Related papers: Identifying Reaction Pathways in Phase Space via A…
Reaction-diffusion-advection media on semi-infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling…
We develop tools from computational algebraic geometry for the study of steady state features of autonomous polynomial dynamical systems via elimination of variables. In particular, we obtain nontrivial bounds for the steady state…
The evolution of chemical reaction networks is often analyzed through kinetic models and energy landscapes, but these approaches fail to capture the deeper structural constraints governing complexity growth. In chemical reaction networks,…
Contemporary work implies generative machine learning models are capable of learning the phase behavior in condensed matter systems such as the Ising model. In this Letter, we utilize a score-based modeling procedure called Thermodynamic…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We consider steady-state diffusion in a three-dimensional bounded domain with a smooth reflecting boundary that is partially covered by small partially reactive patches. By using the method of matched asymptotic expansions, we investigate…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the…
A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…
Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a linear Lineweaver-Burk plot. While such a graphical plot is sometimes good to achieve the end, it is always better to go for a few…
A L{\'e}vy walk of order $\beta$ is studied on an interval of length $L$, driven out of equilibrium by different-density boundary baths. The anomalous current generated under these settings is nonlocally related to the density profile…
We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We provide conditions on the microscopic…
A theory for chemical reaction dynamics in condensed phase systems based on the generalized Langevin formalism of Grote and Hynes is presented. A microscopic approach to calculate the dynamic friction is developed within the framework of a…
Topological band theory has transformed our understanding of crystalline materials by classifying the connectivity and crossings of electronic energy levels. Extending these concepts to molecular systems has therefore attracted significant…
In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This…
A three-dimensional phase-field approach to martensitic transformations that uses reaction pathways in place of a Landau potential is introduced and applied to a model of Fe3Ni. Pathway branching involves an unbounded set of variants…
The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…
We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From…
Reaction-diffusion processes play an important role in a variety of physical, chemical, and biological systems. Conventionally, the kinetics of these processes are described by the law of mass action. However, there are various cases where…