A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Crystal structures of the co-crystalline adduct 5-(4-bromophenyl)-1,3,4-thiadiazol-2-amine--4-nitrobenzoic acid (1/1) and the salt 2-amino-5-(4-bromophenyl)-1,3,4-thiadiazol-3-ium 2-carboxy-4,6-dinitrophenolate

The structures of the 1:1 co-crystalline adduct C8H6BrN3S . C7H5NO4 (I) and the salt C8H7BrN3S+ C7H3N2O7- (II) from the interaction of 5-(4-bromophenyl)-1,3,4-thiadiazol-2-amine with 4-nitrobenzoic acid and 3,5-dinitrosalicylic acid, respectively, have been determined. The primary inter-species association in both (I) and (II) is through duplex R2/2(8) (N-H...O/O-H...O) or (N-H...O/N-H...O) hydrogen bonds, respectively, giving heterodimers. In (II), these are close to planar [dihedral angles between the thiadiazole ring and the two phenyl rings are 2.1(3)deg. (intra) and 9.8(2)deg. (inter)], while in (I) these angles are 22.11(15) and 26.08(18)deg., respectively. In the crystal of (I), the heterodimers are extended into a one-dimensional chain along b through an amine N-...N(thiadiazole) hydrogen bond but in (II), a centrosymmetric cyclic heterotetramer structure is generated through N-H...O hydrogen bonds to phenol and nitro O-atom acceptors and features, together with the primary R2/2(8) interaction, conjoined R4/6(12), R2/1(6) and S(6) ring motifs. Also present in (I) are pi--pi interactions between thiadiazole rings [minimum ring centroid separation, 3.4624(16)deg.] as well as short Br...O(nitro) interactions in both (I) and (II) [3.296(3)A and 3.104(3)A, respectively].

Crystal structure of N,N-diethylbenzene-1,4-diaminium dinitrate

In the structure of the title compound, (C10H18N2)2+, 2(NO3)-, the nitrate salt of 4-(N,N-diethylamino)aniline, the two ethyl groups lie almost perpendicular to the plane of the benzene ring [ring to ethyl C-C-N-C torsion angles, -59.5(2) and 67.5(3)deg.]. The aminium groups of the cation form inter-species N-H...O hydrogen bonds with the nitro O-atoms of both anions giving one-dimensional chains extending along c and are extended into a two-dimensional network structure lying parallel to (010). Weak C-H...O hydrogen-bonding associations are also present.

Crystal structures and hydrogen bonding in the anhydrous tryptaminium salts of the isomeric (2,4-dichlorophenoxy)acetic and (3,5-dichlorophenoxy)acetic acids

The anhydrous salts of 1H-indole-3-ethanamine (tryptamine) with isomeric (2,4-dichlorophenoxy)acetic acid (2,4-D) and (3,5-dichlorophenoxy)acetic (3,5-D), C10H13N2+ (C8H5Cl2O3)-, [(I) and (II), respectively] have been determined and their one-dimensional hydrogen-bonded polymeric structures are described. In the crystal of (I),the aminium H-atoms are involved in three separate inter-species N-H...O hydrogen-bonding interactions, two with carboxyl O-atom acceptors and the third in an asymmetric three-centre bidentate carboxyl O,O' chelate [graph set R2/1(4)]. The indole H-atom forms an N-H...O~carboxyl~ hydrogen bond, extending the chain structure along the b axial direction. In (II), two of the three aminium H-atoms are also involved in N-H...O(carboxyl) hydrogen bonds similar to (I) but with the third, a three-centre asymmetric interaction with carboxyl and phenoxy O-atoms is found [graph set R2/1(5)]. The chain polymeric extension is also along b. There are no pi--pi ring interactions in either of the structures. The aminium side chain conformations differ significantly between the two structures, reflecting the conformational ambivalence of the tryptaminium cation, as found also in the benzoate salts.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Biological application of carbon nanotubes and graphene

