MICRO AND MESO SCALES OF DESCRIPTION CORRESPONDING TO A MODEL OF TISSUE INVASION BY SOLID TUMOURS

2005 ◽  
Vol 15 (11) ◽  
pp. 1667-1683 ◽  
Author(s):  
MIROSŁAW LACHOWICZ
Keyword(s):  
Mathematical Models ◽  
Type Equation ◽  
Reaction Diffusion ◽  
Solid Tumours ◽  
Macroscopic Model ◽  
Scale Level ◽  
Micro Scale ◽  
Tissue Invasion ◽  
Mathematical Relationships ◽  
Meso Scale

In this paper two new mathematical models are proposed that correspond to a macroscopic model of tissue invasion of solid tumours, in terms of a system of reaction-diffusion-chemotaxis equations. The first model is defined at the micro-scale level of a large number of interacting individual entities, and is in terms of a linear (Markov) equation. The second model refers to the meso-scale level of description of test-entities and is given in terms of a bilinear Boltzmann-type equation. Mathematical relationships among these three possible descriptions are formulated. Explicit error estimates are given.

Analysis of smallholder farmers’ vulnerability to climate change and variability in south Wollo, north east highlands of Ethiopia: An agro-ecological system-based approach

2021 ◽  
Author(s):  
Yimer Mohammed ◽  
Kindie Tesfaye ◽  
Menfese Tadesse ◽  
Fantaw Yimer
Keyword(s):  
Climate Change ◽  
Adaptive Capacity ◽  
Smallholder Farmers ◽  
Contributing Factors ◽  
Scale Level ◽  
Ecological Zones ◽  
Micro Scale ◽  
Climate Change And Variability ◽  
North East ◽  
Agro Ecological Zones

Abstract Background: Climate change and variability has been significantly affecting the Ethiopian agricultural production and thereby smallholder farmers livelihoods. The level of vulnerability varied across agro-ecological zones (AEZs). Identification of difference in the level of vulnerability of a system is important in selecting appropriate and effective adaption options to climate change. Therefore, the aim of this study was to analyze the level of vulnerability of agricultural communities to climate change and variability at micro-scale level in five agro-ecological zones (AEZs) of south Wollo, north east highlands of Ethiopia. Data was collected from a representative of 502 sample households from five AEZs through multi stage random sampling methods. Focus group discussion and key informant interviews were also carried out to supplement and substantiate the quantitative data. The indicator based approach was used to empirically calculate vulnerability. Principal Component Analysis (PCA) was applied to give weight for indicators and generate index of vulnerability contributing factors. Results: The results showed that each of the vulnerability contributing factors (exposure, sensitivity and adaptive capacity) varied across the AEZs. M3, SM2 and SM3 are the most exposed AEZs but having a relatively better adaptive capacity whereas M1, M2 and M3 are the most sensitive AEZs with relatively low adaptive capacity to climate variability and change. Overall, SM2 is the most vulnerable AEZ which exhibited high sensitivity and low adaptive capacity followed by M1. Conclusions: The study explored sources and levels of vulnerability to each agro-ecology. Since the study is conducted at micro-scale level, it helps decision makers and development partners to have context-specific understanding of the impact of climate change and variability and design appropriate adaptation measures to address the specific situations.

Effect of micro-scale morphological parameters on meso-scale response of Asphalt Concrete

2014 ◽  
pp. 1775-1784 ◽  
Author(s):  
Ibrahim Onifade ◽  
Denis Jelagin ◽  
Alvaro Guarin ◽  
Björn Birgisson ◽  
Nicole Kringos
Keyword(s):  
Asphalt Concrete ◽  
Morphological Parameters ◽  
Micro Scale ◽  
Scale Response ◽  
Meso Scale

Multi-Scale Analysis of Viscoelastic Behavior of Laminated Composite Structures

2010 ◽  
Vol 430 ◽  
pp. 115-132
Author(s):  
Y. Shibuya ◽  
Hideki Sekine
Keyword(s):  
Viscoelastic Properties ◽  
Composite Structures ◽  
Viscoelastic Behavior ◽  
Laminated Composite ◽  
Scale Analysis ◽  
Scale Level ◽  
Micro Scale ◽  
Multi Scale ◽  
Laminated Composite Structures ◽  
Multi Scale Analysis

For high temperature applications of laminated composite structures, viscoelastic behavior of laminated composite structures is investigated by multi-scale analysis based on a homogenization theory. Effective viscoelastic properties of the laminas are evaluated by a boundary integral method at a micro-scale level, and viscoelastic analysis for laminated composite structures is performed by a finite element method at a macro-scale level using the effective viscoelastic properties of lamina obtained by the micro-scale analysis. In the multi-scale analysis, the Laplace transformation is adopted and the correspondence principle between elastic and viscoelastic solutions in the Laplace domain is applied. The inverse Laplace transform is formulated by the Duhamel integral, and is calculated numerically. As a numerical example, a laminated composite plate with a hole is treated and the viscoelastic behavior of the laminated composite structure is elucidated.

scholarly journals Measurement of Spindle Thermal Growth on a Machine Intended for Micro/Meso Scale Milling

2010 ◽  
Vol 447-448 ◽  
pp. 55-60 ◽  
Author(s):  
J.B. Saedon ◽  
Sein Leung Soo ◽  
David K. Aspinwall
Keyword(s):  
Control System ◽  
Literature Review ◽  
Injection Moulding ◽  
Micro Milling ◽  
Measuring Systems ◽  
Warm Up ◽  
Micro Scale ◽  
Thermal Growth ◽  
Acceleration And Deceleration ◽  
Meso Scale

Micro milling is gaining ground as the preferred process for the manufacture of micro/meso-scale components in conventional workpiece materials, in particular for miniature moulds and tooling inserts (~ 60HRC), for the plastics injection moulding industry. Following a brief literature review on microscale milling and associated machine tool/tooling developments, experimental results are presented in relation to spindle thermal growth for a compensated/cooled spindle operating at up to 60,000 rpm, designed to accommodate the machining of meso-scale/micro-scale components. The work involved investigation of spindle warm up and cool down rates for speeds ranging from 30,000 - 60,000 rpm and subsequently the evaluation of spindle growth using both non-contact and contact measuring systems. Growth levels of up to 16µm were detected despite active spindle cooling and the incorporation of a standard compensation algorithm within the control system. Modification to spindle acceleration and deceleration rates reduced error levels by up to 50%.

scholarly journals Fabrication of beam structures with micro-scale cross-sections and meso-scale spans

2007 ◽  
Vol 17 (12) ◽  
pp. 2516-2521 ◽  
Author(s):  
Michael James Martin ◽  
Robert D White ◽  
Katsuo Kurabayashi ◽  
Iain D Boyd
Keyword(s):  
Cross Sections ◽  
Beam Structures ◽  
Micro Scale ◽  
Meso Scale

Modeling of Mechanical Behavior of Ceramic Nanocomposites

2015 ◽  
Vol 756 ◽  
pp. 187-195 ◽  
Author(s):  
Irina K. Vaganova ◽  
Evgeniya G. Skripnyak ◽  
Vladimir V. Skripnyak ◽  
Vladimir A. Skripnyak
Keyword(s):  
Particle Velocity ◽  
Fracture Stress ◽  
Computational Models ◽  
Ceramic Composites ◽  
Scale Level ◽  
Resonance Behavior ◽  
Critical Fracture ◽  
Critical Fracture Stress ◽  
Meso Scale ◽  
Ceramic Nanocomposites

Deformation and damage occurring at the meso-scale level in structured representative volumes (RVE) of modern nanocomposites in wide loading conditions were simulated. The computational models of a structured RVE of ceramic nanocomposites were developed using the data of structure researches on meso-, micro -, and nanoscale levels. The critical fracture stress on meso-scale level depends not only on relative volumes of voids and inclusions, but also on the parameters of inclusion clusters. The critical fracture stress at the meso-scale level depends not only on relative volumes of voids and strengthened phases, but also on sizes of corresponding structure elements. In the studied ceramic composites the critical failure stress is changed non-monotonically with growth of the volume concentration of strengthening phase particles. At identical porosity, concentration of nanovoids in the vicinity of grain boundaries causes the decrease in the shear strength of nanostructured and ultrafine-grained ceramics. It is revealed that the occurrence of bimodal distributions of the local particle velocity at the meso-scale level precedes the nucleation of microcracks. At mesoscale level of ceramic nanocomposites the pressure and particle velocity distribution don’t display a resonance behavior under submicrosecond single shock pulse loading or repeated pulse loadings.

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