25 papers · ranked by Valyu relevance
Giorgio Kaniadakis, Dionissios T. Hristopulos
Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear…
G. Kaniadakis, Dionissios T. Hristopulos
Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear…
Camran Ali, Donna G. Blackmond, Jordi Burés
Catalytic Cascade Reactions under Curtin–Hammett Conditions Authors: ['Camran Ali' 'Donna G. Blackmond' 'Jordi Burés'] Observations of nonlinear effects of catalyst enantiopurity on product enantiomeric excess in asymmetric catalysis are often used to infer that more than one catalyst species is involved in one or more…
Didier Sornette, Virgile Troude
Life is commonly described as a self-organized, far-from-equilibrium process that maintains internal order by consuming free energy and exporting entropy. This thermodynamic view underlies diverse theoretical frameworks—from autopoiesis and relational biology to autocatalytic sets and hypercycles—yet dissipation is…
W. H. Matthaeus, S. Oughton, K. T. Osman, S. Servidio + 7 more
'S. Peter Gary' 'M. A. Shay' 'F. Valentini' 'V. Roytershteyn' 'H. Karimabadi' 'S. C. Chapman'] The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the…
Denis S. Grebenkov, Anan Yaghmur
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the…
Wei-Hsiang Lin, Edo Kussell, Lai-Sang Young, Christine Jacobs-Wagner
Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of…
Jeremy Gunawardena, Kumar Selvarajoo
Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights…
Authors not listed
Dynamics of population growth or enzyme kinetics do not follow a constant rate making them difficult to quantify. Therefore, a single measure of dynamics is desired to profile the kinetic activities of enzymes with respect to various substrates. In this work, we use a growth model to model enzyme kinetics and provide a…
William Green
A longstanding project of the chemical kinetics community is to predict reaction rates and the behavior of reacting systems, even for systems where there are no experimental data. Many important reacting systems (atmosphere, combustion, pyrolysis, partial oxidations) involve a large number of reactions occurring…
S. N. Patitsas
A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic…
Stuart T. Johnston, Ruth E. Baker, Sean D.L McElwain, Matthew J. Simpson
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based process that models the birth, death and movement of individuals. The model distinguishes between individuals…
Ruud Stoof, Ángel Goñi-Moreno
Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Thomas E. Woolley
Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is…
L. M. Martyushev, В. Д. Селезнев
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces has been proposed. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces…
Santosh Manicka, Kathleen Johnson, Michael Levin, David Murrugarra
The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed ‘regulatory nonlinearity’, we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear…
Yijie Deng, Douglas Raymond Beahm, Xinping Ran, Tanner G Riley + 1 more
Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical…
Evangelos Bakalis, Francesco Zerbetto
Kinetics: Classical, Fractal, or Fractional? Authors: ['Evangelos Bakalis' 'Francesco Zerbetto'] Adsorption-limited kinetics may be described by phenomenological pseudo-order models. Such models leverage on the general principle that the rate of change of the adsorbed material depends on some power of its…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a reaction mechanism of zymogen activation. The reaction consists of a primary non-observable zymogen activation reaction that it is coupled to an indicator (observable) reaction. The product of the first…
Mariona Fucho-Rius, Smitha Maretvadakethope, Rubén Pérez-Carrasco, Àlex Haro + 2 more
The behavior of nonlinear systems close to critical transitions has relevant implications in assessing complex systems’ stability, transient properties, and resilience. Transient times become extremely long near phase transitions (or bifurcations) in a phenomenon generically known as critical slowing down, observed in…
E. N. Miranda
The empirical laws of chemical kinetics are studied from a microscopic point of view. An analysis based on elementary probability theory and combinatorics is enough to explain the kinetics law observed in experiments. Thus, an out of equilibrium system may be examined with tools available to a student who begins the…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…