A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Elevated fetal steroidogenic activity in autism

Autism affects males more than females, giving rise to the idea that the influence of steroid hormones on early fetal brain development may be one important early biological risk factor. Utilizing the Danish Historic Birth Cohort and Danish Psychiatric Central Register, we identified all amniotic fluid samples of males born between 1993 and 1999 who later received ICD-10 (International Classification of Diseases, 10th Revision) diagnoses of autism, Asperger syndrome or PDD-NOS (pervasive developmental disorder not otherwise specified) (n=128) compared with matched typically developing controls. Concentration levels of Δ4 sex steroids (progesterone, 17α-hydroxy-progesterone, androstenedione and testosterone) and cortisol were measured with liquid chromatography tandem mass spectrometry. All hormones were positively associated with each other and principal component analysis confirmed that one generalized latent steroidogenic factor was driving much of the variation in the data. The autism group showed elevations across all hormones on this latent generalized steroidogenic factor (Cohen's d=0.37, P=0.0009) and this elevation was uniform across ICD-10 diagnostic label. These results provide the first direct evidence of elevated fetal steroidogenic activity in autism. Such elevations may be important as epigenetic fetal programming mechanisms and may interact with other important pathophysiological factors in autism.

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Bile salt composition is secondary to bile salt concentration in determining hydrocortisone and progesterone solubility in intestinal mimetic fluids.

Simulated intestinal fluids (SIFs) used to assay the solubility of orally administered drugs are typically based on a single bile salt; sodium taurocholate (STC). The aim of this study was to develop mimetic intestinal fluids with a closer similarity to physiological fluids than those reported to date by developing a mixed bile salt (MBS) system (STC, sodium glycodeoxycholate, sodium deoxycholate; 60:39:1) with different concentrations of lecithin, the preponderant intestinal phospholipid. Hydrocortisone and progesterone were used as model drugs to evaluate systematically the influence of SIF composition on solubility. Increasing total bile salt concentration from 0 to 30 mM increased hydrocortisone and progesterone solubility by 2- and ∼25-fold, respectively. Accordingly, higher solubilities were measured in the fed-state compared to the fasted-state SIFs. Progesterone showed the greatest increases in solubility in STC and MBS systems (2-7-fold) compared to hydrocortisone (no significant change; P>0.05) as lecithin concentration was increased. Overall, MBS systems gave similar solubility profiles to STC. In conclusion, the addenda of MBS and lecithin were found to be secondary to the influence of BS concentration. These data provide a foundation for the design of more bio-similar media for pivotal decision-guiding assays in drug development and quality control settings.

Use of simulated intestinal fluids with Caco-2 cells and rat ileum

In most in vitro studies of oral drug permeability, little attempt is made to reproduce the gastrointestinal lumenal environment. The aim of this study was to evaluate the compatibility of simulated intestinal fluid (SIF) solutions with Caco-2 cell monolayers and Ussing chamber-mounted rat ileum under standard permeability experiment protocols. In preliminary experiments, fasted-state simulated intestinal fluid (FaSSIF) and fed-state simulated intestinal fluid (FeSSIF) solutions based on the dissolution medium formulae of Dressman and co-workers (1998) were modified for compatibility with Caco-2 cells to produce FaS-SIF and FeSSIF "transport" solutions for use with in vitro permeability models. For Caco-2 cells exposed to FaSSIF and FESSIF transport solutions, the transepithelial electrical resistance was maintained for over 4 h and mannitol permeability was equivalent to that in control (Hank's Balanced Salt Solution-treated) cell layers. Scanning electron microscopy revealed that microvilli generally maintained a normal distribution, although some shortening of microvilli and occasional small areas of denudation were observed. For rat ileum in the Ussing chambers, the potential difference (PD) collapsed to zero over 120 min when exposed to the FaSSIF transport solution and an even faster collapse of the PD was observed when the FeSSIF transport solution was used. Electron micrographs revealed erosion of the villi tips and substantial denudation of the microvilli after exposure of ileal tissue to FaSSIF and FeSSIF solutions, and permeability to mannitol was increased by almost two-fold. This study indicated that FaSSIF and FeSSIF transport solutions can be used with Caco-2 monolayers to evaluate drug permeability, but rat ileum in Ussing chambers is adversely affected by these solutions. Metoprolol permeability in Caco-2 experiments was reduced by 33% using the FaSSIF and 75% using the FeSSIF compared to permeability measured using HBSS. This illustrates that using physiological solutions can influence permeability measurements.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.

