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Editorial
No full textThis Editorial is a FOREWORD to a special issue (Vol 193) of the Journal Eur. Phys. J. Special Topics edited by C.P Li and F. Mainardi.
The contributions, all peer reviewd, are partly based on a successful international workshop entitled “Academic Day of Fractional Dynamics and Control” organized by C.P. Li (one of the Guest Editors of this issue) and W. Chen, held at Shanghai University in May 16-18, 2010, under the chair by Y.Q. Chen
Prof Kurths of the Scientif committe of the Journal was so kind to invite the Guest Editors to publish this resulting Special Topics issue, partly based on selected original contributions from the meeting as well as including some additionally invited contributions from well known experts of Fractional Dynamics and Control.
The aim of the issue is to provide an up-dated state-of-art of some topics in Fractional Dynamics and Control
An historical perspective on fractional calculus in linear viscoelasticity
No full textThe article provides an historical survey of early contributions on the applications of fractional calculus in linear viscoelasticty. The period
under examination covers four decades, since 1930’s up to 1970’s, and authors are from both Western and Eastern countries. References to more recent contributions may be found in the bibliography of the author’s book.
This paper reproduces, with Publisher’s permission, Section 3.5 of the
book: F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press-London and World Scienific-Singapore, 2010
Computer assisted programme for the use of IHCD-II: a software for the general practitioners
No full textSympathy for Pontius Pilate. Hemicrania in M.A. Bulgakov's The Master and Margarita.
No full textThe aim of this study was to explore the description of the migraine attack of Pontius Pilate (a character in the novel The Master and Margarita by M. A. Bulgakov). Some of its features are analysed in light of current migraine literature. It is hypothesized that, at least in part, this description is based on the personal experience of the novel's author. We studied and analysed the text of the novel, other works by Bulgakov, his biography, including his medical training and practice, and the recently published diaries of Bulgakov and his wife E. S. Bulgakova. The novel contains a comprehensive description of a migraine attack. It includes a prodrome/aura of osmophobia. Olfactory perception during or shortly before the migraine attack is altered to the point where neutral or even pleasant odours become unbearable. Bulgakov's extensive history of migraines is seen in his diary, the diary of his wife, letters and other literary works. This is one of the most detailed and extensive depictions of a migraine attack in literature, with osmophobia described with great emphasis. It is likely that Pilate's migraine is described based on the personal history of the novel's author
Airplane headache: a neurologistâ€TMs personal experience.
No full textWe describe the airplane-related headache
of one of the authors (Fa.M.) and offer a joint
consideration of it.
When the author in question was 7 years old, he
had a first episode of acute frontal bilateral sinusitis
with fever, and two further episodes at 14 and
22 years. Since then he suffered no further symptom
of rhinitis or sinusitis. At the age of 29 years, he
flew for the first time; it was November, and the
flight was from Milan to Maldives Islands and
lasted 10 h; it was very pleasant and he experienced
no problems. Some months later, in June, during a
short air journey from Verona to Neaples lasting
about 1.5 h, while approaching the landing (the
plane was approximatively 500 m above the
airport), he experienced a sudden, sharp pain of
very high intensity located in the right periorbital
region, associated with profuse tearing, conjunctival
injection and ptosis. He did not check for the presence
of miosis in that instance. During the attack he
was irritable and found it difficult to stay in his
seat. He had to strongly press with his hand on the
right fronto-orbital region, but found only very
mild relief. After 5 min, the pain diminished and
disappeared in 15–20 min; a light dysaesthesia persisted
in the same area for 20 min. This was a very
unpleasant experience, as the pain was really
unbearable, and could be described as ‘thunderclap
like’. Three days later, returning home by airplane,
he took sodium naproxene 550 mg, one tablet,
during take off and suffered no disturbance.
Since then, every time he flies (about four times
per year), 1 h before landing he takes a tablet of
sodium naproxene 550 mg and has never experienced
‘airplane headache’ (1–3) again, until 2 years
ago when, returning from a holiday spent in
Greece, he forgot to take his naproxene: during
landing, he then experienced the same signs and
symptoms described above. Brain magnetic resonance
imaging (MR and angio-MRI were normal.
He has a personal and familial history negative for
headache.
The authors deem it worthwhile to share this
personal experience with the readers of Cephalalgia
for several reasons. It adds a new case (the second
Italian case) to the limited series published up until
now (1–4).
With reference to the paper by Mainardi et al. (3),
this experience confirms the fairly stereotyped presentation
of ‘airplane headache’ as far as sex, age of
onset, pain location, unilaterality, intensity, duration
and onset at landing are concerned; however, vegetative
symptoms of the trigeminal autonomic
cephalalgia series and transient dysaesthesia of the
area were also present, somewhat expanding the
spectrum of the clinical presentation of this kind of
headache (4).
An inconsistent action of ibuprofen has been
described (4). This is the first report of the apparent
good effectiveness of naproxene in this condition: a
very simple preventive therapy with this drug
proved successful in avoiding further attacks.
We expect this form of headache not being rare in
the general population: it is probably underreported
due to its short duration and spontaneous
remission. Therefore, this simple therapeutic
measure, if its efficacy is confirmed in other cases,
could be of help, avoiding an unpleasant and worrying
condition that could, as might have been in
the present case, limit the use of air travel for many
people
Subordination pathways to fractional diffusion
No full textThe uncoupled Continuous Time Random Walk (CTRW) in
one space-dimension and under power law regime is splitted into three distinct random walks: (rw1), a random walk along the line of natural time, happening in operational time; (w2), a random walk along the line of space, happening in operational time; (rw3), the inversion of (rw1), namely a random walk along the line of operational time, happening in natural time.
Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out
for each of these three random walks. Combining the limits of (rw1)
and (rw2) we get the method of parametric subordination for generating particle paths, whereas combination of (rw2) and (rw3) yields the subordination integral for the sojourn probability density in space-time fractional diffusion
Creep, relaxation and viscosity properties for basic fractional models in rheology
No full textThe purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin–Voigt, Maxwell, Zener, anti–Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models
On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep
No full textIn 1958, Jeffreys (Geophys J R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0 ≤ α ≤ 1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α ≤ 1 yields a continuous transition from a Hooke elastic solid with no creep (α→−∞) to a Maxwell fluid with linear creep (α=1) passing through the Lomnitz viscoelastic body with logarithmic creep (α=0) , which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α ≤ 1
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