Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

Solutions of singular integral equations from gas dynamics and plasma physics

In this paper we give the explicit form of the solutions of the singular integral equations associated with some models of gas dynamics and plasma physics which are extensively investigated in the existing literature. In particular, we deal with equations on infinite and semi-infinite contours, where the data are assumed to be meromorphic functions. In this context we rederive some published results and present some new results which show how our method can be successfully used to obtain the explicit form of the solutions in much more general cases than those found in the literature.     

An exploration of fractal-based prognostic model and comparative analysis for second wave of COVID-19 diffusion

Nonlinear Dynamics - The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being...     

Reduction of Protein Networks Models by Passivity Preserving Projection

Reduction of complex protein networks models is of great importance. The accuracy of a passivity preserving algorithm (PRIMA) for model order reduction (MOR) is here tested on protein networks, introducing innovative variations of the standard PRIMA method to fit the problem at hand. The reduction method does not require to solve the complete system, resulting in a promising tool for studying very large-scale models for which the full solution cannot be computed. The mathematical structure of the considered kinetic equations is preserved. Keeping constant the reduction factor, the approximation error is lower for larger systems.     

Onset of diffusive behavior in confined transport systems

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size, modeling simple microporous membranes. It is well established that the point-particle case displays anomalous transport, because of slow correlation decay in the absence of defocusing collisions. We investigate which features of point-particle transport survive in the case of finite-sized particles (which undergo defocusing collisions). A similar question was investigated by Lansel, Porter, and Bunimovich [Chaos 16, 013129 (2006)], who found that certain integrals of motion and multiple ergodic components, characteristic of the point-particle case, remain in "mushroom"-like systems with few finite-sized particles. We quantify the time scales over which the transport of disks shows features typical of the point particles, or is driven toward diffusive behavior. In particular, we find that interparticle collisions drive the system toward diffusive behavior more strongly than defocusing boundary collisions. We illustrate how, and at what stage, typical thermodynamic behavior (consistent with kinetic theory) is observed, as particle numbers grow and mean free paths diminish. These results have both applied (e.g., nanotechnological) and theoretical interest.     

The nonequilibrium Lorentz gas

We study the conductivity of a Lorentz gas system, composed of a regular array of fixed scatterers and a point-like moving particle, as a function of the strength of an applied external field. In order to obtain a nonequilibrium stationary state, the speed of the point particle is fixed by the action of a Gaussian thermostat. For small fields the system is ergodic and the diffusion coefficient is well defined. We show that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At larger values of the field we observe a variety of possible dynamics, including the breakdown of ergodic behavior, and later the existence of a single stable trajectory for the largest fields. We also study the behavior of the system as a function of the orientation of the array of scatterers with respect to the external field. Finally, we present a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain. The consequences of this behavior for the ergodicity of the system are explored. (c) 1995 American Institute of Physics.     

Temporal asymmetry of fluctuations in nonequilibrium steady states: links with correlation functions and nonlinear response

The presence of temporal asymmetries in fluctuation paths of nonequilibrium systems has recently been confirmed numerically in nonequilibrium molecular dynamics simulations of particular deterministic systems. Here we show that this is a common feature of homogeneously driven and thermostatted, reversible, deterministic, chaotic, nonequilibrium systems of interacting particles. This is done by expressing fluctuation paths as correlation functions. The theoretical arguments look rather general, and we expect them to easily extend to other forms of driving and thermostats. The emergence of asymmetry is also justified using the transient time correlation function expression of nonlinear response theory. Numerical simulations are used to verify our arguments.