News Waves: Hard News, Soft News, Fake News, Rumors, News Wavetrains.

We discuss the spread of a piece of news in a population. This is modeled by SIR model of epidemic spread. The model can be reduced to a nonlinear differential equation for the number of people affected by the news of interest.

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics.

The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM).

Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations.

Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method.

Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity.

We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate transformation at Step (1.) of SEsM.

Simple Equations Method (SEsM): Algorithm, Connection with Hirota Method, Inverse Scattering Transform Method, and Several Other Methods.

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials.

On the Possibility of Chaos in a Generalized Model of Three Interacting Sectors.

In this study we extend a model, proposed by Dendrinos, which describes dynamics of change of influence in a social system containing a public sector and a private sector. The novelty is that we reconfigure the system and consider a system consisting of a public sector, a private sector, and a non-governmental organizations (NGO) sector. The additional sector changes the model's system of equations with an additional equation, and additional interactions must be taken into account.

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions.

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network.

Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms.

We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations.

Release of Graphene and Carbon Nanotubes from Biodegradable Poly(Lactic Acid) Films during Degradation and Combustion: Risk Associated with the End-of-Life of Nanocomposite Food Packaging Materials.

Nanoparticles of graphene and carbon nanotubes are attractive materials for the improvement of mechanical and barrier properties and for the functionality of biodegradable polymers for packaging applications. However, the increase of the manufacture and consumption increases the probability of exposure of humans and the environment to such nanomaterials; this brings up questions about the risks of nanomaterials, since they can be toxic. For a risk assessment, it is crucial to know whether airborne nanoparticles of graphene and carbon nanotubes can be released from nanocomposites into the environment at their end-life, or whether they remain embedded in the matrix.

Release of carbon nanoparticles of different size and shape from nanocomposite poly(lactic) acid film into food simulants.

Poly(lactic) acid (PLA) film with 2 wt% mixed carbon nanofillers of graphene nanoplates (GNPs) and multiwall carbon nanotubes (MWCNTs) in a weight ratio of 1:1 with impurities of fullerene and carbon black (CB) was produced by layer-to-layer deposition and hot pressing. The release of carbon nanoparticles from the film was studied at varying time-temperature conditions and simulants. Migrants in simulant solvents were examined with laser diffraction analysis and transmission electron microscopy (TEM).

Role of surfactants on the approaching velocity of two small emulsion drops.

Here we present the exact solution of two approaching spherical droplets problem, at small Reynolds and Peclet numbers, taking into account surface shear and dilatational viscosities, Gibbs elasticity, surface and bulk diffusivities due to the presence of surfactant in both disperse and continuous phases. For large interparticle distances, the drag force coefficient, f, increases only about 50% from fully mobile to tangentially immobile interfaces, while at small distances, f can differ several orders of magnitude. There is significant influence of the degree of surface coverage, θ, on hydrodynamic resistance β for insoluble surfactant monolayers.

Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture.

This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively.

Chaotic pairwise competition.

We investigate a kind of competition possible in a system of at least three populations competing for the same limited resource. As a model we use generalised Volterra equations in which the growth rates and competition coefficients of populations depend on the number of members of all populations. Because of the nonconstant values of the last quantities the system could be repelled from the state of cyclic pairwise competition described by May and Leonard (SIAM J.

Convective heat transport in a rotating fluid layer of infinite Prandtl number: optimum fields and upper bounds on Nusselt number.

By means of the Howard-Busse method of the optimum theory of turbulence we investigate numerically upper bounds on convective heat transport for the case of infinite fluid layer with stress-free vertical boundaries rotating about a vertical axis. We discuss the case of infinite Prandtl number, 1-alpha solution of the obtained variational problem and optimum fields possessing internal, intermediate, and boundary layers. We investigate regions of Rayleigh and Taylor numbers R and Ta, where no analytical bounds can be derived, and compare the analytical and numerical bounds for these regions of R and Ta where such comparison is possible.

Low-dimensional chaos in zero-Prandtl-number Bénard-Marangoni convection.

Three-dimensional surface-tension-driven Bénard convection at zero Prandtl number is computed in the smallest possible doubly periodic rectangular domain that is compatible with the hexagonal flow structure at the linear stability threshold of the quiescent state. Upon increasing the Marangoni number beyond this threshold, the initially stationary flow becomes quickly time dependent. We investigate the transition to chaos for the case of a free-slip bottom wall by means of an analysis of the kinetic energy time series.