Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Real-time power line extraction from unmanned aerial system video images

In this paper a real-time vision based power line extraction solution is investigated for active UAV guidance. The line extraction algorithm starts from ridge points detected by steerable filters. A collinear line segments fitting algorithm is followed up by considering global and local information together with multiple collinear measurements. GPU boosted algorithm implementation is also investigated in the experiment. The experimental result shows that the proposed algorithm outperforms two baseline line detection algorithms and is able to fitting long collinear line segments. The low computational cost of the algorithm make suitable for real-time applications.

Wind-energy based path planning for unmanned aerial vehicles using Markov decision processes

Exploiting wind-energy is one possible way to extend flight duration for Unmanned Arial Vehicles. Wind-energy can also be used to minimise energy consumption for a planned path. In this paper, we consider uncertain time-varying wind fields and plan a path through them. A Gaussian distribution is used to determine uncertainty in the Time-varying wind fields. We use Markov Decision Process to plan a path based upon the uncertainty of Gaussian distribution. Simulation results that compare the direct line of flight between start and target point and our planned path for energy consumption and time of travel are presented. The result is a robust path using the most visited cell while sampling the Gaussian distribution of the wind field in each cell.

Fast power line detection and localization using steerable filter for active UAV guidance

In this paper we present a fast power line detection and localisation algorithm as well as propose a high-level guidance architecture for active vision-based Unmanned Aerial Vehicle (UAV) guidance. The detection stage is based on steerable filters for edge ridge detection, followed by a line fitting algorithm to refine candidate power lines in images. The guidance architecture assumes an UAV with an onboard Gimbal camera. We first control the position of the Gimbal such that the power line is in the field of view of the camera. Then its pose is used to generate the appropriate control commands such that the aircraft moves and flies above the lines. We present initial experimental results for the detection stage which shows that the proposed algorithm outperforms two state-of-the-art line detection algorithms for power line detection from aerial imagery.

Supramolecular selection in molecular alloys

Complexes of the type \[M(phen)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and phen = 1,10-phenanthroline) were found to co-crystallize to form molecular alloys (solid solutions of molecules) with general formula \[MAxMB1–x(phen)3](PF6)2·0.5H2O in which the relative concentrations of the metal complexes in the crystals closely match those in the crystallizing solution. Consequently, the composition of the co-crystals can be accurately predicted and controlled by modulating the relative concentrations of the metal complexes in the crystallizing solution. Although they are chemically and structurally similar, complexes of the type \[M(bipy)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and bipy = 2,2′-bipyridine) display markedly different behavior upon co-crystallization. In this case, the resulting co-crystals of general formula \[MAxMB1–x(bipy)3](PF6)2 have relative concentrations of the constituent complexes that are markedly different from the relative concentrations of the complexes initially present in the crystallizing solution. For example, when the nickel and iron complexes are co-crystallized from a solution containing a 50:50 ratio of each, the result is the formation of some crystals with a higher proportion of iron and others with a higher proportion of nickel. The relative concentrations of the metal complexes in the crystals can vary from those in the crystallizing solutions by as much as 15%. This result was observed for a range of combinations of metal complexes (Ni/Fe, Ni/Ru, and Fe/Ru) and a range of starting concentrations in the crystallizing solutions (90:10 through to 10:90 in 10% increments). To explain this remarkable result, we introduce the concept of “supramolecular selection”, which is a process driven by molecular recognition that leads to the partially selective aggregation of like molecules during crystallization.

Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Statistical and scientometric analysis of international research in geographical and environmental education

Certain statistic and scientometric features of articles published in the journal “International Research in Geographical and Environmental Education” are examined in this paper, for the period 1992-2009, by applying nonparametric statistics and Shannon’s entropy (diversity) formula. The main findings of this analysis are: a) after 2004 the research priorities of researchers in geographical and environmental education seem to have changed, b) “teacher education” has been the most recurrent theme throughout these 18 years, followed by “values & attitudes” and “inquiry & problem solving” c) the themes “GIS” and “Sustainability” were the most “stable” throughout the 18 years, meaning that they maintained their ranks as publication priorities more than other themes, d) citations of IRGEE increase annually, e) the average thematic diversity of articles published during the period 1992-2009 is 82.7% of the maximum thematic diversity (very high), meaning that the Journal has the capacity to attract a wide readership for the 10 themes it has successfully covered throughout the 18 years of its publication.

Eigenvoice modeling for cross likelihood ratio based speaker clustering : a Bayesian approach

This paper proposes the use of Bayesian approaches with the cross likelihood ratio (CLR) as a criterion for speaker clustering within a speaker diarization system, using eigenvoice modeling techniques. The CLR has previously been shown to be an effective decision criterion for speaker clustering using Gaussian mixture models. Recently, eigenvoice modeling has become an increasingly popular technique, due to its ability to adequately represent a speaker based on sparse training data, as well as to provide an improved capture of differences in speaker characteristics. The integration of eigenvoice modeling into the CLR framework to capitalize on the advantage of both techniques has also been shown to be beneficial for the speaker clustering task. Building on that success, this paper proposes the use of Bayesian methods to compute the conditional probabilities in computing the CLR, thus effectively combining the eigenvoice-CLR framework with the advantages of a Bayesian approach to the diarization problem. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, resulting in a 33.5% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.

