130 research outputs found
Singularity Structure, Symmetries and Integrability of Generalized Fisher Type Nonlinear Diffusion Equation
In this letter, the integrability aspects of a generalized Fisher type
equation with modified diffusion in (1+1) and (2+1) dimensions are studied by
carrying out a singularity structure and symmetry analysis. It is shown that
the Painlev\'e property exists only for a special choice of the parameter
(). A B\"acklund transformation is shown to give rise to the linearizing
transformation to the linear heat equation for this case (). A Lie
symmetry analysis also picks out the same case () as the only system among
this class as having nontrivial infinite dimensional Lie algebra of symmetries
and that the similarity variables and similarity reductions lead in a natural
way to the linearizing transformation and physically important classes of
solutions (including known ones in the literature), thereby giving a group
theoretical understanding of the system. For nonintegrable cases in (2+1)
dimensions, associated Lie symmetries and similarity reductions are indicated.Comment: 8 page
Quantum Cellular Neural Networks
We have previously proposed a way of using coupled quantum dots to construct
digital computing elements - quantum-dot cellular automata (QCA). Here we
consider a different approach to using coupled quantum-dot cells in an
architecture which, rather that reproducing Boolean logic, uses a physical
near-neighbor connectivity to construct an analog Cellular Neural Network
(CNN).Comment: 7 pages including 3 figure
Control of scroll wave turbulence using resonant perturbations
Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in
three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky
reaction are examples of such media. In cardiac tissue, chaotic behaviour is
believed to underlie fibrillation which, without intervention, precedes cardiac
death. In this study we investigate suppression of the turbulence using
stimulation of two different types, "modulation of excitability" and "extra
transmembrane current". With cardiac defibrillation in mind, we used a single
pulse as well as repetitive extra current with both constant and feedback
controlled frequency. We show that turbulence can be terminated using either a
resonant modulation of excitability or a resonant extra current. The turbulence
is terminated with much higher probability using a resonant frequency
perturbation than a non-resonant one. Suppression of the turbulence using a
resonant frequency is up to fifty times faster than using a non-resonant
frequency, in both the modulation of excitability and the extra current modes.
We also demonstrate that resonant perturbation requires strength one order of
magnitude lower than that of a single pulse, which is currently used in
clinical practice to terminate cardiac fibrillation. Our results provide a
robust method of controlling complex chaotic spatio-temporal processes.
Resonant drift of spiral waves has been studied extensively in two dimensions,
however, these results show for the first time that it also works in three
dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last
version: 2008/09/18, after revie
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
How to infer gene networks from expression profiles
Inferring, or ‘reverse-engineering', gene networks can be defined as the process of identifying gene interactions from experimental data through computational analysis. Gene expression data from microarrays are typically used for this purpose. Here we compared different reverse-engineering algorithms for which ready-to-use software was available and that had been tested on experimental data sets. We show that reverse-engineering algorithms are indeed able to correctly infer regulatory interactions among genes, at least when one performs perturbation experiments complying with the algorithm requirements. These algorithms are superior to classic clustering algorithms for the purpose of finding regulatory interactions among genes, and, although further improvements are needed, have reached a discreet performance for being practically useful
Buckling of scroll waves
A scroll wave in a sufficiently thin layer of an excitable medium with
negative filament tension can be stable nevertheless due to filament rigidity.
Above a certain critical thickness of the medium, such scroll wave will have a
tendency to deform into a buckled, precessing state. Experimentally this will
be seen as meandering of the spiral wave on the surface, the amplitude of which
grows with the thickness of the layer, until a break-up to scroll wave
turbulence happens. We present a simplified theory for this phenomenon and
illustrate it with numerical examples.Comment: 4 pages main text + 5 pages appendix, 4+2 figures and a movie, as
accepted by Phys Rev Letters 2012/09/2
Oxidation resistance of nano-reinforced PC-refractories modified with phenol formaldehyde resin. Part 4. Thermodynamic evaluation of phase formation within Mg–O–C–Al, Mg–O–C–Ni and МgO‒Al₂O₃‒NiO‒SiO₂ systems using SiC + Al + Ni (NiO) complex antioxidant
Results are given for the synthesis and co-existence of phases formed from components of complex organic-
inorganic antioxidant formed during modification of phenol-formaldehyde resin (PFR) and graphite with silica alkoxide and inorganic or organic nickel precursors. Thermodynamic analysis is given for the Mg–Al–C and Mg–O–Ni–C systems. It is shown that the periclase and carbon can coexist with aluminum and nickel, and also that oxidized antioxidants Al₂O₃ and NiO can interact respectively with the periclase and with the synthesized SiC formed during modification of PFR with silica. In considering the NiO‒MgO‒Al₂O₃‒SiO₂ system it is established that during service noble spinel will be synthesized from the complex antioxidant components, facilitating an increase in PC-refractory durability in service
Effects of a nanoscopic filler on the structure and dynamics of a simulated polymer melt and the relationship to ultra-thin films
We perform molecular dynamics simulations of an idealized polymer melt
surrounding a nanoscopic filler particle to probe the effects of a filler on
the local melt structure and dynamics. We show that the glass transition
temperature of the melt can be shifted to either higher or lower
temperatures by appropriately tuning the interactions between polymer and
filler. A gradual change of the polymer dynamics approaching the filler surface
causes the change in the glass transition. We also find that while the bulk
structure of the polymers changes little, the polymers close to the surface
tend to be elongated and flattened, independent of the type of interaction we
study. Consequently, the dynamics appear strongly influenced by the
interactions, while the melt structure is only altered by the geometric
constraints imposed by the presence of the filler. Our findings show a strong
similarity to those obtained for ultra-thin polymer films (thickness nm) suggesting that both ultra-thin films and filled-polymer systems might
be understood in the same context
Temporal Controls of the Asymmetric Cell Division Cycle in Caulobacter crescentus
The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network, centered on three major control proteins, DnaA, GcrA and CtrA. The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic, biochemical and physiological properties of proliferating bacteria. Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme. The model is validated against observed phenotypes of wild-type cells and relevant mutants, and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions. Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria, the model we are proposing here may be applicable to other genera of importance to agriculture and medicine (e.g., Rhizobium, Brucella)
Petri Nets with Fuzzy Logic (PNFL): Reverse Engineering and Parametrization
Background:
The recent DREAM4 blind assessment provided a particularly realistic and challenging setting for network reverse engineering methods. The in silico part of DREAM4 solicited the inference of cycle-rich gene regulatory networks from heterogeneous, noisy expression data including time courses as well as knockout, knockdown and multifactorial perturbations.
Methodology and Principal Findings:
We inferred and parametrized simulation models based on Petri Nets with Fuzzy Logic (PNFL). This completely automated approach correctly reconstructed networks with cycles as well as oscillating network motifs. PNFL was evaluated as the best performer on DREAM4 in silico networks of size 10 with an area under the precision-recall curve (AUPR) of 81%. Besides topology, we inferred a range of additional mechanistic details with good reliability, e.g. distinguishing activation from inhibition as well as dependent from independent regulation. Our models also performed well on new experimental conditions such as double knockout mutations that were not included in the provided datasets.
Conclusions:
The inference of biological networks substantially benefits from methods that are expressive enough to deal with diverse datasets in a unified way. At the same time, overly complex approaches could generate multiple different models that explain the data equally well. PNFL appears to strike the balance between expressive power and complexity. This also applies to the intuitive representation of PNFL models combining a straightforward graphical notation with colloquial fuzzy parameters
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