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We use tools of bifurcation theory to characterize dynamics of astrocytic~IP$_3$ and~Ca$^{2+}$ for different~IP$_3$ regimes from a mathematical point of view. We do so following a bottom-up approach, starting from a compact, well-stirred…
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of…
Our understanding of how molecular clouds form in the interstellar medium (ISM) would be greatly helped if we had a reliable observational tracer of the gas flows responsible for forming the clouds. Fine structure emission from singly…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
We formulate and explore a generic continuum model of a polarizable active layer with neo-Hookean elasticity and chemo-mechanical interactions. Homogeneous solutions of the model equations exhibit a stationary long-wave instability when the…
The density structure of the interstellar medium (ISM) determines where stars form and release energy, momentum, and heavy elements, driving galaxy evolution. Density variations are seeded and amplified by gas motion, but the exact nature…
Coupling between chemical fuel consumption and phase separation can lead to condensation at a nonequilibrium steady state, resulting in phase behaviors that are not described by equilibrium thermodynamics. Theoretical models of such…
Any distortion of a chemical structure causes new features to appear in the absorption spectrum of the structure, especially in the visible and near UV (see Paper I). Chemical modeling, using molecular orbital theory, showed that the…
Ion sound instabilities driven by the ion flow in a system of a finite length are considered by analytical and numerical methods. The ion sound waves are modified by the presence of stationary ion flow resulting in negative and positive…
A one-dimensional Particle-In-Cell Monte Carlo Collisions (PIC-MCC) method has been used to model the development and propagation of ionization waves in neon and argon positive columns. Low current conditions are considered, i.e. conditions…
During the last ice age there were several quasi-periodic abrupt warming events. The climatic effects of the so-called Dansgaard-Oeschger (DO) events were felt globally, although the North Atlantic experienced the largest and most abrupt…
Understanding the chemical evolution in star-forming cores is a necessary pre-condition to correctly assess physical conditions when using molecular emission. We follow the evolution of chemistry and molecular line profiles through the…
We carry out direct numerical simulations of turbulent astrophysical media that explicitly track ionizations, recombinations, and species-by-species radiative cooling. The simulations assume solar composition and follows the evolution of…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Much of what we know about molecular clouds, and by extension star formation, comes from molecular line observations. Interpreting these correctly requires knowledge of the underlying molecular abundances. Simulations of molecular clouds…
We consider the evolution of an isentropic thermal instability in the atomic zone of a photodissociation region (PDR). In this zone, gas heating and cooling are associated mainly with photoelectric emission from dust grains and…
We study chemical oscillators in the presence of phase separation. By imposing timescale separation between slow reactions and fast diffusion, we define a dynamics at phase equilibrium for the relevant degrees of freedom. We demonstrate…
Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…