Carbon nanotubes (CNTs) and graphene are two representative nanomaterials comprised of purely element carbon [1,2]. Graphene is the two-dimensional, hexagonal sp2-carbon ring networks with one atomic layer thickness, while CNTs can be envisaged as one or several graphene sheets concentrically rolled up into a one-dimensional cylindrical structure, so-called singlewalled (SW) or multi-walled (MW) CNTs, respectively. Figure 12.1 shows the schematic diagram of structures of graphene, SWCNT and MWCNT. Owing to their exceptional mechanical, electrical, optical and thermal properties, CNTs and graphene have been widely considered as a new type of materials with great potentials to revolutionalize many of the biological and medical fields [3–5].

Validation of a Spanish version of the Spine Functional Index

Background The Spine Functional Index (SFI) is a recently published, robust and clinimetrically valid patient reported outcome measure. Objectives The purpose of this study was the adaptation and validation of a Spanish-version (SFI-Sp) with cultural and linguistic equivalence. Methods A two stage observational study was conducted. The SFI was cross-culturally adapted to Spanish through double forward and backward translation then validated for its psychometric characteristics. Participants (n = 226) with various spine conditions of >12 weeks duration completed the SFI-Sp and a region specific measure: for the back, the Roland Morris Questionnaire (RMQ) and Backache Index (BADIX); for the neck, the Neck Disability Index (NDI); for general health the EQ-5D and SF-12. The full sample was employed to determine internal consistency, concurrent criterion validity by region and health, construct validity and factor structure. A subgroup (n = 51) was used to determine reliability at seven days. Results The SFI-Sp demonstrated high internal consistency (α = 0.85) and reliability (r = 0.96). The factor structure was one-dimensional and supported construct validity. Criterion specific validity for function was high with the RMQ (r = 0.79), moderate with the BADIX (r = 0.59) and low with the NDI (r = 0.46). For general health it was low with the EQ-5D and inversely correlated (r = −0.42) and fair with the Physical and Mental Components of the SF-12 and inversely correlated (r = −0.56 and r = −0.48), respectively. The study limitations included the lack of longitudinal data regarding other psychometric properties, specifically responsiveness. Conclusions The SFI-Sp was demonstrated as a valid and reliable spine-regional outcome measure. The psychometric properties were comparable to and supported those of the English-version, however further longitudinal investigations are required.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

The production mechanisms of OH radicals in a pulsed direct current plasma jet

The production mechanism of OH radicals in a pulsed DC plasma jet is studied by a two-dimensional (2-D) plasma jet model and a one-dimensional (1-D) discharge model. For the plasma jet in the open air, electron-impact dissociation of H2O, electron neutralization of H2O+, as well as dissociation of H2O by O(1D) are found to be the main reactions to generate the OH species. The contribution of the dissociation of H2O by electron is more than the others. The additions of N2, O2, air, and H2O into the working gas increase the OH density outside the tube slightly, which is attributed to more electrons produced by Penning ionization. On the other hand, the additions of O2 and H2O into the working gas increase the OH density inside the tube substantially, which is attributed to the increased O (1D) and H2O concentration, respectively. The gas flow will transport high density OH out of the tube during pulse off period. It is also shown that the plasma chemistry and reactivity can be effectively controlled by the pulse numbers. These results are supported by the laser induced fluorescence measurements and are relevant to several applications of atmospheric-pressure plasmas in health care, medicine, and materials processing.

Crystal structures and hydrogen bonding in the morpholinium salts of four phenoxyacetic acid analogues

The anhydrous salts morpholinium (tetrahydro-2-H-1,4-oxazine) phenxyacetate, C4H10NO+ C8H7O3- (I), (4-fluorophenoxy)acetate, C4H10NO+ C8H6FO3- (II) and isomeric morpholinium (3,5-dichlorophenoxy)acetate (3,5-D) (III) and morpholinium (2,4-dichlorophenoxy)acetate (2,4-D), C4H10NO+ C8H5Cl2O3- (IV), have been determined and their hydrogen-bonded structures are described. In the crystals of (I), (III) and (IV), one of the the aminium H atoms is involved in a three-centre asymmetric cation-anion N-H...O,O' R2/1(4) hydrogen-bonding interaction with the two carboxyl O-atom acceptors of the anion. With the structure of (II), the primary N---H...O interaction is linear. In the structures of (I), (II) and (III), the second N-H...O(carboxyl) hydrogen bond generates one-dimensional chain structures extending in all cases along [100]. With (IV), the ion pairs are linked though inversion-related N-H...O hydrogen bonds [graph set R2/4(8)], giving a cyclic heterotetrameric structure.

Crystal structure of morpholin-4-ium cinnamate

In the anhydrous salt formed from the reaction of morpholine with cinnamic acid, C4H10NO+ C9H7O2-, the acid side chain in the trans-cinnamate anion is significantly rotated out of the benzene plane [C-C-C-C torsion angle = 158.54(17)deg. In the crystal, one of the the aminium H atoms is involved in a asymmetric three-centre cation-anion N-H...(O,O') R2/1(4) hydrogen-bonding interaction with the two carboxyl O-atom acceptors of the anion. The second aminium H atom forms an inter-species N-H...O(carboxyl) hydrogen bond, generating a one-dimensional chain structure extending along [100]. Chains are linked by C-H...O interactions forming a supramolecular layer parallel to (01-1).

New Curriculum History

"Rereading the historical record indicates that it is no longer so easy to argue that history is simply prior to its forms. Since the mid-1990s a new wave of research has formed around wider debates in the humanities and social sciences, such as decentering the subject, new analytics of power, reconsideration of one-dimensional time and three-dimensional space, attention to beyond-archival sources, alterity, Otherness, the invisible, and more. In addition, broader and contradictory impulses around the question of the nation - transnational, post-national, proto-national, and neo-national movements – have unearthed a new series of problematics and focused scholarly attention on traveling discourses, national imaginaries, and less formal processes of socialization, bonding, and subjectification. New Curriculum History challenges prior occlusions in the field, building upon and departing from previous waves of scholarship, extending the focus beyond the insularity of public schooling, the traditional framework of the self-contained nation-state, and the psychology of the schooled individual. Drawing on global studies, historical sociology, postcolonial studies, critical race theory, visual culture theory, disability studies, psychoanalytics, Cambridge school structuralisms, poststructuralisms, and infra- and transnational approaches the volume holds together not despite but because of differences and incommensurabilities in rereading historical records. Audience: Scholars and students in curriculum studies, history, education, philosophy, and cultural studies will be interested in these chapters for their methodological range, their innovations and their deterritorializations."--publisher website

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

Self-Absorption and Focusing Effects in Carrier Relaxation Dynamics under Depletion Conditions

The effect of a one-dimensional field (1) on the self-absorption characteristics and (2) when we have a finite numerical aperture for the objective lens that focuses the laser beam on the solid are considered here. Self-absorption, in particular its manifestation as an inner filter for the emitted signal, has been observed in luminescence experiments. Models for this effect exist and have been analyzed, but only in the absence of space charge. Using our previous results on minority carrier relaxation in the presence of a field, we obtain expressions incorporating inner filter effects. Focusing of a light beam on the sample, by an objective lens, results in a three-dimensional source and consequently a three-dimensional continuity equation to be solved for the minority carrier concentration. Assuming a one-dimensional electric field and employing Fourier-Bessel transforms, we recast the problem of carrier relaxation and solve the same via an identity that relates it to solutions obtained in the absence of focusing effects. The inner filter effect as well as focusing introduces new time scales in the problem of carrier relaxation. The interplay between the electric field and the parameters which characterize these effects and the consequent modulation of the intensity and time scales of carrier decay signals are analyzed and discussed.