Symmetry analysis of the two-dimensional diffusion equation with a source term

A symmetry analysis is performed on a (2+1)-dimensional linear diffusion equation with a nonlinear source term involving the dependent variable and its spatial derivatives. In the first part of the paper, we use the classical method to classify source terms where the original equation admits a nontrivial symmetry. In the second part of the paper, we use the nonclassical method and show that we simply recover the classical symmetries.     

Perturbation Theory for the Asymptotic Decay Rates in the Queues with Markovian Arrival Process and/or Markovian Service Process

Three kinds of queues with Markovian arrival process and/or Markovian service process, are considered in this paper. In great generality, their basic steady-state distributions have asymptotically exponential tails. We investigate the sensitivity of these asymptotic decay rates to the small entrywise perturbations in the parameter matrices of the Markovian arrival process.     

Reciprocity between the cerebellum and the cerebral cortex: Nonlinear dynamics in microscopic modules for generating voluntary motor commands

The cerebellum and basal ganglia are reciprocally connected with the cerebral cortex, forming many loops that function as distributed processing modules. Here we present a detailed model of one microscopic loop between the motor cortex and the cerebellum, and we show how small arrays of these microscopic loops (CB modules) can be used to generate biologically plausible motor commands for controlling movement. A fundamental feature of CB modules is the presence of positive feedback loops between the cerebellar nucleus and the motor cortex. We use nonlinear dynamics to model one microscopic loop and to investigate its bistable properties. Simulations demonstrate an ability to program a motor command well in advance of command generation and an ability to vary command duration. However, control of command intensity is minimal, which could interfere with the control of movement velocity. To assess these hypotheses, we use a minimal nonlinear model of the neuromuscular (NM) system that translates motor commands into actual movements. Simulations of the combined CB‐NM modular model indicate that movement duration is readily controlled, whereas velocity is poorly controlled. We then explore how an array of eight CB‐NM modules can be used to control the direction and endpoint of a planar movement. In actuality, thousands of such microscopic loops function together as an array of adjustable pattern generators for programming and regulating the composite motor commands that control limb movements. We discuss the biological plausibility and limitations of the model. We also discuss ways in which an agent‐based representation can take advantage of the modularity in order to model this complex system. © 2008 Wiley Periodicals, Inc. Complexity, 2008     

The ν9 Band of Propyne-d3

A high-resolution Fourier transform spectrum of the ν₉ band of CD₃CCH has been recorded at an apodized resolution of 0.004 cm−1 and analyzed. More than 1700 lines in the spectrum have been assigned and the parameters of the ν₉ state derived. The standard deviation of the fit was 0.00034 cm⁻¹. In order to achieve this fit it was necessary to include l-type doubling interaction and Fermi resonance between ν₉ and the E component of 2ν₁₀.     

Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models

In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent values for the entire state probability vector. From this vector, most performance parameters such as expected waiting time and expected number in the system can be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of transient time. With these two solution methods one can examine any transient associated with the MAP(t)/PH(t)/1/K model including time-varying arrival and/or service patterns. Four test cases are used to demonstrate the effectiveness of these methods. Results from these cases indicate that both methods provide fast and accurate solutions to a wide range of transient scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

Biosorption of radiostrontium by alginate beads: application of isotherm models and thermodynamic studies

Radioactive strontium is one of the major radioactive contaminant and its contamination is a very serious concern. Therefore, there is a need for economic, effective, non-toxic, readily available and abundant adsorbent or biosorbent to remove strontium from solutions. In this study, biosorption of ⁸⁵Sr as a surrogate for ⁹⁰Sr onto alginate beads was investigated in a batch system. Alginate beads were prepared from Na-alginate via cross-linking with divalent calcium ions according to the egg box model. The effect of several parameters such as pH, initial strontium concentration, contact time, dosage of alginate beads and temperature were investigated. In order to optimize the design of biosorption system for the removal of strontium, it is important to establish the most appropriate correlation for equilibrium curves. The experimental isotherm data were described by 6 different biosorption isotherm models, namely Langmuir, Freundlich, Dubinin–Radushkevich, Temkin, Flory–Huggins and Brunauer, Emmer and Teller, with constants obtained from linear and non-linear regression methods. The thermodynamic parameters (?H°, ?S° and ?G°) for strontium biosorption were also determined. The results indicate that these alginate beads have a good potential for the biosorption of strontium from solutions.     

Some decomposition results for a class of vacation queues

We analyze the MAP/PH/1 vacation system at arbitrary times using the matrix-analytic method, and obtain decomposition results for the R$R$ and G$G$ matrices. The decomposition results reduce the amount of computational effort needed to obtain these matrices. The results for the G$G$ matrix are extended to the BMAP/PH/1 system. We also show that in the case of the Geo/PH/1 and M/PH/1 systems with PH vacations both the G$G$ and R$R$ matrices can be obtained explicitly.     

An ab initio investigation of the O(3P)-H2(1sigma(g)+) van der Waals well

We report an ab initio study of the van der Waals region of the O(3P)-H2 potential energy surface based on RCCSD(T) calculations with an aug-cc-pVQZ basis supplemented by bond functions. In addition, an open-shell implementation of symmetry-adapted perturbation theory (SAPT) is used to corroborate the RCCSD(T) calculations and to investigate the relative magnitudes of the various contributions to the van der Waals interaction. We also investigate the effect of the spin-orbit coupling on the position and depth of the van der Waals well. We predict the van der Waals minimum to occur in perpendicular geometry, and located at a closer distance than a secondary well in colinear geometry. The potentials obtained in the present study confirm the previous calculations of Alexander [M. H. Alexander, J. Chem. Phys., 1998, 108, 4467], but disagree with the earlier work of Harding and co-workers [Z. Li, V. A. Apkarian and L. B. Harding, J. Chem. Phys., 1997, 106, 942] as well as with recently refitted surfaces of Brand?o and coworkers [J. Brand?o, C. Mogo and B. C. Silva, J. Chem. Phys., 2004, 121, 8861]. Inclusion of spin-orbit coupling reduces the depth of the van der Waals minimum without causing a change in its position.     

The effects of thermal quenching on the excited-state intramolecular proton transfer reaction in 3-hydroxyflavones

The 3-hydroxyflavone (3HF) and its derivatives are the classical objects in the studies of the mechanisms of excited-state intramolecular proton transfer (ESIPT) reaction due to very frequent observation of two separate bands in fluorescence emission belonging to reactant and reaction product. Those of them possessing electron-donor groups in 4' position find many applications as fluorescence sensors and probes because of their much higher sensitivity of their two-band ratiometric response to interactions with the environment. We report on the strong differences between 3HF and such derivatives in the behavior of their fluorescence spectra as a function of temperature. The thermal quenching changes the intensity ratio of two bands strongly for 3HF but does not change it for its studied derivatives. These results are interpreted in terms of different kinetic mechanisms of ESIPT reaction. In 3HF the equilibrium between the two excited-state species is not established prior to emission, so that the ESIPT reaction is under kinetic control, but in these derivatives the equilibrium is established faster than the emission and the reaction is under thermodynamic control. We suggest that the thermal perturbation of fluorescence spectra can be an extremely simple and convenient alternative to time-resolved spectroscopy for determining if slow irreversible or fast reversible ESIPT reaction gives rise to two bands of fluorescence spectra of similar magnitude. This is essential for the development of new wavelength-ratiometric fluorescence sensors and probes.