deformation Based on cGNSS Time Series Following the 2015 Lefkas (W. Greece) Mw6.5 Earthquake

Applied Sciences ◽

10.3390/app11114817 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4817

Author(s):

Filippos Vallianatos ◽

Vassilis Sakkas

Keyword(s):

Time Series ◽

Relaxation Time ◽

Relaxation Times ◽

Relaxation Mechanism ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Epicentral Area ◽

Arrhenius Dependence ◽

Seismic Deformation ◽

Logarithmic Type

In the present work, a multiscale post-seismic relaxation mechanism, based on the existence of a distribution in relaxation time, is presented. Assuming an Arrhenius dependence of the relaxation time with uniform distributed activation energy in a mesoscopic scale, a generic logarithmic-type relaxation in a macroscopic scale results. The model was applied in the case of the strong 2015 Lefkas Mw6.5 (W. Greece) earthquake, where continuous GNSS (cGNSS) time series were recorded in a station located in the near vicinity of the epicentral area. The application of the present approach to the Lefkas event fits the observed displacements implied by a distribution of relaxation times in the range τmin ≈3.5 days to τmax ≈350 days.

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Escalas do tempo

Revista Acta Semiotica ◽

10.23925/2763-700x.2021n2.56802 ◽

2021 ◽

pp. 306-317

Author(s):

Eric Landowski

Keyword(s):

Great Effort ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Essential Variable ◽

Physiological Processes ◽

Long Duration ◽

Singular Event ◽

History Of ◽

Mesoscopic Level ◽

Different Time Scales

Viral epidemics are processes in which temporality obviously constitutes an essential variable. But different time scales must be distinguished. To see the current pandemic as a singular event is but an illusion due to the “mesoscopic” timescale we are embracing. There is a microscopic scale — that of physiological processes —, a mesoscopic scale, which only allows to see the closest evidence, and a macroscopic scale, that of the ecological determinisms which explain the emergence of the disease in the history of the relationships between species. The article focuses on the mesoscopic level and highlights some semiotic specificities of today’s experience : a temporal suspension, the threat of pure, dramatic and final discontinuity, the behavior of a virus that appears to have “intentionality”, a strong intensity coupled with a long duration, a time of exception, drawn to a final end, and a victory which will only be achieved with great effort.

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Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics

Symmetry ◽

10.3390/sym11081024 ◽

2019 ◽

Vol 11 (8) ◽

pp. 1024 ◽

Cited By ~ 7

Author(s):

Mirosław Lachowicz ◽

Henryk Leszczyński ◽

Elżbieta Puźniakowska–Gałuch

Keyword(s):

Differential Equations ◽

Kinetic Models ◽

Essential Role ◽

Opinion Dynamics ◽

Individual State ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Rigorous Result ◽

Numerical Examples ◽

Political Sciences

In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = - 1 ). The essential role is played by the symmetric nature of interactions. The class may be related to the mesoscopic scale of description. This means that we are going to statistically describe an individual state of an agent of the system. We show that the corresponding equations result at the macroscopic scale in two different pictures: anti-diffusive ( σ = 1 ) and diffusive ( σ = - 1 ). We provide a rigorous result on the convergence. The result captures the macroscopic behavior resulting from the mesoscopic one. In numerical examples, we observe both unipolar and bipolar behavior known in political sciences.

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A distributional approach to 2D Volterra dislocations at the continuum scale

European Journal of Applied Mathematics ◽

10.1017/s0956792512000010 ◽

2012 ◽

Vol 23 (3) ◽

pp. 417-439 ◽

Cited By ~ 11

Author(s):

NICOLAS VAN GOETHEM ◽

FRANÇOIS DUPRET

Keyword(s):

Single Crystals ◽

Strain Field ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Fundamental Identity ◽

Rigorous Framework ◽

Line Defects ◽

Continuum Scale ◽

Defect Densities ◽

The Continuum

We develop a theory to represent dislocations and disclinations in single crystals at the continuum (or mesoscopic) scale by directly modelling the defect densities as concentrated effects governed by the distribution theory. The displacement and rotation multi-valuedness is resolved by introducing the intrinsic and single-valued Frank and Burgers tensors from the distributional gradients of the strain field. Our approach provides a new understanding of the theory of line defects as developed by Kröner [10] and other authors [6, 9]. The fundamental identity relating the incompatibility tensor to the Frank and Burgers vectors (and which is a cornerstone of the theory of dislocations in single crystals) is proved in the 2D case under appropriate assumptions on the strain and strain curl growth in the vicinity of the assumed isolated defect lines. In general, our theory provides a rigorous framework for the treatment of crystal line defects at the mesoscopic scale and a basis to strengthen the theory of homogenisation from mesoscopic to macroscopic scale.

