391 research outputs found
Locally Perturbed Random Walks with Unbounded Jumps
In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively
scaled, simple symmetric random walk, weak convergence to the Brownian motion
holds even in the case of local impurities if . The extension of their
result to finite range random walks is straightforward. Here, however, we are
interested in the situation when the random walk has unbounded range.
Concretely we generalize the statement of \cite{SzT} to unbounded random walks
whose jump distribution belongs to the domain of attraction of the normal law.
We do this first: for diffusively scaled random walks on having finite variance; and second: for random walks with distribution
belonging to the non-normal domain of attraction of the normal law. This result
can be applied to random walks with tail behavior analogous to that of the
infinite horizon Lorentz-process; these, in particular, have infinite variance,
and convergence to Brownian motion holds with the superdiffusive scaling.Comment: 16 page
Chaos in cylindrical stadium billiards via a generic nonlinear mechanism
We describe conditions under which higher-dimensional billiard models in
bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium
to dimensions above two. An example is a three-dimensional stadium bounded by a
cylinder and several planes; the combination of these elements may give rise to
defocusing, allowing large chaotic regions in phase space. By studying families
of marginally-stable periodic orbits that populate the residual part of phase
space, we identify conditions under which a nonlinear instability mechanism
arises in their vicinity. For particular geometries, this mechanism rather
induces stable nonlinear oscillations, including in the form of
whispering-gallery modes.Comment: 4 pages, 4 figure
A mechanical model of normal and anomalous diffusion
The overdamped dynamics of a charged particle driven by an uniform electric
field through a random sequence of scatterers in one dimension is investigated.
Analytic expressions of the mean velocity and of the velocity power spectrum
are presented. These show that above a threshold value of the field normal
diffusion is superimposed to ballistic motion. The diffusion constant can be
given explicitly. At the threshold field the transition between conduction and
localization is accompanied by an anomalous diffusion. Our results exemplify
that, even in the absence of time-dependent stochastic forces, a purely
mechanical model equipped with a quenched disorder can exhibit normal as well
as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure
On extensions of nilpotent torsion rings by semisimple rings
A class of rings in which each member is the extension of a nilpotent torsion ring by a semisimple semiartinian ring is presented. © 1981, Australian Mathematical Society. All rights reserved
Hyperthermia versus oncothermia: Cellular effects in complementary cancer therapy
Hyperthermia means overheating of the living object completely or partly. Hyperthermia, the procedure of raising the temperature of a part of or the whole body above normal for a defined period of time, is applied alone or as an adjunctive with various established cancer treatment modalities such as radiotherapy and chemotherapy. However, hyperthermia is not generally accepted as conventional therapy. The problem is its controversial performance. The controversy is originated from the complications of the deep heating and the focusing of the heat effect. The idea of oncothermia solves the selective deep action on nearly cellular resolution. We would like to demonstrate the force and perspectives of oncothermia, as a highly specialized hyperthermia in clinical oncology. Our aim is to prove the ability of oncothermia to be a candidate to become a widely accepted modality of the standard cancer care. We would like to show the proofs and the challenges of the hyperthermia and oncothermia applications to provide the presently available data and summarize the knowledge in the topic. Like many early stage therapies, oncothermia lacks adequate treatment experience and long-range, comprehensive statistics that can help us optimize its use for all indications. © 2013 Gabriella Hegyi et al
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