Related papers: Duality Between Chemical Potential Dynamics and Re…
Experimental studies of protein-pattern formation have stimulated new interest in the dynamics of reaction-diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially extended…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation…
Modern materials are often synthesized or operated in complex chemical environments, where there can be numerous elemental species, competing phases, and reaction pathways. When analyzing reactions using the Gibbs free energy, which has a…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…
Employing a two-species Cahn-Hilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the robust coexistence of uniform stationary and oscillatory phases as well as of…
Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that…
We study chemical pattern formation in a fluid between two flat plates and the effect of such patterns on the formation of convective cells. This patterning is made possible by assuming the plates are chemically reactive or release reagents…
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…
We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second…
Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we…
Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD,…
By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically-symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex…
Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered from the point of view of interface motion. A dissipative nonlocal equation of motion for the boundary between high and low…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…