Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

Simultaneous determination of multibenzodiazepines by HPLC/UV: Investigation of liquid-liquid and solid-phase extractions in human plasma

A method for simultaneous determination of seven benzodiazepines (BZPs) (flunitrazepam, clonazepam, oxazepam, lorazepam, chlordiazepoxide, nordiazepam and diazepam using N-desalkylflurazepam as internal standard) in human plasma using liquid-liquid and solid-phase extractions followed by high-performance liquid chromatography (HPLC) is described. The analytes were separated employing a LC-18 DB column (250 mm x 4.6 mm, 5 mu m) at 35 degrees C under isocratic conditions using 5 mM KH(2)PO(4) buffer solution pH 6.0: methanol: diethyl ether (55:40:5, v/v/v) as mobile phase at a flow rate of 0.8 mL min(-1). UV detection was carried out at 245 nm. Employing LLE, the best conditions were achieved with double extraction of 0.5 mL, plasma using ethyl acetate and Na(2)HPO(4) pH 9.5 for pH adjusting. Employing SPE, the best conditions were achieved with 0.5 mL plasma plus 3 mL 0.1 M borate buffer pH 9.5, which were then passed through a C18 cartridge previously conditioned, washed for 3 times with these solvents: 3 mL 0.1 M borate buffer pH 9.5,4 mL Milli-Q water and 1 mL acetonitrile 5%, finally the BZPs elution was carried with diethyl ether: n-hexane: methanol (50:30:20). In both methods the solvent was evaporated at 40 degrees C under nitrogen flow. The validation parameters obtained in LLE were linearity range of 50-1200 ng mL(-1) plasma (r >= 0.9927), limits of quantification of 50 ng mL(-1) plasma, within-day and between-day CV% and E% for precision and accuracy lower than 15%, and recovery above 65% for all BZPs. In SPE, the parameter obtained were linearity range of 30-1200 ng mL(-1) plasma (r >= 0.9900), limits of quantification of 30 ng mL(-1) plasma, within-day and between-day CV% and E% for precision and accuracy lower than 15% and recovery above 55% for all BZPs. These extracting procedures followed by HPLC analysis showed their suitable applicability in order to examine one or more BZPs in human plasma. Moreover, it could be suggested that these procedures might be employed in various analytical applications, in special for toxicological/forensic analysis. (c) 2008 Elsevier B.V. All rights reserved.

Molecular dynamics, density functional, ADMET predictions, virtual screening, and molecular interaction field studies for identification and evaluation of novel potential CDK2 inhibitors in cancer therapy

In this work, we have used molecular dynamics, density functional theory, virtual screening, ADMET predictions, and molecular interaction field studies to design and propose eight novel potential inhibitors of CDK2. The eight molecules proposed showed interesting structural characteristics that are required for inhibiting the CDK2 activity and show potential as drug candidates for the treatment of cancer. The parameters related to the Rule of Five were calculated, and only one of the molecules violated more than one parameter. One of the proposals and one of the drug-like compounds selected by virtual screening indicated to be promising candidates for CDK2-based cancer therapy.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.