Angular scattering functions for subchains defined by a generator matrix treatment of simple chains with excluded volume

1982 ◽  
Vol 15 (2) ◽  
pp. 579-582
Author(s):  
Wayne L. Mattice
Keyword(s):  
Excluded Volume ◽  
Generator Matrix ◽  
Angular Scattering

A Field Theory for Polymeric Networks with Excluded Volume

1995 ◽  
Vol 5 (10) ◽  
pp. 1241-1246 ◽  
Author(s):  
Thomas A. Vilgis ◽  
Michael P. Solf
Keyword(s):  
Field Theory ◽  
Excluded Volume ◽  
Polymeric Networks

scholarly journals Angular Scattering Properties of Metasurfaces

2020 ◽  
Vol 68 (1) ◽  
pp. 432-442
Author(s):  
Karim Achouri ◽  
Olivier J. F. Martin
Keyword(s):  
Angular Scattering

scholarly journals An interplay of excluded-volume and polymer–(co)solvent attractive interactions regulates polymer collapse in mixed solvents

2021 ◽  
Vol 154 (13) ◽  
pp. 134903
Author(s):  
Swaminath Bharadwaj ◽  
Divya Nayar ◽  
Cahit Dalgicdir ◽  
Nico F. A. van der Vegt
Keyword(s):  
Mixed Solvents ◽  
Excluded Volume ◽  
Polymer Collapse

scholarly journals Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
J. S. Kłos ◽  
J. Paturej
Keyword(s):  
Electrostatic Interactions ◽  
Spatial Separation ◽  
Excluded Volume ◽  
The Core ◽  
Bjerrum Length ◽  
Two Component ◽  
Conformational Properties ◽  
Dynamics Simulations ◽  
Two Parameters ◽  
Swelling Factor

AbstractLangevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, $$\lambda _B^*$$ λ B ∗ , which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, $$f_b$$ f b , which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by $$f_b$$ f b . For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing $$f_b$$ f b . For strong electrostatic couplings the dendrimer deswells correspondingly to $$f_b$$ f b . In this regime a spatial separation of the counterions into core–shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

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