Dynamic simulation studies of structural formation and transition in electro-magneto-rheological fluids

The computer simulation method has been used to study the structural formation and transition of electro-magneto-rheological (EMR) fluids under compatible electric and magnetic fields. When the fields are applied simultaneously and perpendicularly to each other, the particles rapidly arrange into two-dimensional close-packed layer structures parallel to both fields. The layers then combine together to form thicker sheet-like structures, which finally relax into three-dimensional close-packed structures with the help of the thermal fluctuations. On the other hand, if the electric field is applied firstly to induce the body-centered tetragonal (BCT) columns in the system, and then the magnetic field is applied in the perpendicular direction. the BCT to face-centered cubic (FCC) structure transition is observed in very short time. Following that. the structure keeps on evolving due to the demagnetization effect and finally form the three-dimensional close-packed structures.

Resonance response of electrorheological fluids in vertical oscillation squeeze flow

The resonance effect of microcrystalline cellulose/castor oil electrorheological (ER) suspensions was studied in a compressed oscillatory squeeze flow under external electric fields. The resonance frequency first increases linearly with increasing external held, and then shift to high-field plateau. The amplitudes of resonance peak increase sharply with the applied fields in the range of 0.17-1.67kV/mm. The phase difference of the reduced displacement relative to the excitation force inverses in the case of resonance. A viscoelasticity model of the ER suspensions, which offers both the equivalent stiffness and the viscous damping, should be responsible for the appearance of resonance. The influence of the electric field on the resonance frequency and the resonance hump is consistent qualitatively with the interpretation of our proposed model. Storage modulus G' was presented for the purpose of investigating this influence.

Squeeze flow viscoelasticity of electrorheological fluids based on microcrystalline cellulose

Dynamic viscoelasticity of electrorheological fluids based on microcrystalline cellulose/castor oil suspensions was experimentally investigated in squeeze flow. The dependence of storage modulus G' and loss modulus G" parallel to external electric field on electric fields and strain amplitudes is presented. The experiments show that, when external electric field is higher than the critical field, the viscoelasticity of the ER fluids converts from linear to nonlinear, and the ER fluids transfer from solid-like state to fluid state with the growth of strain amplitude. The influences of strain amplitude and oscillatory frequency on the nonlinearity of viscoelasticity were also studied.

Lattice dynamics study of microstructures of electrorheological fluids

The lattice dynamics method is used to study the stability of the chain structures formed in electrorheological (ER) fluids. The appearance of the soft modes in the phonon dispersion of the structures indicates that the chains tend to distort and aggregate into thicker columns due to the electrostatic attractive forces and thermal generated forces between them. The results show that the stability of the chains relies on their width and the separation between them. The complete chain structures are more stable than the chains with defects. The results can be used to elucidate the densification phenomenon of the chains in the structuring process of ER fluids in the quiescent state.

Dynamic response times of electrorheological fluids in steady shear

Transient responses of electrorheological fluids to square-wave electric fields in steady shear are investigated by computational simulation method. The structure responses of the fluids to the field with high frequency are found to be very similar to that to the field with very low frequency or the sudden applied direct current field. The stress rise processes are also similar in both cases and can be described by an exponential expression. The characteristic time tau of the stress response is found to decrease with the increase of the shear rate (gamma) over dot and the area fraction of the particles phi(2). The relation between them can be roughly expressed as tau proportional to(gamma) over dot(-3/4)phi(2)(-3/2). The simulation results are compared with experimental measurements. The aggregation kinetics of the particles in steady shear is also discussed according to these results.

Computer simulation study of equilibrium properties of magnetic dipolar fluids

Langevin dynamics simulations are used to investigate the equilibrium magnetization properties and structure of magnetic dipolar fluids. The influence of using different boundary conditions are systematically studied. Simulation results on the initial susceptibility and magnetization curves are compared with theoretical predictions. The effect of particle aggregation is discussed in detail by performing a cluster analysis of the microstructure.

Active control of rod vibrations using magnetic fluids

The use of magnetic fluids in controlling rod vibrations is investigated. A prototype of ferrofluid vibration damper is designed and experimentally set up based on the principle of anti-resonance. The efficiency of this damping system is verified in experiments and well explained with classical equations of motion. The improvement of the present system towards active control of rod vibration is also discussed.

The effect of electric field direction on the-shear stress of ER fluids

The effect of the direction of external electric field on the shear stress of an ER fluid has been studied by molecular-dynamics simulation. Due to the formation of inclined chains, the shear stress strongly depends on the direction of the field, and it may be very large under some special field direction. And theoretical model of ideal microstructure of ER fluids has proved this result. Thus the ER effect may be greatly enhanced just by choosing an optimum direction for the field without any additional requirement, suggesting a promising way to the practical application of ER fluids.