A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]

Optical waveguide propagation loss measurement using multiple reflections method

Optical waveguide propagation loss measurement method based on optical multiple reflections detection is presented in this paper. By using a precision reflectometer, uncertain influence on waveguide propagation loss measurement caused by fiber-waveguide coupling can be eliminated effectively and the waveguide net propagation loss can be measured accurately. To demonstrate this, the propagation loss of a Silicon-on-Insulator (SOI) rib waveguide fabricated by RIE is measured with the obtained value being 4.3 dB/cm. This method provides a non-destructive means for evaluating waveguide propagation loss. (c) 2005 Elsevier B.V. All rights reserved.

Focus group method and methodology:current practice and recent debate

This paper considers the contemporary use of focus groups as a method of data collection within qualitative research settings. The authors draw upon their own experiences of using focus groups in educational and 'community' user-group environments in order to provide an overview of recent issues and debates surrounding the deployment of focus group methods and to pick out specific areas of contention in relation to both their epistemological and practical implications. Accordingly, the paper reflects on some of the realities of 'doing' focus groups whilst, at the same time, highlighting common problems and dilemmas which beginning researchers might encounter in their application. In turn, the paper raises a number of related issues around which there appears to have been a lack of academic discussion to date.

Phobic anxiety in 11 nations: Part I: Dimensional constancy of the five-factor model

The Fear Survey Schedule-III (FSS-III) was administered to a total of 5491 students in Australia, East Germany, Great Britain, Greece, Guatemala, Hungary, Italy, Japan, Spain, Sweden, and Venezuela, and submitted to the multiple group method of confirmatory analysis (MGM) in order to determine the cross-national dimensional constancy of the five-factor model of self-assessed fears originally established in Dutch, British, and Canadian samples. The model comprises fears of bodily injury-illness-death, agoraphobic fears, social fears, fears of sexual and aggressive scenes, and harmless animals fears. Close correspondence between the factors was demonstrated across national samples. In each country, the corresponding scales were internally consistent, were intercorrelated at magnitudes comparable to those yielded in the original samples, and yielded (in 93% of the total number of 55 comparisons) sex differences in line with the usual finding (higher scores for females). In each country, the relatively largest sex differences were obtained on harmless animals fears. The organization of self-assessed fears is sufficiently similar across nations to warrant the use of the same weight matrix (scoring key) for the FSS-III in the different countries and to make cross-national comparisons feasible. This opens the way to further studies that attempt to predict (on an a priori basis) cross-national variations in fear levels with dimensions of national cultures. (C) 2002 Elsevier Science Ltd. All rights reserved.

Optimized group replacement scheduling for water pipeline network

Replacement of deteriorated water pipes is a capital-intensive activity for utility companies. Replacement planning aims to minimize total costs while maintaining a satisfactory level of service and is usually conducted for individual pipes. Scheduling replacement in groups is seen to be a better method and has the potential to provide benefits such as the reduction of maintenance costs and service interruptions. However, developing group replacement schedules is a complex task and often beyond the ability of a human expert, especially when multiple or conflicting objectives need to be catered for, such as minimization of total costs and service interruptions. This paper describes the development of a novel replacement decision optimization model for group scheduling (RDOM-GS), which enables multiple group-scheduling criteria by integrating new cost functions, a service interruption model, and optimization algorithms into a unified procedure. An industry case study demonstrates that RDOM-GS can improve replacement planning significantly and reduce costs and service interruptions.

Neuroethologic differences in sleep deprivation induced by the single- and multiple-platform methods

