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The Role of Charge Regulation in Weak Polyampholytes
Lunkad, Raju ; Košovan, Peter (advisor) ; de Sousa Dias, Rita (referee) ; Gonzalez, Jose Luis Garces (referee)
A weak polyampholyte is a polymer that consists of both acid and base groups along the chain. In aqueous solutions, these groups dissociate in a certain pH range, leading to a dramatic change in the overall charge of the polyampholyte from positive to negative as the pH increases. The ability of weak ampholytes to switch their charge in response to changes in pH makes them useful in various applications. Despite the considerable research on weak polyampholytes, the understanding of some aspects is still insufficient. To address this, I systematically investigated the charge regulation of weak polyam- pholytes, specifically peptides, both in solution and during their interaction with polyelectrolytes. Furthermore, I also looked at the charge regulation of polyzwitterions. All these studies were carried out using a simple coarse-grained bead-spring model in Langevin dynamics simulations. In addition, I used the constant-pH ensemble to account for the ionization reactions of acid and base groups in the implicit solvent. Through our simulations, we made significant advancements in understanding how charges and the ionization states of acid and base groups in various peptides and polyzwitterions respond to pH changes. By comparing simulation results with the ideal results predicted by the...
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Inverse mass matrix for higher-order finite element method in linear free-vibration problems
Kolman, Radek ; González, J.G. ; Cimrman, Robert ; Kopačka, Ján ; Cho, S.S. ; Park, B.G.
In the paper, we present adirect inverse mass matrix in the higher-orderfinite element method forsolid mechanics. The direct inverse mass matrix is sparse, has the same structure as the consistent mass matrixand preserves the total mass. The core of derivation of the semi-discrete mixed form is based on the Hamilton’s principle of leastaction. The cardinal issue is finding the relationship between discretized velocities and discretized linear momentum. Finally, the simple formula for the direct inversemass matrix is presented as well as thechoice of density-weighted dual shape functions for linear momentum with respect to the displacement shape functionwith achoice of the lumping mass method for obtaining the correct and positive definitive velocity-linear momentum operator. The application of Dirichlet boundaryconditions into the direct inversemass matrix forafloating system is achieved usingthe projection operator. The suggested methodology is tested on a free-vibration problem of heterogeneous bar for different ordersof shape functions.
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An explicit time scheme with local time stepping for one-dimensional wave propagation in a bimaterial bar
Kolman, Radek ; Cho, S.S. ; Gonzalez, J.G. ; Park, K.C. ; Berezovski, A.
In this paper, we test a two-time step explicit scheme with local time stepping. The standard explicit time scheme in finite element analysis is not able to keep accuracy of stress distribution through meshes with different local Courant numbers for each finite element. The used two-time step scheme with the diagonal mass matrix is based on the modification of the central difference method with pullback interpolation. We present a numerical example of one-dimensional wave propagation in a bimaterial elastic bar. Based on numerical tests, the employed time scheme with pullback interpolation and local stepping technique is able to eliminate spurious oscillations in stress distribution in numerical modelling of shock wave propagation in heterogeneous materials.
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