Fractional Chemotaxis Diffusion Equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page

AN ANALYSIS OF IODINE DEFICIENCY DISORDER AND ERADICATION STRATEGIES IN THE HIGH ATLAS MOUNTAINS OF MOROCCO

Food Consumption/Nutrition/Food Safety, Health Economics and Policy,

On the Consistency of the Solutions of the Space Fractional Schr\"odinger Equation

Recently it was pointed out that the solutions found in literature for the space fractional Schr\"odinger equation in a piecewise manner are wrong, except the case with the delta potential. We reanalyze this problem and show that an exact and a proper treatment of the relevant integral proves otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schr\"odinger equation in general coordinates in terms of Fox's H-functions

Mapping the landscape of climate engineering.

In the absence of a governance framework for climate engineering technologies such as solar radiation management (SRM), the practices of scientific research and intellectual property acquisition can de facto shape the development of the field. It is therefore important to make visible emerging patterns of research and patenting, which we suggest can effectively be done using bibliometric methods. We explore the challenges in defining the boundary of climate engineering, and set out the research strategy taken in this study. A dataset of 825 scientific publications on climate engineering between 1971 and 2013 was identified, including 193 on SRM; these are analysed in terms of trends, institutions, authors and funders. For our patent dataset, we identified 143 first filings directly or indirectly related to climate engineering technologies-of which 28 were related to SRM technologies-linked to 910 family members. We analyse the main patterns discerned in patent trends, applicants and inventors. We compare our own findings with those of an earlier bibliometric study of climate engineering, and show how our method is consistent with the need for transparency and repeatability, and the need to adjust the method as the field develops. We conclude that bibliometric monitoring techniques can play an important role in the anticipatory governance of climate engineering

Time evolution of the reaction front in a subdiffusive system

Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result is derived for the system where the subdiffusion coefficients of reactants differ from each other. It includes the case of one static reactant. As an application of our results, we compare the time evolution of reaction front extracted from experimental data with the theoretical formula and we find that the transport process of organic acid particles in the tooth enamel is subdiffusive.Comment: 18 pages, 3 figure

Cyclic hypoxia exposure accelerates the progression of amoebic gill disease

Amoebic gill disease (AGD), caused by the amoeba Neoparamoeba perurans, has led to considerable economic losses in every major Atlantic salmon producing country, and is increasing in frequency. The most serious infections occur during summer and autumn, when temperatures are high and poor dissolved oxygen (DO) conditions are most common. Here, we tested if exposure to cyclic hypoxia at DO saturations of 40–60% altered the course of infection with N. perurans compared to normoxic controls maintained at ≥90% DO saturation. Although hypoxia exposure did not increase initial susceptibility to N. perurans, it accelerated progression of the disease. By 7 days post-inoculation, amoeba counts estimated from qPCR analysis were 1.7 times higher in the hypoxic treatment than in normoxic controls, and cumulative mortalities were twice as high (16 ± 4% and 8 ± 2%), respectively. At 10 days post-inoculation, however, there were no differences between amoeba counts in the hypoxic and normoxic treatments, nor in the percentage of filaments with AGD lesions (control = 74 ± 2.8%, hypoxic = 69 ± 3.3%), or number of lamellae per lesion (control = 30 ± 0.9%, hypoxic = 27.9 ± 0.9%) as determined by histological examination. Cumulative mortalities at the termination of the experiment were similarly high in both treatments (hypoxic = 60 ± 2%, normoxic = 53 ± 11%). These results reveal that exposure to cyclic hypoxia in a diel pattern, equivalent to what salmon are exposed to in marine aquaculture cages, accelerated the progression of AGD in post-smolts

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

Weyl Quantization of Fractional Derivatives

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.Comment: 9 pages, LaTe

Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with quadratic dependence on the spectral parameter $\omega$. We derive asymptotics of the spectral density in this problem and show how to compute coefficients of its asymptotic expansion from coefficients of the asymptotic expansion of the trace of the heat kernel of $L(\omega)$. The leading term in the spectral asymptotics is the same as for a Laplacian in a cavity. The results have a number of physical applications. We illustrate them by examples of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page