Continuum Limits of Discrete Models via $$\varGamma $$ Γ -Convergence

2016 ◽  
pp. 145-186
Author(s):  
Lucia Scardia
Keyword(s):  
Discrete Models ◽  
Γ Convergence

Discrete Models of Financial Markets

2009 ◽  
Author(s):  
Marek Capinski ◽  
Ekkehard Kopp
Keyword(s):  
Financial Markets ◽  
Discrete Models

Pathway Complexity in the Stacking of Imine-linked Macrocycles Related to Two-Dimensional Covalent Organic Frameworks

2019 ◽  
Author(s):  
Shiwei Wang ◽  
Anton Chavez ◽  
Simil Thomas ◽  
Hong Li ◽  
Nathan C. Flanders ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
Structural Similarity ◽  
Discrete Models ◽  
Side Chains ◽  
Two Dimensional ◽  
Assembly Process ◽  
Covalent Organic Frameworks ◽  
Electron Systems ◽  
Monomer Structure ◽  
Kinetic Traps

This work reports on the assembly of imine-linked macrocycles that serve as models of two-dimensional covalent organic frameworks (2D COFs). Interlayer interactions play an important role in the formation of 2D COFs, yet the effect of monomer structure on COF formation, crystallinity, and susceptibility to exfoliation are not well understood. For example, monomers with both electron-rich and electron-poor π-electron systems have been proposed to strengthen interlayer inter-actions and improve crystallinity. Here we probe these effects by studying the stacking behavior of imine-linked macrocycles that represent discrete models of 2D COFs. <div><br></div><div>Specifically, macrocycles based on terephthaldehyde (PDA) or 2,5-dimethoxyterephthaldehyde (DMPDA) stack upon cooling molecularly dissolved solutions. Both macrocycles assemble cooperatively with similar ΔHe values of -97 kJ/mol and -101 kJ/mol, respectively, although the DMPDA macrocycle assembly process showed a more straightforward temperature dependence. Circular dichroism spectroscopy performed on macrocycles bearing chiral side chains revealed a helix reversion process for the PDA macrocycles that was not observed for the DMPDA macrocycles. <br></div><div><br></div><div>Given the structural similarity of these monomers, these findings demonstrate that the stacking processes associated with nanotubes derived from these macrocycles, as well as for the corresponding COFs, are complex and susceptible to kinetic traps, casting doubt on the relevance of thermodynamic arguments for improving materials quality. <br></div>

scholarly journals Determination of Load-Carrying Capacity of C-Profile Glued Ti-Al Column under Temperature Environment

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3013
Author(s):  
Leszek Czechowski
Keyword(s):  
Carrying Capacity ◽  
Tensile Tests ◽  
Discrete Models ◽  
Image Correlation ◽  
Load Carrying Capacity ◽  
Lagrange Equations ◽  
Load Carrying ◽  
Different Temperatures ◽  
Influence Of Temperature On

The paper deals with an examination of the behaviour of glued Ti-Al column under compression at elevated temperature. The tests of compressed columns with initial load were performed at different temperatures to obtain their characteristics and the load-carrying capacity. The deformations of columns during tests were registered by employing non-contact Digital Image Correlation Aramis® System. The numerical computations based on finite element method by using two different discrete models were carried out to validate the empirical results. To solve the problems, true stress-logarithmic strain curves of one-directional tensile tests dependent on temperature both for considered metals and glue were implemented to software. Numerical estimations based on Green–Lagrange equations for large deflections and strains were conducted. The paper reveals the influence of temperature on the behaviour of compressed C-profile Ti-Al columns. It was verified how the load-carrying capacity of glued bi-metal column decreases with an increase in the temperature increment. The achieved maximum loads at temperature 200 °C dropped by 2.5 times related to maximum loads at ambient temperature.

Role of Surface RGD Patterns on Protein Nanocages in Tumor Targeting Revealed Using Precise Discrete Models

Small ◽  
2019 ◽  
Vol 15 (51) ◽  
pp. 1904838 ◽  
Author(s):  
Ti Fang ◽  
Weiwei Zhu ◽  
Chaoqun Li ◽  
Fan Zhang ◽  
Ding Gao ◽  
...  
Keyword(s):  
Tumor Targeting ◽  
Discrete Models

Continuous and discrete models for masonry like material: A critical comparative study

2015 ◽  
Vol 50 ◽  
pp. 39-58 ◽  
Author(s):  
Daniele Baraldi ◽  
Antonella Cecchi ◽  
Antonio Tralli
Keyword(s):  
Comparative Study ◽  
Discrete Models

scholarly journals From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

2014 ◽  
Vol 25 (01) ◽  
pp. 1-38 ◽  
Author(s):  
V. Agostiniani ◽  
T. Blass ◽  
K. Koumatos
Keyword(s):  
Coercivity Conditions ◽  
Coercivity Condition ◽  
Nematic Elastomers ◽  
Linearized Elasticity ◽  
Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

Sign in / Sign up

Export Citation Format

Share Document