It has been proposed that the multiple-platform method (MP) for desynchronized sleep (DS) deprivation eliminates the stress induced by social isolation and by the restriction of locomotion in the single-platform (SP) method. MP, however, induces a higher increase in plasma corticosterone and ACTH levels than SP. Since deprivation is of heuristic value to identify the functional role of this state of sleep, the objective of the present study was to determine the behavioral differences exhibited by rats during sleep deprivation induced by these two methods. All behavioral patterns exhibited by a group of 7 albino male Wistar rats submitted to 4 days of sleep deprivation by the MP method (15 platforms, spaced 150 mm apart) and by 7 other rats submitted to sleep deprivation by the SP method were recorded in order to elaborate an ethogram. The behavioral patterns were quantitated in 10 replications by naive observers using other groups of 7 rats each submitted to the same deprivation schedule. Each quantification session lasted 35 min and the behavioral patterns presented by each rat over a period of 5 min were counted. The results obtained were: a) rats submitted to the MP method changed platforms at a mean rate of 2.62 ± 1.17 platforms h-1 animal-1; b) the number of episodes of noninteractive waking patterns for the MP animals was significantly higher than that for SP animals (1077 vs 768); c) additional episodes of waking patterns (26.9 ± 18.9 episodes/session) were promoted by social interaction in MP animals; d) the cumulative number of sleep episodes observed in the MP test (311) was significantly lower (chi-square test, 1 d.f., P<0.05) than that observed in the SP test (534); e) rats submitted to the MP test did not show the well-known increase in ambulatory activity observed after the end of the SP test; f) comparison of 6 MP and 6 SP rats showed a significantly shorter latency to the onset of DS in MP rats (7.8 ± 4.3 and 29.0 ± 25.0 min, respectively; Student t-test, P<0.05). We conclude that the social interaction occurring in the MP test generates additional stress since it increases the time of forced wakefulness and reduces the time of rest promoted by synchronized sleep.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

A Multicast Authentication Protocol (MAP) for Dynamic Multicast Groups in Wireless Networks

In this paper, we have proposed a centralized multicast authentication protocol (MAP) for dynamic multicast groups in wireless networks. In our protocol, a multicast group is defined only at the time of the multicasting. The authentication server (AS) in the network generates a session key and authenticates it to each of the members of a multicast group using the computationally inexpensive least common multiple (LCM) method. In addition, a pseudo random function (PRF) is used to bind the secret keys of the network members with their identities. By doing this, the AS is relieved from storing per member secrets in its memory, making the scheme completely storage scalable. The protocol minimizes the load on the network members by shifting the computational tasks towards the AS node as far as possible. The protocol possesses a membership revocation mechanism and is protected against replay attack and brute force attack. Analytical and simulation results confirm the effectiveness of the proposed protocol.

Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

Optical properties of a square-lattice photonic crystal within the partial bandgap

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann-Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method. (c) 2007 Optical Society of America

Efeito da privação de sono paradoxal na expressão de receptores para glicocorticoides no hipocampo e no aprendizado e memória

Vários trabalhos têm demonstrado uma relação entre sono e memória. Desta forma, tem sido descrito um papel importante do sono na consolidação da memória e um efeito negativo pela privação do mesmo. O hipocampo é uma região importante para a formação e consolidação da memória espacial, e contém uma alta expressão de receptores para corticosteróides. As ações dos corticosteróides no hipocampo são fundamentais para a aquisição de memória e dependem de um balanço adequado entre receptores de Glicocorticóides (RGc) e Mineralocorticóides (RMn). Assim é descrito na literatura que um aumento na expressão de RMn é promotor de aquisição de memória, enquanto que um aumento na expressão de RGc produz um efeito negativo. Apesar dos níveis circulantes de glicocorticóides na privação de sono paradoxal (PSP), não serem responsáveis pelo enfraquecimento de memória, não existem dados sobre a expressão dos receptores para corticosteróides no hipocampo, após PSP. Neste trabalho tivemos como objetivo investigar a expressão de receptores de Glicocorticóides no hipocampo, bem como avaliar aprendizado e memória em ratos privados de sono paradoxal. Ratos Wistar machos (250- 350g) foram submetidos à PSP, utilizando-se o método de múltiplas plataformas por um período de 96 horas. Após 96h de privação os animais foram anestesiados e perfundidos. Secções de 25 μm na área do hipocampo foram obtidas e reagidas com anticorpos para receptores de Glicocortidóides. Avaliamos as áreas CA1, CA3 e Giro Denteado. O aprendizado e memória espacial foram avaliados através do teste do labirinto aquático de oito braços, antes e após o período de privação de sono. Avaliou-se a latência de escape e o número de erros obtidos. O grupo PSP apresentou um aumento na expressão de RGc nas regiões: CA1 e Giro Denteado, não se observando diferença significativa na região CA3. A PSP prévia aos testes de aprendizado e memória não provocou alterações significativas. A privação de sono pós-aprendizado também não produziu diferenças estatisticamente significativas, mas um aumento no tempo de latência de escape e número de erros sugere um enfraquecimento na consolidação da memória. O aumento na expressão de RGc nas áreas estudadas, pode ser consequente a uma alteração no balanço entre os receptores para corticosteróides no hipocampo e ser responsável por alterações no aprendizado e memória em ratos PSP.