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Heat Transfer at Aluminum–Water Interfaces: Effect of Surface Roughness

Journal of Nanotechnology in Engineering and Medicine ◽

10.1115/1.4007584 ◽

2012 ◽

Vol 3 (3) ◽

Cited By ~ 4

Author(s):

H. Sam Huang ◽

Vikas Varshney ◽

Jennifer L. Wohlwend ◽

Ajit K. Roy

Keyword(s):

Heat Transfer ◽

Surface Roughness ◽

Finite Element ◽

Md Simulations ◽

Boundary Resistance ◽

Thermal Boundary Resistance ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Microscopic Scale ◽

Thermal Boundary Conductance

In this paper, we studied the effect of microscopic surface roughness on heat transfer between aluminum and water by molecular dynamic (MD) simulations and macroscopic surface roughness on heat transfer between aluminum and water by finite element (FE) method. It was observed that as the microscopic scale surface roughness increases, the thermal boundary conductance increases. At the macroscopic scale, different degrees of surface roughness were studied by finite element method. The heat transfer was observed to enhance as the surface roughness increases. Based on the studies of thermal boundary conductance as a function of system size at the molecular level, a procedure was proposed to obtain the thermal boundary conductance at the mesoscopic scale. The thermal boundary resistance at the microscopic scale obtained by MD simulations and the thermal boundary resistance at the mesoscopic scale obtained by the extrapolation procedure can be included and implemented at the interfacial elements in the finite element method at the macroscopic scale. This provides us a useful model, in which different scales of surface roughness can be included, for heat transfer analysis.

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Modeling and simulation of filling in dual-scale fibrous reinforcements: state of the art and new methodology to quantify the sink effect

Journal of Composite Materials ◽

10.1177/0021998317734038 ◽

2017 ◽

Vol 52 (14) ◽

pp. 1915-1946 ◽

Cited By ~ 4

Author(s):

Iván D Patiño-Arcila ◽

Juan D Vanegas-Jaramillo

Keyword(s):

Modeling And Simulation ◽

State Of The Art ◽

Void Formation ◽

Free Fluid ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Sink Effect ◽

Original Contribution ◽

Dual Scale

The main advances in the modeling and simulation of the filling phenomenon that takes place in dual-scale fibrous reinforcements used in liquid composites molding processes are grouped and classified in the present work. Special emphasis is done in the classification of the simulation methods according to the dimension of the mesh, the identification of the interface conditions porous medium-free fluid, the comparison between the most used fluid-front tracking techniques and the survey of researches dealing with the non-uniform filling of representative unitary cells, which in turn is responsible for the void formation at mesoscopic scale and the sink effect at macroscopic scale. As an original contribution to this field of study, a new methodology to quantify the sink effect in macroscopic fillings is presented and subsequently assessed by comparing the results of experimental radial injections with numerical results obtained by the dual reciprocity-boundary element method. The proposed methodology is physically consistent and leads to results that are closer to the experimental ones than the results obtained when the sink effect is neglected; however, the accuracy is liable to be improved.

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Introduction

10.1093/oso/9780199595068.003.0001 ◽

2017 ◽

Author(s):

Jochen Rau

Keyword(s):

Probability Theory ◽

Phase Transitions ◽

Statistical Mechanics ◽

Conservation Laws ◽

Law Of Large Numbers ◽

Macroscopic Scale ◽

Classical Probability ◽

Large Numbers ◽

Microscopic World ◽

New Phenomena

Statistical mechanics concerns the transition from the microscopic to the macroscopic realm. On a macroscopic scale new phenomena arise that have no counterpart in the microscopic world. For example, macroscopic systems have a temperature; they might undergo phase transitions; and their dynamics may involve dissipation. How can such phenomena be explained? This chapter discusses the characteristic differences between the microscopic and macroscopic realms and lays out the basic challenge of statistical mechanics. It suggests how, in principle, this challenge can be tackled with the help of conservation laws and statistics. The chapter reviews some basic notions of classical probability theory. In particular, it discusses the law of large numbers and illustrates how, despite the indeterminacy of individual events, statistics can make highly accurate predictions about totals and averages.

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