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Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple". Here we consider a very simple mixture of two colloidal and one non-adsorbing polymer species which can be…

It is well known that for a large class of coagulation kernels, Smoluchowski coagulation equations have particular power law solutions which yield a constant flux of mass along all scales of the system. In this paper, we prove that for some…

Analysis of PDEs · Mathematics 2022-07-26 Marina A. Ferreira , Jani Lukkarinen , Alessia Nota , Juan J. L. Velázquez

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

Numerical Analysis · Mathematics 2018-03-09 D. Jodlbauer , U. Langer , T. Wick

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j} = i^{\nu}j^{\mu} + j^{\nu}i^{\mu}$ homogeneous in masses $i$ and $j$ of…

Statistical Mechanics · Physics 2023-07-18 N. V. Brilliantov , W. Otieno , S. A. Matveev , A. P. Smirnov , E. E. Tyrtyshnikov , P. L. Krapivsky

We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster…

Statistical Mechanics · Physics 2020-10-28 N. V. Brilliantov , A. I. Osinsky , P. L. Krapivsky

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than…

Analysis of PDEs · Mathematics 2009-11-11 Alan Hammond , Fraydoun Rezakhanlou

In this paper, we employ Molecular Dynamics computer simulations to study and compare the statics and dynamics of linear and circular (ring) polymer chains in entangled solutions of different densities. While we confirm that linear chain…

Soft Condensed Matter · Physics 2016-02-17 Negar Nahali , Angelo Rosa

In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or \textit{soft}…

Analysis of PDEs · Mathematics 2019-03-05 Maxime Laborde

Coagulation-flocculation, the physicochemical process widely used for purification a wastewater, is affected both by chemical details of involved polymers and by the statistics of their conformations on a large scale. The latter aspect is…

Soft Condensed Matter · Physics 2024-07-23 V. Blavatska , Ja. Ilnytskyi , E. Lähderanta

We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a particle has been grabbed then it cannot be…

Probability · Mathematics 2009-06-04 Jean Bertoin , Vladas Sidoravicius , Maria Eulalia Vares

An off-lattice Monte Carlo algorithm for solutions of equilibrium polymers (EP) is proposed. At low and moderate densities this is shown to reproduce faithfully the (static) properties found recently for flexible linear EP using a lattice…

Statistical Mechanics · Physics 2009-10-31 A. Milchev , J. P. Wittmer , D. P. Landau

Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume…

Statistical Mechanics · Physics 2010-11-24 N. Dorsaz , C. De Michele , F. Piazza , P. De Los Rios , G. Foffi

Proteinaceous aggregation occurs through self-assembly-- a process not entirely understood. In a recent article [1], an analytical theory for amyloid fibril growth via secondary rather than primary nucleation was presented. Remarkably, with…

Biological Physics · Physics 2010-06-16 Barry D. Ganapol

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom…

Soft Condensed Matter · Physics 2009-11-11 Yu. B. Gaididei , P. L. Christiansen , W. J. Zakrzewski

The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding…

Soft Condensed Matter · Physics 2013-05-30 D. Zeb Rocklin , Shina Tan , Paul M. Goldbart

We provide a new proof for the global well-posedness of systems coupling fluids and polymers in two space dimensions. Compared to the well-known existing method based on the losing a priori estimates, our method is more direct and much…

Analysis of PDEs · Mathematics 2012-03-14 Zhen Lei , Yun Wang

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…

Analysis of PDEs · Mathematics 2008-03-19 Jens Jonasson

A co-polycondensation reaction is discussed analytically and by Monte-Carlo simulations where two reactive units compete for reactions with an alternating third reactive unit, whereby irreversible reactions replace bonds which are able to…

Soft Condensed Matter · Physics 2021-05-26 Michael Lang , Frank Böhme

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…

Analysis of PDEs · Mathematics 2021-05-28 José A. Carrillo , David Gómez-Castro , Yao Yao , Chongchun Zeng

We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…

Probability · Mathematics 2023-08-22 Suprio Bhar , Rajeev Bhaskaran , Arvind Kumar Nath