Related papers: An Analytical Model for Molecular Communication ov…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
This paper studies the problem of receiver modeling in molecular communication systems. We consider the diffusive molecular communication channel between a transmitter nano-machine and a receiver nano-machine in a fluid environment. The…
In this paper, we construct approximations of the microscopic solution of a nonlinear reaction--diffusion equation in a domain consisting of two bulk-domains, which are separated by a thin layer with a periodic heterogeneous structure. The…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
This paper focuses on molecular communication (MC) systems where the signaling molecules may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept…
In this paper, we apply dimensional analysis to study a diffusive molecular communication system that uses diffusing enzymes in the propagation environment to mitigate intersymbol interference. The enzymes bind to information molecules and…
We consider linear reaction--diffusion problems with mixed Diriclet-Neumann-Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow…
In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by…
A molecular communication channel is determined by the received signal. Received signal models form the basis for studies focused on modulation, receiver design, capacity, and coding depend on the received signal models. Therefore, it is…
In this paper, we propose a new mathematical model nonlinear reaction-diffusion PDE's describing the dynamics of propagation of cancer. Here the mixed problem for the proposed PDE's is investigated and by applying obtained results…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
Reaction-advection-diffusion equations, in periodic settings and with general type nonlinearities, admit a threshold known as the minimal speed of propagation. The minimal speed does not have an accessible formula when the nonlinearity is…
In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
Molecular communication emerges as a promising communication paradigm for nanotechnology. However, solid mathematical foundations for information-theoretic analysis of molecular communication have not yet been built. In particular, no one…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…