The Smoluchowski coagulation-diffusion PDE is a system of partial differential equations modelling the evolution in time of mass-bearing Brownian particles which are subject to shortrange pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE from a microscopic model of many coagulating Brownian particles that was undertak...

background : effects of electromagnetic fields on healing have been investigated for centuries. substantial data indicates that exposure to electromagnetic field can lead to enhanced healing in both soft and hard tissues. helmholtz coil is a device that generates pulsed electromagnetic fields. objective : in this study, a pair of helmholtz coils for enhancing the healing process in periodontiti...

Thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations. For computationally intensive problems such as the simulation of biomolecules, we propose to average over fast momentum degrees of freedom and construct thermostat equations in configuration space. The equations of motion are deterministic analogues of the Smoluch...

This paper explores the combined effects of Coriolis force and electric on rotating boundary layer flow heat transfer in a viscoplastic hybrid nanofluid from vertical exponentially accelerated plate. The comprises two different types metallic nanoparticles, namely silver (Ag) magnesium oxide (MgO) suspended an aqueous base fluid. Casson model is deployed for non-Newtonian effects. An empirical ...

We discuss equilibria, dynamics and regularity for Smoluchowski equations coupled to Navier-Stokes equations. Introduction We consider mixtures of fluids and microscopic inclusions. The microscopic inclusions are characterized by state variables m ∈ M , where M is a compact smooth Riemannian manifold without boundary. The simplest example is that of microscopic rods with directors m ∈ S. The mi...

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algor...

abstract background: given the fact of irrecoverable consequences of noise in industrial societies and the environment, acoustic filter (silencer) is an instrument which obstacles the transmission of sound waves. a sort of this silencer is helmholtz resonator (branch amplifier) which comes to sound appropriate for low and below 200 hz frequencies in fan and channel noise. the purpose of this ar...

We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples theMaier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field...