Approximate solution to a hybrid model with stochastic volatility: a singular-perturbation strategy

We study a hybrid model of Schobel-Zhu-Hull-White-type from a singular-perturbation-analysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast

Can the Services Sector Be an Engine of Economic Growth for the Philippines?

With the services sector outpacing the Philippines' manufacturing sector in terms of growth and contribution to the country's gross domestic product (GDP) for decades now, is it prudent, as some quarters propose, for the government to "abandon" the manufacturing sector and shift its policy in support of the services sector as the engine of economic growth for the Philippines? This Policy Notes emphatically says "no" and highlights the arguments against such policy shift.services sector, manufacturing sector, deindustrialization

Multiscale reaction-diffusion systems describing concrete corrosion : modeling and analysis

This thesis deals with the modeling and multiscale analysis of reaction-diffusion systems describing concrete corrosion processes due to the aggressive chemical reactions occurring in concrete. We develop a mathematical framework that can be useful in forecasting the service life of sewer pipes. We aim at identifying reliable and easy-to-use multiscale models able to forecast the penetration of sulfuric acid into sewer pipes walls. For modeling of corrosion processes, we take into account balance equations expressing physico-chemical processes that take place in the microstructures (pores) of the partially saturated concrete. We consider two dierent modeling strategies: (1) we propose microscopic reaction-diusion systems to delineate the corrosion processes at the pore level and (2) we consider a distributed microstructure model containing information from two separated spatial scales (micro and macro). All systems of dierential equations are semi-linear, weakly coupled, and partially diusive. Since the precise microstructure of the material is far too complex to be described accurately, we consider two approximations, namely uniformly-periodic and locally-periodic array of microstructures, which are tractable by using averaging mathematical tools. We use different homogenization techniques to obtain the effective behavior of the microscopically oscillating quantities. For the formal derivation of our multiscale models, we apply the asymptotic expansion method to the microscopic reaction-diffusion systems defined in locally-periodic domains for two special choices of scaling in ¿ of the diffusion coefficients. We end up with (i) upscaled systems and (ii) distributed-microstructure systems. As far as rigorous derivations are concerned, we apply the notion of two-scale convergence to the PDE system defined in the uniformly periodic domain. To deal with the non-diffusive object, i.e. the ordinary dierential equation tracking the damage-by-reaction, we combine the two-scale convergence idea with the periodic-boundary-unfolding technique. Additionally, we use the periodic unfolding techniques to obtain corrector estimates assessing the quality of the averaging method. These estimates are convergence rates measuring the error contribution produced while approximating macroscopic solutions by microscopic ones. We derive these estimates under minimal regularity assumptions on the solutions to the microscopic and macroscopic systems, microstructure boundaries, and to the corresponding auxiliary cell problems. We prove the well-posedness of a distributed-microstructure reaction-diusion system which includes transport (diusion) and reaction effects emerging from two separated spatial scales. We perform this analysis by incorporating a variational inequality requiring minimal regularity assumptions on the initial data. We ensure basic estimates like positivity and L8-bounds on the solution to the system. Then we prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions. To predict the position of the corrosion front penetrating the concrete, we use our distributed-microstructure model to perform simulations at macroscopic length scales while taking into account transport and reactions occurring at small length scales. Using an ad hoc logarithmic expression, we approximate numerically macroscopic pH proles dropping down with the onset of corrosion. We extract from the gypsum proles the approximate position of the corrosion front penetrating the uncorroded concrete. We illustrate numerically that as the macroscopic mass-transfer Biot number BiM -> 8, BiM naturally connects two different multiscale reaction-diusion scenarios: the solution of the distributed-microstructure system having the Henry's law acting as micro-macro transmission condition converges to the solution of the matched distributed-microstructure system

