Valuing Asian options using the finite element method and duality techniques

The main objective of this paper is to develop an adaptive finite element method for computation of the values, and different sensitivity measures, of the Asian option with both fixed and floating strike. The pricing is based on Black–Scholes PDE-model and a method developed by Ve?e? where the resulting PDEs are of parabolic type in one spatial dimension and can be applied to both continuous and discrete Asian options. We propose using an adaptive finite element method which is based on a posteriori estimates of the error in desired quantities, which we derive using duality techniques. The a posteriori error estimates are tested and verified, and are used to calculate optimal meshes for each type of option. The use of adapted meshes gives superior accuracy and performance with less degrees of freedom than using uniform meshes. The suggested adaptive finite element method is stable, gives fast and accurate results, and can be applied to other types of options as well.     

Dendrimers in thiol‐ene crosslinked networks and the effect of subsequent generations on thermoset properties

A series of well‐defined allyl‐ether functionalized polyester dendrimers has been synthesized via the divergent approach using traditional esterification reactions. Two commercially available trifunctional thiols, trimethylolpropane tri(3‐mercaptopropanoate) (TRIS) and ethoxylated trimethylolpropane tri(3‐mercaptopropanoate) (ETTMP), were incorporated with the dendrimers into the thiol‐ene polymer networks. The thiol‐ene reactions were conducted at room temperature and cured by UV light without the addition of photoinitiatior. Highly crosslinked films were obtained and characterized with respect to mechanical (DMA) and thermal (DSC and TGA) properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 589–601, 2009     

Synthesis and thiol–ene photopolymerization of allyl‐ether functionalized dendrimers

Well‐defined, allyl‐ether functional, first‐generation dendrimers have been synthesized. The convergent growth approach was utilized, using the anhydride of the allyl‐ether terminated building block. Three different core moieties were used: trimethylolpropane, trisphenol, and ditrimethylolpropane. The coupling reactions proceeded in good yields and all compounds were characterized by NMR, MALDI‐TOF, and SEC. The allyl‐terminated dendrimers were crosslinked by thiol–ene chemistry, using a multifunctional thiol, TriThiol, to give clear and smooth films. The photopolymerization was conducted in the presence of a photoinitiator, Irgacure 651, and no traces of either allyl‐ether groups or thiols were observed by FT‐Raman after cure. All crosslinked films were characterized with respect to mechanical (DMA) and thermal (DSC) properties. It was found that homogeneous networks were formed and that the core functionality and structure had little effect on the network properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1339–1348, 2008     

Theoretical investigations on the chemical bonding, electronic structure, and optical properties of the metal-organic framework MOF-5

The chemical bonding, electronic structure, and optical properties of metal-organic framework-5 (MOF-5) were systematically investigated using ab initio density functional calculations. The unit cell volume and atomic positions were optimized with the Perdew-Burke-Ernzerhof (PBE) functional leading to a good agreement between the experimental and the theoretical equilibrium structural parameters. The calculated bulk modulus indicates that MOF-5 is a soft material. The estimated band gap from a density of state (DOS) calculation for MOF-5 is about 3.4 eV, indicating a nonmetallic character. As MOFs are considered as potential materials for photocatalysts, active components in hybrid solar cells, and electroluminescence cells, the optical properties of this material were investigated. The detailed analysis of chemical bonding in MOF-5 reveals the nature of the Zn-O, O-C, H-C, and C-C bonds, that is, Zn-O having mainly ionic interaction whereas O-C, H-C, and C-C exhibit mainly covalent interactions. The findings in this paper may contribute to a comprehensive understanding about this kind of material and shed insight into the synthesis and application of novel and stable MOFs.     

Two new layered oxohalides in the system Cu–Yb–Te–O–Cl

Two complex lanthanide(III) transition metal(II) tellurium(IV) oxyhalides, Cu₃Yb₂(TeO₃)₄Cl₄ and Cu₃Yb₃(TeO₃)₄Cl₆ have been synthesized and the crystal structures were determined by single-crystal X-ray diffraction. Both compounds are layered with only weak connections in between the layers. The layers are made up of [YbO₈], [TeO₃] and [CuO_xCl_y] polyhedra. In both compounds the strong Lewis acid cations Yb³⁺ and Te⁴⁺ only form bonds to oxygen while Cu²⁺ form bonds to both oxygen and chlorine. This leads the Cl^? ions to be expelled from the bonding volumes of the crystal structures and protrude from the layers. Magnetic susceptibility measurements were performed on a powder sample of Cu₃Yb₂(TeO₃)₄Cl₄. The Curie–Weiss law found at low temperatures indicates a Curie–Weiss temperature of ca. ?5(1) K. However, indication for long-range magnetic ordering could not be observed down to 1.87 K. The two new phases are to the best of our knowledge the first containing all three of Cu, Yb and Te.     

Quasi-steady model of the acoustic scattering properties of a T-junction

T-junctions are common elements in flow duct networks. It is shown that for low Strouhal numbers, based on the duct diameter, their acoustic scattering properties can be described using an incompressible quasi-steady model. Models are derived for systems subjected to combinations of grazing and bias mean flow, and are shown to work in both the limiting cases—that is, grazing or bias flow alone—as well as for the joining or dividing flow configurations. The upper Strouhal number for which the quasi-steady models are applicable is limited by flow-acoustic interaction effects, which differ significantly between the different flow configurations. Generally the models are applicable up to Strouhal numbers of approximately 0.1-0.2, which is comparable with previous published models for other configurations such as bends and orifices. This range is sufficient to make the model useful in many important engineering applications.     

Subwavelength terahertz spin-flip laser based on a magnetic point-contact array

We present a theoretical design for a single-mode, truly subwavelength terahertz disk laser based on a nanocomposite gain medium comprising an array of normal-metal/ferromagnetic (FM) point contacts embedded in a thin dielectric layer. Stimulated emission of light occurs due to spin-flip relaxation of spin-polarized electrons injected from the FM side of the contacts. Ultrahigh electrical current densities in the contacts and a dielectric material with a large refractive index, neither condition being achievable in conventional semiconductor media, enables the thresholds of lasing to be overcome for the lowest-order modes of the disk, making single-mode operation possible.     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.     

Operators with smooth functional calculi

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, which contains all operators of Helffer-Sjöstrand type and is closed under the action of smooth proper mappings. Moreover, the class is closed under tensor product of commuting operators. In general, and operator in this class has no resolvent in the usual sense, so the spectrum must be defined in terms of the functional calculus. We also consider invariant subspaces and spectral decompositions.     

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.