On the Optimal Control of a Random Walk with Jumps and Barriers

The modeling and optimal control of a class of random walks (RWs) is investigated in the framework of the Chapman-Kolmogorov (CK) and Fokker-Planck (FP) equations. This class of RWs includes jumps driven by a compound Poisson process and are subject to different barriers. A control mechanism is investigated that is included in the CK stochastic transition matrix and the purpose of the control is to track a desired discrete probability density function and attain a desired terminal density configuration. Existence and characterization of optimal controls are discussed. The proposed approach allows the derivation of a new FP model that accommodates the presence of the jumps and guarantees conservation of total probability in the case of reflecting barriers, which are modelled by appropriate operators. Results of numerical experiments are presented that successfully validate the proposed control framework.     

Numerical analysis of the Navier–Stokes/Darcy coupling

We consider a differential system based on the coupling of the Navier–Stokes and Darcy equations for modeling the interaction between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming finite element approximation of the coupled problem.     

Fast Solvers of Fredholm Optimal Control Problems

<正>The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented.Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed.Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.     

Seasonal Minimum and Maximum Solar Ultraviolet Exposure Measurements of Classroom Teachers Residing in Tropical North Queensland,Australia

The risk of keratinocyte skin cancer, malignant melanoma and ultraviolet radiation (UVR)‐induced eye disease is disproportionately higher in Australia and New Zealand compared to equivalent northern hemisphere latitudes. While many teachers are aware of the importance of reinforcing sun safety messages to students, many may not be aware of the considerable personal exposure risk while performing outdoor duties in locations experiencing high to extreme ambient UVR year‐round. Personal erythemally effective exposure of classroom teachers in tropical Townsville (19.3°S) was measured to establish seasonal extremes in exposure behavior. Mean daily personal exposure was higher in winter (91.2 J m^‐2, 0.91 Standard Erythema Dose [SED]) than summer (63.3 J m^?2, 0.63 SED). The range of exposures represents personal exposures that approximate current national guidelines for Australian workers at the study latitude of approximately 1.2 SED (30 J m^?2 effective to the International Commission on Non‐Ionizing Radiation Protection). Similar proportions of teachers spent more than 1 h outdoors per day in winter (28.6%) and summer (23.6%) as part of their teaching duties with seasonal differences having little effect on the time of exposure. Personal exposures for teachers peaked during both seasons near school meal break times at 11:00 am and 1:00 pm, respectively.     

Self-assembly in complex mixed surfactant solutions: the impact of dodecyl triethylene glycol on dihexadecyl dimethyl ammonium bromide

The impact of the nonionic surfactant, dodecyl triethyleneglycol ether (C(12)E(3)) on the solution microstructure of the dialkyl chain cationic surfactant, dihexadecyl dimethyl ammonium bromide, (DHDAB) has been investigated. The variation in solution microstructure has been studied using a combination of small angle neutron scattering, ultra small angle neutron scattering, optical texture and photon correlation spectroscopy. At low surfactant concentrations (1.5 mM) the microstructure takes the form of bilamellar vesicles (BLV) for compositions containing less than 20 mol % of added C(12)E(3). Multilamellar vesicles (MLV) are the predominant microstructure for solutions richer in composition than 20 mol % C(12)E(3). At more than 80 mol % C(12)E(3), the solution microstructure reverts to that of a lamellar phase dispersion consistent with studies on the pure nonionic surfactant. At higher concentrations (60 mM) a wide continuous L beta phase region is observed for compositions in the range 20 to 80 mol % C(12)E(3). The fine details of the phase diagram were obtained from quantitative analysis of the SANS data using a well-established lamellar membrane model. Irrespective of the nonionic content, the bilayers are in general highly rigid, consistent with those stabilized by charge interactions. Furthermore estimates of the product of membrane moduli (compressibility and bending modulus) indicate that the different phase regions have very different membrane properties, however the magnitude of the variations observed are not predicted using existing theoretical treatments.     

Controlling aggregation of nonionic surfactants using mixed glycol media

The extent of aggregation of nonionic surfactants can be controlled by the composition of mixed solvents with two miscible glycols, ethylene glycol (EG)/propylene glycol (PG). Three nonionic surfactants bearing a common E8 ethoxylated headgroup, but with variations in the hydrocarbon chain, have been investigated: octaethylene monododecyl ether (C12E8), octaethylene monotetradecyl ether (C14E8), and octaethylene monohexadecyl ether (C16E8). The hydrogen-bonding solvents were EG/PG mixtures at different PG levels, defined in terms of the concentration (mol %) of PG. Aggregation was investigated using small-angle neutron scattering (SANS) with h-CiE8 surfactants, at 10 and 5 wt %, in deuterated glycol solvents to improve contrast. Increasing PG concentration (mol %) in the background EG/PG solvent leads to a consistent decrease in the SANS intensity, until in pure d-PG only very weak scattering is observed. These SANS data were analyzed using cylinder or ellipsoidal form factors for the EG-rich and PG-rich systems, respectively, hence demonstrating an aggregate shape change as a function of solvent composition. The results show that aggregation of nonionic surfactants occurs in glycol solvents and that the EG:PG ratio may be used as an effective means to switch aggregation "on" or "off", as required.     

Electrostastic control of spontaneous curvature in catanionic reverse micelles

By means of small-angle neutron scattering and conductivity measurements, we study the microstructure of octylammoniumoctanoate/octane/water catanionic reverse microemulsions with an excess of anionic or cationic surfactant. Increasing the surface charge makes the microemulsion able to incorporate much more water than in the neutral case, up to 10 water molecules per surfactant. Even with charges in the surfactant film, wormlike micelles are present in the microemulsion domain. Along water dilution lines, the classical rod-to-sphere transition due to the minimization of the curvature energy of the rigid surfactant film is observed. When temperature is decreased, a re-entrant phase transition associated with the liquid-gas equilibrium of attractive cylinders is observed. Using the framework of the Tlusty-Safran theory, attraction could originate from junctions between wormlike reverse micelles. In any case, the spontaneous curvature of the catanionic surfactant film depends on both the temperature and the net charge, whatever the sign of the latter.     

Polyurethane Based Materials for the Production of Biomedical Materials

Polyurethanes (PUs) composed by hard and soft segments have been extensively used in the manufacturing of biocompatible prosthesis and medical devices. A broad variety of PUs can be obtained by modifying the balance between both segments. In the present work, different basically-flexible PUs have been prepared by employing different combinations of aliphatic hexamethylene diisocyanate, poly(ethylene glycol) (Mw 400 Da), poly(ϵ-caprolactone) diol (Mw 530 Da), and 1,4-butanediol. Thermal analysis of the synthesized PUs demonstrated high thermal stability and the assumption of glassy state well below room temperature, in agreement with their marked flexibility. Morphological characterization of PUs films indicated that films prepared by spin coating were smoother and more homogeneous than those obtained by casting. Biological assays performed by using 3T3/BALB-C mouse embryo fibroblast cell line confirmed the absence of toxicity and hence the biocompatibility of PU-films.     

A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems

A finite-element multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The multigrid computational framework implements a nonlinear multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the multigrid scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.