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See detailUniaxial negative thermal expansion and metallophilicity in Cu3[Co(CN)6]
Sapnik, A. F.; Liu, X.; Böstrom, H. L. B. et al

in Journal of Solid State Chemistry (2018), 258

We report the synthesis and structural characterisation of the molecular framework copper(I) hexacyanocobaltate(III), Cu3[Co(CN)6], which we find to be isostructural to H3[Co(CN)6] and the colossal ... [more ▼]

We report the synthesis and structural characterisation of the molecular framework copper(I) hexacyanocobaltate(III), Cu3[Co(CN)6], which we find to be isostructural to H3[Co(CN)6] and the colossal negative thermal expansion material Ag3[Co(CN)6]. Using synchrotron X-ray powder diffraction measurements, we find strong positive and negative thermal expansion behaviour respectively perpendicular and parallel to the trigonal crystal axis: α = 25.4(5) MK a −1 and α = − 43.5(8) MK c −1. These opposing effects collectively result in a volume expansivity α = 7.4(11) MK V −1 that is remarkably small for an anisotropic molecular framework. This thermal response is discussed in the context of the behaviour of the analogous H- and Ag-containing systems. We make use of density-functional theory with many-body dispersion interactions (DFT + MBD) to demonstrate that Cu+…Cu+ metallophilic (‘cuprophilic’) interactions are significantly weaker in Cu3[Co(CN)6] than Ag+…Ag+ interactions in Ag3[Co(CN)6], but that this lowering of energy scale counterintuitively translates to a more moderate—rather than enhanced—degree of structural flexibility. The same conclusion is drawn from consideration of a simple GULP model, which we also present here. Our results demonstrate that strong interactions can actually be exploited in the design of ultra-responsive materials if those interactions are set up to act in tension. [less ▲]

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See detailA force-based large increment method for 2D continuum solids and the mesh convergence study
Long, D.; Guo, Z.; Liu, X. et al

in AIP Conference Proceedings (2012), 1504

In this paper, a triangular plane stress element is implemented based on the large increment method (LIM) to solve 2D continuum mechanics problems. In the LIM, after the governing equations are ... [more ▼]

In this paper, a triangular plane stress element is implemented based on the large increment method (LIM) to solve 2D continuum mechanics problems. In the LIM, after the governing equations are established using the generalized elemental force variables as primary unknowns, an iteration procedure is employed to obtain an optimised approximate solution of the problem. Two numerical examples are investigated to study the mesh convergence of the proposed triangular LIM element. Structured meshes as well as unstructured meshes with different element densities are generated to illustrate the convergence of the total strain energy in both examples. The numerical results obtained from the LIM (including the total strain energy, the displacement and the stress) are compared with the analytical solutions as well as the results from the commercial FEM software ABAQUS. All the results show that the performance of the LIM is as good as the FEM in linear elastic problems. A simple elastoplastic example suggests that the LIM may obtain better result than the FEM. © 2012 American Institute of Physics. [less ▲]

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See detailMonostability and multistability of genetic regulatory networks with different types of regulation functions
Pan, Wei UL; Wang, Z; Gao, H. et al

in Nonlinear Analysis : Real World Applications (2010), 11(4), 31703185

Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by ... [more ▼]

Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]

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See detailApplication of robust model validation using SOSTOOLS to the study of G-Protein signalling in yeast
Yi, T.; Fazel, M.; Liu, X. et al

Scientific Conference (2005)

Two major methodological challenges in modeling biological systems are model (in)validation and parameter estimation. The traditional approach is to fit the model parameters to data. An alternative ... [more ▼]

Two major methodological challenges in modeling biological systems are model (in)validation and parameter estimation. The traditional approach is to fit the model parameters to data. An alternative approach pioneered by Packard, Frenklach, Seiler and colleagues (Frenklach et al., 2002) defines the range of parameter values that is consistent with the data while taking into account parametric and data uncertainty. If an invalidation certificate is found, the feasible parameter space is proved empty; otherwise, attempts to describe the feasible parameter space are carried out. We refer to this methodology as Robust Model Validation (RMV). Here we perform RMV using sum of squares (SOS) programs implemented by the MATLAB toolbox SOSTOOLS (Prajna et al., 2002). The principal advantage of SOS over conventional semidefinite programming (SDP) techniques such as the Sprocedure is the possibility of using higher-order multipliers to obtain tighter parameter bounds. We applied SOSTOOLS to a simple model of the yeast heterotrimeric G-protein cycle. We were able to invalidate the model based on real experimental data. Furthermore, using synthetic data that did not invalidate the model, we explored different techniques for representing the feasible parameter space. [less ▲]

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