An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-squared value of the solution at the boundaries and is defined as ∂Ψ ∂t |b ≈ i Im[ 1 Ψb−1 ∂Ψ ∂t |b−1] Ψb, where Ψ is the complex field and ...

A numerical method is proposed to calculate damping properties for sound-proof structures involving elastic body, viscoelastic body, and porous media. For elastic and viscoelastic body displacement is modeled using conventional finite elements including complex modulus of elasticity. Both effective density and bulk modulus have complex quantities to represent damped sound fields in the porous m...

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting su...

We show that, in perturbative string models where the source of CP violation is a complex vacuum expectation value (v.e.v.) for one or more compactification moduli, CP is conserved if a CP transformation acting on the modulus values is an element of a target-space (self-)duality group. Where the duality group is SL(2, Z) the result confirms a conjecture of Bailin et al. that CP is conserved for...

Biological cells display viscoelastic mechanical properties that are a key factor in the regulation of cell processes, such as migration, adhesion and deformability. One interesting tool to probe the mechanical properties of living cells and other complex systems is the Atomic Force Microscopy (AFM). Rheological properties of the sample are obtained usually from the force-indentation (F-δ) meas...

Periodontal ligament is a thin layer of soft tissue that connects root of a tooth to the surrounding alveolar bone. These ligaments play an important role in initiating tooth movement when loads are applied to teeth with orthodontic appliances. The majority of such soft tissues exhibit as viscoelastic bodies or have a time-dependent behavior. Due to the viscoelastic behavior of the periodontal ...

A novel mixing approach for achieving a good dispersion of multi-walled carbon nanotubes (MWCNTs) in ethylene- propylene diene monomer (EPDM) matrix has been investigated. In this approach EPDM was modified with vinyltrimethoxysilane (VTMS) during melt mixing. In addition the effect of MWCNT concentration on mechanical and rheological properties of modified EPDM has been studied. The formulated...

In the current paper, finite element method is employed for numerical simulations and the study of influential parameters on elastic modulus of polymer-matrix nano-composites. Effects of different key parameters including particle elastic modulus, interphase elastic modulus, matrix elastic modulus, interphase thickness and particle volume fraction on total elastic modulus of nano-composite mate...

As usual, R denotes the real numbers, Z denotes the integers, and C denotes the complex numbers. Thus each α ∈ C can be expressed as a + b i, where a, b are real numbers and i = −1. We call a, b the real and imaginary parts of α, and denote them Reα, Imα, respectively. If z is a complex number, with z = x + y i where x, y are the real and imaginary parts of z, then we write z for the complex co...

in the current paper, finite element method is employed for numerical simulations and the study of influential parameters on elastic modulus of polymer-matrix nano-composites. effects of different key parameters including particle elastic modulus, interphase elastic modulus, matrix elastic modulus, interphase thickness and particle volume fraction on total elastic modulus of nano-composite mate...