Mixed convection along a vertical flat plate in a non-absorbing medium

Here mixed convection boundary layer flow of a viscous fluid along a heated vertical semi-infinite plate is investigated in a non-absorbing medium. The relationship between convection and thermal radiation is established via boundary condition of second kind on the thermally radiating vertical surface. The governing boundary layer equations are transformed into dimensionless parabolic partial differential equations with the help of appropriate transformations and the resultant system is solved numerically by applying straightforward finite difference method along with Gaussian elimination technique. It is worthy to note that Prandlt number, Pr, is taken to be small (<< 1) which is appropriate for liquid metals. Moreover, the numerical results are demonstrated graphically by showing the effects of important physical parameters, namely, the modified Richardson number (or mixed convection parameter), Ri*, and surface radiation parameter, R, in terms of local skin friction and local Nusselt number coefficients.

Determination of creep behaviour of concrete made by brick chips in Bangladesh

Concrete made of brick chips as coarse aggregate are extensively used in Bangladesh for construction of different types of structures from residential and commercial buildings to industrial complex. As creep is influenced among many factors including the constituents’ materials, relative humidity and temperature, it is essential to examine the creep behavior for Bangladeshi brick chips made concrete in Bangladeshi environment. In this work, investigation on the behaviour of creep in concrete of same grade made with brick chips collected from various locations under single stage loading was done. With these investigations, a formula was derived to get theoretical creep values for 24 MPa brick chips made concrete in Bangladeshi environment.

On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

Predicting the localized surface plasmon resonances of spherical nanoparticles on substrate : electrostatic eigenmode method

We present experimental results that demonstrate that the wavelength of the fundamental localised surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple, one line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined, and the role of local environment refractive indices on the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.

On robust face recognition via sparse encoding : the good, the bad, and the ugly

In the field of face recognition, Sparse Representation (SR) has received considerable attention during the past few years. Most of the relevant literature focuses on holistic descriptors in closed-set identification applications. The underlying assumption in SR-based methods is that each class in the gallery has sufficient samples and the query lies on the subspace spanned by the gallery of the same class. Unfortunately, such assumption is easily violated in the more challenging face verification scenario, where an algorithm is required to determine if two faces (where one or both have not been seen before) belong to the same person. In this paper, we first discuss why previous attempts with SR might not be applicable to verification problems. We then propose an alternative approach to face verification via SR. Specifically, we propose to use explicit SR encoding on local image patches rather than the entire face. The obtained sparse signals are pooled via averaging to form multiple region descriptors, which are then concatenated to form an overall face descriptor. Due to the deliberate loss spatial relations within each region (caused by averaging), the resulting descriptor is robust to misalignment & various image deformations. Within the proposed framework, we evaluate several SR encoding techniques: l1-minimisation, Sparse Autoencoder Neural Network (SANN), and an implicit probabilistic technique based on Gaussian Mixture Models. Thorough experiments on AR, FERET, exYaleB, BANCA and ChokePoint datasets show that the proposed local SR approach obtains considerably better and more robust performance than several previous state-of-the-art holistic SR methods, in both verification and closed-set identification problems. The experiments also show that l1-minimisation based encoding has a considerably higher computational than the other techniques, but leads to higher recognition rates.

Assessment of the molecular structure of the borate mineral boracite Mg3B7O13Cl using vibrational spectroscopy

Boracite is a magnesium borate mineral with formula: Mg3B7O13Cl and occurs as blue green, colorless, gray, yellow to white crystals in the orthorhombic – pyramidal crystal system. An intense Raman band at 1009 cm−1 was assigned to the BO stretching vibration of the B7O13 units. Raman bands at 1121, 1136, 1143 cm−1 are attributed to the in-plane bending vibrations of trigonal boron. Four sharp Raman bands observed at 415, 494, 621 and 671 cm−1 are simply defined as trigonal and tetrahedral borate bending modes. The Raman spectrum clearly shows intense Raman bands at 3405 and 3494 cm−1, thus indicating that some Cl anions have been replaced with OH units. The molecular structure of a natural boracite has been assessed by using vibrational spectroscopy.

Chemistry, Raman and infrared spectroscopic characterization of the phosphate mineral reddingite: (MnFe)3(PO4)2(H2O,OH)3, a mineral found in lithium-bearing pegmatite

Detailed investigation of an intermediate member of the reddingite–phosphoferrite series, using infrared and Raman spectroscopy, scanning electron microcopy and electron microprobe analysis, has been carried out on a homogeneous sample from a lithium-bearing pegmatite named Cigana mine, near Conselheiro Pena, Minas Gerais, Brazil. The determined formula is (Mn1.60Fe1.21Ca0.01Mg0.01)∑2.83(PO4)2.12⋅(H2O2.85F0.01)∑2.86 indicating predominance in the reddingite member. Raman spectroscopy coupled with infrared spectroscopy supports the concept of phosphate, hydrogen phosphate and dihydrogen phosphate units in the structure of reddingite-phosphoferrite. Infrared and Raman bands attributed to water and hydroxyl stretching modes are identified. Vibrational spectroscopy adds useful information to the molecular structure of reddingite–phosphoferrite.