Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model

In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is widely used in the population dynamics, combustion theory and plasma physics. By employing the suitable transformation, this equation was mapped to the anomalous diffusion equation where the nonlinear reaction term was eliminated. Due to its simpler form, some exact self-similar solutions with the compact support have been obtained. The solutions, evolving from an initial state, converge to the usual traveling wave at a certain transition time. Hence, it is quite clear the connection between the self-similar solution and the traveling wave solution from these results. Moreover, the solutions were found in the manner that either propagates to the right or propagates to the left. Furthermore, the two solutions form a symmetric solution, expanding in both directions. The application on the spatiotemporal pattern formation in biological population has been mainly focused.Comment: 5 pages, 2 figures, accepted by Phys. Rev.

Field tuned critical fluctuations in YFe2Al10: Evidence from magnetization, 27Al (NMR, NQR) investigations

We report magnetization, specific heat, and NMR investigations on YFe2Al10 over a wide range in temperature and magnetic field and zero field (NQR) measurements. Magnetic susceptibility, specific heat and spin-lattice relaxation rate divided by T (1/T1T) follow a weak power law (T^-0.4) temperature dependence, which is a signature of critical fluctuations of Fe moments. The value of the Sommerfeld-Wilson ratio and linear relation between 1/T1T and chi(T) suggest the existence of ferromagnetic correlations in this system. No magnetic ordering down to 50 mK in Cp(T) and the unusual temperature and field scaling of the bulk and NMR data are associated with a magnetic instability which drives the system to quantum criticality. The magnetic properties of the system are tuned by field wherein ferromagnetic fluctuations are suppressed and a crossover from quantum critical to FL behavior is observed with increasing magnetic field

A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$ when $f'(0)=0$ is included as an extension of the results.Comment: Latex, postcript figure availabl

Neutron diffraction in a model itinerant metal near a quantum critical point

Neutron diffraction measurements on single crystals of Cr1-xVx (x=0, 0.02, 0.037) show that the ordering moment and the Neel temperature are continuously suppressed as x approaches 0.037, a proposed Quantum Critical Point (QCP). The wave vector Q of the spin density wave (SDW) becomes more incommensurate as x increases in accordance with the two band model. At xc=0.037 we have found temperature dependent, resolution limited elastic scattering at 4 incommensurate wave vectors Q=(1+/-delta_1,2, 0, 0)*2pi/a, which correspond to 2 SDWs with Neel temperatures of 19 K and 300 K. Our neutron diffraction measurements indicate that the electronic structure of Cr is robust, and that tuning Cr to its QCP results not in the suppression of antiferromagnetism, but instead enables new spin ordering due to novel nesting of the Fermi surface of Cr.Comment: Submitted as a part of proceedings of LT25 (Amsterdam 2008

The Galam Model of Minority Opinion Spreading and the Marriage Gap

In 2002, Serge Galam designed a model of a minority opinion spreading. The effect is expected to lead a conservative minority to prevail if the issue is discussed long enough. Here we analyze the marriage gap, i.e. the difference in voting for Bush and Kerry in 2004 between married and unmarried people. It seems possible to interpret this marriage gap in terms of the Galam model.Comment: 6 page

Towards Constructing a Corpus for Studying the Effects of Treatments and Substances Reported in PubMed Abstracts

We present the construction of an annotated corpus of PubMed abstracts reporting about positive, negative or neutral effects of treatments or substances. Our ultimate goal is to annotate one sentence (rationale) for each abstract and to use this resource as a training set for text classification of effects discussed in PubMed abstracts. Currently, the corpus consists of 750 abstracts. We describe the automatic processing that supports the corpus construction, the manual annotation activities and some features of the medical language in the abstracts selected for the annotated corpus. It turns out that recognizing the terminology and the abbreviations is key for determining the rationale sentence. The corpus will be applied to improve our classifier, which currently has accuracy of 78.80% achieved with normalization of the abstract terms based on UMLS concepts from specific semantic groups and an SVM with a linear kernel. Finally, we discuss some other possible applications of this corpus.Comment: medical relation extraction, rationale extraction, effects and treatments, bioNL