Effect Of Electrospun Nanofibers On Flexural Properties Of Fiberglass Composites

In the present study, sintered electrospun TEOS nanofibers were interleaved in S2 fiberglass woven fabric layers, and composite panels were fabricated using the heated vacuum assisted resin transfer molding (H-VARTM) process. Cured panels were water jet cut to obtain the flexural test coupons. Flexural coupons were then tested using ASTM D7264 standard. The mechanical properties such as flexural strength, ultimate flexural failure strains, flexural modulus, and fiber volume fraction were measured. The S-2 fiberglass composite with the sintered TEOS electrospun nanofibers displayed lower flexural stiffness and strength as compared to the composites that were fabricated using S-2 fiberglass composite without the TEOS electrospun nanofibers. The present study also indicated that the composites fabricated with sintered TEOS electrospun nanofibers have larger failure strains as compared to the ones that were fabricated without the presence of electrospun nanofibers. The study indicates that the nanoengineered composites have better energy absorbing mechanism under flexural loading as compared to conventional fiberglass composites without presence of nanofibers

Effect Of Electrospun Nanofibers On Flexural Properties Of Fiberglass Composites

In the present study, sintered electrospun TEOS nanofibers were interleaved in S2 fiberglass woven fabric layers, and composite panels were fabricated using the heated vacuum assisted resin transfer molding (H-VARTM) process. Cured panels were water jet cut to obtain the flexural test coupons. Flexural coupons were then tested using ASTM D7264 standard. The mechanical properties such as flexural strength, ultimate flexural failure strains, flexural modulus, and fiber volume fraction were measured. The S-2 fiberglass composite with the sintered TEOS electrospun nanofibers displayed lower flexural stiffness and strength as compared to the composites that were fabricated using S-2 fiberglass composite without the TEOS electrospun nanofibers. The present study also indicated that the composites fabricated with sintered TEOS electrospun nanofibers have larger failure strains as compared to the ones that were fabricated without the presence of electrospun nanofibers. The study indicates that the nanoengineered composites have better energy absorbing mechanism under flexural loading as compared to conventional fiberglass composites without presence of nanofibers

An Investigation of the Effects of Categorization and Discrimination Training on Auditory Perceptual Space

Psychophysical phenomena such as categorical perception and the perceptual magnet effect indicate that our auditory perceptual spaces are warped for some stimuli. This paper investigates the effects of two different kinds of training on auditory perceptual space. It is first shown that categorization training, in which subjects learn to identify stimuli within a particular frequency range as members of the same category, can lead to a decrease in sensitivity to stimuli in that category. This phenomenon is an example of acquired similarity and apparently has not been previously demonstrated for a category-relevant dimension. Discrimination training with the same set of stimuli was shown to have the opposite effect: subjects became more sensitive to differences in the stimuli presented during training. Further experiments investigated some of the conditions that are necessary to generate the acquired similarity found in the first experiment. The results of these experiments are used to evaluate two neural network models of the perceptual magnet effect. These models, in combination with our experimental results, are used to generate an experimentally testable hypothesis concerning changes in the brain's auditory maps under different training conditions.Alfred P. Sloan Foundation and the National institutes of Deafness and other Communication Disorders (R29 02852); Air Force Office of Scientific Research (F49620-98-1-0108

Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality : a well-posedness study

This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is semilinear, partially dissipative, and coupled via the solid-water interface at the microstructure (pore) level. The structure of the model equations is obtained in \cite{tasnim1} by upscaling of the physical and chemical processes taking place within the microstructure of the concrete. Herein we ensure the positivity and $L^\infty-$bounds on concentrations, and then prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions that are stable with respect to the two-scale data and model parameters. The main ingredient to prove existence include fixed-point arguments and convergent two-scale Galerkin approximations

Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality : a well-posedness study

This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: x - macro and y - micro. The system’s origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is semilinear, partially dissipative, and coupled via the solid-water interface at the microstructure (pore) level. The structure of the model equations is obtained in [7] by upscaling of the physical and chemical processes taking place within the microstructure of the concrete. Herein we ensure the positivity and L8-bounds on concentrations, and then prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions that are stable with respect to the two-scale data and model parameters. The main ingredient to prove existence include fixed-point arguments and convergent two-scale Galerkin approximations. Keywords: Reaction and diffusion in heterogeneous media, two-scale Galerkin approximations, parabolic variational inequality, well-posednes