Related papers: The minimal model of Hahn for the Calvin cycle
This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are…
The dynamics of a mathematical model of the Calvin cycle, which is part of photosynthesis, is analysed. Since diffusion of ATP is included in the model a system of reaction-diffusion equations is obtained. It is proved that for a suitable…
Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric…
In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in a…
In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural…
A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arXiv:2510.17296 we introduced a novel…
We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the…
We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to…
A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of the process of condensation in such a system is constructed. The free energy of formation of the…
In our recent work we found a surprising breakdown of symmetry conservation: using standard numerical discretization with very high precision the computed numerical solutions corresponding to very nice initial data may converge to…
Implicit-Explicit methods have been widely used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due to the lack of maximum principle and stiffness caused by the…
Traditional mathematical models of photosynthesis are based on mass action kinetics of light reactions. This approach requires the modeller to enumerate all the possible state combinations of the modelled chemical species. This leads to…
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are…
We consider the Schr\"odinger--Poisson--Newton equations for crystals with a cubic lattice and one ion per cell. We linearize this dynamics at the ground state and introduce a novel class of the ion charge densities which provide the…
We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn model with a nonlocal constraint for crystal growth that conserves the mass of each phase. Solvability conditions are established for the…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…
While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We propose a scheme for continuous generation and stabilization…