Related papers: Singular perturbations and scaling
Quasi-steady state (QSS) reduction is a commonly used method to lower the dimension of a differential equation model of a chemical reaction network. From a mathematical perspective, QSS reduction is generally interpreted as a special type…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
The estimation of the kinetic parameters requires the careful design of experiments under a constrained set of conditions. Many estimates reported in the literature incorporate protocols that leverage simplified mathematical models known as…
In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their…
We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and may depend on many parameters, it is frequently of interest to obtain…
The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $\lambda_{m}$, exhibits…
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory…
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…
We elucidate the effects of chiral quenched disorder on the scaling properties of pure systems by considering a reduced model that is a variant of the quenched disordered cubic anisotropic O(N) model near its second order phase transition.…
Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from…
This paper is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this…
The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of…
Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wavenumber k like k^q. Alternatively, initial conditions are generated from a driven turbulence…