A Note on a Boundary Value Problem

In this note, we prove that, for Robins boundary value problem, a unique solution exists if f_x(t, x, x), f_x(t, x, x), (t), and (t) are continuous, and f_x -(t), f_x -(t), 4(t) ² + ²(t) ++ 2(t), and 4(t) ² + ²(t) + 2(t).AMS Subject Classification (2000) 34B15     

An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions

The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data.     

Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D.J. Watts et al., Science 296, 1302 (2002)) as a hierarchy of groups, each of 5 individuals. A homophily parameter α controls the probability proportional to exp (-αx) of selection of neighbours against distance x. The network nodes are endowed with spin-like variables s_i = ± 1, with Ising interaction J > 0. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature T_c is close to 3.8 for α < 0.0 and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action via weak ties, as discussed by Granovetter in 1973.     

Measuring particle size-dependent physicochemical structure in airborne single walled carbon nanotube agglomerates

As-produced single-walled carbon nanotube (SWCNT) material is a complex matrix of carbon nanotubes, bundles of nanotubes (nanoropes), non-tubular carbon and metal catalyst nanoparticles. The pulmonary toxicity of material released during manufacture and handling will depend on the partitioning and arrangement of these components within airborne particles. To probe the physicochemical structure of airborne SWCNT aggregates, a new technique was developed and applied to aerosolized as-produced material. Differential Mobility Analysis-classified aggregates were analyzed using an Aerosol Particle Mass Monitor, and a structural parameter Γ (proportional to the square of particle mobility diameter, divided by APM voltage) derived. Using information on the constituent components of the SWCNT, modal values of Γ were estimated for specific particle compositions and structures, and compared against measured values. Measured modal values of Γ for 150 nm mobility diameter aggregates suggested they were primarily composed of non-tubular carbon from one batch of material, and thin nanoropes from a second batch of material – these findings were confirmed using Transmission Electron Microscopy. Measured modal values of Γ for 31 nm mobility diameter aggregates indicated that they were comprised predominantly of thin carbon nanoropes with associated nanometer-diameter metal catalyst particles; there was no indication that either catalyst particles or non-tubular carbon particles were being preferentially released into the air. These results indicate that the physicochemistry of aerosol particles released while handling as-produced SWCNT may vary significantly by particle size and production batch, and that evaluations of potential health hazards need to account for this. Disclaimer: The mention of any company or product does not constitute an endorsement by the Centers for Disease Control and Prevention. The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health.     

Waveform preservation of the backscattered stimulated Brillouin scattering wave by using a prepulse injection

We have found that it is possible to preserve the temporal waveform of the reflected wave generated from stimulated Brillouin scattering (SBS) by using a prepulse technique. The waveform of the SBS wave usually shows a steep rising edge in the ordinary SBS process. It has been found that the waveform of the reflected wave depends on both the prepulse energy and the time delay between the main pulse and the prepulses. A prepulse energy of 5 mJ and a time delay of 5 ns have been measured to be the optimum values under the experimental conditions. This prepulse method is useful in developing a multistage system employing several SBS cells in series for high-power laser applications.     

Review of fluorescence anisotropy decay analysis by frequency-domain fluorescence spectroscopy

This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry.     

Direct experimental limit on neutron-mirror-neutron oscillations

In case a mirror world with a copy of our ordinary particle spectrum would exist, the neutron n and its degenerate partner, the mirror neutron n', could potentially mix and undergo nn' oscillations. The interaction of an ordinary magnetic field with the ordinary neutron would lift the degeneracy between the mirror partners, diminish the n' amplitude in the n wave function and, thus, suppress its observability. We report an experimental comparison of ultracold neutron storage in a trap with and without superimposed magnetic field. No influence of the magnetic field is found and, assuming negligible mirror magnetic fields, a limit on the oscillation time taunn' > 103 s (95% C.L.) is derived.     

Pointwise error estimates for a stabilized Galerkin method: non-selfadjoint problems

Highly localized pointwise error estimates for a stabilized Galerkin method are provided for second-order non-selfadjoint elliptic partial differential equations. The estimates show a local dependence of the error on the derivative of the solution u and weak dependence on the global norm. The results in this paper are an extension of the previous pointwise error estimates for the self-adjoint problems. In order to provide pointwise error estimates in the presence of the first-order term in the differential equations, we prove that the stabilized Galerkin solution is higher order perturbation to the Ritz projection of the true solutions. Then, we proceed to obtain pointwise estimates using the so-called discrete Green’s function. Application to error expansion inequalities and a posteriori error estimators are briefly discussed.     

Temperature-sensitive behaviour of poly(glycidol)-b-poly(N-isopropylacrylamide) block copolymers

Temperature-sensitive poly(glycidol)-b-poly(N-isopropylacrylamide) block copolymers (PGl₅₅PNIPAAm_y) were synthesised and their aqueous solutions investigated by different methods including differential scanning calorimetry (DSC), UV-VIS spectroscopy as well as dynamic and static light scattering. The cloud point temperature (T _c) depended on the composition of the investigated block copolymers and increased with decreasing length of the PNIPAAm block in PGl₅₅PNIPAAm_y copolymers. In contrast, the enthalpy of phase separation of PNIPAAm segments measured by DSC decreased with decreasing length of the PNIPAAm block in the polymer. These findings can be correlated with the behaviour of homo-PNIPAAm with similar molecular weights indicating that the influence of PGl on the local environment and phase separation of PNIPAAm chains is similar to the influence observed for PNIPAAm chains bearing different low molecular weight end group. Using DLS measurement, it was shown that the aggregation process depended on the PGl/PNIPAAm block ratio. If the PGl/PNIPAAm ratio was low, stable core-shell aggregates were formed. In contrast, the tendency to formation of large unstable, loose aggregates was observed for copolymers with high PGl/PNIPAAm ratio.     

The K-Quotient

The Rayleigh Quotient and a recently proposed Timoshenko Quotient [1] are upper bounds to the fundamental eigenvalue of a discrete dynamic system. The closeness of these upper bounds to the fundamental eigenvalue depends on the closeness of the trial vectors to the eigenmode used in the calculation. In the present paper, a new quotient is presented. This quotient does not require the closeness of the trial vector to the eigenmode and its accuracy is improvable by raising the numerical value of the parameter p.