Effects of quantum vacuum fluctuations of the electric field on DNA condensation

By assuming that not only counter-ions but DNA molecules as well are thermally distributed according to a Boltzmann law, we propose a modified Poisson-Boltzmann equation, at the classical level, as a starting point to compute the effects of quantum fluctuations of the electric field on the interaction among DNA-cation complexes. The latter are modeled here as infinite one-dimensional wires (δ-functions). Our goal is to single out such quantum-vacuum-driven interaction from the counterion-induced and water-related interactions. We obtain a universal, frustration-free Casimir-like (codimension 2) interaction that extensive numerical analysis show to be a good candidate to explain the formation and stability of DNA aggregates. Such Casimir energy is computed for a variety of configurations of up to 19 DNA strands in a hexagonal array. It is found to be many-body.     

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of S²×S¹.     

KINETIC FUNCTIONS IN MAGNETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we design a new class of ＂schemes with eontroled dissipation＂, following recent work by LeFloch and Mohammadian. It is now recognized that the equivalent equation associated with a scheme provides a guideline to design schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on high-order entropy conservative, finite differences for the hyperbolic flux, and high-order central differences for the resistivity and Hall terms. These schemes are tested for several regimes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in magnetohydrodynamics.     

Modifications of nano-titania surface for in vitro evaluations of hemolysis,cytotoxicity, and nonspecific protein binding

In the past decade, a variety of drug carriers based on mesoporous silica nanoparticles has been extensively reported. However, their biocompatibility still remains debatable, which motivated us to explore the porous nanostructures of other metal oxides, for example titanium dioxide (TiO₂), as potential drug delivery vehicles. Herein, we report the in vitro hemolysis, cytotoxicity, and protein binding of TiO₂ nanoparticles, synthesized by a sol–gel method. The surface of the TiO₂ nanoparticles was modified with hydroxyl, amine, or thiol containing moieties to examine the influence of surface functional groups on the toxicity and protein binding aspects of the nanoparticles. Our study revealed the superior hemocompatibility of pristine, as well as functionalized TiO₂ nanoparticles, compared to that of mesoporous silica, the present gold standard. Among the functional groups studied, aminosilane moieties on the TiO₂ surface substantially reduced the degree of hemolysis (down to 5%). Further, cytotoxicity studies by MTT assay suggested that surface functional moieties play a crucial role in determining the biocompatibility of the nanoparticles. The presence of NH₂– functional groups on the TiO₂ nanoparticle surface enhanced the cell viability by almost 28% as compared to its native counterpart (at 100 μg/ml), which was in agreement with the hemolysis assay. Finally, nonspecific protein adsorption on functionalized TiO₂ surfaces was examined using human serum albumin and it was found that negatively charged surface moieties, like –OH and –SH, could mitigate protein adsorption to a significant extent.

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On stability of numerical schemes via frozen coefficients and the magnetic induction equations

We study finite difference discretizations of initial boundary value problems for linear symmetric hyperbolic systems of equations in multiple space dimensions. The goal is to prove stability for SBP-SAT (Summation by Parts—Simultaneous Approximation Term) finite difference schemes for equations with variable coefficients. We show stability by providing a proof for the principle of frozen coefficients, i.e., showing that variable coefficient discretization is stable provided that all corresponding constant coefficient discretizations are stable.     

A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections

It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V₁(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P, is also simply connected. In this paper we establish that the region V₂(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V₃(s), the region of P visible from s after at most three diffuse reflections, can have (n) holes.A part of this work was done when this author was visiting the University of Miami, Coral Gables, Florida, USA.     

Expansiveness of algebraic actions on connected groups

We study endomorphism actions of a discrete semigroup on a connected group . We give a necessary and sufficient condition for expansiveness of such actions provided is either a Lie group or a solenoid.

     

A General Method for Estimating Dynamic Parameters of Spatial Mechanisms

Dynamic equations of motion require a large number of parameters for each element of the system. These can include for each part their mass, location of center of mass, moment of inertia, spring stiffnesses and damping coefficients. This paper presents a technique for estimating these parameters in spatial mechanisms using any joint type, based on measurements of displacements, velocities and accelerations and of external forces and torques, for the purpose of building accurate multibody models of mechanical systems. A form of the equations of spatial motion is derived, which is linear in the dynamic parameters and based on multibody simulation code methodologies. Singular value decomposition is used to find the essential parameter set, and minimum parameter set. It is shown that a simulation of a four-bar mechanism (with spherical, universal, and revolute joints) and based on the estimated parameters gives accurate response.     

Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function

We deal with single conservation laws with a spatially varying and possibly discontinuous coefficient. This equation includes as a special case single conservation laws with conservative and possibly singular source terms. We extend the framework of optimal entropy solutions for these classes of equations based on a two-step approach. In the first step, an interface connection vector is used to define infinite classes of entropy solutions. We show that each of these classes of solutions is stable in . This allows for the possibility of choosing one of these classes of solutions based on the physics of the problem. In the second step, we define optimal entropy solutions based on the solution of a certain optimization problem at the discontinuities of the coefficient. This method leads to optimal entropy solutions that are consistent with physically observed solutions in two-phase flows in heterogeneous porous media. Another central aim of this paper is to develop suitable numerical schemes for these equations. We develop and analyze a set of Godunov type finite volume methods that are based on exact solutions of the corresponding Riemann problem. Numerical experiments are shown comparing the performance of these schemes on a set of test problems.