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...     

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.     

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.     

Modulation of output power in the spatio-temporal analysis of a semi conductor laser

This paper examines the spatio temporal patterns of a set of a (2 + 1) dimensional partial differential equations (PDE) describing the dynamics of semiconductor external cavity THz lasers. The study is conducted in two phases: (a) first we show that the behaviour of the single mode system may be periodic or chaotic; (b) the output power may be optimized by proper choices of parameters, such as cavity length and injected current, which lead to high dimensional spatio-temporal chaotic regimes. This conclusion applies to systems with one and with two external cavities, and is robust with respect to variations of parameter values and initial-boundary conditions.     

Fluctuation Relations for Dissipative Systems in Constant External Magnetic Field: Theory and Molecular Dynamics Simulations

We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields—an interesting but less commonly investigated geometry—and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.