1,555 research outputs found
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 evolves in time according to the formula
, with 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
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
Measuring subdiffusion parameters
We propose a method to extract from experimental data the subdiffusion
parameter and subdiffusion coefficient which are defined by
means of the relation where
denotes a mean square displacement of a random walker starting from
at the initial time . The method exploits a membrane system where a
substance of interest is transported in a solvent from one vessel to another
across a thin membrane which plays here only an auxiliary role. Using such a
system, we experimentally study a diffusion of glucose and sucrose in a gel
solvent. We find a fully analytic solution of the fractional subdiffusion
equation with the initial and boundary conditions representing the system under
study. Confronting the experimental data with the derived formulas, we show a
subdiffusive character of the sugar transport in gel solvent. We precisely
determine the parameter , which is smaller than 1, and the subdiffusion
coefficient .Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.
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
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
Hyperbolic subdiffusive impedance
We use the hyperbolic subdiffusion equation with fractional time derivatives
(the generalized Cattaneo equation) to study the transport process of
electrolytes in media where subdiffusion occurs. In this model the flux is
delayed in a non-zero time with respect to the concentration gradient. In
particular, we obtain the formula of electrochemical subdiffusive impedance of
a spatially limited sample in the limit of large and of small pulsation of the
electric field. The boundary condition at the external wall of the sample are
taken in the general form as a linear combination of subdiffusive flux and
concentration of the transported particles. We also discuss the influence of
the equation parameters (the subdiffusion parameter and the delay time) on the
Nyquist impedance plots.Comment: 10 pages, 5 figure
Stationarity-conservation laws for certain linear fractional differential equations
The Leibniz rule for fractional Riemann-Liouville derivative is studied in
algebra of functions defined by Laplace convolution. This algebra and the
derived Leibniz rule are used in construction of explicit form of
stationary-conserved currents for linear fractional differential equations. The
examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1
dimensions are discussed in detail. The results are generalized to the mixed
fractional-differential and mixed sequential fractional-differential systems
for which the stationarity-conservation laws are obtained. The derived currents
are used in construction of stationary nonlocal charges.Comment: 28 page
Levi-Civita cylinders with fractional angular deficit
The angular deficit factor in the Levi-Civita vacuum metric has been
parametrized using a Riemann-Liouville fractional integral. This introduces a
new parameter into the general relativistic cylinder description, the
fractional index {\alpha}. When the fractional index is continued into the
negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder
and in an Israel shell.Comment: 5 figure
Homeless drug users' awareness and risk perception of peer "Take Home Naloxone" use – a qualitative study
BACKGROUND
Peer use of take home naloxone has the potential to reduce drug related deaths. There appears to be a paucity of research amongst homeless drug users on the topic. This study explores the acceptability and potential risk of peer use of naloxone amongst homeless drug users. From the findings the most feasible model for future treatment provision is suggested.
METHODS
In depth face-to-face interviews conducted in one primary care centre and two voluntary organisation centres providing services to homeless drug users in a large UK cosmopolitan city. Interviews recorded, transcribed and analysed thematically by framework techniques.
RESULTS
Homeless people recognise signs of a heroin overdose and many are prepared to take responsibility to give naloxone, providing prior training and support is provided. Previous reports of the theoretical potential for abuse and malicious use may have been overplayed.
CONCLUSION
There is insufficient evidence to recommend providing "over the counter" take home naloxone" to UK homeless injecting drug users. However a programme of peer use of take home naloxone amongst homeless drug users could be feasible providing prior training is provided. Peer education within a health promotion framework will optimise success as current professionally led health promotion initiatives are failing to have a positive impact amongst homeless drug users
Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
The classical fields with fractional derivatives are investigated by using
the fractional Lagrangian formulation.The fractional Euler-Lagrange equations
were obtained and two examples were studied.Comment: 9 page
- …