Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Using complex network metrics to predict the persistence of metapopulations with asymmetric connectivity patterns

Almost all metapopulation modelling assumes that connectivity between patches is only a function of distance, and is therefore symmetric. However, connectivity will not depend only on the distance between the patches, as some paths are easy to traverse, while others are difficult. When colonising organisms interact with the heterogeneous landscape between patches, connectivity patterns will invariably be asymmetric. There have been few attempts to theoretically assess the effects of asymmetric connectivity patterns on the dynamics of metapopulations. In this paper, we use the framework of complex networks to investigate whether metapopulation dynamics can be determined by directly analysing the asymmetric connectivity patterns that link the patches. Our analyses focus on “patch occupancy” metapopulation models, which only consider whether a patch is occupied or not. We propose three easily calculated network metrics: the “asymmetry” and “average path strength” of the connectivity pattern, and the “centrality” of each patch. Together, these metrics can be used to predict the length of time a metapopulation is expected to persist, and the relative contribution of each patch to a metapopulation’s viability. Our results clearly demonstrate the negative effect that asymmetry has on metapopulation persistence. Complex network analyses represent a useful new tool for understanding the dynamics of species existing in fragmented landscapes, particularly those existing in large metapopulations.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Anthropogenic landscape change promotes asymmetric dispersal and limits regional patch occupancy in a spatially structured bird population

1. Local extinctions in habitat patches and asymmetric dispersal between patches are key processes structuring animal populations in heterogeneous environments. Effective landscape conservation requires an understanding of how habitat loss and fragmentation influence demographic processes within populations and movement between populations. 2. We used patch occupancy surveys and molecular data for a rainforest bird, the logrunner (Orthonyx temminckii), to determine (i) the effects of landscape change and patch structure on local extinction; (ii) the asymmetry of emigration and immigration rates; (iii) the relative influence of local and between-population landscapes on asymmetric emigration and immigration; and (iv) the relative contributions of habitat loss and habitat fragmentation to asymmetric emigration and immigration. 3. Whether or not a patch was occupied by logrunners was primarily determined by the isolation of that patch. After controlling for patch isolation, patch occupancy declined in landscapes experiencing high levels of rainforest loss over the last 100 years. Habitat loss and fragmentation over the last century was more important than the current pattern of patch isolation alone, which suggested that immigration from neighbouring patches was unable to prevent local extinction in highly modified landscapes. 4. We discovered that dispersal between logrunner populations is highly asymmetric. Emigration rates were 39% lower when local landscapes were fragmented, but emigration was not limited by the structure of the between-population landscapes. In contrast, immigration was 37% greater when local landscapes were fragmented and was lower when the between-population landscapes were fragmented. Rainforest fragmentation influenced asymmetric dispersal to a greater extent than did rainforest loss, and a 60% reduction in mean patch area was capable of switching a population from being a net exporter to a net importer of dispersing logrunners. 5. The synergistic effects of landscape change on species occurrence and asymmetric dispersal have important implications for conservation. Conservation measures that maintain large patch sizes in the landscape may promote asymmetric dispersal from intact to fragmented landscapes and allow rainforest bird populations to persist in fragmented and degraded landscapes. These sink populations could form the kernel of source populations given sufficient habitat restoration. However, the success of this rescue effect will depend on the quality of the between-population landscapes.

The iatrogenic reflex and belief that repression can coercively suppress asymmetric coercive violence : does very robust action by the government decrease functional support for insurgents?

Non-state insurgent actors are too weak to compel powerful adversaries to their will, so they use violence to coerce. A principal objective is to grow and sustain violent resistance to the point that it either militarily challenges the state, or more commonly, generates unacceptable political costs. To survive, insurgents must shift popular support away from the state and to grow they must secure it. State actor policies and actions perceived as illegitimate and oppressive by the insurgent constituency can generate these shifts. A promising insurgent strategy is to attack states in ways that lead angry publics and leaders to discount the historically established risks and take flawed but popular decisions to use repressive measures. Such decisions may be enabled by a visceral belief in the power of coercion and selective use of examples of where robust measures have indeed suppressed resistance. To avoid such counterproductive behaviours the cases of apparent 'successful repression' must be understood. This thesis tests whether robust state action is correlated with reduced support for insurgents, analyses the causal mechanisms of such shifts and examines whether such reduction is because of compulsion or coercion? The approach is founded on prior research by the RAND Corporation which analysed the 30 insurgencies most recently resolved worldwide to determine factors of counterinsurgent success. This new study first re-analyses their data at a finer resolution with new queries that investigate the relationship between repression and insurgent active support. Having determined that, in general, repression does not correlate with decreased insurgent support, this study then analyses two cases in which the data suggests repression seems likely to be reducing insurgent support: the PKK in Turkey and the insurgency against the Vietnamese-sponsored regime after their ousting of the Khmer Rouge. It applies 'structured-focused' case analysis with questions partly built from the insurgency model of Leites and Wolf, who are associated with the advocacy of US robust means in Vietnam. This is thus a test of 'most difficult' cases using a 'least likely' test model. Nevertheless, the findings refute the deterrence argument of 'iron fist' advocates. Robust approaches may physically prevent effective support of insurgents but they do not coercively deter people from being willing to actively support the insurgency.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Higher harmonic large-amplitude fourier transformed alternating current voltammetry : analytical attributes derived from studies of the oxidation of ferrocenemethanol and uric acid at a glassy carbon electrode

An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s−1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e− rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast.