465 research outputs found
Some results on injectivity and multistationarity in chemical reaction networks
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasise the connections between the results, and where possible, present elementary proofs which rely solely on basic linear algebra and calculus. A number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper
Development of overturning circulation in sloping waterbodies due to surface cooling
This work was supported by the Swiss National Science Foundation (project Buoyancy driven nearshore transport in lakes, HYPOlimnetic THErmal SIphonS, HYPOTHESIS, reference 175919) and by the Physics of Aquatic Systems Laboratory (APHYS), EPFL.Cooling the surface of freshwater bodies, whose temperatures are above the temperature
of maximum density, can generate differential cooling between shallow and deep regions.
When surface cooling occurs over a long enough period, the thermally induced cross-shore
pressure gradient may drive an overturning circulation, a phenomenon called ‘thermal
siphon’. However, the conditions under which this process begins are not yet fully
characterised. Here, we examine the development of thermal siphons driven by a uniform
loss of heat at the air–water interface in sloping, stratified basins. For a two-dimensional
framework, we derive theoretical time and velocity scales associated with the transition
from Rayleigh–Bénard type convection to a horizontal overturning circulation across
the shallower sloping basin. This transition is characterised by a three-way horizontal
momentum balance, in which the cross-shore pressure gradient balances the inertial terms
before reaching a quasi-steady regime. We performed numerical and field experiments to
test and show the robustness of the analytical scaling, describe the convective regimes and
quantify the cross-shore transport induced by thermal siphons. Our results are relevant
for understanding the nearshore fluid dynamics induced by nighttime or seasonal surface
cooling in lakes and reservoirs.Swiss National Science Foundation (SNSF)
European Commission 175919Physics of Aquatic Systems Laboratory (APHYS), EPF
Some results on injectivity and multistationarity in chemical reaction networks
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasise the connections between the results, and where possible, present elementary proofs which rely solely on basic linear algebra and calculus. A number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper
Persistence and stability of generalized ribosome flow models with time-varying transition rates
In this paper the qualitative dynamical properties of so-called generalized
ribosome flow models are studied. Ribosome flow models known from the
literature are generalized by allowing an arbitrary directed network structure
between the compartments and secondly, by assuming a general time-varying rate
function describing the compartmental transitions. Persistence of the dynamics
is shown using the chemical reaction network (CRN) representation of the
system. We show the stability of different compartmental structures including
strongly connected ones with an entropy-like logarithmic Lyapunov function. The
L1 contractivity of solutions is also studied in the case of periodic reaction
rates having the same period. It is also shown that different Lyapunov
functions may be assigned to the same model depending on the factorization of
the reaction rates.Comment: 28 pages, 8 figure
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